diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml index 2ddd0138d..73c300ab2 100644 --- a/.github/workflows/test.yml +++ b/.github/workflows/test.yml @@ -28,7 +28,7 @@ jobs: strategy: fail-fast: false matrix: - model: [pcsaft, gc_pcsaft, pets, uvtheory] + model: [pcsaft, gc_pcsaft, pets, uvtheory, saftvrqmie] steps: - uses: actions/checkout@v3 diff --git a/CHANGELOG.md b/CHANGELOG.md index 0bac36a7a..2236aba7e 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -5,6 +5,9 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/), and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html). ## [Unreleased] +### Added +- Added SAFT-VRQ Mie equation of state and Helmholtz energy functional for first order Feynman-Hibbs corrected Mie fluids. [#79](https://github.com/feos-org/feos/pull/79) + ### Changed - Export `EosVariant` and `FunctionalVariant` directly in the crate root instead of their own modules. [#62](https://github.com/feos-org/feos/pull/62) diff --git a/Cargo.toml b/Cargo.toml index 7d4446da0..aa5ccd923 100644 --- a/Cargo.toml +++ b/Cargo.toml @@ -56,6 +56,7 @@ pcsaft = ["association"] gc_pcsaft = ["association"] uvtheory = ["lazy_static"] pets = [] +saftvrqmie = [] rayon = ["dep:rayon", "ndarray/rayon", "feos-core/rayon", "feos-dft?/rayon"] python = ["pyo3", "numpy", "feos-core/python", "feos-dft?/python", "rayon"] -all_models = ["dft", "estimator", "pcsaft", "gc_pcsaft", "uvtheory", "pets"] +all_models = ["dft", "estimator", "pcsaft", "gc_pcsaft", "uvtheory", "pets", "saftvrqmie"] diff --git a/README.md b/README.md index 13096ec46..9e561eb04 100644 --- a/README.md +++ b/README.md @@ -36,6 +36,7 @@ The following models are currently published as part of the `FeOs` framework |`gc-pcsaft`|(heterosegmented) group contribution PC-SAFT|✓|✓| |`pets`|perturbed truncated and shifted Lennard-Jones mixtures|✓|✓| |`uvtheory`|equation of state for Mie fluids and mixtures|✓|| +|`saftvrqmie`|equation of state for quantum fluids and mixtures|✓|✓| The list is being expanded continuously. Currently under development are implementations of ePC-SAFT, a Helmholtz energy functional for the UV theory, and SAFT-VRQ-Mie. diff --git a/docs/api/dft.md b/docs/api/dft.md index 423f46550..4fc092700 100644 --- a/docs/api/dft.md +++ b/docs/api/dft.md @@ -15,6 +15,7 @@ Implementations of Helmholtz energy functionals for DFT. HelmholtzEnergyFunctional.pcsaft HelmholtzEnergyFunctional.gcpcsaft HelmholtzEnergyFunctional.pets + HelmholtzEnergyFunctional.saftvrqmie HelmholtzEnergyFunctional.fmt ``` diff --git a/docs/api/eos.md b/docs/api/eos.md index e3d04a4a5..ccf4bd0fe 100644 --- a/docs/api/eos.md +++ b/docs/api/eos.md @@ -18,6 +18,7 @@ The `State` and `PhaseEquilibrium` objects are used to define thermodynamic cond EquationOfState.pets EquationOfState.python EquationOfState.uvtheory + EquationOfState.saftvrqmie ``` ## Other data types diff --git a/docs/api/index.md b/docs/api/index.md index f493a776c..308d3aa10 100644 --- a/docs/api/index.md +++ b/docs/api/index.md @@ -24,4 +24,5 @@ These modules contain the objects to e.g. read parameters from files or build pa peng_robinson pets uvtheory + saftvrqmie ``` \ No newline at end of file diff --git a/docs/api/saftvrqmie.md b/docs/api/saftvrqmie.md new file mode 100644 index 000000000..57f705f05 --- /dev/null +++ b/docs/api/saftvrqmie.md @@ -0,0 +1,28 @@ +# `feos.saftvrqmie` + +Utilities to build `SaftVRQMieParameters`. + +## Example + +```python +from feos.saftvrqmie import SaftVRQMieParameters + +parameters = SaftVRQMieParameters.from_json(['hydrogen', 'neon'], 'parameters.json') +``` + +## Data types + +```{eval-rst} +.. currentmodule:: feos.saftvrqmie + +.. autosummary:: + :toctree: generated/ + + FeynmanHibbsOrder + Identifier + JobackRecord + PureRecord + BinaryRecord + SaftVRQMieRecord + SaftVRQMieParameters +``` \ No newline at end of file diff --git a/docs/api/uvtheory.md b/docs/api/uvtheory.md index 750dd10e4..8a266ed5f 100644 --- a/docs/api/uvtheory.md +++ b/docs/api/uvtheory.md @@ -21,9 +21,7 @@ parameters = UVParameters.from_json(['methane', 'ethane'], 'parameters.json') Identifier ChemicalRecord PureRecord - SegmentRecord BinaryRecord - BinarySegmentRecord Perturbation UVRecord UVParameters diff --git a/examples/saftvrqmie/deuterium_32K.table b/examples/saftvrqmie/deuterium_32K.table new file mode 100644 index 000000000..3a7790a85 --- /dev/null +++ b/examples/saftvrqmie/deuterium_32K.table @@ -0,0 +1,5005 @@ +# DATE: YYYY-MM-DD UNITS: real CONTRIBUTOR: YOUR NAME +# FH1 potential for deuterium at T = 32 K +FH1_deuterium +N 5000 + +1 0.10000000 2992268387138745344.00000000 388821963225074761728.00000000 +2 0.10238048 2204134613096212480.00000000 279744747075187605504.00000000 +3 0.10476095 1635046766926236416.00000000 202797325462083895296.00000000 +4 0.10714143 1221067095675391488.00000000 148082546204575629312.00000000 +5 0.10952190 917778752412293120.00000000 108880189793970733056.00000000 +6 0.11190238 694073872985799808.00000000 80587576192366854144.00000000 +7 0.11428286 527995593645931072.00000000 60026163169319436288.00000000 +8 0.11666333 403930296894495232.00000000 44983460346953818112.00000000 +9 0.11904381 310695597428795648.00000000 33907698943375126528.00000000 +10 0.12142428 240227765208270688.00000000 25702578135821774848.00000000 +11 0.12380476 186673662824662368.00000000 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a/examples/saftvrqmie/deuterium_neon_32K.rdf b/examples/saftvrqmie/deuterium_neon_32K.rdf new file mode 100644 index 000000000..b07e9bf2c --- /dev/null +++ b/examples/saftvrqmie/deuterium_neon_32K.rdf @@ -0,0 +1,504 @@ +# g(r) for ${substance1} ${substance2} at rho=${initial_density}, t=${t} +i r g11 c11 g12 c12 g21 c21 g22 c22 +# Row c_gr[1] c_gr[2] c_gr[3] c_gr[4] c_gr[5] c_gr[6] c_gr[7] c_gr[8] c_gr[9] +# 1000000 500 +1 0.012 0 0 0 0 0 0 0 0 +2 0.036 0 0 0 0 0 0 0 0 +3 0.06 0 0 0 0 0 0 0 0 +4 0.084 0 0 0 0 0 0 0 0 +5 0.108 0 0 0 0 0 0 0 0 +6 0.132 0 0 0 0 0 0 0 0 +7 0.156 0 0 0 0 0 0 0 0 +8 0.18 0 0 0 0 0 0 0 0 +9 0.204 0 0 0 0 0 0 0 0 +10 0.228 0 0 0 0 0 0 0 0 +11 0.252 0 0 0 0 0 0 0 0 +12 0.276 0 0 0 0 0 0 0 0 +13 0.3 0 0 0 0 0 0 0 0 +14 0.324 0 0 0 0 0 0 0 0 +15 0.348 0 0 0 0 0 0 0 0 +16 0.372 0 0 0 0 0 0 0 0 +17 0.396 0 0 0 0 0 0 0 0 +18 0.42 0 0 0 0 0 0 0 0 +19 0.444 0 0 0 0 0 0 0 0 +20 0.468 0 0 0 0 0 0 0 0 +21 0.492 0 0 0 0 0 0 0 0 +22 0.516 0 0 0 0 0 0 0 0 +23 0.54 0 0 0 0 0 0 0 0 +24 0.564 0 0 0 0 0 0 0 0 +25 0.588 0 0 0 0 0 0 0 0 +26 0.612 0 0 0 0 0 0 0 0 +27 0.636 0 0 0 0 0 0 0 0 +28 0.66 0 0 0 0 0 0 0 0 +29 0.684 0 0 0 0 0 0 0 0 +30 0.708 0 0 0 0 0 0 0 0 +31 0.732 0 0 0 0 0 0 0 0 +32 0.756 0 0 0 0 0 0 0 0 +33 0.78 0 0 0 0 0 0 0 0 +34 0.804 0 0 0 0 0 0 0 0 +35 0.828 0 0 0 0 0 0 0 0 +36 0.852 0 0 0 0 0 0 0 0 +37 0.876 0 0 0 0 0 0 0 0 +38 0.9 0 0 0 0 0 0 0 0 +39 0.924 0 0 0 0 0 0 0 0 +40 0.948 0 0 0 0 0 0 0 0 +41 0.972 0 0 0 0 0 0 0 0 +42 0.996 0 0 0 0 0 0 0 0 +43 1.02 0 0 0 0 0 0 0 0 +44 1.044 0 0 0 0 0 0 0 0 +45 1.068 0 0 0 0 0 0 0 0 +46 1.092 0 0 0 0 0 0 0 0 +47 1.116 0 0 0 0 0 0 0 0 +48 1.14 0 0 0 0 0 0 0 0 +49 1.164 0 0 0 0 0 0 0 0 +50 1.188 0 0 0 0 0 0 0 0 +51 1.212 0 0 0 0 0 0 0 0 +52 1.236 0 0 0 0 0 0 0 0 +53 1.26 0 0 0 0 0 0 0 0 +54 1.284 0 0 0 0 0 0 0 0 +55 1.308 0 0 0 0 0 0 0 0 +56 1.332 0 0 0 0 0 0 0 0 +57 1.356 0 0 0 0 0 0 0 0 +58 1.38 0 0 0 0 0 0 0 0 +59 1.404 0 0 0 0 0 0 0 0 +60 1.428 0 0 0 0 0 0 0 0 +61 1.452 0 0 0 0 0 0 0 0 +62 1.476 0 0 0 0 0 0 0 0 +63 1.5 0 0 0 0 0 0 0 0 +64 1.524 0 0 0 0 0 0 0 0 +65 1.548 0 0 0 0 0 0 0 0 +66 1.572 0 0 0 0 0 0 0 0 +67 1.596 0 0 0 0 0 0 0 0 +68 1.62 0 0 0 0 0 0 0 0 +69 1.644 0 0 0 0 0 0 0 0 +70 1.668 0 0 0 0 0 0 0 0 +71 1.692 0 0 0 0 0 0 0 0 +72 1.716 0 0 0 0 0 0 0 0 +73 1.74 0 0 0 0 0 0 0 0 +74 1.764 0 0 0 0 0 0 0 0 +75 1.788 0 0 0 0 0 0 0 0 +76 1.812 0 0 0 0 0 0 0 0 +77 1.836 0 0 0 0 0 0 0 0 +78 1.86 0 0 0 0 0 0 0 0 +79 1.884 0 0 0 0 0 0 0 0 +80 1.908 0 0 0 0 0 0 0 0 +81 1.932 0 0 0 0 0 0 0 0 +82 1.956 0 0 0 0 0 0 0 0 +83 1.98 0 0 0 0 0 0 0 0 +84 2.004 0 0 0 0 0 0 0 0 +85 2.028 0 0 0 0 0 0 0 0 +86 2.052 0 0 0 0 0 0 0 0 +87 2.076 0 0 0 0 0 0 0 0 +88 2.1 0 0 0 0 0 0 0 0 +89 2.124 0 0 0 0 0 0 0 0 +90 2.148 0 0 0 0 0 0 0 0 +91 2.172 0 0 0 0 0 0 0 0 +92 2.196 0 0 0 0 0 0 0 0 +93 2.22 0 0 0 0 0 0 0 0 +94 2.244 0 0 0 0 0 0 0 0 +95 2.268 0 0 0 0 0 0 0 0 +96 2.292 0 0 0 0 0 0 0 0 +97 2.316 0 0 0 0 0 0 0 0 +98 2.34 0 0 0 0 0 0 0 0 +99 2.364 0 0 0 0 0 0 0 0 +100 2.388 0 0 0 0 0 0 0 0 +101 2.412 0 0 0 0 0 0 0 0 +102 2.436 0 0 0 0 0 0 0 0 +103 2.46 0 0 0 0 0 0 0 0 +104 2.484 0 0 0 0 0 0 5.81491e-06 2.49975e-07 +105 2.508 0 0 0 0 0 0 6.41717e-05 3.06219e-06 +106 2.532 0 0 0 0 0 0 0.000351182 1.87481e-05 +107 2.556 0 0 0 0 0 0 0.00124392 7.53675e-05 +108 2.58 0 0 0 0 0 0 0.0043863 0.000278785 +109 2.604 0 0 7.93451e-06 3.74963e-07 7.93451e-06 9.37406e-08 0.0121171 0.000851227 +110 2.628 0 0 5.1935e-05 2.87471e-06 5.1935e-05 7.18678e-07 0.0304058 0.00231427 +111 2.652 0 0 0.000239697 1.46235e-05 0.000239697 3.65588e-06 0.0649793 0.00549826 +112 2.676 0 0 0.000954188 6.22438e-05 0.000954188 1.55609e-05 0.124374 0.0117034 +113 2.7 0 0 0.00297673 0.000213479 0.00297673 5.33697e-05 0.215153 0.022631 +114 2.724 0 0 0.00810402 0.000632562 0.00810402 0.00015814 0.344792 0.0404556 +115 2.748 0 0 0.0189542 0.00163009 0.0189542 0.000407522 0.509719 0.0672729 +116 2.772 3.73902e-05 4.9995e-07 0.0397965 0.00376125 0.0397965 0.000940312 0.711764 0.105377 +117 2.796 0.000294009 4.49955e-06 0.0752616 0.00786171 0.0752616 0.00196543 0.938872 0.156513 +118 2.82 0.000541923 1.19988e-05 0.131182 0.0151321 0.131182 0.00378303 1.18324 0.222071 +119 2.844 0.00165173 3.52465e-05 0.210731 0.0270109 0.210731 0.00675273 1.43069 0.302693 +120 2.868 0.00480274 0.00010399 0.316055 0.0451287 0.316055 0.0112822 1.67249 0.398538 +121 2.892 0.0144277 0.000313969 0.447811 0.0712309 0.447811 0.0178077 1.89915 0.509202 +122 2.916 0.0299873 0.000757674 0.602433 0.106931 0.602433 0.0267327 2.09682 0.63342 +123 2.94 0.0584178 0.00163634 0.772834 0.153486 0.772834 0.0383715 2.26571 0.769862 +124 2.964 0.104732 0.00323743 0.957251 0.212095 0.957251 0.0530238 2.40641 0.917153 +125 2.988 0.179708 0.0060294 1.14017 0.283039 1.14017 0.0707598 2.50969 1.07326 +126 3.012 0.280239 0.0104535 1.32603 0.366878 1.32603 0.0917196 2.58686 1.23677 +127 3.036 0.408705 0.0170088 1.49887 0.463162 1.49887 0.115791 2.63263 1.40583 +128 3.06 0.573394 0.0263516 1.65725 0.571309 1.65725 0.142827 2.64697 1.57851 +129 3.084 0.761971 0.0389626 1.79795 0.690486 1.79795 0.172621 2.64672 1.75389 +130 3.108 0.968606 0.055244 1.9151 0.819411 1.9151 0.204853 2.62658 1.93066 +131 3.132 1.2022 0.0757652 2.01352 0.957064 2.01352 0.239266 2.58575 2.10738 +132 3.156 1.43795 0.100688 2.088 1.102 2.088 0.275501 2.53566 2.28334 +133 3.18 1.6774 0.130205 2.13997 1.25282 2.13997 0.313205 2.47678 2.45783 +134 3.204 1.89201 0.164003 2.17289 1.40828 2.17289 0.352069 2.40814 2.63007 +135 3.228 2.09057 0.20191 2.19196 1.56745 2.19196 0.391864 2.33849 2.79983 +136 3.252 2.27093 0.243701 2.1903 1.72889 2.1903 0.432221 2.2659 2.96678 +137 3.276 2.42073 0.288909 2.17864 1.89184 2.17864 0.472959 2.19054 3.13057 +138 3.3 2.55662 0.337357 2.15607 2.05547 2.15607 0.513868 2.11344 3.29092 +139 3.324 2.66351 0.388567 2.12292 2.21894 2.12292 0.554736 2.03693 3.44772 +140 3.348 2.7346 0.441906 2.08736 2.382 2.08736 0.595501 1.96512 3.60119 +141 3.372 2.7873 0.497056 2.04097 2.54374 2.04097 0.635934 1.89302 3.75115 +142 3.396 2.80648 0.553378 1.99215 2.70386 1.99215 0.675964 1.82226 3.89757 +143 3.42 2.81716 0.610716 1.9371 2.86176 1.9371 0.715439 1.75689 4.04074 +144 3.444 2.80913 0.668696 1.88116 3.01726 1.88116 0.754315 1.69345 4.18068 +145 3.468 2.78647 0.727013 1.83031 3.17068 1.83031 0.792669 1.63067 4.31732 +146 3.492 2.74706 0.785303 1.77329 3.32138 1.77329 0.830344 1.57253 4.45091 +147 3.516 2.69679 0.843317 1.71656 3.46927 1.71656 0.867317 1.51607 4.58149 +148 3.54 2.63481 0.900773 1.665 3.61468 1.665 0.90367 1.46399 4.70931 +149 3.564 2.58002 0.9578 1.61621 3.75775 1.61621 0.939438 1.41346 4.83439 +150 3.588 2.51217 1.01408 1.56353 3.89803 1.56353 0.974508 1.36726 4.95703 +151 3.612 2.44019 1.06948 1.51451 4.03574 1.51451 1.00893 1.32354 5.07733 +152 3.636 2.37093 1.12402 1.46584 4.1708 1.46584 1.0427 1.28283 5.19549 +153 3.66 2.29416 1.1775 1.42044 4.3034 1.42044 1.07585 1.24269 5.31147 +154 3.684 2.21708 1.22986 1.37727 4.43367 1.37727 1.10842 1.20609 5.42551 +155 3.708 2.14555 1.28119 1.33323 4.56143 1.33323 1.14036 1.17095 5.53768 +156 3.732 2.07152 1.3314 1.29673 4.68729 1.29673 1.17182 1.13677 5.64798 +157 3.756 2.01462 1.38085 1.2576 4.81094 1.2576 1.20273 1.10644 5.75673 +158 3.78 1.9323 1.4289 1.21859 4.93228 1.21859 1.23307 1.07901 5.86415 +159 3.804 1.88226 1.47629 1.18416 5.0517 1.18416 1.26293 1.05207 5.97021 +160 3.828 1.81327 1.52253 1.15403 5.16956 1.15403 1.29239 1.02535 6.07489 +161 3.852 1.75455 1.56783 1.12413 5.2858 1.12413 1.32145 1.00141 6.17841 +162 3.876 1.69639 1.61218 1.09328 5.40027 1.09328 1.35007 0.978105 6.28079 +163 3.9 1.63889 1.65556 1.06668 5.51334 1.06668 1.37834 0.956739 6.38217 +164 3.924 1.58918 1.69814 1.03952 5.62489 1.03952 1.40622 0.938049 6.48281 +165 3.948 1.53708 1.73983 1.01521 5.73517 1.01521 1.43379 0.91897 6.5826 +166 3.972 1.50191 1.78106 0.992228 5.84427 0.992228 1.46107 0.902484 6.6818 +167 3.996 1.44377 1.82118 0.971575 5.95239 0.971575 1.4881 0.886128 6.78038 +168 4.02 1.39805 1.86049 0.950733 6.05947 0.950733 1.51487 0.870963 6.87844 +169 4.044 1.36082 1.89922 0.931445 6.16563 0.931445 1.54141 0.856515 6.97603 +170 4.068 1.31669 1.93714 0.912752 6.2709 0.912752 1.56772 0.843853 7.07332 +171 4.092 1.29377 1.97483 0.892769 6.37508 0.892769 1.59377 0.832479 7.17044 +172 4.116 1.2535 2.01179 0.878455 6.4788 0.878455 1.6197 0.821422 7.26739 +173 4.14 1.22073 2.04819 0.863234 6.58191 0.863234 1.64548 0.812116 7.36437 +174 4.164 1.19077 2.08412 0.847667 6.68434 0.847667 1.67109 0.80203 7.46126 +175 4.188 1.15862 2.11948 0.835214 6.78643 0.835214 1.69661 0.791673 7.558 +176 4.212 1.13312 2.15447 0.823616 6.88827 0.823616 1.72207 0.785015 7.65503 +177 4.236 1.1061 2.189 0.810795 6.98966 0.810795 1.74741 0.777099 7.75217 +178 4.26 1.0807 2.22313 0.799657 7.0908 0.799657 1.7727 0.770209 7.84956 +179 4.284 1.05525 2.25683 0.789703 7.1918 0.789703 1.79795 0.764312 7.94728 +180 4.308 1.03897 2.29038 0.780178 7.29271 0.780178 1.82318 0.759629 8.0455 +181 4.332 1.01795 2.32363 0.773094 7.39382 0.773094 1.84845 0.753712 8.14405 +182 4.356 0.997472 2.35656 0.762422 7.49464 0.762422 1.87366 0.750008 8.2432 +183 4.38 0.979195 2.38925 0.756814 7.59583 0.756814 1.89896 0.747146 8.34306 +184 4.404 0.963515 2.42177 0.749039 7.69708 0.749039 1.92427 0.743735 8.44356 +185 4.428 0.945897 2.45404 0.742668 7.79856 0.742668 1.94964 0.740216 8.54467 +186 4.452 0.933095 2.48622 0.73742 7.90042 0.73742 1.9751 0.738393 8.64664 +187 4.476 0.917093 2.5182 0.73173 8.00259 0.73173 2.00065 0.73774 8.74961 +188 4.5 0.903293 2.55002 0.727073 8.1052 0.727073 2.0263 0.736885 8.85357 +189 4.524 0.894275 2.58187 0.723225 8.20835 0.723225 2.05209 0.735621 8.95847 +190 4.548 0.88359 2.61368 0.7192 8.31203 0.7192 2.07801 0.735546 9.06447 +191 4.572 0.872716 2.64542 0.71819 8.41665 0.71819 2.10416 0.736215 9.17168 +192 4.596 0.860742 2.67706 0.713909 8.52175 0.713909 2.13044 0.738539 9.28037 +193 4.62 0.852395 2.70872 0.712507 8.62774 0.712507 2.15693 0.739479 9.39034 +194 4.644 0.846991 2.74051 0.711357 8.73466 0.711357 2.18366 0.741438 9.50174 +195 4.668 0.838798 2.77231 0.710443 8.84255 0.710443 2.21064 0.745005 9.61484 +196 4.692 0.828634 2.80406 0.709362 8.95138 0.709362 2.23785 0.747674 9.72952 +197 4.716 0.823167 2.83591 0.711163 9.06161 0.711163 2.2654 0.751868 9.84602 +198 4.74 0.817653 2.86788 0.708975 9.17262 0.708975 2.29316 0.75545 9.96428 +199 4.764 0.807827 2.89978 0.711133 9.2851 0.711133 2.32128 0.760308 10.0845 +200 4.788 0.810665 2.93212 0.711916 9.39885 0.711916 2.34971 0.76446 10.2066 +201 4.812 0.804913 2.96456 0.715027 9.51423 0.715027 2.37856 0.76968 10.3308 +202 4.836 0.802294 2.99721 0.714904 9.63075 0.714904 2.40769 0.776528 10.4573 +203 4.86 0.79549 3.0299 0.71954 9.7492 0.71954 2.4373 0.782143 10.586 +204 4.884 0.796098 3.06295 0.720585 9.86899 0.720585 2.46725 0.789321 10.7172 +205 4.908 0.796347 3.09633 0.723709 9.99048 0.723709 2.49762 0.796653 10.8509 +206 4.932 0.794509 3.12996 0.72822 10.1139 0.72822 2.52848 0.804442 10.9872 +207 4.956 0.789862 3.16372 0.730945 10.2391 0.730945 2.55976 0.811648 11.1261 +208 4.98 0.793702 3.19797 0.737779 10.3666 0.737779 2.59164 0.819887 11.2678 +209 5.004 0.792469 3.2325 0.741603 10.496 0.741603 2.624 0.82824 11.4122 +210 5.028 0.794871 3.26747 0.74733 10.6277 0.74733 2.65691 0.839414 11.5601 +211 5.052 0.796517 3.30284 0.75347 10.7617 0.75347 2.69042 0.846816 11.7107 +212 5.076 0.795582 3.33851 0.760391 10.8982 0.760391 2.72456 0.857766 11.8647 +213 5.1 0.799765 3.37471 0.767017 11.0373 0.767017 2.75931 0.867476 12.0219 +214 5.124 0.803567 3.41142 0.775067 11.1791 0.775067 2.79477 0.877268 12.1823 +215 5.148 0.804001 3.4485 0.780588 11.3233 0.780588 2.83081 0.886865 12.3461 +216 5.172 0.806937 3.48606 0.789411 11.4704 0.789411 2.8676 0.898687 12.5136 +217 5.196 0.810993 3.52416 0.795894 11.6202 0.795894 2.90504 0.908659 12.6845 +218 5.22 0.812547 3.56269 0.806248 11.7733 0.806248 2.94332 0.919244 12.859 +219 5.244 0.823927 3.60212 0.815603 11.9296 0.815603 2.9824 0.930597 13.0373 +220 5.268 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+variable molarweight2 equal 20.17969806457545 + +# thermodynamic state +variable x1 equal 0.2 +variable initial_density equal 813.43 # kg / m3 @ p = 8 bar +variable t equal 32 +variable natoms equal 4000 +variable n1 equal v_x1*v_natoms +variable n2 equal v_natoms-v_n1 + +variable molarweight_mix equal v_x1*v_molarweight1+(1-v_x1)*v_molarweight2 +variable avogadro equal 6.022*10^23 +variable initial_density_mol equal v_initial_density/v_molarweight_mix*v_avogadro*10^(-27) # N / V +variable unit_cell_volume equal 1/v_initial_density_mol +variable box_length equal v_unit_cell_volume^(1/3)*v_natoms^(1/3) + +variable rc equal 12.0 + +# setting up the simulation box +region simulation_box block 0.0 ${box_length} 0.0 ${box_length} 0.0 ${box_length} +create_box 2 simulation_box +create_atoms 1 random ${n1} 1234 NULL +create_atoms 2 random ${n2} 4321 NULL +mass 1 ${molarweight1} +mass 2 ${molarweight2} + +# pair potentials +pair_style table linear 5000 +pair_coeff 1 1 ${substance1}_${t}K.table FH1_${substance1} ${rc} +pair_coeff 2 2 ${substance2}_${t}K.table FH1_${substance2} ${rc} +pair_coeff 1 2 ${substance1}_${substance2}_${t}K.table FH1_${substance1}_${substance2} ${rc} + +neighbor 0.3 bin +neigh_modify delay 0 every 1 + +# energy minimization +print "Running Minimization" +minimize 1.0e-4 1.0e-6 100 1000 + +# generate temperatures +velocity all create $t 12345 + +# Define output +thermo_style custom step temp pe ke vol density + +print "Running Equilibration" +fix 1 all nvt temp $t $t 500 +run 100000 +reset_timestep 0 + +# RDF +compute gr all rdf 500 1 1 1 2 2 1 2 2 +fix 1111 all ave/time 100 1 100 c_gr[*] & + file ${substance1}_${substance2}_${t}K.rdf & + mode vector ave running overwrite & + title1 "# g(r) for ${substance1} ${substance2} at rho=${initial_density}, t=${t}" & + title2 "i r g11 c11 g12 c12 g21 c21 g22 c22" + +thermo 1000 +fix 1 all nvt temp $t $t 500 +dump trj all atom 1000 ${substance1}_${substance2}_${t}K.lammpstrj +dump_modify trj sort id +dump xtctrj all xtc 1000 ${substance1}_${substance2}_${t}K.xtc +dump_modify xtctrj sort id +print "Running Production" + +run 100000 + + + + + + diff --git a/examples/saftvrqmie/neon_32K.table b/examples/saftvrqmie/neon_32K.table new file mode 100644 index 000000000..050e90e82 --- /dev/null +++ b/examples/saftvrqmie/neon_32K.table @@ -0,0 +1,5005 @@ +# DATE: YYYY-MM-DD UNITS: real CONTRIBUTOR: YOUR NAME +# FH1 potential for neon at T = 32 K +FH1_neon +N 5000 + +1 0.10000000 155306043023154610176.00000000 23264422075199584731136.00000000 +2 0.10238048 109180029639509065728.00000000 15973568977151704694784.00000000 +3 0.10476095 77379466039583440896.00000000 11063016031874713649152.00000000 +4 0.10714143 55268488968446615552.00000000 7725705181634525921280.00000000 +5 0.10952190 39769571227175911424.00000000 5437984753859370680320.00000000 +6 0.11190238 28820886430146617344.00000000 3856785960851494404096.00000000 +7 0.11428286 21028933964986486784.00000000 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-0.00004191 -0.00002101 +4990 11.97619524 -0.00004186 -0.00002098 +4991 11.97857572 -0.00004181 -0.00002095 +4992 11.98095619 -0.00004176 -0.00002092 +4993 11.98333667 -0.00004171 -0.00002089 +4994 11.98571714 -0.00004166 -0.00002086 +4995 11.98809762 -0.00004161 -0.00002083 +4996 11.99047810 -0.00004156 -0.00002081 +4997 11.99285857 -0.00004151 -0.00002078 +4998 11.99523905 -0.00004146 -0.00002075 +4999 11.99761952 -0.00004141 -0.00002072 +5000 12.00000000 -0.00004136 -0.00002069 diff --git a/examples/saftvrqmie/radial_distribution_function.ipynb b/examples/saftvrqmie/radial_distribution_function.ipynb new file mode 100644 index 000000000..b9501b152 --- /dev/null +++ b/examples/saftvrqmie/radial_distribution_function.ipynb @@ -0,0 +1,613 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "66146e02-48f2-4b2d-b2e3-50bda5cf345f", + "metadata": {}, + "outputs": [], + "source": [ + "from feos import *\n", + "from feos.si import *\n", + "from feos.dft import *\n", + "from feos.saftvrqmie import *\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas as pd\n", + "import seaborn as sns\n", + "\n", + "sns.set_palette(\"Paired\")\n", + "colors = sns.color_palette(\"Dark2\", 3)\n", + "sns.set_context(\"talk\")\n", + "sns.set_style(\"ticks\")" + ] + }, + { + "cell_type": "markdown", + "id": "88ead60a-eb91-4d29-8f0a-00aaef3a2e71", + "metadata": {}, + "source": [ + "# Radial distribution function: comparison between Molecular Dynamics and DFT\n", + "\n", + "In this notebook, we compare the radial distribution function (rdf) as obtained from Molecular Dynamics (MD) simulations using LAMMPS and classical DFT.\n", + "The steps needed are:\n", + "\n", + "1. Read parameters of the SAFT-VRQ Mie equation of state from files, including binary parameters $k_{ij}$ and $l_ {ij}$.\n", + "2. Once the parameters are defined, we can initialize the functional.\n", + "3. We calculate the phase diagram of the mixture. We then select thermodynamic conditions for the simulation in the stable liquid phase.\n", + "4. Generate the LAMMPS tables for energies and forces for all interaction pairs. Run the simulation (not done here; we provide the simulation output).\n", + "5. Read in LAMMPS simulation results. Calculate the rdf using 1D DFT in spherical coordinates.\n", + "6. Plot the results." + ] + }, + { + "cell_type": "markdown", + "id": "31f54a8d-9128-42bf-8ffe-ecfbaec5d370", + "metadata": { + "tags": [] + }, + "source": [ + "## Example system: Deuterium-Neon\n", + "\n", + "In this example, we will take a look at the binary system consisting of deuterium and neon.\n", + "When you run this example, make sure to adjust the relative path to the parameter files.\n", + "Parameters are published in the [FeO$_\\mathrm{s}$ github repository](https://github.com/feos-org/feos) in the `parameters` directory.\n", + "\n", + "As part of the SI you will find LAMMPS input files for all binary systems that we presented in the main article.\n", + "The procedure to calculate the rdf's is the same as presented in this document." + ] + }, + { + "cell_type": "markdown", + "id": "acefbecf-e020-44cf-bcc9-401773638ef2", + "metadata": {}, + "source": [ + "### Read in parameters\n", + "\n", + "We can read parameter from a *json* file using the `SaftVRQMieParameters.from_json` method.\n", + "By default, a list of *names* to define a mixture of substances has to be provided.\n", + "We also have to provide a file with the SAFT-VRQ Mie parameters and optionally another file with binary interaction parameters.\n", + "If we wanted to use other identifiers instead of the name (CAS, SMILES, ...), we could change the `IdentifierOption` to the appropriate data type." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "0f0a312b-5b2b-40ad-a2b4-f5edd9d30b70", + "metadata": {}, + "outputs": [ + { + "data": { + "text/markdown": [ + "|component|molarweight|$\\sigma$|$\\varepsilon$|$\\lambda_r$|$\\lambda_a$|\n", + "|-|-|-|-|-|-|\n", + "|deuterium|4.028209954364|3.0087|39.2388|11|7|\n", + "|neon|20.17969806457545|2.7778|37.501|13|6|" + ], + "text/plain": [ + "SaftVRQMieParameters(\n", + "\tmolarweight=[4.028209954364, 20.17969806457545]\n", + "\tm=[1, 1]\n", + "\tsigma=[3.0087, 2.7778]\n", + "\tepsilon_k=[39.2388, 37.501]\n", + "\tk_ij=\n", + "[[0, 0.13],\n", + " [0.13, 0]]\n", + ")" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "parameters = SaftVRQMieParameters.from_json(\n", + " [\"deuterium\", \"neon\"], \n", + " \"../../../parameters/saftvrqmie/hammer2023.json\",\n", + " \"../../../parameters/saftvrqmie/hammer2023_binary.json\",\n", + " search_option=IdentifierOption.Name\n", + ")\n", + "parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7a677dd4-9271-4b12-bbb8-fe3f3825f2c3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([[0. , 0.13],\n", + " [0.13, 0. ]]),\n", + " array([[0., 0.],\n", + " [0., 0.]]))" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "parameters.k_ij, parameters.l_ij" + ] + }, + { + "cell_type": "markdown", + "id": "81301dbd-b4e7-4db1-80b9-14ee24af7573", + "metadata": {}, + "source": [ + "### Define the functional\n", + "\n", + "Once the parameters are set, we can define the functional.\n", + "This is done by the `HelmholtzEnergyFunctional.saftvrqmie` method.\n", + "We will use most of the default options in this example; note however that we can include or ignore the non-additive correction to the hard-sphere reference.\n", + "To calculate the phase diagram, we will **include the correction term**. \n", + "Later we will use both cases and compare the effect on the rdf." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1ad06f2f-3190-4d10-897b-8f1b359602b6", + "metadata": {}, + "outputs": [], + "source": [ + "functional = HelmholtzEnergyFunctional.saftvrqmie(parameters, inc_nonadd_term=True)" + ] + }, + { + "cell_type": "markdown", + "id": "5f1c838c-1dfd-4d1c-a986-7ff6e81ae82c", + "metadata": {}, + "source": [ + "### Phase diagram\n", + "\n", + "First, we generate the phase diagram ($p-x,y$ diagram) from which we then select appropriate thermodynamic conditions for our simulation in the stable liquid phase.\n", + "The phase diagram is constructed using the `PhaseDiagram.binary_vle` method.\n", + "We can either provide a temperature or a pressure as input (FeO$_\\mathrm{s}$ checks the actual unit to decide which diagram to compute), in conjunction with the numper of VLE's to be included.\n", + "Here, we use a constant temperature of $T = 32$K.\n", + "We can access all thermodynamic states of the VLE using the `liquid` and `vapor` fields.\n", + "With that, we can generate a nice plot." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "9e2b7efd-fb69-4275-b168-df0c4dfbddfd", + "metadata": {}, + "outputs": [], + "source": [ + "temperature = 32 * KELVIN\n", + "dia = PhaseDiagram.binary_vle(functional, temperature, npoints=50)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "1c41dbca-fdd1-478b-bb2a-944ef77b801c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(12, 7))\n", + "plt.title(r\"{} (0), {} (1) at T = {}\".format(\n", + " parameters.pure_records[0].identifier.name,\n", + " parameters.pure_records[1].identifier.name,\n", + " temperature))\n", + "\n", + "plt.plot(dia.liquid.molefracs[:, 0], dia.liquid.pressure / BAR, label=\"liquid\")\n", + "plt.plot(dia.vapor.molefracs[:, 0], dia.vapor.pressure / BAR, label=\"vapor\")\n", + "plt.xlim(0, 1.0)\n", + "plt.ylim(3, 9)\n", + "plt.xlabel(r\"$x_0$\")\n", + "plt.ylabel(r\"$p$ / bar\")\n", + "plt.legend(frameon=False);" + ] + }, + { + "cell_type": "markdown", + "id": "565cc63a-2c10-495b-996a-ac012b6b2ae9", + "metadata": {}, + "source": [ + "We can now specify the thermodynamic condition for our simulation.\n", + "Here, we use a pressure of $p = 8$ bar with a molefraction for deuterium of $x_0 = 0.2$.\n", + "Note that the order of the indices is the order in which we defined our substances when we read our parameters from files.\n", + "\n", + "In LAMMPS, we conduct a NVT simulation, i.e. at constant temperature ($T = 32$ K), volume and number of molecules.\n", + "Thus, given temperature, pressure and the composition, we can calculate the mass density.\n", + "We will use the density and composition to later calculate the appropriate volume of our simulation box for a specific number of molecules, here $N=4000$.\n", + "\n", + "The density for given $T, p, \\mathbf{x}$ can be calculated using the `State` constructor.\n", + "The mass density and the temperature will be inputs for our LAMMPS input file." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "739c6bf6-bbaf-44fb-a75e-a828a35fc5ba", + "metadata": {}, + "outputs": [], + "source": [ + "pressure = 8 * BAR\n", + "x0 = 0.2\n", + "molefracs = np.array([x0, 1-x0])" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "97413ca2-802d-48ec-857f-5c6805c74394", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$812.99\\,\\mathrm{\\frac{kg}{m^{3}}}$" + ], + "text/plain": [ + "812.9908034253764 kg/m³" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state = State(functional, temperature, pressure=pressure, molefracs=molefracs)\n", + "state.mass_density()" + ] + }, + { + "cell_type": "markdown", + "id": "8405fa0c-7a8f-4a3a-a2d7-4e34bfbdc6b6", + "metadata": {}, + "source": [ + "### Generate LAMMPS energy and force tables\n", + "\n", + "In FeO$_\\mathrm{s}$ we provide an utility function to directly export LAMMPS `table` files from the parameters via the `lammps_tables` method of the `SaftVRQMieParameters` object.\n", + "This method will create files for all interaction pairs. Here, three files will be generated, one for deuterium-deuterium interactions, one for neon-neon and one for deuterium-neon.\n", + "\n", + "We have to provide the temperature (32 K), the number of points to store in the table (5000), and the minimum and maximum distance (0.1 and 12 Angstrom, respectively)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "3b074123-73bc-4fce-94d1-60ae739afaf6", + "metadata": {}, + "outputs": [], + "source": [ + "parameters.lammps_tables(temperature, 5000, 0.1 * ANGSTROM, 12.0 * ANGSTROM)" + ] + }, + { + "cell_type": "markdown", + "id": "5956e018-19a4-407b-8ef1-6a05af60f3b2", + "metadata": {}, + "source": [ + "We provide an input file for the LAMMPS simulation that you can use or adjust for your system.\n", + "There are several adjustments necessary, depending on the system of interest.\n", + "\n", + "This is how the LAMMPS input file starts (here it is named `in.binary_deuterium_neon`)\n", + "\n", + "```\n", + "units real\n", + "atom_style atomic\n", + "\n", + "# substance\n", + "variable substance1 string deuterium\n", + "variable substance2 string neon\n", + "variable molarweight1 equal 4.028209954364\n", + "variable molarweight2 equal 20.17969806457545\n", + "\n", + "# thermodynamic state\n", + "variable x1 equal 0.2\n", + "variable initial_density equal 812.99 # kg / m3 @ p = 8 bar\n", + "variable t equal 32\n", + "variable natoms equal 4000\n", + "variable n1 equal v_x1*v_natoms\n", + "variable n2 equal v_natoms-v_n1\n", + "\n", + "variable molarweight_mix equal v_x1*v_molarweight1+(1-v_x1)*v_molarweight2\n", + "variable avogadro equal 6.022*10^23\n", + "variable initial_density_mol equal v_initial_density/v_molarweight_mix*v_avogadro*10^(-27) # N / V\n", + "variable unit_cell_volume equal 1/v_initial_density_mol\n", + "variable box_length equal v_unit_cell_volume^(1/3)*v_natoms^(1/3)\n", + "\n", + "variable rc equal 12.0\n", + "\n", + "```\n", + "\n", + "When changing to other substances, the following changes have to be done\n", + "\n", + "- Adjust the name of the `substance1` and `substance2` variables. The order has to match the order of the parameters for the functional (this will be the filename we generate with `lammps_table`)\n", + "- Adjust the molar weights accordingly. Those will be used to calculate the number density from which the volume of the simulation box is calculated.\n", + "- Adjust the mole fraction `x1`. Note that in this input we start indexing at `1`.\n", + "- Adjust the density (`initial_density`) and temperature variables.\n", + "- Adjust the cut-off radius `rc` above which the potential energies and forces are set to zero. That value should match the upper bound that we used to generate our LAMMPS tables.\n", + "\n", + "The substance names are used for the filenames that are generated during the simulation.\n", + "\n", + "You should always **check** the simulation log or output. **A simple consistency check is the density** reported by LAMMPS which has to match the density we computed from the `State` object above.\n", + "\n", + "*Example log output after equilibration:* \n", + "```\n", + "Step Temp PotEng KinEng Volume Density \n", + " 0 31.487142 -1205.8191 375.3349 138480.42 0.81297093 \n", + " 1000 31.608622 -1204.7169 376.78297 138480.42 0.81297093 \n", + " 2000 31.951485 -1198.6872 380.86999 138480.42 0.81297093 \n", + " 3000 32.182406 -1201.8826 383.62263 138480.42 0.81297093 \n", + " 4000 31.835575 -1200.741 379.48831 138480.42 0.81297093 \n", + " 5000 31.941999 -1206.9745 380.75691 138480.42 0.81297093 \n", + " 6000 31.438711 -1208.0502 374.75759 138480.42 0.81297093 \n", + " 7000 31.62501 -1207.2402 376.97832 138480.42 0.81297093\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "e0fa60a1-aebd-4d8f-936d-a1ef8a718252", + "metadata": {}, + "source": [ + "### Read simulation results and compute rdf via DFT\n", + "\n", + "Simulation results can be read using `pandas.read_csv`.\n", + "To make parsing easier, we can add a `#` in the fourth line and define it as comment when reading the lammps results." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "61208cab-04c8-408c-a1d1-c97db8701577", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " i r g11 c11 g12 c12 g21 c21 g22 c22\n", + "0 1 0.012 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n", + "1 2 0.036 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n", + "2 3 0.060 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n", + "3 4 0.084 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0\n", + "4 5 0.108 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "simulation = pd.read_csv(\n", + " 'deuterium_neon_32K.rdf', \n", + " delim_whitespace=True, \n", + " comment=\"#\",\n", + ")\n", + "simulation.head()" + ] + }, + { + "cell_type": "markdown", + "id": "e91537d2-3c3f-4129-9621-b0952a0600f5", + "metadata": {}, + "source": [ + "For DFT, we construct a second functional without the non-additive correction term (called `functional_additive`).\n", + "FeO$_\\mathrm{s}$ provides an object to calculate the rdf, the `PairCorrelation`.\n", + "\n", + "`PairCorrelation` takes a `State` as input, which we generate for given $T, p, \\mathbf{x}$ for both functionals.\n", + "We can then define the index of the substance that acts as fixed particle, the number of grid points and the maximum radial distance.\n", + "Once defined, we call the `solve` method to run the DFT calculation.\n", + "\n", + "After solving the equilibrium density profile, we can access the rdf for each substance given a fixed particle $i$ where $i$ is the index we used to initialize the `PairCorrelation` object.\n", + "To get all rdf for a binary system, two DFT calculations have to be conducted: one for substance 0 and one for substance 1 acting as fixed particle." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "1d0d0f49-be2b-4784-a630-9c2343768a63", + "metadata": {}, + "outputs": [], + "source": [ + "functional_additive = HelmholtzEnergyFunctional.saftvrqmie(parameters, inc_nonadd_term=False)\n", + "state_additive = State(functional_additive, temperature, pressure=pressure, molefracs=molefracs)\n", + "\n", + "state = State(functional, temperature, pressure=pressure, molefracs=molefracs)\n", + "\n", + "rdf0_additive = PairCorrelation(state_additive, 0, 1024, 12 * ANGSTROM).solve()\n", + "rdf1_additive = PairCorrelation(state_additive, 1, 1024, 12 * ANGSTROM).solve()\n", + "\n", + "rdf0 = PairCorrelation(state, 0, 1024, 12 * ANGSTROM).solve()\n", + "rdf1 = PairCorrelation(state, 1, 1024, 12 * ANGSTROM).solve()" + ] + }, + { + "cell_type": "markdown", + "id": "67956e16-8add-4042-8d0b-a66cb0e73ee5", + "metadata": {}, + "source": [ + "### Plot the results" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "d3b96038-d595-4d36-9823-f15458766bfc", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(13, 7))\n", + "plt.plot(rdf0_additive.r / ANGSTROM, rdf0_additive.pair_correlation_function[0], color=colors[0], linestyle='dashed', label=r\"$g_{00}$ (DFT)\")\n", + "plt.plot(rdf0.r / ANGSTROM, rdf0.pair_correlation_function[0], color=colors[0], linestyle='dotted', label=r\"$g_{00}$ (DFT, nonadditive)\")\n", + "plt.plot(simulation.r, simulation.g11, color=colors[0], label=r\"$g_{00}$ (MD)\")\n", + "\n", + "plt.plot(rdf1_additive.r / ANGSTROM, rdf1_additive.pair_correlation_function[1], color=colors[1], linestyle='dashed', label=r\"$g_{11}$ (DFT)\")\n", + "plt.plot(rdf1.r / ANGSTROM, rdf1.pair_correlation_function[1], color=colors[1], linestyle='dotted', label=r\"$g_{11}$ (DFT, nonadditive)\")\n", + "plt.plot(simulation.r, simulation.g22, color=colors[1], label=r\"$g_{11}$ (MD)\")\n", + "\n", + "plt.plot(rdf0_additive.r / ANGSTROM, rdf0_additive.pair_correlation_function[1], color=colors[2], linestyle='dashed', label=r\"$g_{01}$ (DFT)\")\n", + "plt.plot(rdf0.r / ANGSTROM, rdf0.pair_correlation_function[1], color=colors[2], linestyle='dotted', label=r\"$g_{01}$ (DFT, nonadditive)\")\n", + "plt.plot(simulation.r, simulation.g12, color=colors[2], label=r\"$g_{01}$ (MD)\")\n", + "\n", + "plt.hlines(1.0, 0, 15, color=\"black\", linestyle=\"dashed\", alpha=0.5)\n", + "plt.xlim(2, 12)\n", + "plt.ylim(0, 4.0)\n", + "\n", + "plt.xlabel(r\"r / $\\mathrm{\\AA}$\")\n", + "plt.ylabel(\"$g(r)$\")\n", + "\n", + "plt.legend(frameon=False, loc=\"best\", ncol=3);\n", + "plt.tight_layout()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/parameters/saftvrqmie/README.md b/parameters/saftvrqmie/README.md new file mode 100644 index 000000000..4c66fd86c --- /dev/null +++ b/parameters/saftvrqmie/README.md @@ -0,0 +1,22 @@ +# Parameters + +This directory contains files with parameters for SAFT-VRQ Mie equation of state. +The files named according to the pattern `NameYear.json` correspond to published parameters. The corresponding publication is provided in the [`literature.bib`](literature.bib) file. + +## Notes + +- Para-hydrogen, ortho-hydrogen, and normal hydrogen (3:1 mixture of ortho- and para-hydrogen) have different parameters. **Use the `name` field of the identifier to distinguish between the different versions**. Using other identifier fields (e.g. `formula` or `smiles`) may lead to the wrong set of parameters being used. +- Following [Aasen et al. (2019)](https://aip.scitation.org/doi/full/10.1063/1.5111364) we provide separate parameters for the **specific orders** of the Feynman-Hibbs correction. The compatible order is denoted in the "model" column. + + +## Pure Substance Parameters +|file|model|publication| +|-|-|:-:| +[`aasen2019.json`](aasen2019.json) | first-order Feynman-Hibbs correction parameters. | [🔗](https://doi.org/10.1063/1.5111364) +[`hammer2023.json`](hammer2023.json) | first-order Feynman-Hibbs correction parameters used for (but not adjusted to) surface tensions. | TBD + +## Binary Parameters + +|file|model|publication| +|-|-|:-:| +[`aasen2020_binary.json`](aasen2020_binary.json) | first-order Feynman-Hibbs correction binary interaction parameters. Compatible with [`aasen2019.json`](aasen2019.json) and [`hammer2023.json`](hammer2023.json) | [🔗](https://doi.org/10.1063/1.5136079) diff --git a/parameters/saftvrqmie/aasen2019.json b/parameters/saftvrqmie/aasen2019.json new file mode 100644 index 000000000..3769fb1c6 --- /dev/null +++ b/parameters/saftvrqmie/aasen2019.json @@ -0,0 +1,110 @@ +[ + { + "identifier": { + "cas": "1333-74-0", + "name": "hydrogen", + "iupac_name": "hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0243, + "epsilon_k": 26.706, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 2.0157309551872 + }, + { + "identifier": { + "cas": "1333-74-0", + "name": "para-hydrogen", + "iupac_name": "para-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0235, + "epsilon_k": 26.5860, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 2.0157309551872 + }, + { + "identifier": { + "cas": "1333-74-0", + "name": "ortho-hydrogen", + "iupac_name": "ortho-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0239, + "epsilon_k": 26.7160, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 2.0157309551872 + }, + { + "identifier": { + "cas": "7440-01-9", + "name": "neon", + "iupac_name": "neon", + "smiles": "[Ne]", + "inchi": "InChI=1S/Ne", + "formula": "Ne" + }, + "model_record": { + "m": 1.0, + "sigma": 2.7778, + "epsilon_k": 37.501, + "lr": 13.0, + "la": 6.0 + }, + "molarweight": 20.17969806457545 + }, + { + "identifier": { + "cas": "7440-59-7", + "name": "helium", + "iupac_name": "helium", + "smiles": "[He]", + "inchi": "InChI=1S/He", + "formula": "He" + }, + "model_record": { + "m": 1.0, + "sigma": 2.7443, + "epsilon_k": 5.4195, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 4.002601643881807 + }, + { + "identifier": { + "cas": "7782-39-0", + "name": "deuterium", + "iupac_name": "deuterium", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H/i1+1D", + "formula": "D2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0203, + "epsilon_k": 30.273, + "lr": 10.0, + "la": 6.0 + }, + "molarweight": 4.028209954364 + } +] diff --git a/parameters/saftvrqmie/aasen2020_binary.json b/parameters/saftvrqmie/aasen2020_binary.json new file mode 100644 index 000000000..7bb0d5376 --- /dev/null +++ b/parameters/saftvrqmie/aasen2020_binary.json @@ -0,0 +1,288 @@ +[ + { + "id1": { + "cas": "1333-74-0", + "name": "hydrogen", + "iupac_name": "hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7440-01-9", + "name": "neon", + "iupac_name": "neon", + "smiles": "[Ne]", + "inchi": "InChI=1S/Ne", + "formula": "Ne" + }, + "model_record": { + "k_ij": 0.105, + "l_ij": 0.0 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "hydrogen", + "iupac_name": "hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7440-59-7", + "name": "helium", + "iupac_name": "helium", + "smiles": "[He]", + "inchi": "InChI=1S/He", + "formula": "He" + }, + "model_record": { + "k_ij": 0.08, + "l_ij": -0.05 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "hydrogen", + "iupac_name": "hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7782-39-0", + "name": "deuterium", + "iupac_name": "deuterium", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H/i1+1D", + "formula": "D2" + }, + "model_record": { + "k_ij": 0.0, + "l_ij": 0.0 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "ortho-hydrogen", + "iupac_name": "ortho-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7440-01-9", + "name": "neon", + "iupac_name": "neon", + "smiles": "[Ne]", + "inchi": "InChI=1S/Ne", + "formula": "Ne" + }, + "model_record": { + "k_ij": 0.105, + "l_ij": 0.0 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "ortho-hydrogen", + "iupac_name": "ortho-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7440-59-7", + "name": "helium", + "iupac_name": "helium", + "smiles": "[He]", + "inchi": "InChI=1S/He", + "formula": "He" + }, + "model_record": { + "k_ij": 0.08, + "l_ij": -0.05 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "ortho-hydrogen", + "iupac_name": "ortho-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7782-39-0", + "name": "deuterium", + "iupac_name": "deuterium", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H/i1+1D", + "formula": "D2" + }, + "model_record": { + "k_ij": 0.0, + "l_ij": 0.0 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "para-hydrogen", + "iupac_name": "para-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7440-01-9", + "name": "neon", + "iupac_name": "neon", + "smiles": "[Ne]", + "inchi": "InChI=1S/Ne", + "formula": "Ne" + }, + "model_record": { + "k_ij": 0.105, + "l_ij": 0.0 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "para-hydrogen", + "iupac_name": "para-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7440-59-7", + "name": "helium", + "iupac_name": "helium", + "smiles": "[He]", + "inchi": "InChI=1S/He", + "formula": "He" + }, + "model_record": { + "k_ij": 0.08, + "l_ij": -0.05 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "para-hydrogen", + "iupac_name": "para-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "7782-39-0", + "name": "deuterium", + "iupac_name": "deuterium", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H/i1+1D", + "formula": "D2" + }, + "model_record": { + "k_ij": 0.0, + "l_ij": 0.0 + } + }, + { + "id1": { + "cas": "1333-74-0", + "name": "para-hydrogen", + "iupac_name": "para-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "id2": { + "cas": "1333-74-0", + "name": "ortho-hydrogen", + "iupac_name": "ortho-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "k_ij": 0.0, + "l_ij": 0.0 + } + }, + { + "id1": { + "cas": "7440-59-7", + "name": "helium", + "iupac_name": "helium", + "smiles": "[He]", + "inchi": "InChI=1S/He", + "formula": "He" + }, + "id2": { + "cas": "7782-39-0", + "name": "deuterium", + "iupac_name": "deuterium", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H/i1+1D", + "formula": "D2" + }, + "model_record": { + "k_ij": 0.0, + "l_ij": -0.05 + } + }, + { + "id1": { + "cas": "7440-59-7", + "name": "helium", + "iupac_name": "helium", + "smiles": "[He]", + "inchi": "InChI=1S/He", + "formula": "He" + }, + "id2": { + "cas": "7440-01-9", + "name": "neon", + "iupac_name": "neon", + "smiles": "[Ne]", + "inchi": "InChI=1S/Ne", + "formula": "Ne" + }, + "model_record": { + "k_ij": -0.22, + "l_ij": 0.0 + } + }, + { + "id1": { + "cas": "7440-01-9", + "name": "neon", + "iupac_name": "neon", + "smiles": "[Ne]", + "inchi": "InChI=1S/Ne", + "formula": "Ne" + }, + "id2": { + "cas": "7782-39-0", + "name": "deuterium", + "iupac_name": "deuterium", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H/i1+1D", + "formula": "D2" + }, + "model_record": { + "k_ij": 0.13, + "l_ij": 0.0 + } + } +] diff --git a/parameters/saftvrqmie/hammer2023.json b/parameters/saftvrqmie/hammer2023.json new file mode 100644 index 000000000..e5e201906 --- /dev/null +++ b/parameters/saftvrqmie/hammer2023.json @@ -0,0 +1,110 @@ +[ + { + "identifier": { + "cas": "1333-74-0", + "name": "hydrogen", + "iupac_name": "hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0243, + "epsilon_k": 26.706, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 2.0157309551872 + }, + { + "identifier": { + "cas": "1333-74-0", + "name": "para-hydrogen", + "iupac_name": "para-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0235, + "epsilon_k": 26.5860, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 2.0157309551872 + }, + { + "identifier": { + "cas": "1333-74-0", + "name": "ortho-hydrogen", + "iupac_name": "ortho-hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0239, + "epsilon_k": 26.7160, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 2.0157309551872 + }, + { + "identifier": { + "cas": "7440-01-9", + "name": "neon", + "iupac_name": "neon", + "smiles": "[Ne]", + "inchi": "InChI=1S/Ne", + "formula": "Ne" + }, + "model_record": { + "m": 1.0, + "sigma": 2.7778, + "epsilon_k": 37.501, + "lr": 13.0, + "la": 6.0 + }, + "molarweight": 20.17969806457545 + }, + { + "identifier": { + "cas": "7440-59-7", + "name": "helium", + "iupac_name": "helium", + "smiles": "[He]", + "inchi": "InChI=1S/He", + "formula": "He" + }, + "model_record": { + "m": 1.0, + "sigma": 2.7443, + "epsilon_k": 5.4195, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 4.002601643881807 + }, + { + "identifier": { + "cas": "7782-39-0", + "name": "deuterium", + "iupac_name": "deuterium", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H/i1+1D", + "formula": "D2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0087, + "epsilon_k": 39.2388, + "lr": 11.0, + "la": 7.0 + }, + "molarweight": 4.028209954364 + } +] diff --git a/parameters/saftvrqmie/literature.bib b/parameters/saftvrqmie/literature.bib new file mode 100644 index 000000000..826468611 --- /dev/null +++ b/parameters/saftvrqmie/literature.bib @@ -0,0 +1,42 @@ +@article{aasen2019, + author = {Aasen, Ailo and Hammer, Morten and Ervik, {\AA}smund + and M{\"u}ller, Erich A. and Wilhelmsen, {\O}ivind}, + title = {Equation of State and Force Fields for + {{Feynman}}\textendash{{Hibbs-corrected Mie}} + Fluids. {{I}}. {{Application}} to Pure Helium, Neon, + Hydrogen, and Deuterium}, + journal = {Journal of Chemical Physics}, + month = aug, + number = {6}, + pages = {064508}, + volume = {151}, + year = {2019}, + doi = {10.1063/1.5111364}, + url = {https://doi.org/10.1063/1.5111364} +} + +@article{aasen2020, + author = {Aasen, Ailo and Hammer, Morten and M{\"u}ller, Erich + A. and Wilhelmsen, {\O}ivind}, + title = {Equation of State and Force Fields for + {{Feynman}}\textendash{{Hibbs-corrected Mie}} + Fluids. {{II}}. {{Application}} to Mixtures of + Helium, Neon, Hydrogen, and Deuterium}, + journal = {Journal of Chemical Physics}, + month = feb, + number = {7}, + pages = {074507}, + volume = {152}, + year = {2020}, + doi = {10.1063/1.5136079}, + url = {https://doi.org/10.1063/1.5136079} +} + +@article{hammer2023, + author = {Hammer, Morten and Bauer, Gernot and Stierle, Rolf + and Gross, Joachim and Wilhelmsen, {\O}ivind}, + title = {Classical density functional theory for interfacial + properties of hydrogen, helium, deuterium, neon and + their mixtures}, + journal = {To be published}, +} diff --git a/src/dft.rs b/src/dft.rs index 71c03eac8..352ce0c27 100644 --- a/src/dft.rs +++ b/src/dft.rs @@ -5,6 +5,8 @@ use crate::hard_sphere::FMTFunctional; use crate::pcsaft::PcSaftFunctional; #[cfg(feature = "pets")] use crate::pets::PetsFunctional; +#[cfg(feature = "saftvrqmie")] +use crate::saftvrqmie::SaftVRQMieFunctional; use feos_core::*; use feos_derive::HelmholtzEnergyFunctional; use feos_dft::adsorption::*; @@ -32,4 +34,7 @@ pub enum FunctionalVariant { Pets(PetsFunctional), #[implement(fluid_parameters, pair_potential)] Fmt(FMTFunctional), + #[cfg(feature = "saftvrqmie")] + #[implement(fluid_parameters, molar_weight, pair_potential)] + SaftVRQMie(SaftVRQMieFunctional), } diff --git a/src/eos.rs b/src/eos.rs index 7ed8ac1e5..c93505db5 100644 --- a/src/eos.rs +++ b/src/eos.rs @@ -4,6 +4,8 @@ use crate::gc_pcsaft::GcPcSaft; use crate::pcsaft::PcSaft; #[cfg(feature = "pets")] use crate::pets::Pets; +#[cfg(feature = "saftvrqmie")] +use crate::saftvrqmie::SaftVRQMie; #[cfg(feature = "uvtheory")] use crate::uvtheory::UVTheory; use feos_core::cubic::PengRobinson; @@ -31,6 +33,9 @@ pub enum EosVariant { #[cfg(feature = "python")] #[implement(molar_weight)] Python(PyEoSObj), + #[cfg(feature = "saftvrqmie")] + #[implement(molar_weight)] + SaftVRQMie(SaftVRQMie), #[cfg(feature = "pets")] #[implement(molar_weight)] Pets(Pets), diff --git a/src/lib.rs b/src/lib.rs index c60009313..24af2ff02 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -54,6 +54,8 @@ pub mod gc_pcsaft; pub mod pcsaft; #[cfg(feature = "pets")] pub mod pets; +#[cfg(feature = "saftvrqmie")] +pub mod saftvrqmie; #[cfg(feature = "uvtheory")] pub mod uvtheory; diff --git a/src/python/dft.rs b/src/python/dft.rs index 1965a6cc3..7f8bfcaa4 100644 --- a/src/python/dft.rs +++ b/src/python/dft.rs @@ -16,6 +16,11 @@ use crate::pcsaft::{DQVariants, PcSaftFunctional, PcSaftOptions}; use crate::pets::python::PyPetsParameters; #[cfg(feature = "pets")] use crate::pets::{PetsFunctional, PetsOptions}; +#[cfg(feature = "saftvrqmie")] +use crate::saftvrqmie::python::PySaftVRQMieParameters; +#[cfg(feature = "saftvrqmie")] +use crate::saftvrqmie::{FeynmanHibbsOrder, SaftVRQMieFunctional, SaftVRQMieOptions}; + use feos_core::*; use feos_dft::adsorption::*; use feos_dft::interface::*; @@ -58,7 +63,7 @@ impl PyFunctionalVariant { /// /// Returns /// ------- - /// Functional + /// HelmholtzEnergyFunctional #[cfg(feature = "pcsaft")] #[args( fmt_version = "FMTVersion::WhiteBear", @@ -107,7 +112,7 @@ impl PyFunctionalVariant { /// /// Returns /// ------- - /// Functional + /// HelmholtzEnergyFunctional #[cfg(feature = "gc_pcsaft")] #[args( fmt_version = "FMTVersion::WhiteBear", @@ -150,7 +155,7 @@ impl PyFunctionalVariant { /// /// Returns /// ------- - /// Functional + /// HelmholtzEnergyFunctional #[cfg(feature = "pets")] #[args(fmt_version = "FMTVersion::WhiteBear", max_eta = "0.5")] #[staticmethod] @@ -173,7 +178,7 @@ impl PyFunctionalVariant { /// /// Returns /// ------- - /// Functional + /// HelmholtzEnergyFunctional #[staticmethod] #[pyo3(text_signature = "(sigma, version)")] fn fmt(sigma: &PyArray1, fmt_version: FMTVersion) -> Self { @@ -181,6 +186,51 @@ impl PyFunctionalVariant { FMTFunctional::new(&sigma.to_owned_array(), fmt_version).into(), )) } + + /// SAFT-VRQ Mie Helmholtz energy functional. + /// + /// Parameters + /// ---------- + /// parameters : SaftVRQMieParameters + /// The parameters of the SAFT-VRQ Mie Helmholtz energy functional to use. + /// fmt_version: FMTVersion, optional + /// The specific variant of the FMT term. Defaults to FMTVersion.WhiteBear + /// max_eta : float, optional + /// Maximum packing fraction. Defaults to 0.5. + /// fh_order : FeynmanHibbsOrder, optional + /// Which Feyman-Hibbs correction order to use. Defaults to FeynmanHibbsOrder.FH1. + /// Currently, only the first order is implemented. + /// inc_nonadd_term : bool, optional + /// Include non-additive correction to the hard-sphere reference. Defaults to True. + /// + /// Returns + /// ------- + /// HelmholtzEnergyFunctional + #[cfg(feature = "saftvrqmie")] + #[staticmethod] + #[args( + fmt_version = "FMTVersion::WhiteBear", + max_eta = "0.5", + fh_order = "FeynmanHibbsOrder::FH1", + inc_nonadd_term = "true" + )] + #[pyo3(text_signature = "(parameters, fmt_version, max_eta, fh_order, inc_nonadd_term)")] + fn saftvrqmie( + parameters: PySaftVRQMieParameters, + fmt_version: FMTVersion, + max_eta: f64, + fh_order: FeynmanHibbsOrder, + inc_nonadd_term: bool, + ) -> Self { + let options = SaftVRQMieOptions { + max_eta, + fh_order, + inc_nonadd_term, + }; + Self(Arc::new( + SaftVRQMieFunctional::with_options(parameters.0, fmt_version, options).into(), + )) + } } impl_equation_of_state!(PyFunctionalVariant); diff --git a/src/python/eos.rs b/src/python/eos.rs index 1c44ebd83..8a549866e 100644 --- a/src/python/eos.rs +++ b/src/python/eos.rs @@ -17,10 +17,15 @@ use crate::pcsaft::{DQVariants, PcSaft, PcSaftOptions}; use crate::pets::python::PyPetsParameters; #[cfg(feature = "pets")] use crate::pets::{Pets, PetsOptions}; +#[cfg(feature = "saftvrqmie")] +use crate::saftvrqmie::python::PySaftVRQMieParameters; +#[cfg(feature = "saftvrqmie")] +use crate::saftvrqmie::{FeynmanHibbsOrder, SaftVRQMie, SaftVRQMieOptions}; #[cfg(feature = "uvtheory")] use crate::uvtheory::python::PyUVParameters; #[cfg(feature = "uvtheory")] use crate::uvtheory::{Perturbation, UVTheory, UVTheoryOptions}; + use feos_core::cubic::PengRobinson; use feos_core::python::cubic::PyPengRobinsonParameters; use feos_core::python::user_defined::PyEoSObj; @@ -228,6 +233,50 @@ impl PyEosVariant { options, )))) } + + /// SAFT-VRQ Mie equation of state. + /// + /// Parameters + /// ---------- + /// parameters : SaftVRQMieParameters + /// The parameters of the SAFT-VRQ Mie equation of state to use. + /// max_eta : float, optional + /// Maximum packing fraction. Defaults to 0.5. + /// fh_order : FeynmanHibbsOrder, optional + /// Which Feyman-Hibbs correction order to use. Defaults to FeynmanHibbsOrder.FH1. + /// Currently, only the first order is implemented. + /// inc_nonadd_term : bool, optional + /// Include non-additive correction to the hard-sphere reference. Defaults to True. + /// + /// Returns + /// ------- + /// EquationOfState + /// The SAFT-VRQ Mie equation of state that can be used to compute thermodynamic + /// states. + #[cfg(feature = "saftvrqmie")] + #[staticmethod] + #[args( + max_eta = "0.5", + fh_order = "FeynmanHibbsOrder::FH1", + inc_nonadd_term = "true" + )] + #[pyo3(text_signature = "(parameters, max_eta, fh_order, inc_nonadd_term)")] + fn saftvrqmie( + parameters: PySaftVRQMieParameters, + max_eta: f64, + fh_order: FeynmanHibbsOrder, + inc_nonadd_term: bool, + ) -> Self { + let options = SaftVRQMieOptions { + max_eta, + fh_order, + inc_nonadd_term, + }; + Self(Arc::new(EosVariant::SaftVRQMie(SaftVRQMie::with_options( + parameters.0, + options, + )))) + } } impl_equation_of_state!(PyEosVariant); diff --git a/src/python/mod.rs b/src/python/mod.rs index bc0142571..2ab8abf5f 100644 --- a/src/python/mod.rs +++ b/src/python/mod.rs @@ -4,8 +4,11 @@ use crate::gc_pcsaft::python::__PYO3_PYMODULE_DEF_GC_PCSAFT; use crate::pcsaft::python::__PYO3_PYMODULE_DEF_PCSAFT; #[cfg(feature = "pets")] use crate::pets::python::__PYO3_PYMODULE_DEF_PETS; +#[cfg(feature = "saftvrqmie")] +use crate::saftvrqmie::python::__PYO3_PYMODULE_DEF_SAFTVRQMIE; #[cfg(feature = "uvtheory")] use crate::uvtheory::python::__PYO3_PYMODULE_DEF_UVTHEORY; + use pyo3::prelude::*; use pyo3::wrap_pymodule; use quantity::python::__PYO3_PYMODULE_DEF_QUANTITY; @@ -37,6 +40,8 @@ pub fn feos(py: Python<'_>, m: &PyModule) -> PyResult<()> { m.add_wrapped(wrap_pymodule!(pets))?; #[cfg(feature = "uvtheory")] m.add_wrapped(wrap_pymodule!(uvtheory))?; + #[cfg(feature = "saftvrqmie")] + m.add_wrapped(wrap_pymodule!(saftvrqmie))?; set_path(py, m, "feos.si", "quantity")?; set_path(py, m, "feos.eos", "eos")?; @@ -55,6 +60,8 @@ pub fn feos(py: Python<'_>, m: &PyModule) -> PyResult<()> { set_path(py, m, "feos.pets", "pets")?; #[cfg(feature = "uvtheory")] set_path(py, m, "feos.uvtheory", "uvtheory")?; + #[cfg(feature = "saftvrqmie")] + set_path(py, m, "feos.saftvrqmie", "saftvrqmie")?; py.run( "\ diff --git a/src/saftvrqmie/dft/dispersion.rs b/src/saftvrqmie/dft/dispersion.rs new file mode 100644 index 000000000..c824385bf --- /dev/null +++ b/src/saftvrqmie/dft/dispersion.rs @@ -0,0 +1,101 @@ +use crate::saftvrqmie::eos::dispersion::{dispersion_energy_density, Alpha}; +use crate::saftvrqmie::parameters::SaftVRQMieParameters; +use feos_core::EosResult; +use feos_dft::{ + FunctionalContributionDual, WeightFunction, WeightFunctionInfo, WeightFunctionShape, +}; +use ndarray::*; +use num_dual::DualNum; +use std::fmt; +use std::sync::Arc; + +/// psi Parameter for DFT (Sauer2017) +const PSI_DFT: f64 = 1.3862; +/// psi Parameter for pDGT (Rehner2018) +const PSI_PDGT: f64 = 1.3286; + +#[derive(Clone)] +pub struct AttractiveFunctional { + parameters: Arc, + // Store stuff here +} + +impl AttractiveFunctional { + pub fn new(parameters: Arc) -> Self { + Self { parameters } + } +} + +fn att_weight_functions + ScalarOperand>( + p: &SaftVRQMieParameters, + psi: f64, + temperature: N, +) -> WeightFunctionInfo { + let d = p.hs_diameter(temperature); + WeightFunctionInfo::new(Array1::from_shape_fn(d.len(), |i| i), false).add( + WeightFunction::new_scaled(d * psi, WeightFunctionShape::Theta), + false, + ) +} + +impl + ScalarOperand> FunctionalContributionDual for AttractiveFunctional { + fn weight_functions(&self, temperature: N) -> WeightFunctionInfo { + att_weight_functions(&self.parameters, PSI_DFT, temperature) + } + + fn weight_functions_pdgt(&self, temperature: N) -> WeightFunctionInfo { + att_weight_functions(&self.parameters, PSI_PDGT, temperature) + } + + fn calculate_helmholtz_energy_density( + &self, + temperature: N, + density: ArrayView2, + ) -> EosResult> { + // auxiliary variables + let p = &self.parameters; + let n = p.m.len(); + + // temperature dependent segment radius // calc & store this in struct + let s_eff_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.calc_sigma_eff_ij(i, j, temperature)); + + // temperature dependent segment radius // calc & store this in struct + let d_hs_ij = Array2::from_shape_fn((n, n), |(i, j)| { + p.hs_diameter_ij(i, j, temperature, s_eff_ij[[i, j]]) + }); + + // temperature dependent well depth // calc & store this in struct + let epsilon_k_eff_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.calc_epsilon_k_eff_ij(i, j, temperature)); + + // temperature dependent well depth // calc & store this in struct + let dq_ij = Array2::from_shape_fn((n, n), |(i, j)| p.quantum_d_ij(i, j, temperature)); + + // alphas .... // calc & store this in struct + let alpha = Alpha::new(p, &s_eff_ij, &epsilon_k_eff_ij, temperature); + + let phi = density + .axis_iter(Axis(1)) + .map(|rho_lane| { + dispersion_energy_density( + p, + &d_hs_ij, + &s_eff_ij, + &epsilon_k_eff_ij, + &dq_ij, + &alpha, + &rho_lane.into_owned(), + temperature, + ) + }) + .collect(); + Ok(phi) + } +} + +impl fmt::Display for AttractiveFunctional { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Attractive functional") + } +} diff --git a/src/saftvrqmie/dft/mod.rs b/src/saftvrqmie/dft/mod.rs new file mode 100644 index 000000000..1d0e4acd5 --- /dev/null +++ b/src/saftvrqmie/dft/mod.rs @@ -0,0 +1,154 @@ +use crate::hard_sphere::{FMTContribution, FMTVersion, HardSphereProperties, MonomerShape}; +use crate::saftvrqmie::eos::SaftVRQMieOptions; +use crate::saftvrqmie::parameters::SaftVRQMieParameters; +use dispersion::AttractiveFunctional; +use feos_core::joback::Joback; +use feos_core::parameter::Parameter; +use feos_core::{IdealGasContribution, MolarWeight}; +use feos_dft::adsorption::FluidParameters; +use feos_dft::solvation::PairPotential; +use feos_dft::{FunctionalContribution, HelmholtzEnergyFunctional, MoleculeShape, DFT}; +use ndarray::{Array, Array1, Array2}; +use non_additive_hs::NonAddHardSphereFunctional; +use num_dual::DualNum; +use pure_saft_functional::*; +use quantity::si::*; +use std::f64::consts::FRAC_PI_6; +use std::sync::Arc; + +//mod association; +mod dispersion; +mod non_additive_hs; +mod pure_saft_functional; + +/// SAFT-VRQ Mie Helmholtz energy functional. +pub struct SaftVRQMieFunctional { + pub parameters: Arc, + fmt_version: FMTVersion, + options: SaftVRQMieOptions, + contributions: Vec>, + joback: Joback, +} + +impl SaftVRQMieFunctional { + pub fn new(parameters: Arc) -> DFT { + Self::with_options( + parameters, + FMTVersion::WhiteBear, + SaftVRQMieOptions::default(), + ) + } + + pub fn new_full(parameters: Arc, fmt_version: FMTVersion) -> DFT { + Self::with_options(parameters, fmt_version, SaftVRQMieOptions::default()) + } + + pub fn with_options( + parameters: Arc, + fmt_version: FMTVersion, + saft_options: SaftVRQMieOptions, + ) -> DFT { + let mut contributions: Vec> = Vec::with_capacity(3); + + if matches!( + fmt_version, + FMTVersion::WhiteBear | FMTVersion::AntiSymWhiteBear + ) && parameters.m.len() == 1 + { + let fmt_assoc = PureFMTAssocFunctional::new(parameters.clone(), fmt_version); + contributions.push(Box::new(fmt_assoc)); + let att = PureAttFunctional::new(parameters.clone()); + contributions.push(Box::new(att)); + } else { + // Hard sphere contribution + let hs = FMTContribution::new(¶meters, fmt_version); + contributions.push(Box::new(hs)); + + // Non-additive hard-sphere contribution + if saft_options.inc_nonadd_term { + let non_add_hs = NonAddHardSphereFunctional::new(parameters.clone()); + contributions.push(Box::new(non_add_hs)); + } + + // Dispersion + let att = AttractiveFunctional::new(parameters.clone()); + contributions.push(Box::new(att)); + } + + let joback = match ¶meters.joback_records { + Some(joback_records) => Joback::new(joback_records.clone()), + None => Joback::default(parameters.m.len()), + }; + + (Self { + parameters, + fmt_version, + options: saft_options, + contributions, + joback, + }) + .into() + } +} + +impl HelmholtzEnergyFunctional for SaftVRQMieFunctional { + fn subset(&self, component_list: &[usize]) -> DFT { + Self::with_options( + Arc::new(self.parameters.subset(component_list)), + self.fmt_version, + self.options, + ) + } + + fn compute_max_density(&self, moles: &Array1) -> f64 { + self.options.max_eta * moles.sum() + / (FRAC_PI_6 * &self.parameters.m * self.parameters.sigma.mapv(|v| v.powi(3)) * moles) + .sum() + } + + fn contributions(&self) -> &[Box] { + &self.contributions + } + + fn ideal_gas(&self) -> &dyn IdealGasContribution { + &self.joback + } + + fn molecule_shape(&self) -> MoleculeShape { + MoleculeShape::NonSpherical(&self.parameters.m) + } +} + +impl MolarWeight for SaftVRQMieFunctional { + fn molar_weight(&self) -> SIArray1 { + self.parameters.molarweight.clone() * GRAM / MOL + } +} + +impl HardSphereProperties for SaftVRQMieParameters { + fn monomer_shape>(&self, _: N) -> MonomerShape { + MonomerShape::Spherical(self.m.len()) + } + + fn hs_diameter>(&self, temperature: D) -> Array1 { + self.hs_diameter(temperature) + } +} + +impl FluidParameters for SaftVRQMieFunctional { + fn epsilon_k_ff(&self) -> Array1 { + self.parameters.epsilon_k.clone() + } + + fn sigma_ff(&self) -> &Array1 { + &self.parameters.sigma + } +} + +impl PairPotential for SaftVRQMieFunctional { + fn pair_potential(&self, i: usize, r: &Array1, temperature: f64) -> Array2 { + Array::from_shape_fn((self.parameters.m.len(), r.len()), |(j, k)| { + self.parameters.qmie_potential_ij(i, j, r[k], temperature)[0] + }) + } +} diff --git a/src/saftvrqmie/dft/non_additive_hs.rs b/src/saftvrqmie/dft/non_additive_hs.rs new file mode 100644 index 000000000..fe94e362e --- /dev/null +++ b/src/saftvrqmie/dft/non_additive_hs.rs @@ -0,0 +1,189 @@ +use crate::saftvrqmie::parameters::SaftVRQMieParameters; +use feos_core::EosResult; +use feos_dft::{ + FunctionalContributionDual, WeightFunction, WeightFunctionInfo, WeightFunctionShape, +}; +use ndarray::*; +use num_dual::DualNum; +use std::f64::consts::PI; +use std::fmt; +use std::sync::Arc; + +pub const N0_CUTOFF: f64 = 1e-9; + +#[derive(Clone)] +pub struct NonAddHardSphereFunctional { + parameters: Arc, +} + +impl NonAddHardSphereFunctional { + pub fn new(parameters: Arc) -> Self { + Self { parameters } + } +} + +impl FunctionalContributionDual for NonAddHardSphereFunctional +where + N: DualNum + ScalarOperand, +{ + fn weight_functions(&self, temperature: N) -> WeightFunctionInfo { + let p = &self.parameters; + let r = p.hs_diameter(temperature) * 0.5; + WeightFunctionInfo::new(Array1::from_shape_fn(r.len(), |i| i), false) + .add( + WeightFunction::new_scaled(r.clone(), WeightFunctionShape::Delta), + false, + ) + .add( + WeightFunction { + prefactor: p.m.mapv(N::from), + kernel_radius: r.clone(), + shape: WeightFunctionShape::DeltaVec, + }, + false, + ) + .add( + WeightFunction { + prefactor: p.m.mapv(N::from), + kernel_radius: r, + shape: WeightFunctionShape::Theta, + }, + true, + ) + } + + fn calculate_helmholtz_energy_density( + &self, + temperature: N, + weighted_densities: ArrayView2, + ) -> EosResult> { + let p = &self.parameters; + // number of components + let n = p.m.len(); + // number of dimensions + let dim = (weighted_densities.shape()[0] - 1) / n - 1; + + // weighted densities + let n0i = weighted_densities.slice_axis(Axis(0), Slice::new(0, Some(n as isize), 1)); + let n2vi: Vec<_> = (0..dim) + .into_iter() + .map(|i| { + weighted_densities.slice_axis( + Axis(0), + Slice::new((n * (i + 1)) as isize, Some((n * (i + 2)) as isize), 1), + ) + }) + .collect(); + let n3 = weighted_densities.index_axis(Axis(0), n * (dim + 1)); + + // calculate rho0 + let r = p.hs_diameter(temperature) * 0.5; + let mut n2i = Array::zeros(n0i.raw_dim()); + for i in 0..n { + n2i.index_axis_mut(Axis(0), i) + .assign(&(&n0i.index_axis(Axis(0), i) * (r[i].powi(2) * (p.m[i] * 4.0 * PI)))); + } + let mut rho0: Array2 = (n2vi + .iter() + .map(|n2vi| n2vi * n2vi) + .fold(Array::zeros(n0i.raw_dim()), |acc, x| acc + x) + / -(&n2i * &n2i) + + 1.0) + * n0i; + rho0.iter_mut().zip(&n0i).for_each(|(rho0, &n0i)| { + if n0i.re() < N0_CUTOFF { + *rho0 = n0i; + } + }); + + // calculate xi + let n2v: Vec<_> = n2vi.iter().map(|n2vi| n2vi.sum_axis(Axis(0))).collect(); + let n2 = n2i.sum_axis(Axis(0)); + let mut xi = n2v + .iter() + .map(|n2v| n2v * n2v) + .fold(Array::zeros(n3.raw_dim()), |acc, x| acc + x) + / -(&n2 * &n2) + + 1.0; + xi.iter_mut() + .zip(&n0i.sum_axis(Axis(0))) + .for_each(|(xi, &n0i)| { + if n0i.re() < N0_CUTOFF { + *xi = N::one(); + } + }); + + // auxiliary variables + let n3i = n3.mapv(|n3| (-n3 + 1.0).recip()); + + // temperature dependent segment radius // calc & store this in struct + let s_eff_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.calc_sigma_eff_ij(i, j, temperature)); + + // temperature dependent segment radius // calc & store this in struct + let d_hs_ij = Array2::from_shape_fn((n, n), |(i, j)| { + p.hs_diameter_ij(i, j, temperature, s_eff_ij[[i, j]]) + }); + + // Additive hard-sphere diameter + let d_hs_add_ij = + Array2::from_shape_fn((n, n), |(i, j)| (d_hs_ij[[i, i]] + d_hs_ij[[j, j]]) * 0.5); + + Ok(rho0 + .view() + .into_shape([n, rho0.len() / n]) + .unwrap() + .axis_iter(Axis(1)) + .zip(n2.iter()) + .zip(n3i.iter()) + .zip(xi.iter()) + .map(|(((rho0, &n2), &n3i), &xi)| { + non_additive_hs_energy_density(p, &d_hs_ij, &d_hs_add_ij, &rho0, n2, n3i, xi) + }) + .collect::>() + .into_shape(n2.raw_dim()) + .unwrap()) + } +} + +pub fn non_additive_hs_energy_density + ScalarOperand>( + parameters: &SaftVRQMieParameters, + d_hs_ij: &Array2, + d_hs_add_ij: &Array2, + rho0: &ArrayBase, + n2: N, + n3i: N, + xi: N, +) -> N +where + S: Data, +{ + // auxiliary variables + let n = rho0.len(); + let p = parameters; + let d = Array1::from_shape_fn(n, |i| d_hs_ij[[i, i]]); + let g_hs_ij = Array2::from_shape_fn((n, n), |(i, j)| { + let mu = d[i] * d[j] / (d[i] + d[j]); + n3i + mu * n2 * xi * n3i.powi(2) / 2.0 + (mu * n2 * xi).powi(2) * n3i.powi(3) / 18.0 + }); + + // segment densities + let rho0_s = Array1::from_shape_fn(n, |i| -> N { rho0[i] * p.m[i] }); + + Array2::from_shape_fn((n, n), |(i, j)| { + -rho0_s[i] + * rho0_s[j] + * d_hs_add_ij[[i, j]].powi(2) + * g_hs_ij[[i, j]] + * (d_hs_add_ij[[i, j]] - d_hs_ij[[i, j]]) + * 2.0 + * PI + }) + .sum() +} + +impl fmt::Display for NonAddHardSphereFunctional { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Non-additive hard-sphere functional") + } +} diff --git a/src/saftvrqmie/dft/pure_saft_functional.rs b/src/saftvrqmie/dft/pure_saft_functional.rs new file mode 100644 index 000000000..1ab95e8ff --- /dev/null +++ b/src/saftvrqmie/dft/pure_saft_functional.rs @@ -0,0 +1,198 @@ +use crate::hard_sphere::FMTVersion; +use crate::saftvrqmie::eos::dispersion::{dispersion_energy_density, Alpha}; +use crate::saftvrqmie::parameters::SaftVRQMieParameters; +use feos_core::{EosError, EosResult}; +use feos_dft::{ + FunctionalContributionDual, WeightFunction, WeightFunctionInfo, WeightFunctionShape, +}; +use ndarray::*; +use num_dual::*; +use std::f64::consts::PI; +use std::fmt; +use std::sync::Arc; + +const PI36M1: f64 = 1.0 / (36.0 * PI); +const N3_CUTOFF: f64 = 1e-5; + +#[derive(Clone)] +pub struct PureFMTAssocFunctional { + parameters: Arc, + version: FMTVersion, +} + +impl PureFMTAssocFunctional { + pub fn new(parameters: Arc, version: FMTVersion) -> Self { + Self { + parameters, + version, + } + } +} + +impl + ScalarOperand> FunctionalContributionDual for PureFMTAssocFunctional { + fn weight_functions(&self, temperature: N) -> WeightFunctionInfo { + let r = self.parameters.hs_diameter(temperature) * 0.5; + WeightFunctionInfo::new(arr1(&[0]), false).extend( + vec![ + WeightFunctionShape::Delta, + WeightFunctionShape::Theta, + WeightFunctionShape::DeltaVec, + ] + .into_iter() + .map(|s| WeightFunction { + prefactor: self.parameters.m.mapv(|m| m.into()), + kernel_radius: r.clone(), + shape: s, + }) + .collect(), + false, + ) + } + + fn calculate_helmholtz_energy_density( + &self, + temperature: N, + weighted_densities: ArrayView2, + ) -> EosResult> { + //let p = &self.parameters; + + // weighted densities + let n2 = weighted_densities.index_axis(Axis(0), 0); + let n3 = weighted_densities.index_axis(Axis(0), 1); + let n2v = weighted_densities.slice_axis(Axis(0), Slice::new(2, None, 1)); + + // temperature dependent segment radius + let r = self.parameters.hs_diameter(temperature)[0] * 0.5; + + // auxiliary variables + if n3.iter().any(|n3| n3.re() > 1.0) { + return Err(EosError::IterationFailed(String::from( + "PureFMTAssocFunctional", + ))); + } + let ln31 = n3.mapv(|n3| (-n3).ln_1p()); + let n3rec = n3.mapv(|n3| n3.recip()); + let n3m1 = n3.mapv(|n3| -n3 + 1.0); + let n3m1rec = n3m1.mapv(|n3m1| n3m1.recip()); + let n1 = n2.mapv(|n2| n2 / (r * 4.0 * PI)); + let n0 = n2.mapv(|n2| n2 / (r * r * 4.0 * PI)); + let n1v = n2v.mapv(|n2v| n2v / (r * 4.0 * PI)); + + let (n1n2, n2n2) = match self.version { + FMTVersion::WhiteBear => ( + &n1 * &n2 - (&n1v * &n2v).sum_axis(Axis(0)), + &n2 * &n2 - (&n2v * &n2v).sum_axis(Axis(0)) * 3.0, + ), + FMTVersion::AntiSymWhiteBear => { + let mut xi2 = (&n2v * &n2v).sum_axis(Axis(0)) / n2.map(|n| n.powi(2)); + xi2.iter_mut().for_each(|x| { + if x.re() > 1.0 { + *x = N::one() + } + }); + ( + &n1 * &n2 - (&n1v * &n2v).sum_axis(Axis(0)), + &n2 * &n2 * xi2.mapv(|x| (-x + 1.0).powi(3)), + ) + } + _ => unreachable!(), + }; + + // The f3 term contains a 0/0, therefore a taylor expansion is used for small values of n3 + let mut f3 = (&n3m1 * &n3m1 * &ln31 + n3) * &n3rec * n3rec * &n3m1rec * &n3m1rec; + f3.iter_mut().zip(n3).for_each(|(f3, &n3)| { + if n3.re() < N3_CUTOFF { + *f3 = (((n3 * 35.0 / 6.0 + 4.8) * n3 + 3.75) * n3 + 8.0 / 3.0) * n3 + 1.5; + } + }); + let phi = -(&n0 * &ln31) + n1n2 * &n3m1rec + n2n2 * n2 * PI36M1 * f3; + + Ok(phi) + } +} + +impl fmt::Display for PureFMTAssocFunctional { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Pure FMT+association") + } +} + +#[derive(Clone)] +pub struct PureAttFunctional { + parameters: Arc, +} + +impl PureAttFunctional { + pub fn new(parameters: Arc) -> Self { + Self { parameters } + } +} + +impl + ScalarOperand> FunctionalContributionDual for PureAttFunctional { + fn weight_functions(&self, temperature: N) -> WeightFunctionInfo { + let d = self.parameters.hs_diameter(temperature); + const PSI: f64 = 1.3862; // Homosegmented DFT (Sauer2017) + WeightFunctionInfo::new(arr1(&[0]), false).add( + WeightFunction::new_scaled(d * PSI, WeightFunctionShape::Theta), + false, + ) + } + + fn weight_functions_pdgt(&self, temperature: N) -> WeightFunctionInfo { + let d = self.parameters.hs_diameter(temperature); + const PSI: f64 = 1.3286; // pDGT (Rehner2018) + WeightFunctionInfo::new(arr1(&[0]), false).add( + WeightFunction::new_scaled(d * PSI, WeightFunctionShape::Theta), + false, + ) + } + + fn calculate_helmholtz_energy_density( + &self, + temperature: N, + weighted_densities: ArrayView2, + ) -> EosResult> { + let p = &self.parameters; + let rho = weighted_densities.index_axis(Axis(0), 0); + let n = p.m.len(); + + // temperature dependent segment radius + let s_eff_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.calc_sigma_eff_ij(i, j, temperature)); + + // temperature dependent segment radius + let d_hs_ij = Array2::from_shape_fn((n, n), |(i, j)| { + p.hs_diameter_ij(i, j, temperature, s_eff_ij[[i, j]]) + }); + + // temperature dependent well depth + let epsilon_k_eff_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.calc_epsilon_k_eff_ij(i, j, temperature)); + + // temperature dependent well depth + let dq_ij = Array2::from_shape_fn((n, n), |(i, j)| p.quantum_d_ij(i, j, temperature)); + + // alphas .... + let alpha = Alpha::new(p, &s_eff_ij, &epsilon_k_eff_ij, temperature); + + let phi = rho.mapv(|rho_cell| { + dispersion_energy_density( + p, + &d_hs_ij, + &s_eff_ij, + &epsilon_k_eff_ij, + &dq_ij, + &alpha, + &arr1(&[rho_cell]), + temperature, + ) + }); + Ok(phi) + } +} + +impl fmt::Display for PureAttFunctional { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Pure attractive") + } +} diff --git a/src/saftvrqmie/eos/dispersion.rs b/src/saftvrqmie/eos/dispersion.rs new file mode 100644 index 000000000..1723cfde2 --- /dev/null +++ b/src/saftvrqmie/eos/dispersion.rs @@ -0,0 +1,788 @@ +use crate::saftvrqmie::parameters::SaftVRQMieParameters; +use feos_core::{HelmholtzEnergyDual, StateHD}; +use ndarray::{Array1, Array2}; +use num_dual::DualNum; +use std::f64::consts::FRAC_PI_6; +use std::fmt; +use std::sync::Arc; + +const LAM_COEFF: [[f64; 4]; 4] = [ + [0.81096, 1.7888, -37.578, 92.284], + [1.0205, -19.341, 151.26, -463.50], + [-1.9057, 22.845, -228.14, 973.92], + [1.0885, -6.1962, 106.98, -677.64], +]; + +const PHI: [[f64; 7]; 6] = [ + [ + 7.5365557, -37.60463, 71.745953, -46.83552, -2.467982, -0.50272, 8.0956883, + ], + [-359.44, 1825.6, -3168.0, 1884.2, -0.82376, -3.1935, 3.709], + [1550.9, -5070.1, 6534.6, -3288.7, -2.7171, 2.0883, 0.0], + [ + -1.19932, 9.063632, -17.9482, 11.34027, 20.52142, -56.6377, 40.53683, + ], + [ + -1911.28, 21390.175, -51320.7, 37064.54, 1103.742, -3264.61, 2556.181, + ], + [ + 9236.9, -129430.0, 357230.0, -315530.0, 1390.2, -4518.2, 4241.6, + ], +]; + +pub struct Alpha> { + alpha_ij: Array2, +} + +impl> Alpha { + pub fn new( + parameters: &SaftVRQMieParameters, + sigma_eff_ij: &Array2, + epsilon_k_eff_ij: &Array2, + temperature: D, + ) -> Self { + let p = parameters; + let nc = sigma_eff_ij.shape()[0]; + let mut alpha_ij: Array2 = Array2::zeros((nc, nc)); + + for i in 0..nc { + for j in 0..nc { + let sigma_ratio = D::one() * p.sigma_ij[[i, j]] / sigma_eff_ij[[i, j]]; + let eps_ratio = D::one() * p.epsilon_k_ij[[i, j]] / epsilon_k_eff_ij[[i, j]]; + let la = p.lambda_a_ij[[i, j]]; + let lr = p.lambda_r_ij[[i, j]]; + let sigma_ratio_a = sigma_ratio.powf(la); + let sigma_ratio_r = sigma_ratio.powf(lr); + let dmt = p.quantum_d_ij(i, j, temperature) / p.sigma_ij[[i, j]].powi(2); + let ma = sigma_ratio_a / (la - 3.0); + let mr = sigma_ratio_r / (lr - 3.0); + let q1a = sigma_ratio_a * sigma_ratio.powi(2) * la * (la - 1.0) / (la - 1.0); + let q1r = sigma_ratio_r * sigma_ratio.powi(2) * lr * (lr - 1.0) / (lr - 1.0); + alpha_ij[[i, j]] = (dmt * (q1a - q1r) + ma - mr) * p.c_ij[[i, j]] * eps_ratio; + } + } + Self { alpha_ij } + } + + fn f(&self, k: usize, i: usize, j: usize) -> D { + let a_ij = self.alpha_ij[[i, j]]; + let phi = PHI[k]; + (a_ij * phi[1] + a_ij.powi(2) * phi[2] + a_ij.powi(3) * phi[3] + phi[0]) + / (a_ij * phi[4] + a_ij.powi(2) * phi[5] + a_ij.powi(3) * phi[6] + 1.0) + } +} + +pub struct Dispersion { + pub parameters: Arc, +} + +impl> HelmholtzEnergyDual for Dispersion { + fn helmholtz_energy(&self, state: &StateHD) -> D { + // auxiliary variables + let n = self.parameters.m.len(); + let p = &self.parameters; + let rho = &state.partial_density; + // temperature dependent segment radius + let s_eff_ij = Array2::from_shape_fn((n, n), |(i, j)| -> D { + p.calc_sigma_eff_ij(i, j, state.temperature) + }); + + // temperature dependent segment radius + let d_hs_ij = Array2::from_shape_fn((n, n), |(i, j)| -> D { + p.hs_diameter_ij(i, j, state.temperature, s_eff_ij[[i, j]]) + }); + + // temperature dependent well depth + let epsilon_k_eff_ij = Array2::from_shape_fn((n, n), |(i, j)| -> D { + p.calc_epsilon_k_eff_ij(i, j, state.temperature) + }); + + // temperature dependent well depth + let dq_ij = Array2::from_shape_fn((n, n), |(i, j)| -> D { + p.quantum_d_ij(i, j, state.temperature) + }); + + // segment fractions + let mut x_s = Array1::from_shape_fn(n, |i| -> D { state.molefracs[i] * p.m[i] }); + let inv_x_s_sum = x_s.sum().recip(); + for i in 0..n { + x_s[i] *= inv_x_s_sum; + } + // Segment density + let mut rho_s = D::zero(); + for i in 0..n { + rho_s += rho[i] * p.m[i]; + } + // packing fractions + let zeta = zeta_saft_vrq_mie(&p.m, &x_s, &d_hs_ij, rho_s); + let zeta_bar = zeta_saft_vrq_mie(&p.m, &x_s, &s_eff_ij, rho_s); + + // alphas .... + let alpha = Alpha::new(p, &s_eff_ij, &epsilon_k_eff_ij, state.temperature); + + let a1 = first_order_perturbation(p, &x_s, zeta, rho_s, &d_hs_ij, &s_eff_ij, &dq_ij); + let a2 = second_order_perturbation( + p, &alpha, &x_s, zeta, zeta_bar, rho_s, &d_hs_ij, &s_eff_ij, &dq_ij, + ); + let a3 = third_order_perturbation(p, &alpha, &x_s, zeta_bar, &epsilon_k_eff_ij); + + let mut n_s = D::zero(); + for i in 0..n { + n_s += state.moles[i] * p.m[i]; + } + let inv_t = state.temperature.recip(); + n_s * (a1 * inv_t + a2 * inv_t.powi(2) + a3 * inv_t.powi(3)) + } +} + +#[cfg(feature = "dft")] +pub fn dispersion_energy_density>( + parameters: &SaftVRQMieParameters, + d_hs_ij: &Array2, + s_eff_ij: &Array2, + epsilon_k_eff_ij: &Array2, + dq_ij: &Array2, + alpha: &Alpha, + rho: &Array1, + temperature: D, +) -> D { + // auxiliary variables + let n = rho.len(); + let p = ¶meters; + + // Segment density + let mut rho_s = D::zero(); + for i in 0..n { + rho_s += rho[i] * p.m[i]; + } + // segment fractions + let x_s = Array1::from_shape_fn(n, |i| -> D { rho[i] * p.m[i] * rho_s.recip() }); + + // packing fractions + let zeta = zeta_saft_vrq_mie(&p.m, &x_s, d_hs_ij, rho_s); + let zeta_bar = zeta_saft_vrq_mie(&p.m, &x_s, s_eff_ij, rho_s); + + let a1 = first_order_perturbation(p, &x_s, zeta, rho_s, d_hs_ij, s_eff_ij, dq_ij); + let a2 = second_order_perturbation( + p, alpha, &x_s, zeta, zeta_bar, rho_s, d_hs_ij, s_eff_ij, dq_ij, + ); + let a3 = third_order_perturbation(p, alpha, &x_s, zeta_bar, epsilon_k_eff_ij); + + let inv_t = temperature.recip(); + rho_s * (a1 * inv_t + a2 * inv_t.powi(2) + a3 * inv_t.powi(3)) +} + +fn zeta_saft_vrq_mie>( + m: &Array1, + x_s: &Array1, + diameter: &Array2, + rho_s: D, +) -> D { + let mut zeta = D::zero(); + for i in 0..m.len() { + for j in 0..m.len() { + zeta += x_s[i] * x_s[j] * diameter[[i, j]].powi(3); + } + } + zeta * FRAC_PI_6 * rho_s +} + +fn first_order_perturbation>( + parameters: &SaftVRQMieParameters, + x_s: &Array1, + zeta: D, + rho_s: D, + d_hs_ij: &Array2, + s_eff_ij: &Array2, + dq_ij: &Array2, +) -> D { + let n = parameters.sigma.len(); + let mut a1 = D::zero(); + for i in 0..n { + for j in 0..n { + let x0 = d_hs_ij[[i, j]].recip() * parameters.sigma_ij[[i, j]]; + let x0_eff = s_eff_ij[[i, j]] / d_hs_ij[[i, j]]; + let dq_div_sigma_2 = dq_ij[[i, j]] / parameters.sigma_ij[[i, j]].powi(2); + a1 += x_s[i] + * x_s[j] + * FRAC_PI_6 + * rho_s + * d_hs_ij[[i, j]].powi(3) + * first_order_perturbation_ij( + parameters.lambda_a_ij[[i, j]], + parameters.lambda_r_ij[[i, j]], + parameters.epsilon_k_ij[[i, j]], + zeta, + x0, + x0_eff, + parameters.c_ij[[i, j]], + dq_div_sigma_2, + ) + } + } + a1 +} + +fn first_order_perturbation_ij>( + lambda_a: f64, + lambda_r: f64, + epsilon_k: f64, + zeta: D, + x0: D, + x0_eff: D, + c: f64, + dq_div_sigma_2: D, +) -> D { + let int_a = combine_sutherland_and_b(lambda_a, epsilon_k, zeta, x0, x0_eff); + let int_r = combine_sutherland_and_b(lambda_r, epsilon_k, zeta, x0, x0_eff); + // Quantum correction + let int_qa = combine_sutherland_and_b(lambda_a + 2.0, epsilon_k, zeta, x0, x0_eff); + let int_qr = combine_sutherland_and_b(lambda_r + 2.0, epsilon_k, zeta, x0, x0_eff); + let qa1 = dq_div_sigma_2 * quantum_prefactor(lambda_a); + let qr1 = dq_div_sigma_2 * quantum_prefactor(lambda_r); + + (int_qa * qa1 - int_qr * qr1 + int_a - int_r) * c +} + +fn eta_eff>(lambda: f64, zeta: D) -> D { + let inv_lambda = Array1::from(vec![ + 1.0, + 1.0 / lambda, + 1.0 / lambda.powi(2), + 1.0 / lambda.powi(3), + ]); + let c = Array1::from_shape_fn(4, |i| { + inv_lambda[0] * LAM_COEFF[i][0] + + inv_lambda[1] * LAM_COEFF[i][1] + + inv_lambda[2] * LAM_COEFF[i][2] + + inv_lambda[3] * LAM_COEFF[i][3] + }); + zeta * (zeta * (zeta * (zeta * c[3] + c[2]) + c[1]) + c[0]) +} + +fn sutherland>(lambda: f64, epsilon_k: f64, zeta: D, x0: D) -> D { + let ef = eta_eff(lambda, zeta); + (-ef * 0.5 + 1.0) * -12.0 * x0.powf(lambda) * epsilon_k / (lambda - 3.0) / (-ef + 1.0).powi(3) +} + +fn ilambda>(lambda: f64, x0: D) -> D { + -(x0.powf(3.0 - lambda) - 1.0) / (lambda - 3.0) +} + +fn jlambda>(lambda: f64, x0: D) -> D { + -(x0.powf(4.0 - lambda) * (lambda - 3.0) - x0.powf(3.0 - lambda) * (lambda - 4.0) - 1.0) + / ((lambda - 3.0) * (lambda - 4.0)) +} + +/// Calculate equation 33 of Lafitte 2013 +/// B is divided by the packing fraction +/// +/// \author Morten Hammer, February 2018 +fn b>(lambda: f64, epsilon_k: f64, zeta: D, x0: D, x0_eff: D) -> D { + let ilambda = ilambda(lambda, x0_eff); + let jlambda = jlambda(lambda, x0_eff); + let denum = (-zeta + 1.0).powi(3); + x0.powf(lambda) + * ((-zeta + 2.0) / denum * ilambda + -zeta * 9.0 * (zeta + 1.0) / denum * jlambda) + * 6.0 + * epsilon_k +} + +#[inline] +fn combine_sutherland_and_b>( + lambda: f64, + epsilon_k: f64, + zeta: D, + x0: D, + x0_eff: D, +) -> D { + let int_as = sutherland(lambda, epsilon_k, zeta, x0); + let int_b = b(lambda, epsilon_k, zeta, x0, x0_eff); + int_as + int_b +} + +fn second_order_perturbation>( + parameters: &SaftVRQMieParameters, + alpha: &Alpha, + x_s: &Array1, + zeta: D, + zeta_bar: D, + rho_s: D, + d_hs_ij: &Array2, + s_eff_ij: &Array2, + dq_ij: &Array2, +) -> D { + let n = parameters.sigma.len(); + let mut a2 = D::zero(); + + // Calculate isothermal hard sphere compressibillity factor + let k = (-zeta + 1.0).powi(4) + / (zeta * 4.0 + zeta.powi(2) * 4.0 - zeta.powi(3) * 4.0 + zeta.powi(4) + 1.0); + + for i in 0..n { + for j in 0..n { + let chi = alpha.f(0, i, j) * zeta_bar + + alpha.f(1, i, j) * zeta_bar.powi(5) + + alpha.f(2, i, j) * zeta_bar.powi(8); + let x0 = d_hs_ij[[i, j]].recip() * parameters.sigma_ij[[i, j]]; + let x0_eff = s_eff_ij[[i, j]] / d_hs_ij[[i, j]]; + let dq_div_sigma_2 = dq_ij[[i, j]] / parameters.sigma_ij[[i, j]].powi(2); + a2 += x_s[i] + * x_s[j] + * FRAC_PI_6 + * rho_s + * d_hs_ij[[i, j]].powi(3) + * (chi + 1.0) + * second_order_perturbation_ij( + parameters.lambda_a_ij[[i, j]], + parameters.lambda_r_ij[[i, j]], + parameters.epsilon_k_ij[[i, j]], + zeta, + x0, + x0_eff, + parameters.c_ij[[i, j]], + dq_div_sigma_2, + ) + } + } + a2 * k +} + +#[inline] +fn quantum_prefactor(lambda: f64) -> f64 { + lambda * (lambda - 1.0) +} + +fn second_order_perturbation_ij>( + lambda_a: f64, + lambda_r: f64, + epsilon_k: f64, + zeta: D, + x0: D, + x0_eff: D, + c: f64, + dq_div_sigma_2: D, +) -> D { + let lambda_2r = 2.0 * lambda_r; + let lambda_2a = 2.0 * lambda_a; + let lambda_ar = lambda_a + lambda_r; + // Quantum contributions + let qa1 = dq_div_sigma_2 * quantum_prefactor(lambda_a); + let qr1 = dq_div_sigma_2 * quantum_prefactor(lambda_r); + + let mut a2_ij = D::zero(); + let mut afac = D::one(); + let mut rfac = D::one(); + let mut arfac = -D::one() * 2.0; + // Loop all contributions + // 0: Mie contribution + // 1,2: Quantum corrections + for q in 0..3 { + let int_a = + combine_sutherland_and_b(lambda_2a + 2.0 * q as f64, epsilon_k, zeta, x0, x0_eff); + let int_r = + combine_sutherland_and_b(lambda_2r + 2.0 * q as f64, epsilon_k, zeta, x0, x0_eff); + let int_ar = + combine_sutherland_and_b(lambda_ar + 2.0 * q as f64, epsilon_k, zeta, x0, x0_eff); + if q == 1 { + rfac = qr1 * 2.0; + afac = qa1 * 2.0; + arfac = -(rfac + afac); + } else if q == 2 { + rfac = qr1 * qr1; + afac = qa1 * qa1; + arfac = -qa1 * qr1 * 2.0; + } + a2_ij += int_a * afac + int_ar * arfac + int_r * rfac; + } + a2_ij * 0.5 * epsilon_k * c.powi(2) +} + +fn third_order_perturbation>( + parameters: &SaftVRQMieParameters, + alpha: &Alpha, + x_s: &Array1, + zeta_bar: D, + epsilon_k_eff_ij: &Array2, +) -> D { + let n = parameters.sigma.len(); + let mut a3 = D::zero(); + for i in 0..n { + for j in 0..n { + a3 += x_s[i] + * x_s[j] + * third_order_perturbation_ij(i, j, epsilon_k_eff_ij[[i, j]], alpha, zeta_bar) + } + } + a3 +} + +fn third_order_perturbation_ij>( + i: usize, + j: usize, + epsilon_k_eff: D, + alpha: &Alpha, + zeta_bar: D, +) -> D { + -epsilon_k_eff.powi(3) + * alpha.f(3, i, j) + * zeta_bar + * (alpha.f(4, i, j) * zeta_bar + alpha.f(5, i, j) * zeta_bar.powi(2)).exp() +} + +impl fmt::Display for Dispersion { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Dispersion") + } +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::saftvrqmie::parameters::utils::h2_ne_fh1; + use crate::saftvrqmie::parameters::utils::hydrogen_fh1; + use approx::assert_relative_eq; + use ndarray::arr1; + use num_dual::Dual2; + use num_dual::DualNum; + use num_traits::Zero; + + #[test] + fn test_eta_eff() { + let lambda_6 = 6.0; + let lambda_12 = 12.0; + let mut zeta = 0.45; + let e_eff_6_045 = eta_eff(lambda_6, zeta); + let e_eff_12_045 = eta_eff(lambda_12, zeta); + zeta = 0.1; + let e_eff_6_01 = eta_eff(lambda_6, zeta); + let e_eff_12_01 = eta_eff(lambda_12, zeta); + assert_relative_eq!(e_eff_6_045, 0.19401806958333320, epsilon = 1e-7); + assert_relative_eq!(e_eff_12_045, 0.32193464807291666, epsilon = 1e-7); + assert_relative_eq!(e_eff_6_01, 4.7840898518518506E-002, epsilon = 1e-7); + assert_relative_eq!(e_eff_12_01, 7.6226364537037058E-002, epsilon = 1e-7); + } + + #[test] + fn test_alpha() { + let temperature = Dual2::from_re(26.7060).derive(); + let parameters = hydrogen_fh1(); + let n = 1; + let s_eff_ij = Array2::from_shape_fn((n, n), |(i, j)| { + parameters.calc_sigma_eff_ij(i, j, temperature) + }); + let epsilon_k_eff_ij = Array2::from_shape_fn((n, n), |(i, j)| { + parameters.calc_epsilon_k_eff_ij(i, j, temperature) + }); + let alpha = Alpha::new(¶meters, &s_eff_ij, &epsilon_k_eff_ij, temperature); + assert_relative_eq!( + alpha.alpha_ij[[0, 0]].re(), + 1.0239374984636636, + epsilon = 5e-8 + ); + } + + #[test] + fn test_sutherland() { + let x0 = Dual2::from_re(1.1).derive(); + let zeta = Dual2::from_re(0.333).derive(); + let lambda = 13.77; + let eps_div_k = 13.88; + let asa = sutherland(lambda, eps_div_k, zeta, x0); + assert_relative_eq!(asa.re(), -122.12017536923423, epsilon = 1e-12); + } + + #[test] + fn test_b() { + let x0 = Dual2::from_re(1.1).derive(); + let zeta = Dual2::from_re(0.333).derive(); + let lambda = 13.77; + let eps_div_k = 13.88; + let ba = b(lambda, eps_div_k, zeta, x0, x0); + assert_relative_eq!(ba.re(), 93.436438943866293, epsilon = 1e-12); + } + + #[test] + fn test_quantum_d_ij() { + let p = hydrogen_fh1(); + let temperature = Dual2::from_re(26.7060).derive(); + let dq_ij = p.quantum_d_ij(0, 0, temperature); + assert_relative_eq!(dq_ij.re(), 7.5092605940987542e-2, epsilon = 5e-8); + } + + #[test] + fn test_first_order_perturbation_ij() { + let p = hydrogen_fh1(); + let temperature = Dual2::from_re(26.7060).derive(); + let zeta = Dual2::from_re(0.333).derive(); + let dq_div_s2 = p.quantum_d_ij(0, 0, temperature) / p.sigma_ij[[0, 0]].powi(2); + let s_eff = p.calc_sigma_eff_ij(0, 0, temperature); + let d_hs = p.hs_diameter_ij(0, 0, temperature, s_eff); + let x0 = d_hs.recip() * p.sigma_ij[[0, 0]]; + let x0_eff = s_eff / d_hs; + + let a1_ij = first_order_perturbation_ij( + p.lambda_a_ij[[0, 0]], + p.lambda_r_ij[[0, 0]], + p.epsilon_k_ij[[0, 0]], + zeta, + x0, + x0_eff, + p.c_ij[[0, 0]], + dq_div_s2, + ); + let rel_err = (a1_ij.re() + 332.00915966785539) / 332.00915966785539; + assert_relative_eq!(rel_err, 0.0, epsilon = 1e-7); + } + + #[test] + fn test_second_order_perturbation_ij() { + let p = hydrogen_fh1(); + let temperature = Dual2::from_re(26.7060).derive(); + let zeta = Dual2::from_re(0.333).derive(); + let dq_div_s2 = p.quantum_d_ij(0, 0, temperature) / p.sigma_ij[[0, 0]].powi(2); + let s_eff = p.calc_sigma_eff_ij(0, 0, temperature); + let d_hs = p.hs_diameter_ij(0, 0, temperature, s_eff); + let x0 = d_hs.recip() * p.sigma_ij[[0, 0]]; + let x0_eff = s_eff / d_hs; + + let a2_ij = second_order_perturbation_ij( + p.lambda_a_ij[[0, 0]], + p.lambda_r_ij[[0, 0]], + p.epsilon_k_ij[[0, 0]], + zeta, + x0, + x0_eff, + p.c_ij[[0, 0]], + dq_div_s2, + ); + let rel_err = (a2_ij.re() + 1907.5055256805874) / 1907.5055256805874; + assert_relative_eq!(rel_err, 0.0, epsilon = 1e-7); + } + + #[test] + fn test_third_order_perturbation_ij() { + let p = hydrogen_fh1(); + let temperature = Dual2::from_re(26.7060).derive(); + let zeta_bar = Dual2::from_re(0.333).derive(); + let n = 1; + let s_eff_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.calc_sigma_eff_ij(i, j, temperature)); + let epsilon_k_eff_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.calc_epsilon_k_eff_ij(i, j, temperature)); + let alpha = Alpha::new(&p, &s_eff_ij, &epsilon_k_eff_ij, temperature); + + let a3_ij = third_order_perturbation_ij(0, 0, epsilon_k_eff_ij[[0, 0]], &alpha, zeta_bar); + + let rel_err = (a3_ij.re() + 25.807966819127916) / 25.807966819127916; + assert_relative_eq!(rel_err, 0.0, epsilon = 5e-7); + } + + #[test] + fn test_zeta_saft_vrq_mie() { + let p = hydrogen_fh1(); + let t = Dual2::from_re(26.7060).derive(); + let v = Dual2::from_re(1.0e26).derive(); + let n = Dual2::from_re(6.02214076e23).derive(); + let state = StateHD::new(t, v, arr1(&[n])); + let nc = 1; + // temperature dependent sigma + let s_eff_ij = Array2::from_shape_fn((nc, nc), |(i, j)| { + p.calc_sigma_eff_ij(i, j, state.temperature) + }); + // temperature dependent segment diameter + let d_hs_ij = Array2::from_shape_fn((nc, nc), |(i, j)| { + p.hs_diameter_ij(i, j, state.temperature, s_eff_ij[[i, j]]) + }); + + // segment fractions + let mut x_s = Array1::from_shape_fn(nc, |i| state.molefracs[i] * p.m[i]); + let inv_x_s_sum = x_s.sum().recip(); + for i in 0..nc { + x_s[i] *= inv_x_s_sum; + } + // Segment density + let mut rho_s = Dual2::zero(); + for i in 0..nc { + rho_s += state.partial_density[i] * p.m[i]; + } + // packing fractions + let zeta = zeta_saft_vrq_mie(&p.m, &x_s, &d_hs_ij, rho_s); + let zeta_bar = zeta_saft_vrq_mie(&p.m, &x_s, &s_eff_ij, rho_s); + assert_relative_eq!(zeta.re(), 9.7717457994590765E-002, epsilon = 5e-9); + assert_relative_eq!(zeta_bar.re(), 0.10864364645845238, epsilon = 5e-9); + } + + #[test] + fn test_perturbation_terms() { + let p = hydrogen_fh1(); + let t = Dual2::from_re(26.7060).derive(); + let v = Dual2::from_re(1.0e26).derive(); + let n = Dual2::from_re(6.02214076e23).derive(); + let state = StateHD::new(t, v, arr1(&[n])); + let nc = 1; + // temperature dependent sigma + let s_eff_ij = Array2::from_shape_fn((nc, nc), |(i, j)| { + p.calc_sigma_eff_ij(i, j, state.temperature) + }); + // temperature dependent segment diameter + let d_hs_ij = Array2::from_shape_fn((nc, nc), |(i, j)| { + p.hs_diameter_ij(i, j, state.temperature, s_eff_ij[[i, j]]) + }); + + // segment fractions + let mut x_s = Array1::from_shape_fn(nc, |i| state.molefracs[i] * p.m[i]); + let inv_x_s_sum = x_s.sum().recip(); + for i in 0..nc { + x_s[i] *= inv_x_s_sum; + } + + // Segment density + let mut rho_s = Dual2::zero(); + for i in 0..nc { + rho_s += state.partial_density[i] * p.m[i]; + } + + // packing fractions + let zeta = zeta_saft_vrq_mie(&p.m, &x_s, &d_hs_ij, rho_s); + let zeta_bar = zeta_saft_vrq_mie(&p.m, &x_s, &s_eff_ij, rho_s); + + // temperature dependent well depth + let epsilon_k_eff_ij = Array2::from_shape_fn((nc, nc), |(i, j)| { + p.calc_epsilon_k_eff_ij(i, j, state.temperature) + }); + + // alphas .... + let alpha = Alpha::new(&p, &s_eff_ij, &epsilon_k_eff_ij, state.temperature); + + // temperature dependent well depth + let dq_ij = + Array2::from_shape_fn((nc, nc), |(i, j)| p.quantum_d_ij(i, j, state.temperature)); + + let a1 = first_order_perturbation(&p, &x_s, zeta, rho_s, &d_hs_ij, &s_eff_ij, &dq_ij); + let a2 = second_order_perturbation( + &p, &alpha, &x_s, zeta, zeta_bar, rho_s, &d_hs_ij, &s_eff_ij, &dq_ij, + ); + let a3 = third_order_perturbation(&p, &alpha, &x_s, zeta_bar, &epsilon_k_eff_ij); + + let rel_err_a1 = (a1.re() + 30.702499892515764) / 30.702499892515764; + let rel_err_a2 = (a2.re() + 67.046957636607587) / 67.046957636607587; + let rel_err_a3 = (a3.re() + 470.96241656623727) / 470.96241656623727; + assert_relative_eq!(rel_err_a1.re(), 0.0, epsilon = 5e-7); + assert_relative_eq!(rel_err_a2.re(), 0.0, epsilon = 5e-7); + assert_relative_eq!(rel_err_a3.re(), 0.0, epsilon = 5e-7); + } + + #[test] + fn test_dispersion() { + let disp = Dispersion { + parameters: hydrogen_fh1(), + }; + let a_ref = [ + -1.2683816065838103, + -0.61628364979962436, + -0.40740884837300861, + -0.30420171646199534, + -0.24264152651314486, + ]; + let na = 6.02214076e23; + for it in 0..a_ref.len() { + let t = Dual2::from_re(26.7060 * (it + 1) as f64).derive(); + let v = Dual2::from_re(1.0e26).derive(); + let n = Dual2::from_re(na).derive(); + let state = StateHD::new(t, v, arr1(&[n])); + let a_disp = disp.helmholtz_energy(&state) / na; + assert_relative_eq!(a_disp.re(), a_ref[it], epsilon = 1e-7); + } + let t = Dual2::from_re(26.7060).derive(); + let v = Dual2::from_re(1.0e26 * 2.0).derive(); + let n = Dual2::from_re(na * 2.0).derive(); + let state = StateHD::new(t, v, arr1(&[n])); + let a_disp = disp.helmholtz_energy(&state) / na; + assert_relative_eq!(a_disp.re(), a_ref[0] * 2.0, epsilon = 1e-7); + } + + #[test] + fn test_parameters_mix() { + let disp = Dispersion { + parameters: h2_ne_fh1(), + }; + let p = disp.parameters; + assert_relative_eq!(p.c_ij[[0, 1]], 4.7303195840057679, epsilon = 1e-7); + assert_relative_eq!(p.epsilon_k_ij[[0, 1]], 28.246978839971383, epsilon = 1e-7); + assert_relative_eq!(p.lambda_a_ij[[0, 1]], 6.0, epsilon = 1e-7); + assert_relative_eq!(p.lambda_r_ij[[0, 1]], 10.745966692414834, epsilon = 1e-7); + } + + #[test] + fn test_dispersion_mix() { + let disp = Dispersion { + parameters: h2_ne_fh1(), + }; + let a_ref = [ + -4.4340438372333235, + -2.1563424617699911, + -1.4211021562556054, + -1.0581654195146963, + -0.84210863940206726, + ]; + let na = 6.02214076e23; + let n = [Dual2::from_re(1.1 * na), Dual2::from_re(1.0 * na)]; + let v = Dual2::from_re(1.0e26).derive(); + for it in 0..a_ref.len() { + let t = Dual2::from_re(30.0 * (it + 1) as f64).derive(); + let state = StateHD::new(t, v, arr1(&n)); + let a_disp = disp.helmholtz_energy(&state) / na; + dbg!(it); + assert_relative_eq!(a_disp.re(), a_ref[it], epsilon = 1e-7); + } + let t = Dual2::from_re(30.0).derive(); + let v = Dual2::from_re(1.0e26 * 2.0).derive(); + let n = [Dual2::from_re(2.2 * na), Dual2::from_re(2.0 * na)]; + let state = StateHD::new(t, v, arr1(&n)); + let a_disp = disp.helmholtz_energy(&state) / na; + assert_relative_eq!(a_disp.re(), a_ref[0] * 2.0, epsilon = 1e-7); + } + + #[cfg(feature = "dft")] + #[test] + fn test_dispersion_energy_density() { + let disp = Dispersion { + parameters: hydrogen_fh1(), + }; + let p = &disp.parameters; + let n = p.m.len(); + let rho = Array1::from_shape_fn(n, |_i| Dual2::from_re(0.01)); + let t = Dual2::from_re(25.0).derive(); + // temperature dependent segment radius // calc & store this in struct + let s_eff_ij = Array2::from_shape_fn((n, n), |(i, j)| p.calc_sigma_eff_ij(i, j, t)); + + // temperature dependent segment radius // calc & store this in struct + let d_hs_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.hs_diameter_ij(i, j, t, s_eff_ij[[i, j]])); + + // temperature dependent well depth // calc & store this in struct + let epsilon_k_eff_ij = + Array2::from_shape_fn((n, n), |(i, j)| p.calc_epsilon_k_eff_ij(i, j, t)); + + // temperature dependent well depth // calc & store this in struct + let dq_ij = Array2::from_shape_fn((n, n), |(i, j)| p.quantum_d_ij(i, j, t)); + + // alphas .... // calc & store this in struct + let alpha = Alpha::new(&p, &s_eff_ij, &epsilon_k_eff_ij, t); + let a_disp = dispersion_energy_density( + p, + &d_hs_ij, + &s_eff_ij, + &epsilon_k_eff_ij, + &dq_ij, + &alpha, + &rho, + t, + ); + + dbg!(rho); + dbg!(a_disp.re()); + assert_relative_eq!(a_disp.re(), -0.022349175545184223, epsilon = 1e-7); + } +} diff --git a/src/saftvrqmie/eos/hard_sphere.rs b/src/saftvrqmie/eos/hard_sphere.rs new file mode 100644 index 000000000..649928595 --- /dev/null +++ b/src/saftvrqmie/eos/hard_sphere.rs @@ -0,0 +1,358 @@ +use crate::saftvrqmie::parameters::SaftVRQMieParameters; +use feos_core::{HelmholtzEnergyDual, StateHD}; +use ndarray::*; +use num_dual::DualNum; +use std::f64::consts::TAU; +use std::fmt; +use std::sync::Arc; + +/// Boltzmann's constant in J/K +const KB: f64 = 1.380649e-23; +const PLANCK: f64 = 6.62607015e-34; +const D_QM_PREFACTOR: f64 = PLANCK * PLANCK / (TAU * TAU) / 12.0 * 1e20 / KB; + +const X_K21: [f64; 21] = [ + -0.995657163025808080735527280689003, + -0.973906528517171720077964012084452, + -0.930157491355708226001207180059508, + -0.865063366688984510732096688423493, + -0.780817726586416897063717578345042, + -0.679409568299024406234327365114874, + -0.562757134668604683339000099272694, + -0.433395394129247190799265943165784, + -0.294392862701460198131126603103866, + -0.148874338981631210884826001129720, + 0.000000000000000000000000000000000, + 0.148874338981631210884826001129720, + 0.294392862701460198131126603103866, + 0.433395394129247190799265943165784, + 0.562757134668604683339000099272694, + 0.679409568299024406234327365114874, + 0.780817726586416897063717578345042, + 0.865063366688984510732096688423493, + 0.930157491355708226001207180059508, + 0.973906528517171720077964012084452, + 0.995657163025808080735527280689003, +]; + +const W_K21: [f64; 21] = [ + 0.011694638867371874278064396062192, + 0.032558162307964727478818972459390, + 0.054755896574351996031381300244580, + 0.075039674810919952767043140916190, + 0.093125454583697605535065465083366, + 0.109387158802297641899210590325805, + 0.123491976262065851077958109831074, + 0.134709217311473325928054001771707, + 0.142775938577060080797094273138717, + 0.147739104901338491374841515972068, + 0.149445554002916905664936468389821, + 0.147739104901338491374841515972068, + 0.142775938577060080797094273138717, + 0.134709217311473325928054001771707, + 0.123491976262065851077958109831074, + 0.109387158802297641899210590325805, + 0.093125454583697605535065465083366, + 0.075039674810919952767043140916190, + 0.054755896574351996031381300244580, + 0.032558162307964727478818972459390, + 0.011694638867371874278064396062192, +]; + +impl SaftVRQMieParameters { + #[inline] + pub fn hs_diameter>(&self, temperature: D) -> Array1 { + Array1::from_shape_fn(self.m.len(), |i| -> D { + let sigma_eff = self.calc_sigma_eff_ij(i, i, temperature); + self.hs_diameter_ij(i, i, temperature, sigma_eff) + }) + } + + #[inline] + pub fn hs_diameter_ij>( + &self, + i: usize, + j: usize, + temperature: D, + sigma_eff: D, + ) -> D { + let r0 = self.zero_integrand(i, j, temperature, sigma_eff); + let mut d_hs = r0; + for k in 0..21 { + let width = (sigma_eff - r0) * 0.5; + let r = width * X_K21[k] + width + r0; + let u = self.qmie_potential_ij(i, j, r, temperature); + let f_u = -(-u[0] / temperature).exp() + 1.0; + d_hs += width * f_u * W_K21[k]; + } + d_hs + } + + pub fn zero_integrand>( + &self, + i: usize, + j: usize, + temperature: D, + sigma_eff: D, + ) -> D { + let mut r = sigma_eff * 0.7; + let mut f = D::zero(); + for _k in 1..20 { + let u_vec = self.qmie_potential_ij(i, j, r, temperature); + f = u_vec[0] / temperature + f64::EPSILON.ln(); + if f.re().abs() < 1.0e-12 { + break; + } + let dfdr = u_vec[1] / temperature; + let mut dr = -(f / dfdr); + if dr.re().abs() > 0.5 { + dr *= 0.5 / dr.re().abs(); + } + r += dr; + } + if f.re().abs() > 1.0e-12 { + println!("zero_integrand calculation failed {}", f.re().abs()); + } + r + } + + #[inline] + pub fn epsilon_k_eff>(&self, temperature: D) -> Array1 { + Array1::from_shape_fn(self.m.len(), |i| -> D { + self.calc_epsilon_k_eff_ij(i, i, temperature) + }) + } + + pub fn calc_epsilon_k_eff_ij>(&self, i: usize, j: usize, temperature: D) -> D { + let mut r = D::one() * self.sigma_ij[[i, j]]; + let mut u_vec = [D::zero(), D::zero(), D::zero()]; + for _k in 1..20 { + u_vec = self.qmie_potential_ij(i, j, r, temperature); + if u_vec[1].re().abs() < 1.0e-12 { + break; + } + r += -u_vec[1] / u_vec[2]; + } + if u_vec[1].re().abs() > 1.0e-12 { + println!("calc_epsilon_k_eff_ij calculation failed"); + } + -u_vec[0] + } + + #[inline] + pub fn sigma_eff>(&self, temperature: D) -> Array1 { + Array1::from_shape_fn(self.m.len(), |i| -> D { + self.calc_sigma_eff_ij(i, i, temperature) + }) + } + + pub fn calc_sigma_eff_ij>(&self, i: usize, j: usize, temperature: D) -> D { + let mut r = D::one() * self.sigma_ij[[i, j]]; + let mut u_vec = [D::zero(), D::zero(), D::zero()]; + for _k in 1..20 { + u_vec = self.qmie_potential_ij(i, j, r, temperature); + if u_vec[0].re().abs() < 1.0e-12 { + break; + } + r += -u_vec[0] / u_vec[1]; + } + if u_vec[0].re().abs() > 1.0e-12 { + println!("calc_sigma_eff_ij calculation failed"); + } + r + } + + #[inline] + pub fn quantum_d_ij>(&self, i: usize, j: usize, temperature: D) -> D { + quantum_d_mass(self.mass_ij[[i, j]], temperature) + } + + /// Feynman-Hibbs corrected potential + pub fn qmie_potential_ij>( + &self, + i: usize, + j: usize, + r: D, + temperature: D, + ) -> [D; 3] { + let lr = self.lambda_r_ij[[i, j]]; + let la = self.lambda_a_ij[[i, j]]; + let s = self.sigma_ij[[i, j]]; + let eps = self.epsilon_k_ij[[i, j]]; + let c = self.c_ij[[i, j]]; + let q1r = lr * (lr - 1.0); + let q1a = la * (la - 1.0); + let d = self.quantum_d_ij(i, j, temperature); + let u = (d + * (r.powf(lr + 2.0).recip() * q1r * s.powf(lr) + - r.powf(la + 2.0).recip() * q1a * s.powf(la)) + + r.powf(lr).recip() * s.powf(lr) + - r.powf(la).recip() * s.powf(la)) + * c + * eps; + + let u_r = (d + * (r.powf(lr + 3.0).recip() * -q1r * (lr + 2.0) * s.powf(lr) + + r.powf(la + 3.0).recip() * q1a * (la + 2.0) * s.powf(la)) + - r.powf(lr + 1.0).recip() * lr * s.powf(lr) + + r.powf(la + 1.0).recip() * la * s.powf(la)) + * c + * eps; + let u_rr = (d + * (r.powf(lr + 4.0).recip() * q1r * (lr + 2.0) * (lr + 3.0) * s.powf(lr) + - r.powf(la + 4.0).recip() * q1a * (la + 2.0) * (la + 3.0) * s.powf(la)) + + r.powf(lr + 2.0).recip() * lr * (lr + 1.0) * s.powf(lr) + - r.powf(la + 2.0).recip() * la * (la + 1.0) * s.powf(la)) + * c + * eps; + [u, u_r, u_rr] + } +} + +#[inline] +pub fn quantum_d_mass>(mass: f64, temperature: D) -> D { + temperature.recip() / mass * D_QM_PREFACTOR +} + +pub struct HardSphere { + pub parameters: Arc, +} + +impl> HelmholtzEnergyDual for HardSphere { + fn helmholtz_energy(&self, state: &StateHD) -> D { + let d = self.parameters.hs_diameter(state.temperature); + let zeta = zeta(&self.parameters.m, &state.partial_density, &d); + let frac_1mz3 = -(zeta[3] - 1.0).recip(); + let zeta_23 = zeta_23(&self.parameters.m, &state.molefracs, &d); + state.volume * 6.0 / std::f64::consts::PI + * (zeta[1] * zeta[2] * frac_1mz3 * 3.0 + + zeta[2].powi(2) * frac_1mz3.powi(2) * zeta_23 + + (zeta[2] * zeta_23.powi(2) - zeta[0]) * (zeta[3] * (-1.0)).ln_1p()) + } +} + +impl fmt::Display for HardSphere { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Hard Sphere") + } +} + +pub fn zeta>( + m: &Array1, + partial_density: &Array1, + diameter: &Array1, +) -> [D; 4] { + let mut zeta: [D; 4] = [D::zero(), D::zero(), D::zero(), D::zero()]; + for i in 0..m.len() { + for (k, z) in zeta.iter_mut().enumerate() { + *z += partial_density[i] + * diameter[i].powi(k as i32) + * (std::f64::consts::PI / 6.0 * m[i]); + } + } + zeta +} + +pub fn zeta_23>(m: &Array1, molefracs: &Array1, diameter: &Array1) -> D { + let mut zeta: [D; 2] = [D::zero(), D::zero()]; + for i in 0..m.len() { + for (k, z) in zeta.iter_mut().enumerate() { + *z += molefracs[i] * diameter[i].powi((k + 2) as i32) * m[i]; + } + } + zeta[0] / zeta[1] +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::saftvrqmie::parameters::utils::h2_ne_fh1; + use crate::saftvrqmie::parameters::utils::hydrogen_fh1; + use approx::assert_relative_eq; + use ndarray::arr1; + use num_dual::Dual2; + + #[test] + fn test_quantum_d_mass() { + let parameters = hydrogen_fh1(); + let temperature = Dual2::from_re(26.7060).derive(); + let r = Dual2::from_re(3.5); + let u0 = parameters.qmie_potential_ij(0, 0, r, temperature); + let eps = 1.0e-5; + let u2 = parameters.qmie_potential_ij(0, 0, r + eps, temperature); + let u1 = parameters.qmie_potential_ij(0, 0, r - eps, temperature); + let dudr_num = (u2[0].re() - u1[0].re()) / eps / 2.0; + let d2udr2_num = (u2[1].re() - u1[1].re()) / eps / 2.0; + assert!(((dudr_num - u0[1].re()) / u0[1].re()).abs() < 1.0e-9); + assert!(((d2udr2_num - u0[2].re()) / u0[2].re()).abs() < 1.0e-9); + } + + #[test] + fn test_sigma_effective() { + let parameters = hydrogen_fh1(); + let temperature = Dual2::from_re(26.7060).derive(); + let sigma_eff = parameters.calc_sigma_eff_ij(0, 0, temperature); + println!("{}", sigma_eff.re() - 3.2540054024660556); + assert!((sigma_eff.re() - 3.2540054024660556).abs() < 5.0e-7) + } + + #[test] + fn test_eps_div_k_effective() { + let parameters = hydrogen_fh1(); + let temperature = Dual2::from_re(26.7060).derive(); + let epsilon_k_eff = parameters.calc_epsilon_k_eff_ij(0, 0, temperature); + println!("{}", epsilon_k_eff.re() - 21.654396207986697); + assert!((epsilon_k_eff.re() - 21.654396207986697).abs() < 1.0e-6) + } + + #[test] + fn test_zero_integrand() { + let parameters = hydrogen_fh1(); + let temperature = Dual2::from_re(26.706).derive(); + let sigma_eff = parameters.calc_sigma_eff_ij(0, 0, temperature); + let r0 = parameters.zero_integrand(0, 0, temperature, sigma_eff); + println!("{}", r0.re() - 2.5265031901173732); + assert!((r0.re() - 2.5265031901173732).abs() < 5.0e-7) + } + + #[test] + fn test_hs_diameter() { + let parameters = hydrogen_fh1(); + let temperature = Dual2::from_re(26.7060).derive(); + let sigma_eff = parameters.calc_sigma_eff_ij(0, 0, temperature); + let d_hs = parameters.hs_diameter_ij(0, 0, temperature, sigma_eff); + assert!((d_hs.re() - 3.1410453883283341).abs() < 5.0e-8); + assert!((d_hs.v1[0] + 8.4528823966252661e-3).abs() < 1.0e-9); + } + + #[test] + fn test_hs_helmholtz_energy() { + let hs = HardSphere { + parameters: hydrogen_fh1(), + }; + let na = 6.02214076e23; + let t = 26.7060; + let v = 1.0e26; + let n = na * 1.1; + let s = StateHD::new(t, v, arr1(&[n])); + let a_rust = hs.helmholtz_energy(&s); + dbg!(a_rust / na); + assert_relative_eq!(a_rust / na, 0.54586730268029837, epsilon = 5e-7); + } + + #[test] + fn test_hs_helmholtz_energy_mix() { + let hs = HardSphere { + parameters: h2_ne_fh1(), + }; + let na = 6.02214076e23; + let t = 30.0; + let v = 1.0e26; + let n = [na * 1.1, na * 1.0]; + let s = StateHD::new(t, v, arr1(&n)); + let a_rust = hs.helmholtz_energy(&s); + dbg!(a_rust / na); + // non-additive: 1.8249307925054206 + assert_relative_eq!(a_rust / na, 1.8074833133403905, epsilon = 5e-7); + } +} diff --git a/src/saftvrqmie/eos/mod.rs b/src/saftvrqmie/eos/mod.rs new file mode 100644 index 000000000..e1bea6703 --- /dev/null +++ b/src/saftvrqmie/eos/mod.rs @@ -0,0 +1,309 @@ +use super::parameters::SaftVRQMieParameters; +use feos_core::parameter::Parameter; +use feos_core::{ + Contributions, EntropyScaling, EosError, EosResult, EquationOfState, HelmholtzEnergy, + MolarWeight, State, +}; +use ndarray::Array1; +use quantity::si::*; +use std::f64::consts::{FRAC_PI_6, PI}; +use std::sync::Arc; + +pub(crate) mod dispersion; +pub(crate) mod hard_sphere; +pub(crate) mod non_additive_hs; +use dispersion::Dispersion; +use hard_sphere::HardSphere; +use non_additive_hs::NonAddHardSphere; + +/// Customization options for the SAFT-VRQ Mie equation of state and functional. +#[derive(Copy, Clone)] +pub struct SaftVRQMieOptions { + pub max_eta: f64, + pub fh_order: FeynmanHibbsOrder, + pub inc_nonadd_term: bool, +} + +impl Default for SaftVRQMieOptions { + fn default() -> Self { + Self { + max_eta: 0.5, + fh_order: FeynmanHibbsOrder::FH1, + inc_nonadd_term: true, + } + } +} + +/// Order of Feynman-Hibbs potential +#[derive(Copy, Clone)] +#[cfg_attr(feature = "python", pyo3::pyclass)] +pub enum FeynmanHibbsOrder { + /// First order correction + FH1, + /// Second order correction + FH2, +} + +/// SAFT-VRQ Mie equation of state. +/// +/// # Note +/// Currently, only the first-order Feynman-Hibbs term is implemented. +pub struct SaftVRQMie { + parameters: Arc, + options: SaftVRQMieOptions, + contributions: Vec>, +} + +impl SaftVRQMie { + pub fn new(parameters: Arc) -> Self { + Self::with_options(parameters, SaftVRQMieOptions::default()) + } + + pub fn with_options(parameters: Arc, options: SaftVRQMieOptions) -> Self { + match options.fh_order { + FeynmanHibbsOrder::FH1 => (), + FeynmanHibbsOrder::FH2 => unimplemented!(), + }; + let mut contributions: Vec> = Vec::with_capacity(4); + contributions.push(Box::new(HardSphere { + parameters: parameters.clone(), + })); + contributions.push(Box::new(Dispersion { + parameters: parameters.clone(), + })); + if parameters.m.len() > 1 && options.inc_nonadd_term { + contributions.push(Box::new(NonAddHardSphere { + parameters: parameters.clone(), + })); + } + + Self { + parameters: parameters, + options, + contributions, + } + } +} + +impl EquationOfState for SaftVRQMie { + fn components(&self) -> usize { + self.parameters.pure_records.len() + } + + fn subset(&self, component_list: &[usize]) -> Self { + Self::with_options( + Arc::new(self.parameters.subset(component_list)), + self.options, + ) + } + + fn compute_max_density(&self, moles: &Array1) -> f64 { + self.options.max_eta * moles.sum() + / (FRAC_PI_6 * &self.parameters.m * self.parameters.sigma.mapv(|v| v.powi(3)) * moles) + .sum() + } + + fn residual(&self) -> &[Box] { + &self.contributions + } +} + +impl MolarWeight for SaftVRQMie { + fn molar_weight(&self) -> SIArray1 { + self.parameters.molarweight.clone() * GRAM / MOL + } +} + +fn omega11(t: f64) -> f64 { + 1.06036 * t.powf(-0.15610) + + 0.19300 * (-0.47635 * t).exp() + + 1.03587 * (-1.52996 * t).exp() + + 1.76474 * (-3.89411 * t).exp() +} + +fn omega22(t: f64) -> f64 { + 1.16145 * t.powf(-0.14874) + 0.52487 * (-0.77320 * t).exp() + 2.16178 * (-2.43787 * t).exp() + - 6.435e-4 * t.powf(0.14874) * (18.0323 * t.powf(-0.76830) - 7.27371).sin() +} + +#[inline] +fn chapman_enskog_thermal_conductivity( + temperature: SINumber, + molarweight: SINumber, + m: f64, + sigma: f64, + epsilon_k: f64, +) -> SINumber { + let t = temperature.to_reduced(KELVIN).unwrap(); + 0.083235 * (t * m / molarweight.to_reduced(GRAM / MOL).unwrap()).sqrt() + / sigma.powi(2) + / omega22(t / epsilon_k) + * WATT + / METER + / KELVIN +} + +impl EntropyScaling for SaftVRQMie { + fn viscosity_reference( + &self, + temperature: SINumber, + _: SINumber, + moles: &SIArray1, + ) -> EosResult { + let p = &self.parameters; + let mw = &p.molarweight; + let x = moles.to_reduced(moles.sum())?; + let sigma_eff = p.sigma_eff(temperature.to_reduced(KELVIN)?); + let epsilon_k_eff = p.epsilon_k_eff(temperature.to_reduced(KELVIN)?); + let ce: Array1 = (0..self.components()) + .map(|i| { + let tr = (temperature / epsilon_k_eff[i] / KELVIN) + .into_value() + .unwrap(); + 5.0 / 16.0 + * (mw[i] * GRAM / MOL * KB / NAV * temperature / PI) + .sqrt() + .unwrap() + / omega22(tr) + / (sigma_eff[i] * ANGSTROM).powi(2) + }) + .collect(); + let mut ce_mix = 0.0 * MILLI * PASCAL * SECOND; + for i in 0..self.components() { + let denom: f64 = (0..self.components()) + .map(|j| { + x[j] * (1.0 + + (ce[i] / ce[j]).into_value().unwrap().sqrt() + * (mw[j] / mw[i]).powf(1.0 / 4.0)) + .powi(2) + / (8.0 * (1.0 + mw[i] / mw[j])).sqrt() + }) + .sum(); + ce_mix += ce[i] * x[i] / denom + } + Ok(ce_mix) + } + + fn viscosity_correlation(&self, s_res: f64, x: &Array1) -> EosResult { + let coefficients = self + .parameters + .viscosity + .as_ref() + .expect("Missing viscosity coefficients."); + let m = (x * &self.parameters.m).sum(); + let s = s_res / m; + let pref = (x * &self.parameters.m) / m; + let a: f64 = (&coefficients.row(0) * x).sum(); + let b: f64 = (&coefficients.row(1) * &pref).sum(); + let c: f64 = (&coefficients.row(2) * &pref).sum(); + let d: f64 = (&coefficients.row(3) * &pref).sum(); + Ok(a + b * s + c * s.powi(2) + d * s.powi(3)) + } + + fn diffusion_reference( + &self, + temperature: SINumber, + volume: SINumber, + moles: &SIArray1, + ) -> EosResult { + if self.components() != 1 { + return Err(EosError::IncompatibleComponents(self.components(), 1)); + } + let p = &self.parameters; + let density = moles.sum() / volume; + let res: Array1 = (0..self.components()) + .map(|i| { + let tr = (temperature / p.epsilon_k[i] / KELVIN) + .into_value() + .unwrap(); + 3.0 / 8.0 / (p.sigma[i] * ANGSTROM).powi(2) / omega11(tr) / (density * NAV) + * (temperature * RGAS / PI / (p.molarweight[i] * GRAM / MOL)) + .sqrt() + .unwrap() + }) + .collect(); + Ok(res[0]) + } + + fn diffusion_correlation(&self, s_res: f64, x: &Array1) -> EosResult { + if self.components() != 1 { + return Err(EosError::IncompatibleComponents(self.components(), 1)); + } + let coefficients = self + .parameters + .diffusion + .as_ref() + .expect("Missing diffusion coefficients."); + let m = (x * &self.parameters.m).sum(); + let s = s_res / m; + let pref = (x * &self.parameters.m).mapv(|v| v / m); + let a: f64 = (&coefficients.row(0) * x).sum(); + let b: f64 = (&coefficients.row(1) * &pref).sum(); + let c: f64 = (&coefficients.row(2) * &pref).sum(); + let d: f64 = (&coefficients.row(3) * &pref).sum(); + let e: f64 = (&coefficients.row(4) * &pref).sum(); + Ok(a + b * s - c * (1.0 - s.exp()) * s.powi(2) - d * s.powi(4) - e * s.powi(8)) + } + + // Equation 4 of DOI: 10.1021/acs.iecr.9b04289 + fn thermal_conductivity_reference( + &self, + temperature: SINumber, + volume: SINumber, + moles: &SIArray1, + ) -> EosResult { + if self.components() != 1 { + return Err(EosError::IncompatibleComponents(self.components(), 1)); + } + let p = &self.parameters; + let mws = self.molar_weight(); + let state = State::new_nvt(&Arc::new(Self::new(p.clone())), temperature, volume, moles)?; + let res: Array1 = (0..self.components()) + .map(|i| { + let tr = (temperature / p.epsilon_k[i] / KELVIN) + .into_value() + .unwrap(); + let s_res_reduced = state + .molar_entropy(Contributions::ResidualNvt) + .to_reduced(RGAS) + .unwrap() + / p.m[i]; + let ref_ce = chapman_enskog_thermal_conductivity( + temperature, + mws.get(i), + p.m[i], + p.sigma[i], + p.epsilon_k[i], + ); + let alpha_visc = (-s_res_reduced / -0.5).exp(); + let ref_ts = (-0.0167141 * tr / p.m[i] + 0.0470581 * (tr / p.m[i]).powi(2)) + * (p.m[i] * p.m[i] * p.sigma[i].powi(3) * p.epsilon_k[i]) + * 1e-5 + * WATT + / METER + / KELVIN; + ref_ce + ref_ts * alpha_visc + }) + .collect(); + Ok(res[0]) + } + + fn thermal_conductivity_correlation(&self, s_res: f64, x: &Array1) -> EosResult { + if self.components() != 1 { + return Err(EosError::IncompatibleComponents(self.components(), 1)); + } + let coefficients = self + .parameters + .thermal_conductivity + .as_ref() + .expect("Missing thermal conductivity coefficients"); + let m = (x * &self.parameters.m).sum(); + let s = s_res / m; + let pref = (x * &self.parameters.m).mapv(|v| v / m); + let a: f64 = (&coefficients.row(0) * x).sum(); + let b: f64 = (&coefficients.row(1) * &pref).sum(); + let c: f64 = (&coefficients.row(2) * &pref).sum(); + let d: f64 = (&coefficients.row(3) * &pref).sum(); + Ok(a + b * s + c * (1.0 - s.exp()) + d * s.powi(2)) + } +} diff --git a/src/saftvrqmie/eos/non_additive_hs.rs b/src/saftvrqmie/eos/non_additive_hs.rs new file mode 100644 index 000000000..26f17120c --- /dev/null +++ b/src/saftvrqmie/eos/non_additive_hs.rs @@ -0,0 +1,117 @@ +use crate::saftvrqmie::eos::hard_sphere::zeta; +use crate::saftvrqmie::parameters::SaftVRQMieParameters; +use feos_core::{HelmholtzEnergyDual, StateHD}; +use ndarray::*; +use num_dual::DualNum; +use std::f64::consts::PI; +use std::fmt; +use std::sync::Arc; + +pub struct NonAddHardSphere { + pub parameters: Arc, +} + +impl> HelmholtzEnergyDual for NonAddHardSphere { + fn helmholtz_energy(&self, state: &StateHD) -> D { + let p = &self.parameters; + let n = p.m.len(); + // temperature dependent segment radius + let s_eff_ij = Array2::from_shape_fn((n, n), |(i, j)| -> D { + p.calc_sigma_eff_ij(i, j, state.temperature) + }); + + // temperature dependent segment radius + let d_hs_ij = Array2::from_shape_fn((n, n), |(i, j)| -> D { + p.hs_diameter_ij(i, j, state.temperature, s_eff_ij[[i, j]]) + }); + + // Additive hard-sphere diameter + let d_hs_add_ij = + Array2::from_shape_fn((n, n), |(i, j)| (d_hs_ij[[i, i]] + d_hs_ij[[j, j]]) * 0.5); + + let n_s = Array1::from_shape_fn(n, |i| state.moles[i] * p.m[i]).sum(); + n_s * reduced_non_additive_hs_energy(p, &d_hs_ij, &d_hs_add_ij, &state.partial_density) + } +} + +impl fmt::Display for NonAddHardSphere { + fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { + write!(f, "Non-additive Hard Sphere") + } +} + +pub fn reduced_non_additive_hs_energy>( + parameters: &SaftVRQMieParameters, + d_hs_ij: &Array2, + d_hs_add_ij: &Array2, + rho: &Array1, +) -> D { + // auxiliary variables + let n = rho.len(); + let p = ¶meters; + let d = Array1::from_shape_fn(n, |i| d_hs_ij[[i, i]]); + let zeta = zeta(&p.m, rho, &d); + let frac_1mz3 = -(zeta[3] - 1.0).recip(); + let g_hs_ij = Array2::from_shape_fn((n, n), |(i, j)| { + let mu = d[[i]] * d[[j]] / (d[[i]] + d[[j]]); + frac_1mz3 + + mu * zeta[2] * frac_1mz3.powi(2) * 3.0 + + (mu * zeta[2]).powi(2) * frac_1mz3.powi(3) * 2.0 + }); + + // overall density + let rho_s = Array1::from_shape_fn(n, |i| -> D { rho[i] * p.m[i] }).sum(); + // segment fractions + let x_s = Array1::from_shape_fn(n, |i| -> D { rho[i] * p.m[i] / rho_s }); + + Array2::from_shape_fn((n, n), |(i, j)| { + -rho_s + * x_s[i] + * x_s[j] + * d_hs_add_ij[[i, j]].powi(2) + * g_hs_ij[[i, j]] + * (d_hs_add_ij[[i, j]] - d_hs_ij[[i, j]]) + * 2.0 + * PI + }) + .sum() +} + +#[cfg(test)] +mod tests { + use super::*; + use crate::saftvrqmie::parameters::utils::h2_ne_fh1; + use crate::saftvrqmie::parameters::utils::hydrogen_fh1; + use approx::assert_relative_eq; + use ndarray::arr1; + + #[test] + fn test_non_add_hs_helmholtz_energy() { + let hs = NonAddHardSphere { + parameters: hydrogen_fh1(), + }; + let na = 6.02214076e23; + let t = 26.7060; + let v = 1.0e26; + let n = na * 1.1; + let s = StateHD::new(t, v, arr1(&[n])); + let a_rust = hs.helmholtz_energy(&s); + dbg!(a_rust / na); + assert_relative_eq!(a_rust / na, 0.0, epsilon = 1e-12); + } + + #[test] + fn test_non_add_hs_helmholtz_energy_mix() { + let hs = NonAddHardSphere { + parameters: h2_ne_fh1(), + }; + let na = 6.02214076e23; + let t = 30.0; + let v = 1.0e26; + let n = [na * 1.1, na * 1.0]; + let s = StateHD::new(t, v, arr1(&n)); + let a_rust = hs.helmholtz_energy(&s); + dbg!(a_rust / na); + assert_relative_eq!(a_rust / na, 1.7874359117834266E-002, epsilon = 5e-7); + } +} diff --git a/src/saftvrqmie/mod.rs b/src/saftvrqmie/mod.rs new file mode 100644 index 000000000..f05095813 --- /dev/null +++ b/src/saftvrqmie/mod.rs @@ -0,0 +1,23 @@ +//! SAFT-VRQ Mie equation of state. +//! +//! Quantum effects are described by the first order Feynman–Hibbs corrections to Mie fluids. +//! The model accurately predicts properties for pure substances and mixtures down to 20K. +//! For mixtures, the additive hard-sphere reference contribution is extended with a non-additive correction. +//! +//! # Literature +//! - Pure substances: [Aasen et al. (2019)](https://aip.scitation.org/doi/10.1063/1.5111364) +//! - Binary mixtures: [Aasen et al. (2020)](https://aip.scitation.org/doi/10.1063/1.5136079) +#![warn(clippy::all)] +#![allow(clippy::too_many_arguments)] +#[cfg(feature = "dft")] +mod dft; +mod eos; +mod parameters; + +#[cfg(feature = "dft")] +pub use dft::SaftVRQMieFunctional; +pub use eos::{FeynmanHibbsOrder, SaftVRQMie, SaftVRQMieOptions}; +pub use parameters::{SaftVRQMieBinaryRecord, SaftVRQMieParameters, SaftVRQMieRecord}; + +#[cfg(feature = "python")] +pub mod python; diff --git a/src/saftvrqmie/parameters.rs b/src/saftvrqmie/parameters.rs new file mode 100644 index 000000000..ede95fc81 --- /dev/null +++ b/src/saftvrqmie/parameters.rs @@ -0,0 +1,540 @@ +use feos_core::joback::JobackRecord; +use feos_core::parameter::{Parameter, ParameterError, PureRecord}; +use ndarray::{Array, Array1, Array2}; +use num_traits::Zero; +use quantity::si::{SINumber, ANGSTROM, CALORIE, GRAM, KELVIN, KILO, KILOGRAM, MOL, NAV, RGAS}; +use serde::{Deserialize, Serialize}; +use std::collections::HashMap; +use std::convert::TryFrom; +use std::fmt::Write; +use std::fs::File; +use std::io::BufWriter; + +/// SAFT-VRQ Mie pure-component parameters. +#[derive(Serialize, Deserialize, Clone, Default)] +pub struct SaftVRQMieRecord { + /// Segment number + pub m: f64, + /// Segment diameter in units of Angstrom + pub sigma: f64, + /// Energetic parameter in units of Kelvin + pub epsilon_k: f64, + /// Repulsive Mie exponent + pub lr: f64, + /// Attractive Mie exponent + pub la: f64, + /// Entropy scaling coefficients for the viscosity + #[serde(skip_serializing_if = "Option::is_none")] + pub viscosity: Option<[f64; 4]>, + /// Entropy scaling coefficients for the diffusion coefficient + #[serde(skip_serializing_if = "Option::is_none")] + pub diffusion: Option<[f64; 5]>, + /// Entropy scaling coefficients for the thermal conductivity + #[serde(skip_serializing_if = "Option::is_none")] + pub thermal_conductivity: Option<[f64; 4]>, +} + +impl std::fmt::Display for SaftVRQMieRecord { + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + write!(f, "SaftVRQMieRecord(m={}", self.m)?; + write!(f, ", sigma={}", self.sigma)?; + write!(f, ", epsilon_k={}", self.epsilon_k)?; + if let Some(n) = &self.viscosity { + write!(f, ", viscosity={:?}", n)?; + } + if let Some(n) = &self.diffusion { + write!(f, ", diffusion={:?}", n)?; + } + if let Some(n) = &self.thermal_conductivity { + write!(f, ", thermal_conductivity={:?}", n)?; + } + write!(f, ")") + } +} + +impl SaftVRQMieRecord { + pub fn new( + m: f64, + sigma: f64, + epsilon_k: f64, + lr: f64, + la: f64, + viscosity: Option<[f64; 4]>, + diffusion: Option<[f64; 5]>, + thermal_conductivity: Option<[f64; 4]>, + ) -> SaftVRQMieRecord { + SaftVRQMieRecord { + m, + sigma, + epsilon_k, + lr, + la, + viscosity, + diffusion, + thermal_conductivity, + } + } +} + +/// SAFT-VRQ Mie binary mixture parameters. +#[derive(Serialize, Deserialize, Clone, Default)] +pub struct SaftVRQMieBinaryRecord { + /// correction to energy parameters + pub k_ij: f64, + /// correction to diameter + pub l_ij: f64, +} + +impl std::fmt::Display for SaftVRQMieBinaryRecord { + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + write!(f, "SaftVRQMieBinaryParameters(")?; + write!(f, "\n\tk_ij={}", self.k_ij)?; + write!(f, "\n\tl_ij={}", self.l_ij)?; + write!(f, "\n)") + } +} + +impl TryFrom for SaftVRQMieBinaryRecord { + type Error = ParameterError; + + fn try_from(_f: f64) -> Result { + Err(ParameterError::IncompatibleParameters( + "Cannot infer k_ij and l_ij from single float.".to_string(), + )) + } +} + +impl TryFrom for f64 { + type Error = ParameterError; + + fn try_from(_f: SaftVRQMieBinaryRecord) -> Result { + Err(ParameterError::IncompatibleParameters( + "Cannot infer k_ij and l_ij from single float.".to_string(), + )) + } +} + +/// Parameter set required for the SAFT-VRQ Mie equation of state and Helmholtz energy functional. +pub struct SaftVRQMieParameters { + pub molarweight: Array1, + pub m: Array1, + pub sigma: Array1, + pub epsilon_k: Array1, + pub k_ij: Array2, + pub l_ij: Array2, + pub sigma_ij: Array2, + pub epsilon_k_ij: Array2, + pub e_k_ij: Array2, + pub lr: Array1, + pub la: Array1, + pub c_ij: Array2, + pub lambda_r_ij: Array2, + pub lambda_a_ij: Array2, + pub mass_ij: Array2, + pub viscosity: Option>, + pub diffusion: Option>, + pub thermal_conductivity: Option>, + pub pure_records: Vec>, + pub binary_records: Array2, + pub joback_records: Option>, +} + +impl Parameter for SaftVRQMieParameters { + type Pure = SaftVRQMieRecord; + type IdealGas = JobackRecord; + type Binary = SaftVRQMieBinaryRecord; + + fn from_records( + pure_records: Vec>, + binary_records: Array2, + ) -> Self { + let n = pure_records.len(); + + let mut molarweight = Array::zeros(n); + let mut m = Array::zeros(n); + let mut sigma = Array::zeros(n); + let mut epsilon_k = Array::zeros(n); + let mut lr = Array::zeros(n); + let mut la = Array::zeros(n); + let mut viscosity = Vec::with_capacity(n); + let mut diffusion = Vec::with_capacity(n); + let mut thermal_conductivity = Vec::with_capacity(n); + + let mut component_index = HashMap::with_capacity(n); + + for (i, record) in pure_records.iter().enumerate() { + component_index.insert(record.identifier.clone(), i); + let r = &record.model_record; + m[i] = r.m; + sigma[i] = r.sigma; + epsilon_k[i] = r.epsilon_k; + lr[i] = r.lr; + la[i] = r.la; + viscosity.push(r.viscosity); + diffusion.push(r.diffusion); + thermal_conductivity.push(r.thermal_conductivity); + molarweight[i] = record.molarweight; + } + + let k_ij = binary_records.map(|br| br.k_ij); + let l_ij = binary_records.map(|br| br.l_ij); + let mut epsilon_k_ij = Array::zeros((n, n)); + let mut sigma_ij = Array::zeros((n, n)); + let mut e_k_ij = Array::zeros((n, n)); + let mut lambda_r_ij = Array::zeros((n, n)); + let mut lambda_a_ij = Array::zeros((n, n)); + let mut c_ij = Array::zeros((n, n)); + let mut mass_ij = Array::zeros((n, n)); + let to_mass_per_molecule = (GRAM / MOL / NAV).to_reduced(KILOGRAM).unwrap(); + for i in 0..n { + for j in 0..n { + sigma_ij[[i, j]] = (1.0 - l_ij[[i, j]]) * 0.5 * (sigma[i] + sigma[j]); + e_k_ij[[i, j]] = (sigma[i].powi(3) * sigma[j].powi(3)).sqrt() + / sigma_ij[[i, j]].powi(3) + * (epsilon_k[i] * epsilon_k[j]).sqrt(); + epsilon_k_ij[[i, j]] = (1.0 - k_ij[[i, j]]) * e_k_ij[[i, j]]; + lambda_r_ij[[i, j]] = ((lr[i] - 3.0) * (lr[j] - 3.0)).sqrt() + 3.0; + lambda_a_ij[[i, j]] = ((la[i] - 3.0) * (la[j] - 3.0)).sqrt() + 3.0; + c_ij[[i, j]] = lambda_r_ij[[i, j]] / (lambda_r_ij[[i, j]] - lambda_a_ij[[i, j]]) + * (lambda_r_ij[[i, j]] / lambda_a_ij[[i, j]]) + .powf(lambda_a_ij[[i, j]] / (lambda_r_ij[[i, j]] - lambda_a_ij[[i, j]])); + mass_ij[[i, j]] = 2.0 * molarweight[i] * molarweight[j] + / (molarweight[i] + molarweight[j]) + * to_mass_per_molecule; + } + } + + let viscosity_coefficients = if viscosity.iter().any(|v| v.is_none()) { + None + } else { + let mut v = Array2::zeros((4, viscosity.len())); + for (i, vi) in viscosity.iter().enumerate() { + v.column_mut(i).assign(&Array1::from(vi.unwrap().to_vec())); + } + Some(v) + }; + + let diffusion_coefficients = if diffusion.iter().any(|v| v.is_none()) { + None + } else { + let mut v = Array2::zeros((5, diffusion.len())); + for (i, vi) in diffusion.iter().enumerate() { + v.column_mut(i).assign(&Array1::from(vi.unwrap().to_vec())); + } + Some(v) + }; + + let thermal_conductivity_coefficients = if thermal_conductivity.iter().any(|v| v.is_none()) + { + None + } else { + let mut v = Array2::zeros((4, thermal_conductivity.len())); + for (i, vi) in thermal_conductivity.iter().enumerate() { + v.column_mut(i).assign(&Array1::from(vi.unwrap().to_vec())); + } + Some(v) + }; + + let joback_records = pure_records + .iter() + .map(|r| r.ideal_gas_record.clone()) + .collect(); + + Self { + molarweight, + m, + sigma, + epsilon_k, + k_ij, + l_ij, + sigma_ij, + epsilon_k_ij, + e_k_ij, + lr, + la, + c_ij, + lambda_r_ij, + lambda_a_ij, + mass_ij, + viscosity: viscosity_coefficients, + diffusion: diffusion_coefficients, + thermal_conductivity: thermal_conductivity_coefficients, + pure_records, + binary_records, + joback_records, + } + } + + fn records( + &self, + ) -> ( + &[PureRecord], + &Array2, + ) { + (&self.pure_records, &self.binary_records) + } +} + +impl SaftVRQMieParameters { + pub fn to_markdown(&self) -> String { + let mut output = String::new(); + let o = &mut output; + write!( + o, + "|component|molarweight|$\\sigma$|$\\varepsilon$|$\\lambda_r$|$\\lambda_a$|\n|-|-|-|-|-|-|" + ) + .unwrap(); + for i in 0..self.m.len() { + let component = self.pure_records[i].identifier.name.clone(); + let component = component.unwrap_or(format!("Component {}", i + 1)); + write!( + o, + "\n|{}|{}|{}|{}|{}|{}|", + component, + self.molarweight[i], + self.sigma[i], + self.epsilon_k[i], + self.lr[i], + self.la[i] + ) + .unwrap(); + } + + output + } + + /// Generate energy and force tables to be used with LAMMPS' `pair_style table` command. + /// + /// For a given `temperature`, `n` values between `r_min` and `r_max` (both including) are tabulated. + /// + /// Files for all pure substances and all unique pairs are generated, + /// where filenames use either the "name" field of the identifier or the index if no name is present. + /// + /// # Example + /// + /// For a hydrogen-neon mixture at 30 K, three files will be created. + /// + /// - "hydrogen_30K.table" for H-H interactions, + /// - "neon_30K.table" for Ne-Ne interactions, + /// - "hydrogen_neon_30K.table" for H-Ne interactions. + pub fn lammps_tables( + &self, + temperature: SINumber, + n: usize, + r_min: SINumber, + r_max: SINumber, + ) -> std::io::Result<()> { + let t = temperature.to_reduced(KELVIN).unwrap(); + let rs = Array1::linspace( + r_min.to_reduced(ANGSTROM).unwrap(), + r_max.to_reduced(ANGSTROM).unwrap(), + n, + ); + let energy_conversion = (KELVIN * RGAS / (KILO * CALORIE / MOL)) + .into_value() + .unwrap(); + let force_conversion = (KELVIN * RGAS / (KILO * CALORIE / MOL)) + .into_value() + .unwrap(); + + let n_components = self.sigma.len(); + for i in 0..n_components { + for j in i..n_components { + let name_i = self.pure_records[i] + .identifier + .name + .clone() + .unwrap_or(i.to_string()); + let name_j = self.pure_records[j] + .identifier + .name + .clone() + .unwrap_or(j.to_string()); + + let name = if i == j { + name_i + } else { + format!("{}_{}", name_i, name_j) + }; + let f = File::create(format!("{}_{}K.table", name, t))?; + let mut stream = BufWriter::new(f); + + std::io::Write::write( + &mut stream, + b"# DATE: YYYY-MM-DD UNITS: real CONTRIBUTOR: YOUR NAME\n", + )?; + std::io::Write::write( + &mut stream, + format!("# FH1 potential for {} at T = {}\n", name, temperature).as_bytes(), + )?; + std::io::Write::write(&mut stream, format!("FH1_{}\n", name).as_bytes())?; + std::io::Write::write(&mut stream, format!("N {}\n\n", n).as_bytes())?; + + for (k, &r) in rs.iter().enumerate() { + let [u, du, _] = self.qmie_potential_ij(i, j, r, t); + std::io::Write::write( + &mut stream, + format!( + "{} {:12.8} {:12.8} {:12.8}\n", + k + 1, + r, + u * energy_conversion, + -du * force_conversion + ) + .as_bytes(), + )?; + } + std::io::Write::flush(&mut stream)?; + } + } + Ok(()) + } +} + +impl std::fmt::Display for SaftVRQMieParameters { + fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { + write!(f, "SaftVRQMieParameters(")?; + write!(f, "\n\tmolarweight={}", self.molarweight)?; + write!(f, "\n\tm={}", self.m)?; + write!(f, "\n\tsigma={}", self.sigma)?; + write!(f, "\n\tepsilon_k={}", self.epsilon_k)?; + + if !self.k_ij.iter().all(|k| k.is_zero()) { + write!(f, "\n\tk_ij=\n{}", self.k_ij)?; + } + write!(f, "\n)") + } +} + +#[cfg(test)] +pub mod utils { + use super::*; + use std::sync::Arc; + + pub fn hydrogen_fh1() -> Arc { + let hydrogen_json = r#" + { + "identifier": { + "cas": "1333-74-0", + "name": "hydrogen", + "iupac_name": "hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0243, + "epsilon_k": 26.706, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 2.0157309551872 + }"#; + let hydrogen_record: PureRecord = + serde_json::from_str(hydrogen_json).expect("Unable to parse json."); + Arc::new(SaftVRQMieParameters::new_pure(hydrogen_record)) + } + + #[allow(dead_code)] + pub fn helium_fh1() -> Arc { + let helium_json = r#" + { + "identifier": { + "cas": "1333-74-0", + "name": "helium", + "iupac_name": "helium", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "He" + }, + "model_record": { + "m": 1.0, + "sigma": 2.7443, + "epsilon_k": 5.4195, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 4.002601643881807 + }"#; + let helium_record: PureRecord = + serde_json::from_str(helium_json).expect("Unable to parse json."); + Arc::new(SaftVRQMieParameters::new_pure(helium_record)) + } + + #[allow(dead_code)] + pub fn neon_fh1() -> Arc { + let neon_json = r#" + { + "identifier": { + "cas": "1333-74-0", + "name": "neon", + "iupac_name": "neon", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "Ne" + }, + "model_record": { + "m": 1.0, + "sigma": 2.7778, + "epsilon_k": 37.501, + "lr": 13.0, + "la": 6.0 + }, + "molarweight": 20.17969806457545 + }"#; + let neon_record: PureRecord = + serde_json::from_str(neon_json).expect("Unable to parse json."); + Arc::new(SaftVRQMieParameters::new_pure(neon_record)) + } + + pub fn h2_ne_fh1() -> Arc { + let binary_json = r#"[ + { + "identifier": { + "cas": "1333-74-0", + "name": "hydrogen", + "iupac_name": "hydrogen", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 3.0243, + "epsilon_k": 26.706, + "lr": 9.0, + "la": 6.0 + }, + "molarweight": 2.0157309551872 + }, + { + "identifier": { + "cas": "1333-74-0", + "name": "neon", + "iupac_name": "neon", + "smiles": "[HH]", + "inchi": "InChI=1S/H2/h1H", + "formula": "H2" + }, + "model_record": { + "m": 1.0, + "sigma": 2.7778, + "epsilon_k": 37.501, + "lr": 13.0, + "la": 6.0 + }, + "molarweight": 20.17969806457545 + } + ]"#; + let binary_record: Vec> = + serde_json::from_str(binary_json).expect("Unable to parse json."); + Arc::new(SaftVRQMieParameters::new_binary( + binary_record, + Some(SaftVRQMieBinaryRecord { + k_ij: 0.105, + l_ij: 0.0, + }), + )) + } +} diff --git a/src/saftvrqmie/python.rs b/src/saftvrqmie/python.rs new file mode 100644 index 000000000..699269d29 --- /dev/null +++ b/src/saftvrqmie/python.rs @@ -0,0 +1,240 @@ +//! Python bindings for the SAFT-VRQ Mie equation of state. +use crate::saftvrqmie::eos::FeynmanHibbsOrder; +use crate::saftvrqmie::parameters::{ + SaftVRQMieBinaryRecord, SaftVRQMieParameters, SaftVRQMieRecord, +}; +use feos_core::joback::JobackRecord; +use feos_core::parameter::{ + BinaryRecord, Identifier, IdentifierOption, Parameter, ParameterError, PureRecord, +}; +use feos_core::python::joback::PyJobackRecord; +use feos_core::python::parameter::PyIdentifier; +use feos_core::*; +use ndarray::Array2; +use numpy::{PyArray2, PyReadonlyArray2, ToPyArray}; +use pyo3::exceptions::{PyIOError, PyTypeError}; +use pyo3::prelude::*; +use quantity::python::PySINumber; +use std::convert::{TryFrom, TryInto}; +use std::sync::Arc; + +/// Create a set of Saft-VRQ Mie parameters from records. +#[pyclass(name = "SaftVRQMieRecord")] +#[pyo3( + text_signature = "(m, sigma, epsilon_k, viscosity=None, diffusion=None, thermal_conductivity=None)" +)] +#[derive(Clone)] +pub struct PySaftVRQMieRecord(SaftVRQMieRecord); + +#[pymethods] +impl PySaftVRQMieRecord { + #[new] + fn new( + m: f64, + sigma: f64, + epsilon_k: f64, + lr: f64, + la: f64, + viscosity: Option<[f64; 4]>, + ) -> Self { + Self(SaftVRQMieRecord::new( + m, sigma, epsilon_k, lr, la, viscosity, None, None, + )) + } + + #[getter] + fn get_m(&self) -> f64 { + self.0.m + } + + #[getter] + fn get_sigma(&self) -> f64 { + self.0.sigma + } + + #[getter] + fn get_epsilon_k(&self) -> f64 { + self.0.epsilon_k + } + + #[getter] + fn get_lr(&self) -> f64 { + self.0.lr + } + + #[getter] + fn get_la(&self) -> f64 { + self.0.la + } + + #[getter] + fn get_viscosity(&self) -> Option<[f64; 4]> { + self.0.viscosity + } + + #[getter] + fn get_diffusion(&self) -> Option<[f64; 5]> { + self.0.diffusion + } + + #[getter] + fn get_thermal_conductivity(&self) -> Option<[f64; 4]> { + self.0.thermal_conductivity + } + + fn __repr__(&self) -> PyResult { + Ok(self.0.to_string()) + } +} + +/// Create a set of Saft-VRQ Mie parameters from records. +#[pyclass(name = "SaftVRQMieBinaryRecord")] +#[pyo3(text_signature = "(k_ij, l_ij)")] +#[derive(Clone)] +pub struct PySaftVRQMieBinaryRecord(SaftVRQMieBinaryRecord); + +#[pymethods] +impl PySaftVRQMieBinaryRecord { + #[new] + fn new(k_ij: f64, l_ij: f64) -> Self { + Self(SaftVRQMieBinaryRecord { k_ij, l_ij }) + } + + #[getter] + fn get_k_ij(&self) -> f64 { + self.0.k_ij + } + + #[getter] + fn get_l_ij(&self) -> f64 { + self.0.l_ij + } + + #[setter] + fn set_k_ij(&mut self, k_ij: f64) { + self.0.k_ij = k_ij + } + + #[setter] + fn set_l_ij(&mut self, l_ij: f64) { + self.0.l_ij = l_ij + } +} + +/// Create a set of SAFT-VRQ Mie parameters from records. +/// +/// Parameters +/// ---------- +/// pure_records : List[PureRecord] +/// pure substance records. +/// binary_records : List[BinaryRecord], optional +/// binary saft parameter records +/// substances : List[str], optional +/// The substances to use. Filters substances from `pure_records` according to +/// `search_option`. +/// When not provided, all entries of `pure_records` are used. +/// search_option : {'Name', 'Cas', 'Inchi', 'IupacName', 'Formula', 'Smiles'}, optional, defaults to 'Name'. +/// Identifier that is used to search substance. +/// +/// Returns +/// ------- +/// SaftVRQMieParameters +#[pyclass(name = "SaftVRQMieParameters")] +#[pyo3( + text_signature = "(pure_records, binary_records=None, substances=None, search_option='Name')" +)] +#[derive(Clone)] +pub struct PySaftVRQMieParameters(pub Arc); + +impl_json_handling!(PySaftVRQMieRecord); +impl_pure_record!( + SaftVRQMieRecord, + PySaftVRQMieRecord, + JobackRecord, + PyJobackRecord +); +impl_binary_record!(SaftVRQMieBinaryRecord, PySaftVRQMieBinaryRecord); +impl_parameter!(SaftVRQMieParameters, PySaftVRQMieParameters); + +#[pymethods] +impl PySaftVRQMieParameters { + #[getter] + fn get_k_ij<'py>(&self, py: Python<'py>) -> &'py PyArray2 { + self.0.k_ij.view().to_pyarray(py) + } + + #[getter] + fn get_l_ij<'py>(&self, py: Python<'py>) -> &'py PyArray2 { + self.0.l_ij.view().to_pyarray(py) + } + + /// Generate energy and force tables to be used with LAMMPS' `pair_style table` command. + /// + /// Parameters + /// ---------- + /// temperature : SINumber + /// temperature at which the Feynman-Hibbs corrected Mie potential + /// is evaluated. + /// n : int + /// total number of points to calculate in the table between r_min and r_max. + /// r_min : SINumber + /// minimum distance (included) + /// r_max : SINumber + /// maximum distance (included) + /// + /// Raises + /// ------ + /// IOError + /// if there are issues with writing to a file. + /// + /// Notes + /// ----- + /// + /// For a given `temperature`, `n` values between `r_min` and `r_max` (both including) are tabulated. + /// + /// Files for all pure substances and all unique pairs are generated, + /// where filenames use either the "name" field of the identifier or the index if no name is present. + /// + /// Example + /// ------- + /// + /// For a hydrogen-neon mixture at 30 K, three files will be created. + /// + /// - "hydrogen_30K.table" for H-H interactions, + /// - "neon_30K.table" for Ne-Ne interactions, + /// - "hydrogen_neon_30K.table" for H-Ne interactions. + #[pyo3(text_signature = "($self, temperature, n, r_min, r_max)")] + fn lammps_tables( + &self, + temperature: PySINumber, + n: usize, + r_min: PySINumber, + r_max: PySINumber, + ) -> PyResult<()> { + self.0 + .lammps_tables(temperature.into(), n, r_min.into(), r_max.into()) + .map_err(|e| PyIOError::new_err(e)) + } + + fn _repr_markdown_(&self) -> String { + self.0.to_markdown() + } + + fn __repr__(&self) -> PyResult { + Ok(self.0.to_string()) + } +} + +#[pymodule] +pub fn saftvrqmie(_py: Python<'_>, m: &PyModule) -> PyResult<()> { + m.add_class::()?; + m.add_class::()?; + m.add_class::()?; + m.add_class::()?; + + m.add_class::()?; + m.add_class::()?; + m.add_class::()?; + m.add_class::()?; + Ok(()) +}