Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions
The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculati...
Saved in:
| Published in | The Journal of chemical physics Vol. 148; no. 24; pp. 241725 - 241735 |
|---|---|
| Main Authors | , , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
28.06.2018
|
| Online Access | Get full text |
Cover
Loading…
| Abstract | The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms. |
|---|---|
| AbstractList | The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms. The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms. |
| Author | Ceriotti, Michele Paesani, Francesco Imbalzano, Giulio Csányi, Gábor Nguyen, Thuong T. Székely, Eszter Götz, Andreas W. Behler, Jörg |
| Author_xml | – sequence: 1 givenname: Thuong T. surname: Nguyen fullname: Nguyen, Thuong T. organization: 5Universität Göttingen, Institut für Physikalische Chemie, Theoretische Chemie, Tammannstr. 6, 37077 Göttingen, Germany – sequence: 2 givenname: Eszter surname: Székely fullname: Székely, Eszter organization: Engineering Department, University of Cambridge – sequence: 3 givenname: Giulio surname: Imbalzano fullname: Imbalzano, Giulio organization: Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne – sequence: 4 givenname: Jörg surname: Behler fullname: Behler, Jörg organization: Universität Göttingen, Institut für Physikalische Chemie, Theoretische Chemie – sequence: 5 givenname: Gábor surname: Csányi fullname: Csányi, Gábor organization: Engineering Department, University of Cambridge – sequence: 6 givenname: Michele surname: Ceriotti fullname: Ceriotti, Michele organization: Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne – sequence: 7 givenname: Andreas W. surname: Götz fullname: Götz, Andreas W. organization: San Diego Supercomputer Center, University of California, San Diego – sequence: 8 givenname: Francesco surname: Paesani fullname: Paesani, Francesco email: fpaesani@ucsd.edu organization: 5Universität Göttingen, Institut für Physikalische Chemie, Theoretische Chemie, Tammannstr. 6, 37077 Göttingen, Germany |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/29960316$$D View this record in MEDLINE/PubMed |
| BookMark | eNp9kc9u1DAQxi1URLeFAy-AfARE2nH-eXNEK1qQKnGBszV2Jm0gsYPttM0z8ZJ12N0LQlxmpG9-3yfNzBk7sc4SY68FXAioi0txUUFeVlI-YxsB2yaTdQMnbAOQi6ypoT5lZyH8AAAh8_IFO82bpBai3rDfOzdO6PvgLHcdn8iPc8TYO4vDsPDe3qch2sgnNyzWjT0O4QO3NHscUosPzv9MAtqWX-McQmI5TpN3j_34JyYZI9m4-lIa9zR5Cqtgb_kDRvJJTRXNCgce77ybb-_4iHbJtGsXTo8T2rAOX7LnXYqhV4d-zr5fffq2-5zdfL3-svt4k5kyFzGrtzlViFTUxVY2BrQ0ett1oI0RUmpBRpu2aAuASpda1AZaDQZLg3Ury4KKc_Z2n5vW-DVTiGrsg6FhQEtuDipPN5d5BU2V0DcHdNYjtWryaW2_qOOBE3C5B4x3IXjqlOn3940e-0EJUOsLlVCHFybHu78cx9B_se_3bDim_gd-AkiarwQ |
| CODEN | JCPSA6 |
| CitedBy_id | crossref_primary_10_1063_5_0031215 crossref_primary_10_1021_acs_jctc_2c00731 crossref_primary_10_1021_acsenergylett_1c00194 crossref_primary_10_1021_acs_est_1c05970 crossref_primary_10_1063_5_0080506 crossref_primary_10_1063_1_5114618 crossref_primary_10_1063_5_0197105 crossref_primary_10_1021_acs_jpca_9b08723 crossref_primary_10_1038_s41570_019_0080_8 crossref_primary_10_1021_acs_jctc_9b00884 crossref_primary_10_1021_acs_jpcb_0c01218 crossref_primary_10_1063_5_0089200 crossref_primary_10_1021_acs_chemrev_0c00665 crossref_primary_10_1063_5_0041022 crossref_primary_10_1016_j_commatsci_2021_110481 crossref_primary_10_1021_acs_jpca_1c03709 crossref_primary_10_1063_5_0055779 crossref_primary_10_1016_j_coche_2019_04_003 crossref_primary_10_1021_acs_jctc_1c00595 crossref_primary_10_1021_acs_jpca_1c09786 crossref_primary_10_1063_5_0026133 crossref_primary_10_1021_acs_jpcc_0c05831 crossref_primary_10_1103_PhysRevMaterials_5_063804 crossref_primary_10_1088_1361_648X_abf6e2 crossref_primary_10_1063_5_0007473 crossref_primary_10_1021_acscentsci_8b00913 crossref_primary_10_1063_1_5078394 crossref_primary_10_1103_PhysRevB_105_165141 crossref_primary_10_1002_jcc_26004 crossref_primary_10_1088_2632_2153_aca1f8 crossref_primary_10_1021_acs_jctc_4c01333 crossref_primary_10_1063_5_0154989 crossref_primary_10_1021_acs_jpcc_2c07423 crossref_primary_10_1016_j_matdes_2022_111162 crossref_primary_10_1021_acs_jctc_1c00541 crossref_primary_10_1021_acs_chemrev_1c00021 crossref_primary_10_1021_acs_jpcb_0c04473 crossref_primary_10_1039_D0CP06135B crossref_primary_10_1103_PhysRevB_107_174106 crossref_primary_10_1063_5_0007166 crossref_primary_10_1021_acs_jpca_0c05979 crossref_primary_10_1063_5_0139245 crossref_primary_10_1038_s41570_022_00416_3 crossref_primary_10_1002_jcc_26037 crossref_primary_10_1021_acs_jpca_4c05873 crossref_primary_10_1063_1_5086358 crossref_primary_10_1063_5_0201241 crossref_primary_10_1088_2632_2153_abc9fd crossref_primary_10_1146_annurev_physchem_090519_051837 crossref_primary_10_1039_C8FD00085A crossref_primary_10_1021_acs_jctc_8b00179 crossref_primary_10_1063_1674_0068_cjcp2201005 crossref_primary_10_1021_acs_jctc_1c01241 crossref_primary_10_1021_acs_jctc_8b00298 crossref_primary_10_1021_acs_jctc_4c00858 crossref_primary_10_1063_5_0015872 crossref_primary_10_1063_1_5100141 crossref_primary_10_1021_acs_jctc_2c00645 crossref_primary_10_1088_2632_2153_abd51e crossref_primary_10_1063_5_0002162 crossref_primary_10_1080_01621459_2019_1654876 crossref_primary_10_1021_acs_jctc_1c00813 crossref_primary_10_1063_5_0024210 crossref_primary_10_1021_acs_jpca_9b04087 crossref_primary_10_1039_D3DD00011G crossref_primary_10_1016_j_jcp_2022_110946 crossref_primary_10_1016_j_cpc_2019_106949 crossref_primary_10_1021_acs_jpclett_9b03664 crossref_primary_10_1063_1_5114652 crossref_primary_10_1021_acs_jctc_0c00837 crossref_primary_10_1021_acsphyschemau_4c00004 crossref_primary_10_1088_2515_7655_abc96f crossref_primary_10_1039_C9FD00030E crossref_primary_10_1063_1_5123999 crossref_primary_10_1103_PhysRevB_110_064101 crossref_primary_10_1063_5_0101280 crossref_primary_10_1021_acs_jctc_9b01241 crossref_primary_10_1039_D4CP02989E crossref_primary_10_1557_mrc_2019_80 crossref_primary_10_1021_acsomega_9b02968 crossref_primary_10_1063_5_0079314 crossref_primary_10_1103_PhysRevMaterials_4_045602 crossref_primary_10_1021_acs_jctc_8b00636 crossref_primary_10_1146_annurev_physchem_062422_023532 crossref_primary_10_1021_acs_jctc_3c00344 crossref_primary_10_1039_D4SC05955G crossref_primary_10_1016_j_coche_2019_03_005 crossref_primary_10_1126_sciadv_aav1190 crossref_primary_10_1021_acs_jctc_3c00187 crossref_primary_10_1039_D0CP04221H crossref_primary_10_1021_acs_jpcb_8b11905 crossref_primary_10_1063_5_0044689 crossref_primary_10_1021_acs_jcim_1c01125 crossref_primary_10_1021_acs_chemrev_0c00868 crossref_primary_10_1021_acs_jctc_4c01005 crossref_primary_10_1063_5_0207567 crossref_primary_10_1021_acs_jpclett_0c00989 crossref_primary_10_1021_acs_jctc_9b01256 crossref_primary_10_1021_acs_jpca_3c07104 crossref_primary_10_1002_pssb_202000416 crossref_primary_10_1021_acs_jpca_0c04473 crossref_primary_10_1021_acs_jpca_2c00601 crossref_primary_10_1021_acs_jctc_4c00039 crossref_primary_10_1021_acs_jpcb_3c00693 crossref_primary_10_1103_PhysRevB_99_014104 crossref_primary_10_1039_C8CP05921G crossref_primary_10_1103_RevModPhys_91_045002 crossref_primary_10_1021_acs_jctc_8b00869 crossref_primary_10_1063_1_5092794 crossref_primary_10_1088_2632_2153_ac9a9d crossref_primary_10_1063_5_0007276 crossref_primary_10_1063_1_5088393 crossref_primary_10_1063_5_0129613 crossref_primary_10_1063_5_0021955 crossref_primary_10_1021_acs_jctc_0c00698 crossref_primary_10_1039_D0FD00028K crossref_primary_10_1063_5_0032362 crossref_primary_10_1103_PhysRevB_107_144103 crossref_primary_10_1038_s41597_020_0473_z crossref_primary_10_1039_D0CP05089J crossref_primary_10_1021_acs_jctc_1c00046 crossref_primary_10_1021_acs_jpcb_3c04629 crossref_primary_10_1021_acs_jpca_3c06823 crossref_primary_10_52396_JUSTC_2024_0031 crossref_primary_10_1021_acs_jctc_2c00396 crossref_primary_10_1021_acs_jpclett_0c01061 crossref_primary_10_1039_D2CP00719C crossref_primary_10_1002_wcms_1645 crossref_primary_10_1063_5_0176709 crossref_primary_10_1021_acs_jpcc_2c06341 crossref_primary_10_1038_s41467_021_21376_0 crossref_primary_10_1039_D2DD00057A crossref_primary_10_1021_acs_jpca_2c02243 crossref_primary_10_1063_5_0063534 crossref_primary_10_1002_qua_27389 crossref_primary_10_1063_1_5091842 crossref_primary_10_1063_5_0027643 crossref_primary_10_1021_acs_jctc_4c00660 crossref_primary_10_1088_2515_7639_ab084b crossref_primary_10_1088_1367_2630_ac3261 crossref_primary_10_1063_5_0128780 crossref_primary_10_1007_s00214_021_02773_6 crossref_primary_10_1039_D1CP01544C crossref_primary_10_1063_5_0072004 crossref_primary_10_1021_acs_jctc_1c00069 crossref_primary_10_1063_1_5043213 |
| Cites_doi | 10.1021/j100296a048 10.1021/ct300913g 10.1063/1.1423940 10.1002/qua.24927 10.1063/1.2386157 10.1039/c6cp00415f 10.1021/acs.accounts.6b00285 10.1063/1.432402 10.1063/1.473987 10.1137/0206041 10.1021/j100308a038 10.1063/1.1447904 10.1002/qua.560360845 10.1063/1.1423942 10.1103/physrevb.88.054104 10.1039/c7sc04665k 10.1021/jp2069489 10.1021/jp8001614 10.1080/01442350903234923 10.1021/jp027815+ 10.1063/1.2817618 10.1021/jp403802c 10.1021/acs.jpclett.6b00729 10.1103/physrevlett.98.146401 10.1063/1.1676585 10.1063/1.473820 10.1021/jp8105919 10.1063/1.3664730 10.1021/acs.jpclett.7b01106 10.1021/acs.chemrev.5b00644 10.1021/ct5004115 10.1039/df9572400133 10.1016/0009-2614(69)80119-3 10.1002/jcc.540160413 10.1063/1.445869 10.1063/1.4967719 10.1103/physrevb.87.184115 10.1063/1.436773 10.1063/1.3553717 10.1063/1.4930194 10.1126/science.aae0012 10.1063/1.1423941 10.1063/1.1683075 10.1021/jacs.7b03143 10.1002/qua.24890 10.1103/physreva.33.2679 10.1016/s0009-2614(00)00592-3 10.1016/0009-2614(87)80416-5 10.1021/jacs.6b00893 10.1103/physrevlett.104.136403 10.1126/sciadv.1701816 10.1021/cr068037a 10.1073/pnas.1602375113 10.1021/ct500079y 10.1016/j.fluid.2015.07.040 10.1063/1.3554905 10.1186/s13321-017-0192-4 10.1126/science.1136371 10.1021/ct400863t 10.1126/science.aad8625 10.1021/jz3017733 10.1063/1.4973380 10.1016/s0167-7322(02)00094-6 10.1063/1.5003074 10.1063/1.2136877 10.1073/pnas.0803205106 10.1021/j100383a037 10.1063/1.2831537 10.1063/1.2895750 10.1021/acs.jpcb.6b02366 10.1063/1.1731425 10.1002/anie.201703114 10.1063/1.2837299 10.1063/1.449246 10.1063/1.1699114 10.1063/1.1743822 10.1063/1.1730376 10.1021/jp208946p 10.1021/ct501131j 10.1021/ct3010563 10.1039/c1cp22168j 10.1021/acs.jctc.6b01248 10.1063/1.481505 10.1063/1.3167790 10.1021/ct9004917 10.1073/pnas.1108486108 |
| ContentType | Journal Article |
| Copyright | Author(s) |
| Copyright_xml | – notice: Author(s) |
| DBID | AAYXX CITATION NPM 7X8 |
| DOI | 10.1063/1.5024577 |
| DatabaseName | CrossRef PubMed MEDLINE - Academic |
| DatabaseTitle | CrossRef PubMed MEDLINE - Academic |
| DatabaseTitleList | PubMed MEDLINE - Academic CrossRef |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Chemistry Physics |
| EISSN | 1089-7690 |
| ExternalDocumentID | 29960316 10_1063_1_5024577 jcp |
| Genre | Journal Article |
| GrantInformation_xml | – fundername: H2020 European Research Council grantid: 677013-HBMAP funderid: http://dx.doi.org/10.13039/100010663 – fundername: National Science Foundation grantid: ACI-1548562; ACI-1642336 funderid: http://dx.doi.org/10.13039/100000001 – fundername: Deutsche Forschungsgemeinschaft grantid: Be3264/11-2 funderid: http://dx.doi.org/10.13039/501100001659 |
| GroupedDBID | --- -DZ -ET -~X 123 1UP 2-P 29K 4.4 53G 5VS 85S AAAAW AABDS AAEUA AAPUP AAYIH ABPPZ ABZEH ACBRY ACLYJ ACNCT ACZLF ADCTM AEJMO AENEX AFATG AFHCQ AGKCL AGLKD AGMXG AGTJO AHSDT AJJCW AJQPL ALEPV ALMA_UNASSIGNED_HOLDINGS AQWKA ATXIE AWQPM BPZLN CS3 D-I DU5 EBS EJD ESX F5P FDOHQ FFFMQ HAM M6X M71 M73 N9A NPSNA O-B P2P RIP RNS RQS TN5 TWZ UPT WH7 YQT YZZ ~02 AAGWI AAYXX ABJGX ADMLS BDMKI CITATION NPM 7X8 |
| ID | FETCH-LOGICAL-c421t-682e5aae363879c0b7cb8ff0bcc177b1ecbcd3d3005b4b16c0db0ca4ca6d743e3 |
| ISSN | 0021-9606 1089-7690 |
| IngestDate | Thu Jul 10 23:21:17 EDT 2025 Wed Feb 19 02:43:08 EST 2025 Tue Jul 01 00:27:15 EDT 2025 Thu Apr 24 23:00:43 EDT 2025 Fri Jun 21 00:14:57 EDT 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 24 |
| Language | English |
| License | 0021-9606/2018/148(24)/241725/11/$30.00 Published by AIP Publishing. |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c421t-682e5aae363879c0b7cb8ff0bcc177b1ecbcd3d3005b4b16c0db0ca4ca6d743e3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ORCID | 0000-0002-1220-1542 0000-0003-2571-2832 0000-0002-4451-1203 0000000212201542 0000000325712832 0000000244511203 |
| OpenAccessLink | http://infoscience.epfl.ch/record/272592 |
| PMID | 29960316 |
| PQID | 2063725095 |
| PQPubID | 23479 |
| PageCount | 11 |
| ParticipantIDs | scitation_primary_10_1063_1_5024577 pubmed_primary_29960316 crossref_citationtrail_10_1063_1_5024577 proquest_miscellaneous_2063725095 crossref_primary_10_1063_1_5024577 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2018-06-28 |
| PublicationDateYYYYMMDD | 2018-06-28 |
| PublicationDate_xml | – month: 06 year: 2018 text: 2018-06-28 day: 28 |
| PublicationDecade | 2010 |
| PublicationPlace | United States |
| PublicationPlace_xml | – name: United States |
| PublicationTitle | The Journal of chemical physics |
| PublicationTitleAlternate | J Chem Phys |
| PublicationYear | 2018 |
| References | Ball (c5) 2008; 108 Lyubartsev, Laaksonen (c29) 2000; 325 Richardson, Pérez, Lobsiger, Reid, Temelso, Shields, Kisiel, Wales, Pate, Althorpe (c54) 2016; 351 De, Musil, Ingram, Baldauf, Ceriotti (c88) 2017; 9 Wood, Parker (c2) 1957; 27 Bartók, Gillan, Manby, Csányi (c43) 2013; 88 Dang, Pettitt (c16) 1987; 91 Lie, Clementi (c28) 1986; 33 Moberg, Straight, Knight, Paesani (c64) 2017; 8 Dang, Chang (c34) 1997; 106 Guillot (c6) 2002; 101 Rahman, Stillinger (c11) 1971; 55 Burnham, Xantheas (c35) 2002; 116 Jorgensen, Chandrasekhar, Madura, Impey, Klein (c14) 1983; 79 Góra, Podeszwa, Cencek, Szalewicz (c74) 2011; 135 Cheng, Behler, Ceriotti (c59) 2016; 7 Wu, Tepper, Voth (c20) 2006; 124 Xie, Bowman (c68) 2010; 6 Niesar, Corongiu, Huang, Dupuis, Clementi (c31) 1989; 36 Paesani (c53) 2016; 49 Stillinger, David (c33) 1978; 69 Bukowski, Szalewicz, Groenenboom, van der Avoird (c47) 2007; 315 Wang, Head-Gordon, Ponder, Ren, Chodera, Eastman, Martinez, Pande (c42) 2013; 117 Babin, Medders, Paesani (c51) 2014; 10 Burnham, Xantheas (c38) 2002; 116 Park, Lin, Paesani (c23) 2011; 116 Yao, Herr, Parkhill (c70) 2017; 146 Kamath, Vargas-Hernández, Krems, Carrington, Manzhos (c71) 2018; 148 Burnham, Anick, Mankoo, Reiter (c40) 2008; 128 Behler (c46) 2017; 56 Babin, Leforestier, Paesani (c50) 2013; 9 Lybrand, Kollman (c26) 1985; 83 Fanourgakis, Xantheas (c39) 2008; 128 De, Bartók, Csányi, Ceriotti (c85) 2016; 18 Frank, Wen (c25) 1957; 24 Bates, Tschumper (c72) 2009; 113 Burnham, Xantheas (c37) 2002; 116 Mahoney, Drineas (c87) 2009; 106 Ferguson (c17) 1995; 16 Horn, Swope, Pitera, Madura, Dick, Hura, Head-Gordon (c19) 2004; 120 Reddy, Straight, Bajaj, Huy Pham, Riera, Moberg, Morales, Knight, Götz, Paesani (c58) 2016; 145 Bartók, Csányi (c69) 2015; 115 Musil, De, Yang, Campbell, Day, Ceriotti (c92) 2018; 9 Ren, Ponder (c41) 2003; 107 Behler, Parrinello (c66) 2007; 98 Medders, Paesani (c61) 2015; 11 Pham, Reddy, Chen, Knight, Paesani (c60) 2017; 13 Adler, Knizia, Werner (c75) 2007; 127 Bartók, Payne, Kondor, Csányi (c82) 2010; 104 Bartok, De, Poelking, Bernstein, Kermode, Csanyi, Ceriotti (c86) 2017; 3 Joung, Cheatham (c24) 2008; 112 Berendsen, Grigera, Straatsma (c15) 1987; 91 Wang, Huang, Shepler, Braams, Bowman (c48) 2011; 134 Peterson, Adler, Werner (c76) 2008; 128 Matsuoka, Clementi, Yoshimine (c27) 1976; 64 Xantheas, Burnham, Harrison (c36) 2002; 116 Cole, Farrell, Wales, Saykally (c55) 2016; 352 Medders, Babin, Paesani (c57) 2013; 9 Rosenkrantz, Stearns, Lewis (c89) 1977; 6 Barker, Watts (c10) 1969; 3 Honda, Kitaura (c30) 1987; 140 Vega, Abascal (c7) 2011; 13 Shvab, Sadus (c8) 2016; 407 Brown, Götz, Cheng, Steele, Mandelshtam, Paesani (c56) 2017; 139 Partridge, Schwenke (c65) 1997; 106 Straight, Paesani (c62) 2016; 120 Paesani, Zhang, Case, Cheatham, Voth (c21) 2006; 125 Habershon, Markland, Manolopoulos (c22) 2009; 131 Niesar, Corongiu, Clementi, Kneller, Bhattacharya (c32) 1990; 94 Bartók, Kondor, Csányi (c83) 2013; 87 Alder, Wainwright (c4) 1960; 33 Medders, Götz, Morales, Paesani (c93) 2015; 143 Medders, Babin, Paesani (c52) 2014; 10 Behler (c78) 2011; 134 Babin, Medders, Paesani (c49) 2012; 3 Mahoney, Jorgensen (c18) 2000; 112 Alder, Wainwright (c3) 1959; 31 Braams, Bowman (c45) 2009; 28 Medders, Paesani (c63) 2016; 138 Metropolis, Rosenbluth, Rosenbluth, Teller, Teller (c1) 1953; 21 Temelso, Archer, Shields (c73) 2011; 115 Cisneros, Wikfeldt, Ojamäe, Lu, Xu, Torabifard, Bartók, Csányi, Molinero, Paesani (c9) 2016; 116 Ceriotti, Tribello, Parrinello (c90) 2011; 108 Ceriotti, Tribello, Parrinello (c91) 2013; 9 Behler (c67) 2015; 115 Morawietz, Singraber, Dellago, Behler (c44) 2016; 113 (2023080301095653800_c20) 2006; 124 (2023080301095653800_c67) 2015; 115 (2023080301095653800_c81) 1990 (2023080301095653800_c14) 1983; 79 Theano Development Team (2023080301095653800_c80) 2016 (2023080301095653800_c63) 2016; 138 (2023080301095653800_c31) 1989; 36 (2023080301095653800_c90) 2011; 108 (2023080301095653800_c74) 2011; 135 (2023080301095653800_c1) 1953; 21 (2023080301095653800_c82) 2010; 104 (2023080301095653800_c89) 1977; 6 (2023080301095653800_c3) 1959; 31 (2023080301095653800_c50) 2013; 9 (2023080301095653800_c26) 1985; 83 (2023080301095653800_c28) 1986; 33 (2023080301095653800_c52) 2014; 10 (2023080301095653800_c58) 2016; 145 (2023080301095653800_c59) 2016; 7 (2023080301095653800_c64) 2017; 8 (2023080301095653800_c71) 2018; 148 (2023080301095653800_c5) 2008; 108 (2023080301095653800_c25) 1957; 24 (2023080301095653800_c45) 2009; 28 (2023080301095653800_c47) 2007; 315 (2023080301095653800_c15) 1987; 91 (2023080301095653800_c69) 2015; 115 (2023080301095653800_c85) 2016; 18 (2023080301095653800_c60) 2017; 13 (2023080301095653800_c93) 2015; 143 (2023080301095653800_c35) 2002; 116 (2023080301095653800_c24) 2008; 112 (2023080301095653800_c30) 1987; 140 (2023080301095653800_c39) 2008; 128 (2023080301095653800_c41) 2003; 107 (2023080301095653800_c17) 1995; 16 (2023080301095653800_c55) 2016; 352 (2023080301095653800_c6) 2002; 101 (2023080301095653800_c84) 2017 (2023080301095653800_c86) 2017; 3 (2023080301095653800_c43) 2013; 88 (2023080301095653800_c87) 2009; 106 (2023080301095653800_c51) 2014; 10 (2023080301095653800_c70) 2017; 146 (2023080301095653800_c44) 2016; 113 (2023080301095653800_c79) 2015 (2023080301095653800_c65) 1997; 106 (2023080301095653800_c54) 2016; 351 (2023080301095653800_c32) 1990; 94 (2023080301095653800_c27) 1976; 64 (2023080301095653800_c62) 2016; 120 (2023080301095653800_c34) 1997; 106 (2023080301095653800_c57) 2013; 9 (2023080301095653800_c19) 2004; 120 (2023080301095653800_c2) 1957; 27 (2023080301095653800_c16) 1987; 91 (2023080301095653800_c53) 2016; 49 (2023080301095653800_c77) 1963 (2023080301095653800_c75) 2007; 127 (2023080301095653800_c36) 2002; 116 (2023080301095653800_c78) 2011; 134 (2023080301095653800_c8) 2016; 407 (2023080301095653800_c12) 1940 (2023080301095653800_c10) 1969; 3 (2023080301095653800_c91) 2013; 9 (2023080301095653800_c22) 2009; 131 (2023080301095653800_c18) 2000; 112 (2023080301095653800_c42) 2013; 117 (2023080301095653800_c46) 2017; 56 (2023080301095653800_c33) 1978; 69 (2023080301095653800_c11) 1971; 55 (2023080301095653800_c48) 2011; 134 (2023080301095653800_c61) 2015; 11 (2023080301095653800_c68) 2010; 6 (2023080301095653800_c40) 2008; 128 (2023080301095653800_c92) 2018; 9 (2023080301095653800_c66) 2007; 98 (2023080301095653800_c13) 1981 (2023080301095653800_c83) 2013; 87 (2023080301095653800_c38) 2002; 116 (2023080301095653800_c73) 2011; 115 (2023080301095653800_c4) 1960; 33 (2023080301095653800_c7) 2011; 13 (2023080301095653800_c88) 2017; 9 (2023080301095653800_c29) 2000; 325 (2023080301095653800_c76) 2008; 128 (2023080301095653800_c56) 2017; 139 (2023080301095653800_c23) 2011; 116 (2023080301095653800_c72) 2009; 113 (2023080301095653800_c37) 2002; 116 (2023080301095653800_c49) 2012; 3 (2023080301095653800_c21) 2006; 125 (2023080301095653800_c9) 2016; 116 |
| References_xml | – volume: 112 start-page: 8910 year: 2000 ident: c18 publication-title: J. Chem. Phys. – volume: 116 start-page: 5115 year: 2002 ident: c38 publication-title: J. Chem. Phys. – volume: 139 start-page: 7082 year: 2017 ident: c56 publication-title: J. Am. Chem. Soc. – volume: 91 start-page: 6269 year: 1987 ident: c15 publication-title: J. Phys. Chem. – volume: 13 start-page: 19663 year: 2011 ident: c7 publication-title: Phys. Chem. Chem. Phys. – volume: 124 start-page: 024503 year: 2006 ident: c20 publication-title: J. Chem. Phys. – volume: 140 start-page: 53 year: 1987 ident: c30 publication-title: Chem. Phys. Lett. – volume: 407 start-page: 7 year: 2016 ident: c8 publication-title: Fluid Phase Equilib. – volume: 9 start-page: 5395 year: 2013 ident: c50 publication-title: J. Chem. Theory Comput. – volume: 3 start-page: 144 year: 1969 ident: c10 publication-title: Chem. Phys. Lett. – volume: 146 start-page: 014106 year: 2017 ident: c70 publication-title: J. Chem. Phys. – volume: 9 start-page: 6 year: 2017 ident: c88 publication-title: J. Cheminf. – volume: 116 start-page: 343 year: 2011 ident: c23 publication-title: J. Phys. Chem. B – volume: 120 start-page: 8539 year: 2016 ident: c62 publication-title: J. Phys. Chem. B – volume: 11 start-page: 1145 year: 2015 ident: c61 publication-title: J. Chem. Theory Comput. – volume: 6 start-page: 563 year: 1977 ident: c89 publication-title: SIAM J. Comput. – volume: 101 start-page: 219 year: 2002 ident: c6 publication-title: J. Mol. Liq. – volume: 115 start-page: 1051 year: 2015 ident: c69 publication-title: Int. J. Quantum Chem. – volume: 134 start-page: 074106 year: 2011 ident: c78 publication-title: J. Chem. Phys. – volume: 351 start-page: 1310 year: 2016 ident: c54 publication-title: Science – volume: 33 start-page: 1439 year: 1960 ident: c4 publication-title: J. Chem. Phys. – volume: 36 start-page: 421 year: 1989 ident: c31 publication-title: Int. J. Quantum Chem. – volume: 116 start-page: 1493 year: 2002 ident: c36 publication-title: J. Chem. Phys. – volume: 145 start-page: 194504 year: 2016 ident: c58 publication-title: J. Chem. Phys. – volume: 148 start-page: 241702 year: 2018 ident: c71 publication-title: J. Chem. Phys. – volume: 108 start-page: 13023 year: 2011 ident: c90 publication-title: Proc. Natl. Acad. Sci. U. S. A. – volume: 33 start-page: 2679 year: 1986 ident: c28 publication-title: Phys. Rev. A – volume: 31 start-page: 459 year: 1959 ident: c3 publication-title: J. Chem. Phys. – volume: 10 start-page: 1599 year: 2014 ident: c51 publication-title: J. Chem. Theory Comput. – volume: 24 start-page: 133 year: 1957 ident: c25 publication-title: Discuss. Faraday Soc. – volume: 3 start-page: e1701816 year: 2017 ident: c86 publication-title: Sci. Adv. – volume: 143 start-page: 104102 year: 2015 ident: c93 publication-title: J. Chem. Phys. – volume: 10 start-page: 2906 year: 2014 ident: c52 publication-title: J. Chem. Theory Comput. – volume: 138 start-page: 3912 year: 2016 ident: c63 publication-title: J. Am. Chem. Soc. – volume: 115 start-page: 1032 year: 2015 ident: c67 publication-title: Int. J. Quantum Chem. – volume: 108 start-page: 74 year: 2008 ident: c5 publication-title: Chem. Rev. – volume: 27 start-page: 720 year: 1957 ident: c2 publication-title: J. Chem. Phys. – volume: 7 start-page: 2210 year: 2016 ident: c59 publication-title: J. Phys. Chem. Lett. – volume: 352 start-page: 1194 year: 2016 ident: c55 publication-title: Science – volume: 120 start-page: 9665 year: 2004 ident: c19 publication-title: J. Chem. Phys. – volume: 125 start-page: 184507 year: 2006 ident: c21 publication-title: J. Chem. Phys. – volume: 56 start-page: 12828 year: 2017 ident: c46 publication-title: Angew. Chem., Int. Ed. – volume: 315 start-page: 1249 year: 2007 ident: c47 publication-title: Science – volume: 135 start-page: 224102 year: 2011 ident: c74 publication-title: J. Chem. Phys. – volume: 9 start-page: 1103 year: 2013 ident: c57 publication-title: J. Chem. Theory Comput. – volume: 116 start-page: 1479 year: 2002 ident: c35 publication-title: J. Chem. Phys. – volume: 134 start-page: 094509 year: 2011 ident: c48 publication-title: J. Chem. Phys. – volume: 8 start-page: 2579 year: 2017 ident: c64 publication-title: J. Phys. Chem. Lett. – volume: 3 start-page: 3765 year: 2012 ident: c49 publication-title: J. Phys. Chem. Lett. – volume: 115 start-page: 12034 year: 2011 ident: c73 publication-title: J. Phys. Chem. A – volume: 117 start-page: 9956 year: 2013 ident: c42 publication-title: J. Phys. Chem. B – volume: 325 start-page: 15 year: 2000 ident: c29 publication-title: Chem. Phys. Lett. – volume: 106 start-page: 8149 year: 1997 ident: c34 publication-title: J. Chem. Phys. – volume: 6 start-page: 26 year: 2010 ident: c68 publication-title: J. Chem. Theory Comput. – volume: 113 start-page: 3555 year: 2009 ident: c72 publication-title: J. Phys. Chem. A – volume: 131 start-page: 024501 year: 2009 ident: c22 publication-title: J. Chem. Phys. – volume: 55 start-page: 3336 year: 1971 ident: c11 publication-title: J. Chem. Phys. – volume: 83 start-page: 2923 year: 1985 ident: c26 publication-title: J. Chem. Phys. – volume: 128 start-page: 074506 year: 2008 ident: c39 publication-title: J. Chem. Phys. – volume: 9 start-page: 1289 year: 2018 ident: c92 publication-title: Chem. Sci. – volume: 18 start-page: 13754 year: 2016 ident: c85 publication-title: Phys. Chem. Chem. Phys. – volume: 16 start-page: 501 year: 1995 ident: c17 publication-title: J. Comput. Chem. – volume: 98 start-page: 146401 year: 2007 ident: c66 publication-title: Phys. Rev. Lett. – volume: 113 start-page: 8368 year: 2016 ident: c44 publication-title: Proc. Natl. Acad. Sci. U. S. A. – volume: 13 start-page: 1778 year: 2017 ident: c60 publication-title: J. Chem. Theory Comput. – volume: 128 start-page: 154519 year: 2008 ident: c40 publication-title: J. Chem. Phys. – volume: 106 start-page: 4618 year: 1997 ident: c65 publication-title: J. Chem. Phys. – volume: 116 start-page: 7501 year: 2016 ident: c9 publication-title: Chem. Rev. – volume: 79 start-page: 926 year: 1983 ident: c14 publication-title: J. Chem. Phys. – volume: 127 start-page: 221106 year: 2007 ident: c75 publication-title: J. Chem. Phys. – volume: 21 start-page: 1087 year: 1953 ident: c1 publication-title: J. Chem. Phys. – volume: 112 start-page: 9020 year: 2008 ident: c24 publication-title: J. Phys. Chem. B – volume: 94 start-page: 7949 year: 1990 ident: c32 publication-title: J. Phys. Chem. – volume: 87 start-page: 184115 year: 2013 ident: c83 publication-title: Phys. Rev. B – volume: 116 start-page: 1500 year: 2002 ident: c37 publication-title: J. Chem. Phys. – volume: 91 start-page: 3349 year: 1987 ident: c16 publication-title: J. Phys. Chem. – volume: 69 start-page: 1473 year: 1978 ident: c33 publication-title: J. Chem. Phys. – volume: 9 start-page: 1521 year: 2013 ident: c91 publication-title: J. Chem. Theory Comput. – volume: 107 start-page: 5933 year: 2003 ident: c41 publication-title: J. Phys. Chem. B – volume: 88 start-page: 054104 year: 2013 ident: c43 publication-title: Phys. Rev. B – volume: 104 start-page: 136403 year: 2010 ident: c82 publication-title: Phys. Rev. Lett. – volume: 49 start-page: 1844 year: 2016 ident: c53 publication-title: Acc. Chem. Res. – volume: 128 start-page: 084102 year: 2008 ident: c76 publication-title: J. Chem. Phys. – volume: 64 start-page: 1351 year: 1976 ident: c27 publication-title: J. Chem. Phys. – volume: 28 start-page: 577 year: 2009 ident: c45 publication-title: Int. Rev. Phys. Chem. – volume: 106 start-page: 697 year: 2009 ident: c87 publication-title: Proc. Natl. Acad. Sci. U. S. A. – volume: 91 start-page: 3349 year: 1987 ident: 2023080301095653800_c16 publication-title: J. Phys. Chem. doi: 10.1021/j100296a048 – volume: 9 start-page: 1103 year: 2013 ident: 2023080301095653800_c57 publication-title: J. Chem. Theory Comput. doi: 10.1021/ct300913g – volume: 116 start-page: 1479 year: 2002 ident: 2023080301095653800_c35 publication-title: J. Chem. Phys. doi: 10.1063/1.1423940 – year: 2015 ident: 2023080301095653800_c79 – volume: 115 start-page: 1051 year: 2015 ident: 2023080301095653800_c69 publication-title: Int. J. Quantum Chem. doi: 10.1002/qua.24927 – volume: 125 start-page: 184507 year: 2006 ident: 2023080301095653800_c21 publication-title: J. Chem. Phys. doi: 10.1063/1.2386157 – volume: 18 start-page: 13754 year: 2016 ident: 2023080301095653800_c85 publication-title: Phys. Chem. Chem. Phys. doi: 10.1039/c6cp00415f – volume: 49 start-page: 1844 year: 2016 ident: 2023080301095653800_c53 publication-title: Acc. Chem. Res. doi: 10.1021/acs.accounts.6b00285 – volume: 64 start-page: 1351 year: 1976 ident: 2023080301095653800_c27 publication-title: J. Chem. Phys. doi: 10.1063/1.432402 – volume: 106 start-page: 4618 year: 1997 ident: 2023080301095653800_c65 publication-title: J. Chem. Phys. doi: 10.1063/1.473987 – volume: 6 start-page: 563 year: 1977 ident: 2023080301095653800_c89 publication-title: SIAM J. Comput. doi: 10.1137/0206041 – volume: 91 start-page: 6269 year: 1987 ident: 2023080301095653800_c15 publication-title: J. Phys. Chem. doi: 10.1021/j100308a038 – volume: 116 start-page: 5115 year: 2002 ident: 2023080301095653800_c38 publication-title: J. Chem. Phys. doi: 10.1063/1.1447904 – volume: 36 start-page: 421 year: 1989 ident: 2023080301095653800_c31 publication-title: Int. J. Quantum Chem. doi: 10.1002/qua.560360845 – volume: 116 start-page: 1500 year: 2002 ident: 2023080301095653800_c37 publication-title: J. Chem. Phys. doi: 10.1063/1.1423942 – volume: 88 start-page: 054104 year: 2013 ident: 2023080301095653800_c43 publication-title: Phys. Rev. B doi: 10.1103/physrevb.88.054104 – volume: 9 start-page: 1289 year: 2018 ident: 2023080301095653800_c92 publication-title: Chem. Sci. doi: 10.1039/c7sc04665k – volume: 115 start-page: 12034 year: 2011 ident: 2023080301095653800_c73 publication-title: J. Phys. Chem. A doi: 10.1021/jp2069489 – volume: 112 start-page: 9020 year: 2008 ident: 2023080301095653800_c24 publication-title: J. Phys. Chem. B doi: 10.1021/jp8001614 – volume: 28 start-page: 577 year: 2009 ident: 2023080301095653800_c45 publication-title: Int. Rev. Phys. Chem. doi: 10.1080/01442350903234923 – volume: 107 start-page: 5933 year: 2003 ident: 2023080301095653800_c41 publication-title: J. Phys. Chem. B doi: 10.1021/jp027815+ – volume: 127 start-page: 221106 year: 2007 ident: 2023080301095653800_c75 publication-title: J. Chem. Phys. doi: 10.1063/1.2817618 – volume: 117 start-page: 9956 year: 2013 ident: 2023080301095653800_c42 publication-title: J. Phys. Chem. B doi: 10.1021/jp403802c – volume: 7 start-page: 2210 year: 2016 ident: 2023080301095653800_c59 publication-title: J. Phys. Chem. Lett. doi: 10.1021/acs.jpclett.6b00729 – volume: 98 start-page: 146401 year: 2007 ident: 2023080301095653800_c66 publication-title: Phys. Rev. Lett. doi: 10.1103/physrevlett.98.146401 – volume: 55 start-page: 3336 year: 1971 ident: 2023080301095653800_c11 publication-title: J. Chem. Phys. doi: 10.1063/1.1676585 – volume: 106 start-page: 8149 year: 1997 ident: 2023080301095653800_c34 publication-title: J. Chem. Phys. doi: 10.1063/1.473820 – volume: 113 start-page: 3555 year: 2009 ident: 2023080301095653800_c72 publication-title: J. Phys. Chem. A doi: 10.1021/jp8105919 – volume: 135 start-page: 224102 year: 2011 ident: 2023080301095653800_c74 publication-title: J. Chem. Phys. doi: 10.1063/1.3664730 – volume: 8 start-page: 2579 year: 2017 ident: 2023080301095653800_c64 publication-title: J. Phys. Chem. Lett. doi: 10.1021/acs.jpclett.7b01106 – volume: 116 start-page: 7501 year: 2016 ident: 2023080301095653800_c9 publication-title: Chem. Rev. doi: 10.1021/acs.chemrev.5b00644 – volume: 10 start-page: 2906 year: 2014 ident: 2023080301095653800_c52 publication-title: J. Chem. Theory Comput. doi: 10.1021/ct5004115 – volume: 24 start-page: 133 year: 1957 ident: 2023080301095653800_c25 publication-title: Discuss. Faraday Soc. doi: 10.1039/df9572400133 – year: 2016 ident: 2023080301095653800_c80 – volume: 3 start-page: 144 year: 1969 ident: 2023080301095653800_c10 publication-title: Chem. Phys. Lett. doi: 10.1016/0009-2614(69)80119-3 – volume: 16 start-page: 501 year: 1995 ident: 2023080301095653800_c17 publication-title: J. Comput. Chem. doi: 10.1002/jcc.540160413 – volume: 79 start-page: 926 year: 1983 ident: 2023080301095653800_c14 publication-title: J. Chem. Phys. doi: 10.1063/1.445869 – volume: 145 start-page: 194504 year: 2016 ident: 2023080301095653800_c58 publication-title: J. Chem. Phys. doi: 10.1063/1.4967719 – volume: 87 start-page: 184115 year: 2013 ident: 2023080301095653800_c83 publication-title: Phys. Rev. B doi: 10.1103/physrevb.87.184115 – volume: 69 start-page: 1473 year: 1978 ident: 2023080301095653800_c33 publication-title: J. Chem. Phys. doi: 10.1063/1.436773 – volume: 134 start-page: 074106 year: 2011 ident: 2023080301095653800_c78 publication-title: J. Chem. Phys. doi: 10.1063/1.3553717 – volume: 143 start-page: 104102 year: 2015 ident: 2023080301095653800_c93 publication-title: J. Chem. Phys. doi: 10.1063/1.4930194 – volume: 351 start-page: 1310 year: 2016 ident: 2023080301095653800_c54 publication-title: Science doi: 10.1126/science.aae0012 – volume: 116 start-page: 1493 year: 2002 ident: 2023080301095653800_c36 publication-title: J. Chem. Phys. doi: 10.1063/1.1423941 – volume: 120 start-page: 9665 year: 2004 ident: 2023080301095653800_c19 publication-title: J. Chem. Phys. doi: 10.1063/1.1683075 – volume: 139 start-page: 7082 year: 2017 ident: 2023080301095653800_c56 publication-title: J. Am. Chem. Soc. doi: 10.1021/jacs.7b03143 – volume: 115 start-page: 1032 year: 2015 ident: 2023080301095653800_c67 publication-title: Int. J. Quantum Chem. doi: 10.1002/qua.24890 – volume: 33 start-page: 2679 year: 1986 ident: 2023080301095653800_c28 publication-title: Phys. Rev. A doi: 10.1103/physreva.33.2679 – volume: 325 start-page: 15 year: 2000 ident: 2023080301095653800_c29 publication-title: Chem. Phys. Lett. doi: 10.1016/s0009-2614(00)00592-3 – volume: 140 start-page: 53 year: 1987 ident: 2023080301095653800_c30 publication-title: Chem. Phys. Lett. doi: 10.1016/0009-2614(87)80416-5 – volume: 138 start-page: 3912 year: 2016 ident: 2023080301095653800_c63 publication-title: J. Am. Chem. Soc. doi: 10.1021/jacs.6b00893 – volume: 104 start-page: 136403 year: 2010 ident: 2023080301095653800_c82 publication-title: Phys. Rev. Lett. doi: 10.1103/physrevlett.104.136403 – volume: 3 start-page: e1701816 year: 2017 ident: 2023080301095653800_c86 publication-title: Sci. Adv. doi: 10.1126/sciadv.1701816 – volume: 108 start-page: 74 year: 2008 ident: 2023080301095653800_c5 publication-title: Chem. Rev. doi: 10.1021/cr068037a – start-page: 1035 volume-title: Soviet Mathematics Doklady year: 1963 ident: 2023080301095653800_c77 – volume: 113 start-page: 8368 year: 2016 ident: 2023080301095653800_c44 publication-title: Proc. Natl. Acad. Sci. U. S. A. doi: 10.1073/pnas.1602375113 – start-page: 21 year: 1990 ident: 2023080301095653800_c81 – volume: 10 start-page: 1599 year: 2014 ident: 2023080301095653800_c51 publication-title: J. Chem. Theory Comput. doi: 10.1021/ct500079y – volume: 407 start-page: 7 year: 2016 ident: 2023080301095653800_c8 publication-title: Fluid Phase Equilib. doi: 10.1016/j.fluid.2015.07.040 – volume-title: Statistical Mechanics year: 1940 ident: 2023080301095653800_c12 – volume: 134 start-page: 094509 year: 2011 ident: 2023080301095653800_c48 publication-title: J. Chem. Phys. doi: 10.1063/1.3554905 – volume: 9 start-page: 6 year: 2017 ident: 2023080301095653800_c88 publication-title: J. Cheminf. doi: 10.1186/s13321-017-0192-4 – volume: 315 start-page: 1249 year: 2007 ident: 2023080301095653800_c47 publication-title: Science doi: 10.1126/science.1136371 – volume: 9 start-page: 5395 year: 2013 ident: 2023080301095653800_c50 publication-title: J. Chem. Theory Comput. doi: 10.1021/ct400863t – volume: 352 start-page: 1194 year: 2016 ident: 2023080301095653800_c55 publication-title: Science doi: 10.1126/science.aad8625 – volume: 3 start-page: 3765 year: 2012 ident: 2023080301095653800_c49 publication-title: J. Phys. Chem. Lett. doi: 10.1021/jz3017733 – volume: 146 start-page: 014106 year: 2017 ident: 2023080301095653800_c70 publication-title: J. Chem. Phys. doi: 10.1063/1.4973380 – volume: 101 start-page: 219 year: 2002 ident: 2023080301095653800_c6 publication-title: J. Mol. Liq. doi: 10.1016/s0167-7322(02)00094-6 – volume: 148 start-page: 241702 year: 2018 ident: 2023080301095653800_c71 publication-title: J. Chem. Phys. doi: 10.1063/1.5003074 – volume: 124 start-page: 024503 year: 2006 ident: 2023080301095653800_c20 publication-title: J. Chem. Phys. doi: 10.1063/1.2136877 – volume: 106 start-page: 697 year: 2009 ident: 2023080301095653800_c87 publication-title: Proc. Natl. Acad. Sci. U. S. A. doi: 10.1073/pnas.0803205106 – volume: 94 start-page: 7949 year: 1990 ident: 2023080301095653800_c32 publication-title: J. Phys. Chem. doi: 10.1021/j100383a037 – volume: 128 start-page: 084102 year: 2008 ident: 2023080301095653800_c76 publication-title: J. Chem. Phys. doi: 10.1063/1.2831537 – volume: 128 start-page: 154519 year: 2008 ident: 2023080301095653800_c40 publication-title: J. Chem. Phys. doi: 10.1063/1.2895750 – volume: 120 start-page: 8539 year: 2016 ident: 2023080301095653800_c62 publication-title: J. Phys. Chem. B doi: 10.1021/acs.jpcb.6b02366 – volume: 33 start-page: 1439 year: 1960 ident: 2023080301095653800_c4 publication-title: J. Chem. Phys. doi: 10.1063/1.1731425 – start-page: 331 volume-title: Intermolecular Forces year: 1981 ident: 2023080301095653800_c13 – volume: 56 start-page: 12828 year: 2017 ident: 2023080301095653800_c46 publication-title: Angew. Chem., Int. Ed. doi: 10.1002/anie.201703114 – volume: 128 start-page: 074506 year: 2008 ident: 2023080301095653800_c39 publication-title: J. Chem. Phys. doi: 10.1063/1.2837299 – volume: 83 start-page: 2923 year: 1985 ident: 2023080301095653800_c26 publication-title: J. Chem. Phys. doi: 10.1063/1.449246 – volume: 21 start-page: 1087 year: 1953 ident: 2023080301095653800_c1 publication-title: J. Chem. Phys. doi: 10.1063/1.1699114 – volume: 27 start-page: 720 year: 1957 ident: 2023080301095653800_c2 publication-title: J. Chem. Phys. doi: 10.1063/1.1743822 – year: 2017 ident: 2023080301095653800_c84 – volume: 31 start-page: 459 year: 1959 ident: 2023080301095653800_c3 publication-title: J. Chem. Phys. doi: 10.1063/1.1730376 – volume: 116 start-page: 343 year: 2011 ident: 2023080301095653800_c23 publication-title: J. Phys. Chem. B doi: 10.1021/jp208946p – volume: 11 start-page: 1145 year: 2015 ident: 2023080301095653800_c61 publication-title: J. Chem. Theory Comput. doi: 10.1021/ct501131j – volume: 9 start-page: 1521 year: 2013 ident: 2023080301095653800_c91 publication-title: J. Chem. Theory Comput. doi: 10.1021/ct3010563 – volume: 13 start-page: 19663 year: 2011 ident: 2023080301095653800_c7 publication-title: Phys. Chem. Chem. Phys. doi: 10.1039/c1cp22168j – volume: 13 start-page: 1778 year: 2017 ident: 2023080301095653800_c60 publication-title: J. Chem. Theory Comput. doi: 10.1021/acs.jctc.6b01248 – volume: 112 start-page: 8910 year: 2000 ident: 2023080301095653800_c18 publication-title: J. Chem. Phys. doi: 10.1063/1.481505 – volume: 131 start-page: 024501 year: 2009 ident: 2023080301095653800_c22 publication-title: J. Chem. Phys. doi: 10.1063/1.3167790 – volume: 6 start-page: 26 year: 2010 ident: 2023080301095653800_c68 publication-title: J. Chem. Theory Comput. doi: 10.1021/ct9004917 – volume: 108 start-page: 13023 year: 2011 ident: 2023080301095653800_c90 publication-title: Proc. Natl. Acad. Sci. U. S. A. doi: 10.1073/pnas.1108486108 |
| SSID | ssj0001724 |
| Score | 2.6245291 |
| Snippet | The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems.... |
| SourceID | proquest pubmed crossref scitation |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 241725 |
| Title | Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions |
| URI | http://dx.doi.org/10.1063/1.5024577 https://www.ncbi.nlm.nih.gov/pubmed/29960316 https://www.proquest.com/docview/2063725095 |
| Volume | 148 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3ZbtQwFLWGqVDhAUHZhk1meUCiKVmc7bEMpaWiFRJTqW-R7ThQmE2dBDHzS3wJf8W9ceykpZWAl2iUxYlyzjjX9r3nEPJCsCTlPlb0uLFwWJHi-m4oIZBL41QqiEkFFgofHEZ7R2z_ODzu9X51spaqUmzJ1YV1Jf-DKuwDXLFK9h-QtY3CDvgN-MIWEIbtX2E87JoIogLxpCqbyb0x1vN9h4Pw5tCJYYnlx_BA-EpRwxKQmeoM8IVJ4Nzl1aIuqax1xn-c6KJGuLjEjCKUWa5rX-a6YKmexOUosYiKE6e6PmJhfX8m0Mk4YpYv0UMAPod2WvBrS89OMCyNboGeabGB_uHnaqk7xtGXCm2RWk3JlV7j_6a0V_bOYtXJNH4_EXy84rWv-Kvdk2qs0810RZIxfN7HFt5EjcRXM_XhJZii1ZSSK91du0nqxJE2HLX9OUs6xPVZt3tmEK-FF345IFTDSYytENeitbNMh0HzSU0hH7VsAu-cdncdDZhDV8iaDyMWv0_Wtt8efPhkwwK4MzPSVlHw2t4J5aiba8_GRn8MeK6TdQiLNI86QdDoJrnRAEa3NRVvkZ6abpD1oTEN3CBXP2r8bpOfLTnprKDnyEktOWmHnJtUU5Maam5SICY1xKRniElbYkJrtEtMWhOTdolJG2JSS0zaEvMOOXq3MxruOY0ziCOZ75VOlPgq5FwF8PWALsUVsRRJUbhCSi-OhaekkHmQoxWDYMKLpJsLV3ImeZRDyKyCu6Q_nU3VfULTVIRFKHjEi4Jh5iUTAoY5KsxjBYMTOSAvDSaZefno3jLO6vSNKMi8rEFyQJ7ZU-daK-aik54aYDPABpfn-FTNqkXmw3nAThjzDMg9jbhtxjBkQJ5bClx-jweXXv-QXGv_SI9Ivzyt1GOIqkvxpOHrbzp52Ng |
| linkProvider | EBSCOhost |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Comparison+of+permutationally+invariant+polynomials%2C+neural+networks%2C+and+Gaussian+approximation+potentials+in+representing+water+interactions+through+many-body+expansions&rft.jtitle=The+Journal+of+chemical+physics&rft.au=Nguyen%2C+Thuong+T&rft.au=Sz%C3%A9kely%2C+Eszter&rft.au=Imbalzano%2C+Giulio&rft.au=Behler%2C+J%C3%B6rg&rft.date=2018-06-28&rft.eissn=1089-7690&rft.volume=148&rft.issue=24&rft.spage=241725&rft_id=info:doi/10.1063%2F1.5024577&rft_id=info%3Apmid%2F29960316&rft.externalDocID=29960316 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9606&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9606&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9606&client=summon |