DOI: 10.1063/1.5020710. Alchemical and structural distribution based representation for universal quantum machine learning

Alchemical and structural distribution based representation for universal quantum machine learning

10.1063/1.5020710

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We introduce a representation of any atom in any chemical environment for the automatized generation of universal kernel ridge regression-based quantum machine learning (QML) models of electronic properties, trained throughout chemical compound space. The representation is based on Gaussian distribution functions, scaled by power laws and explicitly accounting for structural as well as elemental degrees of freedom. The elemental components help us to lower the QML model’s learning curve, and, through interpolation across the periodic table, even enable “alchemical extrapolation” to covalent bonding between elements not part of training. This point is demonstrated for the prediction of covalent binding in single, double, and triple bonds among main-group elements as well as for atomization energies in organic molecules. We present numerical evidence that resulting QML energy models, after training on a few thousand random training instances, reach chemical accuracy for out-of-sample compounds. Compound datasets studied include thousands of structurally and compositionally diverse organic molecules, non-covalently bonded protein side-chains, (H2O)40-clusters, and crystalline solids. Learning curves for QML models also indicate competitive predictive power for various other electronic ground state properties of organic molecules, calculated with hybrid density functional theory, including polarizability, heat-capacity, HOMO-LUMO eigenvalues and gap, zero point vibrational energy, dipole moment, and highest vibrational fundamental frequency.

Bibliography

Faber, F. A., Christensen, A. S., Huang, B., & von Lilienfeld, O. A. (2018). Alchemical and structural distribution based representation for universal quantum machine learning. The Journal of Chemical Physics, 148(24).

Authors 4

Felix A. Faber (first)
Anders S. Christensen (additional)
Bing Huang (additional)
O. Anatole von Lilienfeld (additional)

References 57 Referenced 308

{'volume-title': 'Introduction to Computational Chemistry', 'year': '2007', 'key': '2023080305134788100_c1'} / Introduction to Computational Chemistry (2007)
10.1038/s41467-017-00839-3 / Nat. Commun. (2017)
10.1021/acs.jctc.7b00577 / J. Chem. Theory Comput. (2017)
10.1038/ncomms13890 / Nat. Commun. (2017)
{'key': '2023080305134788100_c5'}
{'year': '2015', 'first-page': '2215', 'key': '2023080305134788100_c6'} (2015)
10.1103/physrevlett.108.058301 / Phys. Rev. Lett. (2012)
10.1021/acs.jpclett.5b00831 / J. Phys. Chem. Lett. (2015)
10.1063/1.4964627 / J. Chem. Phys. (2016)
10.1103/physrevlett.98.146401 / Phys. Rev. Lett. (2007)
10.1021/ci100050t / J. Chem. Inf. Model. (2010)
10.1002/qua.24375 / Int. J. Quantum Chem. (2013)
10.1103/physrevb.89.205118 / Phys. Rev. B (2014)
B. Huang and O. A. von Lilienfeld, preprint arXiv:1707.04146 (2017).
H. Huo and M. Rupp, preprint arXiv:1704.06439 (2017).
10.1007/978-3-319-06379-9_9 / Many-Electron Approaches in Physics, Chemistry and Mathematics (2014)
10.1063/1.4947217 / J. Chem. Phys. (2016)
10.1002/qua.24912 / Int. J. Quantum Chem. (2015)
10.1103/physrevlett.117.135502 / Phys. Rev. Lett. (2016)
10.1039/c6cp00415f / Phys. Chem. Chem. Phys. (2016)
10.1109/72.914517 / IEEE Trans. Neural Networks (2001)
{'volume-title': 'Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond', 'year': '2002', 'key': '2023080305134788100_c22'} / Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (2002)
10.1007/978-3-642-41136-6 / Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik / Kernel ridge regression by Schölkopf (2013)
{'volume-title': 'The Elements of Statistical Learning: Data Mining, Inference, and Prediction', 'year': '2011', 'edition': '2nd ed.', 'key': '2023080305134788100_c24'} / The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2011)
S. Mathias, M.Sc. thesis, University of Bonn, 2015, http://wissrech.ins.uni-bonn.de/teaching/master/masterthesis_mathias_revised.pdf.
{'volume-title': 'Scientific Computing and Algorithms in Industrial Simulations', 'year': '2017', 'article-title': 'LC-GAP: Localized Coulomb descriptors for the Gaussian approximation potential', 'key': '2023080305134788100_c26'} / Scientific Computing and Algorithms in Industrial Simulations / LC-GAP: Localized Coulomb descriptors for the Gaussian approximation potential (2017)
10.1002/qua.24927 / Int. J. Quantum Chem. (2015)
10.2533/chimia.2015.182 / Chimia Int. J. Chem. (2015)
10.1063/1.1723844 / J. Chem. Phys. (1943)
{'key': '2023080305134788100_c30', 'first-page': '629', 'volume': '17', 'year': '1943', 'journal-title': 'Proc. Phys. Math. Soc. Japan'} / Proc. Phys. Math. Soc. Japan (1943)
10.1063/1.4929335 / J. Chem. Phys. (2015)
10.1016/j.commatsci.2016.12.004 / Comput. Mater. Sci. (2017)
10.1038/sdata.2014.22 / Sci. Data (2014)
10.1021/j100096a001 / J. Phys. Chem. (1993)
10.1021/ci300415d / J. Chem. Inf. Model. (2012)
10.1088/1367-2630/15/9/095003 / New J. Phys. (2013)
10.1021/ja902302h / J. Am. Chem. Soc. (2009)
10.1063/1.478401 / J. Chem. Phys. (1999)
10.1063/1.478522 / J. Chem. Phys. (1999)
10.1063/1.5001028 / J. Chem. Phys. (2017)
10.1021/ct200600p / J. Chem. Theory Comput. (2011)
10.1063/1.445869 / J. Chem. Phys. (1983)
10.1002/jcc.540040211 / J. Comput. Chem. (1983)
10.1063/1.4927476 / J. Chem. Phys. (2015)
10.1107/s0108768102006948 / Acta Crystallogr., Sect. B: Struct. Sci. (2002)
10.1021/ci00038a003 / J. Chem. Inf. Comput. Sci. (1983)
10.1038/npjcompumats.2015.10 / npj Comput. Mater. (2015)
10.1007/s11837-013-0755-4 / JOM (2013)
10.1103/physrevb.96.024104 / Phys. Rev. B (2017)
10.1103/physrevlett.77.3865 / Phys. Rev. Lett. (1996)
10.1162/neco.1996.8.5.1085 / Neural Comput. (1996)
10.1021/acs.jctc.5b00099 / J. Chem. Theory Comput. (2015)
10.1126/sciadv.1701816 / Sci. Adv. (2017)
10.1103/physrevb.87.184115 / Phys. Rev. B (2013)
10.1002/qua.24917 / Int. J. Quantum Chem. (2015)
10.1021/ct400195d / J. Chem. Theory Comput. (2013)
10.1063/1.3249969 / J. Chem. Phys. (2009)

Dates

Type	When
Created	7 years, 5 months ago (March 20, 2018, 10:44 a.m.)
Deposited	2 months, 3 weeks ago (May 27, 2025, 4:20 p.m.)
Indexed	2 weeks, 6 days ago (Aug. 2, 2025, 12:40 a.m.)
Issued	7 years, 5 months ago (March 20, 2018)
Published	7 years, 5 months ago (March 20, 2018)
Published Online	7 years, 5 months ago (March 20, 2018)
Published Print	7 years, 1 month ago (June 28, 2018)

Funders 0

None

BibTeX

@article{Faber_2018, title={Alchemical and structural distribution based representation for universal quantum machine learning}, volume={148}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.5020710}, DOI={10.1063/1.5020710}, number={24}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Faber, Felix A. and Christensen, Anders S. and Huang, Bing and von Lilienfeld, O. Anatole}, year={2018}, month=mar }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        2
      ]
    ],
    "date-time": "2025-08-02T04:40:44Z",
    "timestamp": 1754109644707,
    "version": "3.41.2"
  },
  "reference-count": 57,
  "publisher": "AIP Publishing",
  "issue": "24",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2018,
            3,
            20
          ]
        ],
        "date-time": "2018-03-20T00:00:00Z",
        "timestamp": 1521504000000
      },
      "content-version": "vor",
      "delay-in-days": 0,
      "URL": "https://creativecommons.org/licenses/by/4.0/"
    },
    {
      "start": {
        "date-parts": [
          [
            2018,
            3,
            20
          ]
        ],
        "date-time": "2018-03-20T00:00:00Z",
        "timestamp": 1521504000000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://creativecommons.org/licenses/by/4.0/"
    }
  ],
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2018,
        6,
        28
      ]
    ]
  },
  "abstract": "<jats:p>We introduce a representation of any atom in any chemical environment for the automatized generation of universal kernel ridge regression-based quantum machine learning (QML) models of electronic properties, trained throughout chemical compound space. The representation is based on Gaussian distribution functions, scaled by power laws and explicitly accounting for structural as well as elemental degrees of freedom. The elemental components help us to lower the QML model\u2019s learning curve, and, through interpolation across the periodic table, even enable \u201calchemical extrapolation\u201d to covalent bonding between elements not part of training. This point is demonstrated for the prediction of covalent binding in single, double, and triple bonds among main-group elements as well as for atomization energies in organic molecules. We present numerical evidence that resulting QML energy models, after training on a few thousand random training instances, reach chemical accuracy for out-of-sample compounds. Compound datasets studied include thousands of structurally and compositionally diverse organic molecules, non-covalently bonded protein side-chains, (H2O)40-clusters, and crystalline solids. Learning curves for QML models also indicate competitive predictive power for various other electronic ground state properties of organic molecules, calculated with hybrid density functional theory, including polarizability, heat-capacity, HOMO-LUMO eigenvalues and gap, zero point vibrational energy, dipole moment, and highest vibrational fundamental frequency.</jats:p>",
  "DOI": "10.1063/1.5020710",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2018,
        3,
        20
      ]
    ],
    "date-time": "2018-03-20T14:44:17Z",
    "timestamp": 1521557057000
  },
  "update-policy": "https://doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 308,
  "title": "Alchemical and structural distribution based representation for universal quantum machine learning",
  "prefix": "10.1063",
  "volume": "148",
  "author": [
    {
      "given": "Felix A.",
      "family": "Faber",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel , Basel, Switzerland"
        }
      ]
    },
    {
      "ORCID": "https://orcid.org/0000-0002-7253-6897",
      "authenticated-orcid": false,
      "given": "Anders S.",
      "family": "Christensen",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel , Basel, Switzerland"
        }
      ]
    },
    {
      "given": "Bing",
      "family": "Huang",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel , Basel, Switzerland"
        }
      ]
    },
    {
      "given": "O. Anatole",
      "family": "von Lilienfeld",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel , Basel, Switzerland"
        }
      ]
    }
  ],
  "member": "317",
  "published-online": {
    "date-parts": [
      [
        2018,
        3,
        20
      ]
    ]
  },
  "reference": [
    {
      "volume-title": "Introduction to Computational Chemistry",
      "year": "2007",
      "key": "2023080305134788100_c1"
    },
    {
      "key": "2023080305134788100_c2",
      "doi-asserted-by": "publisher",
      "first-page": "872",
      "DOI": "10.1038/s41467-017-00839-3",
      "volume": "8",
      "year": "2017",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "2023080305134788100_c3",
      "doi-asserted-by": "publisher",
      "first-page": "5255",
      "DOI": "10.1021/acs.jctc.7b00577",
      "volume": "13",
      "year": "2017",
      "journal-title": "J. Chem. Theory Comput."
    },
    {
      "key": "2023080305134788100_c4",
      "doi-asserted-by": "publisher",
      "first-page": "13890",
      "DOI": "10.1038/ncomms13890",
      "volume": "8",
      "year": "2017",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "2023080305134788100_c5"
    },
    {
      "year": "2015",
      "first-page": "2215",
      "key": "2023080305134788100_c6"
    },
    {
      "key": "2023080305134788100_c7",
      "doi-asserted-by": "publisher",
      "first-page": "058301",
      "DOI": "10.1103/physrevlett.108.058301",
      "volume": "108",
      "year": "2012",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2023080305134788100_c8",
      "doi-asserted-by": "publisher",
      "first-page": "2326",
      "DOI": "10.1021/acs.jpclett.5b00831",
      "volume": "6",
      "year": "2015",
      "journal-title": "J. Phys. Chem. Lett."
    },
    {
      "key": "2023080305134788100_c9",
      "doi-asserted-by": "publisher",
      "first-page": "161102",
      "DOI": "10.1063/1.4964627",
      "volume": "145",
      "year": "2016",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c10",
      "doi-asserted-by": "publisher",
      "first-page": "146401",
      "DOI": "10.1103/physrevlett.98.146401",
      "volume": "98",
      "year": "2007",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2023080305134788100_c11",
      "doi-asserted-by": "publisher",
      "first-page": "742",
      "DOI": "10.1021/ci100050t",
      "volume": "50",
      "year": "2010",
      "journal-title": "J. Chem. Inf. Model."
    },
    {
      "key": "2023080305134788100_c12",
      "doi-asserted-by": "publisher",
      "first-page": "1676",
      "DOI": "10.1002/qua.24375",
      "volume": "113",
      "year": "2013",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "2023080305134788100_c13",
      "doi-asserted-by": "publisher",
      "first-page": "205118",
      "DOI": "10.1103/physrevb.89.205118",
      "volume": "89",
      "year": "2014",
      "journal-title": "Phys. Rev. B"
    },
    {
      "unstructured": "B.\u2008Huang and O. A.\u2008von Lilienfeld, preprint arXiv:1707.04146 (2017).",
      "key": "2023080305134788100_c14"
    },
    {
      "unstructured": "H.\u2008Huo and M.\u2008Rupp, preprint arXiv:1704.06439 (2017).",
      "key": "2023080305134788100_c15"
    },
    {
      "key": "2023080305134788100_c16",
      "doi-asserted-by": "crossref",
      "first-page": "169",
      "DOI": "10.1007/978-3-319-06379-9_9",
      "volume-title": "Many-Electron Approaches in Physics, Chemistry and Mathematics",
      "year": "2014"
    },
    {
      "key": "2023080305134788100_c17",
      "doi-asserted-by": "publisher",
      "first-page": "174110",
      "DOI": "10.1063/1.4947217",
      "volume": "144",
      "year": "2016",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c18",
      "doi-asserted-by": "publisher",
      "first-page": "1084",
      "DOI": "10.1002/qua.24912",
      "volume": "115",
      "year": "2015",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "2023080305134788100_c19",
      "doi-asserted-by": "publisher",
      "first-page": "135502",
      "DOI": "10.1103/physrevlett.117.135502",
      "volume": "117",
      "year": "2016",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2023080305134788100_c20",
      "doi-asserted-by": "publisher",
      "first-page": "13754",
      "DOI": "10.1039/c6cp00415f",
      "volume": "18",
      "year": "2016",
      "journal-title": "Phys. Chem. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c21",
      "doi-asserted-by": "publisher",
      "first-page": "181",
      "DOI": "10.1109/72.914517",
      "volume": "12",
      "year": "2001",
      "journal-title": "IEEE Trans. Neural Networks"
    },
    {
      "volume-title": "Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond",
      "year": "2002",
      "key": "2023080305134788100_c22"
    },
    {
      "key": "2023080305134788100_c23",
      "doi-asserted-by": "crossref",
      "first-page": "105",
      "DOI": "10.1007/978-3-642-41136-6",
      "article-title": "Kernel ridge regression",
      "volume-title": "Empirical Inference: Festschrift in Honor of Vladimir N. Vapnik",
      "author": "Sch\u00f6lkopf",
      "year": "2013"
    },
    {
      "volume-title": "The Elements of Statistical Learning: Data Mining, Inference, and Prediction",
      "year": "2011",
      "edition": "2nd ed.",
      "key": "2023080305134788100_c24"
    },
    {
      "unstructured": "S.\u2008Mathias, M.Sc. thesis, University of Bonn, 2015, http://wissrech.ins.uni-bonn.de/teaching/master/masterthesis_mathias_revised.pdf.",
      "key": "2023080305134788100_c25"
    },
    {
      "volume-title": "Scientific Computing and Algorithms in Industrial Simulations",
      "year": "2017",
      "article-title": "LC-GAP: Localized Coulomb descriptors for the Gaussian approximation potential",
      "key": "2023080305134788100_c26"
    },
    {
      "key": "2023080305134788100_c27",
      "doi-asserted-by": "publisher",
      "first-page": "1051",
      "DOI": "10.1002/qua.24927",
      "volume": "115",
      "year": "2015",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "2023080305134788100_c28",
      "doi-asserted-by": "publisher",
      "first-page": "182",
      "DOI": "10.2533/chimia.2015.182",
      "volume": "69",
      "year": "2015",
      "journal-title": "Chimia Int. J. Chem."
    },
    {
      "key": "2023080305134788100_c29",
      "doi-asserted-by": "publisher",
      "first-page": "299",
      "DOI": "10.1063/1.1723844",
      "volume": "11",
      "year": "1943",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c30",
      "first-page": "629",
      "volume": "17",
      "year": "1943",
      "journal-title": "Proc. Phys. Math. Soc. Japan"
    },
    {
      "key": "2023080305134788100_c31",
      "doi-asserted-by": "publisher",
      "first-page": "084123",
      "DOI": "10.1063/1.4929335",
      "volume": "143",
      "year": "2015",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c32",
      "doi-asserted-by": "publisher",
      "first-page": "156",
      "DOI": "10.1016/j.commatsci.2016.12.004",
      "volume": "129",
      "year": "2017",
      "journal-title": "Comput. Mater. Sci."
    },
    {
      "key": "2023080305134788100_c33",
      "doi-asserted-by": "publisher",
      "first-page": "140022",
      "DOI": "10.1038/sdata.2014.22",
      "volume": "1",
      "year": "2014",
      "journal-title": "Sci. Data"
    },
    {
      "key": "2023080305134788100_c34",
      "doi-asserted-by": "publisher",
      "first-page": "11623",
      "DOI": "10.1021/j100096a001",
      "volume": "98",
      "year": "1993",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2023080305134788100_c35",
      "doi-asserted-by": "publisher",
      "first-page": "2864",
      "DOI": "10.1021/ci300415d",
      "volume": "52",
      "year": "2012",
      "journal-title": "J. Chem. Inf. Model."
    },
    {
      "key": "2023080305134788100_c36",
      "doi-asserted-by": "publisher",
      "first-page": "095003",
      "DOI": "10.1088/1367-2630/15/9/095003",
      "volume": "15",
      "year": "2013",
      "journal-title": "New J. Phys."
    },
    {
      "key": "2023080305134788100_c37",
      "doi-asserted-by": "publisher",
      "first-page": "8732",
      "DOI": "10.1021/ja902302h",
      "volume": "131",
      "year": "2009",
      "journal-title": "J. Am. Chem. Soc."
    },
    {
      "key": "2023080305134788100_c38",
      "doi-asserted-by": "publisher",
      "first-page": "5029",
      "DOI": "10.1063/1.478401",
      "volume": "110",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c39",
      "doi-asserted-by": "publisher",
      "first-page": "6158",
      "DOI": "10.1063/1.478522",
      "volume": "110",
      "year": "1999",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c40",
      "doi-asserted-by": "publisher",
      "first-page": "161727",
      "DOI": "10.1063/1.5001028",
      "volume": "147",
      "year": "2017",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c41",
      "doi-asserted-by": "publisher",
      "first-page": "3978",
      "DOI": "10.1021/ct200600p",
      "volume": "7",
      "year": "2011",
      "journal-title": "J. Chem. Theory Comput."
    },
    {
      "key": "2023080305134788100_c42",
      "doi-asserted-by": "publisher",
      "first-page": "926",
      "DOI": "10.1063/1.445869",
      "volume": "79",
      "year": "1983",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c43",
      "doi-asserted-by": "publisher",
      "first-page": "187",
      "DOI": "10.1002/jcc.540040211",
      "volume": "4",
      "year": "1983",
      "journal-title": "J. Comput. Chem."
    },
    {
      "key": "2023080305134788100_c44",
      "doi-asserted-by": "publisher",
      "first-page": "054107",
      "DOI": "10.1063/1.4927476",
      "volume": "143",
      "year": "2015",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023080305134788100_c45",
      "doi-asserted-by": "publisher",
      "first-page": "364",
      "DOI": "10.1107/s0108768102006948",
      "volume": "58",
      "year": "2002",
      "journal-title": "Acta Crystallogr., Sect. B: Struct. Sci."
    },
    {
      "key": "2023080305134788100_c46",
      "doi-asserted-by": "publisher",
      "first-page": "66",
      "DOI": "10.1021/ci00038a003",
      "volume": "23",
      "year": "1983",
      "journal-title": "J. Chem. Inf. Comput. Sci."
    },
    {
      "key": "2023080305134788100_c47",
      "doi-asserted-by": "publisher",
      "first-page": "15010",
      "DOI": "10.1038/npjcompumats.2015.10",
      "volume": "1",
      "year": "2015",
      "journal-title": "npj Comput. Mater."
    },
    {
      "key": "2023080305134788100_c48",
      "doi-asserted-by": "publisher",
      "first-page": "1501",
      "DOI": "10.1007/s11837-013-0755-4",
      "volume": "65",
      "year": "2013",
      "journal-title": "JOM"
    },
    {
      "key": "2023080305134788100_c49",
      "doi-asserted-by": "publisher",
      "first-page": "024104",
      "DOI": "10.1103/physrevb.96.024104",
      "volume": "96",
      "year": "2017",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023080305134788100_c50",
      "doi-asserted-by": "publisher",
      "first-page": "3865",
      "DOI": "10.1103/physrevlett.77.3865",
      "volume": "77",
      "year": "1996",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2023080305134788100_c51",
      "doi-asserted-by": "publisher",
      "first-page": "1085",
      "DOI": "10.1162/neco.1996.8.5.1085",
      "volume": "8",
      "year": "1996",
      "journal-title": "Neural Comput."
    },
    {
      "key": "2023080305134788100_c52",
      "doi-asserted-by": "publisher",
      "first-page": "2087",
      "DOI": "10.1021/acs.jctc.5b00099",
      "volume": "11",
      "year": "2015",
      "journal-title": "J. Chem. Theory Comput."
    },
    {
      "issue": "12",
      "key": "2023080305134788100_c53",
      "doi-asserted-by": "publisher",
      "first-page": "e1701816",
      "DOI": "10.1126/sciadv.1701816",
      "volume": "3",
      "year": "2017",
      "journal-title": "Sci. Adv."
    },
    {
      "key": "2023080305134788100_c54",
      "doi-asserted-by": "publisher",
      "first-page": "184115",
      "DOI": "10.1103/physrevb.87.184115",
      "volume": "87",
      "year": "2013",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2023080305134788100_c55",
      "doi-asserted-by": "publisher",
      "first-page": "1094",
      "DOI": "10.1002/qua.24917",
      "volume": "115",
      "year": "2015",
      "journal-title": "Int. J. Quantum Chem."
    },
    {
      "key": "2023080305134788100_c56",
      "doi-asserted-by": "publisher",
      "first-page": "3404",
      "DOI": "10.1021/ct400195d",
      "volume": "9",
      "year": "2013",
      "journal-title": "J. Chem. Theory Comput."
    },
    {
      "key": "2023080305134788100_c57",
      "doi-asserted-by": "publisher",
      "first-page": "164102",
      "DOI": "10.1063/1.3249969",
      "volume": "131",
      "year": "2009",
      "journal-title": "J. Chem. Phys."
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.5020710/16654916/241717_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.5020710/16654916/241717_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/1.5020710/16654916/241717_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2025,
        5,
        27
      ]
    ],
    "date-time": "2025-05-27T20:20:26Z",
    "timestamp": 1748377226000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/148/24/241717/961132/Alchemical-and-structural-distribution-based"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2018,
        3,
        20
      ]
    ]
  },
  "references-count": 57,
  "journal-issue": {
    "issue": "24",
    "published-print": {
      "date-parts": [
        [
          2018,
          6,
          28
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.5020710",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2018,
        6,
        28
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2018,
        3,
        20
      ]
    ]
  },
  "article-number": "241717"
}