DOI: 10.1063/1.4986081. Improving the accuracy of Møller-Plesset perturbation theory with neural networks

Improving the accuracy of Møller-Plesset perturbation theory with neural networks

10.1063/1.4986081

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Noncovalent interactions are of fundamental importance across the disciplines of chemistry, materials science, and biology. Quantum chemical calculations on noncovalently bound complexes, which allow for the quantification of properties such as binding energies and geometries, play an essential role in advancing our understanding of, and building models for, a vast array of complex processes involving molecular association or self-assembly. Because of its relatively modest computational cost, second-order Møller-Plesset perturbation (MP2) theory is one of the most widely used methods in quantum chemistry for studying noncovalent interactions. MP2 is, however, plagued by serious errors due to its incomplete treatment of electron correlation, especially when modeling van der Waals interactions and π-stacked complexes. Here we present spin-network-scaled MP2 (SNS-MP2), a new semi-empirical MP2-based method for dimer interaction-energy calculations. To correct for errors in MP2, SNS-MP2 uses quantum chemical features of the complex under study in conjunction with a neural network to reweight terms appearing in the total MP2 interaction energy. The method has been trained on a new data set consisting of over 200 000 complete basis set (CBS)-extrapolated coupled-cluster interaction energies, which are considered the gold standard for chemical accuracy. SNS-MP2 predicts gold-standard binding energies of unseen test compounds with a mean absolute error of 0.04 kcal mol−1 (root-mean-square error 0.09 kcal mol−1), a 6- to 7-fold improvement over MP2. To the best of our knowledge, its accuracy exceeds that of all extant density functional theory- and wavefunction-based methods of similar computational cost, and is very close to the intrinsic accuracy of our benchmark coupled-cluster methodology itself. Furthermore, SNS-MP2 provides reliable per-conformation confidence intervals on the predicted interaction energies, a feature not available from any alternative method.

Bibliography

McGibbon, R. T., Taube, A. G., Donchev, A. G., Siva, K., HernÃ¡ndez, F., Hargus, C., Law, K.-H., Klepeis, J. L., & Shaw, D. E. (2017). Improving the accuracy of MÃ¸ller-Plesset perturbation theory with neural networks. The Journal of Chemical Physics, 147(16).

Authors 9

Robert T. McGibbon (first)
Andrew G. Taube (additional)
Alexander G. Donchev (additional)
Karthik Siva (additional)
Felipe Hernández (additional)
Cory Hargus (additional)
Ka-Hei Law (additional)
John L. Klepeis (additional)
David E. Shaw (additional)

References 79 Referenced 86

10.1146/annurev.biophys.36.040306.132550 / Annu. Rev. Biophys. Biomol. Struct. / Calculation of protein-ligand binding affinities (2007)
10.1126/science.1071063 / Science / Toward self-organization and complex matter (2002)
{'volume-title': 'The Theory of Intermolecular Forces', 'year': '2013', 'key': '2023061919341570400_c3'} / The Theory of Intermolecular Forces (2013)
10.1016/0009-2614(88)85250-3 / Chem. Phys. Lett. / MP2 energy evaluation by direct methods (1988)
10.1016/0009-2614(93)87156-w / Chem. Phys. Lett. / Use of approximate integrals in ab initio theory. An application in MP2 energy calculations (1993)
10.1063/1.1564816 / J. Chem. Phys. / Fast linear scaling second-order Møller–Plesset perturbation theory (MP2) using local and density fitting approximations (2003)
10.1063/1.479957 / J. Chem. Phys. / Low-order scaling local electron correlation methods. I. Linear scaling local MP2 (1999)
10.1063/1.480512 / J. Chem. Phys. / Closely approximating second-order Møller–Plesset perturbation theory with a local triatomics in molecules model (2000)
10.1021/ct050126s / J. Chem. Theory Comput. / A resolution-of-the-identity implementation of the local triatomics-in-molecules model for second-order Møller–Plesset perturbation theory with application to alanine tetrapeptide conformational energies (2005)
10.1002/wcms.58 / Wiley Interdiscip. Rev.: Comput. Mol. Sci. / Møller–plesset perturbation theory: From small molecule methods to methods for thousands of atoms (2011)
10.1063/1.2795693 / J. Chem. Phys. / The origin of deficiency of the supermolecule second-order Møller–Plesset approach for evaluating interaction energies (2007)
10.1039/b600027d / Phys. Chem. Chem. Phys. / Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs (2006)
10.1021/ja025896h / J. Am. Chem. Soc. / Estimates of the ab initio limit for pi-pi interactions: The benzene dimer (2002)
10.1080/00268977000101561 / Mol. Phys. / The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors (1970)
10.1021/ct400057w / J. Chem. Theory Comput. / Describing noncovalent interactions beyond the common approximations: How accurate is the “gold standard,” CCSD(T) at the complete basis set limit? (2013)
10.1063/1.1569242 / J. Chem. Phys. / Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies (2003)
10.1021/cr00031a008 / Chem. Rev. / Perturbation theory approach to intermolecular potential energy surfaces of van der Waals complexes (1994)
10.1002/wcms.84 / Wiley Interdiscip. Rev.: Comput. Mol. Sci. / Wavefunction methods for noncovalent interactions (2012)
10.1021/ct2002946 / J. Chem. Theory Comput. / S66: A well-balanced database of benchmark interaction energies relevant to biomolecular structures (2011)
10.1039/c6cp00688d / Phys. Chem. Chem. Phys. / The S66x8 benchmark for noncovalent interactions revisited: Explicitly correlated ab initio methods and density functional theory (2016)
10.1063/1.4961095 / J. Chem. Phys. / Blind test of density-functional-based methods on intermolecular interaction energies (2016)
10.1021/ct9005882 / J. Chem. Theory Comput. / Accurate intermolecular interaction energies from a combination of MP2 and TDDFT response theory (2010)
10.1063/1.3213194 / J. Chem. Phys. / Dispersion-corrected Møller–Plesset second-order perturbation theory (2009)
10.1021/ct6002737 / J. Chem. Theory Comput. / Spin-component scaling methods for weak and stacking interactions (2007)
10.1080/00268970701283781 / Mol. Phys. / Optimized spin-component scaled second-order Møller-Plesset perturbation theory for intermolecular interaction energies (2007)
10.1063/1.1809602 / J. Chem. Phys. / Scaled opposite-spin second order Møller-Plesset correlation energy: An economical electronic structure method (2004)
10.1039/b910905f / Phys. Chem. Chem. Phys. / Coulomb-only second-order perturbation theory in long-range-corrected hybrid density functionals (2009)
10.1080/00268978800100171 / Mol. Phys. / On the connection between the supermolecular Møller-Plesset treatment of the interaction energy and the perturbation theory of intermolecular forces (1988)
10.1063/1.457743 / J. Chem. Phys. / On decomposition of second-order Møller–Plesset supermolecular interaction energy and basis set effects (1990)
10.1080/00268970802641242 / Mol. Phys. / On the accuracy of spin-component-scaled perturbation theory (SCS-MP2) for the potential energy surface of the ethylene dimer (2009)
10.1063/1.4975326 / J. Chem. Phys. / Generalized spin-ratio scaled MP2 method for accurate prediction of intermolecular interactions for neutral and ionic species (2017)
10.1103/physrevlett.108.058301 / Phys. Rev. Lett. / Fast and accurate modeling of molecular atomization energies with machine learning (2012)
10.1137/16M1075454 / Multiscale Model. Simul. / Wavelet scattering regression of quantum chemical energies (2017)
10.1063/1.3553717 / J. Chem. Phys. / Atom-centered symmetry functions for constructing high-dimensional neural network potentials (2011)
10.1039/c1cp21668f / Phys. Chem. Chem. Phys. / Neural network potential-energy surfaces in chemistry: A tool for large-scale simulations (2011)
10.1021/acs.jpclett.5b00831 / J. Phys. Chem. Lett. / Machine learning predictions of molecular properties: Accurate many-body potentials and nonlocality in chemical space (2015)
10.1038/ncomms13890 / Nat. Commun. / Quantum-chemical insights from deep tensor neural networks (2016)
{'volume-title': 'Deep Learning', 'year': '2016', 'key': '2023061919341570400_c38'} / Deep Learning (2016)
10.1016/s0009-2614(99)00179-7 / Chem. Phys. Lett. / Basis-set convergence of the energy in molecular Hartree–Fock calculations (1999)
{'first-page': '55', 'article-title': 'Estimating the mean and variance of the target probability distribution', 'year': '1994', 'key': '2023061919341570400_c40'} / Estimating the mean and variance of the target probability distribution (1994)
{'volume-title': 'Neural Networks for Pattern Recognition', 'year': '1995', 'key': '2023061919341570400_c41'} / Neural Networks for Pattern Recognition (1995)
{'edition': '2nd ed.', 'volume-title': 'The Elements of Statistical Learning: Data Mining, Inference, and Prediction', 'year': '2009', 'key': '2023061919341570400_c42'} / The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2009)
{'first-page': '315', 'article-title': 'Deep sparse rectifier neural networks', 'year': '2011', 'key': '2023061919341570400_c43'} / Deep sparse rectifier neural networks (2011)
{'key': '2023061919341570400_c44', 'first-page': '1929', 'article-title': 'Dropout: A simple way to prevent neural networks from overfitting', 'volume': '15', 'year': '2014', 'journal-title': 'J. Mach. Learn. Res.'} / J. Mach. Learn. Res. / Dropout: A simple way to prevent neural networks from overfitting (2014)
{'year': '2015', 'key': '2023061919341570400_c45', 'article-title': 'Dropout as a Bayesian approximation: Representing model uncertainty in deep learning'} / Dropout as a Bayesian approximation: Representing model uncertainty in deep learning (2015)
{'key': '2023061919341570400_c46', 'first-page': '2575', 'article-title': 'Variational dropout and the local reparameterization trick', 'volume': '28', 'year': '2015', 'journal-title': 'Adv. Neural. Inf. Process. Syst.'} / Adv. Neural. Inf. Process. Syst. / Variational dropout and the local reparameterization trick (2015)
10.1021/ct200523a / J. Chem. Theory Comput. / Extensions of the S66 data set: More accurate interaction energies and angular-displaced nonequilibrium geometries (2011)
10.1063/1.4952647 / J. Chem. Phys. / ωB97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation (2016)
10.1021/ct100651f / J. Chem. Theory Comput. / Parameterization of a B3LYP specific correction for non-covalent interactions and basis set superposition error on a gigantic dataset of CCSD(T) quality non-covalent interaction energies (2011)
10.1002/wcms.82 / Wiley Interdiscip. Rev.: Comput. Mol. Sci. / Molpro: A general-purpose quantum chemistry program package (2012)
H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz, P. Celani, T. Korona, R. Lindh, A. Mitrushenkov, G. Rauhut, K. R. Shamasundar, T. B. Adler, R. D. Amos, A. Bernhardsson, A. Berning, D. L. Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert, E. Goll, C. Hampel, A. Heßelmann, G. Hetzer, T. Hrenar, G. Jansen, C. Köppl, Y. Liu, A. W. Lloyd, R. A. Mata, A. J. May, S. J. McNicholas, W. Meyer, M. E. Mura, A. Nicklass, D. P. O’Neill, P. Palmieri, D. Peng, K. Pflüger, R. Pitzer, M. Reiher, T. Shiozaki, H. Stoll, A. J. Stone, R. Tarroni, T. Thorsteinsson, and M. Wang, molpro, version 2012.1, a package of ab initio programs, 2012, see http://www.molpro.net.
H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz, P. Celani, W. Györffy, D. Kats, T. Korona, R. Lindh, A. Mitrushenkov, G. Rauhut, K. R. Shamasundar, T. B. Adler, R. D. Amos, A. Bernhardsson, A. Berning, D. L. Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert, E. Goll, C. Hampel, A. Heßelmann, G. Hetzer, T. Hrenar, G. Jansen, C. Köppl, Y. Liu, A. W. Lloyd, R. A. Mata, A. J. May, S. J. McNicholas, W. Meyer, M. E. Mura, A. Nicklass, D. P. O’Neill, P. Palmieri, D. Peng, K. Pflüger, R. Pitzer, M. Reiher, T. Shiozaki, H. Stoll, A. J. Stone, R. Tarroni, T. Thorsteinsson, and M. Wang, molpro, version 2015.1, a package of ab initio programs, 2015, see http://www.molpro.net.
10.1002/wcms.93 / Wiley Interdiscip. Rev.: Comput. Mol. Sci. / Psi4: An open-source ab initio electronic structure program (2012)
10.1002/9781119092919 / The Data Science Handbook (2017)
F. Chollet, Keras, GitHub repository, 2015, https://github.com/fchollet/keras.
R. Al-Rfou, G. Alain, A. Almahairi, C. Angermueller, D. Bahdanau, N. Ballas, F. Bastien, J. Bayer, A. Belikov, A. Belopolsky, Y. Bengio, A. Bergeron, J. Bergstra, V. Bisson, J. B. Snyder, N. Bouchard, N. Boulanger-Lewandowski, X. Bouthillier, A. de Brébisson, O. Breuleux, P.-L. Carrier, K. Cho, J. Chorowski, P. Christiano, T. Cooijmans, “Theano: A Python framework for fast computation of mathematical expressions,” e-print arXiv:1605.02688 (2016).
{'key': '2023061919341570400_c57'}
10.1063/1.4903765 / J. Chem. Phys. / Appointing silver and bronze standards for noncovalent interactions: A comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches (2014)
10.1063/1.3054300 / J. Chem. Phys. / Simplified CCSD(T)-F12 methods: Theory and benchmarks (2009)
10.1063/1.2889388 / J. Chem. Phys. / Explicitly correlated RMP2 for high-spin open-shell reference states (2008)
10.1063/1.4967424 / J. Chem. Phys. / Note: The performance of new density functionals for a recent blind test of non-covalent interactions (2016)
{'volume-title': 'Handbook of Molecular Descriptors', 'year': '2000', 'key': '2023061919341570400_c62'} / Handbook of Molecular Descriptors (2000)
{'first-page': '1263', 'article-title': 'Neural message passing for quantum chemistry', 'year': '2017', 'key': '2023061919341570400_c63'} / Neural message passing for quantum chemistry (2017)
10.1021/acs.jctc.5b00099 / J. Chem. Theory Comput. / Big data meets quantum chemistry approximations: The Δ-machine learning approach (2015)
10.1146/annurev.pc.32.100181.002043 / Annu. Rev. Phys. Chem. / Many-body perturbation theory and coupled cluster theory for electron correlation in molecules (1981)
10.1063/1.462569 / J. Chem. Phys. / Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions (1992)
10.1063/1.1367373 / J. Chem. Phys. / Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited (2001)
10.1063/1.1520138 / J. Chem. Phys. / Accurate correlation consistent basis sets for molecular core–valence correlation effects: The second row atoms Al–Ar, and the first row atoms B–Ne revisited (2002)
10.1063/1.2768602 / J. Chem. Phys. / Behavior of density functionals with respect to basis set. VI. Truncation of the correlation consistent basis sets (2007)
10.1063/1.1785145 / J. Chem. Phys. / Truncation of the correlation consistent basis sets: An effective approach to the reduction of computational cost? (2004)
10.1063/1.1867412 / J. Chem. Phys. / Truncation of the correlation consistent basis sets: Extension to third-row (Ga–Kr) molecules (2005)
10.1021/ct200106a / J. Chem. Theory Comput. / Perspectives on basis sets beautiful: Seasonal plantings of diffuse basis functions (2011)
10.1039/b204199p / Phys. Chem. Chem. Phys. / A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency (2002)
10.1002/jcc.20702 / J. Comput. Chem. / Hartree–Fock exchange fitting basis sets for H to Rn (2008)
10.1063/1.1856451 / J. Chem. Phys. / All-electron and relativistic pseudopotential studies for the group 1 element polarizabilities from K to element 119 (2005)
10.1063/1.2148945 / J. Chem. Phys. / Relativistic small-core energy-consistent pseudopotentials for the alkaline-earth elements from Ca to Ra (2006)
{'key': '2023061919341570400_c77'}
{'key': '2023061919341570400_c78'}
{'key': '2023061919341570400_c79'}

Dates

Type	When
Created	8 years ago (Sept. 6, 2017, 5:28 p.m.)
Deposited	3 months, 1 week ago (May 27, 2025, 4:20 p.m.)
Indexed	1 week, 2 days ago (Aug. 29, 2025, 6:06 a.m.)
Issued	8 years ago (Sept. 6, 2017)
Published	8 years ago (Sept. 6, 2017)
Published Online	8 years ago (Sept. 6, 2017)
Published Print	7 years, 10 months ago (Oct. 28, 2017)

Funders 0

None

BibTeX

@article{McGibbon_2017, title={Improving the accuracy of Møller-Plesset perturbation theory with neural networks}, volume={147}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.4986081}, DOI={10.1063/1.4986081}, number={16}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={McGibbon, Robert T. and Taube, Andrew G. and Donchev, Alexander G. and Siva, Karthik and Hernández, Felipe and Hargus, Cory and Law, Ka-Hei and Klepeis, John L. and Shaw, David E.}, year={2017}, month=sep }

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  "abstract": "<jats:p>Noncovalent interactions are of fundamental importance across the disciplines of chemistry, materials science, and biology. Quantum chemical calculations on noncovalently bound complexes, which allow for the quantification of properties such as binding energies and geometries, play an essential role in advancing our understanding of, and building models for, a vast array of complex processes involving molecular association or self-assembly. Because of its relatively modest computational cost, second-order M\u00f8ller-Plesset perturbation (MP2) theory is one of the most widely used methods in quantum chemistry for studying noncovalent interactions. MP2 is, however, plagued by serious errors due to its incomplete treatment of electron correlation, especially when modeling van der Waals interactions and \u03c0-stacked complexes. Here we present spin-network-scaled MP2 (SNS-MP2), a new semi-empirical MP2-based method for dimer interaction-energy calculations. To correct for errors in MP2, SNS-MP2 uses quantum chemical features of the complex under study in conjunction with a neural network to reweight terms appearing in the total MP2 interaction energy. The method has been trained on a new data set consisting of over 200 000 complete basis set (CBS)-extrapolated coupled-cluster interaction energies, which are considered the gold standard for chemical accuracy. SNS-MP2 predicts gold-standard binding energies of unseen test compounds with a mean absolute error of 0.04 kcal mol\u22121 (root-mean-square error 0.09 kcal mol\u22121), a 6- to 7-fold improvement over MP2. To the best of our knowledge, its accuracy exceeds that of all extant density functional theory- and wavefunction-based methods of similar computational cost, and is very close to the intrinsic accuracy of our benchmark coupled-cluster methodology itself. Furthermore, SNS-MP2 provides reliable per-conformation confidence intervals on the predicted interaction energies, a feature not available from any alternative method.</jats:p>",
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      "year": "2007",
      "journal-title": "Annu. Rev. Biophys. Biomol. Struct."
    },
    {
      "key": "2023061919341570400_c2",
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      "first-page": "2400",
      "DOI": "10.1126/science.1071063",
      "article-title": "Toward self-organization and complex matter",
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      "year": "2002",
      "journal-title": "Science"
    },
    {
      "volume-title": "The Theory of Intermolecular Forces",
      "year": "2013",
      "key": "2023061919341570400_c3"
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      "article-title": "Use of approximate integrals in ab initio theory. An application in MP2 energy calculations",
      "volume": "208",
      "year": "1993",
      "journal-title": "Chem. Phys. Lett."
    },
    {
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      "article-title": "Fast linear scaling second-order M\u00f8ller\u2013Plesset perturbation theory (MP2) using local and density fitting approximations",
      "volume": "118",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
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      "article-title": "Low-order scaling local electron correlation methods. I. Linear scaling local MP2",
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      "year": "1999",
      "journal-title": "J. Chem. Phys."
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      "year": "2000",
      "journal-title": "J. Chem. Phys."
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      "volume": "1",
      "year": "2005",
      "journal-title": "J. Chem. Theory Comput."
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      "volume": "1",
      "year": "2011",
      "journal-title": "Wiley Interdiscip. Rev.: Comput. Mol. Sci."
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      "article-title": "The origin of deficiency of the supermolecule second-order M\u00f8ller\u2013Plesset approach for evaluating interaction energies",
      "volume": "127",
      "year": "2007",
      "journal-title": "J. Chem. Phys."
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      "issue": "17",
      "key": "2023061919341570400_c12",
      "doi-asserted-by": "publisher",
      "first-page": "1985",
      "DOI": "10.1039/b600027d",
      "article-title": "Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs",
      "volume": "8",
      "year": "2006",
      "journal-title": "Phys. Chem. Chem. Phys."
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    {
      "issue": "36",
      "key": "2023061919341570400_c13",
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      "first-page": "10887",
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      "article-title": "Estimates of the ab initio limit for pi-pi interactions: The benzene dimer",
      "volume": "124",
      "year": "2002",
      "journal-title": "J. Am. Chem. Soc."
    },
    {
      "issue": "4",
      "key": "2023061919341570400_c14",
      "doi-asserted-by": "publisher",
      "first-page": "553",
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      "article-title": "The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors",
      "volume": "19",
      "year": "1970",
      "journal-title": "Mol. Phys."
    },
    {
      "issue": "5",
      "key": "2023061919341570400_c15",
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      "first-page": "2151",
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      "article-title": "Describing noncovalent interactions beyond the common approximations: How accurate is the \u201cgold standard,\u201d CCSD(T) at the complete basis set limit?",
      "volume": "9",
      "year": "2013",
      "journal-title": "J. Chem. Theory Comput."
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      "issue": "20",
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      "first-page": "9095",
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      "article-title": "Improved second-order M\u00f8ller\u2013Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies",
      "volume": "118",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
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    {
      "issue": "7",
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      "first-page": "1887",
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      "article-title": "Perturbation theory approach to intermolecular potential energy surfaces of van der Waals complexes",
      "volume": "94",
      "year": "1994",
      "journal-title": "Chem. Rev."
    },
    {
      "issue": "2",
      "key": "2023061919341570400_c18",
      "doi-asserted-by": "publisher",
      "first-page": "304",
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      "year": "2012",
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      "issue": "8",
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      "article-title": "S66: A well-balanced database of benchmark interaction energies relevant to biomolecular structures",
      "volume": "7",
      "year": "2011",
      "journal-title": "J. Chem. Theory Comput."
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    {
      "issue": "31",
      "key": "2023061919341570400_c20",
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      "first-page": "20905",
      "DOI": "10.1039/c6cp00688d",
      "article-title": "The S66x8 benchmark for noncovalent interactions revisited: Explicitly correlated ab initio methods and density functional theory",
      "volume": "18",
      "year": "2016",
      "journal-title": "Phys. Chem. Chem. Phys."
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      "issue": "12",
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      "DOI": "10.1063/1.4961095",
      "article-title": "Blind test of density-functional-based methods on intermolecular interaction energies",
      "volume": "145",
      "year": "2016",
      "journal-title": "J. Chem. Phys."
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    {
      "issue": "1",
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      "volume": "6",
      "year": "2010",
      "journal-title": "J. Chem. Theory Comput."
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    {
      "issue": "9",
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      "article-title": "Dispersion-corrected M\u00f8ller\u2013Plesset second-order perturbation theory",
      "volume": "131",
      "year": "2009",
      "journal-title": "J. Chem. Phys."
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    {
      "issue": "1",
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      "doi-asserted-by": "publisher",
      "first-page": "80",
      "DOI": "10.1021/ct6002737",
      "article-title": "Spin-component scaling methods for weak and stacking interactions",
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      "year": "2007",
      "journal-title": "J. Chem. Theory Comput."
    },
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      "issue": "8",
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      "year": "2007",
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    {
      "issue": "20",
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      "volume": "121",
      "year": "2004",
      "journal-title": "J. Chem. Phys."
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    {
      "issue": "42",
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      "volume": "11",
      "year": "2009",
      "journal-title": "Phys. Chem. Chem. Phys."
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    {
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      "volume": "63",
      "year": "1988",
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      "issue": "7",
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      "first-page": "4357",
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      "volume": "92",
      "year": "1990",
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      "volume": "107",
      "year": "2009",
      "journal-title": "Mol. Phys."
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      "issue": "6",
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      "volume": "146",
      "year": "2017",
      "journal-title": "J. Chem. Phys."
    },
    {
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      "article-title": "Fast and accurate modeling of molecular atomization energies with machine learning",
      "volume": "108",
      "year": "2012",
      "journal-title": "Phys. Rev. Lett."
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      "issue": "2",
      "key": "2023061919341570400_c33",
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      "first-page": "827",
      "DOI": "10.1137/16M1075454",
      "article-title": "Wavelet scattering regression of quantum chemical energies",
      "volume": "15",
      "year": "2017",
      "journal-title": "Multiscale Model. Simul."
    },
    {
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      "article-title": "Atom-centered symmetry functions for constructing high-dimensional neural network potentials",
      "volume": "134",
      "year": "2011",
      "journal-title": "J. Chem. Phys."
    },
    {
      "issue": "40",
      "key": "2023061919341570400_c35",
      "doi-asserted-by": "publisher",
      "first-page": "17930",
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      "volume": "13",
      "year": "2011",
      "journal-title": "Phys. Chem. Chem. Phys."
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      "issue": "12",
      "key": "2023061919341570400_c36",
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      "first-page": "2326",
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      "article-title": "Machine learning predictions of molecular properties: Accurate many-body potentials and nonlocality in chemical space",
      "volume": "6",
      "year": "2015",
      "journal-title": "J. Phys. Chem. Lett."
    },
    {
      "key": "2023061919341570400_c37",
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      "first-page": "13890",
      "DOI": "10.1038/ncomms13890",
      "article-title": "Quantum-chemical insights from deep tensor neural networks",
      "volume": "8",
      "year": "2016",
      "journal-title": "Nat. Commun."
    },
    {
      "volume-title": "Deep Learning",
      "year": "2016",
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    {
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      "article-title": "Basis-set convergence of the energy in molecular Hartree\u2013Fock calculations",
      "volume": "302",
      "year": "1999",
      "journal-title": "Chem. Phys. Lett."
    },
    {
      "first-page": "55",
      "article-title": "Estimating the mean and variance of the target probability distribution",
      "year": "1994",
      "key": "2023061919341570400_c40"
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    {
      "volume-title": "Neural Networks for Pattern Recognition",
      "year": "1995",
      "key": "2023061919341570400_c41"
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    {
      "edition": "2nd ed.",
      "volume-title": "The Elements of Statistical Learning: Data Mining, Inference, and Prediction",
      "year": "2009",
      "key": "2023061919341570400_c42"
    },
    {
      "first-page": "315",
      "article-title": "Deep sparse rectifier neural networks",
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    {
      "key": "2023061919341570400_c44",
      "first-page": "1929",
      "article-title": "Dropout: A simple way to prevent neural networks from overfitting",
      "volume": "15",
      "year": "2014",
      "journal-title": "J. Mach. Learn. Res."
    },
    {
      "year": "2015",
      "key": "2023061919341570400_c45",
      "article-title": "Dropout as a Bayesian approximation: Representing model uncertainty in deep learning"
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    {
      "key": "2023061919341570400_c46",
      "first-page": "2575",
      "article-title": "Variational dropout and the local reparameterization trick",
      "volume": "28",
      "year": "2015",
      "journal-title": "Adv. Neural. Inf. Process. Syst."
    },
    {
      "issue": "11",
      "key": "2023061919341570400_c47",
      "doi-asserted-by": "publisher",
      "first-page": "3466",
      "DOI": "10.1021/ct200523a",
      "article-title": "Extensions of the S66 data set: More accurate interaction energies and angular-displaced nonequilibrium geometries",
      "volume": "7",
      "year": "2011",
      "journal-title": "J. Chem. Theory Comput."
    },
    {
      "issue": "21",
      "key": "2023061919341570400_c48",
      "doi-asserted-by": "publisher",
      "first-page": "214110",
      "DOI": "10.1063/1.4952647",
      "article-title": "\u03c9B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation",
      "volume": "144",
      "year": "2016",
      "journal-title": "J. Chem. Phys."
    },
    {
      "issue": "3",
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      "doi-asserted-by": "publisher",
      "first-page": "658",
      "DOI": "10.1021/ct100651f",
      "article-title": "Parameterization of a B3LYP specific correction for non-covalent interactions and basis set superposition error on a gigantic dataset of CCSD(T) quality non-covalent interaction energies",
      "volume": "7",
      "year": "2011",
      "journal-title": "J. Chem. Theory Comput."
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      "issue": "2",
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      "doi-asserted-by": "publisher",
      "first-page": "242",
      "DOI": "10.1002/wcms.82",
      "article-title": "Molpro: A general-purpose quantum chemistry program package",
      "volume": "2",
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      "journal-title": "Wiley Interdiscip. Rev.: Comput. Mol. Sci."
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      "year": "2014",
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      "year": "2009",
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      "year": "2008",
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      "volume": "145",
      "year": "2016",
      "journal-title": "J. Chem. Phys."
    },
    {
      "volume-title": "Handbook of Molecular Descriptors",
      "year": "2000",
      "key": "2023061919341570400_c62"
    },
    {
      "first-page": "1263",
      "article-title": "Neural message passing for quantum chemistry",
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