Application of a Two-Component Neural Network for Interchange Correlation Functional Interpolation

  • Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Round. 136B864 (1964).

    ADS
    MathSciNet

    Google Scholar

  • Kohn, W. & Sham, LJ Self-consistent equations including trade and correlation effects. Phys. Round. 140A1133 (1965).

    ADS
    MathSciNet

    Google Scholar

  • Ceperley, DM & Alder, B. Ground state of electron gas by a stochastic method. Phys. Rev. Lett. 45566 (1980).

    ADS
    CASE
    Article

    Google Scholar

  • Zhao, Y., Schultz, NE and Truhlar, DG Functional exchange correlation with high accuracy for metallic and non-metallic compounds, kinetics and non-covalent interactions (2005).

  • Vosko, SH, Wilk, L. & Nusair, M. Accurate spin-dependent liquid electron correlation energies for local spin density calculations: a critical analysis. Box. J.Phys. 581200-1211 (1980).

    ADS
    CASE
    Article

    Google Scholar

  • Perdew, JP & Zunger, A. Self-interaction correction to density functional approximations for many-electron systems. Phys. Rev. B 235048 (1981).

    ADS
    CASE
    Article

    Google Scholar

  • Perdew, JP & Wang, Y. Accurate and simple analytical representation of electron-gas correlation energy. Phys. Rev. B 4513244 (1992).

    ADS
    CASE
    Article

    Google Scholar

  • Wang, Y. & Perdew, JP Spin scale of electron-gas correlation energy in the high-density limit. Phys. Rev. B 438911 (1991).

    ADS
    CASE
    Article

    Google Scholar

  • Perdew, JP et al. Atoms, molecules, solids and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 466671 (1992).

    ADS
    CASE
    Article

    Google Scholar

  • Perdew, JP, Burke, K. & Ernzerhof, M. The Generalized Gradient Approximation Simplified. Phys. Rev. Lett. 773865 (1996).

    ADS
    CASE
    Article

    Google Scholar

  • Mardirossian, N. & Head-Gordon, M. Thirty Years of Density Functional Theory in Computational Chemistry: An Overview and Extensive Evaluation of 200 Density Functionals. Mol. Phys. 1152315-2372 (2017).

    ADS
    CASE
    Article

    Google Scholar

  • Lani, G., Di Marino, S., Gerolin, A., van Leeuwen, R. & Gori-Giorgi, P. The adiabatic functional with strictly correlated electrons: kernel and exact properties. Phys. Chem. Chem. Phys. 1821092–21101 (2016).

    CASE
    Article

    Google Scholar

  • Maier, TM, Haasler, M., Arbuznikov, AV & Kaupp, M. New approaches for calibrating exchange energy densities in local hybrid functionals. Phys. Chem. Chem. Phys. 1821133–21144 (2016).

    CASE
    Article

    Google Scholar

  • Mori-Sánchez, P. & Cohen, AJ The discontinuity derived from the exchange-correlation functional. Phys. Chem. Chem. Phys. 1614378–14387 (2014).

    Article

    Google Scholar

  • Mori-Sánchez, P. & Cohen, AJ Exact density functional obtained via constrained sampling search. J.Phys. Chem. Lett. 94910–4914 (2018).

    Article

    Google Scholar

  • Needs, R., Towler, M., Drummond, N. & Ríos, PL Continuous variational Monte Carlo calculations and diffusion quantum. J.Phys. Condens. Question 22023201 (2009).

    ADS
    Article

    Google Scholar

  • Kolorenč, J. & Mitas, L. Applications of quantum Monte Carlo methods in condensed systems. Rep. Prog. Phys. 74026502 (2011).

    ADS
    Article

    Google Scholar

  • Cremer, D. Møller – Plesset’s perturbation theory: from small molecule methods to methods for thousands of atoms. Wiley Interdiscip. Rev. Computer. Mol. Science. 1509-530 (2011).

    CASE
    Article

    Google Scholar

  • Cybenko, G. Approximation by superpositions of a sigmoid function. Math. System control signals 2303–314 (1989).

    MathSciNet
    Article

    Google Scholar

  • Tozer, DJ, Ingamells, VE & Handy, NC Exchange Correlation Potentials. J. Chem. Phys. 1059200–9213 (1996).

    ADS
    CASE
    Article

    Google Scholar

  • Nagai, R., Akashi, R., Sasaki, S. & Tsuneyuki, S. Neural Network Kohn-Sham Exchange Correlation Potential and Its Out-of-Training Transferability. J. Chem. Phys. 148241737 (2018).

    ADS
    Article

    Google Scholar

  • Nagai, R., Akashi, R. & Sugino, O. Complementing Density Functional Theory with Machine Learning of Molecules’ Hidden Messages. NPJ calculation. Mater. 61–8 (2020).

    Article

    Google Scholar

  • Lei, X. & Medford, AJ Design and Analysis of Machine Learning Exchange-Correlation Functionals via Rotation-Invariant Convolutional Descriptors. Phys. Rev. Mater. 3063801 (2019).

    CASE
    Article

    Google Scholar

  • Ramos, P. & Pavanello, M. Static Correlation Density Functional Theory. arXiv preprint arXiv:1906.06661 (2019).

  • Ryabov, A., Akhatov, I. & Zhilyaev, P. Neural Network Interpolation of Exchange Correlation Function. Science. representing ten1–7 (2020).

    ADS
    Article

    Google Scholar

  • Lil. et al. Kohn-sham equations as a regularizer: building prior knowledge in machine-learned physics. Phys. Rev. Lett. 126036401 (2021).

    ADS
    CASE
    Article

    Google Scholar

  • Kirkpatrick, J. et al. Pushing the boundaries of density functionals by solving the fractional electron problem. Science 3741385-1389 (2021).

    ADS
    CASE
    Article

    Google Scholar

  • Perdew, JP, Burke, K. & Ernzerhof, M. The Generalized Gradient Approximation Simplified [phys. rev. lett. 77, 3865 (1996)]. Phys. Rev. Lett. 781396–1396 (1997).

    ADS
    CASE
    Article

    Google Scholar

  • Andrade, X. et al. Real-space grids and octopus code as tools for the development of new simulation approaches for electronic systems. Phys. Chem. Chem. Phys. 1731371–31396 (2015).

    CASE
    Article

    Google Scholar

  • Andrade, X. et al. Time-dependent density functional theory in massively parallel computer architectures: the Octopus project. J.Phys. Condens. Question 24233202 (2012).

    ADS
    Article

    Google Scholar

  • Andrade, X. & Aspuru-Guzik, A. Real-space density functional theory on graphics processing units: a computational approach and comparison with Gaussian basis ensemble methods. J. Chem. Theoretical calculation. 94360–4373 (2013).

    CASE
    Article

    Google Scholar

  • Lynch, BJ & Truhlar, DG Robust and affordable multicoefficient methods for thermochemistry and thermochemical kinetics: the mccm/3 and sac/3 suite. J.Phys. Chem. A 1073898–3906 (2003).

    CASE
    Article

    Google Scholar

  • Balbás, L., Martins, JL & Soler, JM Assessing the Energy, Potential, and Stress of Exchange Correlation. Phys. Rev. B 64165110 (2001).

    ADS
    Article

    Google Scholar

  • Lehtola, S., Steigemann, C., Oliveira, MJ & Marques, MA Recent developments in libxc – a comprehensive library of functionals for density functional theory. SoftwareX seven1–5 (2018).

    ADS
    Article

    Google Scholar

  • Schlipf, M. & Gygi, F. Optimization algorithm for generating oncv pseudopotentials. Calculation. Phys. Common. 19636–44 (2015).

    ADS
    CASE
    Article

    Google Scholar

  • Paszke, A. et al. Pytorch: A high-performance, imperative-style deep learning library. In Advances in Neural Information Processing Systems 32 (eds. Wallach, H. et al.) 8024–8035 (Curran Associates, Inc., 2019).

  • Clevert, D.-A., Unterthiner, T. & Hochreiter, S. Fast and Accurate Deep Network Learning by Exponential Linear Units (elus) (2016).

  • Cuierrier, E., Roy, P.-O. & Ernzerhof, M. Constructing and representing exchange correlation holes through artificial neural networks. J. Chem. Phys. 155174121 (2021).

    ADS
    CASE
    Article

    Google Scholar

  • Nagai, R., Akashi, R. & Sugino, O. Functional machine learning-based exchange correlation with physical asymptotic constraints. arXiv preprint arXiv:2111.15593 (2021).

  • Gong, W. et al. Incorporation of density scale constraint into density functional design via contrastive representation learning. arXiv preprint arXiv:2205.15071 (2022).

  • Schmidt, J., Benavides-Riveros, CL & Marques, MA Machine Learning the Nonlocal Physical Exchange-Correlation Functional of Density Functional Theory. J.Phys. Chem. Lett. ten6425–6431 (2019).

    CASE
    Article

    Google Scholar

  • Gaiduk, AP & Staroverov, VN How to tell when a Kohn-Sham potential model is not a functional derivative. J. Chem. Phys. 131044107 (2009).

    ADS
    Article

    Google Scholar