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Abstract Density functional theory (DFT) has been a critical component of computational materials research and discovery for decades. However, the computational cost of solving the central Kohn–Sham equation remains a major obstacle for dynamical studies of complex phenomena at-scale. Here, we propose an end-to-end machine learning (ML) model that emulates the essence of DFT by mapping the atomic structure of the system to its electronic charge density, followed by the prediction of other properties such as density of states, potential energy, atomic forces, and stress tensor, by using the atomic structure and charge density as input. Our deep learning model successfully bypasses the explicit solution of the Kohn-Sham equation with orders of magnitude speedup (linear scaling with system size with a small prefactor), while maintaining chemical accuracy. We demonstrate the capability of this ML-DFT concept for an extensive database of organic molecules, polymer chains, and polymer crystals.
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Towards a density functional theory of molecular fragments. What is the shape of atoms in molecules?
In some sense, quantum mechanics solves all the problems in chemistry: The only thing one has to do is solve the Schrödinger equation for the molecules of interest. Unfortunately, the computational cost of solving this equation grows exponentially with the number of electrons and for more than ~100 electrons, it is impossible to solve it with chemical accuracy (~ 2 kcal/mol). The Kohn-Sham (KS) equations of density functional theory (DFT) allow us to reformulate the Schrödinger equation using the electronic probability density as the central variable without having to calculate the Schrödinger wave functions. The cost of solving the Kohn-Sham equations grows only as N3, where N is the number of electrons, which has led to the immense popularity of DFT in chemistry. Despite this popularity, even the most sophisticated approximations in KS-DFT result in errors that limit the use of methods based exclusively on the electronic density. By using fragment densities (as opposed to total densities) as the main variables, we discuss here how new methods can be developed that scale linearly with N while providing an appealing answer to the subtitle of the article: What is the shape of atoms in molecules
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- Award ID(s):
- 1900301
- PAR ID:
- 10182067
- Date Published:
- Journal Name:
- Revista de la Academia Colombiana de Ciencias Exactas Físicas y Naturales
- Volume:
- 44
- Issue:
- 170
- ISSN:
- 0370-3908
- Page Range / eLocation ID:
- 269-279
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/http://dx.doi.org/10.18257/raccefyn.960
