Automatic differentiation approach for obtaining exchange-correlation functional derivatives
ORAL
Abstract
Obtaining explicit analytical expressions for exchange-correlation (XC) functional derivatives in density functional theory (DFT) can be tedious. Automatic differentiation methods like those implemented in the JAX framework allow us to take derivatives to the n-th order of a defined function. Here, we start from the analytical form of a known exchange-correlation energy density (εxc) and use automatic differentiation to get function descriptions of the first (vxc) and second (fxc) derivatives, known as the potential and kernel, respectively. The kernel is required for excited-state linear-response calculations in the Casida formulation of time-dependent density functional theory (TD-DFT). Simulated electronic excitation spectra using our functionals obtained from automatic differentiation show excellent agreement with the same using analytical descriptions stored within the widely-used libxc library. We scale this framework for use with meta-GGAs, orbital (OEP) and hybrid functionals, many-body dispersion functionals, as well as functionals that include electron-photon interactions (QEDFT). Newly derived functionals that only have an εxc expression could also make use of this framework for easier implementation in higher-order applications.
*J.C.U. and M.M. are supported by the CCQ graduate fellowships in computational quantum physics at their respective institutions. The Flatiron Institute is a division of the Simons Foundation.
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Presenters
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Jaylyn C Umana
- The Graduate Center, City University of New York; Center for Computational Quantum Physics, Flatiron Institute
- The Graduate Center, City University of New York