Machine-Learning Electron Dynamics with Moment Propagation Theory: Application to Optical Absorption Spectrum Computation using Real-Time TDDFT

TL;DR

This paper introduces a machine-learning-enhanced moment propagation theory for simulating electron dynamics efficiently, demonstrated through optical absorption spectrum calculations in molecules and condensed matter systems using real-time TDDFT data.

Contribution

The work develops a novel approach combining machine learning with moment propagation theory and real-time TDDFT to efficiently simulate quantum electron dynamics.

Findings

Successfully computed optical absorption spectra for molecules and solids.

Demonstrated efficiency improvements over traditional RT-TDDFT methods.

Explored the application of electron nearsightedness principle in this context.

Abstract

We present an application of our new theoretical formulation of quantum dynamics, moment propagation theory (MPT) (Boyer et al., J. Chem. Phys. 160, 064113 (2024)), for employing machine-learning techniques to simulate the quantum dynamics of electrons. In particular, we use real-time time-dependent density functional theory (RT-TDDFT) simulation in the gauge of the maximally localized Wannier functions (MLWFs) for training the MPT equation of motion. Spatially-localized time-dependent MLWFs provide a concise representation that is particularly convenient for the MPT expressed in terms of increasing orders of moments. The equation of motion for these moments can be integrated in time while the analytical expressions are quite involved. In this work, machine-learning techniques were used to train the the second-order time derivatives of the moments using first-principles data from the RT-TDDFT simulation, and this MPT enabled us to perform electron dynamics efficiently. The application to computing optical absorption spectrum for various systems was demonstrated as a proof-of-principles example of this approach. In addition to isolated molecules (water, benzene, and ethene), condensed matter systems (liquid water and crystalline silicon) were studied, and we also explored how the principle of the nearsightedness of electrons can be employed in this context.