Machine-Learning\nElectron Dynamics with Moment Propagation\nTheory: Application to Optical Absorption Spectrum Computation Using\nReal-Time TDDFT

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