UC Merced

Time-dependent electronic structure is an important means to understand the dynamics of electrons, and thus the associated time-dependent mechanisms, in chemical systems of interest. A popular method to model and study electron dynamics is real-time time-dependent density-functional theory, or RT-TDDFT. In practice, the implementation of RT-TDDFT (as well as linear response TDDFT) makes an approximation known as the adiabatic approximation, where the dependence of electron density at the current moment of time on that at previous moments in time (as well as the many-body interacting and non-interacting Kohn-Sham wave-functions) is completely ignored. Maitra et al have shown that this approximation fails for model systems, but the eects of this approximation with varying system-size are not known. We study electron dynamics of systems exhibiting charge-transfer by resonantly perturbing them and conclude that size-dependent errors, evaluated in terms of peak-shifting in linear absorption spectra and Rabi cycle dynamics, get progressively smaller as the system-size increases. Statistical learning methods have been shown to have an increasingly wide scope with respect to property prediction in quantum chemical problems in recent times. However, their use for predicting electron dynamics has been relatively underexplored. In collaboration with Dr. Bhat and his group (Applied Math, UC Merced), with a goal to train a Hamiltonian model for predicting accurate density evolution, we demonstrate that one can use time-dependent density-matrix trajectories to learn molecular electronic Hamiltonians which can be used to propagate density-matrices under arbitrary electric-eld perturbations. In an eort to apply such learning methods to density-matrix data obtained from accurate wave-function methods such as time-dependent configuration interaction (TDCI), we explore the amount of memory required to reproduce accurate TDCI singles (TDCIS) density-matrix evolution in some molecular systems for various perturbations. In doing so successfully, we hope to explore the structure and application of statistical learning methods for training Hamiltonian models on accurate time-dependent electron density data, predicting single reference density-matrix evolution and informing the construction of memory-inclusive exchange-correlation functionals in TDDFT.