Gaussian-based techniques for quantum propagation from the time-dependent variational principle: Formulation in terms of trajectories of coupled classical and quantum variables

Abstract

Published paper

GPU-Accelerated State-Averaged Complete Active Space Self-Consistent Field Interfaced with Ab Initio Multiple Spawning Unravels the Photodynamics of Provitamin D3

“…[12][13][14][15][16][17][18][19][20][21] Quantum mechanical effects related to surface crossing can be described either by a swarm of classical trajectories that can hop between electronic states -trajectory surface hopping (TSH) [22][23][24] -or by an expansion of the nuclear wavefunctions in terms of frozen Gaussians following classical trajectories called "trajectory basis functions" -Full Multiple Spawning (FMS) [12][13][25][26][27] and related methods. 19,[28][29][30] The propagation of trajectories substantially reduces the cost of the nuclear propagation compared to grid-based solution of the time-dependent Schrödinger equation. [10][11] However, when implemented in a context where the electronic structure is solved simultaneously with the nuclear dynamics, a large number of electronic structure calculations will be required to compute electronic energies, nuclear gradients, and nonadiabatic coupling vectors between electronic states.…”

Photoionization dynamics and angular squeezing phenomenon in intense long-wavelength laser fields

“…. ,N p } as |ψ n (t) = |χ n (1) |χ n (2) · · · |χ n (N p ) , as in the CCS method [14][15][16][17][18]. In coordinate space, the 3D CS of the j th particle in the nth TDBS, x|χ n (j ) , is given by [14,18] x|χ n (j ) = 1…”

“…Another kind of method to reduce N is to change the relation between N and M by developing novel approaches. One such approach is the coupled coherent state (CCS) method that makes use of time-dependent coherent states (CSs) as the basis set [10,[15][16][17]. In the CCS method, N is greatly reduced because it scales up quadratically with M as N ∼ M 2 .…”

“…In the CCS method, N is greatly reduced because it scales up quadratically with M as N ∼ M 2 . The CCS method has been successfully applied to a number of multidimensional calculations [10,[14][15][16][17][18].…”

“…In this work, we develop a more feasible coherent-state Ehrenfest trajectory (CSET) approach for the study of full dynamics of molecules in intense laser fields based on the coherent-state trajectories [17] that are determined by coupled Ehrenfest equations. In this approach, the electrons and nuclei in real space are mapped to the phase space.…”