Dynamical pruning of static localized basis sets in time-dependent quantum dynamics

Abstract

We investigate the viability of dynamical pruning of localized basis sets in time-dependent quantum wave packet methods. Basis functions that have a very small population at any given time are removed from the active set. The basis functions themselves are time independent, but the set of active functions changes in time. Two different types of localized basis functions are tested: discrete variable representation ͑DVR͒ functions, which are localized in position space, and phase-space localized ͑PSL͒ functions, which are localized in both position and momentum. The number of functions active at each point in time can be as much as an order of magnitude less for dynamical pruning than for static pruning, in reactive scattering calculations of H 2 on the Pt͑211͒ stepped surface. Scaling of the dynamically pruned PSL ͑DP-PSL͒ bases with dimension is considerably more favorable than for either the primitive ͑direct product͒ or DVR bases, and the DP-PSL basis set is predicted to be three orders of magnitude smaller than the primitive basis set in the current state-of-the-art six-dimensional reactive scattering calculations.

Resonance dynamics of DCO (X̃ A′2) simulated with the dynamically pruned discrete variable representation (DP-DVR)

“…47,62 This direct-product basis is then pruned using our DP-DVR approach, 44 which is related to previous pruning methods. 43,[63][64][65][66] In contrast to those, we could show that our approach is actually faster than conventional methods. If the absolute value of a coefficient of a direct-product basis function is larger than a predefined wave-amplitude threshold, this basis function and its nearest neighbors become active.…”

A Continuous Spawning Method for Nonadiabatic Dynamics and Validation for the Zero‐Temperature Spin‐Boson Problem

“…This behavior is crucial to the success of the procedure, since it ensures that this “continuous spawning” procedure does not result in spawning new basis functions at each time step (which would rapidly become unmanageable). Furthermore, it is anticipated that the computational effort can be significantly reduced by incorporating adaptive basis set truncation techniques, as explored recently by others 54,55 . We have not yet explored this possibility.…”

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

“…only coefficients whose magnitude is of a certain percentage of the maximal coefficient value are kept, which leads to time-dependent thresholds (as suggested in ref. 27). Fig.…”