title: Basis set generation for quantum dynamics simulations using simple trajectory-based methods.
abstract: Methods for solving the time-dependent Schrödinger equation generally employ either a global static basis set, which is fixed at the outset, or a dynamic basis set, which evolves according to classical-like or variational equations of motion; the former approach results in the well-known exponential scaling with system size, while the latter can suffer from challenging numerical problems, such as singular matrices, as well as violation of energy conservation. Here, we suggest a middle road: building a basis set using trajectories to place time-independent basis functions in the regions of phase space relevant to wave function propagation. This simple approach, which potentially circumvents many of the problems traditionally associated with global or dynamic basis sets, is successfully demonstrated for two challenging benchmark problems in quantum dynamics, namely, relaxation dynamics following photoexcitation in pyrazine, and the spin Boson model.
authors.affiliation: Department of Chemistry and Centre for Scientific Computing, University of Warwick , Coventry, CV4 7AL, United Kingdom.
authors.forename: Maximilian A C
authors.initials: MA
authors.lastname: Saller
authors.affiliation: Department of Chemistry and Centre for Scientific Computing, University of Warwick , Coventry, CV4 7AL, United Kingdom.
authors.forename: Scott
authors.initials: S
authors.lastname: Habershon