Long-time and unitary properties of semiclassical initial value representations

Abstract

We numerically compare the semiclassical "frozen Gaussian" Herman-Kluk propagator [Chem. Phys. 91, 27 (1984)] and the "thawed Gaussian" propagator put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by studying the quantum dynamics in some nonlinear onedimensional potentials. The reasons for the lack of long time accuracy and norm conservation in the latter method are uncovered. We amend the thawed Gaussian propagator with a global harmonic approximation for the stability of the trajectories and demonstrate that this revised propagator is a true alternative to the Herman-Kluk propagator with similar accuracy.

Semiclassical on-the-fly computation of the S→S1 absorption spectrum of formaldehyde

“…Due to our use of a unit prefactor there is a rapid loss of unitarity with time. 35 This is also seen by comparing the SCIVR and the harmonic correlation functions, which are shown as insets in Figs. 1 and 2.…”

Semiclassical dynamics of open quantum systems: Comparing the finite with the infinite perspective

“…(8). This approach has been discussed already in the first of the seminal papers of Kay [34] and has since then been used with different levels of success, e.g., in [42] and [43]. While in [42] the original HK approach according to Eq.…”

“…This approach has been discussed already in the first of the seminal papers of Kay [34] and has since then been used with different levels of success, e.g., in [42] and [43]. While in [42] the original HK approach according to Eq. (8) was shown to be superior, the opposite is true in the surface scattering study by Moix and Pollak [43].…”

“…Also, in the case of the SCBM the norm deviates on the order of 10-20% from unity for both, high temperatures and low temperatures with strong coupling. The results presented in the corresponding graphs are thus obtained via renormalization [50,42,44].…”

Accelerated direct semiclassical molecular dynamics using a compact finite difference Hessian scheme

“…[1][2][3] In particular, semiclassical initial value representation (SC-IVR) theories have proven to be quite accurate, as demonstrated by numerous applications. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] The fundamental advantage of the SC-IVR propagator over basis set evaluations of the quantum propagator, such as the multiconfigurational time-dependent Hartree 21 or the coupled coherent states methodology, 22 is that it exclusively relies on classical trajectories and, therefore, it can be straightforwardly implemented with "on the fly" direct molecular dynamics calculations. In addition, basis sets and other 23,24 approximate evaluations of the quantum propagator need a global potential energy surface, while SC-IVR depends only on the local potential.…”