Optimization of the semiclassical initial value representation of the exact quantum-mechanical real time propagator

Self Cite

Thawed Gaussian wavepackets have been used in recent years to compute approximations to the thermal density matrix. From a numerical point of view, it is cheaper to employ frozen Gaussian wavepackets. In this paper, we provide the formalism for the computation of thermal densities using frozen Gaussian wavepackets. We show that the exact density may be given in terms of a series, in which the zeroth order term is the frozen Gaussian. A numerical test of the methodology is presented for deep tunneling in the quartic double well potential. In all cases, the series is observed to converge. The convergence of the diagonal density matrix element is much faster than that of the antidiagonal one, suggesting that the methodology should be especially useful for the computation of partition functions. As a by product of this study, we find that the density matrix in configuration space can have more than two saddle points at low temperatures. This has implications for the use of the quantum instanton theory.

Section: Frozen Gaussian Series Representation Of the Imaginary Time mentioning

confidence: 99%

Frozen Gaussian series representation of the imaginary time propagator theory and numerical tests

Zhang

Shao

Pollak

2009

Self Cite

“…[15][16][17][18] To this end, we proposed a means of reducing the computational cost associated with the generation of classical trajectories via the introduction of constraints in SC-IVR by reducing the effec-tive number of degrees of freedom. As a result, the number of trajectories required in order to achieve converged results grows as a function of the complexity and dimensionality of the problem.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical initial value representation treatment of a hydrogen bonded complex of rigid water molecules from a single trajectory in Cartesian coordinates

Issack

Roy

2007

A semiclassical initial value representation approach for molecular systems in Cartesian coordinates is combined with a recently proposed time averaging technique [J. Chem. Phys. 118, 7174 (2003)]. It is shown that a single trajectory can yield the zero-point energy of the water dimer with good accuracy for the model chosen when compared to fully constrained Cartesian semiclassical calculations. The convergence with respect to the number of averaging time origins is discussed.

“…To our knowledge, the only general procedure to estimate the error arising from semiclassical approximations other than a direct comparison with the exact quantum eigenfunctions, is a perturbative series correction of the propagator. [30][31][32][33] In this paper, a set of semiclassical molecular dynamics methods will be employed to calculate vibrational eigenfunctions. First, the methods will be tested on analytical potentials where exact calculations can be performed, and then coupled with a first principles approach, in which the potential energy surfaces are computed on-the-fly using density functional theory (DFT).…”

Section: Introductionmentioning

confidence: 99%

First principles semiclassical calculations of vibrational eigenfunctions

Ceotto

Valleau

Tantardini

et al. 2011

Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational eigenfunctions are calculated for the CO 2 molecule and its accuracy evaluated. The multiple coherent states initial value representations semiclassical method recently developed by us has shown with only six ab initio trajectories to evaluate eigenvalues and eigenfunctions at the accuracy level of thousands trajectory semiclassical initial value representation simulations.