First-principles semiclassical initial value representation molecular dynamics

Michele Ceotto,Gian Franco Tantardini,Sangwoo Shim,Sule Atahan,Alán Aspuru-Guzik

doi:10.1039/b820785b

Abstract

In this work, we explore the use of the semiclassical initial value representation (SC-IVR) method with first-principles electronic structure approaches to carry out classical molecular dynamics. The proposed approach can extract the vibrational power spectrum of carbon dioxide from a single trajectory providing numerical results that agree with experiment and quantum calculations. The computational demands of the method are comparable to those of classical single-trajectory calculations, while describing uniquely quantum features such as the zero-point energy and Fermi resonances. The method can also be used to identify symmetry properties of given vibrational peaks and investigate vibrational couplings by selected classical trajectories. The accuracy of the method degrades for the reproduction of anharmonic shifts for high-energy vibrational levels.

Highlights

Algorithms for the simulation of molecular dynamics belong to the fundamental toolset of modern theoretical chemical physics
We explore the use of the semiclassical initial value representation (SC-IVR) method with firstprinciples electronic structure approaches to carry out classical molecular dynamics
We show how the semiclassical initial value representation (SC-IVR) [12] method can be coupled tightly and naturally, without any mayor change in formulation, with first principles electronic structure approaches to carry out classical molecular dynamics

Summary

Re π h T

× χ | p (t2) , q (t2) ei(St2 (p(0),q(0))+Et2)/hχ | p (t1) , q (t1) ei(St1 (p(0),q(0))+Et1)/h ∗. Where (p (t1) , q (t1)) and (p (t2) , q (t2)) are variables that evolve from the same initial conditions but to different times, and T is the total simulation time The advantage of this approach is that the additional time integral can in principle replace the need for phase-space averaging in the large-time limit of a single trajectory. Our numerical tests show that the results of carrying out this approximation are essentially identical to the double time integral approach when using a single trajectory. The potential, nuclear gradient and Hessian are used to calculate the action, pre-factor and coherent state overlaps necessary for the TA-SC-IVR method (Eqs. 4 and 5). To evaluate the FP-SC-IVR method, we compare vibrational spectrum of CO2 molecule from FP-SC-IVR method to numerically-exact discrete variable representation (DVR) eigenvalue calculations on a potential fitted to a set of first-principles points obtained at the same level of theory. We continue on the discussion of the FP-SC-IVR method

POTENTIAL FITTING AND GRID CALCULATIONS

CONCLUSIONS