Abstract
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.
Highlights
Quantum effects in the nuclear dynamics.8–17 there has been great development in this field, to our knowledge, calculations of molecular eigenfunctions using on-the-fly approaches have not been explored
As an alternative to EBK and JWKB approaches, as we expose below, the spectral quantum features can be better understood in terms of the underlying dynamics, in particular within the semiclassical approximation, since periodic orbits set a correspondence between stationary states and their corresponding dynamics
Semiclassical methods are based on a linear superposition of Gaussian coherent states that lie along the quantized classical trajectories
Summary
Quantum effects in the nuclear dynamics. there has been great development in this field, to our knowledge, calculations of molecular eigenfunctions using on-the-fly approaches have not been explored. Semiclassical methods are based on a linear superposition of Gaussian coherent states that lie along the quantized classical trajectories Such approach is free of any caustic problems and the agreement with the exact calculations is good in the tunneling region. We employ a recent implementation 34,35 of the original time-averaging filtering of the semiclassical initial value representation method (SC-IVR) (Ref. 36) and extend it for the purpose of calculating vibrational eigenfunctions This method uses a suitable set of delocalized coherent states that resembles a linear combination of the eigenfunctions of the system to reproduce quantum spectral features. In this way, the multiple coherent states SC-IVR (MC-SC-IVR) mimics the multiple vibrational components and successfully reproduce well-defined spectra for the several systems which have been tested.. IV, first principles semiclassical eigenfunctions are calculated for the carbon dioxide molecule and, conclusions are drawn in Sec V
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