Determination of molecular vibrational state energies using the ab initio semiclassical initial value representation: Application to formaldehyde

Abstract

We have demonstrated the use of ab initio molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.

A novel Gaussian Binning (1GB) analysis of vibrational state distributions in highly excited ${\rm H}_\text{2}$H2O from reactive quenching of OH* by ${\rm H}_\text{2}$H2

“…In the case of FFT, momenta and positions are expressed in their Fourier series representations, while AS is based on a time-dependent perturbation of the initial normal mode Hamiltonian, which is smoothly increasing in time until the true Hamiltonian is obtained. AS has been successfully applied even to the reactive abstraction of hydrogen in the Cl+CH 4 reaction 11 and to H 2 CO. 12 Also, impressive calculations of quantum vibrational energies using the Semiclassical Initial Value Representation of Miller were recently reported for H 2 CO. 13,14 Nevertheless, the application of these methods to highly vibrationally excited states remains practically an unsolved problem.…”

Fighting the curse of dimensionality in first-principles semiclassical calculations: Non-local reference states for large number of dimensions

“…In a very recent paper Roy et al 23 performed ab initio semiclassical simulation of the formaldehyde molecule, using SC-IVR methodology. 44 This simulation provides a good benchmark for different first-principles semiclassical molecular dynamics approaches.…”

“…19 In order to approximately bypass the dimensionality restrictions mentioned above, semiclassical molecular dynamics has been an attractive alternative. [20][21][22][23] Regarding the first limitation about the requirement of a fitted PES, semiclassical molecular dynamics has the advantage of relying on classical trajectories obtained from first-principles simulations of nuclear dynamics. In order to bypass the second limitation associated with the dimensionality of the basis set, the semiclassical initial value representation (SC-IVR) (Ref.…”

“…So far, these simulations have been restricted to very few dimensions. [21][22][23] In order to extend the applicability of the method, we explore the development of improved reference states. The reference state is usually defined as the direct product of the harmonic ground state approximation of each degree of freedom, or more generally as a direct product of one-dimensional wavefunctions,…”

First principles semiclassical calculations of vibrational eigenfunctions

“…34,35,37 The major advantages of the method are that very few trajectories can accurately reproduce SC-IVR spectra obtained with thousands of trajectories and further that it can easily be implemented into a first principles molecular dynamics calculation. More recently Roy et al 38 also used such delocalization of coherent states for the calculation of the vibrational power spectrum of formaldehyde. This is another example of first-principles SC-IVR, as well as it is the work of Pollak and Tatchen on the absorption spectrum of the same molecule.…”