Predicting accurate vibrational frequencies for highly anharmonic systems

Abstract

Improvements in the manner in which the potential energy surface (PES) is generated in the vibrational selfconsistent field (VSCF) method have been implemented. The PES can now be computed over a flexible range of displacements and following normal mode displacement vectors expressed in internal rather than Cartesian coordinates, leading to higher accuracy of the calculated vibrational frequencies. The coarse-grained parallelization of the PES calculations, which is computationally by far the most expensive part of the VSCF method, enables the usage of higher levels of theory and larger basis sets. The new VSCF procedure is discussed and applied to three examples, H+3, HNO2, and HNO3, to illustrate its accuracy and applicability. KeywordsNormal modes, Set theory, OzoneBasis sets, Potential energy surfaces Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 129 (2008) Improvements in the manner in which the potential energy surface ͑PES͒ is generated in the vibrational self-consistent field ͑VSCF͒ method have been implemented. The PES can now be computed over a flexible range of displacements and following normal mode displacement vectors expressed in internal rather than Cartesian coordinates, leading to higher accuracy of the calculated vibrational frequencies. The coarse-grained parallelization of the PES calculations, which is computationally by far the most expensive part of the VSCF method, enables the usage of higher levels of theory and larger basis sets. The new VSCF procedure is discussed and applied to three examples, H 3 + , HNO 2 , and HNO 3 , to illustrate its accuracy and applicability.

Ab initio molecular geometry and anharmonic vibrational spectra of thiourea and thiourea‐d4

“…Although higher-order coupling terms in the expression defining VSCF system potential (like mode triples) can have non-negligible influence on the accuracy of transitions computed by the VSCF method based on a grid derived from normal-mode displacement vectors expressed in Cartesian coordinates, their significance is greatly reduced when properly selected internal coordinates are used as the basis in such expansion. 25 Evaluation of the PESs and dipole moment surfaces needed in the direct and 2-MR-QFF VSCF calculations was done on a one-dimensional (single mode) or rectangular (mode pairs) grid covering the range between maximum displacement points of the harmonic oscillator along each normal mode, 34 namely within (24x i 20.5 , 1 4x i…”

“…Proper selection of the internal coordinate set used in the grid preparation was verified at the initial stage of the VSCF run by assuring that iterative conversion to Cartesian coordinate displacements converges for all 39,456 grid points. 34 QFF-VSCF method using 2-MR-QFF mode coupling representation 26 was used to compute wavenumbers of fundamental transitions of C 2 symmetry conformers of thiourea and thiourea-d 4 at MP2/TZV1(2d,2p) and MP2/6-3111G(3df,2p) levels. Direct CC-VSCF method based on 39,456 PES points evaluated at MP2/6-311G(2d,p) level was used to calculate fundamental, overtone, and combination transitions of both thiourea isotopomers of C 2 symmetry.…”

“…Grid size of 16 points (single mode) or 16 3 16 points (mode pairs) was used in the direct VSCF calculation, whereas QFF-VSCF computation used six-point and 12-point grids, respectively. 34 Cartesian coordinates of the individual grid points, required to compute energy (and dipole moment) on the PES, were evaluated by expanding normal-mode displacement vector of a given mode in the basis of 18 nonredundant internal coordinates and subsequently con-verting thus obtained internal coordinates of a grid point into Cartesian coordinates by an iterative procedure. 34 Set of internal coordinates used in the grid generation consisted of all bond distances, two \(N-C-S), two \(H-N-C), and two \(H 0 -N-C) angles, s(N-C-S-N), two s(H-N-C-S), and two s(H 0 -N-C-S) dihedral angles (Fig.…”

Optimized coordinates in vibrational coupled cluster calculations

“…It has been shown that the local coordinates provide a Hamiltonian that is less coupled and beneficial in describing, for example, stretching vibrations of X-H (X=C, N, O) bonds, [27][28][29][30] the wagging of −NH 2 group, 31 the torsion of −OH group, [32][33][34][35] −CH 3 group, 36 etc. Although the curved motion of the internal coordinates gives rise to complex kinematic coupling in the kinetic energy operator, the techniques to automatically compute the kinetic energy terms have recently evolved.…”

Entropy Contributions to Transition State Modeling

“…In a series of later papers, they further refined the method to solve the Schrödinger equation for potentials that were obtained by curvilinear distortions of the normal modes rather than using rectilinear Cartesian distortions. It was shown that this procedure allowed to minimize anharmonic couplings between the one-dimensional oscillators [72][73][74][75]. The new routines were implemented in a series of codes that interface with the popular VASP program for solid state calculations [76][77][78][79].…”