Anharmonic vibrational computations with a quartic force field for curvilinear coordinates

Abstract

The direct vibrational self-consistent field (VSCF) method, which combines anharmonic vibrational theory with electronic structure calculations, is a sophisticated theoretical approach to calculate the vibrational spectra of molecules from first principles. Combining the VSCF approach with the quartic force field (QFF) is a good alternative to direct VSCF, with a lower computational cost. QFF is a 4th-order Taylor expansion of the potential energy surface near an equilibrium geometry. In this study, a new strategy is proposed to derive the QFF in terms of normal coordinates; the QFF coefficients are determined through numerical differentiations of the energy by representing the normal coordinates in internal rather than Cartesian coordinates. The VSCF/QFF-internal method was implemented in the General Atomic and Molecular Electronic Structure System electronic structure program and applied to the evaluations of the fundamental vibrational frequencies of HNO2, HNO3, H2O dimer, and H2O trimer, using Møller-Plesset second order perturbation theory and the aug-cc-pVDZ and aug-cc-pVTZ basis sets. The results are much improved, especially for the intermolecular vibrational modes, compared with the Cartesian coordinate representation of the normal coordinates in the VSCF/QFF approach.