An efficient approach for calculating vibrational wave functions and zero-point vibrational corrections to molecular properties of polyatomic molecules

Abstract

We have recently presented a formalism for calculating zero-point vibrational corrections to molecular properties of polyatomic molecules in which the contribution to the zero-point vibrational correction from the anharmonicity of the potential is included in the calculations by performing a perturbation expansion of the vibrational wave function around an effective geometry. In this paper we describe an implementation of this approach, focusing on computational aspects such as the definition of normal coordinates at a nonequilibrium geometry and the use of the Eckart frame in order to obtain accurate nonisotropic molecular properties. The formalism allows for a black-box evaluation of zero-point vibrational corrections, completed in two successive steps, requiring a total of two molecular Hessians, 6K–11 molecular gradients, and 6K–11 property evaluations, K being the number of atoms. We apply the approach to the study of a number of electric and magnetic properties—the dipole and quadrupole moments, the static and frequency-dependent polarizability, the magnetizability, the rotational g tensor and the nuclear shieldings—of the molecules hydrogen fluoride, water, ammonia, and methane. Particular attention is paid to the importance of electron correlation and of the importance of the zero-point vibrational corrections for obtaining accurate estimates of molecular properties for a direct comparison with experiment.