Nuclear Corrections to Electronic Expectation Values: Zero-Point Vibrational Effects in the Water Molecule

Abstract

A variation–perturbation approach is used to determine nuclear corrections to electronic properties of polyatomic molecules. To illustrate the technique, general expressions for the first‐order zero‐point vibrational corrections are derived and applied to various one‐electron properties of the water molecule. These include the electric dipole and molecular quadrupole moments, the diamagnetic susceptibility, the diamagnetic shielding constants, the quadrupole coupling constants, and the Hellmann–Feynman forces. The numerical results, which depend upon the combined use of the LCAO MO CI wavefunctions of Reeves and Boys and of the experimental data of Papous̆ek and Pliva, show that electronic expectation values need to be vibrationally corrected for quantitative comparisons of theory with experiment. For the water molecule, these corrections are typically about 1%, but can be as large as 10%, of the equilibrium values. The net sign of each correction is determined by the symmetric stretching mode in H2O and D2O, and the O–H and/or O–D stretch in HDO. Of particular importance to the proper treatment of the vibrational average is a potential surface containing the proper number of appropriately chosen symmetric and asymmetric configurations of nuclei.