Nuclear corrections to molecular properties. IV. Theory for low-lying vibrational states of polyatomic molecules with application to the water molecule near the Hartree-Fock limit

Perturbation theory is used in conjunction with ab initio electronic structure calculations to obtain information about the effects of pure vibration on properties of polyatomic molecules. It is shown that any property $\mathcal{P}$ can be developed in the form $<\mathcal{P}{>}_{\nu }=\mathcal{P}{\prime }_0{\mathrm{+\Sigma }}_{\text{i=1}}^N{A}_i{\mathrm{(\nu }}_i{\text{+1/2)+Σ}}_{\mathrm{i\le \; j}}^N{B}_{\mathrm{ij}}{\mathrm{(\nu }}_i{\text{+1/2)(ν}}_j\text{+1/2)+ ⋯}$ , where $\mathcal{P}{\prime }_0{\mathrm{,\{A}}_j\}$ , and {B_ij} are certain constants and (ν₁, ν₂, ⋯ ν_N) are the quantum numbers for N modes of vibration. Several isotopic variants of the water molecule with Σ_iν_i ≤ 3 are used to illustrate the utility of the method at the Hartree‐Fock level of approximation. The properties examined include the energy, the dipole moment, and the nuclear quadrupole coupling constants.