The multipole polarizabilities and hyperpolarizabilities of the water molecule in liquid state: an ab initio study

A charge perturbation variant of the finite-field method has been used to c alculate dipole and quadrupole moments, dipole polarizability, hyper- and p rincipal components of high-order polarizabilities of the water molecule in gas and in liquid phase conditions. Calculations were performed for the gr ound-state water molecule at the MP2 and MP4 levels of theory. The gas phas e values determined allow our methodology for extracting polarizabilities t o be tested and a properly balanced, moderate-sized basis set to be selecte d; the results obtained are in very good agreement with experiment and the most accurate previous theoretical estimates. A local field approach is int roduced to mimic the electrostatic environment experienced by a water molec ule in the liquid. Within this approach, sets of fixed charges are used to generate the desired electric fields and field gradients. Three different l iquid phase models and the corresponding sets of electrical properties are examined. The values obtained from these models and for gas-phase are compa red. The magnitudes of the dipole and the quadrupole moments increase movin g from gas to liquid phase, where the latter shows greater sensitivity to t he choice of liquid model. For a liquid phase water molecule the first hype rpolarizability (beta) and first higher polarizability (A) increase markedl y, actually changing sign, the second hyperpolarizability (gamma) also incr eases but much less dramatically, and components of the second high-order p olarizability tensor (B) demonstrate a rearrangement of contributions. The values reported for the hyper- and high-order polarizability tensors are th e first such theoretical estimates for liquid water.