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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 calculate dipole and quadrupole moments, dipole polarizability, hyper- and principal components of high-order polarizabilities of the water molecule in gas and in liquid phase conditions. Calculations were performed for the ground-state water molecule at the MP2 and MP4 levels of theory. The gas phase values determined allow our methodology for extracting polarizabilities to be tested and a properly balanced, moderate-sized basis set to be selected; the results obtained are in very good agreement with experiment and the most accurate previous theoretical estimates. A local field approach is introduced to mimic the electrostatic environment experienced by a water molecule in the liquid. Within this approach, sets of fixed charges are used to generate the desired electric fields and field gradients. Three different liquid phase models and the corresponding sets of electrical properties are examined. The values obtained from these models and for gas-phase are compared. The magnitudes of the dipole and the quadrupole moments increase moving from gas to liquid phase, where the latter shows greater sensitivity to the choice of liquid model. For a liquid phase water molecule the first hyperpolarizability (β) and first higher polarizability (A) increase markedly, actually changing sign, the second hyperpolarizability (γ) also increases but much less dramatically, and components of the second high-order polarizability tensor (B) demonstrate a rearrangement of contributions. The values reported for the hyper- and high-order polarizability tensors are the first such theoretical estimates for liquid water.