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Vibrational motions can play an important role in determining electrical, magnetic, and spectroscopic properties through so-called nuclear relaxation, zero-point vibrational averaging, or a combination of the two. Recent advances in the analysis and computational treatment of these phenomena include the finite field/nuclear relaxation technique and field-induced coordinates. These methodologies, which were originally developed for non-resonant electric dipole (hyper)polarizabilities, are reviewed and extended to magnetic properties as well as properties involving simultaneous electric and magnetic fields. In addition, spectroscopic applications such as two-photon absorption, circular dichroism, and infrared/Raman vibrational intensities are considered. With the finite field/nuclear relaxation technique and field-induced coordinates computations are now feasible for much larger molecules than before The authors are indebted to Prof. D. M. Bishop for helpful discussions. J. M. L. acknowledges the financial assistance provided through Spanish DGICYT Project No. PB98-0457-C02-1

A new response theory formulation for calculating second-order vibrational nonlinear optical properties has recently been presented by Hansen, et al. J. Chem. Phys. 2009, 131, 154101. For so-called mixed terms this method contains a correction to account for an approximation made in the classic Bishop and Kirtman, J. Chem. Phys. 1991, 15, 2646 perturbation treatment. This correction vanishes in the static limit and is here shown to vanish also in the high frequency limit. The response theory formulation is extended to third-order properties and, in that case, vanishes in both limits as well Financial help has been furnished by the Spanish MEC Project No. CTQ2008-06696/BQU and by the catalan Departament d’Universitats, Recerca i Societat de la Informació (DURSI) through project No. 2009SGR637

The zero-point static vibrational averaging (ZPVA) correction to the (hyper)polarizability is written in first-order as the sum of two contributions, one involving electric field derivatives and the other a sum over normal coordinate derivatives of the zero-point energy. It is shown that the sum over 3N-6 normal modes can be replaced by a single term using field-induced coordinates (FICs). A computational strategy that takes advantage of this simplification is presented and applied to a typical push-pull polyene NH2-(CH = CH)3-NO2. From the dependence of the first-order ZPVA on the field-dependent equilibrium geometry, we also obtain other low-order static and dynamic vibrational curvature contributions to the (hyper)polarizabilities. The entire set of electronic and vibrational terms is partitioned into two different sequences, each of which exhibits rapid initial convergence for NH2(CH = CH)3NO2 at the Hartree-Fock/6-31G+p level. Including electron correlation at the second-order Moller-Plesset (MP2) level, and the frequency dependence of the ZPVA correction is discussed.