Variational calculation of vibrational linear and nonlinear optical properties

Abstract

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment ͑i.e., vibrational Møller-Plesset perturbation theory͒. Our results indicate when the conventional BishopKirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.

Linear response functions for a vibrational configuration interaction state

“…Of course, the ␣ nr approximation would have a far worse performance for more anharmonic systems. 31 In addition to our results for ␣ nr we have for comparison also included the results of ␣ nr obtained by Torrent-Sucarrat et al 31 Table III show that, in complete agreement with our FVCI linear response results, when this correction is added to ␣ nr the value of the zz component of the PV polarizability increases by about 9%. Torrent-Sucarrat et al.…”

“…Concerning the variation in the potential we observe that almost converged results may be obtained at the V͓2M4T͔ level. Finite field MP2/Pol FVCI calculations performed by Torrent-Sucarrat et al 31 showed that the inclusion of fifth and sixth order terms in the Taylor expansion for the potential ͑V͓3M6T͔͒ causes a decrease of 2% to the total vibrational polarizability ͑PV+ ZPVA͒. Thus, we expect that our error due to the exclusion of such fifth and sixth order terms has a similar effect.…”

“…Torrent-Sucarrat et al. 31 also found an excellent agreement between variational and perturbation theory water vibrational polarizabilities, although their results were computed using finite field nuclear relaxation techniques instead of the analytical linear response method. However, for more anharmonic systems perturbation theory based procedures diverge and only explicit variational wave function methods give reliable results for vibrational polarizabilities.…”

“…Finite field variational approaches have also been suggested and applied to the calculation of total static ͑hyper͒polarizabilities. 31 In this paper we implement analytical response theoretical methods for vibrational configuration interaction ͑VCI͒ methods. VCI has a long history and has been applied in many studies of vibrational energies, in particular, see Refs.…”

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

“…19 The ZPVA, in turn, can be obtained by applying variational procedures to solve the vibrational Schrödinger equation. 20,21 Experimental measurements are often carried out at optical frequencies much larger than the frequencies of the relevant vibrational excitations. In that event, one may invoke the infinite optical frequency approximation [22][23][24] ͑IOFA͒ in calculating vibrational NLO properties.…”