摘要:

I.IntroductionIn the field of nonlinear optics, the importance of the nuclear motion on the observed nonlinear optical response has become well known and accepted since Bishop first drew particular attention to it in a 19901review, and several review articles have recently been devoted to this topic.2–5To a large extent, the acknowledgement of the importance of vibrational motion on linear and nonlinear electric properties is due to recent progress in the development of efficientab initioprograms for calculating nonlinear optical properties accurately,4–7as well as programs that can study the effects of vibrational motion on these properties. A list of programs capable of evaluating the necessary property derivatives is given in the review by Bishop and Norman.5Dedicated to Professor Reinhart Ahlrichs on the occasion of his 60th birthday.Vibrational effects on molecular properties are often partitioned into zero‐point vibrational contributions, arising from the averaging of the molecular properties over the vibrational zero‐point motion of the molecule, and pure vibrational contributions, arising from vibrational excitations.5In a conventional sum‐over‐states (SOS) expression for a molecular property, the process is described by excitations into a number of virtual excited states. The introduction of vibrational excited states in the SOS expressions will result in formulas (after the invocation of certain approximations) for the pure vibrational contributions that involve lower‐order optical processes evaluated as vibrational transition moments.Responses to an applied electric field usually appear at the lowest orders in the field strength, since most molecules have a permanent electric dipole moment, or at least a change in the dipole moment with respect to some vibrational modes for nonpolar molecules. On the other hand, most molecules are diamagnetic (have no permanent magnetic dipole moment), and in such cases there will be no pure vibrational contributions to magnetic response properties through third order in an applied magnetic field. This does not exclude the possibility of pure vibrational contributions in nonlinear processes involving a mixture of electric and magnetic fields, where the combination of electric dipole moments with the magnetizability will give rise to pure vibrational contributions.8Indeed, Bishop and Cybulski have shown that these pure vibrational contributions to the hypermagnetizability may be substantial in diatomic molecules, amounting to about 10% of the electronic contribution.8In a study of the hypermagnetizability of O2, the pure vibrational contributions to the diamagnetic part of the hypermagnetizability tensor were found to be almost 60% of the electronic counterpart.9Unfortunately, in this study no estimate was made for the pure vibrational contributions arising from the presence of the permanent magnetic moments in the oxygen molecule.For diatomic molecules one can solve the vibrational problem numerically,8and the evaluation of the pure vibrational contributions is then easily done by summation over excited vibrational states, in particular since this summation has been shown to converge rapidly.8However, this approach cannot be applied to polyatomic molecules. Bishop and coworkers have derived expressions for the pure vibrational contributions to the polarizability and the first and second hyperpolarizabilities using perturbation theory.10–12The full derivation is quite tedious and cumbersome: for our purposes we will simply recapitulate their derivation and then specialize it to the case of the hypermagnetizability.We apply the formulas to the evaluation of zero‐point vibrational averaging (ZPVA) and pure vibrational (PV) contributions to the hypermagnetizability of the water molecule. Although there are no available experiments for the hypermagnetizability of water in the gas phase, it has been shown that water is unique in the sense that the observable Cotton–Mouton effect is dominated by the contribution from the hypermagnetizability anisotropy, rather than the polarizability and magnetizability contribution, which dominates for most molecules.13,14Any vibrational effect on the hypermagnetizability can therefore be expected also to influence the Cotton–Mouton constant. We will also evaluate the vibrational contributions to the polarizability and magnetizability, and discuss the importance of vibrational contributions to the Cotton–Mouton effect of water. To the best of our knowledge, this is the first investigation of pure and zero‐point vibrational effects on the hypermagnetizability of a polyatomic molecule.In Section II we derive the expressions for the pure vibrational contributions to the hypermagnetizability for a diamagnetic molecule using perturbation theory. In Section III we summarize briefly the basis sets and configuration spaces we have used, together with the computational methodology employed. In Section IV we summarize the results of our findings and give some concluding remarks in Section V.

ISSN:1463-9076     

出版商:RSC    

年代:2000

数据来源: RSC