NR Contribution to Vibrational NLO Properties

In this section we present the nuclear relaxation (NR) contributions to the vibrational (hyper)polarizabilities of Li C6o and [Li C6o]. As previously stated our treatment requires a geometry optimization in the presence of a finite field. A problem can arise when there are multiple minima on the PES separated by low energy barriers. The finite field method works satisfactorily in that event as long as the field-dependent optimized structure corresponds to the same minimum as the field-free optimized structure. This was the case in previous work on ammonia [42], which has a double minimum potential. However, it is sometimes not the case for the endohedral fullerenes considered here, especially Li C6o- In fact, we were unable to determine the NR contribution in the x direction, i.e. perpendicular to the symmetry plane, for that molecule. It was possible to obtain based on the alternative analytical formulation [32-34], utilizing field-free dipole (first) derivatives and the Hessian. The analytical polarizability components in the other two directions were, then, used to confirm the values of the corresponding finite field method for those properties. 

In addition to the situation just discussed, it was also found that the electric field can sometimes lead to a change of electronic state, as detected by a sudden jump in the computed polarizability. This further limited the range of applicable field strengths and, thus, the range of properties that could be computed with sufficient statistical confidence. 

In contrast to a, the NR contributions to (3 and 7, are quite large. For the cation, in particular, two diagonal components of 7 are larger than the correspond- 

We have computed both electronic and NR vibrational contributions to the (hyper) polarizabilities of the prototype endohedral fullereneLi C60 and its cation. A number of these properties were obtained for the first time. In other cases our results differ quite signicantly from those previously determined using more approximate approaches. The latter include the static electronic properties calculated by Campbell et al. [5, 6], Although, for the cation, there is a large difference between our values of the static vibrational conffibution to a and those reported by Whitehouse and 

Buckingham [4], these results are not really comparable because their calculations include the effect of temperature. In addition, they applied several strong approximations, such as assuming a spherical field-free potential inside the cage. On the other hand, our calculations do not include higher-order vibrational contributions omitted in the NR treatment. It would be worthwhile to add temperature-dependence to the NR approach as we plan to do in the future. Whereas the NR contribution to the static a is quite small for both endohedral fullerenes, it becomes quite large for the static hyperpolarizabilities. This contribution is reduced for the dynamic Pockels effect, computed in the infinite optical frequency approximation, but is still not negligible. 

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