Page 310 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

COUPLED HARTREE-FOCK APPROACH 293

ranges from 42.305 to 45.284 a.u.. Sadlej basis sets give _ and
a.u., see Table 2 in Ref. [39]. These results are close to the estimated Hartree-Fock
limits, ,, and [39]; accordingly they are much more accurate
than those reported by Perrin et al. [16], i.e., and Our
estimates are also more accurate than the best ones from Ref. 18, and
These findings imply that our basis sets are definitely more reliable than those
adopted in Ref. 16 and Ref. 18 for studying second-order electric properties. Ac-
cordingly, it seems quite difficult to understand that theoretical obtained via
relatively small ad hoc basis sets are closer to the HF limit, if the same basis sets
provide less accurate polarizabilities. This feature would mean that the problem of
constructing suitable basis sets for the simultaneous evaluation of second-, third-,
and fourth-rank electric properties of HF quality ought to be carefully reconsidered.
Comparison with a few experimental values, obtained corresponding to different wave-
lengths [41–47], seems however to suggest that nuclear vibration [3] and electron cor-
relation [15–18] play an important role. In particular, the correlation contributions
estimated via second-order Moeller-Plesset techniques [16] are large. Accordingly, the
present work confirms that CHF level of accuracy is insufficient to predict accurate
hyperpolarizability of benzene molecule.
In any event, we are confident that the computational approach developed in this
study, owing to its efficient use of molecular symmetry, can help develop large basis
sets for first and second hyperpolarizabilities. An important aim would be that of
estimating, at least at empirical level, Hartree-Fock limits for these quantities. To
this end the use of basis sets polarized two times, according to the recipe developed
by Sadlej [37], would seem very promising.