Page 309 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

292 P. LAZZERETTI ET AL.
7. Second hyperpolarizability of benzene

The computational scheme outlined in Secs. IV and V has been applied to the cal-
culation of the hyperpolarizability of benzene molecule, for which a number of
ab initio studies have been already reported [15–18]. The computer program imple-
menting the CHF algorithm has been checked with respect to corresponding finite-
perturbation theory calculations [28]. For a number of molecular systems, belonging
to several point groups, the results from calculations exploiting the full symmetry
have been matched with corresponding ones, obtained by using lower subsymmetries
for the same molecule [11], including
In particular the results of Ref. [16], obtained via a 4-31g polarized basis set, have
been reproduced on an 486 IBM compatible PC, with a hard disk memory of 100
Mbyte. As a matter of fact, in that calculation, only 1 180 752 symmetry unique
two-electron integrals . had to be stored within our method.
Five large basis sets have been employed in the present study of benzene; basis set
I, which has been taken from Sadlej’s tables [37], is a (10s6p4d/6s4p) contracted to
[5s3p2d/3s2p], and contains 210 CGTOs. It has been previously adopted by us in a
near Hartree-Fock calculation of electric dipole polarizability of benzene molecule [38].
According to our experience, Sadlej’s basis sets [37] provide accurate estimates of
first-, second-, and third-order electric properties of large molecules [39].
Basis sets II-V have been employed in estimating the Hartree-Fock limit of a number
of second-order properties in the benzene molecule [40]. The primitive GTO sets range
from (11s7p2d/5s2p) to (14s8p4d/8s3p), contracted respectively to [6s5p1d/3s1p]
and [9s6p4d/6s3p]. Although the exponents for the polarization functions of these
basis sets were chosen in that paper to maximize the paramagnetic susceptibility,
the extension of the basis sets (from 252 to 396 CGTO) guarantees a remarkable
flexibility and excellent overall characteristics. The number of symmetry unique
two-electron integrals range from The calculations have been carried
out on a CONVEX C-220 and on an IBM 3090.
The ability of Sadlej basis sets [37] to provide reliable values of has been tested
in a limited number of cases with encouraging results [11]. In the present work on
benzene the Sadlej basis set yields theoretical estimates close to those obtained by
Perrin et al. [16] and Kama et al. [17], but smaller than those reported by Augspurger
and Dykstra [18]. The C-C bond distance retained in [18], however, is
compared to used by us, see Refs. [38] and [40].
The theoretical results provided by the large basis sets II-V are much smaller than
those from previous references [15–18]: the present findings confirm that the second-
hyperpolarizability is largely affected by the basis set characteristics. It is very dif-
ficult to assess the accuracy of a given CHF calculation of and it may well
happen that smaller basis sets provide theoretical values of apparently better qual-
ity. Whereas the diagonal components of the electric dipole polarizability are
quadratic properties for which the Hartree-Fock limit can be estimated with relative
accuracy a posteriori, e.g., via extended calculations [38], it does not seem possible to
establish a variational principle for, and/or upper and lower bounds to, either
and
As a matter of fact, the electric dipole polarizabilities obtained via basis sets II-IV
are larger than those reported in Ref. 16 and Ref. 18: from Table 1 of Ref. 39 it can
be seen that from those basis sets ranges from 78.352 to 79.142 a.u., and that