Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems
Authors: Champagne Benoît , Botek Edith , Nakano Masayoshi , Nitta Tomoshige , Yamaguchi Kizashi 
Published: March 2005

The basis set and electron correlation effects on the static polarizability (α) and second hyperpolarizability (γ) are investigated ab initio for two model open-shell π-conjugated systems, the C5H7 radical and the C6H8 radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C6H8 whereas diffuse functions are compulsory for C5H7, in particular, p diffuse functions. In addition to the 6-31G*+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for α and γ of the two model compounds, respectively. For the polarizability, the unrestricted Hartree–Fock and unrestricted second-order Møller–Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Møller–Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree–Fock results. Moreover, the differences between the restricted open-shell Hartree–Fock and restricted open-shell second-order Møller–Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree–Fock and unrestricted second-order Møller–Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order Møller–Plesset method, provide for both compounds γ values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged α and γ values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of α and γ have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree–Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.