Basis set dependence of the vibrational wavenumbers of the out-of-plane modes of conjugated π-electron ring systems

Abstract

Basis set dependence of the vibrational wavenumbers of out-of-plane modes calculated at the MP2 level of ab initio molecular orbital theory is examined for benzene, p-benzoquinodimethane, p-benzoquinone, furan, and thiophene. Various polarization functions up to (3df,p) are used in combination with the 6-31G and 6-311G basis sets. It is shown that, especially in the case of normal modes with alternate out-of-plane motions of the carbon atoms (such as the ν4 (b2g) mode of benzene), the calculated wavenumbers depend strongly on the exponents (αd) of the d functions on the carbon atoms. It is therefore necessary to include d functions with an optimum exponent (αd≅0.4) on the carbon atoms to obtain reasonable out-of-plane vibrational force fields. In a few cases (such as the ν16 (a2) mode of furan), inclusion of a set of f functions on the carbon atoms has some effects on the calculated wavenumbers of out-of-plane modes. However, unless the basis set contains an optimum set of d functions, inclusion of a set of f functions does not improve the agreement between the observed and calculated vibrational wavenumbers. As a case with an exaggerated effect of basis set, it is shown that the wavenumber of the ν41 (b2g) mode of the planar optimized structure of p-benzoquinodimethane is calculated to be imaginary by using the 6-311G(d,p) or 6-311G(df,p) basis set at the MP2 level. For all the molecules treated in the present study, reasonable out-of-plane vibrational force fields are obtained by using the 6-31G(2df,p) and 6-311G(2df,p) basis sets.