Calculation of electric polarizabilities within the CNDO framework including polarization functions in the basis set

Abstract

A semi-empirical method within the CNDO framework is applied to the calculation of the electric polarizabilities for H₂O, H₂CO, NH₃, CH₃OH, C₂H₂, C₂H₄ and N₂. The approach allows for the inclusion of different valence shell orbitals on the same atom and yields results which agree well with experiment. The main features of elaborate ab initio calculations are also reproduced. In most cases the polarization functions have been optimized and account well for the polarization of the molecule. It is shown that a judicious choice of these functions is intimately related with the environmental anisotropy of bonds and is indirectly connected with internal field effects.

The polarization of the hydrogen atoms is an important aspect of molecular polarization, particularly when the symmetry of the molecule increases and the heavy atoms lie in a near-isotropic field of surrounding hydrogen atoms. This hydrogen polarization is well accounted for by the inclusion of 2p hydrogen orbitals obtained from a variational calculation on the hydrogen atom polarizability. In less symmetric molecules the addition of polarization functions to other atoms is necessary. In our work we used carefully chosen 3d functions and this is discussed in detail for H₂O, C₂H₂, C₂H₄ and N₂. The environmental anisotropy of the hydrogen atoms plays a role in the evaluation of polarizability anisotropies and is taken into consideration by the exclusion of one or two p orbitals centred on hydrogen atoms.

Given the small number of basis functions we have used and the simplicity of the semi-empirical approach, the results are encouraging and may easily be extended to larger molecules. As the features of more elaborate ab initio calculations are reproduced rather well it is possible that such calculations would benefit from consideration of these results, in particular from the choice of orbitals and their exponents.