Ab initio calculations of static dipole polarizabilities using improved virtual orbitals and symmetry adapted polarization functions

Abstract

A new method is presented for the calculation of the molecular dipole polarizability tensor. The introduction of the Improved Virtual Orbital concept in the well known (Rayleigh-Schrödinger Perturbation Type) Sum Over States expression leads to a very simple working equation involving only the energies and the transition dipole matrix elements of the occupied and the Improved Virtual Orbitals. The latter can be obtained in a non-iterative way by solving a modified Hartree-Fock-Roothaan equation for each occupied orbital. Computational times involved typically amount to only 10 or 20 per cent of a single SCF calculation. Calculations are reported with a large basis set of Double/Triple Zeta type quality, augmented with diffuse functions and one, respectively two sets of p and d polarization functions on Hydrogen and first row atoms. In view of possible applications to larger systems (Part II) a reduced basis is developed in which only those polarization functions strictly necessary by symmetry are introduced (they account for those irreducible representations not spanned by the s-p basis). This procedure involves a simulation of the p, d, f, ..., type polarization functions needed by a series of all-centre Spherical Gaussian Orbitals. If the relation between geometrical parameters and exponents is transferred from the actual GTOs to its simulation, a criterion of maximal overlap leads in the cases actually needed to a quadratic equation relating the exponent of the SGOs to the exponent of the GTO to be simulated. The value of the overlap integral is very high (>99 per cent) for all cases required indicating, as also shows up in electron density (difference) maps, an extremely high ressemblance between the GTO and its simulation. H₂O is taken as a case study. The IVO technique performs extremely well (as seen by comparing UCHF results with their IVO counterparts for a given basis). For the largest basis [DTZ/DPP] and its reduced version the results are significantly better than for example those obtained with the Finite Field technique, at the SCF level, whereas the computation time is smaller by a factor of 4. The reduced basis [DTZ/DP] is obviously an exciting alternative for very large basis in cases where, due to the size of the molecule, problems with basis set limitations arise.