On the improvement of the gauge invariance in finite basis set coupled hartree—fock calculations of molecular magnetic properties

Abstract

Finite basis set coupled Hartree—Fock calculations of molecular magnetic susceptibilities and nuclear shielding constants show a very large gauge dependence (i.e., a dependence on the origin of the magnetic vector potential). The best agreement with experiment is expected for a gauge origin at the electronic centroid for which choice the so-called paramagnetic cotributions to the above properties are small. However, with a finite basis set agreement with experiment may be fortuitous and some estimate of the contribution of the unknown functions is required. A general scheme is presented for dealing with the above problems. The essence of the method is to apply an average energy approximation to the unknown functions and to determine this energy by enforcing the gauge invariance requirement. Consequently the technique can still be categorised as an ab initio method and a close approach to the Hartree—Fock limit is achieved without the need to employ very large basis sets with extensive optimisation. The method is applied to the hydrogen fluoride molecule which provides numerical justification of the proposed scheme.