Ab initio calculation of molecular properties

Abstract

A review of fundamental problems concerning the ab initio calculation of molecular properties is given. The perturbing operators relevant to many important properties are unbounded, but the application of perturbation theory can be justified, nevertheless. Both first and second-order properties are often better obtained as numerical derivatives of the energy than as expectation values. Some elegant theorems of perturbation theory that hold if the unperturbed problem is solved exactly become invalid for approximate wave functions, but can be ‘saved’ in the framework of ‘stationary perturbation theory’ of which the random phase approximation (RPA) is a special case. The second part of the paper is devoted to magnetic properties of molecules, in particular NMR chemical shifts. The gauge problem and its solution by means of the IGLO method is studied in detail. A formal comparison of the individual gauge for localized orbitals (IGLO) and localized orbital, localized origin (LORG) methods is given. Some selected results on 13C and 31P shifts are presented that demonstrate the practical usefulness of IGLO calculations, e.g. for the full shift tensors.