The change of picture of the Hellmann-Feynman force operator in approximate relativistic methods

The calculation of energy gradients in one- and two-component approximate m ethods of relativistic quantum chemistry which follow from the block-diagon alisation of the Dirac hamiltonian, is considered. It is indicated that the transition to these approximate methods involves the so-called change of p icture for all operators. In particular this applies to the Hellmann-Feynma n force operator. To avoid explicit transformation of this operator to the new picture two schemes for its modelling in terms of the usual Coulomb att raction operators are proposed. One of them is based on the point charge nu clear dipole moment model. The other one, the so-called shifted nucleus mod el, involves a parametrised shift of the nucleus. Both these models lead to a semianalytical method for the evaluation of energy gradients in approxim ate relativistic calculations, in which the relaxation terms is obtained an alytically whereas the matrix elements of the Hellmann-Feynman force are ca lculated by using the finite difference method. The accuracy and relative merits of the two models are analysed. The two mo dels are tested within the one-component Douglas-Kroll method. A large chan ge of picture contribution is found in calculations of intramolecular force s in the coinage metal hydrides. This shows that any approximate relativist ic technique for calculations of the energy gradients and for the relativis tic geometry optimisation must take into account the change of picture cont ribution to the evaluated Hellmann-Feynman force. (C) 2001 Elsevier Science B.V. All rights reserved.