PROJECTS

Development, implementation and application of the analytical calculation of energy derivatives, especially nuclear gradients, of electron-correlation methods employing wavefunctions that depend explicitly on the interelectronic distances

PRINCIPAL INVESTIGATOR

Prof. Dr. Willem Maarten Klopper Universität Karlsruhe Physikalische Chemie Engesserstraße 15 D-76131 Karlsruhe +49-721-608-7263 +49-721-608-3319 klopper@chem-bio.uni-karlsruhe.de

PROJECT RESEARCH ASSISTANT

ABSTRACT

The explicitly-correlated approach in computational quantum chemistry comprises a family of methods using wavefunctions that depend explicitly on all electron-electron distances in the atom or molecule of interest. Today, functions of the interelectronic distances are utilized in various forms. They appear in linear or exponential (Gaussian) terms in the wavefunction, in similarity-transformed Hamiltonians and in the Jastrow functions of Quantum-Monte-Carlo calculations. All of these methods have the potential to compute the ground- and excited-state energies of a molecule with very high accuracy, without the need for an inacceptably large basis set of one-electron orbitals. However, to the best of our knowledge, these accurate energies can only be computed in a prescribed and fixed nuclear configuration and none of the explicitly correlated methods can be used to compute analytically the first derivative of the energy with respect to nuclear displacements. It is the goal of the present project to develop and implement (for the first time) the analytic calculation of nuclear energy gradients at the level of second-order perturbation theory with terms linear in the interelectronic distances (linear-r₁₂ methods or R12 methods). During the first funding period, methods have been developed and implemented for the analytic calculation of first-order one-electron molecular properties (expectation values). These properties can be obtained as the trace of the corresponding property matrix with an effective one-electron density. Furthermore, codes have been written to evaluate the first derivatives of all of the two-electron integrals involved in the second-order perturbation theory with terms linear in the interelectronic distances. The aim of this renewal proposal is to construct effective two-electron densities and to contract the differentiated two-electron integrals with these.