PROJECTS

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

PRINCIPAL INVESTIGATOR

Prof. Dr. Willem Maarten Klopper Universität Karlsruhe Institut für Physikalische Chemie Kaiserstraße 12 76131 Karlsruhe Germany 0721/6087263 0721/6083319 wim.klopper@chemie.uni-karlsruhe.de www: Homepage

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 (Slater or 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 to very high accuracy, without the need for an inacceptably large basis set of one-electron orbitals. However, to the best of our knowledge, none of the explicitly correlated methods can be used to compute analytically the first derivative of the energy with respect to nuclear displacements. In the preceding two funding periods, we have developed and implemented (for the first time) the analytic calculation of 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 in the framework of the DALTON program 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. In the second funding period, codes have been written (again in the framework of the DALTON program) to evaluate the first derivatives with respect to nuclear displacements (molecular gradients) for a selected variant of the R12 methods with linear-r₁₂ terms. The aim of this renewal proposal is to transfer the recently developed techniques to the TURBOMOLE program and, on that occasion, to other variants of the R12 methods (e.g., F12 methods that utilize Slatertype geminals, density fitting, a [T1, f₁₂] commutator-free approach, and a complementary auxiliary basis set, CABS).