Professor Hans-Joachim Werner
Institute for Theoretical Chemistry
University of Stuttgart
Stuttgart, Germany

Friday, April 1, 2011
3:00 pm (CT)
1005 Beckman Institute

Abstract

Accurate electronic structure calculations using wave function methods suffer from two major problems: (i) the computational effort rises very steeply with the molecular size, and (ii) the correlation energy converges very slowly with basis set size per atom. Therefore, highly accurate coupled-cluster calculations of molecular properties have so far been possible only for very small molecules. Here we review new methods that overcome both problems: The steep scaling with molecular size can be much reduced by using local orbitals and applying local approximations. The convergence with basis set size can be very much improved by including terms into the wave function that depend explicitly on the inter-electronic distances rij (so-called F12 methods) [1]. These two approaches have been combined in order to arrive at efficient coupled-cluster methods that can be applied for much larger molecules than so far. It is shown that explicitly correlated terms can be defined in a way that they not only eliminate most of the basis set incompleteness errors, but also remove to a very large extent the errors caused by the local approximations [2,3]. Extensive benchmarks for closed and open-shell systems demonstrate that virtually the same accuracy as with the non-local counterparts is achieved. Using screening techniques and efficient density fitting approximations for the evaluation of all required two-electron integrals almost linear scaling of the computational cost with molecular size is obtained. This makes it possible to carry out LCCSD(T)-F12 calculations with near complete basis set (CBS) accuracy for molecules with 50-100 atoms, and various illustrative applications are presented. Recently, also explicitly correlated multi-reference methods (CASPT2-F12 [4], MRCI-F12 [5,6]) have been developed, which can be applied to systems with strong static correlation effects as well as to electronically excited states. Applications to potential energy surfaces and situations with avoided crossings or conical intersections [6] will be presented.