EU Regional School - Schneider Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Dr. Schneider - The Computation of the electronic Structure - an Introduction into Quantum Chemistry

Institute of Mathematics
TU Berlin

Abstract

The numerical solution of the stationary electronic Schrodinger equation is a fun- damental task in the numerical simulation of atomic and molecular behaviour, with widespread applications in chemistry, molecular biology, solid state physics and material sciences. We present the following topics

  • 1. Introduction
  • 2. Hartree Fock and Density Functional Theory
  • 3. CI, MRSCF and Coupled Cluster Methods
  • 4. Fock space and tensor product states, reduced density matrices and the DMRG algorithm

In Density Functional Theory (DFT) the highdimensional linear Schr"dinger is replaced by a system of nonlinear but low dimensional Kohn Sham equations. This allows the treatment of relativley large systems. We will discuss the numerical treatment of DFT as a constraint optimization problem and present perspectives to treat large systems eciently. Nevertheless, the accuracy of DFT is limited due to modelling errors. To go beyond this limitations, one has to consider the approxima- tion of the high-dimensional wave function directly. We present the Coupled Cluster Method as a most powerful tool whenever highly accurrate results are required. We would like to remark that quantum Monte Carlo methods provide alternatives for computing correlation e ects, but is limited by the xed node approximation.