JournalsowrVol. 8, No. 2pp. 1769–1843

Mathematical Methods in Quantum Chemistry

  • Gero Friesecke

    Technische Universität München, München Garching, Germany
  • Peter Gill

    Australian National University, Canberra, Australia
Mathematical Methods in Quantum Chemistry cover
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Abstract

The field of quantum chemistry is concerned with the analysis and simulation of chemical phenomena on the basis of the fundamental equations of quantum mechanics. Since the ‘exact’ electronic Schrödinger equation for a molecule with NN electrons is a partial differential equation in 3NN dimension, direct discretization of each coordinate direction into KK gridpoints yields K3NK^{3N} gridpoints. Thus a single Carbon atom (N=6N = 6) on a coarse ten point grid in each direction (K=10K = 10) already has a prohibitive 101810^{18} degrees of freedom. Hence quantum chemical simulations require highly sophisticated model-reduction, approximation, and simulation techniques. The workshop brought together quantum chemists and the emerging and fast growing community of mathematicians working in the area, to assess recent advances and discuss long term prospects regarding the overarching challenges of
(1) developing accurate reduced models at moderate computational cost,
(2) developing more systematic ways to understand and exploit the multiscale nature of quantum chemistry problems.
Topics of the workshop included:
• wave function based electronic structure methods,
• density functional theory, and
• quantum molecular dynamics.
Within these central and well established areas of quantum chemistry, the workshop focused on recent conceptual ideas and (where available) emerging mathematical results.

Cite this article

Gero Friesecke, Peter Gill, Mathematical Methods in Quantum Chemistry. Oberwolfach Rep. 8 (2011), no. 2, pp. 1769–1843

DOI 10.4171/OWR/2011/32