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Oberwolfach Reports

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Volume 15, Issue 1, 2018, pp. 631–721
DOI: 10.4171/OWR/2018/13

Published online: 2019-01-04

Mathematical Methods in Quantum Chemistry

Eric Cancès[1], Gero Friesecke[2], Trygve Ulf Helgaker[3] and Lin Lin[4]

(1) Ecole des Ponts ParisTech, Marne-La-Vallée, France
(2) Technische Universität München, Garching, Germany
(3) University of Oslo, Norway
(4) University of California, Berkeley, USA

The field of quantum chemistry is concerned with the modelling and simulation of the behaviour of molecular systems on the basis of the fundamental equations of quantum mechanics. Since these equations exhibit an extreme case of the curse of dimensionality (the Schrödinger equation for $N$ electrons being a partial differential equation on $\mathbb R^{3N}$), the quantum-chemical simulation of even moderate-size molecules already requires highly sophisticated model-reduction, approximation, and simulation techniques. The workshop brought together selected quantum chemists and physicists, and the growing community of mathematicians working in the area, to report and discuss recent advances on topics such as coupled-cluster theory, direct approximation schemes in full configuration-interaction (FCI) theory, interacting Green’s functions, foundations and computational aspects of density-functional theory (DFT), low-rank tensor methods, quantum chemistry in the presence of a strong magnetic field, and multiscale coupling of quantum simulations.

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Cancès Eric, Friesecke Gero, Helgaker Trygve Ulf, Lin Lin: Mathematical Methods in Quantum Chemistry. Oberwolfach Rep. 15 (2018), 631-721. doi: 10.4171/OWR/2018/13