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Rigorous results in electronic structure calculations

Denis Chaykin (tchaikine***at***hotmail.com)
Christian Jansson (jansson***at***tuhh.de)
Frerich Keil (keil***at***tuhh.de)
Marko Lange (m.lange***at***aoni.waseda.jp)
Kai Torben Ohlhus (kai.ohlhus***at***tuhh.de)
Siegfried M. Rump (rump***at***tuhh.de)

Abstract: Electronic structure calculations, in particular the computation of the ground state energy, lead to challenging problems in optimization. These problems are of enormous importance in quantum chemistry for calculations of properties of solids and molecules. Minimization methods for computing the ground state energy can be developed by employing a variational approach, where the second-order reduced density matrix defines the variable. This concept leads to large-scale semidefinite programming problems that provide a lower bound for the ground state energy. Upper bounds of the ground state energy can be calculated for example with the Hartree-Fock method. However, Nakata, Nakatsuji, Ehara, Fukuda, Nakata, and Fujisawa observed, that due to numerical errors the semidefinite solver produced erroneous results with a lower bound significantly larger than the Hartree-Fock upper bound. Violations within one mhartree were observed. We present here a method for solving electronic structure problems where all numerical errors are taken into consideration. In particular this method provides rigorous error bounds without violations as mentioned above.

Keywords: electronic structure calculations, reduced density matrix, semidefinite programming, interval arithmetic, rigorous error bounds

Category 1: Applications -- Science and Engineering (Chemical Engineering )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: 11/2016

Download: [PDF]

Entry Submitted: 11/17/2016
Entry Accepted: 11/17/2016
Entry Last Modified: 12/23/2017

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