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Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle

Pastorczak, E.; Gidopoulos, N.I.; Pernal, K.

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Authors

E. Pastorczak

K. Pernal



Abstract

We show that the Helmholtz free-energy variational principle is the physical principle underlying the ensemble variational theory formulated in seminal papers by Theophilou and by Gross, Oliveira, and Kohn. A method of calculating electronic excitations of atoms and molecules is then proposed, based on the constrained minimization of the free energy. It involves the search for the optimal set of Slater determinant states to describe low electronic excitations and, in a second step, the search for optimal rotations in the space spanned by these states. Boltzmann factors are used as weights of states in the ensemble since for these the free energy achieves a minimum. The proposed method is applied to the Be atom and LiH and BH molecules. The method captures static electron correlation but naturally lacks dynamic correlation. To account for the latter, we describe short-range electron-electron interaction with a density functional, while the long-range part is still expressed by a wave-function method. Using the example of the LiH molecule, we find that the resulting method is able to capture both static and dynamic electron correlations.

Citation

Pastorczak, E., Gidopoulos, N., & Pernal, K. (2013). Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle. Physical Review A, 87(6), Article 062501. https://doi.org/10.1103/physreva.87.062501

Journal Article Type Article
Publication Date Jun 1, 2013
Deposit Date Jan 15, 2014
Publicly Available Date Jul 11, 2014
Journal Physical Review A
Print ISSN 1050-2947
Electronic ISSN 1094-1622
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 87
Issue 6
Article Number 062501
DOI https://doi.org/10.1103/physreva.87.062501
Public URL https://durham-repository.worktribe.com/output/1442470

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Copyright Statement
Reprinted with permission from the American Physical Society: Phys. Rev. A 87, 062501 © (2013) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.






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