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Variational calculations of excited states via direct optimization of the orbitals in DFT

Variational calculations of excited states via direct optimization of the orbitals in DFT


Title: Variational calculations of excited states via direct optimization of the orbitals in DFT
Author: Levi, Gianluca   orcid.org/0000-0002-4542-0653
Ivanov, Aleksei   orcid.org/0000-0001-7403-3508
Jónsson, Hannes   orcid.org/0000-0001-8285-5421
Date: 2020-06
Language: English
Scope: 448-466
University/Institute: Háskóli Íslands
University of Iceland
School: Verkfræði- og náttúruvísindasvið (HÍ)
School of Engineering and Natural Sciences (UI)
Department: Raunvísindastofnun (HÍ)
Science Institute (UI)
Raunvísindadeild (HÍ)
Faculty of Physical Sciences (UI)
Series: Faraday Discussions;224
ISSN: 1359-6640
1364-5498 (eISSN)
DOI: DOI:10.1039/d0fd00064g
Subject: Efnafræði
URI: https://hdl.handle.net/20.500.11815/2418

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Citation:

Levi, G., Ivanov, A. V., & Jónsson, H. (2020). Variational calculations of excited states via direct optimization of the orbitals in DFT. Faraday Discussions, 224(0), 448-466. doi:10.1039/D0FD00064G

Abstract:

A direct optimization method for obtaining excited electronic states using density functionals is presented. It involves selective convergence on saddle points on the energy surface representing the variation of the energy as a function of the electronic degrees of freedom, thereby avoiding convergence to a minimum and corresponding variational collapse to the ground electronic state. The method is based on an exponential transformation of the molecular orbitals, making it possible to use efficient quasi-Newton optimization approaches. Direct convergence on a target nth-order saddle point is guided by an appropriate preconditioner for the optimization as well as the maximum overlap method. Results of benchmark calculations of 52 excited states of molecules indicate that the method is more robust than a standard self-consistent field (SCF) approach especially when degenerate or quasi-degenerate orbitals are involved. The method can overcome challenges arising from rearrangement of closely spaced orbitals in a charge-transfer excitation of the nitrobenzene molecule, a case where the SCF fails to converge. The formulation of the method is general and can be applied to non-unitary invariant functionals, such as self-interaction corrected functionals.

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