Optimization of constrained density functional theory

O'Regan, David D and Teobaldi, Gilberto ORCID: 0000-0001-6068-6786 (2016) Optimization of constrained density functional theory. PHYSICAL REVIEW B, 94 (3). 035159-.

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Official URL: http://dx.doi.org/10.1103/PhysRevB.94.035159

Abstract

Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimisation is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a new, non-perturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill-definition in multi-constraint cDFT.

Item Type:	Article
Additional Information:	15 pages, 6 figures
Uncontrolled Keywords:	cond-mat.other, cond-mat.other, physics.chem-ph
Depositing User:	Symplectic Admin
Date Deposited:	10 Mar 2021 14:03
Last Modified:	18 Jan 2023 23:25
DOI:	10.1103/PhysRevB.94.035159
Open Access URL:	http://journals.aps.org/prb/abstract/10.1103/PhysR...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3105622