Optimization of constrained density functional theory

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.

15 pages, 6 figures

References in corpus (8)

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• Realistic, quantitative descriptions of electron-transfer reactions: diabatic free-energy surfaces from first-principles molecular dynamics
• Resonant transport and electrostatic effects in single-molecule electrical junctions
• Optical Absorption Study by Ab initio Downfolding Approach: Application to GaAs
• Supercell convergence of charge-transfer energies in pentacene molecular crystals from constrained DFT
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• XDFT: an efficient first-principles method for neutral excitations in molecules
• Optimization strategies developed on NiO for Heisenberg exchange coupling calculations using projector augmented wave based first-principles DFT+U+J
• Inapplicability of exact constraints and a minimal two-parameter generalization to the DFT+$U$ based correction of self-interaction error
• Constrained Density Functional Theory Calculation with Iterative Optimization
• Wannier-function-based constrained DFT with nonorthogonality-correcting Pulay forces in application to the reorganization effects in graphene-adsorbed pentacene