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.Comment: 15 pages, 6 figure

Local Moment Instability of Os in Honeycomb Li2.15Os0.85O3

“…In an effort to reconcile the valence state measurements with the magneto-thermal measurements, we have applied density functional theory (DFT) methods including SOC, correlation effects, and a fixed atomic spin moment method in our study of Li 2 OsO 3 (see Methods for the description) 47–52 . Without magnetism, SOC is strong enough to provide a pseudogap but no gap, within the Os t 2g bands.…”

“…A mesh of 9 × 5 × 9 was used for k-sampling and 500 eV for energy cutoff. The constrained atomic spin moment on Os method 52 was used in some calculations to fix moments at or near the observed value. Constraints are managed by the use of Lagrangian multipliers, imposed with constraint parameters; the input parameter λ  = 1.0 was used 48 .…”

Diabatic model for electrochemical hydrogen evolution based on constrained DFT configuration interaction

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“…, the Lagrange multipliers. Apart from being simple, the constraint terms in equation (10) are linear in the density, thus avoiding multiple stationary solutions and/or energy discontinuities [26].…”