Optimization of constrained density functional theory

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

Subspace representations in ab initio methods for strongly correlated systems

We present a generalized definition of subspace occupancy matrices in ab initio methods for strongly correlated materials, such as DFT+U and DFT+DMFT, which is appropriate to the case of nonorthogonal projector functions. By enforcing the tensorial consistency of all matrix operations, we are led to a subspace projection operator for which the occupancy matrix is tensorial and accumulates only contributions which are local to the correlated subspace at hand. For DFT+U in particular, the resulting contributions to the potential and ionic forces are automatically Hermitian, without resort to symmetrization, and localized to their corresponding correlated subspace. The tensorial invariance of the occupancies, energies and ionic forces is preserved. We illustrate the effect of this formalism in a DFT+U study using self-consistently determined projectors.Comment: 15 pages, 8 figures. This version (v2) matches that accepted for Physical Review B on 15th April 201

Generalized Wannier functions: a comparison of molecular electric dipole polarizabilities

Localized Wannier functions provide an efficient and intuitive means by which to compute dielectric properties from first principles. They are most commonly constructed in a post-processing step, following total-energy minimization. Nonorthogonal generalized Wannier functions (NGWFs) [Skylaris et al., Phys. Rev. B 66, 035119 11 (2002); Skylaris et al., J. Chem. Phys. 122, 084119 (2005)] may also be optimized in situ, in the process of solving for the ground-state density. We explore the relationship between NGWFs and orthonormal, maximally localized Wannier functions (MLWFs) [Marzari and Vanderbilt, Phys. Rev. B 56, 12847 (1997); Souza, Marzari, and Vanderbilt, ibid. 65, 035109 (2001)], demonstrating that NGWFs may be used to compute electric dipole polarizabilities efficiently, with no necessity for post-processing optimization, and with an accuracy comparable to MLWFs.Comment: 5 pages, 1 figure. This version matches that accepted for Physical Review B on 4th May 201

Strain-induced Weyl and Dirac states and direct-indirect gap transitions in group-V materials

We perform comprehensive density-functional theory calculations on strained two-dimensional phosphorus (P), arsenic (As) and antimony (Sb) in the monolayer, bilayer, and bulk $\alpha$-phase, from which we compute the key mechanical and electronic properties of these materials. Specifically, we compute their electronic band structures, band gaps, and charge-carrier effective masses, and identify the qualitative electronic and structural transitions that may occur. Moreover, we compute the elastic properties such as the Young's modulus $Y$; shear modulus $G$; bulk modulus $\mathcal{B}$; and Poisson ratio $\nu$ and present their isotropic averages of as well as their dependence on the in-plane orientation, for which the relevant expressions are derived. We predict strain-induced Dirac states in the monolayers of As and Sb and the bilayers of P, As, and Sb, as well as the possible existence of Weyl states in the bulk phases of P and As. These phases are predicted to support charge velocities up to $10^6$~$\textrm{ms}^{-1}$ and, in some highly anisotropic cases, permit one-dimensional ballistic conductivity in the puckered direction. We also predict numerous band gap transitions for moderate in-plane stresses. Our results contribute to the mounting evidence for the utility of these materials, made possible by their broad range in tuneable properties, and facilitate the directed exploration of their potential application in next-generation electronics.Comment: Final version accepted for publication in 2D Materials on 1/9/17. Keywords: phosphorene, arsenene, and antimonene. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence [http://creativecommons.org/licenses/by/3.0]. Any further distribution of this work must maintain attribution to the authors and the title of the work, journal citation and DO