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

In search of the drivers of high growth in manufacturing SMEs

Though considerable attention in the extant literature has been devoted to growth and performance of firms, there is a dearth of research on high growth firms. Furthermore, the majority of literature in this area focuses on large firms while research on high growth small firms is underdeveloped. This paper investigates the drivers of high growth in manufacturing SMEs. Following a number of focus group interviews with six managing directors of manufacturing firms, a number of drivers of high growth were identified and investigated in a sample of 207 manufacturing SMEs. The results of this study indicate that high growth firms place a greater emphasis on external drivers such as strategic orientation, their operating environment and the use of e-commerce compared with firms having static or declining sales. The analysis shows that high growth firms compete largely on the basis of price. While high growth firms have increased their sales by over 30% during the past three years or longer, it is questionable if manufacturing firms can sustain their competitive advantage without recourse to greater research and development, and innovation in the longer term

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

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