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

Ligand Discrimination in Myoglobin from Linear-Scaling DFT+U

Myoglobin modulates the binding of diatomic molecules to its heme group via hydrogen-bonding and steric interactions with neighboring residues, and is an important benchmark for computational studies of biomolecules. We have performed calculations on the heme binding site and a significant proportion of the protein environment (more than 1000 atoms) using linear-scaling density functional theory and the DFT+U method to correct for self-interaction errors associated with localized 3d states. We confirm both the hydrogen-bonding nature of the discrimination effect (3.6 kcal/mol) and assumptions that the relative strain energy stored in the protein is low (less than 1 kcal/mol). Our calculations significantly widen the scope for tackling problems in drug design and enzymology, especially in cases where electron localization, allostery or long-ranged polarization influence ligand binding and reaction.Comment: 15 pages, 3 figures. Supplementary material 8 pages, 3 figures. This version matches that accepted for J. Phys. Chem. Lett. on 10th May 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

Projector self-consistent DFT+U using non-orthogonal generalized Wannier functions

We present a formulation of the density-functional theory + Hubbard model (DFT+U) method that is self-consistent over the choice of Hubbard projectors used to define the correlated subspaces. In order to overcome the arbitrariness in this choice, we propose the use of non-orthogonal generalized Wannier functions (NGWFs) as projectors for the DFT+U correction. We iteratively refine these NGWF projectors and, hence, the DFT+U functional, such that the correlated subspaces are fully self-consistent with the DFT+U ground-state. We discuss the convergence characteristics of this algorithm and compare ground-state properties thus computed with those calculated using hydrogenic projectors. Our approach is implemented within, but not restricted to, a linear-scaling DFT framework, opening the path to DFT+U calculations on systems of unprecedented size.Comment: 4 pages, 3 figures. This version (v2) matches that accepted for Physical Review B Rapid Communications on 26th July 201

Linear-scaling DFT+U with full local orbital optimization

We present an approach to the DFT+U method (Density Functional Theory + Hubbard model) within which the computational effort for calculation of ground state energies and forces scales linearly with system size. We employ a formulation of the Hubbard model using nonorthogonal projector functions to define the localized subspaces, and apply it to a local-orbital DFT method including in situ orbital optimization. The resulting approach thus combines linear-scaling and systematic variational convergence. We demonstrate the scaling of the method by applying it to nickel oxide nano-clusters with sizes exceeding 7,000 atoms.Comment: 10 pages, 4 figures. This version (v3) matches that accepted for Physical Review B on 30th January 201

Renormalization of myoglobin-ligand binding energetics by quantum many-body effects

We carry out a first-principles atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linear-scaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical mean-field theory (DMFT). This combination of methods explicitly accounts for dynamical and multi-reference quantum physics, such as valence and spin fluctuations, of the 3d electrons, whilst treating a significant proportion of the protein (more than 1000 atoms) with density functional theory. The computed electronic structure of the myoglobin complexes and the nature of the Fe-O2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long standing problem related to the quantum-mechanical description of the respiration process, namely that DFT calculations predict a strong imbalance between O2 and CO binding, favoring the latter to an unphysically large extent. We show that the explicit inclusion of many body-effects induced by the Hund's coupling mechanism results in the correct prediction of similar binding energies for oxy- and carbonmonoxymyoglobin.Comment: 7 pages, 5 figures. Accepted for publication in the Proceedings of the National Academy of Sciences of the United States of America (2014). For the published article see http://www.pnas.org/content/early/2014/04/09/1322966111.abstrac

Study of state-of-the-art static inverter design Final report, 6 Jan. - 6 Jun. 1966

Multiple purpose inverter design based on phase demodulated inverter circuit selected from state-of-the-art assessment of ten inverter circuit