Kieron Burke

Restoring the density-gradient expansion for exchange in solids and surfaces.

Popular modern generalized gradient approximations are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of density gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approximation that improves equilibrium properties of densely packed solids and their surfaces.Successful modern generalized gradient approximations (GGAs) are biased toward atomic energies. Restoration of the first-principles gradient expansion for the exchange energy over a wide range of density gradients eliminates this bias. With many collaborators, I introduce PBEsol, a revised Perdew-Burke-Ernzerhof GGA that improves equilibrium properties of densely-packed solids and their surfaces.

Rationale for mixing exact exchange with density functional approximations

Density functional approximations for the exchange‐correlation energy EDFAxc of an electronic system are often improved by admixing some exact exchange Ex: Exc≊EDFAxc+(1/n)(Ex−EDFAx). This procedure is justified when the error in EDFAxc arises from the λ=0 or exchange end of the coupling‐constant integral ∫10 dλ EDFAxc,λ. We argue that the optimum integer n is approximately the lowest order of Gorling–Levy perturbation theory which provides a realistic description of the coupling‐constant dependence Exc,λ in the range 0≤λ≤1, whence n≊4 for atomization energies of typical molecules. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second‐order perturbation theory with the generalized gradient approximation.

Perspective on density functional theory

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science. Electronic structure problems in a dazzling variety of fields are currently being tackled. However, DFT has many limitations in its present form: too many approximations, failures for strongly correlated systems, too slow for liquids, etc. This perspective reviews some recent progress and ongoing challenges.

Time-dependent density functional theory: Past, present, and future

Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope, and yields predictions for many more properties. We discuss some of the challenges involved in making accurate predictions for these properties.

Double excitations within time-dependent density functional theory linear response

Within the adiabatic approximation, time-dependent density functional theory yields only single excitations. Near states of double excitation character, the exact exchange-correlation kernel has a strong dependence on frequency. We derive the exact frequency-dependent kernel when a double excitation mixes with a single excitation, well separated from the other excitations, in the limit that the electron--electron interaction is weak. Building on this, we construct a nonempirical approximation for the general case, and illustrate our results on a simple model.

Self-interaction errors in density-functional calculations of electronic transport.

All density-functional calculations of single-molecule transport to date have used continuous exchange-correlation approximations. The lack of derivative discontinuity in such calculations leads to the erroneous prediction of metallic transport for insulating molecules. A simple and computationally undemanding atomic self-interaction correction (SIC) opens conduction gaps in I-V characteristics that otherwise are predicted metallic, as in the case of the prototype Au/ditholated-benzene/Au junction.

The adiabatic connection method: a non-empirical hybrid

Abstract For systems in which generalized gradient approximations (GGAs) work better for exchange-correlation energies than for exchange alone, a simple hybrid of GGA energies with the exact exchange energy is derived which improves the GGA result. A criterion is given which shows when this hybrid makes the greatest improvement. Results for molecules are given, showing that multiply bonded systems are most improved.

Can optimized effective potentials be determined uniquely

Local (multiplicative) effective exchange potentials obtained from the linear-combination- of-atomic-orbital (LCAO) optimized effective potential (OEP) method are frequently unrealistic in that they tend to exhibit wrong asymptotic behavior (although formally they should have the correct asymptotic behavior) and also assume unphysical rapid oscillations around the nuclei. We give an algebraic proof that, with an infinity of orbitals, the kernel of the OEP integral equation has one and only one singularity associated with a constant and hence the OEP method determines a local exchange potential uniquely, provided that we impose some appropriate boundary condition upon the exchange potential. When the number of orbitals is finite, however, the OEP integral equation is ill-posed in that it has an infinite number of solutions. We circumvent this problem by projecting the equation and the exchange potential upon the function space accessible by the kernel and thereby making the exchange potential unique. The o...

Finding Density Functionals with Machine Learning

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of noninteracting fermions in 1D, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is within the interpolation region. Via principal component analysis, a projected functional derivative finds highly accurate self-consistent densities. The challenges for application of our method to real electronic structure problems are discussed.

Magnetic Properties of Sheet Silicates; 2:1:1 Layer Minerals

Magnetization, susceptibility and Mössbauer spectra are reported for representative chlorite samples with differing iron content. The anisotropy of the susceptibility and magnetization of a clinochlore crystal is explained using the trigonal effective crystal-field model developed earlier for 1:1 and 2:1 layer silicates, with a splitting of theT2g triplet of 1,120K. Predominant exchange interactions in the iron-rich samples are ferromagnetic withJ=1.2 K, as for other trioctahedral ferrous minerals. A peak in the susceptibility of thuringite occurs atTm=5.5 K, and magnetic hyperfine splitting appears at lower temperatures in the Mössbauer spectrum. However neutron diffraction reveals no long-range magnetic order in thuringite (or biotite, which behaves similarly). The only magnetic contribution to the diffraction pattern at 1.6 K is increased small angle scattering (q<0.4 Å−1). A factor favouring this random ferromagnetic ground state over the planar antiferromagnetic state of greenalite and minnesotaite is the presence of pairs of ferric ions on adjacent sites, in conjunction with magnetic vacancies in the octahedral sheets. Monte Carlo simulations of the magnetic ground state of the sheets illustrate how long range ferromagnetic order may be destroyed by vortices forming around the Fe3+-Fe3+ pairs.