S. H. Vosko

Bio: S. H. Vosko is an academic researcher from University of Toronto. The author has contributed to research in topics: Fermi surface & Pseudopotential. The author has an hindex of 22, co-authored 45 publications receiving 21119 citations.

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation.

Abstract: Generalized gradient approximations (GGA's) seek to improve upon the accuracy of the local-spin-density (LSD) approximation in electronic-structure calculations. Perdew and Wang have developed a GGA based on real-space cutoff of the spurious long-range components of the second-order gradient expansion for the exchange-correlation hole. We have found that this density functional performs well in numerical tests for a variety of systems: (1) Total energies of 30 atoms are highly accurate. (2) Ionization energies and electron affinities are improved in a statistical sense, although significant interconfigurational and interterm errors remain. (3) Accurate atomization energies are found for seven hydrocarbon molecules, with a rms error per bond of 0.1 eV, compared with 0.7 eV for the LSD approximation and 2.4 eV for the Hartree-Fock approximation. (4) For atoms and molecules, there is a cancellation of error between density functionals for exchange and correlation, which is most striking whenever the Hartree-Fock result is furthest from experiment. (5) The surprising LSD underestimation of the lattice constants of Li and Na by 3--4 % is corrected, and the magnetic ground state of solid Fe is restored. (6) The work function, surface energy (neglecting the long-range contribution), and curvature energy of a metallic surface are all slightly reduced in comparison with LSD. Taking account of the positive long-range contribution, we find surface and curvature energies in good agreement with experimental or exact values. Finally, a way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects.

Exact exchange-only potentials and the virial relation as microscopic criteria for generalized gradient approximations.

Abstract: The information contained in the exact exchange potential of atoms as calculated in the optimized-potential model is used to analyze generalized approximations (GGA's) from a microscopic viewpoint. It is shown that the GGA recently introduced by Perdew and Wang [in Electronic Structure of Solids 1991, edited by P. Ziesche and H. Eschrig (Akademie Verlag, Berlin, 1991), Vol. 11] does not significantly improve the exchange potential given by the lowest-order gradient correction. This contrasts with its excellent reproduction of atomic exchange energies, which is shown to be mainly due to cancellation of local errors in the integrand of the virial relation for the exchange-energy functional. Utilizing this virial relation a GGA is constructed which reproduces atomic exchange potentials considerably better. This functional does not give as accurately total exchange energies, although it is superior to the second-order gradient expansion. It thus represents a balanced approach aiming at an overall improvement rather than focusing on the exchange energies only. It is concluded that the concept of GGA's due to its simple quasilocal-density dependence is not sufficiently flexible to accurately reproduce exchange potentials and exchange energies simultaneously. It seems that the criteria for judging and constructing approximate exchange functionals put forward in this work and the resulting GGA give a more realistic view of the overall capabilities of GGA's to represent the properties of the true exchange-energy functional, e.g., its functional derivatives, than previous GGA's.

A relativistic density functional formalism

Abstract: A relativistic generalisation of the Hohenberg-Kohn-Sham density functional formalism is presented. Single-particle equations, analogous to those suggested for the non-relativistic formalism are introduced. These equations may take two forms, one analogous to the Dirac-Slater and the other analogous to Dirac-Fock relativistic self-consistent field equations. The complicated relativistic many-body effects are included in the formalism via energy functionals analogous to the exchange-correlation functionals of the non-relativistic formalism. The local density approximation for these functionals is discussed and explicit expressions are given for relativistic corrections. The relation of these corrections to the Breit interaction is mentioned. The description of magnetic effects in the relativistic formalism is discussed briefly.

Accurate optimized-potential-model solutions for spherical spin-polarized atoms: Evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations.

Abstract: We present accurate optimized-potential-model (OPM) results for spherical spin-polarized atoms emphasizing the precise construction of the OPM exchange potential from the numerical solution of the OPM integral equation, especially for large r. The results are used to discuss the quality of the local spin-density approximation (LSDA) and a generalized-gradient expansion (GGA) [A. D. Becke, Phys. Rev. A 38, 3098 (1988)] for describing these atoms. It is shown that the LSDA can produce substantial errors (beyond what is known from unpolarized atoms) for quantities which are directly related to the spin polarization of these systems. In particular, the LSDA overestimates the magnetization density in the interior of Cu by a factor of 2. While the GGA improves integral quantities like total ground-state and exchange energies, remarkably it is less successful for energy differences like ${\mathit{E}}_{\mathit{x}\mathrm{\ensuremath{\uparrow}}}$-${\mathit{E}}_{\mathit{x}\mathrm{\ensuremath{\downarrow}}}$. Most important, however, it is not able to reduce the LSDA's errors for local quantities like the difference between spin-up and spin-down exchange potentials and magnetization densities significantly nor does it reverse the LSDA's incorrect ordering of the two highest occupied majority-spin eigenvalues of Cr and Cu.

Density‐functional thermochemistry. III. The role of exact exchange

Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

Abstract: QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

Self-interaction correction to density-functional approximations for many-electron systems

Abstract: The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

First-principles simulation: ideas, illustrations and the CASTEP code

Abstract: First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.

Chemistry with ADF

Abstract: We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation-strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001