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.

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

A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)

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

Chemistry with ADF

The response of an interacting many-particle system to a time-dependent external field can usually be treated within linear response theory. Due to rapid experimental progress in the field of laser physics, however, ultra-short laser pulses of very high intensity have become available in recent years. The electric field produced in such pulses can reach the strength of the electric field caused by atomic nuclei. If an atomic system is placed in the focus of such a laser pulse one observes a wealth of new phenomena [1] which cannot be explained by traditional perturbation theory. The non-perturbative quantum mechanical description of interacting particles moving in a very strong time-dependent external field therefore has become a prominent problem of theoretical physics. In principle, it requires a full solution of the time-dependent Schrodinger equation for the interacting many-body system, which is an exceedingly difficult task. In view of the success of density functional methods in the treatment of stationary many-body systems and in view of their numerical simplicity, a time-dependent version of density functional theory appears highly desirable, both within and beyond the regime of linear response.

Density-Functional Theory for Time-Dependent Systems

https://www.lct.jussieu.fr/pagesperso/savin/papers/lyp/MieSavStoPre-89.pdf

Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr

We assess various approximate forms for the correlation energy per particle of the spin-polarized homogeneous electron gas that have frequently been used in applications of the local spin density a...

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Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis

The linear augmented plane wave method in the muffin-tin approximation was used to perform self-consistent spin-polarized calculations of the electron number density n(r) and spin (magnetic moment) density m(r) in metallic Be, within the framework of the spin density functional formalism. For the exchange-correlation functional we used the recent accurate results of Vosko et al. in the local spin density approximation. The Fermi contact contribution to the Knight shift is proportional to the sum of three spin densities (evaluated at the nucleus) arising from (i) the valence electrons at the Fermi surface, (ii) the core electrons, and (iii) the valence electrons below the Fermi surface. We find a 90% cancellation between (i) and (ii) which greatly magnifies the significance of the relatively small effect (iii). Although our contact term is still positive in sign, its magnitude is nearly one-fourth of the previous smallest first principles result and thus requires a smaller orbital diamagnetic contribution ...

The Fermi contact contribution to the Knight shift in Be from self-consistent spin-polarized calculations

Spin-density functional theory, in the local spin-density approximation (LSDA) was used to calculate the total Fermi contact contribution Ks, to the Knight shift in solid Mg. The self-consistent spin-polarised Kohn-Sham equations were solved for the spin and number densities by the linear augmented plane wave method in the muffin-tin approximation. For the exchange-correlation energy functional the authors used the recent accurate results of Vosko et al. (1980), Ks was found to consist of the contributions 0.138%, -0.003% and -0.007% due to the Fermi surface, core and valence electrons below the Fermi surface respectively, yielding a total which is 14% larger than the experimental value. The authors compare their results previous LSDA calculations which used an ion-in-jellium model.

S. H. Vosko

Papers

Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis

The Fermi contact contribution to the Knight shift in Be from self-consistent spin-polarized calculations

A comparison of spin-density functional calculations for the Knight shift in Mg