Andreas Savin

Combining long-range configuration interaction with short-range density functionals

Abstract A density functional for short-range electron-electron interaction recently developed by one of us, has been implemented into a multi-reference configuration-interaction code with explicit treatment of long-range interaction only. Possible advantages of such an approach are discussed, using as examples some closed-shell atoms (Be, Ne) and diatomics (H2, Li2, C2, N2, F2).

Long-range-short-range separation of the electron-electron interaction in density-functional theory

By splitting the Coulomb interaction into long-range and short-range components, we decompose the energy of a quantum electronic system into long-range and short-range contributions. We show that the long-range part of the energy can be efficiently calculated by traditional wave function methods, while the short-range part can be handled by a density functional. The analysis of this functional with respect to the range of the associated interaction reveals that, in the limit of a very short-range interaction, the short-range exchange-correlation energy can be expressed as a simple local functional of the on-top pair density and its first derivatives. This provides an explanation for the accuracy of the local density approximation (LDA) for the short-range functional. Moreover, this analysis leads also to new simple approximations for the short-range exchange and correlation energies improving the LDA.

Atomic Shell Structure and Electron Numbers

rn The electron localization function (ELF) was calculated for the atoms Li to Sr. The ELF maxima reveal the atomic shell structure for all these atoms. The shells are separated from each other by ELF minima. The integration of the electron density in a shell gives electron numbers. For the valence shell those are in good agreement with the ones expected from the Periodic Table of Elements. 0 1996 John Wiley & Sons, Inc.

Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation

An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range density-functional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be2 and Ne2.

Double-hybrid density-functional theory made rigorous.

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Møller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter version of the standard double-hybrid approximations. We assess the performance of these double-hybrid schemes on representative test sets of atomization energies and reaction barrier heights, and we compare to other hybrid approximations, including range-separated hybrids. Our best one-parameter double-hybrid approximation, called 1DH-BLYP, roughly reproduces the two parameters of the standard B2-PLYP or B2GP-PLYP double-hybrid approximations, which shows that these methods are not only empirically close to an optimum for general chemical applications but are also theoretically supported.

Relationship of Kohn-Sham eigenvalues to excitation energies

In Kohn-Sham density functional theory, only the highest occupied eigenvalue has a rigorous physical meaning, viz., it is the negative of the lowest ionization energy. Here, we demonstrate that for finite systems, the unoccupied true Kohn-Sham eigenvalues las opposed to the those obtained from the commonly used approximate density functionals) are also meaningful in that good approximations to excitation energies can be obtained from them. We argue that the explanation for this observed behavior is that, at large distances, the Kohn-Sham orbitals and the quasiparticle amplitudes satisfy the same equation to order 1/r(4)

ANALYSIS OF THE DELOCALIZATION IN THE TOPOLOGICAL THEORY OF CHEMICAL BOND

Abstract The topological analysis of the gradient field of the electron localization function provides a convenient theoretical framework for the partition of the molecular space into basins of attractors having a clear chemical meaning. The basin populations are evaluated by integrating the one-electron density over the basins. The variance of the basin population provides a measure of the delocalization. The behavior of the core C(X) and protonated valence basins V(X, H) populations were investigated. The analysis of the population variance in terms of cross-contributions is presented for aromatic and antiaromatic systems, hypervalent molecules and hydrogen-bonded complexes. For hypervalent molecules this analysis emphasizes the importance of the ionic resonance structures.

Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules

Control of near-degeneracy effects and dynamical correlation in atoms and molecules is within sight, thanks to an economical method that mixes configuration interaction (CI) and density functional theory (DFT). The influence of the size of the configuration-space has been studied for light systems including elements of the first and second period of the Periodic Table.

The importance of middle-range Hartree-Fock-type exchange for hybrid density functionals

Hybrid functionals are responsible for much of the utility of modern Kohn-Sham density functional theory. When rigorously applied to solid-state metallic and small band gap systems, however, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally challenging and introduces unphysical effects. This can be remedied by using a range-separated hybrid which only keeps short-range nonlocal exchange, as in the functional of Heyd et al. [J. Chem. Phys. 118, 8207 (2003)]. On the other hand, many molecular properties require full long-range nonlocal exchange, which can also be included by means of a range-separated hybrid such as the recently introduced LC-omegaPBE functional [O. A. Vydrov and G. E. Scuseria, J. Chem. Phys. 125, 234109 (2006)]. In this paper, we show that a three-range hybrid which mainly includes middle-range Hartree-Fock-type exchange and neglects long- and short-range Hartree-Fock-type exchange yields excellent accuracy for thermochemistry, barrier heights, and band gaps, emphasizing that the middle-range part of the 1/r potential seems crucial to accurately model these properties.

Contribution to the electron distribution analysis. I, Shell structure of atoms

Relativistic spherically averaged numerical all‐electron densities ρ were computed for the atoms Be–Ba, B–Tl, C–Pb, Cu–Au, and Zn–Hg. The Laplacian of these densities is not able to resolve the valence shell from the inner shells in case of heavy atoms, starting with the fourth row. The distribution of the local kinetic energy Ekin shows a valence maximum even for these heavy atoms, unfortunately, in a region of negative kinetic energy; i.e., nonclassically allowed. The quantity −‖∇ρ‖/ρ was also investigated. For all computed atoms, the −‖∇ρ‖/ρ diagrams are capable of describing the complete shell structure. −‖∇ρ‖/ρ is sensitive to basis set quality: poor Gaussian basis sets exhibit spurious oscillations and a premature onset of the linear decay. For the atoms B–Tl, Ba, Au, Hg, and Pb, nonrelativistic numerical calculations were performed to examine the effect of the relativity on the aforementioned quantities. Tests with pseudopotential densities reveal that for pseudopotential calculations, it is advisa...