Self-consistent local-density approximation with model Coulomb pair-correlation functions for electronic systems

Abstract

The model Coulomb pair-correlation functions proposed several years ago by Gritsenko, Bagaturyants, Kazansky, and Zhidomirov are incorporated into the self-consistent local-density approximation (LDA) scheme for electronic systems. Different correlation functions satisfying well-established local boundary conditions and integral conditions have been tested by performing LDA calculations for closed-shell atoms. Those correlation functions contain a single parameter which can be optimized by fitting the atomic correlation energies to empirical data. In this way, a single (universal) value of the parameter is found to give a very good fit for all the atoms studied. The results provide a substantial improvement of calculated correlation energies as compared to the usual LDA functionals and the scheme should be useful for molecular and cluster calculations.PACS number(s): 31.20. Sy, 31.20.Tz, 31.10.+z

Weighted-density exchange and local-density Coulomb correlation energy functionals for finite systems: Application to atoms

“…The present exchange paircorrelation function is the spin-polarized generalization of the non-spin-polarized one, recently developed and tested for the case of noble gas atoms [22]. The Coulomb pair-correlation function is an extension of a recent model [23]. The fundamentals of the method are presented in Secs.…”

Linearly scaling direct method for accurately inverting sparse banded matrices

“…The error of the modified version of the New Algorithm is typically less that half of the error of the other two methods. This can be due to the fact that the modified version uses equation (27) instead of (26c). Therefore, fewer numbers (about half of them) are present in the calculation, and hence fewer potential sources of error are present.…”

“…Equation (27) can easily be obtained from (25a) by induction. The reader must also note that, although the coefficients ξ IJ have been obtained by performing the products…”

“…However, banded systems can be solved in O(nm u m l ) floating point operations using very simple recursive formulae, and the explicit form of A −1 can be obtained in O(n 2 ) floating point operations. As mentioned earlier, there exist a number of physical problems whose behaviour is described by banded systems where m u , m l n. This makes it possible to get large computational savings if suitable algorithms are used, what is even more important for computationally heavy problems like those in which the calculation of relevant quantities requires many iterations (Molecular Dynamics [14,24], Monte Carlo simulations [25], quantum properties calculations via self-consistent field equations [26,27], etc. ).…”

Ionization potentials of atoms calculated with a nonlocal exchange and a local correlation functional

“…In this article, we used a newly developed [22,23] nonlocal WDA exchange functional and a local correlation functional [24] to calculate the first ionization potential of atoms (3 5 Z 5 54) and the total energies of the He, Be, and Ne isoelectronic series (Z 15 20). Our results are compared with available experimental IPS 1251 and with other recent self-consistent calculations using density gradient (GGA) functionals [26].…”