Exact-exchange density-functional calculations for noble-gas solids

The electronic structure of noble-gas solids is calculated within density functional theory's exact-exchange method (EXX) and compared with the results from the local-density approximation (LDA). It is shown that the EXX method does not reproduce the fundamental energy gaps as well as has been reported for semiconductors. However, the EXX-Kohn-Sham energy gaps for these materials reproduce about 80 % of the experimental optical gaps. The structural properties of noble-gas solids are described by the EXX method as poorly as by the LDA one. This is due to missing Van der Waals interactions in both, LDA and EXX functionals.Comment: 4 Fig

Unscreened Hartree-Fock calculations for metallic Fe, Co, Ni, and Cu from ab-initio Hamiltonians

Unscreened Hartree-Fock approximation (HFA) calculations for metallic Fe, Co, Ni, and Cu are presented, by using a quantum-chemical approach. We believe that these are the first HFA results to have been done for crystalline 3d transition metals. Our approach uses a linearized muffin-tin orbital calculation to determine Bloch functions for the Hartree one-particle Hamiltonian, and from these obtains maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and two-particle Coulomb matrix elements are calculated. The resulting second-quantized multi-band Hamiltonian with ab-initio parameters is studied within the simplest many-body approximation, namely the unscreened, self-consistent HFA, which takes into account exact exchange and is free of self-interactions. Although the d-bands sit considerably lower within HFA than within the local (spin) density approximation L(S)DA, the exchange splitting and magnetic moments for ferromagnetic Fe, Co, and Ni are only slightly larger in HFA than what is obtained either experimentally or within LSDA. The HFA total energies are lower than the corresponding LSDA calculations. We believe that this same approach can be easily extended to include more sophisticated ab-initio many-body treatments of the electronic structure of solids.Comment: 11 papes, 7 figures, 5 table

Comparative study of density functional theories of the exchange-correlation hole and energy in silicon

We present a detailed study of the exchange-correlation hole and exchange-correlation energy per particle in the Si crystal as calculated by the Variational Monte Carlo method and predicted by various density functional models. Nonlocal density averaging methods prove to be successful in correcting severe errors in the local density approximation (LDA) at low densities where the density changes dramatically over the correlation length of the LDA hole, but fail to provide systematic improvements at higher densities where the effects of density inhomogeneity are more subtle. Exchange and correlation considered separately show a sensitivity to the nonlocal semiconductor crystal environment, particularly within the Si bond, which is not predicted by the nonlocal approaches based on density averaging. The exchange hole is well described by a bonding orbital picture, while the correlation hole has a significant component due to the polarization of the nearby bonds, which partially screens out the anisotropy in the exchange hole.Comment: 16 pages, 5 figures, RevTeX, added conten

Density functional theories and self-energy approaches

A purpose-designed microarray platform (Stressgenes, Phase 1) was utilised to investigate the changes in gene expression within the liver of rainbow trout during exposure to a prolonged period of confinement. Tissue and blood samples were collected from trout at intervals up to 648 h after transfer to a standardised confinement stressor, together with matched samples from undisturbed control fish. Plasma ACTH, cortisol, glucose and lactate were analysed to confirm that the neuroendocrine response to confinement was consistent with previous findings and to provide a phenotypic context to assist interpretation of gene expression data. Liver samples for suppression subtractive hybridisation (SSH) library construction were selected from within the experimental groups comprising “early” stress (2–48 h) and “late” stress (96–504 h). In order to reduce redundancy within the four SSH libraries and yield a higher number of unique clones an additional subtraction was carried out. After printing of the arrays a series of 55 hybridisations were executed to cover 6 time points. At 2 h, 6 h, 24 h, 168 h and 504 h 5 individual confined fish and 5 individual control fish were used with control fish only at 0 h. A preliminary list of 314 clones considered differentially regulated over the complete time course was generated by a combination of data analysis approaches and the most significant gene expression changes were found to occur during the 24 h to 168 h time period with a general approach to control levels by 504 h. Few changes in expression were apparent over the first 6 h. The list of genes whose expression was significantly altered comprised predominantly genes belonging to the biological process category (response to stimulus) and one cellular component category (extracellular region) and were dominated by so-called acute phase proteins. Analysis of the gene expression profile in liver tissue during confinement revealed a number of significant clusters. The major patterns comprised genes that were up-regulated at 24 h and beyond, the primary examples being haptoglobin, β-fibrinogen and EST10729. Two representative genes from each of the six k-means clusters were validated by qPCR. Correlations between microarray and qPCR expression patterns were significant for most of the genes tested. qPCR analysis revealed that haptoglobin expression was up-regulated approximately 8-fold at 24 h and over 13-fold by 168 h.This project was part funded by the European Commission (Q5RS-2001-02211), Enterprise Ireland and the Natural Environment Research Council of the United Kingdom

Basic Methods for Computing Special Functions

This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website