Hartree-Fock band-structure calculations

Hartree-Fock calculations on molecules commonly exploit the symmetry of the molecular point group to simplify calculations such studies on perfectly ordered bulk crystalline solids are possible if one exploits the translational symmetry of the crystalline lattice (see Ashcroft and Mermin, 1976) as well as the local symmetry of the unit cell. From orbitals centered on various nuclei within the unit cell of the crystal Bloch orbitals are generated, as given by the formula (in one dimension)  

Hartree-Fock band calculations were performed by Euwema et al. 

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Calculate G°(E), the Green matrix of the unperturbed system, as defined in equation (4.111) for the elements of F , using as input the results of a Hartree-Fock band-structure calculation of the... 

For the calculation of the Hartree-Fock band structures of polymers a method has been developed including non-local exchange and full-self consistency. It is applicable also in the case of a combined symmetry (e.g., helix). 

The focus then shifts to the delocalized side of Fig. 1.1, first discussing Hartree-Fock band-structure studies, that is, calculations in which the full translational symmetry of a solid is exploited rather than the point-group symmetry of a molecule. A good general reference for such studies is Ashcroft and Mermin (1976). Density-functional theory is then discussed, based on a review by von Barth (1986), and including both the multiple-scattering self-consistent-field method (MS-SCF-ATa) and more accurate basis-function-density-functional approaches. We then describe the success of these methods in calculations on molecules and molecular clusters. Advances in density-functional band theory are then considered, with a presentation based on Srivastava and Weaire (1987). A discussion of the purely theoretical modified electron-gas ionic models is... 

Ab initio SCF LCAO CO calculations on the infinite neutral TCNQ and TTF stacks were performed using a TCNQ (see Figure 2.5a) or TTF (Figure 2.5b) molecule as unit cell. These ab initio Hartree-Fock band structures can serve as a starting point for further improvements, such as the treatment of charge transfer between the stacks and interac-... 

The present paper will first review shortly the way of performing Hartree-Fock (HF) calculations for ground state properties of polymers. By use of the Koopmans theorem, the corresponding HF density of states is of direct interest as an interpretative tool of XPS experiments. A practical way of correlating band structure calculations and XPS spectra is thus presented. In the last part, we illustrate the type of mutual enrichment which can be gained from the interplay between theory and experiment for the understanding of valence electronic properties. ... 

Nikolic G, Shimazaki T, Yoshihiro A (eds) (2011) Fourier transforms, Gaussian and Fourier Transform (GFT) method and screened Hartree-Fock exchange potential for first-principles band structure calculations. 15-36... 

In actual polymer calculations it is necessary to decide how many-neighbor interactions must be taken into account to obtain satisfactory results. This is by no means a trivial question. Experience gained in numerous calculations (see below) indicates that the number of neighbors to be taken into account explicitly is smaller if one performs a band-structure calculation, than if one is interested in the total energy per unit cell. To imderstand the reason for this we now examine the latter quantity for a linear chain obtained by straightforward generalization of the Hartree-Fock-Roothaan expression for molecules, namely... 

The availability of detailed information about the electronic states of PDAs makes them ideal systems to test molecular quantum mechanical theories. The earliest calculation for a model PDA chain with simple sidegroups gave rather poor values for the band-gap, see (7). In most of these calculations Coulomb correlations were neglected so that only band structures were deduced. Further work along these lines has included the use of an ab initio crystal orbital method [105), studies of the ground state geometries [106), a priori Hartree Fock crystal orbital calculations (107) and a non-empirical effective Hamiltonian technique [108). These show... 

Due to the central role of DNA and proteins in biochemistry and biophysics the computation of the electronic structure of periodic polymers built from nucleotide bases, base pairs, nucleotides and amino acids, respectively, had been of high interest since about twenty years. Early calculations of the band structure of DNA related periodic polymers have been performed with the crystal orbital (CO) method on the basis of different semiempirical levels (1). Recently the results of ab initio Hartree-Fock CO (2, 3) band structure calculations for the four nucleotide base stacks (4-6), the two Watson-Crick base pair stacks (6), the sugar-phosphate chain (4,5) and the three nucleotides cytidine (4,5), adenylic acid and th3nnidine (6) have been reported. These computations represent a significant progress but the following improvements are required for a more accurate description of the electronic structure of real DNA and its transport properties ... 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

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