Band structures methodology

Subsequently, Br das et al. [25] calculated the band structures of polyisothianaphthene (1) and the 5,6-di-methyl, 5,6-dimethoxy, and 5,6-dicyano derivatives, 13-15, using the MNDO-optimized geometry of isothia-naphthene (3) corresponding to the aromatic structures and the VEH band structure methodology. 

However, it became evident in the post-war period that, valuable as they were, these band-structure concepts could not be applied even qualitatively to key systems of industrial interest notably steels, nickel-base alloys, and other emerging materials such as titanium and uranium alloys. This led to a resurgence of interest in a more general thermodynamic approach both in Europe (Meijering 1948, Hillert 1953, Lumsden 1952, Andrews 1956, Svechnikov and Lesnik 1956, Meijering 1957) and in the USA (Kaufman and Cohen 1956, Weiss and Tauer 1956, Kaufman and Cohen 1958, Betterton 1958). Initially much of the work related only to relatively simple binary or ternary systems and calculations were performed largely by individuals, each with their own methodology, and there was no attempt to produce a co-ordinated framework. 

For direct Af-electron variational methods, the computational effort increases so rapidly with increasing N that alternative simplified methods must be used for calculations of the electronic structure of large molecules and solids. Especially for calculations of the electronic energy levels of solids (energy-band structure), the methodology of choice is that of independent-electron models, usually in the framework of density functional theory [189, 321, 90], When restricted to local potentials, as in the local-density approximation (LDA), this is a valid variational theory for any A-electron system. It can readily be applied to heavy atoms by relativistic or semirelativistic modification of the kinetic energy operator in the orbital Kohn-Sham equations [229, 384],... 

This chapter reviews the methodologies developed over the years to tackle various aspects of surface photoelectrochemistry. Section 2.2 gives an overview of all the photophysical and photochemical processes operative in semiconductor systems, combining findings from solid-state physics and chemistry. For completeness, the effect of quantisation of the band structure is included. The basic principles are presented to enable a smooth transition from purely molecular to purely sohd-state... 

Infinite stereoregular polymers require special consideration (see Section 8). Band structure techniques that parallel the methodologies formulated for ordinary molecules are evolving rapidly. However, the Finite Field procedures need further development and we recommend that, for the time being, extrapolation of finite oligomer calculations should be employed. 

For the discussion of the physicochemical properties of conductive conjugated polymers, it is most important to set up the appropriate model and to employ the proper method of calculations. In this article most of the analyses have been based on the one-dimensional tight-binding CO methodology for polymers with periodical unit cells. This approach is useful because it gives not only the band structure but also information reflecting the nature of each atomic orbital in the unit cell. 

The methodology of band structure calculations is diverse< >. In general, however, the band structure determined in reciprocal space does not give a straightforward indication of the charge density in real space. Electronic charge densities have recently been calculated, however, for several semicon-ductors,< > with wavefunctions calculated using pseudopotential theory. 

Even though some progress has been made towards understanding electrocatalytic process and screening electrocatalysts from DFT, the method has difficulty in providing quantitative numbers for detailed reaction steps. On one hand, methodological improvements are required to describe the electron transfer at solid-liquid interface, the band structure, and the excited states effectively, which is currently limitation of DFT. On another hand, the model systems in DFT studies are somewhat too simplified to model the real catalysts effectively. For instance, the real catalysts are powders, which may behave differently with size. Recently, efforts have been made to model the nanoparticles with the size of the real catalysts (<5 nm), showing indeed different behaviors from the extended surfaces even in term of trend (Fig. 3), a common model used in DFT studies [24, 25]. Thus, theoretical... 

Band structure calculations of metal hydrides have provided understanding of the bonding characteristics of these materials and clarified the mechanisms involved in various physical properties such as superconductivity. Since the electronic structure of stoichiometric hydrides has been discussed extensively in the literature, in this article we will focus on the methodology and results of disordered hydrides. This disorder can occur on the metal site of the hydride by considering random substitutions of the host metal or on the hydrogen sublattice where vacancies appear. 

In a previous volume[l] of this series one of us described the methodology of performing band structure calculations for metal hydrides and discussed the electronic properties of such systems. In that article, although non-periodic systems were reported, the emphasis was on periodic materials. This paper deals exclusively with disordered materials. 

Recent papers [4-6] of the NRL group have concentrated on a tight-binding methodology that simultaneously fits the energy bands and the total ener — of the fee and bcc structures as a function of volume, and correctly predicts the ground state for those metals that crystallize in the hep or even the Of-Mn structure. 

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