Applications of band theory

The application of band theory to account for detailed electrical, optical and magnetic properties has so far had only limited success (28). Electronic conduction and optical absorption resulting in the onset of u.v.-visible opaqueness involve the transference of electrons from one ion to another, and it would therefore seem worth applying the principles of optical electronegativity to these problems. Any resulting correlations are expected to be of a much more qualitative nature than results given by applying band theory. 

The electronic structure of a solid metal or semiconductor is described by the band theory that considers the possible energy states of delocalized electrons in the crystal lattice. An apparent difficulty for the application of band theory to solid state catalysis is that the theory describes the situation in an infinitely extended lattice whereas the catalytic process is located on an external crystal surface where the lattice ends. In attempting to develop a correlation between catalytic surface processes and the bulk electronic properties of catalysts as described by the band theory, the approach taken in the following pages will be to assume a correlation between bulk and surface electronic properties. For example, it is assumed that lack of electrons in the bulk results in empty orbitals in the surface conversely, excess electrons in the bulk should result in occupied orbitals in the surface (7). This principle gains strong support from the consistency of the description thus achieved. In the following, the principle will be applied to supported catalysts. 

It needs to be stressed that models of the metallic state on which the Band Theory is based suppose an infinite three-dimensional array of ion cores, so that the band structure cannot be expected to persist unchanged to the surface. Moreover the ion cores must be precisely located before theoretical analysis starts, and we shall shortly see that interatomic distances and vibrational amplitudes in the surface differ somewhat from those in the interior. These factors certainly complicate the useful application of Band Theory to the properties of surfaces. 

Discussions of the limitations and applicability of band theory vs oligomer approach in determining... 

In the final section of the present chapter we discuss an application of band theory which is becoming a dominant component in the field of atomic and electronic structure of solids it is the calculation of the total energy of the solid as a function of the arrangement of the atoms. The ability to obtain accurate values for the total energy as a function of atomic configuration is crucial in explaining a number of thermodynamic and mechanical properties of solids. For example,... 

In conclusion it might be said that Wannier functions, although they date back to (at least) 1937, have not yet been at all widely used. Since the topics mentioned above, for which they hold most promise, have been studied intensively only in the last few years, Wannier functions may yet come to the fore as indispensable practical tools in the application of band theory. ... 

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