Band Theory, Valence Bond, and Tight-Binding Calculations
In the theory of the electronic structure of crystals, the fundamental features of the band theory, valence bond method, and tight-binding approximation are reviewed, The band theory is studied on the basis of the Hartree-Fock scheme, and the Bloch functions are formed by a projection technique. The main methods for calculating Hartree-Fock functions in a solid are briefly discussed. The advantages and disadvantages of the band theory and the valence bond method are emphasized, and special attention is paid to the correlation error. In connection with the tight-binding approximation. the importance of the continuum part and of the approximate linear dependencies is stressed. lt is shown that a complete orthonormal set of translation connected atomic orbitals may be constructed as a convenient basis for this approach. The implication of the virial theorem in interpreting the cohesive properties of the ionic crystals is further emphasized. Some recent refinements of band theory are then discussed. lt is shown that a large part of the correlation error can be removed by permitting different orbitals for different spins. This leads to a scheme intermediate between band theory and valence bond method and, by means of a single parameter, an essential lowering of the energy curve and the correct asymptotic behavior for separated atoms or constituents can be obtained. The band theory can be further reflned and connected to the exact solution of the many-electron Schrhdinger equation of the crystal by means of an extension of the self-consistentfield scheme, utilizing the so-called reaction operator here exactly defined by means of a simple partitioning technique. The various types of self-consistent field theories are flnally compared.
- Research Organization:
- Uppsala Univ.; and Univ. of Florida, Gainesville
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-16-007536
- OSTI ID:
- 4818947
- Journal Information:
- Journal of Applied Physics, Journal Name: Journal of Applied Physics Journal Issue: 1 Vol. 33; ISSN JAPIAU; ISSN 0021-8979
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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