Discrete Variational Method for the Energy Band Problem with LCAO Basis and Non-Spherical Local Potential

  • G. S. Painter
  • D. E. Ellis
Part of the The IBM Research Symposia Series book series (IRSS)


While the discrete variational method (DVM)1,2 is not restricted with regard to the form of the basis set, and this is one advantage of the technique, the method has so far been applied to the one electron model Hamiltonian using a linear combination of atomic orbitals (LCAO) basis. The DVM seems most promising for treating compounds, where non-spherical potential terms are significant. The LCAO basis is most appropriate for forming crystal wavefunctions for those systems in which the atomic character of the constituent atoms is maintained to a large degree. The results that have been obtained thus far for bcc Li, diamond, single and multi-layer graphite, LiF, MgO, SiC and TiC show that the DVM is in fact a feasible scheme and works quite well with surprisingly few integration points. Moreover, the LCAO basis has been found to converge the occupied and lower conduction band structures with only slight extensions beyond minimal basis sets.


Integration Point Bloch Function Integration Grid Lower Conduction Band Discrete Variational Method 
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Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • G. S. Painter
    • 1
  • D. E. Ellis
    • 2
  1. 1.Metals and Ceramics DivisionOak Ridge National LaboratoryOak RidgeUSA
  2. 2.Physics DepartmentNorthwestern UniversityEvanstonUSA

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