Generalizations of the Relativistic OPW Method Including Overlapping and Non-Overlapping Atomic Orbitals
The advantages and disadvantages of the standard orthogonalized plane-wave (OPW) method for calculating electronic band structures are briefly examined. Then, following Herring (1940), the possibility of increasing the convergence of the OPW method by including certain ‘outer-core’ auxiliary tight-binding functions in the OPW basis set is investigated. It is argued that, contrary to much recent work, the overlap of core and outer-core functions on neighboring lattice sites is non-negligible in many materials and must be taken into account (either directly or indirectly) if a modified OPW method is to form the basis for a flexible and rapidly convergent scheme for metals and semi-conductors. Detailed expressions are derived for the relativistic OPW and modified OPW matrix elements which include ℓ-dependent potentials and overlapping orbitals.
KeywordsDirac Equation Core State Schroedinger Equation Trial Wave Function Core Core
Unable to display preview. Download preview PDF.
- Dalton, N. W. (1970) “Notes on the Dirac Equation and the Relativistic OPW Method” IBM Research Report RJ 785 (unpublished).Google Scholar
- Dalton, N. W. (1971) “Approximate KKR Band-Structure Schemes for Transition Metals” Computational Methods in Band Theory (Plenum Press) p. 225.Google Scholar
- Euwema, R. N. (1971) “Rapid Convergence of Crystalline Energy Bands by Use of a Plane-Wave-Gaussian Mixed Basis Set” Intern. J. Quantum Chem. 5, 61.Google Scholar
- Gray, D. and Karpien, R. J. (1971) “Some Notes on a Modified OPW Method” Computational Methods in Band Theory (Plenum Press) p. 144.Google Scholar
- Herman, F.,Kortum, R. L., Ortenburger, I. B. and Van Dyke, J. P. (1968) “Relativistic Band Structure of GeTe, SnTe, PbSe and PbS” J. de Phys. C4, sup 11–12, 62.Google Scholar
- Herman, F., Kortum, R. L., Ortenburger, I. B. and Van Dyke, J. P. (1969) “ Electronic Structure and Optical Spectrum of Semi-Conductors” ARL Technical Report ( Aerospace Research Laboratories, ARL 69 - 0080 ).Google Scholar
- Herman, F. and Skillman, S. (1963) “Atomic Structure Calculations” (Prentice-Hall, Englewood Cliffs, New Jersey).Google Scholar
- Kunz, A. B. “Combined Plane-Wave Tight-Binding Method for Energy-Band Calculations with Application to Sodium Iodide and Lithium Iodide” Phys. Rev. 180 934.Google Scholar
- Lipari, N. O. and Deegan, R. A. (1971) “Wave-Functions and Energy-Bands for Narrow Band Materials: A Modified Tight-Binding Calculation for the d-bands in Cu” (preprint).Google Scholar