Computational Solid State Physics pp 113-141 | Cite as

# Generalizations of the Relativistic OPW Method Including Overlapping and Non-Overlapping Atomic Orbitals

## Abstract

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.

## Keywords

Dirac Equation Core State Schroedinger Equation Trial Wave Function Core Core## Preview

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## References

- Anderson, O. K. and Kasowski, R. V. (1971) “Electronic States as Linear Combinations of Muffin-tin Orbitals” Phys. Rev. B. 4 1064.ADSCrossRefGoogle Scholar
- Brown, E. and Krumhansl, J. A. (1958) “Energy Band Structure of Lithium by a Modified Plane-Wave Method” Phys. Rev. 109 30ADSCrossRefGoogle Scholar
- Butler, F. A., Bloom, F. K. and Brown, E. (1969) “Modification of the Orthogonalised Plane-Wave Method Applied to Copper” Phys. Rev. 180 744.ADSCrossRefGoogle Scholar
- Callaway, J. (1955a) “Orthogonalised Plane-Wave Method” Phys. Rev. 91 933.ADSCrossRefGoogle Scholar
- Callaway, J. (1955b) “Electronic Energy Bands in Iron” Phys. Rev. 99 500.ADSMATHCrossRefGoogle Scholar
- Dalton, N. W. (1970) “Notes on the Dirac Equation and the Relativistic OPW Method” IBM Research Report RJ 785 (unpublished).Google Scholar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
- Euwema, R. N. (1971) “Plane1Wave-Gaussian Energy-Band Study of Nb” Phys. Rev. B 4 4332.ADSCrossRefGoogle Scholar
- Gray, D. and Brown, E. (1967) “Electron Energy Levels in Cu3Au” Phys. Rev. 160 567.ADSCrossRefGoogle 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
- Heine, V. (1967) “s-d Interaction in Transition Metals” Phys, Rev. 153 673.ADSCrossRefGoogle 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
- Herring, C. (1940) “A New Method for Calculating Wave-Functions in Crystals” Phys. Rev. 57. 1169.ADSMATHCrossRefGoogle Scholar
- Hubbard, J. (1967) “The Approximate Calculation of Electronic Band-Structures” Proc, Phys. Soc. 92 921.ADSCrossRefGoogle Scholar
- Kleinman, L. and Shurtleff, R. (1969) “Modified Augmented-Plane-Wave Method for Calculating Energy Bands” Phys. Rev. 188 1111.ADSCrossRefGoogle Scholar
- Kohn, W. and Rostkoker, N. (1954) “Solution of the Schroedinger Equation in Periodic Lattices with an Application to Metallic Lithium” Phys. Rev. 94 1111.ADSMATHCrossRefGoogle Scholar
- Korringa, J, (1947) “On the Calculation of a Bloch-Wave in a Metal” Physica 13 392.MathSciNetADSCrossRefGoogle 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
- Liberman, D., Waber, J, T. and Cromer, D. T. (1965) “Self-Consistent-Field Dirac-Slater Wave-Functions for Atoms and Ions. I. Comparison with Previous Calculations” Phys. Rev. 137 A27.ADSCrossRefGoogle 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
- Lowdin, P. (1951) “A Note on the Quantum-Mechanical Perturbation Theory” J. Chem. Phys. 19 1396.MathSciNetADSCrossRefGoogle Scholar
- Miasek, M. (1957) “Tight-Binding Method for Hexagonal Close-Packed Structure” Phys. Rev. 107 92.MathSciNetADSMATHCrossRefGoogle Scholar
- Phillips, J. C. and Kleinman, L. (1959) “New Method for Calculating Wave-Functions in Crystals and Molecules” Phys. Rev. 116 287.ADSMATHCrossRefGoogle Scholar
- Phillips, J. C. (1968) “Significance of Model Hamiltonians in Energy- Band Theory” Adv. in Phys. 65 79.ADSCrossRefGoogle Scholar
- Slater, J. C. (1937) “Wave-Functions in a Periodic Potential” Phys. Rev. 51. 846.ADSMATHCrossRefGoogle Scholar
- Slater, J. C. and Koster, G. F. (1954) “Simplified LCAO Method for the Periodic Potential Problem” Phys. Rev. 94 498.ADSCrossRefGoogle Scholar
- Soven, P. (1965) “Relativistic Band-Structure and Fermi Surface of Thallium” Phys. Rev. A137 1706.ADSCrossRefGoogle Scholar
- Wigner, E. and Seitz, F. (1933) “On the Constitution of Metallic Sodium. I” Phys. Rev. 43 804.ADSMATHCrossRefGoogle Scholar
- Wigner, E. and Seitz, F. (1934) “On the Constitution of Metallic Sodium. II” Phys. Rev. 46 509.ADSMATHCrossRefGoogle Scholar