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Numerical Integration in Density Functional Methods with Linear Combination of Atomic Orbitals

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Quantum-Mechanical Ab-initio Calculation of the Properties of Crystalline Materials

Part of the book series: Lecture Notes in Chemistry ((LNC,volume 67))

Summary

The generalization of Becke’s numerical integration scheme to periodic functions is presented, which allows the LCAO-Kohn-Sham equations for crystals to be solved efficiently. The computational implementation of the scheme and its calibration are briefly discussed.

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References

  1. M.L. Cohen, in Structure and Bonding in Crystals, Vol.1 (M. O’Keeffe and A. Navrotsky, eds), Academic, New York, p. 25 (1981).

    Google Scholar 

  2. A. Zunger, in Structure and Bonding in Crystals, Vol.1 (M. O’Keeffe and A. Navrotsky, eds), Academic, New York, p. 73 (1981).

    Google Scholar 

  3. O.K. Andersen, Phys. Eev. B 12, 3060 (1975).

    Article  CAS  Google Scholar 

  4. T. Ziegler, Chem. Rev, 91, 651 (1991).

    Article  CAS  Google Scholar 

  5. B.G Johnson, P.M.W. Gill, and J.A. Pople, J. Chem. Phys. 98 5612 (1992).

    Article  Google Scholar 

  6. J. Andzeim and E. Wimmer, J. Chem. Phys, 96, 1280 (1992).

    Article  Google Scholar 

  7. P. Durand and J.C. Barthelat, Chem. Phys Lett. 27, 191 (1974).

    Article  CAS  Google Scholar 

  8. A.D. Becke, J. Chem. Phys. 88, 2547 (1988).

    Article  CAS  Google Scholar 

  9. P.W.M. Gill, B.G. Johnson, J.A. Pople, and M.J. Frisch, Chem. Phys. Lett. 197, 499 (1992)

    Article  CAS  Google Scholar 

  10. A.D. Becke, J. Chem. Phys 96, 2155 (1992).

    Article  CAS  Google Scholar 

  11. C. Pisani, E. Dovesi and C. Roetti, Hartree-Fock Ab Initio Treatment of Crystalline Systems, Lecture Notes in Chem. Vol. 48, Springer, Berlin (1988).

    Google Scholar 

  12. R. Dovesi, C. Pisani, C. Roetti, M. Causà, and V.R. Saunders, CRYSTAL 88, Program No. 577, QCPE, Indiana University, Bloomington, IN (1989); R. Dovesi, V.R. Saunders and C. Roetti, CRYSTAL92 User Documentation, University of Torino, Torino (1992).

    Google Scholar 

  13. M.Causa and A. Zupan, Chem. Phys. Lett. 220, 145 (1994).

    Article  CAS  Google Scholar 

  14. M.Causa and A. Zupan, Int. J. Quantum Chem. S28, 633 (1994).

    Article  CAS  Google Scholar 

  15. A. Zupan and M. Causa, Int. J. Quantum Chem, S32, 446 (1995).

    Google Scholar 

  16. F.E. Harris and H.J. Monkhorst, Phys. Rev. Lett. 23, 1026 (1969).

    Article  CAS  Google Scholar 

  17. A. Savin, Int. J. Quantum Chem. S22, 457 (1988).

    Google Scholar 

  18. G. Stroud, Approximate Calculations of Multiple Integrals, Prentice-Hall (1971)

    Google Scholar 

  19. V.I. Lebedev, Zh. Vychisl. Mat. Fiz. 16, 293 (1976).

    Google Scholar 

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© 1996 Springer-Verlag Berlin Heidelberg

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Causà, M. (1996). Numerical Integration in Density Functional Methods with Linear Combination of Atomic Orbitals. In: Pisani, C. (eds) Quantum-Mechanical Ab-initio Calculation of the Properties of Crystalline Materials. Lecture Notes in Chemistry, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61478-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-61478-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61645-0

  • Online ISBN: 978-3-642-61478-1

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