Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

Physical Review B - Condensed Matter and Materials Physics

Volumn 84, Issue 4, 2011, Pages

  Alam, Aftab ^a   Khan, S N ^a,b   Wilson, Brian G ^c   Johnson, D D ^a,b  

^a University of Illinois at Urbana Champaign   (United States)

^b IOWA STATE UNIVERSITY   (United States)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79961238772     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.84.045105     Document Type: Article

References (44)

1. G. F. Voronoi, J. Reine Angew. Math 0075-4102 10.1515/crll.1908.134.198 134, 198 (1908).
2. D. E. Ellis and G. S. Painter, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.2.2887 2, 2887 (1970).
3. P. M. Boerrigter, G. Te. Velde, and J. E. Baerends, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.560330204 33, 87 (1988).
4. F. W. Averill and G. S. Painter, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.39.8115 39, 8115 (1989).
5. G. Te. Velde and E. J. Baerends, J. Comput. Phys. JCTPAH 0021-9991 10.1016/0021-9991(92)90277-6 99, 84 (1992).
6. Daniele Finocchiaro, Marco Pellegrini, and Paolo Bientinesi, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1998.6080 146, 707 (1998).
7. L. Vitos, I. A. Abrikosov, and B. Johansson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.156401 87, 156401 (2001).
8. A. Gonis, Erik C. Sowa, and P. A. Sterne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.2207 66, 2207 (1991).
9. Yang Wang, G. M. Stocks, W. A. Shelton, D. M. C. Nicholson, Z. Szotek, and W. M. Temmerman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75. 2867 75, 2867 (1995).
10. E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.24.864 24, 864 (1981);
11. D. J. Singh and L. Nordstrom, Planewaves, Pseudopotentials and LAPW method, 2nd ed. (Springer, Berlin, 2006).
12. M. Tanemura, T. Ogawa, and N. Ogita, J. Comput. Phys. JCTPAH 0021-9991 10.1016/0021-9991(83)90087-6 51, 191 (1983).
13. T. J. R. Hughes, The Finite Element Method (Dover Publications, Mineola, 2000).
14. B. J. Gellatly and J. L. Finney, J. Non-Cryst. Solids JNCSBJ 0022-3093 10.1016/0022-3093(82)90093-X 50, 313 (1981).
15. F. Aurenhammer, Siam J. Comput. SMJCAT 0097-5397 10.1137/0216006 16, 78 (1987).
16. Aftab Alam and D. D. Johnson, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.80.125123 80, 125123 (2009).
17. J. van W. Morgan, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/10/8/020 10, 1181 (1977).
18. D. D. Johnson, A. Alam, and A. V. Smirnov, MECCA: Multiple-Scattering Electronic-Structure Calculations for Complex Alloys (KKR-CPA Program, ver. 1.9) (University of Illinois, Illinois, 2008).
19. A. Goede, R. Preissner, and C. Frömmel, J. Comput. Chem. JCCHDD 0192-8651 10.1002/(SICI)1096-987X(19970715)18:9<1113::AID-JCC1>3.0.CO;2-U 18, 1113 (1997).
20. Srikanth Sastry, David S. Corti, Pablo G. Debenedetti, and F. H. Stillinger, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.56.5524 56, 5524 (1997).
21. F. M. Richards, J. Mol. Biol. JMOBAK 0022-2836 10.1016/0022-2836(74) 90570-1 82, 1 (1974).
22. N. N. Medvedev, Dokl. Akad. Nauk 337, 776 (1994);
23. N. N. Medvedev, Phys. Dokl. 337, 157 (1994);
24. M. Gerstein, J. Tsay, and M. Levitt, J. Mol. Biol. JMOBAK 0022-2836 10.1006/jmbi.1995.0351 249, 955 (1995).
25. V. Eyert, The Augmented Spherical Wave Method: A Comprehensive Treatment, Lecture Notes in Physics (Springer, Berlin, 2007), Vol. 719.
26. H. Xiao and Z. Gimbutas, Comp. Math. Applications CMAPDK 0898-1221 10.1016/j.camwa.2009.10.027 59, 663 (2001).
27. C. B. Haselgrove, Math. Comp. MCMPAF 0025-5718 10.1090/S0025-5718-1961- 0146960-1 15, 323 (1961);
28. H. Conroy, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1701795 47, 5307 (1967).
29. A. D. Becke, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.454033 88, 2547 (1988).
30. A. H. Stroud and D. Secrest, Gaussian Quadrature Formulas (Prentice-Hall, Englewood Cliffs, 1966).
31. J. C. Slater, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1725697 41, 3199 (1964);
32. E. Clementi, D. L. Raimondi, and Q. P. Reinhardt, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1712084 47, 1300 (1967).
33. Aftab Alam, Brent Kraczek, and D. D. Johnson, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.82.024435 82, 024435 (2010).
34. Javier Bernal, FORTRAN Codes for Voronoi Tessellation and Delauney Triangulations, NIST math webpages [http://math.nist.gov/~JBernal/JBernal-Sft. html].
35. D. D. Johnson, F. J. Pinski, and G. M. Stocks, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.30.5508 30, 5508 (1984).
36. U. von Barth and L. Hedin, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/5/13/012 5, 1629 (1972).
37. H. J. Monkhorst and J. D. Pack, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.13.5188 13, 5188 (1976).
38. D. D. Johnson, D. M. Nicholson, F. J. Pinski, B. L. Gyorffy, and G. M. Stocks, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.2088 56, 2088 (1986).
39. D. D. Johnson and F. J. Pinski, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.48.11553 48, 11553 (1993).
40. A. Gonis and W. H. Butler, Multiple Scattering Theory (Springer, New York, 2000).
41. N. Stefanou, H. Akai, and R. Zeller, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/0010-4655(90)90009-P 60, 231 (1990);
42. Y. Wang, G. M. Stocks, and J. S. Faulkner, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.49.5028 49, 5028 (1994).
43. R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser, and K. K. Kelley, Selected Values of Thermodynamic Properties of Binary Alloys (American Society for Metals, Metals Park, 1973).
44. L. Wang, Z. Fan, A. G. Roy, and D. E. Laughlin, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1669272 95, 7483 (2004).