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Pseudopotentials and Total Energy Calculations: Applications to Crystal Stability, Vibrational Properties, Phase Transformations, and Surface Structures

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Electronic Structure, Dynamics, and Quantum Structural Properties of Condensed Matter

Abstract

A review of the applications of the pseudopotential method and total energy techniques to the electronic and structural properties of solids is presented. With this approach, it has recently become possible to determine with accuracy crystal structures, lattice constants, bulk moduli, shear moduli, cohesive energies, phonon spectra, solid-solid phase transformations, and other static and dynamical properties of solids. The only inputs to these calculations, which are performed either with plane wave or LCAO bases, are the atomic numbers and masses of the constituent atoms. Calculations have also been carried out to study the atomic and electronic structure of surfaces, chemisorption systems, and interfaces. Results for several selected systems including the covalent semiconductors and insulators and the transition metals are discussed. The review is not exhaustive but focuses on specific prototype systems to illustrate recent progress.

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References

  1. For related topics, see articles by K. Kunc and by R. M. Martin in this volume.

    Google Scholar 

  2. Introductory reviews on background materials are available in M. L. Cohen, Phys. Today 32:40 (1979), and M. L. Cohen, Phys. Scripta T1: 5 (1982).

    Google Scholar 

  3. D. R. Hamann, M. Schlüter, and C. Chiang, Phys. Rev. Lett. 43: 1494 (1979).

    Article  CAS  Google Scholar 

  4. G. Kerker, J. Phys. C 13: L189 (1980).

    Article  CAS  Google Scholar 

  5. A. Zunger and M. L. Cohen, Phys. Rev. B 18:5449 (1978); 20: 4082 (1979).

    CAS  Google Scholar 

  6. T. Starkoff and J. D. Joannopoulos, Phys. Rev. B 16: 5212 (1977).

    Article  Google Scholar 

  7. S. G. Louie, S. Froyen, and M. L. Cohen, Phys. Rev. B 26: 1738 (1982).

    Article  CAS  Google Scholar 

  8. P. Hohenberg and W. Kohn, Phys. Rev. 136: B864 (1964).

    Article  Google Scholar 

  9. W. Kohn and L. J. Sham, Phys. Rev. 140: A1133 (1965).

    Article  Google Scholar 

  10. E. Wigner, Phys. Rev. 46: 1002 (1934).

    Article  CAS  Google Scholar 

  11. L. Hedin and B. I. Lundqvist, J. Phys. C 4: 2064 (1971).

    Article  Google Scholar 

  12. U. von Barth and L. Hedin, J. Phys. C 5: 1629 (1972).

    Article  Google Scholar 

  13. O. Gunnarsson, B. I. Lundqvist, and J. W. Wilkens, Phys. Rev. B 10: 1319 (1974).

    Article  CAS  Google Scholar 

  14. D. M. Ceperley, Phys. Rev. B 18:3126 (1978); D. M. Ceperley and B. I. Alder, Phys. Rev. Lett. 45:566 (1980). These results are parameterized in J. P. Perdew and A. Zunger, Phys. Rev. B 23: 5048 (1981).

    Google Scholar 

  15. S. G. Louie, K. M. Ho, and M. L. Cohen, Phys. Rev. B 19: 1774 (1979).

    Article  CAS  Google Scholar 

  16. J. R. Chelikowsky and S. G. Louie, Phys. Rev. B 29: 3470 (1984).

    Google Scholar 

  17. J. Ihm, A. Zunger, and M. L. Cohen, J. Phys. C 12: 4401 (1979).

    Article  Google Scholar 

  18. Z. Levine and S. G. Louie, Phys. Rev. B 25: 6310 (1982).

    Article  CAS  Google Scholar 

  19. D. Vanderbilt and S. G. Louie, Phys. Rev. B (in press).

    Google Scholar 

  20. J. R. Chelikowsky, S. G. Louie, D. Vanderbilt, and C. T. Chan, Int. J. of Quant. Chem. (in press).

    Google Scholar 

  21. M. T. Yin and M. L. Cohen, Phys. Rev. B 26: 5668 (1982).

    Article  CAS  Google Scholar 

  22. S. Froyen and M. L. Cohen, Phys. Rev. B 28: 3258 (1983).

    Article  CAS  Google Scholar 

  23. F. D. Murnaghan, Proc. Nat. Acad. Sci. U.S.A. 3: 244 (1944).

    Article  Google Scholar 

  24. M. T. Yin and M. L. Cohen, Phys. Rev. B 24: 6121 (1981).

    Article  CAS  Google Scholar 

  25. P. K. Lam and M. L. Cohen, Phys. Rev. B 24:4224 (1981); B 25: 6139 (1982).

    CAS  Google Scholar 

  26. M. Y. Chou, P. K. Lam, and M. L. Cohen, Solid State Comm. 42: 861 (1982).

    Article  CAS  Google Scholar 

  27. C. T. Chan, J. R. Chelikowsky, and S. G. Louie (to be published).

    Google Scholar 

  28. K. M. Ho, C. L. Fu, B. N. Harmon, W. Weber, and D. R. Hamann, Phys. Rev. Lett. 49:673 (1982); Phys. Rev. B 29: 1575 (1984).

    CAS  Google Scholar 

  29. N. A. W. Holzwarth, S. G. Louie, and S. Rabíi, Phys. Rev. B 26: 5382 (1982).

    Article  CAS  Google Scholar 

  30. R. Chen, P. Trucano, and R. F. Stewart, Acta Crystallogr. Sec. A 33: 823 (1977).

    Google Scholar 

  31. M. T. Yin and M. L. Cohen, Phys. Rev. Lett. 45:1004 (1980); Phys. Rev. B 26: 3259 (1982).

    CAS  Google Scholar 

  32. K. Kunc and R. M. Martin, Phys. Rev. Lett. 48: 406 (1982).

    Article  CAS  Google Scholar 

  33. B. N. Harmon, W. Weber, and D. R. Hamann, Phys. Rev. B 25: 1109 (1982).

    Article  CAS  Google Scholar 

  34. H. Nielsen and R. M. Martin, Phys. Rev. Lett. 50: 697 (1983).

    Article  Google Scholar 

  35. D. Vanderbilt, S. G. Louie, and M. L. Cohen (to be published).

    Google Scholar 

  36. M. Born and R. Oppenheimer, Ann. Physk 84: 457 (1927).

    Article  CAS  Google Scholar 

  37. K. Kunc and R. M. Martin, J. de Physique, Colloque C 6: 649 (1981).

    Google Scholar 

  38. M. T. Yin and M. L. Cohen, Phys. Rev. B 25: 4317 (1982).

    Article  CAS  Google Scholar 

  39. S. A. Solin and A. K. Ramdas, Phys. Rev. B 1: 1687 (1970).

    Article  Google Scholar 

  40. M. H. Cohen and J. Ruvalds, Phys. Rev. Lett. 23: 1378 (1969)

    Article  Google Scholar 

  41. R. Tubino and J. L. Birman, Phys. Rev. B 15:5843 (1977), and references therein.

    Google Scholar 

  42. R. Biswas and R. M. Martin (to be published).

    Google Scholar 

  43. S. Fahy and S. G. Louie (to be published).

    Google Scholar 

  44. M. T. Yin, Phys. Rev. B (in press).

    Google Scholar 

  45. P. K. Lam and M. L. Cohen, Phys. Rev. B 27: 5986 (1983).

    Article  CAS  Google Scholar 

  46. W. Maysenholder, S. G. Louie, and M. L. Cohen (to be published).

    Google Scholar 

  47. J. A. Moriarty and A. K. McMahan, Phys. Rev. Lett. 48: 809 (1982).

    Google Scholar 

  48. P. K. Lam, M. Y. Chou, and M. L. Cohen, J. Phys. C 17: 2065 (1984).

    Article  CAS  Google Scholar 

  49. F. Aldinger and G. Petzow, Beryllium Science and Technology, ed. D. Webster and G. J. London, Plenum, New York, Vol. 1 (1979), p. 235.

    Google Scholar 

  50. F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York (1965), p. 294.

    Google Scholar 

  51. R. P. Feynman, Statistical Mechanics, Benjamin, Reading (1972), p. 9.

    Google Scholar 

  52. J. A. Appelbaum and D. R. Hamann, Rev. Mod. Phys. 48: 3 (1974).

    Google Scholar 

  53. M. Schluter, J. R. Chelikowsky, S. G. Louie, and M. L. Cohen, Phys. Rev. B 12: 4200 (1975).

    Article  Google Scholar 

  54. For a recent review, see D. Haneman, Adv. Phys. 31: 165 (1982).

    Google Scholar 

  55. F. J. Himpsel, D. E. Eastman, P. Heimann, and J. F. van der Veen, Phys. Rev. B 24: 7270 (1981).

    Article  CAS  Google Scholar 

  56. F. Houzay, G. Guichar, R. Pinchaux, G. Jezequel, F. Solal, A. Barsky, P. Steiner, and Y. Petroff, Surf. Sci. 132:40 (1983), and references therein.

    Google Scholar 

  57. J. M. Nicholls, G. V. Hansson, R. I. G. Uhrberg, and S. A. Flodstrom, Phys. Rev. B 27: 2594 (1983).

    Article  CAS  Google Scholar 

  58. J. E. Northrup. J. Ihm, and M. L. Cohen, Phys. Rev. Lett. 47: 1910 (1981).

    Article  Google Scholar 

  59. J. E. Northrup and M. L. Cohen, Phys. Rev. Lett. 49: 1349 (1982).

    Article  CAS  Google Scholar 

  60. G. Allan and M. Lannoo, Surf. Science 63: 11 (1977).

    Article  CAS  Google Scholar 

  61. C. B. Duke and W. K. Ford, Surf. Sci. 111: L685 (1981).

    Article  CAS  Google Scholar 

  62. R. Del Sole and D. J. Chadi, Phys. Rev. B 24: 7430 (1981).

    Google Scholar 

  63. J. E. Northrup and M. L. Cohen, Phys. Rev. B 29: 5944 (1984).

    Article  CAS  Google Scholar 

  64. K. C. Pandey, Phys. Rev. Lett. 47: 1913 (1981).

    Article  CAS  Google Scholar 

  65. J. E. Northrup and M. L. Cohen, Phys. Rev. B 27: 6553 (1983).

    Article  CAS  Google Scholar 

  66. D. Vanderbilt and S. G. Louie, Phys. Rev. B 29 (in press).

    Google Scholar 

  67. K. C. Pandey, Phys. Rev. B 25: 4338 (1982).

    Google Scholar 

  68. W. S. Yang and F. Jona, Bull. Am. Phys. Soc. 28: 415 (1983).

    Google Scholar 

  69. S. V. Pepper, Surf. Sci. 12: 47 (1982).

    Article  Google Scholar 

  70. D. J. Chadi, Proceedings of the IXth Vacuum Congress/Vth International Conference on Solid Surfaces, Madrid, Spain, 1983; and J. Vac. Sci. Technol. (in press).

    Google Scholar 

  71. D. J. Chadi, Phys. Rev. B 26: 4762 (1982).

    Google Scholar 

  72. R. Seiwatz, Surf. Sci. 2: 473 (1964).

    Article  CAS  Google Scholar 

  73. This unrelaxed Pandey model has all bulk bond lengths except for the graphite length for surface chain bonds.

    Google Scholar 

  74. J. Ihm, M. L. Cohen, and D. J. Chadi, Phys. Rev. B 21:4592 (1980); M. T. Yin and M. L. Cohen, ibid. 24: 2303 (1981).

    Google Scholar 

  75. J. Ihm, D. H. Lee, J. D. Joannopoulos, and J. J. Xiong, Phys. Rev. Lett. 51: 1872 (1983).

    Article  CAS  Google Scholar 

  76. J. Ihm and J. D. Joannopoulos, Phys. Rev. B 26: 4429 (1982).

    Article  CAS  Google Scholar 

  77. S. G. Louie, K. M. Ho, J. R. Chelikowsky, and M. L. Cohen, Phys. Rev. Lett. 37:1289 (1976); Phys. Rev. B 15: 5627 (1977).

    CAS  Google Scholar 

  78. S. G. Louie, Phys. Rev. Lett. 40: 1525 (1978).

    Article  CAS  Google Scholar 

  79. J. A. Appelbaum and D. R. Hamann, Solid State Comm. 27: 881 (1978).

    Article  CAS  Google Scholar 

  80. C. S. Wang and A. J. Freeman, Phys. Rev. B 11: 793 (1979).

    Article  Google Scholar 

  81. J. R. Smith, J. G. Gay, and F. J. Arlinghaus, Phys. Rev. B 21: 2201 (1980).

    Article  CAS  Google Scholar 

  82. H. Krakauer, M. Posternak, and A. J. Freeman, Phys. Rev. B 19: 1706 (1979).

    Article  CAS  Google Scholar 

  83. Jepsen, J. Madsen, and 0. K. Andersen, Phys. Rev. B 18: 605 (1978).

    Article  Google Scholar 

  84. G. P. Kerker, K. M. Ho, and M. L. Cohen, Phys. Rev. Lett. 40: 1593 (1978).

    Article  CAS  Google Scholar 

  85. S. L. Wang, T. Gustafsson, and E. W. Plummer, Phys. Rev. Lett. 39: 822 (1977).

    Article  Google Scholar 

  86. S. G. Louie, Phys. Rev. Lett. 42: 476 (1979).

    Article  CAS  Google Scholar 

  87. W. Eberhardt, S. G. Louie, and E. W. Plummer, Phys. Rev. B 28: 465 (1983).

    Article  CAS  Google Scholar 

  88. P. D. Johnson and N. V. Smith, Phys. Rev. Lett. 49: 290 (1982).

    Article  CAS  Google Scholar 

  89. S. G. Louie, P. Thiry, R. Pinchaux, Y. Petroff, D. Chandesris, J. LeCante, Phys. Rev. Lett. 44: 549 (1980).

    Article  CAS  Google Scholar 

  90. N. A. W. Holzwarth and J. R. Chelikowsky (to be published).

    Google Scholar 

  91. H. Conrad, G. Ertl, J. Kuppers, and E. E. Latta, Surf. Sci. 58: 578 (1976).

    Article  CAS  Google Scholar 

  92. J. E. Demuth, Surf. Sci. 65:369 (1977), and unpublished.

    Google Scholar 

  93. D. M. Newns, Phys. Rev. 178: 1123 (1959).

    Article  Google Scholar 

  94. K. Schonhammer, Solid State Comm. 22: 51 (1977).

    Article  Google Scholar 

  95. For semiconductors, refer, for example, to J. Ihm and J. Joannopoulos, Phys. Rev. B 24:4191 (1981); M. T. Yin and M. L. Cohen, Phys. Rev. B 26:5668 (1982); S. Froyen and M. L. Cohen, Solid State Comm. 43: 447 (1982).

    Google Scholar 

  96. D. R. Hamann, Phys. Rev. Lett. 42: 662 (1979).

    Article  CAS  Google Scholar 

  97. For the case of wide gap insulators, see, for example, R. A. Heaton and C. C. Lin, Phys. Rev. B 22:3629 (1980); S. B. Trickey, F. R. Green, Jr., and F. W. Averill, Phys. Rev. B 8: 4822 (1973).

    Article  Google Scholar 

  98. G. Strinati, H. J. Mattausch, and W. Hanke, Phys. Rev. B 25:2867 (1982), and references therein.

    Google Scholar 

  99. C. S. Wang and W. E. Pickett, Phys. Rev. Lett. 51: 597 (1983).

    Article  CAS  Google Scholar 

  100. L. J. Sham and M. Schluter, Phys. Rev. Lett. 51: 1888 (1983)

    Article  Google Scholar 

  101. M. S. Hybertsen and S. G. Louie, Solid State Comm. (in press).

    Google Scholar 

  102. D. C. Langreth and M. J. Mehl, Phys. Rev. B 28:1809 (1983), and references therein.

    Article  CAS  Google Scholar 

  103. J. P. Perdew and A. Zunger, Phys. Rev. B 23: 5048 (1981).

    Article  CAS  Google Scholar 

  104. J. A. Alonso and L. A. Girifalco, Solid State Comm. 24:135 (1977); Phys. Rev. B 17: 3735 (1978).

    Article  CAS  Google Scholar 

  105. Gunnarsson, M. Jonson, and B. I. Lundqvist, Solid State Comm. 24:765 (1977); Phys. Rev. B 20: 3136 (1979).

    Article  Google Scholar 

  106. F. Manghi, G. Rieglar, C. M. Bertoni, C. Calandra, and G. B. Bachelet, Phys. Rev. B 28: 6157 (1983).

    Article  CAS  Google Scholar 

  107. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13: 4274 (1976).

    Article  Google Scholar 

  108. Gunnarsson and R. 0. Jones, Phys. Scr. 21: 394 (1980).

    Article  Google Scholar 

  109. Landolt-Bornstein, Zahlenwerte und Funktioned aus Naturwissenschaften und Technik, N.S. Vol. 11117a, Springer-Verlag, New York (1982).

    Google Scholar 

  110. W. E. Spicer and R. C. Eden, Proceedings of the Ninth Interna- tional Conference of the Physics of Semiconductors, Moscow, 1968, Nauka, Leningrad, Vol. 1 (1968), p. 61.

    Google Scholar 

  111. R. Hulthen and N. G. Nilsson, Solid State Comm. 18: 1341 (1976).

    Article  CAS  Google Scholar 

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Louie, S.G. (1985). Pseudopotentials and Total Energy Calculations: Applications to Crystal Stability, Vibrational Properties, Phase Transformations, and Surface Structures. In: Devreese, J.T., Van Camp, P. (eds) Electronic Structure, Dynamics, and Quantum Structural Properties of Condensed Matter. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0899-8_8

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