(1.1)

 

 

(1.2)

 

 

(1.3)

 

 

(1.4)

 

 

(1.5)

 

 

(1.6)

 

 

(1.7)

 

 

(1.8)

 

.

(1.9)

 

(1.10)

 

 

(1.11)

 

 

(1.12)

 

 

(1.13)

 

 

(1.14)

 

 

(1.15)

 

 

(1.16)

 

 

(1.17)

 

 

(1.18)

 

(1.19)

 

 

(1.20)

 

 

(1.21)

 

 

(1.22)
.

 

 

(1.23)

 

 

(1.24)

 

 

(1.25)

 

 

(1.26)

 

 

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(1.28)

 

 

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.

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,

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.

(1.37)

 

.

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,

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,

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.

(1.42)

 

 

(1.43)

 

,

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,

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.

(1.46)

 

.

(1.47)

 

,

(1.48)

 

.

(1.49)

 

 

(1.50)

 

 

(1.51)

 

 

(1.52)

 

 

(1.53)

 

 

(1.54)

 

 

(1.55)

 

 

(1.56)

 

 

(1.57)

 

(1.58)

 

 

(1.59)

 

 

(1.60)

 

 

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(1.64)

 

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,

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,

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,

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,

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,

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.

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,

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,

(1.90)

 

.

(1.91)

 

,

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,

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.

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(1.96)

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,

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,

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1.5. Список литературы к Главе 1

  1. Chelikowsky J. R., Louie S. G./ Ed. Quantum Theory of Real Materials. Boston: Kluwer Press, 1996.
  2. Alfe D., Gillan M. J., Price G. D. Melting curve of iron at Earth's core pressures from ab initio calculations// Nature. 1999. V. 401. P. 462.
  3. Slater J. C. The theory of complex spectra// Phys. Rev. 1929. V. 34. P. 1293.
  4. Turner A. A modern valence bond study of charge-transfer processes of astrophysical interest: Ph. D. Thesis, 1995.
  5. Фларри Р. Квантовая химия. М.: Мир, 1985.
  6. Минкин В. И., Симкин Б. Я., Миняев Р. М. Теория строения молекул. Ростов-на-Дону: Феникс, 1997.
  7. Herring C. A new method for calculating wave function in crystals// Phys. Rev. 1940. V. 57. P. 1169.
  8. Slater J. C. Wave function in periodic potential// Ibid. 1937. V. 51. P. 846.
  9. Харрисон У. Теория твердого тела. М.: Мир, 1972.
  10. Dorsett H., White A. Overview of molecular modelling and ab initio molecular orbital methods suitable for use with energetic materials// DSTO Aeronautical and Maritime Research Laboratory. Australia, 2000.
  11. Романова Т. А., Краснов П. О., Качин С. В., Аврамов П. В. Теория и практика компьютерного моделирования нанообъектов. Красноярск: КГТУ, 2002. (Мультимедийное издание.)
  12. Krasheninnikov A. V. Introduction to electronic structure calculations// Lectures notes. 2002
  13. Thomas L. H.// Proc. Cambridge Philos. Soc. 1926. V. 23. P. 542; Fermi E.// Z. Phys. 1928. V. 48. P. 73.
  14. Зиненко В. И., Сорокин Б. П., Турчин П. П. Основы физики твердого тела. М.: Изд-во физ.-мат. лит., 2001.
  15. Kohanoff J., Gidopoulos N. I. Density Functional Theory: Basics, New Trends and Applications/ S. Wilson (Ed.); Handbook of Molecular Physics and Quantum Chemistry. Vol. 2, part 5, chap. 26. Chichester: John Wiley & Sons, Ltd, 2003. P. 532—568.
  16. Jones R. O., Gunnarsson O. The density functional formalism, its applications and prospects// Rev. Mod. Phys. 1989. V. 61. P. 689.
  17. March N. H.// Adv. Phys. 1957. V. 6. P. 1.
  18. March N. H.// Theor. Chem.: A Specialist’s Periodic Report. 1981. V. 4. P. 92.
  19. Lieb E. H., Simon B. Tomas-Fermi Theory Revisited// Phys. Rev. Lett. 1973. V. 31. P. 681.
  20. Lieb E.H. The stability of matter// Rev. Mod. Phys. 1976. V. 48. P. 553; Thomas-Fermi and related theories of atoms and molecules// Rev. Mod. Phys. 1981. V. 53. P. 603.
  21. Кон В. Электронная структура вещества — волновые функции и функционалы плотности// УФН. 2002. Т. 172, № 3. С. 336.
  22. Kohn W., Sham L. J. Self-Consistent equations including exchange and correlation effects// Phys. Rev. 1965. V. 140. P. A1133.
  23. Hohenberg P., Kohn W. Inhomogeneous Electron Gas// Ibid. 1964. V. 136. P. B864.
  24. Kohn W.// Highlights of Condensed-Matter Theory (Proc. of the Intern. School of Physics «Enrico Fermi», Course 89)/ Ed. F. Bassani, F. Fumi, M. P. Tosi. Amsterdam: North-Holland, 1985. P. 4.
  25. Лундквист С., Марч Н. Теория неоднородного электронного газа. М.: Мир, 1987.
  26. Payne M. C., Teter M. P., Allan D. C. et al. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients// Rev. Mod. Phys. 1992. V. 64, N 4. P. 1045.
  27. Wigner E. P. Effects of the electron interaction on the energy levels of electrons in metals// Trans. Faraday. Soc. 1938. V. 34. P. 678.
  28. Ceperly D. M. Ground state of the fermion one-component plasma: A Monte Carlo study in two and three dimensions// Phys. Rev. 1978. V. B18. P. 3126.
  29. Ceperly D. M., Alder B. J. Ground state of the electron gas by a stochastic method// Phys. Rev. Lett. 1980. V. 45. P. 566.
  30. Perdew J. P., Zunger A. Self-interaction correction to density-functional approximations for many-electron systems// Phys. Rev. 1981. V. B23. P. 5048.
  31. Cottenier S. Density Functional Theory and the family of (L)APW-methods: a step-by-step introduction/ Instituut voor Kernen Stralingsfysica, K. U. Leuven. Belgium, 2002.
  32. Fuchs M., Scheffler M. Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory// Comp. Phys. Commun. 1999. V. 119. P. 67.
  33. Perdew J. P. Density-functional approximation for the correlation energy of the inhomogeneous electron gas// Phys. Rev. 1986. V. B33. P. 8822; Perdew J. P., Chevary A., Vosko S. H. et al. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation// Ibid. 1992. V. B46. P. 6671; Perdew J. P., Wang Y. Accurate and simple analytic representation of the electron-gas correlation energy// Phys. Rev. 1992. V. B45. P. 13244; Perdew J. P., Burke K., Ernzerhof M. Generalized Gradient Approximation Made Simple// Phys. Rev. Lett. 1996. V. 77. P. 3865.
  34. Asada T., Terakura K. Generalized-gradient-approximation study of the magnetic and cohesive properties of bcc, fcc, and hcp Mn// Phys. Rev. 1993. V. B47. P. 15992.
  35. Eder M., Moroni E. G., Hafner J. Structure and magnetic properties of thin Mn/Cu(001) and CuMn/Cu(100) films// Surf. Sci. 1999. V. 423, N 1. P. 244.
  36. Pérez-Jordá J. M., Becke A. D. A density-functional study of van der Waals forces: rare gas diatomics// Chem. Phys. Lett. 1995. V. 233. P. 134.
  37. Ястребов Л. И., Кацнельсон А. А. Основы одноэлектронной теории твердого тела. М.: Наука, 1981.
  38. Fermi E.// Nuovo Cimento. 1934. V. 11. P. 157.
  39. Chelikowsky J. R. The Pseudopotential-Density Functional Method (PDFM) Applied to Nanostructures// J. Phys. D: Appl. Phys. 2000. V. 33. P. R33.
  40. Hamann D. R., Schlüter M., Chiang C. Norm-Conserving Pseudopotentials// Phys. Rev. Lett. 1979. V. 43. P. 1494.
  41. Troullier N., Martins J. L. Efficient pseudopotentials for plane-wave calculations// Phys. Rev. 1991. V. B43. P. 1993.
  42. Bachelet G., Hamann D. R., Schlüter M. Pseudopotentials that work: From H to Pu// Ibid. 1982. V. B26. P. 4199.
  43. Kerker G. P. Non-singular atomic pseudopotentials for solid state applications// J. Phys. 1980. V. C13. P. L189.
  44. Greenside H. S., Schlüter M. Pseudopotentials for the 3d transition-metal elements// Phys. Rev. 1983. V. B28. P. 535.
  45. Vanderbilt D. Soft self-consistent pseudopotentials in generalized eigenvalue formalism// Ibid. 1990. V. B41. P. 7892.
  46. Blöchl P. E. Generalized separable potentials for electronic-structure calculations// Ibid. 1990. V. B41. P. 5414.
  47. Kresse G., Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method// Ibid. 1999. V. B59. P. 1758.
  48. Laasonen K., Pasquarello A., Car R. et al. Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials// Ibid. 1993. V. B47. P. 10142.
  49. Kresse G., Hafner J. Ab initio molecular dynamics for open-shell transition metals// Ibid. 1993. V. B48. P. 13115; Kresse G., Hafner J. Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements// J. Phys.: Condens. Matter. 1994. V. 6. P. 8245; Uchiyama T., Tsukada M. Atomic and electronic structures of oxygen-adsorbed Si(001) surfaces// Phys. Rev. 1995. V. B53. P. 7917; Yamauchi J., Tsukada M., Watanabe S., Sugino O. First-principles study on energetics of c-BN(001) reconstructed surfaces// Idid. 1996. V. B54. P. 5586; Sawada H., Morikawa Y., Terakura K., Hamada N. Jahn-Teller distortion and magnetic structures in LaMnO3// Ibid. 1997. V. B56. P. 12154; Сorso D., Pasquarello A., Baldereschi A. Density-functional perturbation theory for lattice dynamics with ultrasoft pseudopotentials// Idid. 1997. V. B56. P. 11369.
  50. Kresse G., Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set// Phys. Rev. 1996. V. B54. P. 11169.
  51. Kresse G., Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set// Comput. Mater. Sci. 1996. V. 6. P. 15.
  52. Moroni E. G., Kresse G., Hafner J., Furthmüller J. Ultrasoft pseudopotentials applied to magnetic Fe, Co, and Ni: From atoms to solids// Phys. Rev. 1997. V. B56. P. 15629.
  53. Louie S. G., Froyen S., Cohen M. L. Nonlinear ionic pseudopotentials in spin-density-functional calculations// Ibid. 1982. V. B26. P. 1738.
  54. http://cst-www.nrl.navy.mil/bind/
  55. Saito R., Dresselhaus G., Dresselhaus M. S. Physical properties of Carbon Nanotubes. London: Imperial College Press, 1999.
  56. Slater J. C., Koster G. F. Simplified LCAO method for the periodic potential problem// Phys. Rev. 1954. V. 94. P. 1498.
  57. Lennard-Jones J. E.// Proc. Roy. Soc. 1924. V. A106. P. 463; Lennard-Jones J. E. Wave functions of many-electron atoms// Proc. Camb. Phil. Soc. 1931. V. 27. P. 469.
  58. Maruyama S. Molecular dynamics method for microscale heat transfer// W. J. Minkowycz, E. M. Sparrow (Eds). Advances in Numerical Heat Transfer. V. 2, Chap. 6. New York: Taylor & Francis, 2000. P. 189—226.
  59. Malescio G. Intermolecular potentials — past, present, future// Nature Materials. 2003. V. 2. P. 501.
  60. Смирнов Б. М. Скейлинг в атомной и молекулярной физике// УФН. 2001. Т. 171, № 12. С. 1291.
  61. Stoddard S. D., Ford J. Numerical Experiments on the Stochastic Behavior of a Lennard-Jones Gas System// Phys. Rev. 1973. V. A8. P. 1504.
  62. Кривцов А. М., Кривцова Н. В. Метод частиц и его использование в механике деформируемого твердого тела// Дальневосточный математический журнал. 2002. Т. 3, № 2. С. 254.
  63. Wilson N. T. The structure and dynamics of noble metal clusters: PhD Thesis, 2000.
  64. Morse P. M. Diatomic molecules according to the wave mechanics. II. Vibrational levels// Phys. Rev. 1929. V. 34. P. 57.
  65. Girifalco L. A., Weizer V. G. Application of the Morse potential function to cubic metals// Ibid. 1959. V. 114. P. 687.
  66. Stillinger F. H., Weber T. A. Computer simulation of local order in condensed phases of silicon// Ibid. 1985. V. B31. P. 5262.
  67. Watanabe T., Ohdomari I. Modeling of SiO2/Si(100) interface structure by using extended-Stillinger-Weber potential// Thin Solid Films. 1999. V. 343—344. P. 370.
  68. Nozaki T., Doyama M., Kogure Y., Yokotsuka T. Micromachining of pure silicon by molecular dynamics// Ibid. 1998. V. 334. P. 221.
  69. Abell G. C. Empirical chemical pseudopotential theory of molecular and metallic bonding// Phys. Rev. 1985. V. B31. P. 6184.
  70. Tersoff J. New empirical model for the structural properties of silicon// Phys. Rev. Lett. 1986. V. 56. P. 632.
  71. Brenner D. W., Shenderova O. A., Harrison J. A. et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons// J. Phys.: Condens. Matter. 2002. V. 14. P. 783.
  72. Brenner D. W. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films// Phys. Rev. 1990. V. B42. P. 9458.
  73. Harrison J. A., Stuart S. J., Robertson D. H., White C. T. Properties of capped nanotubes when used as SPM tips// J. Phys. Chem. 1997. V. B101. P. 9682.
  74. Belova E., Chernozatonskii L. «Spring» behavior of «bough» CNT junctions// Abstracts of 7th Biennial International Workshop Fullerenes and Atomic Clusters «IWFAC», St. Petersburg, Russia, 27 June — 1 July, 2005. P. 191.
  75. Garg A., Han J., Sinnott S. B. Interactions of Carbon-Nanotubule Proximal Probe Tips with Diamond and Graphene// Phys. Rev. Lett. 1998. V. 81. P. 2260.
  76. Garg A., Sinnott S. B. Effect of chemical functionalization on the mechanical properties of carbon nanotubes// Chem. Phys. Lett. 1998. V. 295. P. 273.
  77. Garg A., Sinnott S. B. Generalized dielectric breakdown model// Phys. Rev. 1999. V. B60. P. 786.
  78. Srivastava D., Brenner D. W., Schall J. D. et al. Predictions of enhanced chemical reactivity at regions of local conformational strain on carbon nanotubes: kinky chemistry// J. Phys. Chem. 1999. V. B103. P. 4330.
  79. Cleri F., Rosato V. Tight-binding potentials for transitions metals and alloys// Phys. Rev. 1993. V. B48. P. 22.
  80. Foiles S. M. Application of the embedded-atom method to liquid transition metals// Ibid. 1985. V. B32. P. 3409.
  81. Foiles S. M., Baskes M. I., Daw M. S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys// Ibid. 1986. V. B33. P. 7983.
  82. Daw M. S., Foiles S. M., Baskes M. I. The embedded atom method: a review of theory and applications// Mat. Sci. Rep. 1993. V. 9. P. 251.
  83. Johnson R. A. Analytic nearest-neighbor model for fcc metals// Phys. Rev. 1988. V. B37. P. 3924.
  84. Johnson R. A. Alloy models with embedded-atom method// Ibid. 1989. V. B39. P. 12554.
  85. Ercolessi F., Adams J. B. Interatomic potentials from first-principles calculations: the Force-Matching method// Europhys. Lett. 1994. V. 26. P. 583.
  86. Ercolessi F., Tosatti E., Parrinello M. Au (100) Surface Reconstruction// Phys. Rev. Lett. 1986. V. 57. P. 719.
  87. Ercolessi F., Tosatti E., Parrinello M. Simulation of gold in the glue model. Phil. Mag. 1988. V. A58. P. 213.
  88. Voter A. F., Chen S. P. Accurate interatomic potentials for nickel, aluminum and nickel-aluminum (Ni3Al)// Mater. Res. Soc. Symp. Proc. 1987. V. 82. P. 175.
  89. Chen S. P., Voter A. F., Srolovitz D. J. Computer simulation of grain boundaries in Ni/sub 3/Al: the effect of grain boundary composition// Scr. Metall. 1989. V. 20, N 10. P. 1389.
  90. Oh D., Johnson R. Simple embedded atom method model for fcc and hcp metals// J. Mater. Res. 1988. V. 3, N 3. P. 471.
  91. Pasianot R., Savino E. J. Embedded-atom method interatomic potentials for hcp metals// Phys. Rev. 1992. V. B45. P. 12704.
  92. Finnis M. W., Sinclair J. E. A simple empirical N-body potential for transition metals// Phil. Mag. 1984. V. A50. P. 45.
  93. Ackland G. J., Thetford R. An improved n-body semiempirical model for body-centered cubic transition-metals// Ibid. 1987. V. A56. P. 15.
  94. Oh D., Johnson R. Analytic embedded atom method model for bcc metals// J. Mater. Res. 1989. V. 4, N 5. P. 1195.
  95. Ercolessi F. A molecular dynamics primer// Spring College in Computational Physics/ ICTP, Trieste, June 1997.
  96. Robles M., Mustoneny V., Kaskiz K. Molecular dynamic study of a single dislocation in a two-dimensional Lennard-Jones system// Int. J. of Mod. Phys. 2003. V. C14, N 4. P. 407.
  97. Liu P., Wang Y. Theoretical study on the structure of Cu(110)-p2×1-O reconstruction// J. Phys.: Condens. Matter. 2000. V. 12. P. 3955.
  98. Shimizu A., Tachikawa H. Molecular dynamics simulation on diffusion of lithium atom pair in C150H30 cluster model for glassy carbon at very low temperatures// Electrochimica Acta. 2003. V. 48. P. 1727.
  99. Webb R., Kerford M., Way A., Wilson I. Comparison of gold and carbon cluster impacts on graphite using Molecular Dynamics simulation// Nuclear Instruments and Methods in Physics Research. 1999. V. B153. P. 284.
  100. Романова Т. А., Краснов П. О., Аврамов П. В. Изменение электронной структуры гема при образовании комплекса с оксидом азота и динамика атомного остова при физиологической температуре// Докл. РАН. 2001. Т. 380, № 2. С. 263.
  101. Tuckerman M. E., Martyna G. J. Understanding modern molecular dynamics: techniques and applications// J. Phys. Chem. 2000. V. B104. P. 159.
  102. Verlet L. Computer «experiments» on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules// Phys. Rev. 1967. V. 159. P. 98; Verlet L. Computer «experiments» on classical fluids. II. equilibrium correlation functions// Phys. Rev. 1967. V. 165. P. 201.
  103. Фейнман Р., Лейтон Р., Сэндс М. Фейнмановские лекции по физике. Т. 1. М.: Мир, 1967.
  104. Rahman A. Сorrelations in the motion of atoms in liquid argon// Phys. Rev. 1964. V. 136. P. A405.
  105. Kuronen A. Introduction to atomistic simulations// Lecture notes. 2004.
  106. Car R., Parinello M. Unified approach for molecular dynamics and density-functional theor// Phys. Rev. Lett. 1985. V. 55. P. 2471.
  107. Аврамов П. В., Овчинников С. Г. Квантово-химическое и молекулярно-динамическое моделирование структуры и свойств углеродных наноструктур и их производных. Новосибирск: Изд-во СО РАН, 2000.
  108. Soler J. M., Artacho E., Gale J. D. et al. The SIESTA method for ab-initio order-N materials simulation// J. Phys.: Condens. Matter. 2002. V. 14. P. 2745.
  109. Kim J., Mauri F., Galli G. Total-energy global optimizations using nonorthogonal localized orbitals// Phys.Rev. 1995. V. B52. P. 1640.
  110. Maseras F., Morokuma K. IMOMM: A New Ab Initio + Molecular Mechanics Geometry Optimization Scheme of Equilibrium Structures and Transition States// J. Comp. Chem. 1995. V. 16. P. 1170.
  111. Svensson M., Humbel S., Froese R. D. J. et al. ONIOM: A Multilayered Integrated MO + MM Method for Geometry Optimizations and Single Point Energy Predictions. A Test for Diels-Alder Reactions and Pt(P(t-Bu)3)2 + H2 Oxidative Addition// J. Phys. Chem. 1996. V. 100. P. 19357.
  112. Haynes P. D., Payne M. C. An ab initio linear-scaling scheme// Mol. Simul. 2000. V. 25. P. 257.
  113. Bowler D. R., Gillan M. J. Length-scale ill conditioning in linear-scaling DFT// Comp. Phys. Comm. 1998. V. 112. P. 103.
  114. Briggs E. L., Sullivan D. J., Bernholc J. Large-scale electronic structure calculations with multigrid acceleration// Phys. Rev. 1995. V. B52. P. 5471.
  115. Venkatesh P. K. Ab initio density functional theory calculations in the real space// Physica. 2002. V. B318. P. 121.
  116. Yang W. Direct calculation of electron density in density-functional theory// Phys. Rev. Lett. 1991. V. 66. P. 1438.
  117. Li X. P., Nunes R. W., Vanderbilt D. Density-matrix electronic-structure method with linear system-size scaling// Phys. Rev. 1993. V. B47. P. 10891.
  118. McWeeny R. Some recent advances in density matrix theory//. Rev. Mod. Phys. 1960. V. 32. P. 335.
  119. Kohn W. Density functional and density matrix method scaling linearly with the number of atoms// Phys. Rev. Lett. V. 76. 1996. P. 3168.
  120. Ordejon P. Order-N tight-binding methods for electronic-structure and molecular dynamics// Comput. Mat. Sci. 1998. V. 12. P. 157.
  121. Scuseria G. E. Linear scaling density functional calculations with Gaussian orbitals// J. Phys. Chem. 1999. V. A103. P. 4782.
  122. Kudin K. N., Scuseria G. E. Linear-scaling density-functional theory with Gaussian orbitals and periodic boundary conditions: Efficient evaluation of energy and forces via the fast multipole method// Phys. Rev. 2000. V. B61. P. 16440.
  123. Wannier G. H. The structure of electronic excitation levels in insulating crystals// Ibid. 1937. V. 52. P. 191.

[1] Здесь и далее используется атомная система единиц, где  

[2] См. Приложение 2.

[3] Индекс AE означает All Electron wave function   волновая функция, рассчитанная без применения приближения псевдопотенциала. В данной работе она будет называться «полной».

[4] Экранирование см. [37. с. 85].

[5] Подробности вывода можно посмотреть, например, в [37. с. 32].

[6] В данном параграфе будет подразумеваться, что энергия по Ридбергу, а не по Хартри.

[7] В случае использования схемы Слейтера Костера (Slater Koster) [56] необходимо вычислить только матрицу переноса, так как матрица перекрытия является единичной.

[8] Более подробно о ван-дер-ваальсовом притяжении можно прочесть, например, в [14].

[9] В данном случае речь не идет о поверхностном распределении заряда или о поляризационных полях.