Electronic structure calculations for solids and molecules: Theory and computational methods

Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods

Volumn 9780521815918, Issue , 2006, Pages 1-348

  Kohanoff, Jorge ^a  

^a QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; ELECTRONIC STRUCTURE; MOLECULAR PHYSICS; MOLECULES; STUDENTS; TEXTBOOKS;

COMPUTATIONAL TECHNIQUE; ELECTRONIC STRUCTURE CALCULATIONS; GRADUATE STUDENTS; HARTREE-FOCK APPROACH; HARTREE-FOCK THEORY; PRACTICAL METHOD; THEORETICAL APPROACH; THEORETICAL CHEMISTRY;

DENSITY FUNCTIONAL THEORY;

EID: 84925190172     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511755613     Document Type: Book

References (511)

1. Bloch, F. (1928). Uber die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52, 555–560.
2. Bohr, N. (1913). On the constitution of atoms and molecules. I. Phil. Mag. 26, 1–24.
3. Born, M. and Oppenheimer, J. R. (1927). Quantum theory of the molecules. Ann. d. Physik 84, 457–484.
4. Feynman, R. P. (1939). Forces in molecules. Phys. Rev. 56, 340–343.
5. Habib, S., Shizume, K., and Zurek, W. H. (1998). Decoherence, chaos, and the correspondence principle. Phys. Rev. Lett. 80, 4361–4365.
6. Handy, N. C. and Lee, A. M. (1996). The adiabatic approximation. Chem. Phys. Lett. 252, 425–430.
7. Heitler, W. and London, F. (1927). Wechselwirkung neutraler Atome und homopolare Bindung nach der Quantenmechanik. Z. Phys. 44, 455–472.
8. Hellmann, H. (1937). Einführung in die Quantenchemie. Leipzig, Deuticke.
9. Horsfield, A. P., Bowler, D. R., Fisher, A. J., Todorov, T. N., and Sánchez, C. G.Mendeleyev, D. I. (1869). The relation between the properties and atomic weights of the elements. J. Russian Chem. Soc. 1, 60–77.
10. Messiah, A. (1961). Quantum Mechanics. Amsterdam, North Holland.
11. Schrödinger, E. (1926). Quantisierung als Eigenwertproblem. Ann. d. Physik 79, 361–376.
12. Ceperley, D. M. and Alder, B. J. (1980). Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566–569.
13. Chapman, D. L. (1913). A contribution to the theory of electrocapillarity. Philos. Mag. 25, 475–481.
14. Debye, P. and Hückel, E. (1923). Zur Theorie der Elektrolyte. Phys. Z. 24, 185–206.
15. Fetter, A. and Walecka, J. D. (1971). Quantum Theory of Many-Particle Systems. New York, McGraw-Hill.
16. Feynman, R. P. (1998). Statistical Mechanics: a Set of Lectures. Advanced Book Classics. Reading, MA, Perseus.
17. Gouy, G. (1910). Sur la constitution de la charge électrique à la surface d’un électrolyte. J. Phys. Theor. Appl. 9, 455–468.
18. Hansen, J.-P. and McDonald, I. R. (1976). Theory of Simple Liquids. London, Academic Press.
19. Ortiz, G. and Ballone, P. (1994). Correlation energy, structure factor, radial distribution function, and momentum distribution of the spin-polarized uniform electron gas. Phys. Rev. B 50, 1391–1405.
20. Parr, R. G. and Yang, W. (1989). Density Functional Theory of Atoms and Molecules. Oxford, Oxford University Press.
21. Zaremba, E. and Kohn, W. (1976). Van der Waals interaction between an atom and a solid surface. Phys. Rev. B 13, 2270–2285.
22. Bartlett, R. J. (1989). Coupled-cluster approach to molecular structure and spectra: a step toward predictive quantum chemistry. J. Phys. Chem. 93, 1697–1708.
23. Davidson, E. R. (1975). The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comput. Phys. 17, 87–94.
24. Fetter, A. and Walecka, J. D. (1971). Quantum Theory of Many-Particle Systems. New York, McGraw-Hill.
25. Fock, V. (1930). Näherungsmethode zur Losung des quantenmechanischen Mehrkörperprobleme. Z. Phys. 61, 126–148.
26. Hartree, D. R. (1928). The wave mechanics of an atom with a non-coulomb central field. I. Theory and methods. Proc. Cambridge Phil. Soc. 24, 89–110.
27. Helgaker, T., Jørgensen, P., and Olsen, J. (2000). Molecular Electronic-Structure Theory. Chichester, Wiley.
28. Hylleraas, E. A. (1929). Calculation of the energy of helium. Z. Phys. 54, 347–366.
29. Jensen, F. (1999). Introduction to Computational Chemistry. Chichester, Wiley.
30. Klopper, W., Röhse, R., and Kutzelnigg, W. (1991). CID and CEPA calculations with linear r12 terms. Chem. Phys. Lett. 178, 455–461.
31. Koopmans, T. A. (1933). Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms. Physica 1, 104–113.
32. Messiah, A. (1961). Quantum Mechanics. Amsterdam, North Holland.
33. Møller, C. and Plesset, M. S. (1934). Note on an approximation treatment for many-electron systems. Phys. Rev. 46, 618–622.
34. Pople, J. A. and Beveridge, D. L. (1970). Approximate Molecular Orbital Theory. Advanced Chemistry, London, McGraw-Hill.
35. Slater, J. C. (1928). The self-consistent field and the structure of atoms. Phys. Rev. 32, 339–348.
36. Slater, J. C. (1930). Note on Hartree's method. Phys. Rev. 35, 210–211.
37. Szabo, A. and Ostlund, N. S. (1989). Modern Quantum Chemistry. New York, McGraw-Hill.
38. Dirac, P. A. M. (1930). Note on exchange phenomena in the Thomas atom. Proc. Cambridge Phil. Soc. 26, 376–385.
39. Fermi, E. (1928). A statistical method for the determination of some properties of atoms. II. Application to the periodic system of the elements. Z. Phys. 48, 73–79.
40. Görling, A. (1996). Density-functional theory for excited states. Phys. Rev. A 54, 3912–3915.
41. Hedin, L. (1965). New method for calculating the one-particle Green's function with application to the electron-gas problem. Phys. Rev. 139, A796–823.
42. Hohenberg, P. and Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev. 136, B864–867.
43. Janak, J. F. (1978). Proof that in density-functional theory. Phys. Rev. B 18, 7165–7168.
44. Jones, R. O. and Gunnarsson, O. (1989). The density functional formalism, its applications and prospects. Rev. Mod. Phys. 61, 689–746.
45. Kittel, C. (1996). Introduction to Solid State Physics, 7th edn. New York, Wiley.
46. Kohn, W. (1983). v-representability and density functional theory. Phys. Rev. Lett. 51, 1596–1598.
47. Kohn, W. and Sham, L. (1965). Self-consistent equations including exchange and correlation effects. Phys. Rev. 14, A1133–1138.
48. Koopmans, T. A. (1933). Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms. Physica 1, 104–113.
49. Langreth, D. C. and Perdew, J. P. (1977). Exchange-correlation energy of a metallic surface: wave-vector analysis. Phys. Rev. B 15, 2884–2901.
50. Leininger, T., Stoll, H., Werner, H.-J., and Savin, A. (1997). Combining long-range configuration interaction with short-range density functionals. Chem. Phys. Lett. 275, 151–160.
51. Levy, M. (1982). Electron densities in search of Hamiltonians. Phys. Rev. A 26, 1200–1208.
52. March, N. H. (1992). Electron Density Theory of Atoms and Molecules. London, Academic Press.
53. Oda, T., Pasquarello, A., and Car, R. (1998). Fully unconstrained approach to noncollinear magnetism: application to small Fe clusters. Phys. Rev. Lett. 80, 3622–3625.
54. Pederson, M. and Jackson, K. A. (1991). Pseudoenergies for simulations on metallic systems. Phys. Rev. B 43, 7312–7315.
55. Perdew, J. P. and Wang, Y. (1992). Pair-distribution function and its coupling-constant average for the spin-polarized electron gas. Phys. Rev. B 46, 12947–12954.
56. Perdew, J. P. and Zunger, A. (1981). Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048–5079.
57. Petersilka, M., Gossmann, U. J., and Gross, E. K. U. (1996). Excitation energies from time-dependent density-functional theory. Phys. Rev. Lett. 76, 1212–1215.
58. Pollet, R., Savin, A., Leininger, T., and Stoll, H. (2002). Combining multideterminantal wave functions with density functionals to handle near-degeneracy in atoms and molecules. J. Chem. Phys. 116, 1250–1258.
59. Slater, J. C. (1951). A simplification of the Hartree–Fock method. Phys. Rev. 81, 385–390.
60. Slater, J. C. (1974). Quantum Theory of Molecules and Solids. New York, McGraw-Hill.
61. Stoll, H. and Savin, A. (1985). Density functionals for correlation energies of atoms and molecules. In Density Functional Methods in Physics, R. M. Dreizler and J. da Providencia, eds. New York, Plenum Press.
62. Theophilou, A. K. (1979). The energy density functional formalism for excited states. J. Phys. C 12, 5419–5430.
63. Thomas, L. H. (1927). The calculation of atomic fields. Proc. Cambridge Phil. Soc. 23, 542–548.
64. Valiev, M. M. and Fernando, G. W. (1995). Occupation numbers in density-functional calculations. Phys. Rev. B 52, 10697–10700.
65. Vogel, D., Krüger, P., and Pollmann, J. (1995). Ab initio electronic-structure calculations for II-VI semiconductors using self-interaction-corrected pseudopotentials. Phys. Rev. B 52, 14316–14319.
66. Von Barth, U. and Hedin, L. (1972). A local exchange-correlation potential for the spin polarized case. I. J. Phys. C 5, 1629–1642.
67. Wigner, E. P. (1938). Effects of electron interaction on the energy levels of electrons in metals. Trans. Faraday Soc. 34, 678–685.
68. Adamo, C., Ernzerhof, M., and Scuseria, G. E. (2000). The meta-GGA functional: thermochemistry with a kinetic energy density dependent exchange-correlation functional. J. Chem. Phys. 112, 2643–2649.
69. Alonso, J. A. and Girifalco, L. A. (1978). Nonlocal approximation to the exchange potential and kinetic energy of an inhomogeneous electron gas. Phys. Rev. B 17, 3735–3743.
70. Andersson, Y., Langreth, D. C., and Lundqvist, B. I. (1996). Van der Waals interactions in density-functional theory. Phys. Rev. Lett. 76, 102–105.
71. Anisimov, V. I., Zaanen, J., and Andersen, O. K. (1991). Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 44, 943–954.
72. Anisimov, V. I., Aryasetiawan, F., and Lichtenstein, A. I. (1997). First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+U method. J. Phys. Condens. Matter 9, 767–808.
73. Aryasetiawan, F. (1992). Self-energy of ferromagnetic nickel in the GW approximation. Phys. Rev. B 46, 13051–13064.
74. Aryasetiawan, F. and Gunnarsson, O. (1995). Electronic structure of NiO in the GW approximation. Phys. Rev. Lett. 74, 3221–3224.
75. Aulbur, W. G., Städele, M., and Görling, A. (2000). Exact-exchange-based quasiparticle calculations. Phys. Rev. B 62, 7121–7132.
76. Aziz, R. A. and Slaman, M. J. (1991). An examination of ab initio results for the helium potential energy curve. J. Chem. Phys. 94, 8047–8053.
77. Baroni, S. and Tuncel, E. (1983). Exact-exchange extension of the local-spin-density approximation in atoms: calculation of total energies and electron affinities. J. Chem. Phys. 79, 6140–6144.
78. Becke, A. D. (1986). Density functional calculations of molecular bond energies. J. Chem. Phys. 84, 4524–4529.
79. Becke, A. D. (1988). Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098–3100.
80. Becke, A. D. (1993). Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648–5652.
81. Becke, A. D. (1998). A new inhomogeneity parameter in density-functional theory. J. Chem. Phys. 109, 2092–2098.
82. Biermann, S., Aryasetiawan, F., and Georges, A. (2003). First-principles approach to the electronic structure of strongly correlated systems: combining the GW approximation and dynamical mean-field theory. Phys. Rev. Lett. 90, 086402.
83. Bylander, D. M. and Kleinman, L. (1990). Good semiconductor band gaps with a modified local-density approximation. Phys. Rev. B 41, 7868–7871.
84. Bylander, D. M. and Kleinman, L. (1995). Energy gaps and cohesive energy of Ge from the optimized effective potential. Phys. Rev. Lett. 74, 3660–3663.
85. Ceperley, D. M. and Alder, B. J. (1980). Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566–569.
86. Charlesworth, J. P. A. (1996). Weighted-density approximation in metals and semiconductors. Phys. Rev. B 53, 12666–12673.
87. Colle, R. and Salvetti, D. (1975). Approximate calculation of the correlation energy for the closed shells. Theor. Chim. Acta 37, 329–334.
88. Della Salla, F. and Görling, A. (2001). Efficient localized Hartree–Fock methods as effective exact-exchange Kohn–Sham methods for molecules. J. Chem. Phys. 115, 5718–5732.
89. Denton, A. R. and Ashcroft, N. W. (1989). Modified weighted-density-functional theory of nonuniform classical liquids. Phys. Rev. A 39, 4701–4708.
90. Dobson, J. F. and Dinte, B. P. (1996). Constraint satisfaction in local and gradient susceptibility approximations: application to a van der Waals density functional. Phys. Rev. Lett. 76, 1780–1783.
91. Engel, E. and Vosko, S. H. (1993). Accurate optimized-potential-model solutions for spherical spin-polarized atoms: evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations. Phys. Rev. A 47, 2800–2811.
92. Engel, E., Höck, A., and Dreizler, R. M. (2000). Van der Waals bonds in density-functional theory. Phys. Rev. A 61, 032502.
93. Ernzerhof, M. (1996). Construction of the adiabatic connection. Chem. Phys. Lett. 263, 499–506.
94. Ernzerhof, M. and Scuseria, G. E. (1999). Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional. J. Chem. Phys. 110, 5029–5036.
95. Fetter, A. and Walecka, J. D. (1971). Quantum Theory of Many-Particle Systems. New York, McGraw-Hill.
96. Filippi, C., Umrigar, C. J., and Taut, M. (1994). Comparison of exact and approximate density functionals for an exactly soluble model. J. Chem. Phys. 100, 1290–1295.
97. Filippi, C., Gonze, X., and Umrigar, C. J. (1996). Generalized gradient approximations to density functional theory: comparison with exact results. In Recent Developments and Applications of Density Functional Theory, J. M. Seminario, ed. Amsterdam, Elsevier.
98. García-González, P., Alvarellos, J. E., Chacón, E., and Tarazona, P. (2000). Image potential and the exchange-correlation weighted density approximation functional. Phys. Rev. B 62, 16063–16068.
99. Garza, J., Nichols, J. A., and Dixon, D. A. (2000). The optimized effective potential and the self-interaction correction in density functional theory: application to molecules. J. Chem. Phys. 112, 7880–7890.
100. Gell-Mann, M. and Brueckner, K. A. (1957). Correlation energy of an electron gas at high density. Phys. Rev. 106, 364–368.
101. Ghosh, S. K. and Parr, R. G. (1986). Phase-space approach to the exchange-energy functional of density-functional theory. Phys. Rev. A 34, 785–791.
102. Godby, R. W., Schluter, M., and Sham, L. J. (1986). Accurate exchange-correlation potential for silicon and its discontinuity on addition of an electron. Phys. Rev. Lett. 56, 2415–2418.
103. Görling, A. (1996). Exact treatment of exchange in Kohn–Sham band-structure schemes. Phys. Rev. B 53, 7024–7029.
104. Görling, A. (1999). New KS method for molecules based on an exchange charge density generating the exact local KS exchange potential. Phys. Rev. Lett. 83, 5459–5462.
105. Görling, A. and Ernzerhof, M. (1995). Energy differences between Kohn–Sham and Hartree–Fock wave functions yielding the same electron density. Phys. Rev. A 51, 4501–4513.
106. Görling, A. and Levy, M. (1993). Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion. Phys. Rev. B 47, 13105–13113.
107. Görling, A. and Levy, M. (1994). Exact Kohn–Sham scheme based on perturbation theory. Phys. Rev. A 50, 196–204.
108. Görling, A. and Levy, M. (1997). Hybrid schemes combining the Hartree–Fock method and density-functional theory: underlying formalism and properties of correlation functionals. J. Chem. Phys. 106, 2675–2680.
109. Grabo, T., Kreibich, T., Kurth, S., and Gross, E. K. U. (1998). Orbital functionals in density functional theory: the optimized effective potential method. In Strong Coulomb Correlations in Electronic Structure: Beyond the Local Density Approximation, V. I. Anisimov, ed. Tokyo, Gordon & Breach.
110. Grabowski, I., Hirata, S., Ivanov, S., and Bartlett, R. J. (2002). Ab initio density functional theory: OEP-MBPT(2). A new orbital-dependent correlation functional. J. Chem. Phys. 116, 4415–4425.
111. Gross, E. K. U. and Dreizler, R. M. (1981). Gradient expansion of the Coulomb exchange energy. Z. Phys. A 302, 103–106.
112. Grüning, M., Gritsenko, O. V., and Baerends, E. J. (2004). Improved description of chemical barriers with generalized gradient approximations (GGAs) and meta-GGAs. J. Phys. Chem. A 108, 4459–4469.
113. Gunnarsson, O. and Jones, R. O. (1980). Density functional calculations for atoms, molecules and clusters. Phys. Scr. 21, 394–401.
114. Hammer, B., Hansen, L. B., and Nørskov, J. K. (1999). Improved adsorption energetics within density-functional theory using revised Perdew–Burke–Ernzerhof functionals. Phys. Rev. B 59, 7413–7421.
115. Handy, N. C. and Cohen, A. J. (2001). Left–right correlation energy. Mol. Phys. 99, 403–412.
116. Hedin, L. (1965). New method for calculating the one-particle Green's function with application to the electron-gas problem. Phys. Rev. 139, A796–823.
117. Holm, B. (1999). Total energies from GW calculation. Phys. Rev. Lett. 83, 788–791.
118. Holm, B. and von Barth, U. (1998). Fully self-consistent GW self-energy of the electron gas. Phys. Rev. B 57, 2108–2117.
119. Hubbard, J. (1965). Electron correlations in narrow energy bands. IV. The atomic representation. Proc. Roy. Soc. London 285, 542–560.
120. Hybertsen, M. S. and Louie, S. G. (1985). First-principles theory of quasiparticles: calculation of band gaps in semiconductors and insulators. Phys. Rev. Lett. 55, 1418–1421.
121. Ivanov, S., Hirata, S., and Bartlett, R. J. (1999). Exact exchange treatment for molecules in finite-basis-set Kohn–Sham theory. Phys. Rev. Lett. 83, 5455–5458.
122. Ivanov, S., Hirata, S., Grabowski, I., and Bartlett, R. J. (2003). Connections between second-order Görling–Levy and many-body perturbation approaches in density functional theory. J. Chem. Phys. 118, 461–470.
123. Jones, R. O. and Gunnarsson, O. (1989). The density functional formalism, its applications and prospects. Rev. Mod. Phys. 61, 689–746.
124. Kohanoff, J. and Gidopoulos, N. I. (2003). Density functional theory: basics, new trends and applications. In Handbook of Molecular Physics and Quantum Chemistry, S. Wilson, ed., Vol. 2. Chichester, Wiley, Chapter 26, 532–568.
125. Kohn, W. (1986). Discontinuity of the exchange-correlation potential from a density-functional viewpoint. Phys. Rev. B 33, 4331–4333.
126. Kohn, W. and Sham, L. (1965). Self-consistent equations including exchange and correlation effects. Phys. Rev. 14, A1133–1138.
127. Kohn, W., Meir, Y., and Makarov, D. E. (1998). Van der Waals energies in density functional theory. Phys. Rev. Lett. 80, 4153–4156.
128. Kotani, T. (1994). Exact exchange-potential band-structure calculations by the LMTO-ASA method: MgO and CaO. Phys. Rev. B 50, 14816–14821.
129. Krieger, J. B., Li, Y., and Iafrate, G. J. (1992). Construction and application of an accurate local spin-polarized Kohn–Sham potential with integer discontinuity: exchange-only theory. Phys. Rev. A 45, 101–126.
130. Krieger, J. B., Chen, J., Iafrate, G. J., and Savin, A. (1999). Construction of an accurate self-interaction-corrected correlation energy functional based on an electron gas with a gap. In Electron Correlations and Materials Properties, A. Gonis and N. Kioussis, eds. New York, Plenum Press.
131. Kurth, S. and Perdew, J. P. (1999). Density-functional correction of random-phase approximation correlation with results for jellium surface energies. Phys. Rev. B 59, 10461–10468.
132. Langreth, D. C. and Mehl, M. J. (1981). Easily implementable nonlocal exchange-correlation energy functional. Phys. Rev. Lett. 47, 446–450.
133. Langreth, D. C. and Perdew, J. P. (1977). Exchange-correlation energy of a metallic surface: wave-vector analysis. Phys. Rev. B 15, 2884–2901.
134. Lee, C., Yang, W., and Parr, R. G. (1988). Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785–789.
135. Leininger, T., Stoll, H., Werner, H.-J., and Savin, A. (1997). Combining long-range configuration interaction with short-range density functionals. Chem. Phys. Lett. 275, 151–160.
136. Levy, M. and Perdew, J. P. (1985). Hellmann–Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms. Phys. Rev. A 32, 2010–2021.
137. Levy, M., Perdew, J. P., and Sahni, V. (1984). Exact differential equation for the density and ionization energy of a many-particle system. Phys. Rev. A 30, 2745–2748.
138. Li, Y., Krieger, J. B., and Iafrate, G. J. (1992). Negative ions as described by Kohn–Sham exchange-only theory. Chem. Phys. Lett. 191, 38–46.
139. Li, Y., Krieger, J. B., and Iafrate, G. J. (1993). Self-consistent calculations of atomic properties using self-interaction-free exchange-only Kohn–Sham potentials. Phys. Rev. A 47, 165–181.
140. Lieb, E. H. and Oxford, S. (1981). Improved lower bound on the indirect Coulomb energy. Int. J. Quantum Chem. 19, 427–439.
141. Lutsko, J. F. and Baus, M. (1990). Can the thermodynamic properties of a solid be mapped onto those of a liquid? Phys. Rev. Lett. 64, 761–763.
142. Ma, S.-K. and Brueckner, K. A. (1968). Correlation energy of an electron gas with a slowly varying high density. Phys. Rev. 165, 18–31.
143. Misawa, S. (1965). Ferromagnetism of an electron gas. Phys. Rev. 140, A1645–A1648.
144. Nekovee, M., Foulkes, W. M. C., and Needs, R. J. (2001). Quantum Monte Carlo analysis of exchange and correlation in the strongly inhomogeneous electron gas. Phys. Rev. Lett. 87, 036401.
145. Perdew, J. P. (1985). Accurate density functional for the energy: real-space cutoff of the gradient expansion for the exchange hole. Phys. Rev. Lett. 55, 1665–1668.
146. Perdew, J. P. and Levy, M. (1983). Physical content of the exact Kohn–Sham orbital energies: band gaps and derivative discontinuities. Phys. Rev. Lett. 51, 1884–1887.
147. Perdew, J. P. and Norman, M. R. (1982). Electron removal energies in Kohn–Sham density-functional theory. Phys. Rev. B 26, 5445–5450.
148. Perdew, J. P. and Schmidt, K. (2001). Jacob's ladder of density functional approximations for the exchange-correlation energy. In Density Functional Theory and its Application to Materials. Vol. 577. New York, American Institute of Physics, 1–20.
149. Perdew, J. P. and Wang, Y. (1992a). Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45, 13244–13249.
150. Perdew, J. P. and Wang, Y. (1992b). Pair-distribution function and its coupling-constant average for the spin-polarized electron gas. Phys. Rev. B 46, 12947–12954.
151. Perdew, J. P. and Zunger, A. (1981). Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048–5079.
152. Perdew, J. P., Parr, R. G., Levy, M., and Balduz, J. L. (1982). Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys. Rev. Lett. 49, 1691–1694.
153. Perdew, J. P., Burke, K., and Ernzerhof, M. (1996). Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868.
154. Perdew, J. P., Kurth, S., Zupan, A., and Blaha, P. (1999). Accurate density functional with correct formal properties: a step beyond the generalized gradient approximation. Phys. Rev. Lett. 82, 2544–2547.
155. Perdew, J. P., Tao, J., Staroverov, V. N., and Scuseria, G. E. (2004). Meta-generalized gradient approximation: explanation of a realistic nonempirical density functional. J. Chem. Phys. 120, 6898–6911.
156. Rapcewicz, K. and Ashcroft, N. W. (1991). Fluctuation attraction in condensed matter: a nonlocal functional approach. Phys. Rev. B 44, 4032–4035.
157. Rojas, H. N., Godby, R. W., and Needs, R. J. (1995). Space-time method for ab initio calculations of self-energies and dielectric response functions of solids. Phys. Rev. Lett. 74, 1827–1830.
158. Rushton, P. P., Tozer, D. J., and Clark, S. J. (2002a). Description of exchange and correlation in the strongly inhomogeneous electron gas using a nonlocal density functional. Phys. Rev. B 65, 193106.
159. Rushton, P. P., Tozer, D. J., and Clark, S. J. (2002b). Nonlocal density-functional description of exchange and correlation in silicon. Phys. Rev. B 65, 235203.
160. Sahni, V., Gruenebaum, J., and Perdew, J. P. (1982). Study of the density-gradient expansion for the exchange energy. Phys. Rev. B 26, 4371–4377.
161. Savrasov, S., Kotliar, G., and Abrahams, E. (2000). Correlated electrons in d-plutonium within a dynamical mean-field picture. Nature (London) 410, 793–795.
162. Schindlmayr, A. and Godby, R. W. (1998). Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation. Phys. Rev. Lett. 80, 1702–1705.
163. Seidl, A., Görling, A., Vogl, P., Majewski, J. A., and Levy, M. (1996). Generalized Kohn–Sham schemes and the band-gap problem. Phys. Rev. B 53, 3764–3774.
164. Seidl, M., Perdew, J. P., and Levy, M. (1999). Strictly correlated electrons in density-functional theory. Phys. Rev. A 59, 51–54.
165. Seidl, M., Perdew, J. P., and Kurth, S. (2000a). Density functionals for the strong-interaction limit. Phys. Rev. A 62, 012502.
166. Seidl, M., Perdew, J. P., and Kurth, S. (2000b). Simulation of all-order density-functional perturbation theory, using the second order and the strong-correlation limit. Phys. Rev. Lett. 84, 5070–5073.
167. Sham, L. J. and Schlüter, M. (1983). Density-functional theory of the energy gap. Phys. Rev. Lett. 51, 1888–1891.
168. Sharp, R. T. and Horton, G. K. (1953). A variational approach to the unipotential many-electron problem. Phys. Rev. 90, 317–317.
169. Singh, D. J. (1993). Weighted-density-approximation ground-state studies of solids. Phys. Rev. B 48, 14099–14103.
170. Singwi, K. S., Tosi, M. P., Land, R. H., and Sjölander, A. (1968). Electron correlations at metallic densities. Phys. Rev. 176, 589–599.
171. Slater, J. C. (1951). A simplification of the Hartree–Fock method. Phys. Rev. 81, 385–390.
172. Städele, M., Majewski, J. A., Vogl, P., and Görling, A. (1997). Exact Kohn–Sham exchange potential in semiconductors. Phys. Rev. Lett. 79, 2089–2092.
173. Städele, M., Moukara, M., Majewski, J. A., Vogl, P., and Görling, A. (1999). Exact exchange Kohn–Sham formalism applied to semiconductors. Phys. Rev. B 59, 10031–1043.
174. Staroverov, V. N., Scuseria, G. E., Tao, J., and Perdew, J. P. (2003). Comparative assessment of a new nonempirical density functional: molecules and hydrogen-bonded complexes. J. Chem. Phys. 119, 12129–12137.
175. Svendsen, P. S. and von Barth, U. (1996). Gradient expansion of the exchange energy from second-order density response theory. Phys. Rev. B 54, 17402–17413.
176. Talman, J. D. and Shadwick, W. F. (1976). Optimized effective atomic central potential. Phys. Rev. A 14, 36–40.
177. Tao, J., Gori-Giorgi, P., Perdew, J. P., and McWeeny, R. (2001). Uniform electron gas from the Colle–Salvetti functional: missing long-range correlations. Phys. Rev. A 63, 032513.
178. Tao, J., Perdew, J. P., Staroverov, V. N., and Scuseria, G. E. (2003). Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. Phys. Rev. Lett. 91, 146401.
179. Toulouse, J., Savin, A., and Adamo, C. (2002). Validation and assessment of an accurate approach to the correlation problem in density functional theory: the Krieger–Chen–Iafrate–Savin model. J. Chem. Phys. 117, 10465–10473.
180. Van Gisbergen, S. J. A., Schipper, P. R. T., Gritsenko, O. V., Baerends, E. J., Snijders, J. G., Champagne, B., and Kirtman, B. (1999). Electric field dependence of the exchange-correlation potential in molecular chains. Phys. Rev. Lett. 83, 694–697.
181. Van Voorhis, T. and Scuseria, G. E. (1998). A novel form for the exchange-correlation energy functional. J. Chem. Phys. 109, 400–410.
182. Von Barth, U. and Hedin, L. (1972). A local exchange-correlation potential for the spin polarized case. I. J. Phys. C 5, 1629–1642.
183. Von Weizsäcker, C. F. (1935). Zur Theorie der Kernmassen. Z. Phys. 96, 431–458.
184. Vosko, S. H., Wilk, L., and Nusair, M. (1980). Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 58, 1200–1211.
185. Yan, Z., Perdew, J. P., and Kurth, S. (2000). Density functional for short-range correlation: accuracy of the random-phase approximation for isoelectronic energy changes. Phys. Rev. B 61, 16430–16439.
186. Zaremba, E. and Kohn, W. (1976). Van der Waals interaction between an atom and a solid surface. Phys. Rev. B 13, 2270–2285.
187. Zhang, Y. and Yang, W. (1998). Comment on “generalized gradient approximation made simple”. Phys. Rev. Lett. 80, 890–891.
188. Alavi, A., Kohanoff, J., Parrinello, M., and Frenkel, D. (1995). Ab initio molecular dynamics with excited electrons. Phys. Rev. Lett. 73, 2599–2602.
189. Allen, M. P. and Tildesley, D. J. (1987). Computer Simulation of Liquids. Oxford, Clarendon Press.
190. Arteca, G. A., Cachau, R. E., and Veluri, K. (2000). Structural complexity of hydrogen-bonded networks. Chem. Phys. Lett. 319, 719–724.
191. Baldereschi, A. (1973). Mean-value point in the Brillouin zone. Phys. Rev. B 7, 5212–5215.
192. Bloch, F. (1928). Über die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52, 555–560.
193. Chadi, D. J. and Cohen, M. L. (1973). Special points in the Brillouin zone. Phys. Rev. B 8, 5747–5753.
194. Fu, C.-L. and Ho, K.-M. (1983). First-principles calculation of the equilibrium ground-state properties of transition metals: applications to Nb and Mo. Phys. Rev. B 28, 5480–5486.
195. Fu, C.-L. and Ho, K.-M. (1989). External-charge-induced surface reconstruction on Ag(110). Phys. Rev. Lett. 63, 1617–1620.
196. Gilat, G. and Raubenheimer, L. J. (1966). Accurate numerical method for calculating frequency-distribution functions in solids. Phys. Rev. B 144, 390–395.
197. Harrison, W. A. (1980). Electronic Structure and the Properties of Solids. San Francisco, Freeman.
198. Hockney, R. W. and Eastwood, J. W. (1981). Computer Simulation Using Particles. New York, McGraw-Hill.
199. Jepsen, O. and Andersen, O. K. (1971). The electronic structure of h.c.p. Ytterbium. Solid State Comm. 9, 1763–1767.
200. Kittel, C. (1996). Introduction to Solid State Physics, 7th edn. New York, Wiley.
201. Lehmann, G. and Taut, M. (1972). Numerical calculation of the density of states and related properties. Phys. Status Solidi 54, 469–477.
202. Lozovoi, A. Y. and Alavi, A. (2003). Reconstruction of charged surfaces: general trends and a case study of Pt(110) and Au(110). Phys. Rev. B 68, 245416.
203. Lozovoi, A. Y., Alavi, A., Kohanoff, J., and Lynden-Bell, R. M. (2001). Ab initio simulation of charged slabs at constant chemical potential. J. Chem. Phys. 115, 1661–1669.
204. Makov, G. and Payne, M. (1995). Periodic boundary conditions in ab initio calculations. Phys. Rev. B 51, 4014–4022.
205. Marzari, N., Vanderbilt, D., and Payne, M. C. (1997). Ensemble density-functional theory for ab initio molecular dynamics of metals and finite-temperature insulators. Phys. Rev. Lett. 79, 1337–1340.
206. Mermin, N. D. (1965). Thermal properties of the inhomogeneous electron gas. Phys. Rev. 137, A1441–1443.
207. Methfessel, M. and Paxton, A. T. (1989). High-precision sampling for Brillouin-zone integration in metals. Phys. Rev. B 40, 3616–3621.
208. Monkhorst, H. J. and Pack, J. D. (1976). Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192.
209. Moreno, J. and Soler, J. M. (1992). Optimal meshes for integrals in real- and reciprocal-space unit cells. Phys. Rev. B 45, 13891–13898.
210. Rath, J. and Freeman, A. J. (1975). Generalized magnetic susceptibilities in metals: application of the analytic tetrahedron linear energy method to Sc. Phys. Rev. B 11, 2109–2117.
211. Sánchez, C. G. (2003). Molecular reorientation of water adsorbed on charged Ag(111) surfaces. Surface Science 527, 1–11.
212. Sánchez, C. G., Lozovoi, A. Y., and Alavi, A. (2004). Field evaporation from first principles. Mol. Phys. 102, 1045–1055.
213. Sprik, M., Hutter, J., and Parrinello, M. (1996). Ab initio molecular dynamics simulation of liquid water: comparison of three gradient-corrected density functionals. J. Chem. Phys. 105, 1142–1152.
214. Appelbaum, J. A. and Hamann, D. R. (1973). Self-consistent pseudopotential for Si. Phys. Rev. B 8, 1777–1780.
215. Bachelet, G. B. and Schlüter, M. (1982). Relativistic norm-conserving pseudopotentials. Phys. Rev. B 25, 2103–2108.
216. Bachelet, G. B., Hamann, D. R., and Schlüter, M. (1982). Pseudopotentials that work: from H to Pu. Phys. Rev. B 26, 4199–4228.
217. Blöchl, P. E. (1990). Generalized separable potentials for electronic-structure calculations. Phys. Rev. B 41, 5414–5416.
218. Engel, G. E. and Needs, R. J. (1990). Calculations of the structural properties of cubic zinc sulfide. Phys. Rev. B 41, 7876–7878.
219. Giannozzi, P. (2004). Notes on Pseudopotential Generation. Scuola Normale Superiore di Pisa. www.nest.sns.it/giannozz/software.html.
220. Gonze, X., Käckell, P., and Scheffler, M. (1990). Ghost states for separable, norm-conserving, ab initio pseudopotentials. Phys. Rev. B 41, 12264–12267.
221. Gonze, X., Stumpf, R., and Scheffler, M. (1991). Analysis of separable potentials. Phys. Rev. B 44, 8503–8513.
222. Hamann, D. R. (1989). Generalized norm-conserving pseudopotentials. Phys. Rev. B 40, 2980–2987.
223. Hamann, D. R., Schlüter, M., and Chiang, C. (1979). Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494–1497.
224. Herman, F. and Skillman, S. (1963). Atomic Structure Calculations. New Jersey, Prentice-Hall.
225. Herring, C. (1940). A new method for calculating wave functions in crystals. Phys. Rev. 57, 1169–1177.
226. Kerker, G. P. (1980). Nonsingular atomic pseudopotentials for solid state applications. J. Phys. C 13, L189–L194.
227. Kleinman, L. (1980). Relativistic norm-conserving pseudopotential. Phys. Rev. B 21, 2630–2631.
228. Kleinman, L. and Bylander, D. M. (1982). Efficacious form for model pseudopotentials. Phys. Rev. Lett. 48, 1425–1428.
229. Koelling, D. D. and Harmon, B. N. (1977). A technique for relativistic spin-polarized calculations. J. Phys. C 10, 3107–3114.
230. Koval, S. F., Kohanoff, J., Lasave, J., Colizzi, G., and Migoni, R. L. (2005). Ferroelectricity and isotope effects in hydrogen-bonded crystals: the case of KDP. Phys. Rev. B 71, 184102.
231. Lin, J. S., Qteish, A., Payne, M. C., and Heine, V. (1993). Optimized and transferable nonlocal separable ab initio pseudopotentials. Phys. Rev. B 47, 4174–4180.
232. Louie, S. B., Froyen, S., and Cohen, M. L. (1982). Nonlinear ionic pseudopotentials in spin-density-functional calculations. Phys. Rev. B 26, 1738–1742.
233. MacDonald, A. H. and Vosko, S. H. (1979). A relativistic density functional formalism. J. Phys. C 12, 2977–2990.
234. Philips, J. C. and Kleinman, L. (1959). New method for calculating wave functions in crystals and molecules. Phys. Rev. 116, 287–294.
235. Rappe, A. M., Rabe, M., Kaxiras, E., and Joannopoulos, J. D. (1990). Optimized pseudopotentials. Phys. Rev. B 41, 1227–1230.
236. Schiff, L. I. (1955). Quantum Mechanics. New York, McGraw-Hill.
237. Shaw, R. W. and Harrison, J. W. A. (1967). Reformulation of the screened Heine–Abarenkov model potential. Phys. Rev. 163, 604–611.
238. Slater, J. C. (1937). Wave functions in a periodic potential. Phys. Rev. 51, 846–851.
239. Soler, J. M., Artacho, E., Gale, J. D., García, A. I., Junquera, J., Ordejón, P., and Sánchez-Portal, D. (2002). The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14, 2745–2780.
240. Topp, W. C. and Hopfield, J. J. (1973). Chemically motivated pseudopotential for sodium. Phys. Rev. B 7, 1295–1303.
241. Troullier, N. and Martins, J. L. (1991). Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006.
242. Vanderbilt, D. (1990). Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892–7895.
243. Zhu, J., Wang, X. W., and Louie, S. G. (1992). First-principles pseudopotential calculations for magnetic iron. Phys. Rev. B 45, 8887–8893.
244. Andersen, O. K. (1971). In Computational Methods in Band Theory, J. F. J. P. M. Marcus and A. R. Williams, eds. New York, Plenum Press, 178.
245. Andersen, O. K. (1975). Linear methods in band theory. Phys. Rev. B 12, 3060–3083.
246. Andersen, O. K. (1984). Linear methods in band theory. In The Electronic Structure of Complex Systems, P. Phariseau and W. M. Temmerman, eds. New York, Plenum Press, 11–66.
247. Andersen, O. K. and Jepsen, O. (1984). Explicit, first-principles tight-binding theory. Phys. Rev. Lett. 53, 2571–1574.
248. Andersen, O. K. and Kasowski, R. V. (1971). Electronic states as linear combinations of Muffin Tin orbitals. Phys. Rev. B 4, 1064–1069.
249. Andersen, O. K., Postnikov, A. V., and Savrasov, S. Y. (1992). The muffin-tin-orbital point of view. In Applications of Multiple Scattering Theory to Materials Science, W. H. Butler, P. H. Dederichs, A. Gonis, and R. L. Weaver, eds. MRS Symposium Proceedings, vol. 253. Pittsburgh, Materials Research Society, 37–70.
250. Andersen, O. K., Saha-Dasgupta, T., Tank, R. W., Arcangeli, C., Jepsen, O., and Krier, G. (2000). Developing the MTO formalism. In Electronic Structure and the Physical Properties of Solids: the Uses of the LMTO Method, H. Dreyssé, ed. Lecture Notes in Physics. Berlin, Springer Verlag.
251. Andzelm, J. and Wimmer, E. (1992). Density functional Gaussian-type-orbital approach to molecular geometries, vibrations, and reaction energies. J. Chem. Phys. 96, 1280–1303.
252. Anglada, E., Soler, J. M., Junquera, J., and Artacho, E. (2002). Systematic generation of finite-range atomic basis sets for linear-scaling calculations. Phys. Rev. B 66, 205101.
253. Arias, T. A. (1999). Multiresolution analysis of electronic structure: semicardinal and wavelet bases. Rev. Mod. Phys. 71, 267–311.
254. Binkley, J. S., Pople, J. A., and Hehre, W. J. (1980). Self-consistent molecular orbital methods. XXI. Small split-valence basis sets for first-row elements. J. Am. Chem. Soc. 102, 939–947.
255. Bloch, F. (1928). Über die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52, 555–560.
256. Bowler, D. and Gillan, M. (2002). Recent progress in linear scaling ab initio electronic structure techniques. J. Phys. Condens. Matter 14, 2781–2798.
257. Boys, S. F. (1950). Electron wave functions I. A general method for calculation for the stationary states of any molecular system. Proc. Roy. Soc. London 200, 542–554.
258. Boys, S. F. and Bernardi, F. (1970). The calculations of small molecular interaction by the difference of separate total energies. Some procedures with reduced error. Mol. Phys. 19, 553–566.
259. Chelikowsky, J. R., Troullier, N., and Saad, Y. (1994). Finite-difference pseudopotential method: electronic structure calculations without a basis. Phys. Rev. Lett. 72, 1240–1243.
260. Davenport, J. W. (1984). Linear augmented-Slater-type-orbital method for electronic-structure calculations. Phys. Rev. B 29, 2896–2904.
261. Delley, B. (1990). An all-electron numerical method for solving the local density functional for polyatomic molecules. J. Chem. Phys. 92, 508–517.
262. Dunning, T. H. (1989). Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007–1023.
263. Finnis, M. W. (2003). Interatomic forces in condensed matter. Oxford Series on Materials Modelling, Oxford, Oxford University Press.
264. Gan, C. K., Haynes, P. D., and Payne, M. C. (2001). First-principles density-functional calculations using localized spherical-wave basis sets. Phys. Rev. B 63, 205109.
265. Godbout, N., Salahub, D. R., Andzelm, J., and Wimmer, E. (1992). Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through Neon, optimization technique and validation. Can. J. Chem. 70, 560–571.
266. Gygi, F. (1992). Adaptive riemannian metric for plane-wave electronic-structure calculations. Europhys. Lett. 19, 617–620.
267. Gygi, F. and Galli, G. (1995). Real-space adaptive-coordinate electronic-structure calculations. Phys. Rev. B 52, R2229–R2232.
268. Hall, G. G. (1951). The molecular orbital theory of chemical valency. VIII - A method of calculating ionization potentials. Proc. Roy. Soc. London 205, 541–552.
269. Ham, F. S. and Segall, B. (1961). Energy bands in periodic lattices – Green's function method. Phys. Rev. 124, 1786–1796.
270. Hamann, D. R. (1995). Application of adaptive curvilinear coordinates to the electronic structure of solids. Phys. Rev. B 51, 7337–7340.
271. Hehre, W. J., Stewart, R. F., and Pople, J. A. (1969). Self-consistent molecular-orbital methods. I. Use of Gaussian expansions of Slater-type atomic orbitals. J. Chem. Phys. 51, 2657–2664.
272. Hehre, W. J., Ditchfield, R., and Pople, J. A. (1972). Self-consistent molecular orbital methods. XII. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules. J. Chem. Phys. 56, 2257–2261.
273. Heine, V. (1967). s-d interaction in transition metals. Phys. Rev. 153, 673–682.
274. Helgaker, T., Jørgensen, P., and Olsen, J. (2000). Molecular Electronic-Structure Theory. Chichester, Wiley.
275. Hernandez, E., Gillan, M. J., and Goringe, C. M. (1997). Basis functions for linear-scaling first-principles calculations. Phys. Rev. B 55, 13485–13493.
276. Ho, K. M., Elsässer, C., Chan, C. T., and Fähnle, M. (1992). First-principles pseudopotential calculations for hydrogen in 4d transition metals. I. Mixed-basis method for total energies and forces. J. Phys. Condens. Matter 4, 5189–5206.
277. Huzinaga, S. (1965). Gaussian-type functions for polyatomic systems. I. J. Chem. Phys. 42, 1293–1302.
278. Jackson, J. D. (1975). Classical Electrodynamics, 2nd edn. New York, Wiley.
279. Junquera, J., Paz, O., Sánchez-Portal, D., and Artacho, E. (2001). Numerical atomic orbitals for linear-scaling calculations. Phys. Rev. B 64, 235111.
280. Kittel, C. (1996). Introduction to Solid State Physics, 7th edn. New York, Wiley.
281. Koelling, D. D. (1970). Alternative augmented-plane-wave technique: theory and application to copper. Phys. Rev. B 2, 290–298.
282. Koelling, D. D. and Arbman, G. O. (1975). Use of energy derivative of the radial solution in an augmented plane wave method: application to Cu. J. Phys. F: Metal Phys. 5, 2041–2054.
283. Kohn, W. and Rostoker, N. (1954). Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium. Phys. Rev. 94, 1111–1120.
284. Korringa, J. (1947). On the calculation of the energy of a Bloch wave in a metal. Physica 13, 392–400.
285. Lin, Z. and Harris, J. (1993). A localized-basis scheme for molecular dynamics. J. Phys. Condens. Matter 5, 1055–1080.
286. Loucks, T. L. (1967). The Augmented Plane Wave Method. New York, Benjamin.
287. Louie, S. G., Ho, K. M., and Cohen, M. L. (1979). Self-consistent mixed-basis approach to the electronic structure of solids. Phys. Rev. B 19, 1774–1782.
288. Löwdin, P. O. (1950). On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals. J. Chem. Phys. 18, 365–375.
289. Marcus, P. M. (1967). Int. J. Quantum Chem. 1, 567.
290. Messiah, A. (1961). Quantum Mechanics. Amsterdam, North Holland.
291. Methfessel, M. (1988). Elastic constants and phonon frequencies of Si calculated by a fast full-potential linear-muffin-tin-orbital method. Phys. Rev. B 38, 1537–1540.
292. Pople, J. A. and Nesbet, R. K. (1954). Self-consistent orbitals for radicals. J. Chem. Phys. 22, 571–572.
293. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes. The Art of Scientific Computing. Cambridge, Cambridge University Press.
294. Pulay, P. (1969). Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. I. Theory. Mol. Phys. 17, 197–204.
295. Roothaan, C. C. J. (1951). New developments in molecular orbital theory. Rev. Mod. Phys. 23, 69–89.
296. Saffren, M. M. (1960). Bull. Am. Phys. Soc. 5, 298.
297. Saffren, M. M. and Slater, J. C. (1953). An augmented plane-wave method for the periodic potential problem. II. Phys. Rev. 92, 1126–1128.
298. Sankey, O. F. and Niklewski, D. J. (1989). Ab initio multicenter tight-binding model for molecular dynamics simulations and other applications in covalent systems. Phys. Rev. B 40, 3979–3995.
299. Skriver, H. (1984). The LMTO Method. New York, Springer.
300. Skylaris, C.-K., Diéguez, O., Haynes, P. D., and Payne, M. C. (2002). Comparison of variational real-space representations of the kinetic energy operator. Phys. Rev. B 66, 073103.
301. Slater, J. C. (1930a). Atomic shielding constants. Phys. Rev. 36, 57–64.
302. Slater, J. C. (1930b). Note on Hartree's method. Phys. Rev. 35, 210–211.
303. Slater, J. C. (1932). Analytic atomic wave functions. Phys. Rev. 42, 33–43.
304. Slater, J. C. (1934). The electronic structure of metals. Rev. Mod. Phys. 6, 209–281.
305. Slater, J. C. (1937). Wave functions in a periodic potential. Phys. Rev. 51, 846–851.
306. Slater, J. C. (1953). An augmented plane wave method for the periodic potential problem. Phys. Rev. 92, 603–608.
307. Soler, J. M. and Williams, A. R. (1990). Augmented-plane-wave forces. Phys. Rev. B 42, 9728–9731.
308. Soler, J. M., Artacho, E., Gale, J. D., García, A. I., Junquera, J., Ordejón, P., and Sánchez-Portal, D. (2002). The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14, 2745–2780. www.siesta.org.
309. Sprik, M. and Klein, M. L. (1989). Adiabatic dynamics of the solvated electron in liquid ammonia. J. Chem. Phys. 91, 5665–5671.
310. Trivedi, H. P. and Steinborn, E. O. (1982). Numerical properties of a new translation formula for exponential-type functions and its application to one-electron multicenter integrals. Phys. Rev. A 25, 113–127.
311. Varga, K., Zhang, Z., and Pantelides, S. T. (2004). Lagrange functions: a family of powerful basis sets for real-space order-N electronic structure calculations. Phys. Rev. Lett. 93, 176403.
312. Watson, M. A., Handy, N. C., and Cohen, A. J. (2003). Density functional calculations, using Slater basis sets, with exact exchange. J. Chem. Phys. 119, 6475–6481.
313. Wigner, E. and Seitz, F. (1933). On the constitution of metallic sodium. Phys. Rev. 43, 804–810.
314. Williams, A. R., Kübler, J., and Gelatt Jr., C. D. (1979). Cohesive properties of metallic compounds: augmented-spherical-wave calculations. Phys. Rev. B 19, 6094–6118.
315. Abramowitz, M. and Stegun, I. A. (1965). Handbook of Mathematical Functions. New York, Dover.
316. Allen, M. P. and Tildesley, D. J. (1987). Computer Simulation of Liquids. Oxford, Clarendon Press.
317. Amos, R. D., Alberts, I. L., Andrews, J. S. et al. (1995). CADPAC: The Cambridge Analytic Derivatives Package Issue 6. A Suite of Quantum Chemistry Programs. Cambridge, University of Cambridge. www-theor.ch.cam.ac.uk/software/cadpac.html.
318. Andersen, O. K. (1973). Simple approach to the band-structure problem. Solid State Comm. 13, 133–136.
319. Andersen, O. K. (1975). Linear methods in band theory. Phys. Rev. B 12, 3060–3083.
320. Andersen, O. K. (1984). Linear methods in band theory. In The Electronic Structure of Complex Systems, P. Phariseau and W. M. Temmerman, eds. New York, Plenum Press, 11–66.
321. Andersen, O. K. and Wooley, R. G. (1973). Muffin-tin orbitals and molecular calculations: general formalism. Mol. Phys. 26, 905–927.
322. Andersen, O. K., Postnikov, A. V., and Savrasov, S. Y. (1992). The muffin-tin-orbital point of view. In Applications of Multiple Scattering Theory to Materials Science, W. H. Butler, P. H. Dederichs, A. Gonis, and R. L. Weaver, eds. MRS Symposium Proceedings, vol. 253. Pittsburgh, Materials Research Society, 37–70.
323. Andersen, O. K., Saha-Dasgupta, T., Tank, R. W., Arcangeli, C., Jepsen, O., and Krier, G. (2000). Developing the MTO formalism. In Electronic Structure and the Physical Properties of Solids: the Uses of the LMTO Method, H. Dreyssé, ed. Lecture Notes in Physics. Berlin, Springer Verlag, 1–84.
324. Andzelm, J. and Wimmer, E. (1992). Density functional Gaussian-type-orbital approach to molecular geometries, vibrations, and reaction energies. J. Chem. Phys. 96, 1280–1303.
325. Baroni, S., de Gironcoli, S., Dal Corso, A., and Giannozzi, P. (2001). Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515–562.
326. Blaha, P., Schwarz, K., Sorantini, P., and Trickey, S. B. (1990). Full-potential, linearized augmented plane wave programs for crystalline systems. Comput. Phys. Commun. 59, 399–415.
327. Blöchl, P. (1994). Projector augmented-wave method. Phys. Rev. B 50, 17953–17979.
328. Boys, S. F. (1950). Electron wave functions I. A general method for calculation for the stationary states of any molecular system. Proc. Roy. Soc. London 200, 542–554.
329. Causà, M., Dovesi, R., Orlando, R., Pisani, C., and Saunders, V. R. (1988). Treatment of the exchange interactions in Hartree–Fock LCAO calculation of periodic systems. J. Phys. Chem. 92, 909–913.
330. Dupuis, M., Rys, J., and King, H. F. (1976). Evaluation of molecular integrals over Gaussian basis functions. J. Chem. Phys. 65, 111–116.
331. Estrín, D. A., Corongiu, G., and Clementi, E. (1993). Structure and dynamics of molecular systems using density functional theory. In METECC, Methods and Techniques in Computational Chemistry. Cagliari, Stef, Chapter 12, 541–567.
332. Ewald, P. P. (1921). Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 64, 253–287.
333. Finnis, M. W. (2003). Interatomic Forces in Condensed Matter. Oxford Series on Materials Modelling, Oxford, Oxford University Press.
334. Frisch, M. J., Trucks, G. W., Schlegel, H. B. et al. (2004). Gaussian 03, Revision C.02. Wallingford, CT, Gaussian, Inc. www.gaussian.com.
335. Gill, P. M. W. and Pople, J. A. (1991). The prism algorithm for 2-electron integrals. Int. J. Quantum Chem. 40, 753–772.
336. Godbout, N., Salahub, D. R., Andzelm, J., and Wimmer, E. (1992). Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through Neon, optimization technique and validation. Can. J. Chem. 70, 560–571.
337. Gonis, A. (1992). Green functions for ordered and disordered systems. Amsterdam, North-Holland.
338. Greengard, L. and Rokhlin, V. (1987). A fast algorithm for particle simulations. J. Comput. Phys. 73, 325–348.
339. Ham, F. S. and Segall, B. (1961). Energy bands in periodic lattices – Green's function method. Phys. Rev. 124, 1786–1796.
340. Harris, J. (1985). Simplified method for calculating the energy of weakly interacting fragments. Phys. Rev. B 31, 1770–1779.
341. Head-Gordon, M. and Pople, J. A. (1988). A method for two-electron Gaussian integral and integral derivative evaluation using recurrence relations. J. Chem. Phys. 89, 5777–5786.
342. Helgaker, T., Jorgensen, P., and Olsen, J. (2000). Molecular Electronic Structure Theory. Chichester, Wiley.
343. Herring, C. (1940). A new method for calculating wave functions in crystals. Phys. Rev. 57, 1169–1177.
344. Holtzwarth, N. A. W., Matthews, G. E., Tackett, A. R., and Dunning, R. B. (1997). Comparison of the projector augmented-wave, pseudopotential and linearized augmented-plane-wave formalism for density-functional calculations of solids. Phys. Rev. B 55, 2005–2017.
345. Ihm, J., Zunger, A., and Cohen, M. L. (1979). Momentum-space formalism for the total energy of solids. J. Phys. C: Solid State Phys. 12, 4409–4422.
346. Ishida, K. (1998). Rapid algorithm for computing the electron repulsion integral over higher order Gaussian-type orbitals: accompanying coordinate expansion method. J. Comput. Chem. 19, 923–934.
347. Jackson, J. D. (1975). Classical Electrodynamics, 2nd edn. New York, Wiley.
348. Jensen, F. (1999). Introduction to Computational Chemistry. Chichester, Wiley.
349. Jepsen, O., Madsen, J., and Andersen, O. K. (1982). Spin-polarized electronic structure of the Ni (001) surface and thin films. Phys. Rev. B 26, 2790–2809.
350. Kendall, R. A., Apra, E., Bernholdt, D. E. et al. (2000). High performance computational chemistry: an overview of NWChem a distributed parallel application. Comput. Phys. Commun. 128, 260–283. www.emsl.pnl.gov/docs/nwchem/nwchem.html.
351. King-Smith, R. D., Payne, M. C., and Lin, J. S. (1991). Real-space implementation of nonlocal pseudopotentials for first-principles total-energy calculations. Phys. Rev. B 44, 13063–13066.
352. Kleinman, L. and Bylander, D. M. (1982). Efficacious form for model pseudopotentials. Phys. Rev. Lett. 48, 1425–1428.
353. Koelling, D. D. and Arbman, G. O. (1975). Use of energy derivative of the radial solution in an augmented plane wave method: application to Cu. J. Phys. F: Metal Phys. 5, 2041–2054.
354. Koelling, D. D., Freeman, A. J., and Mueller, F. M. (1970). Shifts in the electronic band structure of metals due to non-muffin-tin potentials. Phys. Rev. B 1, 1318–1324.
355. Kohn, W. and Rostoker, N. (1954). Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium. Phys. Rev. 94, 1111–1120.
356. Korringa, J. (1947). On the calculation of the energy of a Bloch wave in a metal. Physica 13, 392–400.
357. Kresse, G. and Joubert, D. (1999). From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775.
358. Laasonen, K., Pasquarello, A., Car, R., Lee, C., and Vanderbilt, D. (1993). Car–Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials. Phys. Rev. B 47, 10142–10153.
359. Loucks, T. L. (1965). Fermi surfaces of Cr, Mo and W by the augmented-plane-wave method. Phys. Rev. 139, A1181–A1188.
360. Loucks, T. L. (1967). The Augmented Plane Wave Method. New York, Benjamin.
361. McMurchie, L. E. and Davidson, E. R. (1978). One- and two-electron integrals over cartesian Gaussian functions. J. Comput. Phys. 26, 218–231.
362. Methfessel, M. and van Schilfgaarde, M. (1993). Derivation of force theorems in density-functional theory: application to the full-potential LMTO method. Phys. Rev. B 48, 4937–4940.
363. Methfessel, M., Rodriguez, C. O., and Andersen, O. K. (1989). Fast full-potential calculations with a converged basis of atom-centered linear muffin-tin orbitals: structural and dynamic properties of silicon. Phys. Rev. B 40, 2009–2012.
364. Methfessel, M., van Schilfgaarde, M., and Casali, R. A. (2000). A full-potential LMTO method based on smooth Hankel functions. In Electronic Structure and the Physical Properties of Solids: the Uses of the LMTO Method, H. Dreyssé, ed. Lecture Notes in Physics. Berlin, Springer Verlag, 114–147.
365. Nielsen, O. H. and Martin, R. M. (1983). First-principles calculation of stress. Phys. Rev. Lett. 50, 697–700.
366. Nielsen, O. H. and Martin, R. M. (1985a). Quantum-mechanical theory of stress and force. Phys. Rev. B 32, 3780–3791.
367. Nielsen, O. H. and Martin, R. M. (1985b). Stresses in semiconductors: ab initio calculations on Si, Ge, and GaAs. Phys. Rev. B 32, 3792–3805.
368. Obara, S. and Saika, A. (1986). Efficient recursive computation of molecular integrals over Cartesian Gaussian functions. J. Chem. Phys. 84, 3963–3974.
369. Parrinello, M., Hutter, J., Marx, D. et al. (2004). CPMD V3.9. IBM Corp. 1990–2004, MPI für Festkörperforschung Stuttgart 1997–2001. www.cpmd.org.
370. Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. A., and Joannopoulos, J. D. (1992). Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045–1097.
371. Pisani, C. and Dovesi, R. (1980). Exact exchange Hartree–Fock calculations for periodic systems. I. Illustration of the method. Int. J. Quantum Chem. 17, 501–516. www.crystal.unito.it.
372. Pople, J. A. and Beveridge, D. L. (1970). Approximate Molecular Orbital Theory. Advanced Chemistry, London, McGraw-Hill.
373. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes. The Art of Scientific Computing. Cambridge, Cambridge University Press.
374. Pulay, P. (1969). Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. I. Theory. Mol. Phys. 17, 197–204.
375. Rys, J., Dupuis, M., and King, H. F. (1983). Computation of electron repulsion integrals using the Rys quadrature method. J. Comput. Chem. 4, 154–157.
376. Savrasov, S. Y. and Savrasov, D. Y. (1992). Full-potential linear-muffin-tin-orbital method for calculating total energies and forces. Phys. Rev. B 46, 12181–12195.
377. Schmidt, M. W., Baldridge, K. K., Boatz, J. A. et al. (1993). General atomic and molecular electronic structure system. J. Comput. Chem. 14, 1347–1363. www.msg.ameslab.gov/GAMESS/GAMESS.html.
378. Segall, M. D., Lindan, P. J. D., Pickard, C. J. et al. (2002). First-principles simulation: ideas, illustrations and the CASTEP code. J. Phys. Condens. Matter 14, 2717–2744.
379. Skriver, H. (1984). The LMTO Method. New York, Springer.
380. Slater, J. C. (1937). Wave functions in a periodic potential. Phys. Rev. 51, 846–851.
381. Soler, J. M. and Williams, A. R. (1989). Simple formula for the atomic forces in the augmented-plane-wave method. Phys. Rev. B 40, 1560–1564.
382. Soler, J. M. and Williams, A. R. (1990). Augmented-plane-wave forces. Phys. Rev. B 42, 9728–9731.
383. Soler, J. M., Artacho, E., Gale, J. D. et al. (2002). The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14, 2745–2780. www.siesta.org.
384. VandeVondele, J., Krack, M., Mohamed, F., Parrinello, M., Chassaing, T., and Hutter, J. (2005). QUICKSTEP: fast and accurate density functional calculations using a mixed gaussian and plane waves approach. Comput. Phys. Commun. 167, 103–128.
385. White, C. A. and Head-Gordon, M. (1994). Derivation and efficient implementation of the fast multipole method. J. Chem. Phys. 101, 6593–6605.
386. Williams, A. R. (1970). Non-muffin-tin energy bands for silicon by the Korringa–Kohn–Rostoker method. Phys. Rev. B 1, 3417–3426.
387. Wimmer, E., Krakauer, H., Weinert, M., and Freeman, A. J. (1981). Full-potential self-consistent linearized-augmented-plane-wave method for calculating the electronic structure of molecules and surfaces: O2 molecule. Phys. Rev. B 24, 864–875.
388. Yu, R., Singh, D., and Krakauer, H. (1991). All-electron and pseudopotential force calculations using the linearized-augmented-plane-wave method. Phys. Rev. B 93, 6411–6422.
389. Andersen, O. K., Saha-Dasgupta, T., Tank, R. W., Arcangeli, C., Jepsen, O., and Krier, G. (2000). Developing the MTO formalism. In Electronic Structure and the Physical Properties of Solids: the Uses of the LMTO method, H. Dreyssé, ed. Lecture Notes in Physics. Berlin, Springer Verlag.
390. Bester, G. and Fähnle, M. (2001). Interpretation of ab initio total energy results in a chemical language: I. Formalism and implementation into a mixed-basis pseudopotential code. J. Phys. Condens. Matter 13, 11541–11550.
391. Bingham, R. C., Dewar, M. J. S., and Lo, D. H. (1975). Ground states of molecules. XXVI. MINDO/3 calculations for hydrocarbons. J. Am. Chem. Soc. 97, 1294–1301.
392. Børnsen, N., Meyer, B., Grotheer, O., and Fähnle, M. (1999). Ecov – a new tool for the analysis of electronic structure in a chemical language. J. Phys. Condens. Matter 11, L287–L293.
393. Brenner, D. W. (1990). Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B 42, 9458–9471.
394. Brooks, R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminatham, S., and Karplus, M. (1983). CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem. 4, 187–217.
395. Chacón, E., Alvarellos, J. E., and Tarazona, P. (1985). Nonlocal kinetic energy functional form nonhomogeneous electron systems. Phys. Rev. B 32, 7868–7877.
396. Chetty, N., Jacobsen, K. W., and Nørskov, J. K. (1991). Optimized and transferable densities from first principles local density calculations. J. Phys. Condens. Matter 3, 5437–5443.
397. Cornell, W. D., Cieplak, P., Bayly, C. I. et al. (1995). A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc. 117, 5179–5197.
398. Daw, M. S. and Baskes, M. I. (1984). Embedded atom method: derivation and application to impurities, surfaces and other defects in metals. Phys. Rev. B 29, 6443–6453.
399. DePristo, A. E. and Kress, J. D. (1987). Rational function representation for accurate exchange energy functionals. J. Chem. Phys. 86, 1425–1428.
400. Dewar, M. J. S. and Thiel, W. (1977). The MNDO method. Approximations and parameters. J. Am. Chem. Soc. 99, 4899–4907.
401. Dewar, M. J. S., Zoebisch, E. G., Healy, E. F., and Stewart, J. J. P. (1985). AM1: a new general purpose quantum mechanical molecular model. J. Am. Chem. Soc. 107, 3902–3909.
402. Dick, B. G. and Overhauser, J. A. W. (1958). Theory of the dielectric constants of alkali halide crystals. Phys. Rev. 112, 90–103.
403. Ducastelle, F. (1970). Elastic modulus of transition metals. J. de Phys. 31, 1055–1062.
404. Eichinger, M., Tavan, P., Hutter, J., and Parrinello, M. (1999). A hybrid method for solutes in complex solvents: density functional theory combined with empirical force fields. J. Chem. Phys. 110, 10452–10467.
405. Elstner, M., Porezag, D., Jungnickel, G., Elsner, J., Haugk, M., Frauenheim, T., Suhai, S., and Seifert, G. (1998). Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys. Rev. B 58, 7260–7268.
406. Ercolessi, F., Tosatti, E., and Parrinello, M. (1986). Au(100) surface reconstruction. Phys. Rev. Lett. 57, 719–722.
407. Esfarjani, K. and Kawazoe, Y. (1998). Self-consistent tight-binding formalism for charged systems. J. Phys. Condens. Matter 10, 8257–8267.
408. Estrín, D. A., Kohanoff, J., Laría, D. H., and Weht, R. O. (1997). A hybrid quantum and classical mechanical Monte Carlo simulation of the interaction of hydrogen chloride with solid water clusters. Chem. Phys. Lett. 280, 280–286.
409. Fabris, S., Paxton, A. T., and Finnis, M. W. (2001). Free energy and molecular dynamics calculations for the cubic-tetragonal phase transition in zirconia. Phys. Rev. B 63, 094101.
410. Fabris, S., Paxton, A. T., and Finnis, M. W. (2002). A stabilisation mechanism of zirconia based on oxygen vacancies only. Acta Materialia 50, 5171–5178.
411. Field, M. J., Bash, P. A., and Karplus, M. J. (1990). A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J. Comput. Chem. 11, 700–733.
412. Finnis, M. W. (2003). Interatomic Forces in Condensed Matter. Oxford Series on Materials Modelling, Oxford, Oxford University Press.
413. Finnis, M. W. and Sinclair, J. E. (1984). A simple empirical N-body potential for transition metals. Phil. Mag. 50, 45–55.
414. Finnis, M. W., Paxton, A. T., Methfessel, M., and van Schilfgaarde, M. (1998). The crystal structure of zirconia from first principles and self-consistent tight-binding. Phys. Rev. Lett. 81, 5149–5152.
415. Foley, M. and Madden, P. A. (1996). Further orbital-free kinetic-energy functionals for ab initio molecular dynamics. Phys. Rev. B 53, 10589–10598.
416. Foulkes, W. M. C. (1987). Ph.D. thesis, University of Cambridge.
417. García-González, P., Alvarellos, J. E., and Chacón, E. (1996). Kinetic-energy density functional: atoms and shell structure. Phys. Rev. A 54, 1897–1905.
418. Goodwin, L., Skinner, A. J., and Pettifor, D. G. (1989). Generating transferable tight-binding parameters – application to silicon. Europhys. Lett. 9, 701–706.
419. Harris, J. (1985). Simplified method for calculating the energy of weakly interacting fragments. Phys. Rev. B 31, 1770–1779.
420. Harrison, W. A. (1980). Electronic Structure and the Properties of Solids. San Francisco, Freeman.
421. Haydock, R., Heine, V., and Kelly, M. J. (1972). Electronic structure based on the local atomic environment for tight-binding bands. J. Phys. C 5, 2845–2858.
422. Hill, T. L. (1948). Steric effects. I. Van der Waals potential energy curves. J. Chem. Phys. 16, 399–404.
423. Hoffmann, R. (1963). An extended Hückel theory. I. Hydrocarbons. J. Chem. Phys. 39, 1397–1412.
424. Hohenberg, P. and Kohn, W. (1964). Inhomogeneous electron gas. Phys. Rev. 136, B864–867.
425. Jacobsen, K. W., Nørskov, J. K., and Puska, M. J. (1987). Interatomic interaction in the effective medium theory. Phys. Rev. B 35, 7423–7442.
426. Jensen, F. (1999). Introduction to Computational Chemistry. Chichester, Wiley.
427. Jorgensen, W. L. (1998). OPLS force fields. In Encyclopedia of Computational Chemistry, P. v. R. Schleyer, ed. New York, Wiley, 1986–1989.
428. Kim, J., Mauri, F., and Galli, G. (1995). Total-energy global optimizations using nonorthogonal localized orbitals. Phys. Rev. B 52, 1640–1648.
429. King, R. A. and Handy, N. C. (2001). Kinetic energy functionals for molecular calculations. Mol. Phys. 99, 1005–1009.
430. Kirzhnits, D. A. (1957). Quantum corrections to the Thomas–Fermi equation. Zh. Eksp.
431. Teor. Fiz. 32 115. Sov. Phys. JETP 5, 64–72 (1957).
432. Laio, A., VandeVondele, J., and Röthlisberger, U. (2002). A Hamiltonian electrostatic coupling scheme for hybrid Car–Parrinello molecular dynamics simulations. J. Chem. Phys. 116, 6941–6947.
433. Lee, H., Lee, C., and Parr, R. G. (1991). Cojoint gradient correction to the Hartree–Fock kinetic- and exchange-energy density functionals. Phys. Rev. A 44, 768–771.
434. Lennard-Jones, J. E. (1924). The determination of molecular fields. II. From the equation of state of a gas. Proc. Roy. Soc. London 106, 463–477.
435. Miertus, S., Scrocco, E., and Tomasi, J. (1981). Electrostatic interaction of a solute with a continuum. A direct utilization of ab initio molecular potentials for the prevision of solvent effects. Chem. Phys. 55, 117–129.
436. Migoni, R., Bilz, H., and Bauerle, D. (1976). Origin of Raman scattering and ferroelectricity in oxidic perovskites. Phys. Rev. Lett. 37, 1155–1158.
437. Monard, G., Loos, M., Théry, V., Baka, K., and Rivail, J.-L. (1996). Hybrid classical quantum force field for modeling very large molecules. Int. J. Quant. Chem. 58, 153–159.
438. Murdock, S. E., Lynden-Bell, R. M., Kohanoff, J., and Sexton, G. J. (2002). Determining the electronic structure and chemical potentials of molecules in solution. Phys. Chem. Chem. Phys. 4, 3016–3021.
439. Onsager, L. (1936). Electric moments of molecules in liquids. J. Am. Chem. Soc. 58, 1486–1493.
440. Ordejón, P., Drabold, D. A., Grumbach, M. P., and Martin, R. M. (1993). Unconstrained minimization approach for electronic computations that scales linearly with system size. Phys. Rev. B 48, 14646–14649.
441. Perrot, F. (1994). Hydrogen–hydrogen interaction in an electron gas. J. Phys. Condens. Matter 6, 431–446.
442. Pettifor, D. (1989). New many-body potential for the bond order. Phys. Rev. Lett. 63, 2480–2483.
443. Pettifor, D. G. (1995). Bonding and Structure in Molecules and Solids. Oxford, Clarendon Press.
444. Pople, J. A. and Beveridge, D. L. (1970). Approximate Molecular Orbital Theory. Advanced Chemistry, London, McGraw-Hill.
445. Pople, J. A. and Segal, G. A. (1965). Approximate self-consistent molecular orbital theory. II. Calculations with complete neglect of differential overlap. J. Chem. Phys. 43, S136–S151.
446. Pople, J. A. and Segal, G. A. (1966). Approximate self-consistent molecular orbital theory. III. CNDO results for AB2 and AB3 systems. J. Chem. Phys. 44, 3289–3296.
447. Pople, J. A., Santry, D. P., and Segal, G. A. (1965). Approximate self-consistent molecular orbital theory. I. Invariant procedures. J. Chem. Phys. 43, S129–S135.
448. Pople, J. A., Beveridge, D. L., and Dobosh, P. A. (1967). Approximate self-consistent molecular-orbital theory. V. Intermediate neglect of differential overlap. J. Chem. Phys. 47, 2026–2033.
449. Rappe, A. K., Casewit, C. J., Colwell, K. S., Goddard III, W. A., and Skiff, W. M. (1992). UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 114, 10024–10035.
450. Sankey, O. F. and Niklewski, D. J. (1989). Ab initio multicenter tight-binding model for molecular dynamics simulations and other applications in covalent systems. Phys. Rev. B 40, 3979–3995.
451. Schelling, P. K., Yu, N., and Halley, J. W. (1998). Self-consistent tight-binding atomic-relaxation model of titanium dioxide. Phys. Rev. B 58, 1279–1293.
452. Slater, J. C. and Koster, G. F. (1954). Simplified LCAO method for the periodic potential problem. Phys. Rev. 94, 1498–1524.
453. Smargiassi, E. and Madden, P. A. (1994). Orbital-free kinetic-energy functionals for first-principles molecular dynamics. Phys. Rev. B 49, 5220–5226.
454. Stewart, J. J. P. (1989). Optimization of parameters for semiempirical methods. I. Method. J. Comput. Chem. 10, 209–220.
455. Stillinger, F. H. and David, C. W. (1978). Polarization model for water and its ionic dissociation products. J. Chem. Phys. 69, 1473–1484.
456. Stillinger, F. H. and Weber, T. A. (1985). Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 31, 5262–5271.
457. Stone, A. J. (1981). Distributed multipole analysis; or how to describe a molecular charge distribution. Chem. Phys. Lett. 83, 233–239.
458. Svensson, M., Humbel, S., Froesse, R. D. J., Matsubara, T., Sieber, S., and Morokuma, K. (1996). 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. 100, 19357–19363.
459. Tersoff, J. (1986). New empirical model for the structural properties of silicon. Phys. Rev. Lett. 23, 542–548.
460. Thiel, W. (1981). The MNDOC method, a correlated version of the MNDO model. J. Am. Chem. Soc. 103, 1413–1420.
461. Van Gunsteren, W. F. and Berendsen, H. J. C. (1990). Computer Simulation of Molecular Dynamics: Methodology, Applications and Perspectives in Chemistry. www.igc.ethz.ch/gromos.
462. Von Weizsäcker, C. F. (1935). Zur Theorie der Kernmassen. Z. Phys. 96, 431–458.
463. Wang, B., Stott, M. J., and von Barth, U. (2001). Approximate electron kinetic-energy functionals. Phys. Rev. A 63, 052501–1–052501–8.
464. Wang, L.-W. and Teter, M. P. (1992). Kinetic-energy functional of the electron density. Phys. Rev. B 45, 13196–13220.
465. Wang, Y. A., Govind, N., and Carter, E. A. (1999). Orbital-free kinetic-energy density functionals with a density-dependent kernel. Phys. Rev. B 60, 16350–16358.
466. Watson, S. C. and Carter, E. A. (2000). Linear-scaling parallel algorithms for the first principles treatment of metals. Comput. Phys. Commun. 128, 67–92.
467. Zaremba, E. (1990). Extremal properties of the Harris functional. J. Phys. Condens. Matter 2, 2479–2486.
468. Alavi, A., Kohanoff, J., Parrinello, M., and Frenkel, D. (1995). Ab initio molecular dynamics with excited electrons. Phys. Rev. Lett. 73, 2599–2602.
469. Anderson, D. G. (1965). Iterative procedures for non-linear integral equations. Assoc. Comput. Mach. 12, 547–560.
470. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Croz, J. D., Greenbaum, A., Hammarling, S., McKenney, A., and Sorensen, D. (1999). LAPACK Users’ Guide, 3rd edn. Philadelphia, PA, Society for Industrial and Applied Mathematics. www.netlib.org/lapack.
471. Blackford, L. S., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., and Whaley, R. C. (1997). ScaLAPACK Users’ Guide. Philadelphia, PA, Society for Industrial and Applied Mathematics. www.netlib.org/scalapack.
472. Broyden, C. G. (1965). A class of methods for solving nonlinear simultaneous equations. Math. Comput. 19, 577–593.
473. Car, R. and Parrinello, M. (1985). Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474.
474. CPMD Consortium (2004). CPMD V3.9. IBM Corp 1990-2004, MPI für Festkörperforschung Stuttgart. 1997-2001.
475. Cullum, J. K. and Willoughby, R. A. (2002). Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. 1. Philadelphia, Society for Industrial and Applied Mathematics.
476. Davidson, E. R. (1975). The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comput. Phys. 17, 87–94.
477. Hutter, J., Lüthi, H.-P., and Parrinello, M. (1994). Electronic structure optimisation in plane-wave-based density functional calculations by direct inversion in the iterative subspace. Comput. Mater. Sci. 2, 244–248.
478. Johnson, D. D. (1988). Modified Broyden's method for accelerating convergence in self-consistent calculations. Phys. Rev. B 38, 12807–12813.
479. Lanczos, C. (1950). An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Standards 45, 255–282.
480. Marx, D. and Hutter, J. (2000). Ab-initio molecular dynamics: theory and implementation. In Modern Methods and Algorithms in Quantum Chemistry, J. Grotendorst, ed. NIC, vol. 1. Jülich, John von Neumann Institute for Computing, 301–449.
481. Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. A., and Joannopoulos, J. D. (1992). Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045–1097.
482. Pollard, W. T. and Friesner, R. A. (1993). Efficient Fock matrix diagonalization by a Krylov-space method. J. Chem. Phys. 99, 6742–6750.
483. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes. The Art of Scientific Computing. Cambridge, Cambridge University Press.
484. Pulay, P. (1980). Convergence acceleration of iterative sequences. The case of SCF iteration. Chem. Phys. Lett. 73, 393–397.
485. Baroni, S., de Gironcoli, S., dal Corso, A., and Giannozzi, P. (2005). Plane-wave self-consistent field. www.pwscf.org.
486. Bendt, P. and Zunger, A. (1983). Simultaneous relaxation of nuclear geometries and electronic charge densities in electronic structure theories. Phys. Rev. Lett. 50, 1684–1688.
487. Blöchl, P. and Parrinello, M. (1992). Adiabaticity in first-principles molecular dynamics. Phys. Rev. B 45, 9413–9416.
488. Car, R. and Parrinello, M. (1985). Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474.
489. Car, R. and Parrinello, M. (1988). The unified approach for molecular dynamics and density functional theory. In Proceedings of NATO Workshop: Simple Molecular Systems at Very High Density, A. Polian, P. Loubeyre, and N. Boccara, eds. NATO ASI. New York, Plenum Press, 455–476.
490. Ercolessi, F. and Adams, J. (1994). Interatomic potentials from 1st-principles calculations – the force-matching method. Europhys. Lett. 26, 583–588.
491. Estrín, D. A., Corongiu, G., and Clementi, E. (1993). Structure and dynamics of molecular systems using density functional theory. In METECC, Methods and Techniques in Computational Chemistry. Cagliari, Stef, Chapter 12, 541–567.
492. Galli, G. and Parrinello, M. (1991). Ab initio molecular dynamics: principles and practical implementation. In Computer Simulations in Material Science, M. Meyer and V. Pontikis, eds. Dordrecht, Kluwer, 283–304.
493. Hartke, B. and Carter, E. A. (1992). Spin eigenstate-dependent Hartree–Fock molecular dynamics. Chem. Phys. Lett. 189, 358–362.
494. Kohanoff, J. and Hansen, J.-P. (1996). Statistical properties of the dense hydrogen plasma: an ab initio molecular dynamics investigation. Phys. Rev. E 54, 768–781.
495. Kohanoff, J., Andreoni, W., and Parrinello, M. (1992). Zero-point-motion effects on the structure of C60. Phys. Rev. B 46, 4371–4373.
496. Kresse, G. and Furthmüller, J. (1996). Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186. cms.mpi.univie.ac.at/vasp.
497. Marx, D. and Hutter, J. (2000). Ab-initio molecular dynamics: theory and implementation. In Modern Methods and Algorithms in Quantum Chemistry, J. Grotendorst, ed. NIC, vol. 1. Jülich, John von Neumann Institute for Computing, 301–449.
498. Marzari, N., Vanderbilt, D., and Payne, M. C. (1997). Ensemble density-functional theory for ab initio molecular dynamics of metals and finite-temperature insulators. Phys. Rev. Lett. 79, 1337–1340.
499. Mermin, N. D. (1965). Thermal properties of the inhomogeneous electron gas. Phys. Rev. 137, A1441–A1443.
500. Methfessel, M. (1988). Elastic constants and phonon frequencies of Si calculated by a fast full-potential linear-muffin-tin-orbital method. Phys. Rev. B 38, 1537–1540.
501. Nosè, S. (1984). A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52, 255–268.
502. Parker, C. L., Ventura, O. N., Burt, S. K., and Cachau, R. E. (2003). DYNGA: a general purpose QM-MM-MD program. I. Application to water. Mol. Phys. 101, 2659–2668.
503. Pastore, G., Smargiassi, E., and Buda, F. (1991). Theory of ab initio molecular-dynamics calculations. Phys. Rev. A 44, 6334–6347.
504. Pulay, P. (1969). Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. I. Theory. Mol. Phys. 17, 197–204.
505. Remler, D. K. and Madden, P. A. (1990). Molecular dynamics without effective potentials via the Car–Parrinello approach. Mol. Phys. 70, 921–966.
506. Ryckaert, J. P., Ciccotti, G., and Berendsen, H. J. C. (1977). Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. J. Comput. Phys. 23, 327–341.
507. Segall, M. D., Lindan, P. J. D., Pickard, C. J. et al. (2002). First-principles simulation: ideas, illustrations and the CASTEP code. J. Phys. Condens. Matt. 14, 2717–2744.
508. Soler, J. M. and Williams, A. R. (1990). Augmented-plane-wave forces. Phys. Rev. B 42, 9728–9731.
509. Soler, J. M., Artacho, E., Gale, J. D. et al. (2002). The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14, 2745–2780. www.siesta.org.
510. Tangney, P. and Scandolo, S. (2002). How well do Car–Parrinello simulations reproduce the Born–Oppenheimer surface? Theory and examples. J. Chem. Phys. 116, 14–24.
511. Verlet, L. (1967). Computer “experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103.