Density functional theory of electronic structure: A short course for mineralogists and geophysicists

Reviews in Mineralogy and Geochemistry

Volumn 71, Issue , 2010, Pages 1-18

  Perdew, John P ^a   Ruzsinszky, Adrienn ^a  

^a Tulane University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY FUNCTIONALS; EQUATION OF STATE; EQUILIBRIUM STRUCTURES; FIRST-PRINCIPLES; HIGH PRESSURE; INTERMOLECULAR INTERACTIONS; NUCLEAR MOTIONS; SHORT COURSE; TEMPERATURE DEPENDENT; VIBRATIONAL PROPERTIES;

ELECTRONIC STRUCTURE; EQUATIONS OF STATE OF LIQUIDS; EXCITED STATES; GROUND STATE; MOLECULAR DYNAMICS;

DENSITY FUNCTIONAL THEORY;

EID: 78149424386     PISSN: 15296466     EISSN: None     Source Type: Book Series    
DOI: 10.2138/rmg.2010.71.1     Document Type: Article

References (79)

1. Alchagirov AB, Perdew JP, Boettger JC, Albers RC, Fiolhais C (2001) Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model. Phys Rev B 63:224115
2. Alfè D, Price GD, Gillan MJ (2002) Iron under Earth's core conditions: Liquid-state thermodynamics and high-pressure melting curve from ab initio calculations. Phys Rev B 65:165118
3. 0. Phys Rev B 31:6779-6781
4. Armiento R, Mattsson AE (2005) Functional designed to include surface effects in selfconsistent density functional theory. Phys Rev B 72:085108
5. Ashcroft NW, Mermin ND (1976) Solid State Physics. Holt, Rinehart and Winston, New York
6. Becke AD (1988) Density-functional exchange-energy approximation with exact asymptotic behaviour. Phys Rev A 38:3098-3100
7. Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 98:5648
8. Becke AD (1996) Density-functional thermochemistry. IV. A new dynamical correlation functional and implications for exact-exchange mixing. J Chem Phys 104:1040
9. Burke K, Perdew JP, Ernzerhof M (1998) Why semi-local density functionals work: Accuracy of the on-top pair density and importance of system averaging. J Chem Phys 109:3760
10. Carrier P, Wentzcovitch R, Tsuchiya J (2007) First-principles prediction of crystal structures at high temperatures using the quasiharmonic approximation. Phys Rev B 76:064116
11. Ceperley DM, Alder BJ (1980) Ground state of the electron gas by a stochastic method. Phys Rev Lett 45:566-569
12. Constantin LA, Perdew JP, Tao J (2006) Meta-generalized gradient approximation for the exchange-correlation hole, with an application to the jellium surface. Phys Rev B 73:205104
13. Csonka GI, Perdew JP, Ruzsinszky A, Philipsen PHT, Lebegue S, Paier J, Vydrov OA, Angyan JG (2009) Assessing the performance of recent density functionals for solids. Phys Rev B 79:155107
14. Csonka GI, Vydrov OA, Scuseria GE, Ruzsinszky A, Perdew JP (2007) Diminished gradient dependence of density functionals: Constraint satisfaction and self-interaction correction. J Chem Phys 126:244107
15. Dreizler RM (2003) Relativistic density functional theory. In: A Primer in Density Functional Theory. Fiolhais C, Nogueira F, Marques M (eds) Springer, Berlin, p 123-143
16. Dreizler RM, Gross EKU (1990) Density Functional Theory. Springer, Berlin
17. Goerling A, Levy M (1993) Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion. Phys Rev B 47:13105
18. Gunnarsson O, Lundqvist BI (1976) Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys Rev B 13:4274-4298
19. Harl J, Kresse G (2009) Accurate bulk properties from approximate many-body techniques. Phys Rev Lett 103:056401
20. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864-B871
21. Kanhere DG, Panat PV, Rajagopal AK, Callaway J (1986) Exchange-correlation potentials for spin-polarized systems at finite temperature. Phys Rev A 33:490-497
22. Karki BB, Stixrude L, Wentzcovitch R (2001) High-pressure elastic properties of major materials of earth's mantle from first principles. Rev Geophys 39:507-534
23. Kohn W (1999) Nobel lecture: Electronic structure of matter - wave functions and density functionals. Rev Mod Phys 71:1253-1266
24. Kohn W, Sham LJ (1965) Selfconsistent equations including exchange and correlation effects. Phys Rev 140:A1133-A1138
25. Kuemmel S, Perdew JP (2003) Optimized effective potential made simple: Orbital functionals, orbital shifts, and the exact Kohn-Sham exchange potential. Phys Rev B 68:035103
26. Kurth S, Perdew JP (2000) Role of the exchange-correlation energy: Nature's glue. Lit J Quantum Chem 77:814-818
27. Kurth S, Perdew JP, Blaha P (1999) Molecular and solid state tests of density functional approximations: LSD, GGA's, and Meta-GGA's. Int J Quantum Chem 75:889-909
28. Langreth DC, Mehl MJ (1983) Beyond the local-density approximation in calculations of ground-state electronic properties. Phys Rev B 28:1809-1834
29. Langreth DC, Perdew JP (1975) The exchange-correlation energy of a metallic surface. Solid State Commun 17:1425-1429
30. Langreth DC, Perdew JP (1980) Theory of nonuniform electronic systems: I. Analysis of the gradient approximation and a generalization mat works. Phys Rev B 21:5469-5493
31. Langreth DC, Vosko SH (1990) Response functions and non-local functionals. In: Density Functional Theory of Many-Fermion Systems - In celebration of the 25th anniversary of the Hohenberg-Kohn theorem. Trickey SB (ed) Academic, Orlando, p 175-201
32. Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785-789
33. Levy M (1979) Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals, and solution of the v-representability problem. Proc Natl Acad Sci USA 76:6062-6065
34. Levy M (1991) Density functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole. Phys Rev A 43:4637-4646
35. Levy M, Perdew JP (1985) Hellmann-Feynman, virial, and scaling requisites for the exact universal density functional. Shape of the correlation potential and diamagnetic susceptibility for atoms. Phys Rev A 32:2010-2021
36. Lieb EH, Oxford S (1981) Improved lower bound on the indirect Coulomb energy. Int J Quantum Chem 19:427-439
37. Martin RM (2004) Electronic Structure: Basic Theory and Practical Methods. Cambridge University Press
38. Mermin ND (1965) Thermal properties of the inhomogeneous electron gas. Phys Rev 137:A1441-A1443
39. Mori-Sanchez P, Cohen AJ, Yang W (2009) Failure of the random phase approximation correlation energy. eprint axXiv:0903.4403
40. Neaton JB, Ashcroft NW (1999) Pairing in dense lithium. Nature 400:141-144
41. Neumann R, Nobes RH, Handy NC (1996) Exchange functionals and potentials. Mol Phys 87:1-36
42. Parr RG, Yang W (1989) Density-Functional Theory of Atoms and Molecules. Oxford University Press, New York
43. Perdew JP (1991) Unified theory of exchange and correlation beyond the local spin density approximation. In: Electronic Structure of Solids. Ziesche P, Eschrig H (eds) Akademie Verlag, Berlin, p 11
44. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865-3868
45. Perdew JP, Burke K, Wang Y (1998) Generalized gradient approximation for the exchange-correlation hole of a many-electron system. Phys Rev B 54:16533-16539
46. Perdew JP, Kurth S (2003) Density functionals for non-relativistic Coulomb systems in the new century. In: A Primer in Density Functional Theory. Fiolhais C, Noguiera F, Marques M (eds) Springer, Berlin, p 1-55
47. Perdew JP, Levy M (1983) Physical Content of the exact Kohn-Sham orbital energies: Band gaps and derivative discontinuities. Phys Rev Lett 51:1884-1887
48. Perdew JP, Parr RG, Levy M, Balduz JL (1982) Density functional theory for fractional particle number: Derivative discontinuities of the energy. Phys Rev Lett 49:1691-1694
49. Perdew JP, Ruzsinszky A, Constantin LA, Sun J, Csonka GI (2009a) Some fundamental issues in ground-state density functional theory: A guide for the perplexed. J Chem Theory Comput 5:902-908
50. Perdew JP, Ruzsinszky A, Csonka GI, Constantin LA, Sun J (2009b) Workhorse semilocal density functional for condensed matter physics and quantum chemistry. Phys Rev Lett 103:026403
51. Perdew JP, Ruzsinszky A, Csonka GI, Vydrov OA, Scuseria GE, Staroverov VN, Tao J (2007) Exchange and correlation in open systems of fluctuating electron number. Phys Rev A 76:040501
52. Perdew JP, Ruzsinszky A, Tao J, Csonka GI, Constantin LA, Zhou X, Vydrov OA, Scuseria GE, Burke K (2008a) Restoring the gradient expansion for exchange in solids and surfaces. Phys Rev Lett 100:136406
53. Perdew JP, Savin A, Burke K (1995) Escaping the symmetry dilemma through a pair-density interpretation of spin-density functional theory. Phys Rev A 51:4531-4541
54. Perdew JP, Schmidt K (2001) Jacob's ladder of density functional approximations for the exchange-correlation energy. In: Density Functional Theory and its Applications to Materials. Van Doren VE, Van Alsenoy K, Geerlings P (eds) American Institute of Physics, Melville, New York, p 1-20
55. Perdew JP, Staroverov VN, Tao J, Scuseria GE (2008b) Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction. Phys Rev A 78:052513
56. Perdew JP, Wang Y (1986) Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. Phys Rev B 33:8800-8802
57. Perdew JP, Wang Y (1992) Accurate and simple analytic representation of the electron gas correlation energy. Phys Rev B 45:13244-13249
58. Perdew JP, Zunger A (1981) Self-interaction correction to density functional approximations for many-electron systems. Phys Rev B 23:5048-5079
59. Perrot F, Dharma-wardana MWC (2000) Spin-polarized electron liquid at arbitrary temperature: Exchange-correlation energies, electron distribution functions, and the static response functions. Phys Rev B 62:16536-16548
60. Pollock L, Perdew JP (1998) Exchange-correlation corrections to the lattice dynamics of simple metals and a search for soft modes at normal and expanded volumes. Int J Quantum Chem 69:359
61. Ruzsinszky A, Perdew JP, Csonka GI (2005) Binding energy curves from nonempirical density functionals I. Shared-electron bonds in closed-shell and radical molecules. J Phys Chem A 109:11015
62. Ruzsinszky A, Perdew JP, Csonka GI, Vydrov OA, Scuseria GE (2006) Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals. J Chem Phys 125:194112
63. +. J Chem Phys 126:194112
64. Sha X, Cohen RE (2006) Lattice dynamics and thermodynamics of bcc iron under pressure: First-principles linear response theory. Phys Rev B 73:104303
65. Sham LJ, Schlueter M (1983) Density functional theory of the energy gap. Phys Rev Lett 51:1888
66. Slater JC (1974) The Self-Consistent Field for Molecules and Solids. McGraw-Hill, New York
67. Soederlind P, Ross M (2000) Rubidium at high pressure and temperature. J Phys Condens Matter 12:921
68. Steinle-Neumann G, Cohen RE, Stixrude L (2004) Magnetism in iron as a function of pressure. J Phys Condens Matter 16:S1109
69. Stixrude L, Cohen RE, Singh DJ (1994) Iron at high pressure: Linearized-augmented-plane-wave computations in the generalized gradient approximation. Phys Rev B 50:6442
70. Tao J, Perdew JP (2005) Test of a nonempirical density functional: Short-range part of the van der Waals interaction in rare-gas clusters. J Chem Phys 122:114102
71. Tao J, Perdew JP, Staroverov VN, Scuseria GE (2003) Climbing the density functional ladder: Nonempirical meta-generalized gradient approximation designed for molecules and solids. Phys Rev Lett 91:146401 [TPSS]
72. Vitos L, Johansson B, Kollar J (2000) Exchange energy in the local Airy gas approximation. Phys Rev B 62:10046
73. von Barth U, Hedin L (1972) A local exchange-correlation potential for the spin-polarized case, (i) J Phys C 5:1629
74. Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin-density calculations. Can J Phys 58:1200
75. Wu ZG, Cohen RE (2006) More accurate generalized gradient approximation for solids. Phys Rev B 73:235116
76. Young DA (1991) Phase Diagrams of the Elements. University of California Press
77. Zhao Y, Truhlar DG (2006) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals and systematic tests of four M06-class functionals and 12 other functionals. Theor Chem Acc 120:1432
78. Zhao Y, Truhlar DG (2008) Construction of a generalized gradient approximation by restoring the density-gradient expansion and enforcing a tight Lieb-Oxford bond. J Chem Phys 128:184109
79. Ziegler T, Rauk A, Baerends EJ ( 1977) Calculation of multiplet energies by Hartree-Fock-Slater method. Theor Chim Acta 43:261