Innovations in finite-temperature density functionals

Lecture Notes in Computational Science and Engineering

Volumn 96, Issue , 2014, Pages 61-85

  Karasiev, Valentin V ^a   Sjostrom, Travis ^a   Chakraborty, Debajit ^a   Dufty, James W ^b   Runge, Keith ^a   Harris, Frank E ^a   Trickey, S B ^a  

^a UNIVERSITY OF FLORIDA   (United States)

^b NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; COMPUTATION THEORY; FREE ENERGY; MOLECULAR DYNAMICS; QUANTUM CHEMISTRY; SURVEYS; WAVE PLASMA INTERACTIONS;

AB INITIO MOLECULAR DYNAMICS; COMPUTATIONAL BOTTLENECKS; COMPUTATIONAL TECHNIQUE; EFFECTIVE INTERACTIONS; EXCHANGE CORRELATIONS; FINITE TEMPERATURES; HARTREE-FOCK CALCULATIONS; KOHN-SHAM CALCULATIONS;

DENSITY FUNCTIONAL THEORY;

EID: 84908077441     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-319-04912-0__3     Document Type: Article

References (120)

1. K. Gavroglu, Eur. J. Phys. 15, 9 (1994) and References therein
2. P.A. Bauer, E.K. Dabora, N. Manson, in Dynamics of Detonations and Explosions: Detonations, ed. by A.L. Kuhl, J.-C. Leyer, A.A. Borisov, W.A. Siriganano (American Institute of Aeronautics and Astronautics, Washington, DC, 1991), pp. 3ff and References therein
3. Basic Research Needs for High Energy Density Laboratory Physics (Report of the Workshop on Research Needs, Nov. 2009). U.S. Department of Energy, Office of Science and National Nuclear Security Administration (2010); see Chapter 6 and References therein
4. H.F. Wilson, B. Militzer, Phys. Rev. Lett. 108, 111101 (2012)
5. R.P. Drake, Phys. Today 63, 28 (2010) and References therein
6. B.A. Remington, R.P. Drake, D.D. Ryutov, Rev. Mod. Phys. 78, 755 (2006) and References therein
7. R.P. Drake, High-Energy-Density Physics (Springer, Berlin, 2006) and References therein
8. J. Li, C.B. Agee, Nature 381, 686 (1996)
9. M.J. Drake, K. Righter, Nature 416, 39 (2002)
10. E. Jagoutz, H. Palme, H. Baddenhausen, K. Blum, M. Cendales, G. Dreibus, B. Spettel, V. Lorenz, H. Wanke, Proc. Lunar Planet. Sci. Conf. 10, 2031 (1979)
11. H. Wanke, Phil. Trans. Roy. Soc. Lond. A 303, 287 (1981)
12. C.J. Allegre, J.-P. Poirer, E. Humler, A.W. Hofmann, Earth Planet. Sci. Lett. 134, 515 (1995)
13. K. Righter, M.J. Drake, Earth Planet. Sci. Lett. 146, 541 (1997)
14. J.C. Boettger, S.B. Trickey, Phys. Rev. B 51, R15623 (1995)
15. J.C. Boettger, S.B. Trickey, Phys. Rev. B 53, 3007 (1996)
16. R.N. Barnett, U. Landman, Phys. Rev. B 48, 2081 (1993)
17. D. Marx, J. Hutter, Ab initio molecular dynamics: theory and implementation, in Modern Methods and Algorithms of Quantum Chemistry, ed. by J. Grotendorst, NIC Series, vol. 1 (John von Neumann Institute for Computing, J ulich, 2000), pp. 301ff and References therein
18. J.S. Tse, Annu. Rev. Phys. Chem. 53, 249 (2002)
19. D. Marx, J. Hutter, Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods (Cambridge University Press, Cambridge, 2009) and References therein
20. T.D. Kühne, Ab-initio molecular dynamics arXiv:1201.5945 [physics.chem-ph]
21. W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)
22. P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)
23. M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979)
24. E.H. Lieb, Int. J. Quantum Chem. 24, 243 (1983)
25. R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules (Oxford, New York, 1989). For T-dependent theory see Sections 3.6 and 9.1
26. R.M. Dreizler, E.K.U. Gross, Density Functional Theory (Springer, Berlin, 1990)
27. L.A. Collins (Los Alamos National Lab), Equilibrium and non-equilibrium orbital-free molecular dynamics simulations at extreme conditions, CECAM Workshop, Paris, 05 Sept 2012
28. D.O. Gericke (Univ.Warwick), Effective interactions and ion dynamics in warm dense matter, Invited Talk I8, Physics of Non-ideal Plasmas 14, Rostock Germany, 11 Sept 2012
29. N.D. Mermin, Phys. Rev. 137, A1441 (1965)
30. A.K. Rajagopal, A density functional formalism for condensed matter systems, in Density Functional Methods in Physics, ed. by J. da Providencia, R.M. Dreizler, NATO ASI B, vol. 123 (Plenum, New York, 1985), pp. 159ff
31. M.V. Stoitsov, I.Zh. Petkov, Ann. Phys. 184, 121 (1988)
32. R.M. Dreizler, Density functional theory at finite temperatures, in The Nuclear Equation of State, Part A, ed by W. Greiner, H. Stöcker, NATO ASI B, vol. 216 (Plenum, NY, 1989), pp. 521ff
33. J.P. Perdew, K. Schmidt, A.I.P. Conf. Proc. 577, 1 (2001)
34. F. Perrot, M.W.C. Dharma-wardana, Phys. Rev. A 30, 2619 (1984)
35. N.D. Mermin, Ann. Phys. (NY) 21, 99 (1963)
36. J. Sokoloff, Ann. Phys. (NY) 45, 186 (1967)
37. J. Dolbeault, P. Felmer, M. Lewin, Math. Model. Methods Appl. Sci. 19, 347 (2009)
38. Y.A. Wang, E.A. Carter, Orbital-free kinetic-energy density functional theory, Chap. 5 in Theoretical Methods in Condensed Phase Chemistry, ed. by S.D. Schwartz (Kluwer, New York, 2000), pp. 117ff and References therein
39. M. Hodak, W. Lu, J. Bernholc, J. Chem. Phys. 128, 014101 (2008)
40. X. Blanc, E. Cances, J. Chem. Phys. 122, 214106 (2005)
41. E.V. Ludeña, J. Chem. Phys. 79, 6174 (1983)
42. R. Cuevas-Saavedra, D. Chakraborty, P.W. Ayers, Phys. Rev. A 85, 042519 (2012)
43. T.A. Wesołowski, Phys. Rev. A 77, 012504 (2008) and References therein
44. J.W. Kaminski, S. Gusarov, T.A. Wesołowski, A. Kovalenko, J. Phys. Chem. A, 114, 6082 (2010) and References therein
45. V.V. Karasiev, S.B. Trickey, F.E. Harris, J. Comput. Aided Mat. Des. 13, 111 (2006)
46. V.V. Karasiev, R.S. Jones, S.B. Trickey, F.E. Harris, Recent advances in developing orbitalfree kinetic energy functionals, in New Developments in Quantum Chemistry, ed. by J.L. Paz, A.J. Hernández (Transworld Research Network, Kerala, 2009), pp. 25ff
47. V.V. Karasiev, R.S. Jones, S.B. Trickey, F.E. Harris, Phys. Rev. B 80, 245120 (2009)
48. S.B. Trickey, V.V. Karasiev, R.S. Jones, Int. J. Quantum Chem. 109, 2943 (2009)
49. C.F. von Weizsäcker, Z. Phys. 96, 431 (1935)
50. Y. Tal, R.F.W. Bader, Int. J. Quantum Chem. S12, 153 (1978)
51. L.J. Bartolotti, P.K. Acharya, J. Chem. Phys. 77, 4576 (1982)
52. J.E. Harriman, The interface between reduced density matrices and density functional theory, in Density Matrices and Density Functionals, ed. by R. Erdahl, V.H. Smith Jr. (D. Reidel, Dordrecht, 1987), pp. 359ff
53. M. Levy, H. Ou-Yang, Phys. Rev. A 38, 625 (1988)
54. R. Baltin, J. Chem. Phys. 86, 947 (1987)
55. J.W. Dufty, S.B. Trickey, Phys. Rev. B 84, 125118 (2011)
56. R.P. Feynman, N. Metropolis, E. Teller, Phys. Rev. 75, 1561 (1949)
57. J. Bartel, M. Brack, M. Durand, Nucl. Phys. A 445, 263 (1985)
58. M. Brack, C. Guet, H.-B. Hakansson, Phys. Rep. 123, 275 (1985)
59. F. Perrot, Phys. Rev. A 20, 586 (1979)
60. V.V. Karasiev, T. Sjostrom, S.B. Trickey, Phys. Rev. B 86, 115101 (2012)
61. B. Holst, R. Redmer, M. Desjarlais, Phys. Rev. B 77, 184201 (2008)
62. D.A. Horner, F. Lambert, J.D. Kress, L.A. Collins, Phys. Rev. B 80, 024305 (2009)
63. W. Ebeling, W. Richert, W.D. Kraeft, W. Stolzmann, Phys. Stat. Solidi (b) 104, 193 (1981)
64. S. Tanaka, S. Mitake, S. Ichimaru, Phys. Rev. A 32, 1896 (1985)
65. F. Perrot, M.W.C. Dharma-wardana, Phys. Rev. B 62 16536 (2000)
66. F. Perrot, M.W.C. Dharma-wardana, Phys. Rev. B. 67, 079901(E) (2003)
67. D.J.W. Geldart, E. Dunlap, M.L. Glasser, M.R.A. Shegelski, Solid State Commun. 88, 81 (1993)
68. E. Dunlap, D.J.W. Geldart, Can. J. Phys. 72, 1 (1994)
69. M.L. Glasser, D.J.W. Geldart, E. Dunlap, Can. J. Phys. 72, 7 (1994)
70. E. Brown. D. Ceperley, J. Dubois, Simulation of the warm, dense homogeneous electron gas. Paper X24-2, American Physical Society, March meeting, 1 Mar 2012
71. V.V. Karasiev, T. Sjostrom, S.B. Trickey, Phys. Rev. E 86, 056704 (2012)
72. T. Sjostrom, F.E. Harris, S.B. Trickey, Phys. Rev. B 85, 045125 (2012)
73. T. Sjostrom, Finite-temperature hartree-fock exchange and exchange-correlation free energy functionals, IPAM Workshop IV, Computational Challenges in Warm Dense Matter, UCLA, Los Angeles, May 2012, https://www.ipam.ucla.edu/publications/plws4/plws410624.pdf and to be published
74. F. Tran, T.A. Wesołowski, Int. J. Quantum Chem. 89, 441 (2002)
75. V.V. Karasiev, D. Chakraborty, O.A. Shukruto, S.B. Trickey, Phys. Rev. B 88, 161108(R) (2013)
76. M. Levy, J.P. Perdew, Phys. Rev. A 32, 2010 (1985)
77. M. Levy, The coordinate scaling requirements in density functional theory, in Single-Particle Density in Physics and Chemistry, ed. by N.H. March (Academic, London/San Diego, 1987), pp. 45ff
78. M. Levy, Phys. Rev. A 43, 4637 (1991)
79. M. Levy, Coordinate scaling requirements for approximating exchange and correlation, in Density Functional Theory, ed. by E.K.U. Gross, R.M. Dreizler, NATO ASI B, vol. 337 (Plenum, New York, 1995), pp. 11ff
80. S. Pittalis, C.R. Proetto, A. Floris, A. Sanna, C. Bersier, K. Burke, E.K.U. Gross, Phys. Rev. Lett. 107, 163001 (2011)
81. J.W. Dufty, S.B. Trickey, Finite temperature scaling in density functional theory (in preparation)
82. T. Gál, J.W. Dufty, S.B. Trickey, Local density approximation to the kinetic energy functional for finite Ne , in preparation
83. J. Dufty, S. Dutta, Phys. Rev. E 87, 032101 (2013)
84. J. Dufty, S. Dutta, Phys. Rev. E 87, 032102 (2013)
85. L.W. Wang, M.P. Teter, Phys. Rev. B 45, 13196 (1992)
86. B.J. Zhou, V.L. Ligneres, E.A. Carter, J. Chem. Phys. 122, 044103 (2005)
87. C. Huang, E.A. Carter, Phys. Rev. B 81, 045206 (2010)
88. J.W. Dufty, S.B. Trickey, Revised Thomas-Fermi functional for singular potentials, American Physical Society, March 2013 meeting abstract
89. F. Perrot, M.W.C. Dharma-wardana, Phys. Rev. B 62, 16536 (2000)
90. J.W. Dufty, S. Dutta, Contrib. Plasma Phys. 52, 100 (2012)
91. J.W. Dufty, Derivation and context of Kubo-Greenwood transport coefficients (in preparation)
92. S.B. Trickey, V.V. Karasiev, A. Vela, Phys. Rev. B 84, 075146 (2011)
93. A. Vela, J.C. Pacheco-Kato, J.L. Gázquez, J.M. del Campo, S.B. Trickey, J. Chem. Phys. 136, 144115 (2012)
94. J. Martín del Campo, J.L. Gázquez, R.J. Alvarez-Mendez, S.B. Trickey, A. Vela, Analysis of the generalized gradient approximation for the exchange energy, in Concepts and Methods in Modern Theoretical Chemistry, vol. 1, ed. by volume honoring Professor B.M. Deb, S.K. Ghosh and P.K. Chattaraj (Taylor and Francis/CRC, Boca Raton, 2012) in press
95. J.M. del Campo, J.L. Gázquez, S.B. Trickey, A. Vela, J. Chem. Phys. 136, 104108 (2012)
96. J. Martín del Campo, A. Vela, J.L. Gázquez, S.B. Trickey, Chem. Phys. Lett. 543, 179 (2012)
97. P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98, 11623 (1994)
98. J.P. Perdew, A. Ruzsinszky, G.I. Csonka, L.A. Constantin, J.W. Sun, Phys. Rev. Lett. 103, 026403 (2009).
99. J.P. Perdew, A. Ruzsinszky, G.I. Csonka, L.A. Constantin, J.W. Sun, Phys. Rev. Lett. 106, 179902 (2011)
100. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37, 785 (1984)
101. V.V. Karasiev, S.B. Trickey, Comput. Phys. Commun. 183, 2519 (2012)
102. G.K-L. Chan, A.J. Cohen, N.C. Handy, J. Chem. Phys. 114, 631 (2001)
103. X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Cote, T. Deutsch, L. Genovese, Ph. Ghosez, M. Giantomassi, S.G˜ oedecker, D.R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S.M˜ azevet, M.J.T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.-M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M.J. Verstraete, G. Zerah, J.W. Zwanziger, ABINIT: first-principles approach to material and nanosystem properties, Comput. Phys. Commun. 180, 2582 (2009)
104. X. Gonze, G.-M. Rignanese, M. Verstraete, J.-M. Beuken, Y. Pouillon, R. Caracas, F. Jollet, M. Torrent, G. Zerah, M. Mikami, Ph. Ghosez, M. Veithen, J.-Y. Raty, V. Olevano, F. Bruneval, L. Reining, R. Godby, G. Onida, D.R. Hamann, D.C. Allan, A brief introduction to the ABINIT software package, Zeit. Kristallogr. 220, 558 (2005)
105. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, Quantum espresso: a modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter 21, 395502 (2009)
106. G. Kresse, J. Hafner, Phys. Rev. B 47, 558 (1993)
107. G. Kresse, J. Hafner, Phys. Rev. B 49, 14251 (1994)
108. G. Kresse, J. Furthmüller, Comput. Mat. Sci. 6, 15 (1996)
109. G. Kresse, J. Furthmüller, Phys. Rev. B 54, 11169 (1996)
110. V. Heine, I. Abarenkov, Phil. Mag. 9, 451 (1964)
111. L. Goodwin, R.J. Needs, V. Heine, J. Phys. Condens. Matter 2, 351 (1990)
112. G.S. Ho, V.L. Lignères, E.A. Carter, Comput. Phys. Commun. 179, 839 (2008)
113. L. Hung, C. Huang, I. Shin, G.S. Ho, V.L. Lignères, E.A. Carter, Comput. Phys. Commun. 181, 2208 (2010)
114. V.V. Karasiev, T. Sjostrom, S.B. Trickey, Finite-temperature orbital-free DFT molecular dynamics: coupling PROFESS and QUANTUM ESPRESSO (in preparation)
115. Ki-dong Oh, P.A. Deymier, Phys. Rev. B 58, 7577 (1998) and References therein
116. Ki-dong Oh, P.A. Deymier, Phys. Rev. B 59, 11276 (1999) and References therein
117. M.P. Desjarlais, J.D. Kress, L.A. Collins, Phys. Rev. E 66, 025401 (2002)
118. D.A. Liberman, This distinction was recognized in the different values of in the X exchange functional of the late 1960s and early 1970s, Phys. Rev. 171, 1 (1968) as well as References in J.W.D. Connolly, in Semiempirical Methods of Electronic Structure Calculation, Part A: Techniques, ed. by G.A. Segal (Plenum, NY 1977), pp. 105ff
119. D.E. Taylor, V.V. Karasiev, K. Runge, S.B. Trickey, F.E. Harris, Computat. Mat. Sci. 39, 705 (2007)
120. R. Colle, O. Salvetti, Theor. Chim. Acta 37, 329 (1975)