Tensor representation techniques in post-Hartree-Fock methods: Matrix product state tensor format

Molecular Physics

Volumn 111, Issue 16-17, 2013, Pages 2398-2413

  Benedikt, Udo ^a   Auer, Henry ^b   Espig, Mike ^b   Hackbusch, Wolfgang ^b   Auer, Alexander A ^a  

^a MAX PLANCK INSTITUTE FOR CHEMICAL ENERGY CONVERSION   (Germany)

^b MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

canonical polyadic product; configuration interaction; coupled cluster; electronic structure methods; matrix product state; post Hartree Fock; tensor representation

Indexed keywords

CANONICAL POLYADIC PRODUCT; CONFIGURATION INTERACTIONS; COUPLED CLUSTERS; MATRIX PRODUCT STATE; POST-HARTREE-FOCK; TENSOR REPRESENTATION;

ALGORITHMS; CALCULATIONS; ELECTRONIC STRUCTURE; INTEGRAL EQUATIONS; MOLECULAR PHYSICS; NUMERICAL METHODS; QUANTUM CHEMISTRY;

TENSORS;

EID: 84885186999     PISSN: 00268976     EISSN: 13623028     Source Type: Journal    
DOI: 10.1080/00268976.2013.798433     Document Type: Article

References (128)

1. W. Koch and M.C. Holthausen, A Chemist?s Guide to Density Functional Theory (Wiley-VCH, Weinheim, 2001).
2. T. Schwabe,R.Huenerbein, and S.Grimme, Synlett 10(10), 1431 (2010).
3. C.D. Sherrill, J. Chem. Phys. 132(11), 110902 (2010).
4. M. Feyereisen, G. Fitzgerald, and A. Komornicki, Chem. Phys. Lett. 208(5-6), 359 (1993).
5. O.Vahtras, J. Almlof, and M. Feyereisen, Chem. Phys. Lett. 213(5-6), 514 (1993).
6. K. Eichkorn, O. Treutler, H. O hm, M. Haser, and R. Ahlrichs, Chem. Phys. Lett. 240(4), 283 (1995).
7. R. Kendall andH. Fruchtl, Theor. Chem. Acc. 97(1-4), 158 (1997).
8. F. Weigend, M. Haser, H. Patzelt, and R. Ahlrichs, Chem. Phys. Lett. 294(1-3), 143 (1998).
9. C. Hattig and F. Weigend, J. Chem. Phys. 113(13), 5154 (2000).
10. C. Hattig and K. Hald, Phys. Chem. Chem. Phys. 4(11), 2111 (2002).
11. C. Hattig, J. Chem. Phys. 118(17), 7751 (2003).
12. R. Ahlrichs, Phys. Chem. Chem. Phys. 6(22), 5119 (2004).
13. H.J.Werner, F.R. Manby, and P.J. Knowles, J. Chem. Phys. 118(18), 8149 (2003).
14. M. Schutz and F.R. Manby, Phys. Chem. Chem. Phys. 5(16), 3349 (2003).
15. F.R. Manby, J. Chem. Phys. 119(9), 4607 (2003).
16. F.P. Billingsley and J.E. Bloor, J. Chem. Phys. 55(11), 5178 (1971).
17. E.J. Baerends, D.E. Ellis, and P. Ros, Chem. Phys. 2(1), 41 (1973).
18. J.L. Whitten, J. Chem. Phys. 58(10), 4496 (1973).
19. B.I. Dunlap, J.W.D. Connolly, and J.R. Sabin, J. Chem. Phys. 71(12), 4993 (1979).
20. N.H.F. Beebe and J. Linderberg, Int. J. Quantum Chem. 12, 683 (1977).
21. I. Røeggen and E. Wisløff-Nilssen, Chem. Phys. Lett. 132(2), 154 (1986).
22. S. Wilson, Comput. Phys. Commun. 58(1-2), 71 (1990).
23. R. Lindh, U. Ryu, and B. Liu, J. Chem. Phys. 95(8), 5889 (1991).
24. H. Koch, A.S. deMeŕas, and T. B. Pedersen, J. Chem. Phys. 118(21), 9481 (2003).
25. F. Aquilante, T. B. Pedersen, and R. Lindh, J. Chem. Phys. 126(19), 194106 (2007).
26. F. Weigend, M. Kattannek, and R. Ahlrichs, J. Chem. Phys. 130(16), 164106 (2009).
27. J. Zienau, L. Clin, B. Doser, and C. Ochsenfeld, J. Chem. Phys. 130(20), 204112 (2009).
28. J. Almlof, Chem. Phys. Lett. 181(4), 319 (1991).
29. M. Haser and J. Almlof, J. Chem. Phys. 96(1), 489 (1992).
30. M. Haser, Theor. Chim. Acta. 87(1-2), 147 (1993).
31. A.K. Wilson and J. Almlof, Theor. Chim. Acta. 95(1-2), 49 (1997).
32. T.D. Crawford and H.F. Schaefer, Rev. Comp. Chem. 14, 33 (2000).
33. T. Helgaker,W. Klopper, and D.P. Tew,Mol. Phys. 106(16-18), 2107 (2008).
34. R.J. Bartlett, J. Phys. Chem. 93, 1697 (1989).
35. R.J. Bartlett, in Modern Electronic Structure Theory, edited by D. Yarkony (World Scientific, Singapore, 1995).
36. H.Larsen, J.Olsen, C.Hattig, P. Jørgensen,O.Christiansen, and J. Gauss, J. Chem. Phys. 111(5), 1917 (1999).
37. D. Feller and J. A. Sordo, J. Chem. Phys. 112(13), 5604 (2000).
38. J. Pittner and P. Hobza, Chem. Phys. Lett. 390(46), 496 (2004).
39. A. Tajti, P.G. Szalay, A.G. Csaszar, M. Kallay, J. Gauss, E.F. Valeev, B. A. Flowers, J. Vazquez, and J.F. Stanton, J. Chem. Phys. 121(23), 11599 (2004).
40. M. Heckert, M. Ḱallay, and J. Gauss, Mol. Phys. 103(15-16), 2109 (2005).
41. G. Rauhut, G. Knizia, and H.J. Werner, J. Chem. Phys. 130(5), 054105 (2009).
42. C. Hattig, D.P. Tew, and A. Kohn, J. Chem. Phys. 132(23), 231102 (2010).
43. P.O. Lowdin, Phys. Rev. 97(6), 1474 (1955).
44. P.O. Lowdin, Phys. Rev. 97 (6), 1490 (1955).
45. P.O. Lowdin, Phys. Rev. 97(6), 1509 (1955).
46. W. Kutzelnigg, Theor. Chim. Acta 1(4), 327 (1963).
47. R.K. Nesbet, Phys. Rev. 175(1), 2 (1968).
48. W. Meyer, Int. J. Quantum Chem. 5(S5), 341 (1971).
49. F. Neese, A. Hansen, and D.G. Liakos, J. Chem. Phys. 131(6), 064103 (2009).
50. F. Neese, F. Wennmohs, and A. Hansen, J. Chem. Phys. 130(11), 114108 (2009).
51. F. Neese, A. Hansen, F. Wennmohs, and S. Grimme, Acc. Chem. Res. 42(5), 641 (2009).
52. A. Anoop, W. Thiel, and F. Neese, J. Chem. Theory Comput. 6(10), 3137 (2010).
53. J. Yang, Y. Kurashige, F.R. Manby, and G.K.L. Chan, J. Chem. Phys. 134(4), 044123 (2011).
54. J. Yang, G.K.L. Chan, F.R. Manby, M. Schutz, and H.J. Werner, J. Chem. Phys. 136(14), 144105 (2012).
55. Y. Kurashige, J. Yang, G.K.L. Chan, and F.R. Manby, J. Chem. Phys. 136(12), 124106 (2012).
56. P. Pulay, Chem. Phys. Lett. 100(2), 151 (1983).
57. P. Pulay and S. Saebo, Theor. Chim. Acta 69(5-6), 357 (1986).
58. S. Saebø and P. Pulay, J. Chem. Phys. 86(2), 914 (1987).
59. L. Adamowicz and R.J. Bartlett, J. Chem. Phys. 86(11), 6314 (1987).
60. P. Neogŕady, M. Pitońak, and M. Urban, Mol. Phys. 103(15-16), 2141 (2005).
61. M. Pitońak, F. Holka, P. Neogŕady, and M. Urban, J. Mol. Struct. Theochem. 768(1-3), 79 (2006).
62. L. Adamowicz, Mol. Phys. 108(21), 3105 (2010).
63. C. Eckart and G. Young, Psychometrika 1(3), 211 (1936).
64. J.D. Carroll and J.J. Chang, Psychometrika 35(3), 283 (1970).
65. T. Kinoshita, O. Hino, and R.J. Bartlett, J. Chem. Phys. 119(15), 7756 (2003).
66. O. Hino, T. Kinoshita, and R.J. Bartlett, J. Chem. Phys. 121(3), 1206 (2004).
67. E.G. Hohenstein, R.M. Parrish, and T.J. Martinez, J. Chem. Phys. 137(4), 044103 (2012).
68. R. A. Harshman and M.E. Lundy, Comput. Stat. Data Anal. 18(1), 39 (1994).
69. A. Auer, U. Benedikt, M. Espig, and W. Hackbusch, in Oberwolfach Reports: Mathematical Methods in Quantum Chemistry, edited by Gero Friesecke and Peter Gill, Vol. 8, pp. 1808-1812.
70. U. Benedikt, A. A. Auer, M. Espig, and W. Hackbusch, J. Chem. Phys. 134(5), 054118 (2011).
71. W. Hackbusch and S. Kuhn, J. Fourier Anal. Appl. 15(5), 706 (2009).
72. L. Grasedyck, SIMAX 27, 1 (2009).
73. W. Hackbusch, Tensor Spaces and Numerical Tensor Calculus (Springer, Berlin, Heidelberg, 2012).
74. S.R. White and R.M. Noack, Phys. Rev. Lett. 68(24), 3487 (1992).
75. S.R. White, Phys. Rev. Lett. 69(19), 2863 (1992).
76. S. Rommer and S. O stlund, Phys. Rev. B 55(4), 2164 (1997).
77. G.K.L. Chan and M. Head-Gordon, J. Chem. Phys. 116(11), 4462 (2002).
78. G.K.L. Chan, J. Chem. Phys. 120(7), 3172 (2004).
79. U. Schollwock, Rev. Mod. Phys. 77(1), 259 (2005).
80. G.K.-L. Chan, J.J. Dorando, D. Ghosh, J. Hachmann, E. Neuscamman, H.Wang, and T.Yanai, in Frontiers in Quantum Systems in Chemistry and Physics, edited by S.Wilson, P.J. Grout, P. Piecuch, J. Maruani, and G. Delgado-Barrio (Progress in Theoretical Chemistry and Physics, Springer, Heidelberg, 2008).
81. K.H. Marti and M. Reiher, Mol. Phys. 108(3), 501 (2010).
82. K.H. Marti and M. Reiher, Z. Phys. Chem. 224(3-4), 583 (2010).
83. K.H. Marti, B. Bauer, M. Reiher, M. Troyer, and F. Verstraete, New J. Phys. 12, 103008 (2010).
84. U. Schollwock, Ann. Phys. 326(1), 96 (2011).
85. O. Legeza and G. F́ath, Phys. Rev. B 53(21), 14349 (1996).
86. O. Legeza and J. Śolyom, Phys. Rev. B 70, 205118 (2004).
87. O. Legeza, J. Roder, and B. A. Hess, Phys. Rev. B 67(12), 125114 (2003).
88. O. Legeza, J. Roder, and B. A. Hess, Mol. Phys. 101(13), 2019 (2003).
89. O. Legeza and J. Śolyom, Phys. Rev. B 68, 195116 (2003).
90. J. Rissler, R.M. Noack, and S.R. White, Chem. Phys. 323(23), 519 (2006).
91. V. Murg, F. Verstraete, O. Legeza, and R.M. Noack, Phys. Rev. B 82, 205105 (2010).
92. G. Barcza, O. Legeza, K.H. Marti, and M. Reiher, Phys. Rev. A 83, 012508 (2011).
93. R. Bellman, Adaptive Control Processes: A Guided Tour (Princeton University Press, Princeton, NJ, 1961).
94. R. Bellman, Dynamic Programming (Dover Publications, New York, 2003).
95. G. Beylkin and M.J. Mohlenkamp, Proc. Nat. Acad. Sci. USA 99(16), 10246 (2002).
96. G. Beylkin and M.J. Mohlenkamp, SIAM J. Sci. Comput. 26(6), 2133 (2005).
97. T.G. Kolda, SIAM J. Matrix Anal. Appl. 23(1), 243 (2001).
98. S.R. Chinnamsetty, M. Espig, B.N. Khoromskij, W. Hackbusch, and H.J. Flad, J. Chem. Phys. 127(8), 084110 (2007).
99. M. Espig, PhD thesis, Universitat Leipzig, 2008.
100. W. Hackbusch and B. Khoromskij, J. Complex. 23(4-6), 697 (2007).
101. W. Hackbusch and B.N. Khoromskij, SIAM J. Matrix Anal. Appl. 30(3), 1233 (2008).
102. E. Acar and B. Yener, IEEE T. Knowl. Data. En. 21(1), 6 (2009).
103. T.G. Kolda and B.W. Bader, SIAM Rev. 51(3), 455 (2009).
104. M. Espig, L. Grasedyck, and W. Hackbusch, Constr. Approx. 30(3), 557 (2009).
105. M. Espig, W. Hackbusch, A. Litvinenko, H. Matthies, and E. Zander, Efficient Analysis of High Dimensional Data in Tensor Formats, edited by Jochen Garcke and Michael Griebel (Springer, Berlin, Heidelberg, 2013), Vol. 88, pp. 31-56.
106. R. Bro, Chemom. Intell. Lab. Syst. 38(2), 149 (1997).
107. L. De Lathauwer, B. De Moor, and J. Vandewalle, SIAM J. Matrix Anal. Appl. 21(4), 1253 (2000).
108. R. Bro and H. A.L. Kiers, J. Chemom. 17(5), 274 (2003).
109. M. Espig and W. Hackbusch, Numer. Math. 122(3), 489 (2012).
110. M. Espig,W. Hackbusch, T. Rohwedder, and R. Schneider, Numer. Math. 122(3), 469 (2012).
111. L.R. Tucker, Psychometrika 31(3), 279 (1966).
112. L. De Lathauwer, B. De Moor, and J. Vandewalle, SIAM J. Matrix Anal. Appl. 21(4), 1324 (2000).
113. L. Grasedyck, SIAM. J. Matrix Anal. Appl. 31(4), 2029 (2010).
114. I.V. Oseledets and E.E. Tyrtyshnikov, Linear AlgebraAppl. 432(1), 70 (2010).
115. I. Oseledets, SIAM J. Sci. Comput. 33(5), 2295 (2011).
116. D. Perez-Garcia, F. Verstraete, M.Wolf, and J. Cirac, Quantum Inf. Comput. 7(5-6), 401 (2007).
117. G. Vidal, Phys. Rev. Lett. 91(14), 147902 (2003).
118. I.V. Oseledets, SIAM J. Sci. Comput. (2009).
119. M. Bebendorf, Numer. Math. 86, 565 (2000).
120. I. Oseledets, preprint (2009). .
121. I. Gavrilyuk, W. Hackbusch, and B. Khoromskij, Math. Comput. 73(247), 1297 (2004).
122. D. Braess and W. Hackbusch, IMA J. Numer. Anal. 25(4), 685 (2005).
123. Cfour, Coupled Cluster techniques for Computational Chemistry, a quantum-Chemical program package by J.F. Stanton, J. Gauss, M.E. Harding, P.G. Szalay with contributions from A. A. Auer, R.J. Bartlett, U. Benedikt, C. Berger, D.E. Bernholdt, O. Christiansen, M. Heckert, O. Heun, C. Huber, D. Jonsson, J. Juśelius, K. Klein, W.J. Lauderdale, D. Matthews, T. Metzroth, D.P. O?Neill, D.R. Price, E. Prochnow, K. Ruud, F. Schiffmann, S. Stopkowicz, A. Tajti, M.E. Varner, J. V́azquez, F. Wang, J.D. Watts and the integral packages MOLECULE (J. Almlof and P.R. Taylor), PROPS (P.R. Taylor), ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A.V. Mitin and C. Van Wullen. For the current version, see http://www.cfour.de.
124. W.J. Hehre, R. Ditchfie, and J. A. Pople, J. Chem. Phys. 56(5), 2257 (1972).
125. K.P. Huber and G.H. Herzberg, Molecular Spectra and Molecular Structure IV: Constants of Diatomic Molecules (Van Nostrand-Reinhold, New York, 1979).
126. A.R. Hoy, I.M. Mills, and G. Strey, Mol. Phys. 24(6), 1265 (1972).
127. T.H. Dunning, J. Chem. Phys. 90(2), 1007 (1989).
128. V. Khoromskaia, B. Khoromskij, and R. Schneider, Comput. Methods Appl. Math. 11(3), 327 (2011).