Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices

Journal of Chemical Physics

Volumn 140, Issue 17, 2014, Pages

  Leclerc, Arnaud ^a,b   Carrington, Tucker ^a  

^a QUEEN S UNIVERSITY   (Canada)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ITERATIVE METHODS; VIBRATIONAL SPECTRA;

BASIS FUNCTIONS; DIMENSIONAL VECTORS; DIRECT PRODUCT; ITERATIVE APPROACH; LINEAR COMBINATIONS; MODEL HAMILTONIANS; RANK REDUCTION; SUM OF PRODUCTS;

HAMILTONIANS;

EID: 84900003805     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4871981     Document Type: Article

References (102)

1. C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950). 10.6028/jres.045.026
2. J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Vol. I: Theory (SIAM Classics in Applied Mathematics, 2002).
3. D. Neuhauser, J. Chem. Phys. 93, 2611 (1990). 10.1063/1.458900
4. V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 106, 5085 (1997). 10.1063/1.473554
5. R. Chen and H. Guo, J. Chem. Phys. 111, 464 (1999). 10.1063/1.479327
6. S.-W. Huang and T. Carrington, Chem. Phys. Lett. 312, 311 (1999). 10.1016/S0009-2614(99)00889-1
7. H. Koeppel, W. Domcke, and L. S. Cederbaum, Adv. Chem. Phys. 57, 59 (1984).
8. M. Bramley and T. Carrington, J. Chem. Phys. 99, 8519 (1993). 10.1063/1.465576
9. M. Bramley, J. Tromp, T. Carrington, and G. Corey, J. Chem. Phys. 100, 6175 (1994). 10.1063/1.467273
10. C. Leforestier, L. Braly, K. Liu, M. Elrod, and R. Saykally, J. Chem. Phys. 106, 8527 (1997). 10.1063/1.473908
11. F. L. Quere and C. Leforestier, J. Chem. Phys. 94, 1118 (1991). 10.1063/1.460017
12. N. P. P. Sarkar and T. Carrington, J. Chem. Phys. 110, 10269 (1999). 10.1063/1.478960
13. G. M. R. Chen and H. Guo, J. Chem. Phys. 114, 4763 (2001). 10.1063/1.1348274
14. J. C. Tremblay and T. Carrington, J. Chem. Phys. 125, 094311 (2006). 10.1063/1.2234480
15. G. M. R. Chen and H. Guo, Chem. Phys. Lett. 320, 567 (2000). 10.1016/S0009-2614(00)00254-2
16. R. Dawes, X.-G. Wang, A. W. Jasper, and T. Carrington, J. Chem. Phys. 133, 134304 (2010). 10.1063/1.3494542
17. G. Avila and T. Carrington, J. Chem. Phys. 135, 064101 (2011). 10.1063/1.3617249
18. J. C. Light and T. Carrington, Adv. Chem. Phys. 114, 263 (2000).
19. S. Carter, J. M. Bowman, and N. C. Handy, Theor. Chim. Acta 100, 191 (1998). 10.1007/s002140050379
20. D. M. Benoit, J. Chem. Phys. 120, 562 (2004). 10.1063/1.1631817
21. P. Meier, M. Neff, and G. Rauhut, J. Chem. Theory Comput. 7, 148 (2011). 10.1021/ct1004752
22. R. Dawes and T. Carrington, J. Chem. Phys. 122, 134101 (2005). 10.1063/1.1863935
23. R. Dawes and T. Carrington, J. Chem. Phys. 124, 054102 (2006). 10.1063/1.2162168
24. S. Carter and N. C. Handy, Comput. Phys. Rep. 5, 115 (1986).
25. D. T. Colbert and W. H. Miller, J. Chem. Phys. 96, 1982 (1992). 10.1063/1.462100
26. H.-G. Yu, J. Chem. Phys. 117, 2030 (2002). 10.1063/1.1488575
27. C. Iung, C. Leforestier, and R. E. Wyatt, J. Chem. Phys. 98, 6722 (1993). 10.1063/1.464764
28. Z. Bacic and J. C. Light, Annu. Rev. Phys. Chem. 40, 469 (1989). 10.1146/annurev.pc.40.100189.002345
29. J. R. Henderson and J. Tennyson, Chem. Phys. Lett. 173, 133 (1990). 10.1016/0009-2614(90)80066-M
30. M. Mladenovic, Spectrochim. Acta, Part A 58, 795 (2002). 10.1016/S1386-1425(01)00669-2
31. D. Luckhaus, J. Chem. Phys. 113, 1329 (2000). 10.1063/1.481924
32. J. M. Bowman and B. Gazdy, J. Chem. Phys. 94, 454 (1991). 10.1063/1.460361
33. S. Carter and N. C. Handy, Comput. Phys. Commun. 51, 49 (1988). 10.1016/0010-4655(88)90061-6
34. M. J. Bramley and N. C. Handy, J. Chem. Phys. 98, 1378 (1993). 10.1063/1.464305
35. S. Carter and N. C. Handy, Mol. Phys. 100, 681 (2002). 10.1080/00268970110105415
36. Multidimensional Quantum Dynamics: MCTDH Theory and Applications, edited by H.-D. Meyer, F. Gatti, and G. A. Worth (Wiley-VCH, Weinheim, 2009).
37. M. H. Beck, A. Jaeckle, G. A. Worth, and H.-D. Meyer, Phys. Rep. 324, 1 (2000). 10.1016/S0370-1573(99)00047-2
38. M. J. Davis and E. J. Heller, J. Chem. Phys. 71, 3383 (1979). 10.1063/1.438727
39. B. Poirier, J. Theor. Comput. Chem. 2, 65 (2003). 10.1142/ S0219633603000380
40. T. Halverson and B. Poirier, J. Chem. Phys. 137, 224101 (2012). 10.1063/1.4769402
41. A. Shimshovitz and D. J. Tannor, Phys. Rev. Lett. 109, 070402 (2012). 10.1103/PhysRevLett.109.070402
42. X.-G. Wang and T. Carrington, J. Phys. Chem. A 105, 2575 (2001). 10.1021/jp003792s
43. G. Avila and T. Carrington, J. Chem. Phys. 131, 174103 (2009). 10.1063/1.3246593
44. G. Avila and T. Carrington, J. Chem. Phys. 137, 174108 (2012). 10.1063/1.4764099
45. D. Lauvergnat and A. Nauts, Spectrochim. Acta, Part A 119, 18 (2014). 10.1016/j.saa.2013.05.068
46. M. Bramley and T. Carrington, J. Chem. Phys. 101, 8494 (1994). 10.1063/1.468110
47. X.-G. Wang and T. Carrington, J. Chem. Phys. 117, 6923 (2002). 10.1063/1.1506911
48. R. A. Friesner, J. A. Bentley, M. Menou, and C. Leforestier, J. Chem. Phys. 99, 324 (1993). 10.1063/1.465810
49. A. Viel and C. Leforestier, J. Chem. Phys. 112, 1212 (2000). 10.1063/1.480674
50. G. Avila and T. Carrington, J. Chem. Phys. 134, 054126 (2011). 10.1063/1.3549817
51. T. Zhang and G. H. Golub, SIAM J. Matrix Anal. Appl. 23, 534 (2001). 10.1137/S0895479899352045
52. G. Beylkin and M. J. Mohlenkamp, PNAS 99, 10246 (2002). 10.1073/pnas.112329799
53. G. Beylkin and M. J. Mohlenkamp, SIAM J. Sci. Comput. 26, 2133 (2005). 10.1137/040604959
54. U. Benedikt, A. A. Auer, M. Espig, and W. Hackbusch, J. Chem. Phys. 134, 054118 (2011). 10.1063/1.3514201
55. F. A. Bischoff and E. F. Valeev, J. Chem. Phys. 134, 104104 (2011). 10.1063/1.3560091
56. F. A. Bischoff, R. J. Harrison, and E. F. Valeev, J. Chem. Phys. 137, 104103 (2012). 10.1063/1.4747538
57. E. G. Hohenstein, R. M. Parrish, and T. J. Martinez, J. Chem. Phys. 137, 044103 (2012). 10.1063/1.4732310
58. R. M. Parrish, E. G. Hohenstein, T. J. Martinez, and C. D. Sherrill, J. Chem. Phys. 137, 224106 (2012). 10.1063/1.4768233
59. E. G. Hohenstein, R. M. Parrish, C. D. Sherrill, and T. J. Martinez, J. Chem. Phys. 137, 221101 (2012). 10.1063/1.4768241
60. T. G. Kolda and B. W. Bader, SIAM Rev. 51, 455 (2009). 10.1137/07070111X
61. F. L. Hitchcock, J. Math. Phys. 6, 164 (1927).
62. L. R. Tucker, Psychometrika 31, 279 (1966). 10.1007/BF02289464
63. W. Hackbusch and S. Kühn, J. Fourier Anal. Appl. 15, 706 (2009). 10.1007/s00041-009-9094-9
64. L. Grasedyck, SIAM J. Matrix Anal. Appl. 31, 2029 (2010). 10.1137/090764189
65. D. Kressner and C. Tobler, Comput. Methods Appl. Math. 11, 363 (2011). 10.2478/cmam-2011-0020
66. I. V. Oseledets, SIAM J. Sci. Comput. 33, 2295 (2011). 10.1137/090752286
67. H. Wang and M. Thoss, J. Chem. Phys. 119, 1289 (2003). 10.1063/1.1580111
68. D. Pelaez and H.-D. Meyer, J. Chem. Phys. 138, 014108 (2013). 10.1063/1.4773021
69. S. Manzhos and T. Carrington, J. Chem. Phys. 125, 194105 (2006). 10.1063/1.2387950
70. S. Manzhos and T. Carrington, J. Chem. Phys. 127, 014103 (2007). 10.1063/1.2746846
71. S. Manzhos and T. Carrington, J. Chem. Phys. 129, 224104 (2008). 10.1063/1.3021471
72. J. C. M. S. E. Pradhan, J.-L. Carreon-Macedo, and A. Brown, J. Phys. Chem. A 117, 6925 (2013). 10.1021/jp309651r
73. G. Strang, Introduction to Applied Mathematics (Wellesley Cambridge Press, Wellesley, Massachusetts, 1986).
74. Y. Saad, Numerical Methods for Large Eigenvalue Problems, 2nd ed. (SIAM Classics in Applied Mathematics, 2011).
75. B. N. Parlett, The Symmetric Eigenvalue Problem (Prentice Hall, Englewood Cliffs, NJ, 1980), Chap. 4 (republished by SIAM, Philadelphia, 1998).
76. S. R. Chinnamsetty, M. Espig, B. N. Khoromskij, and W. Hackbusch, J. Chem. Phys. 127, 084110 (2007). 10.1063/1.2761871
77. M. Espig, W. Hackbusch, T. Rohwedder, and R. Schneider, Numer. Math. 122, 469 (2012). 10.1007/s00211-012-0464-x
78. S.-W. Huang and T. Carrington Jr., J. Chem. Phys. 112, 8765 (2000). 10.1063/1.481492
79. B. Poirier and T. Carrington Jr., J. Chem. Phys. 114, 9254 (2001). 10.1063/1.1367396
80. B. Poirier and T. Carrington Jr., J. Chem. Phys. 116, 1215 (2002). 10.1063/1.1428752
81. W. Bian and B. Poirier, J. Theor. Comput. Chem. 2, 583 (2003). 10.1142/S0219633603000768
82. D. Begue, P. Carbonnière, and C. Pouchan, J. Phys. Chem. A 109, 4611 (2005). 10.1021/jp0406114
83. J. K. G. Watson, Mol. Phys. 15, 479 (1968). 10.1080/00268976800101381
84. L. Henry and G. Amat, J. Mol. Spectrosc. 5, 319 (1961). 10.1016/0022-2852(61)90096-0
85. L. Henry and G. Amat, J. Mol. Spectrosc. 15, 168 (1965). 10.1016/0022-2852(65)90034-2
86. H. H. Nielsen, Rev. Mod. Phys. 23, 90 (1951). 10.1103/RevModPhys.23.90
87. B. Poirier and T. Halverson, private communication (November 2013).
88. I. Nagawa and T. Shimanouchi, Spectrochim. Acta 18, 513 (1962). 10.1016/S0371-1951(62)80163-5
89. M. Koivusaari, V. M. Horneman, and R. Anttila, J. Mol. Spectrosc. 152, 377 (1992). 10.1016/0022-2852(92)90076-Z
90. A. Tolonen, M. Koivusaari, R. Paso, J. Schroderus, S. Alanko, and R. Anttila, J. Mol. Spectrosc. 160, 554 (1993). 10.1006/jmsp.1993.1201
91. R. Paso, R. Anttila, and M. Koivusaari, J. Mol. Spectrosc. 165, 470 (1994). 10.1006/jmsp.1994.1150
92. J. Duncan, D. McKean, F. Tullini, G. Nivellini, and J. P. Pea, J. Mol. Spectrosc. 69, 123 (1978). 10.1016/0022-2852(78)90033-4
93. B. T. S. Edit Matyus, G. Czako, and A. G. Csaszar, J. Chem. Phys. 127, 084102 (2007). 10.1063/1.2756518
94. H.-G. Yu and J. T. Muckerman, J. Mol. Spectrosc. 214, 11 (2002). 10.1006/jmsp.2002.8569
95. X.-G. Wang, T. Carrington, J. Tang, and A. R. W. McKellar, J. Chem. Phys. 123, 034301 (2005). 10.1063/1.1924408
96. U. Manthe, J. Chem. Phys. 105, 6989 (1996). 10.1063/1.471847
97. F. Huarte-Larraaga and U. Manthe, J. Chem. Phys. 113, 5115 (2000). 10.1063/1.1311802
98. H. Nakatsuji, Acc. Chem. Res. 45, 1480 (2012). 10.1021/ar200340j
99. E. Davidson, J. Comput. Phys. 17, 87 (1975). 10.1016/0021-9991(75)90065-0
100. S.-I. Chu and D. A. Telnov, Phys. Rep. 390, 1 (2004). 10.1016/j.physrep.2003.10.001
101. A. Leclerc, S. Guérin, G. Jolicard, and J. P. Killingbeck, Phys. Rev. A 83, 032113 (2011). 10.1103/PhysRevA.83.032113
102. A. Leclerc, G. Jolicard, D. Viennot, and J. P. Killingbeck, J. Chem. Phys. 136, 014106 (2012). 10.1063/1.3673320