Automatic differentiation method for numerical construction of the rotational-vibrational Hamiltonian as a power series in the curvilinear internal coordinates using the Eckart frame

Journal of Chemical Physics

Volumn 143, Issue 1, 2015, Pages

  Yachmenev, Andrey ^a   Yurchenko, Sergei N ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AMMONIA; CHLORINE COMPOUNDS; HAMILTONIANS; KINETIC ENERGY; KINETICS; MOLECULES; PHOSPHORUS COMPOUNDS;

AUTOMATIC DIFFERENTIATIONS; CURVILINEAR COORDINATE; KINETIC-ENERGY OPERATOR; LARGE POLYATOMIC MOLECULES; POWER SERIES EXPANSIONS; SYMBOLIC DIFFERENTIATION; VIBRATIONAL CALCULATIONS; VIBRATIONAL HAMILTONIAN;

NUMERICAL METHODS;

EID: 84947240185     PISSN: 00219606     EISSN: 10897690     Source Type: Journal    
DOI: 10.1063/1.4923039     Document Type: Article

References (97)

1. D. Luckhaus, J. Chem. Phys. 113, 1329 (2000). 10.1063/1.481924
2. D. Lauvergnat and A. Nauts, J. Chem. Phys. 116, 8560 (2002). 10.1063/1.1469019
3. S. N. Yurchenko, W. Thiel, and P. Jensen, J. Mol. Spectrosc. 245, 126 (2007). 10.1016/j.jms.2007.07.009
4. E. Mátyus, G. Czakó, B. T. Sutcliffe, and A. G. Császár, J. Chem. Phys. 127, 084102 (2007). 10.1063/1.2756518
5. E. Mátyus, G. Czakó, and A. G. Császár, J. Chem. Phys. 130, 134112 (2009). 10.1063/1.3076742
6. E. Mátyus, J. Šimunek, and A. G. Császár, J. Chem. Phys. 131, 074106 (2009). 10.1063/1.3187528
7. X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 130, 094101 (2009). 10.1063/1.3077130
8. G. Avila and T. Carrington, Jr., J. Chem. Phys. 134, 054126 (2011). 10.1063/1.3549817
9. G. Avila and T. Carrington, Jr., J. Chem. Phys. 139, 134114 (2013). 10.1063/1.4821348
10. X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 138, 104106 (2013). 10.1063/1.4793474
11. O. L. Polyansky, I. N. Kozin, R. I. Ovsyannikov, P. Malyszek, J. Koput, J. Tennyson, and S. N. Yurchenko, J. Phys. Chem. A 117, 7367 (2013). 10.1021/jp401216g
12. A. V. Nikitin, M. Rey, and V. G. Tyuterev, J. Mol. Spectrosc. 305, 40 (2014). 10.1016/j.jms.2014.09.010
13. A. F. Al-Refaie, A. Yachmenev, S. N. Yurchenko, and J. Tennyson, Mon. Not. R. Astron. Soc. 448, 1704 (2015). 10.1093/mnras/stv091
14. C. Sousa-Silva, N. Hesketh, S. N. Yurchenko, C. Hill, and J. Tennyson, J. Quant. Spectrosc. Radiat. Transfer 142, 66 (2014). 10.1016/j.jqsrt.2014.03.012
15. X. Huang, R. R. Gamache, R. S. Freedman, D. W. Schwenke, and T. J. Lee, J. Quant. Spectrosc. Radiat. Transfer 147, 134 (2014). 10.1016/j.jqsrt.2014.05.015
16. X. Huang, D. W. Schwenke, and T. J. Lee, J. Chem. Phys. 140, 114311 (2014). 10.1063/1.4868327
17. K. M. Dunn, J. E. Boggs, and P. Pulay, J. Chem. Phys. 86, 5088 (1987). 10.1063/1.452652
18. S. Carter, A. R. Sharma, and J. M. Bowman, J. Chem. Phys. 137, 154301 (2012). 10.1063/1.4758005
19. M. Rey, A. V. Nikitin, and V. G. Tyuterev, Phys. Chem. Chem. Phys. 15, 10049 (2013). 10.1039/c3cp50275a
20. S. N. Yurchenko and J. Tennyson, Mon. Not. R. Astron. Soc. 440, 1649 (2014). 10.1093/mnras/stu326
21. T. Delahaye, A. Nikitin, M. Rey, P. G. Szalay, and V. G. Tyuterev, J. Chem. Phys. 141, 104301 (2014). 10.1063/1.4894419
22. A. I. Pavlyuchko, S. N. Yurchenko, and J. Tennyson, " ExoMol molecular line lists: XI The spectrum of nitric acid," Mon. Not. R. Astron. Soc. (in press).
23. A. V. Nikitin, M. Rey, and V. G. Tyuterev, J. Chem. Phys. 142, 094118 (2015). 10.1063/1.4913520
24. C. Fábri, T. Furtenbacher, and A. G. Császár, Mol. Phys. 112, 2462 (2015). 10.1080/00268976.2014.921341
25. J. K. G. Watson, Mol. Phys. 15, 479 (1968). 10.1080/00268976800101381
26. J. K. G. Watson, Mol. Phys. 19, 465 (1970). 10.1080/00268977000101491
27. J. M. Bowman, T. Carrington, and H.-D. Meyer, Mol. Phys. 106, 2145 (2008). 10.1080/00268970802258609
28. J. Tennyson and B. T. Sutcliffe, J. Chem. Phys. 77, 4061 (1982). 10.1063/1.444316
29. P. Jensen, J. Mol. Spectrosc. 128, 478 (1988). 10.1016/0022-2852(88)90164-6
30. A. G. Császár and N. C. Handy, J. Chem. Phys. 102, 3962 (1995). 10.1063/1.468524
31. M. J. Bramley and T. Carrington, Jr., J. Chem. Phys. 99, 8519 (1993). 10.1063/1.465576
32. L. Halonen, J. Chem. Phys. 106, 831 (1997). 10.1063/1.473228
33. M. Mladenovic, J. Chem. Phys. 112, 1070 (2000). 10.1063/1.480662
34. M. Mladenović, Spectrochim. Acta, Part A 58, 795 (2002). 10.1016/S1386-1425(01)00669-2
35. D. Schwenke, J. Chem. Phys. 118, 10431 (2003). 10.1063/1.1574013
36. T. Rajamaki, A. Miani, and L. Halonen, J. Chem. Phys. 118, 6358 (2003). 10.1063/1.1555801
37. J. Tennyson, M. A. Kostin, P. Barletta, G. J. Harris, J. Ramanlal, O. L. Polyansky, and N. F. Zobov, Comput. Phys. Commun. 163, 85 (2004). 10.1016/j.cpc.2003.10.003
38. I. N. Kozin, M. M. Law, J. Tennyson, and J. M. Hutson, Comput. Phys. Commun. 163, 117 (2004). 10.1016/j.cpc.2004.07.005
39. X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 121, 2937 (2004). 10.1063/1.1767093
40. F. Gatti and C. Iung, Phys. Rep. 484, 1 (2009). 10.1016/j.physrep.2009.05.003
41. M. Rey, A. V. Nikitin, and V. G. Tyuterev, J. Chem. Phys. 136, 244106 (2012). 10.1063/1.4730030
42. M. H. Beck, A. Jäckle, G. A. Worth, and H.-D. Meyer, Phys. Rep. 324, 1 (2000). 10.1016/S0370-1573(99)00047-2
43. D. Lauvergnat and A. Nauts, Chem. Phys. 305, 105 (2004). 10.1016/j.chemphys.2004.06.026
44. H. G. Yu and J. T. Muckerman, J. Mol. Spectrosc. 214, 11 (2002). 10.1006/jmsp.2002.8569
45. J. M. Bowman, S. Carter, and X. C. Huang, Int. Rev. Phys. Chem. 22, 533 (2003). 10.1080/0144235031000124163
46. Y. Scribano, D. M. Lauvergnat, and D. M. Benoit, J. Chem. Phys. 133, 094103 (2010). 10.1063/1.3476468
47. C. Eckart, Phys. Rev. 47, 552 (1935). 10.1103/PhysRev.47.552
48. J. D. Louck and H. W. Galbraith, Rev. Mod. Phys. 48, 69 (1976). 10.1103/RevModPhys.48.69
49. F. Wang, F. R. W. McCourt, and E. I. von Nagy-Felsobuki, J. Mol. Struct.: THEOCHEM 497, 227 (2000). 10.1016/S0166-1280(99)00373-5
50. A. Cejchan and V. Spirko, J. Mol. Spectrosc. 217, 142 (2003). 10.1016/S0022-2852(02)00033-4
51. S. N. Yurchenko, R. J. Barber, A. Yachmenev, W. Thiel, P. Jensen, and J. Tennyson, J. Phys. Chem. 43, 11845 (2009). 10.1021/jp9029425
52. T. Szidarovszky, C. Fábri, and A. G. Császár, J. Chem. Phys. 136, 174112 (2012). 10.1063/1.4707463
53. C. Fábri, E. Mátyus, and A. G. Császár, Spectrochim. Acta A 119, 84 (2014). 10.1016/j.saa.2013.03.090
54. H. Wei and T. Carrington, Jr., Chem. Phys. Lett. 287, 289 (1998). 10.1016/S0009-2614(98)00186-9
55. C. R. le Sueur, S. Miller, J. Tennyson, and B. T. Sutcliffe, Mol. Phys. 76, 1147 (1992). 10.1080/00268979200101941
56. J. M. Luis, M. Duran, J. L. Andrés, B. Champagne, and B. Kirtman, J. Chem. Phys. 111, 875 (1999). 10.1063/1.479373
57. P. R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy, 2nd ed. (NRC Research Press, Ottawa, 1998).
58. H. Wei and T. Carrington, Jr., J. Chem. Phys. 107, 2813 (1997). 10.1063/1.474639
59. H. Wei, J. Chem. Phys. 118, 7202 (2003). 10.1063/1.1562624
60. H. M. Pickett and H. L. Strauss, J. Am. Chem. Soc. 92, 7281 (1970). 10.1021/ja00728a009
61. A. Y. Dymarsky and K. N. Kudin, J. Chem. Phys. 122, 124103 (2005). 10.1063/1.1864872
62. S. V. Krasnoshchekov, E. V. Isayeva, and N. F. Stepanov, J. Chem. Phys. 140, 154104 (2014). 10.1063/1.4870936
63. J. Pesonen, J. Chem. Phys. 140, 074101 (2014). 10.1063/1.4865750
64. V. Szalay, J. Chem. Phys. 140, 234107 (2014). 10.1063/1.4883195
65. V. Szalay, J. Chem. Phys. 142, 174107 (2015). 10.1063/1.4919606
66. K. Sadri, D. Lauvergnat, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 141, 114101 (2014). 10.1063/1.4895557
67. S. A. Smolyak, Sov. Math. Dosl. 4, 240 (1963).
68. E. Novak and K. Ritter, Numer. Math. 75, 79 (1996). 10.1007/s002110050231
69. G. W. Wasilkowski and H. Woniakowski, J. Complexity 11, 1 (1995). 10.1006/jcom.1995.1001
70. H.-J. Bungartz and M. Griebel, Acta Numerica 13, 147269 (2004). 10.1017/S0962492904000182
71. G. Avila and T. Carrington, Jr., J. Chem. Phys. 135, 064101 (2011). 10.1063/1.3617249
72. G. Avila and T. Carrington, Jr., J. Chem. Phys. 134, 054126 (2011). 10.1063/1.3549817
73. D. Lauvergnat and A. Nauts, Phys. Chem. Chem. Phys. 12, 8405 (2010). 10.1039/c001944e
74. J. I. Rodriguez, D. C. Thompson, P. W. Ayers, and A. Koester, J. Chem. Phys. 128, 224103 (2008). 10.1063/1.2931563
75. S. N. Yurchenko, M. Carvajal, P. Jensen, H. Lin, J. J. Zheng, and W. Thiel, Mol. Phys. 103, 359 (2005). 10.1080/002689705412331517255
76. A. I. Pavlyuchko, S. N. Yurchenko, and J. Tennyson, " Hybrid variation-perturbation method for calculating rovibrational energy levels of polyatomic molecules," Mol. Phys. (in press). 10.1080/00268976.2014.992485
77. A. Griewank, in Mathematical Programming, edited by M. Iri and K. Tanabe (Kluwer Academic Publishers, Dordrecht, 1989), pp. 83-108.
78. A. Griewank and A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2nd ed. (SIAM, Philadelphia, PA, 2008).
79. G. O. Sørensen, in Large Amplitude Motion in Molecules II, Topics in Current Chemistry, edited by M. J. Krische et al. (Springer, Berlin Heidelberg, Heidelberg, 1979), Vol. 82, pp. 97-175.
80. M. Hardy, Electron. J. Combinatorics 13, #R1 (2006).
81. J. M. McCarthy, Introduction to Theoretical Kinematics, 2nd ed. (MIT Press, Cambridge, MA, 1990).
82. C. Moler and C. Van Loan, SIAM Rev. 45, 3 (2003). 10.1137/S00361445024180
83. S. N. Yurchenko, W. Thiel, M. Carvajal, H. Lin, and P. Jensen, Adv. Quantum Chem. 48, 209 (2005). 10.1016/s0065-3276(05)48014-4
84. S. N. Yurchenko, W. Thiel, M. Carvajal, and P. Jensen, Chem. Phys. 346, 146 (2008). 10.1016/j.chemphys.2008.01.052
85. A. Yachmenev, S. N. Yurchenko, I. Paidarova, P. Jensen, W. Thiel, and S. P. A. Sauer, J. Chem. Phys. 132, 114305 (2010). 10.1063/1.3359850
86. S. N. Yurchenko, R. J. Barber, A. Yachmenev, W. Thiel, P. Jensen, and J. Tennyson, J. Phys. Chem. A 113, 11845 (2009). 10.1021/jp9029425
87. S. N. Yurchenko, J. Zheng, H. Lin, P. Jensen, and W. Thiel, J. Chem. Phys. 123, 134308 (2005). 10.1063/1.2047572
88. C. Sousa-Silva, S. N. Yurchenko, and J. Tennyson, J. Mol. Spectrosc. 288, 28 (2013). 10.1016/j.jms.2013.04.002
89. J. M. L. Martin, T. J. Lee, and P. R. Taylor, J. Mol. Spectrosc. 160, 105 (1993). 10.1006/jmsp.1993.1161
90. A. Owens, A. Yachmenev, S. N. Yurchenko, W. Thiel, and J. Tennyson, J. Chem. Phys. 142, 244306 (2015). 10.1063/1.4922890
91. S. N. Yurchenko, R. J. Barber, and J. Tennyson, Mon. Not. R. Astron. Soc. 413, 1828-1834 (2011). 10.1111/j.1365-2966.2011.18261.x
92. C. Sousa-Silva, A. F. Al-Refaie, J. Tennyson, and S. N. Yurchenko, Mon. Not. R. Astron. Soc. 446, 2337 (2015). 10.1093/mnras/stu2246
93. J. Tennyson and S. N. Yurchenko, Mon. Not. R. Astron. Soc. 425, 21 (2012). 10.1111/j.1365-2966.2012.21440.x
94. A. Yachmenev, S. N. Yurchenko, P. Jensen, and W. Thiel, J. Chem. Phys. 134, 244307 (2011). 10.1063/1.3599927
95. J. T. Hougen, P. R. Bunker, and J. W. C. Johns, J. Mol. Spectrosc. 34, 136 (1970). 10.1016/0022-2852(70)90080-9
96. X. Huang, D. W. Schwenke, and T. J. Lee, J. Chem. Phys. 134, 044320 (2011). 10.1063/1.3541351
97. A. R. A. Derzi, T. Furtenbacher, J. Tennyson, S. N. Yurchenko, and A. G. Császár, J. Quant. Spectrosc. Radiat. Transfer 161, 117 (2015). 10.1016/j.jqsrt.2015.03.034