An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions

Journal of Chemical Physics

Volumn 134, Issue 10, 2011, Pages

  Liu, Jian ^a,b   Miller, William H ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; OSCILLATORS (ELECTRONIC); PHASE SPACE METHODS; QUANTUM ELECTRONICS; REGRESSION ANALYSIS;

ANHARMONIC MODEL; AUTOCORRELATION FUNCTIONS; CANONICAL DISTRIBUTIONS; COMPLEX SYSTEMS; HARMONIC LIMIT; HARMONIC OSCILLATORS; HIGH TEMPERATURE; MOMENTUM OPERATORS; NONLINEAR FUNCTIONS; NONLINEAR OPERATOR; NUMERICAL TESTS; PHASE SPACE FORMULATION; PHASE SPACES; QUANTUM EFFECTS; QUANTUM MECHANICAL; QUANTUM MECHANICS; THERMAL CORRELATIONS; TIME CORRELATION FUNCTIONS; TRAJECTORY-BASED;

HARMONIC FUNCTIONS;

EID: 85017641784     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3555274     Document Type: Article

References (98)

1. B. J. Berne and G. D. Harp, Adv. Chem. Phys. 17, 63 (1970). 10.1002/SERIES2007
2. W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983). 10.1063/1.445581
3. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics, 2nd ed. (Springer-Verlag, Heidelberg, 1991).
4. H. Wang, X. Sun, and W. H. Miller, J. Chem. Phys. 108, 9726 (1998). 10.1063/1.476447
5. X. Sun, H. Wang, and W. H. Miller, J. Chem. Phys. 109, 7064 (1998). 10.1063/1.477389 (Pubitemid 128674371)
6. J. Liu and W. H. Miller, J. Chem. Phys. 126, 234110 (2007). 10.1063/1.2743023 (Pubitemid 47141469)
7. J. A. Poulsen, G. Nyman, and P. J. Rossky, J. Chem. Phys. 119, 12179 (2003). 10.1063/1.1626631
8. Q. Shi and E. Geva, J. Chem. Phys. 118, 8173 (2003). 10.1063/1.1564814
9. R. Hernandez and G. A. Voth, Chem. Phys. 233, 243 (1998). 10.1016/S0301-0104(98)00027-5 (Pubitemid 128111762)
10. E. Pollak and J. L. Liao, J. Chem. Phys. 108, 2733 (1998). 10.1063/1.475665
11. J. Shao and N. Makri, J. Phys. Chem. A 103, 7753 (1999). 10.1021/jp991433v
12. J. Shao and N. Makri, J. Phys. Chem. A 103, 9479 (1999). 10.1021/jp991837n
13. N. Makri, J. Phys. Chem. B 106, 8390 (2002). 10.1021/jp020907e (Pubitemid 35382948)
14. N. J. Wright and N. Makri, J. Chem. Phys. 119, 1634 (2003). 10.1063/1.1580472
15. A. Nakayama and N. Makri, J. Chem. Phys. 119, 8592 (2003). 10.1063/1.1611473
16. N. J. Wright and N. Makri, J. Phys. Chem. B 108, 6816 (2004). 10.1021/jp037600f
17. A. Nakayama and N. Makri, Chem. Phys. 304, 147 (2004). 10.1016/j.chemphys.2004.06.029
18. N. Makri, A. Nakayama, and N. Wright, J. Theor. Comput. Chem. 3, 391 (2004). 10.1142/S0219633604001112 (Pubitemid 40110359)
19. A. Nakayama and N. Makri, Proc. Natl. Acad Sci. U.S.A. 102, 4230 (2005). 10.1073/pnas.0501127102 (Pubitemid 40397094)
20. J. Liu and N. Makri, Chem. Phys. 322, 23 (2006). 10.1016/j.chemphys.2005. 08.010
21. J. Liu, A. Nakayama, and N. Makri, Mol. Phys. 104, 1267 (2006). 10.1080/00268970500525754
22. J. Liu and W. H. Miller, J. Chem. Phys. 125, 224104 (2006). 10.1063/1.2395941 (Pubitemid 44927405)
23. J. Kegerreis and N. Makri, J. Comput. Chem. 28, 818 (2007). 10.1002/jcc.20608 (Pubitemid 46384194)
24. E. Bukhman and N. Makri, J. Phys. Chem. A 111, 11320 (2007). 10.1021/jp0721907 (Pubitemid 350149925)
25. J. Chen and N. Makri, Mol. Phys. 106, 443 (2008). 10.1080/ 00268970701854797 (Pubitemid 351534348)
26. J. Kegerreis, A. Nakayama, and N. Makri, J. Chem. Phys. 128, 184509 (2008). 10.1063/1.2911925 (Pubitemid 351707258)
27. E. Bukhman and N. Makri, J. Phys. Chem. A 113, 7183 (2009). 10.1021/jp809741x
28. W. H. Miller, J. Chem. Phys. 53, 3578 (1970). 10.1063/1.1674535
29. W. H. Miller, J. Chem. Phys. 61, 1823 (1974). 10.1063/1.1682181
30. W. H. Miller, Adv. Chem. Phys. 30, 77 (1975). 10.1002/SERIES2007
31. E. J. Heller, J. Chem. Phys. 62, 1544 (1975). 10.1063/1.430620
32. E. J. Heller, J. Chem. Phys. 75, 2923 (1981). 10.1063/1.442382
33. M. F. Herman and E. Kluk, Chem. Phys. 91, 27 (1984). 10.1016/0301- 0104(84)80039-7
34. E. J. Heller, J. Chem. Phys. 95, 9431 (1991). 10.1063/1.461178
35. W. H. Miller, J. Chem. Phys. 95, 9428 (1991). 10.1063/1.461177
36. E. J. Heller, J. Chem. Phys. 94, 2723 (1991). 10.1063/1.459848
37. G. Campolieti and P. Brumer, Phys. Rev. A 50, 997 (1994). 10.1103/PhysRevA.50.997
38. K. G. Kay, J. Chem. Phys. 100, 4377 (1994). 10.1063/1.466320
39. K. G. Kay, J. Chem. Phys. 100, 4432 (1994). 10.1063/1.466273
40. D. J. Tannor and S. Garashchuk, Annu. Rev. Phys. Chem. 51, 553 (2000). 10.1146/annurev.physchem.51.1.553
41. M. Baranger, M. A. M. de Aguiar, F. Keck, H. J. Korsch, and B. Schellhaass, J. Phys. A 34, 7227 (2001). 10.1088/0305-4470/34/36/309
42. W. H. Miller, J. Phys. Chem. A 105, 2942 (2001). 10.1021/jp003712k (Pubitemid 35373060)
43. K. G. Kay, Annu. Rev. Phys. Chem. 56, 255 (2005). 10.1146/annurev. physchem.56.092503.141257 (Pubitemid 41156879)
44. W. H. Miller, J. Chem. Phys. 125, 132305 (2006). 10.1063/1.2211608 (Pubitemid 44522308)
45. E. Pollak and J. S. Shao, J. Chem. Phys. 116, 1748 (2002). 10.1063/1.1429650
46. T. Yamamoto, H. B. Wang, and W. H. Miller, J. Chem. Phys. 116, 7335 (2002). 10.1063/1.1464539 (Pubitemid 34599049)
47. J. Liu and W. H. Miller, J. Chem. Phys. 127, 114506 (2007). 10.1063/1.2774990 (Pubitemid 47462019)
48. J. Liu and W. H. Miller, J. Chem. Phys. 128, 144511 (2008). 10.1063/1.2889945 (Pubitemid 351537181)
49. J. Liu and W. H. Miller, J. Chem. Phys. 129, 124111 (2008). 10.1063/1.2981065
50. Q. Shi and E. Geva, J. Phys. Chem. A 107, 9070 (2003). 10.1021/jp0304982
51. B. J. Ka, Q. Shi, and E. Geva, J. Phys. Chem. A 109, 5527 (2005). 10.1021/jp051223k (Pubitemid 41027872)
52. B. J. Ka and E. Geva, J. Phys. Chem. A 110, 9555 (2006). 10.1021/jp062363c (Pubitemid 44318443)
53. I. Navrotskaya and E. Geva, J. Phys. Chem. A 111, 460 (2007). 10.1021/jp066243g
54. J. Liu and W. H. Miller, J. Chem. Phys. 131, 074113 (2009). 10.1063/1.3202438
55. J. Liu, W. H. Miller, F. Paesani, W. Zhang, and D. Case, J. Chem. Phys. 131, 164509 (2009). 10.1063/1.3254372
56. J. A. Poulsen, G. Nyman, and P. J. Rossky, J. Phys. Chem. B 108, 19799 (2004). 10.1021/jp040425y (Pubitemid 40079477)
57. J. A. Poulsen, G. Nyman, and P. J. Rossky, Proc. Natl. Acad. Sci. U.S.A. 102, 6709 (2005). 10.1073/pnas.0408647102 (Pubitemid 40675380)
58. J. A. Poulsen, G. Nyman, and P. J. Rossky, J. Chem. Theory Comput. 2, 1482 (2006). 10.1021/ct600167s
59. J. Cao and G. A. Voth, J. Chem. Phys. 99, 10070 (1993). 10.1063/1.465512
60. S. Jang and G. A. Voth, J. Chem. Phys. 111, 2371 (1999). 10.1063/1.479515
61. T. D. Hone, P. J. Rossky, and G. A. Voth, J. Chem. Phys. 124, 154103 (2006). 10.1063/1.2186636
62. I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 121, 3368 (2004). 10.1063/1.1777575
63. T. F. Miller and D. E. Manolopoulos, J. Chem. Phys. 123, 154504 (2005). 10.1063/1.2074967 (Pubitemid 41716932)
64. B. J. Braams and D. E. Manolopoulos, J. Chem. Phys. 125, 124105 (2006). 10.1063/1.2357599 (Pubitemid 44484188)
65. Q. Shi and E. Geva, J. Chem. Phys. 119, 9030 (2003). 10.1063/1.1613636
66. A. Horikoshi and K. Kinugawa, J. Chem. Phys. 122, 174104 (2005). 10.1063/1.1888576 (Pubitemid 40665961)
67. A. Witt, S. D. Ivanov, M. Shiga, H. Forbert, and D. Marx, J. Chem. Phys. 130, 194510 (2009). 10.1063/1.3125009
68. E. Wigner, Phys. Rev. 40, 749 (1932). 10.1103/PhysRev.40.749
69. E. P. Wigner, Perspectives in Quantum Theory (MIT, Cambridge, 1971).
70. K. Husimi, Proc. Phys. Math. Soc. Japn 22, 264 (1940).
71. R. J. Glauber, Phys. Rev. 131, 2766 (1963). 10.1103/PhysRev.131.2766
72. R. J. Glauber, Quantum Optics and Electronics (Gordon and Breach, New York, 1965).
73. E. C. G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963). 10.1103/PhysRevLett. 10.277
74. J. G. Kirkwood, Phys. Rev. 44, 31 (1933). 10.1103/PhysRev.44.31
75. A. W. Rihaczek, IEEE Trans. Inf. Theory 14, 369 (1968). 10.1109/TIT.1968.1054157
76. C. L. Mehta, J. Math. Phys. 5, 677 (1964). 10.1063/1.1704163
77. D. C. Rivier, Phys. Rev. 83, 862 (1951). 10.1103/PhysRev.83.862
78. H. Margenau and R. N. Hill, Prog. Theor. Phys. 26, 722 (1961). 10.1143/PTP.26.722
79. M. Born and P. Jordan, Z. Phys. 34, 858 (1925). 10.1007/BF01328531
80. L. Cohen and Y. I. Zaparovanny, J. Math. Phys. 21, 794 (1980). 10.1063/1.524501
81. J. Kruger, in Second International Wigner Symposium (Goslar, Germany, 1991).
82. P. D. Drummond and C. W. Gardiner, J. Phys. A 13, 2353 (1980). 10.1088/0305-4470/13/7/018
83. L. Cohen, J. Math. Phys. 7, 781 (1966). 10.1063/1.1931206
84. B. Hellsing, S. I. Sawada, and H. Metiu, Chem. Phys. Lett. 122, 303 (1985). 10.1016/0009-2614(85)80226-8
85. P. Frantsuzov, A. Neumaier, and V. A. Mandelshtam, Chem. Phys. Lett. 381, 117 (2003). 10.1016/j.cplett.2003.09.104
86. P. A. Frantsuzov and V. A. Mandelshtam, J. Chem. Phys. 121, 9247 (2004). 10.1063/1.1804495 (Pubitemid 40001689)
87. J. S. Shao and E. Pollak, J. Chem. Phys. 125, 133502 (2006). 10.1063/1.2207142 (Pubitemid 44522366)
88. E. Jezek and N. Makri, J. Phys. Chem. 105, 2851 (2001). 10.1021/jp003838h (Pubitemid 35373154)
89. M. Thoss, H. Wang, and W. H. Miller, J. Chem. Phys. 114, 9220 (2001). 10.1063/1.1359242 (Pubitemid 32535592)
90. S. Zhang and E. Pollak, J. Chem. Phys. 121, 3384 (2004). 10.1063/1.1772361
91. N. Makri and K. Thompson, Chem. Phys. Lett. 291, 101 (1998). 10.1016/S0009-2614(98)00590-9
92. K. Thompson and N. Makri, J. Chem. Phys. 110, 1343 (1999). 10.1063/1.478011
93. D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995). 10.1103/RevModPhys.67.279
94. R. Giachetti and V. Tognetti, Phys. Rev. Lett. 55, 912 (1985). 10.1103/PhysRevLett.55.912
95. R. P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986). 10.1103/PhysRevA.34.5080
96. A. Cuccoli, R. Giachetti, V. Tognetti, R. Vaia, and P. Verrucchi, J. Phys. Condens. Matter 7, 7891 (1995). 10.1088/0953-8984/7/41/003
97. D. H. Zhang, J. S. Shao, and E. Pollak, J. Chem. Phys. 131, 044116 (2009). 10.1063/1.3190328
98. E. Pollak and E. Martin-Fierro, J. Chem. Phys. 126, 044116 (2007). 10.1063/1.2714518 (Pubitemid 46685437)