Ring-polymer instanton method for calculating tunneling splittings

Journal of Chemical Physics

Volumn 134, Issue 5, 2011, Pages

  Richardson, Jeremy O ^a   Althorpe, Stuart C ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CUT OUT; INFINITE NUMBERS; INSTANTONS; LINEAR POLYMERS; MALONALDEHYDE; MATRIX DETERMINANT; MULTIPLE DIMENSIONS; PARTITION FUNCTIONS; PERIODIC ORBITS; POTENTIAL SURFACES; RING POLYMERS; TUNNELING SPLITTINGS;

ALDEHYDES;

POLYMERS;

EID: 79951548290     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3530589     Document Type: Article

References (56)

1. F. N. Keutsch and R. J. Saykally, Proc. Natl. Acad. Sci. U.S.A. 98, 10533 (2001). 10.1073/pnas.191266498 (Pubitemid 32878656)
2. J. O. Richardson and S. C. Althorpe, J. Chem. Phys. 131, 214106 (2009). 10.1063/1.3267318
3. I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 122, 084106 (2005). 10.1063/1.1850093 (Pubitemid 41047448)
4. I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 123, 034102 (2005). 10.1063/1.1954769 (Pubitemid 41117885)
5. R. Collepardo-Guevara, I. R. Craig, and D. E. Manolopoulos, J. Chem. Phys. 128, 144502 (2008). 10.1063/1.2883593 (Pubitemid 351537173)
6. R. Collepardo-Guevara, Y. V. Suleimanov, and D. E. Manolopoulos, J. Chem. Phys. 130, 174713 (2009); 10.1063/1.3127145
7. R. Collepardo-Guevara, Y. V. Suleimanov, and D. E. Manolopoulos, J. Chem. Phys. 133, 049902 (2010). 10.1063/1.3464477
8. W. H. Miller, J. Chem. Phys. 62, 1899 (1975). 10.1063/1.430676
9. C. G. Callan and S. Coleman, Phys. Rev. D 16, 1762 (1977). 10.1103/PhysRevD.16.1762
10. S. Coleman, in The Whys of Subnuclear Physics, edited by, A. Zichichi, (Plenum, New York, 1979), pp. 805-916.
11. A. I. Vainshtein, V. I. Zakharov, V. A. Novikov, and M. A. Shifman, Sov. Phys. Usp. 25, 195 (1982). 10.1070/PU1982v025n04ABEH004533
12. V. A. Benderskii, D. E. Makarov, and C. A. Wight, Chemical Dynamics at Low Temperatures, Adv. Chem. Phys. Vol. 88 (Wiley, New York, 1994).
13. J. Cao and G. A. Voth, J. Chem. Phys. 105, 6856 (1996). 10.1063/1.471980
14. Z. Smedarchina, W. Siebrand, and A. Fernández-Ramos, J. Chem. Phys. 127, 174513 (2007). 10.1063/1.2785186 (Pubitemid 350075536)
15. G. V. Milnikov and H. Nakamura, J. Chem. Phys. 115, 6881 (2001). 10.1063/1.1406532 (Pubitemid 33028815)
16. G. V. Milnikov and H. Nakamura, J. Chem. Phys. 122, 124311 (2005). 10.1063/1.1869989 (Pubitemid 40537463)
17. G. Milnikov and H. Nakamura, Phys. Chem. Chem. Phys. 10, 1374 (2008).
18. S. Andersson, G. Nyman, A. Arnaldsson, U. Manthe, and H. Jnsson, J. Phys. Chem. A 113, 4468 (2009). 10.1021/jp811070w
19. S. C. Althorpe, D. C. Clary, and P. R. Bunker, Chem. Phys. Lett. 187, 345 (1991). 10.1016/0009-2614(91)80264-X
20. S. C. Althorpe and D. C. Clary, J. Chem. Phys. 101, 3603 (1994). 10.1063/1.467545
21. S. C. Althorpe and D. C. Clary, J. Chem. Phys. 102, 4390 (1995). 10.1063/1.469488
22. R. S. Fellers, L. B. Braly, R. J. Saykally, and C. Leforestier, J. Chem. Phys. 110, 6306 (1999). 10.1063/1.478535
23. T. Hammer, M. D. Coutinho-Neto, A. Viel, and U. Manthe, J. Chem. Phys. 131, 224109 (2009). 10.1063/1.3272610
24. D. F. Coker and R. O. Watts, J. Phys. Chem. 91, 2513 (1987). 10.1021/j100294a015
25. J. K. Gregory and D. C. Clary, J. Chem. Phys. 102, 7817 (1995). 10.1063/1.468982
26. J. K. Gregory and D. C. Clary, J. Chem. Phys. 103, 8924 (1995). 10.1063/1.470082
27. Y. Wang, B. J. Braams, J. M. Bowman, S. Carter, and D. P. Tew, J. Chem. Phys. 128, 224314 (2008). 10.1063/1.2937732
28. A. Kuki and P. G. Wolynes, Science 236, 1647 (1987). 10.1126/science. 3603005
29. D. M. Ceperley and G. Jacucci, Phys. Rev. Lett. 58, 1648 (1987). 10.1103/PhysRevLett.58.1648
30. C. Alexandrou and J. W. Negele, Phys. Rev. C 37, 1513 (1988). 10.1103/PhysRevC.37.1513
31. M. Marchi and D. Chandler, J. Chem. Phys. 95, 889 (1991). 10.1063/1.461096
32. Y. Wang and J. M. Bowman, J. Chem. Phys. 129, 121103 (2008). 10.1063/1.2978230
33. W. H. Miller, J. Phys. Chem. 83, 960 (1979). 10.1021/j100471a015
34. N. Makri and W. H. Miller, J. Chem. Phys. 91, 4026 (1989). 10.1063/1.456833
35. M. Ben-Nun and T. J. Martínez, J. Phys. Chem. A 103, 6055 (1999). 10.1021/jp990904a
36. D. J. Wales, J. Am. Chem. Soc. 115, 11191 (1993). 10.1021/ja00077a017
37. Y. Watanabe, T. Taketsugu, and D. J. Wales, J. Chem. Phys. 120, 5993 (2004). 10.1063/1.1651058
38. M. Takahashi, Y. Watanabe, T. Taketsugu, and D. J. Wales, J. Chem. Phys. 123, 044302 (2005). 10.1063/1.1954768 (Pubitemid 41164725)
39. C. S. Tautermann, A. F. Voegele, T. Loerting, and K. R. Liedl, J. Chem. Phys. 117, 1962 (2002). 10.1063/1.1488924 (Pubitemid 34916774)
40. In Ref. it is demonstrated that, when applied to describe tunneling splitting in the → limit, the instanton approach is equivalent to the WKB approximation, with the energy treated as the first order term with respect to.
41. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
42. D. Chandler and P. G. Wolynes, J. Chem. Phys. 74, 4078 (1981). 10.1063/1.441588
43. M. Parrinello and A. Rahman, J. Chem. Phys. 80, 860 (1984). 10.1063/1.446740
44. D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995). 10.1103/RevModPhys.67.279
45. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 4th ed. (World Scientific, Singapore, 2006).
46. 2+V′ ′[x(t)]x(t)d/dt-x(t)+V′[x(t)], since V[x(t)] is the force due to the inverted potential.
47. C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal, ACM Trans. Math. Softw. 23, 550 (1997). 10.1145/279232.279236
48. J. Cao, Phys. Rev. E 49, 882 (1994). 10.1103/PhysRevE.49.882
49. D. Marx and M. H. Mser, J. Phys.: Condens. Matter 11, R117 (1999). 10.1088/0953-8984/11/11/003
50. M. R. Pastrana, L. A. M. Quintales, J. Brando, and A. J. C. Varandas, J. Phys. Chem. 94, 8073 (1990). 10.1021/j100384a019
51. T. D. Sewell, Y. Guo, and D. L. Thompson, J. Chem. Phys. 103, 8557 (1995). 10.1063/1.470166
52. M. E. Tuckerman and D. Marx, Phys. Rev. Lett. 86, 4946 (2001). 10.1103/PhysRevLett.86.4946 (Pubitemid 32505540)
53. K. Yagi, T. Taketsugu, and K. Hirao, J. Chem. Phys. 115, 10647 (2001). 10.1063/1.1418436 (Pubitemid 34063667)
54. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, 6th ed. (Academic, New York, 2000).
55. D. W. Firth, K. Beyer, M. Dvorak, S. W. Reeve, A. Grushow, and K. R. Leopold, J. Chem. Phys. 94, 1812 (1991). 10.1063/1.459955
56. S. L. Baughcum, Z. Smith, E. B. Wilson, and R. W. Duerst, J. Am. Chem. Soc. 106, 2260 (1984). 10.1021/ja00320a007