메뉴 건너뛰기




Volumn 134, Issue 11, 2011, Pages

On the equivalence of two commonly used forms of semiclassical instanton theory

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE DESCRIPTIONS; COMPLEX PLANES; INSTANTON THEORY; PARTITION FUNCTIONS; PERIODIC ORBITS; QUANTUM TRANSITIONS; RING POLYMERS; SEMICLASSICAL LIMIT; TIME CORRELATION FUNCTIONS;

EID: 79953208641     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3563045     Document Type: Article
Times cited : (94)

References (65)
  • 1
    • 0038287905 scopus 로고    scopus 로고
    • 10.1146/annurev.physchem.54.011002.103750
    • S. C. Althorpe and D. C. Clary, Annu. Rev. Phys. Chem. 54, 493 (2003). 10.1146/annurev.physchem.54.011002.103750
    • (2003) Annu. Rev. Phys. Chem. , vol.54 , pp. 493
    • Althorpe, S.C.1    Clary, D.C.2
  • 6
    • 79953177174 scopus 로고    scopus 로고
    • We cannot do justice here to the large number of calculations in this field, to which the works cited below should provide a good source of references
    • We cannot do justice here to the large number of calculations in this field, to which the works cited below should provide a good source of references.
  • 8
    • 0036572651 scopus 로고    scopus 로고
    • Combining semiclassical time evolution and quantum boltzmann operator to evaluate reactive flux correlation function for thermal rate constants of complex systems
    • DOI 10.1063/1.1464539
    • T. Yamamoto, H. Wang, and W. H. Miller, J. Chem. Phys. 116, 7335 (2002). 10.1063/1.1464539 (Pubitemid 34599049)
    • (2002) Journal of Chemical Physics , vol.116 , Issue.17 , pp. 7335-7349
    • Yamamoto, T.1    Wang, H.2    Miller, W.H.3
  • 9
    • 69249189455 scopus 로고    scopus 로고
    • 10.1063/1.3202438
    • J. Liu and W. H. Miller, J. Chem. Phys. 131, 074113 (2009). 10.1063/1.3202438
    • (2009) J. Chem. Phys. , vol.131 , pp. 074113
    • Liu, J.1    Miller, W.H.2
  • 12
    • 2242445002 scopus 로고    scopus 로고
    • J. Cao and,. 10.1063/1.471980
    • J. Cao and G. A. Voth, J. Chem. Phys. 105, 6856 (1996). 10.1063/1.471980
    • (1996) J. Chem. Phys. , vol.105 , pp. 6856
    • Voth, G.A.1
  • 13
    • 19644367467 scopus 로고
    • 10.1103/PhysRevD.16.1762
    • C. G. Callan and S. Coleman, Phys. Rev. D 16, 1762 (1977). 10.1103/PhysRevD.16.1762
    • (1977) Phys. Rev. D , vol.16 , pp. 1762
    • Callan, C.G.1    Coleman, S.2
  • 14
    • 33744748455 scopus 로고
    • 10.1103/PhysRevLett.46.388
    • I. Affleck, Phys. Rev. Lett. 46, 388 (1981). 10.1103/PhysRevLett.46.388
    • (1981) Phys. Rev. Lett. , vol.46 , pp. 388
    • Affleck, I.1
  • 17
    • 4243272162 scopus 로고
    • 10.1103/PhysRevLett.58.563
    • M. J. Gillan, Phys. Rev. Lett. 58, 563 (1987). 10.1103/PhysRevLett.58.563
    • (1987) Phys. Rev. Lett. , vol.58 , pp. 563
    • Gillan, M.J.1
  • 18
    • 0001053428 scopus 로고
    • 10.1088/0022-3719/20/24/005
    • M. J. Gillan, J. Phys. C 20, 3621 (1987). 10.1088/0022-3719/20/24/005
    • (1987) J. Phys. C , vol.20 , pp. 3621
    • Gillan, M.J.1
  • 22
    • 22944467841 scopus 로고    scopus 로고
    • Chemical reaction rates from ring polymer molecular dynamics
    • DOI 10.1063/1.1850093, 084106
    • I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 122, 084106 (2005). 10.1063/1.1850093 (Pubitemid 41047448)
    • (2005) Journal of Chemical Physics , vol.122 , Issue.8 , pp. 1-12
    • Craig, I.R.1    Manolopoulos, D.E.2
  • 23
    • 23744437908 scopus 로고    scopus 로고
    • A refined ring polymer molecular dynamics theory of chemical reaction rates
    • DOI 10.1063/1.1954769, 034102
    • I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 123, 034102 (2005). 10.1063/1.1954769 (Pubitemid 41117885)
    • (2005) Journal of Chemical Physics , vol.123 , Issue.3 , pp. 1-10
    • Craig, I.R.1    Manolopoulos, D.E.2
  • 25
    • 56849097597 scopus 로고    scopus 로고
    • 10.1063/1.3013357
    • T. F. Miller III, J. Chem. Phys. 129, 194502 (2008). 10.1063/1.3013357
    • (2008) J. Chem. Phys. , vol.129 , pp. 194502
    • Miller III, T.F.1
  • 29
    • 0035886126 scopus 로고    scopus 로고
    • Practical implementation of the instanton theory for the ground-state tunneling splitting
    • DOI 10.1063/1.1406532
    • G. V. Milnikov and H. Nakamura, J. Chem. Phys. 115, 6881 (2001). 10.1063/1.1406532 (Pubitemid 33028815)
    • (2001) Journal of Chemical Physics , vol.115 , Issue.15 , pp. 6881-6897
    • Mil'nikov, G.V.1    Nakamura, H.2
  • 31
    • 18344380226 scopus 로고
    • 10.1016/0003-4916(83)90202-6
    • A. O. Caldeira and A. J. Leggett, Ann. Phys. 149, 374 (1983). 10.1016/0003-4916(83)90202-6
    • (1983) Ann. Phys. , vol.149 , pp. 374
    • Caldeira, A.O.1    Leggett, A.J.2
  • 34
    • 34250105289 scopus 로고
    • 10.1007/BF01304224
    • P. Hnggi, Z. Phys. B 68, 181 (1987). 10.1007/BF01304224
    • (1987) Z. Phys. B , vol.68 , pp. 181
    • Hnggi, P.1
  • 35
    • 36749114243 scopus 로고
    • 10.1063/1.430676
    • W. H. Miller, J. Chem. Phys. 62, 1899 (1975). 10.1063/1.430676
    • (1975) J. Chem. Phys. , vol.62 , pp. 1899
    • Miller, W.H.1
  • 37
    • 0001222359 scopus 로고
    • 10.1063/1.1731099
    • T. Yamamoto, J. Chem. Phys. 33, 281 (1960). 10.1063/1.1731099
    • (1960) J. Chem. Phys. , vol.33 , pp. 281
    • Yamamoto, T.1
  • 38
    • 36749118190 scopus 로고
    • 10.1063/1.1682181
    • W. H. Miller, J. Chem. Phys. 61, 1823 (1974). 10.1063/1.1682181
    • (1974) J. Chem. Phys. , vol.61 , pp. 1823
    • Miller, W.H.1
  • 40
    • 79953228711 scopus 로고    scopus 로고
    • One possible justification of the Im F approach is that it gives (formally) the correct expression for the rate in the limit → . However, this does not satisfactorily explain why the Im F approach works so well at finite temperatures, which are often just below the cross-over between deeand shallow tunneling
    • One possible justification of the Im F approach is that it gives (formally) the correct expression for the rate in the limit →. However, this does not satisfactorily explain why the Im F approach works so well at finite temperatures, which are often just below the cross-over between deep and shallow tunneling.
  • 42
    • 79953224296 scopus 로고    scopus 로고
    • See Appendix A of Ref.
    • See Appendix A of Ref..
  • 45
    • 79953211369 scopus 로고    scopus 로고
    • This approximation will often work, since the instanton is often a straight line. However, it will break down for curved instanton paths, for which the transverse and longitudinal modes become decoupled only in the limit that the temperature tends to absolute-zero: see Ref.
    • This approximation will often work, since the instanton is often a straight line. However, it will break down for curved instanton paths, for which the transverse and longitudinal modes become decoupled only in the limit that the temperature tends to absolute-zero: see Ref..
  • 49
    • 11944260941 scopus 로고
    • 10.1103/RevModPhys.67.279
    • D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995). 10.1103/RevModPhys.67.279
    • (1995) Rev. Mod. Phys. , vol.67 , pp. 279
    • Ceperley, D.M.1
  • 57
    • 0001074253 scopus 로고
    • 10.1103/PhysRev.40.749
    • E. Wigner, Z. Phys. Chem. B 19, 203 (1932). 10.1103/PhysRev.40.749
    • (1932) Z. Phys. Chem. B , vol.19 , pp. 203
    • Wigner, E.1
  • 59
    • 79953221311 scopus 로고    scopus 로고
    • personal communication (7 September)
    • W. H. Miller, personal communication (7 September 2010).
    • (2010)
    • Miller, W.H.1
  • 60
    • 79953229941 scopus 로고    scopus 로고
    • note
    • 1).
  • 61
    • 79953220970 scopus 로고    scopus 로고
    • This is because the value returned by the steepest-descent approximation is the same, regardless of whether one evaluates the steepest-descent integral in one step, or whether one splits the space into two parts X and Y, and evaluates first the integral over X (by steepest descent), and secondly the integral over Y. The two-steprefactor contains a product of two determinants which is equal to the single determinant in the one-steprefactor.
    • This is because the value returned by the steepest-descent approximation is the same, regardless of whether one evaluates the steepest-descent integral in one step, or whether one splits the space into two parts X and Y, and evaluates first the integral over X (by steepest descent), and secondly the integral over Y. The two-step prefactor contains a product of two determinants which is equal to the single determinant in the one-step prefactor.
  • 62
    • 0002911251 scopus 로고
    • 10.1002/SERIES2007
    • W. H. Miller, Adv. Chem. Phys. 25, 69 (1974). 10.1002/SERIES2007
    • (1974) Adv. Chem. Phys. , vol.25 , pp. 69
    • Miller, W.H.1
  • 63
    • 79953210586 scopus 로고    scopus 로고
    • Reference discusses only two- and three-dimensional systems, but the results generalize immediately to systems with more dimensions.
    • Reference discusses only two- and three-dimensional systems, but the results generalize immediately to systems with more dimensions.
  • 65
    • 79953216908 scopus 로고    scopus 로고
    • See Sec. 4.5 of Ref..
    • See Sec. 4.5 of Ref..


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.