Semiclassical chaos in atomic clusters: An exploration with ring-polymer molecular dynamics

Physica D: Nonlinear Phenomena

Volumn 240, Issue 12, 2011, Pages 1001-1007

  Calvo, F ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

Atomic clusters; Isomerization; Lyapunov exponent; Path integral molecular dynamics

Indexed keywords

ATOMIC BEAMS; DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; ISOMERIZATION; ISOMERS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; QUANTUM ELECTRONICS; TEMPERATURE;

ATOMIC CLUSTERS; DETERMINISTIC CHAOS; HAMILTONIAN FORMULATIONS; INTRINSIC FEATURES; LYAPUNOV CHARACTERISTIC EXPONENTS; LYAPUNOV EXPONENT; NUCLEAR DELOCALIZATION; PATH-INTEGRAL MOLECULAR DYNAMICS;

MOLECULAR DYNAMICS;

EID: 79958221792     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2011.02.010     Document Type: Article

References (53)

1. V. Mehra, and R. Ramaswamy Maximal Lyapunov exponent at crises Phys. Rev. E 53 1996 3420 3424 (Pubitemid 126584027)
2. K.-H. Kwon, and B.-Y. Park Lyapunov exponent and the solidfluid phase transition J. Chem. Phys. 107 1997 5171 5177
3. S.K. Nayak, P. Jena, K.D. Ball, and R.S. Berry Dynamics and instabilities near the glass transition: from clusters to crystals J. Chem. Phys. 108 1998 234 239 (Pubitemid 128571228)
4. H.A. Posch, and W.G. Hoover Equilibrium and nonequilibrium Lyapunov spectra for dense fluids and solids Phys. Rev. A 39 1989 2175 2188
5. V. Latora, A. Rapisarda, and S. Ruffo Lyapunov instability and finite size effects in a system with long-range forces Phys. Rev. Lett. 80 1998 692 695 (Pubitemid 128623838)
6. P. Butera, and G. Caravati Phase transitions and Lyapunov characteristic exponents Phys. Rev. A 36 1987 962 964
7. C. Antonopoulos, V. Basios, and T. Bountis Weak chaos and the melting transition in a confined microplasma system Phys. Rev. E 81 2010 016211(19)
8. T.L. Beck, D.M. Leitner, and R.S. Berry Melting and phase space transitions in small clusters: spectral characteristics, dimensions, and K entropy J. Chem. Phys. 89 1988 1681 1694
9. R.J. Hinde, R.S. Berry, and D.J. Wales Chaos in small clusters of inert gas atoms J. Chem. Phys. 96 1992 1376 1390
10. 3) J. Phys. B 24 1991 L351 L357
11. C. Amitrano, and R.S. Berry Probability distributions of local Liapunov exponents for small clusters Phys. Rev. Lett. 68 1992 729 732
12. C. Chakravarty, R.J. Hinde, D.M. Leitner, and D.J. Wales Effects of three-body (AxilrodTeller) forces on the classical and quantum behavior of rare-gas trimers Phys. Rev. E 56 1997 363 377 (Pubitemid 127602049)
13. E. Yurtsever, and N. Elmaci Chaotic behavior of triatomic clusters Phys. Rev. A 55 1997 538 544 (Pubitemid 127604860)
14. F. Calvo Chaos and dynamical coexistence in Lennard-Jones clusters J. Chem. Phys. 108 1998 6861 6868
15. F. Calvo, and P. Labastie Melting and phase space transitions in small ionic clusters J. Phys. Chem. B 102 1998 2051 2059 (Pubitemid 128586662)
16. F. Calvo Largest Lyapunov exponent in molecular systems: linear molecules and application to nitrogen clusters Phys. Rev. E 58 1998 5643 5649 (Pubitemid 128601324)
17. F. Calvo Largest Lyapunov exponent in molecular systems. II: quaternion coordinates and application to methane clusters Phys. Rev. E 60 1999 2771 2778
18. P. Gaspard Lyapunov exponent of ion motion in microplasmas Phys. Rev. E 68 2003 056209(17)
19. J.R. Green, J. Jellinek, and R.S. Berry Space-time properties of GramSchmidt vectors in classical Hamiltonian evolution Phys. Rev. E 80 2009 066205(19)
20. M.C. Gutzwiller Chaos in Classical and Quantum Mechanics 1990 Springer-Verlag Berlin
21. Th. Zimmerman, L.S. Cederbaum, H.-D. Meyer, and H. Kppel Statistical properties of energy levels J. Phys. Chem. 91 1987 4446 4455
22. J.H. Van Vleck The correspondence principle in the statistical interpretation of quantum mechanics Proc. Natl. Acad. Sci. USA 14 1928 178 188
23. M.V. Berry, and M. Tabor Level clustering in regular spectrum Proc. Roy. Soc. London A 356 1977 375 394
24. M.J. Davis, and E.J. Heller Multidimensional wave functions from classical trajectories J. Chem. Phys. 75 1981 3916 3924
25. M.C. Gutzwiller Phase2010Integral approximation in momentum space and the bound states of an atom J. Math. Phys. 8 1967 1979 2000
26. G. Papadopoulos Gaussian path integrals Phys. Rev. D 11 1975 2870 2875
27. I.R. Craig, and D.E. Manolopoulos Quantum statistics and classical mechanics: real time correlation functions from ring polymer molecular dynamics J. Chem. Phys. 121 2004 3368 3373
28. B.J. Braams, and D.E. Manolopoulos On the short-time limit of ring polymer molecular dynamics J. Chem. Phys. 125 2006 124105(19)
29. A. Prez, M.E. Tuckerman, and M.H. Mser A comparative study of the centroid and ring-polymer molecular dynamics methods for approximating quantum time correlation functions from path integrals J. Chem. Phys. 130 2009 184105(113)
30. F. Calvo, J.P.K. Doye, and D.J. Wales Quantum partition functions from classical distributions: application to rare-gas clusters J. Chem. Phys. 114 2001 73127231
31. 38 cluster: quantum mechanics versus classical J. Chem. Phys. 122 2005 154305(112)
32. J. Deckman, P.A. Frantsuzov, and V.A. Mandelshtam Quantum transitions in Lennard-Jones clusters Phys. Rev. E 77 2008 052102(14)
33. T.F. Miller III, and D.E. Manolopoulos Quantum diffusion in liquid para-hydrogen from ring-polymer molecular dynamics J. Chem. Phys. 122 2005 184503(17)
34. T.E. Markland, S. Habershon, and D.E. Manolopoulos Quantum diffusion of hydrogen and muonium atoms in liquid water and hexagonal ice J. Chem. Phys. 128 2008 194506(111)
35. F. Calvo, and D. Costa Diffusion of hydrides in palladium nanoclusters. A ring-polymer molecular dynamics study of quantum finite size effects J. Chem. Theory Comput. 6 2010 508 516
36. M. Shiga, and A. Nakayama Ab initio path integral ring polymer molecular dynamics: vibrational spectra of molecules Chem. Phys. Lett. 451 2008 175 181
37. F. Calvo, P. Parneix, and N.-T. Van-Oanh Finite temperature infrared spectroscopy of polycyclic aromatic hydrocarbon molecules: path-integral molecular dynamics J. Chem. Phys. 132 2010 124308(19)
38. R. Collepardo-Guevara, Y.V. Suleimanov, and D.E. Manolopoulos Bimolecular reaction rates from ring polymer molecular dynamics J. Chem. Phys. 130 2009 174713(114)
39. G. Benettin, L. Galgani, and J.M. Strelcyn Kolmogorov entropy and numerical experiments Phys. Rev. A 14 1976 2338 2345
40. M.E. Tuckerman, B.J. Berne, and G.J. Martyna Reversible multiple time scale molecular dynamics J. Chem. Phys. 97 1992 1990 2001
41. Y. Zhou, M. Karplus, K.D. Ball, and R.S. Berry The distance fluctuation criterion for melting: comparison of square-well and Morse potential models for clusters and homopolymers J. Chem. Phys. 116 2002 2323 2329 (Pubitemid 34159939)
42. J.R. Barker Sums of quantum states of nonseparable degrees of freedom: multidimensional Monte Carlo integration J. Phys. Chem. 91 1987 3849 3854
43. M. Basire, P. Parneix, and F. Calvo Quantum anharmonic densities of states using the WangLandau method J. Chem. Phys. 129 2008 081101(14)
44. F. Calvo, M. Basire, and P. Parneix Quantum densities of states of fluxional polyatomic systems from a superposition approximation J. Chem. Phys. 130 2009 154101(18)
45. A.M. Ferrenberg, and R.H. Swendsen Optimized Monte Carlo data analysis Phys. Rev. Lett. 63 1989 1195 1198
46. F. Calvo, and P. Labastie Configurational density of states from molecular dynamics simulations Chem. Phys. Lett. 247 1995 395 400
47. F. Wang, and D.P. Landau Efficient, multiple-range random walk algorithm to calculate the density of states Phys. Rev. Lett. 86 2001 2050 2053 (Pubitemid 32254758)
48. M. Diem Introduction to Modern Vibrational Spectroscopy 1993 Wiley-Interscience London
49. E. Aurell, G. Boffetta, A. Crisanti, G. Paladin, and A. Vulpiani Growth of noninfinitesimal perturbations in turbulence Phys. Rev. Lett. 77 1996 1262 1265 (Pubitemid 126625663)
50. Y. Matsunaga, C.-B. Li, and T. Komatsuzaki Anomalous diffusion in folding dynamics of minimalist protein landscape Phys. Rev. Lett. 99 2007 238103(14)
51. A.J. Lichtenberg, and M.A. Lieberman Regular and Chaotic Dynamics 1992 Springer-Verlag New York
52. L. Casetti, R. Livi, and M. Pettini Gaussian model for chaotic instability of Hamiltonian flows Phys. Rev. Lett. 74 1995 375 378
53. L. Casetti, C. Clementi, and M. Pettini Riemannian theory of Hamiltonian chaos and Lyapunov exponents Phys. Rev. E 54 1996 59693894