Nonadiabatic molecular dynamics based on trajectories

Entropy

Volumn 16, Issue 1, 2014, Pages 62-85

  De Carvalho, Felipe Franco ^a   Bouduban, Marine E F ^a   Curchod, Basile F E ^a   Tavernelli, Ivano ^a  

^a EPFL   (Switzerland)

Author keywords

Bohmian dynamics; Born Oppenheimer approximation; Ehrenfest dynamics; Nonadiabatic dynamics; Trajectory surface hopping

Indexed keywords

EID: 84893201648     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e16010062     Document Type: Review

References (76)

1. Born, M.; Oppenheimer, R. Zur quantentheorie der molekeln. Annalen der Physik 1927, 389, 457-484, (in German).
2. Ballhausen, C.; Hansen, A. Electronic spectra. Annu. Rev. Phys. Chem. 1972, 23, 15-38.
3. Marx, D.; Hutter, J. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods; Cambridge University Press: Cambridge, UK, 2009.
4. Kapral, R.; Ciccotti, G. Mixed quantum-classical dynamics. J. Chem. Phys. 1999, 110, 8919-8929.
5. Tully, J.C. Mixed quantum classical dynamics. Faraday Discuss. 1998, 110, 407-419.
6. Kapral, R. Progress in the theory of mixed quantum-classical dynimics. Annu. Rev. Phys. Chem. 2006, 57, 129-157.
7. Hohenberg, P.; Kohn, W. Inhomogeneous electron gas. Phys. Rev. B 1964, 136, B864-B871.
8. Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 1965, 140, A1133-A1138.
9. Runge, E.; Gross, E.K.U. Density-functional theory for time-dependent systems. Phys. Rev. Lett. 1984, 52, 997-1000.
10. Casida, M.E. Time-dependent density-functional response theory for molecules. In Recent Advances in Density Functional Methods; Chong, D.P., Ed.; World Scientific: Singapore, Singapore, 1995; p. 155.
11. Petersilka, M.; Gossmann, U.J.; Gross, E.K.U. Excitation energies from time-dependent density-functional theory. Phys. Rev. Lett. 1996, 76, 1212-1215.
12. Appel, H.; Gross, E.K.U.; Burke, K. Excitations in time-dependent density-functional theory. Phys. Rev. Lett. 2003, 90, 043005.
13. Barbatti, M.; Granucci, G.; Ruckenbauer, M.; Plasser, F.; Pittner, J.; Persico, M.; Lischka, H. NEWTON-X, a package for Newtonian dynamics close to the crossing seam, version 1.2. Available online: www.newtonx.org (accessed on 20 December 2013).
14. Tully, J.C.; Preston, R.K. Trajectory surface hopping approach to nonadiabatic molecular collisions: The reaction of H+ with D2. J. Chem. Phys. 1971, 55, 562-572.
15. Tully, J.C. Molecular dynamics with electronic transitions. J. Chem. Phys. 1990, 93, 1061-1071.
16. Nielsen, S.; Kapral, R.; Ciccotti, G. Mixed quantum-classical surface hopping dynamics. J. Chem. Phys. 2000, 112, 6543-6553.
17. Herman, M.F. Nonadiabatic semiclassical scattering. I. Analysis of generalized surface hopping procedures. J. Chem. Phys. 1984, 81, 754-763.
18. Sun, X.; Miller, W.H. Semiclassical initial value representation for electronically nonadiabatic molecular dynamics. J. Chem. Phys. 1997, 106, 6346-6353.
19. Coker, D.; Xiao, L. Methods for molecular dynamics with nonadiabatic transitions. J. Chem. Phys. 1995, 102, 496-510.
20. Bittner, E.R.; Rossky, P.J. Quantum decoherence in mixed quantum-classical systems: Nonadiabatic processes. J. Chem. Phys. 1995, 103, 8130-8143.
21. Donoso, A.; Martens, C.C. Simulation of coherent nonadiabatic dynamics using classical trajectories. J. Phys. Chem. A 1998, 102, 4291-4300.
22. Horenko, I.; Salzmann, C.; Schmidt, B.; Schutte, C. Quantum-classical Liouville approach to molecular dynamics: Surface hopping Gaussian phase-space packets. J. Chem. Phys. 2002, 117, 11075-11088.
23. Burghardt, I.; Cederbaum, L. Hydrodynamic equations for mixed quantum states. II. Coupled electronic states. J. Chem. Phys. 2001, 115, 10312-10322.
24. Bonella, S.; Coker, D.F. LAND-map, a linearized approach to nonadiabatic dynamics using the mapping formalism. J. Chem. Phys. 2005, 122, 194102.
25. McEniry, E.J.; Wang, Y.; Dundas, D.; Todorov, T.N.; Stella, L.; Miranda, R.P.; Fisher, A.J.; Horsfield, A.P.; Race, C.P.; Mason, D.R.; et al. Modelling non-adiabatic processes using correlated electron-ion dynamics. Eur. Phys. J. B 2010, 77, 305-329.
26. Thachuk, M.; Ivanov, M.Y.; Wardlaw, D.M. A semiclassical approach to intense-field above-threshold dissociation in the long wavelength limit. II. Conservation principles and coherence in surface hopping. J. Chem. Phys. 1998, 109, 5747-5760.
27. Fang, J.Y.; Hammes-Schiffer, S. Improvement of the internal consistency in trajectory surface hopping. J. Phys. Chem. A 1999, 103, 9399-9407.
28. Subotnik, J.; Shenvi, N. A new approach to decoherence and momentum rescaling in the surface hopping algorithm. J. Chem. Phys. 2011, 134, 024105.
29. Meyer, H.D.; Manthe, U.; Cederbaum, L.S. The multi-configurational time-dependent hartree approach. Chem. Phys. Lett. 1990, 165, 73-78.
30. Bohm, D. A suggested interpretation of the quantum theory in terms of "hidden" variables. I. Phys. Rev. 1952, 85, 166-179.
31. Bohm, D. A suggested interpretation of the quantum theory in terms of "hidden" variables. II. Phys. Rev. 1952, 85, 180-193.
32. Takabayasi, T. On the formulation of quantum mechanics associated with classical pictures. Prog. Theor. Phys. 1952, 8, 143-182.
33. Holland, P.R. The Quantum Theory of Motion-An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics; Cambridge University Press: Cambridge, UK, 1993.
34. Lopreore, C.L.; Wyatt, R.E. Quantum wave packet dynamics with trajectories. Phys. Rev. Lett. 1999, 82, 5190-5193.
35. Wyatt, R.E. Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics; interdisciplinary applied mathematics; Springer: New York, NY, USA, 2005.
36. Chattaraj, P.K., Ed. Quantum Trajectories; Atoms, Molecules, and Clusters Series; CRC Press: Boca Raton, FL, USA, 2010.
37. Oriols, X., Mompart, J., Eds. Applied Bohmian Mechanics, From Nanoscale Systems to Cosmology; Pan Stanford Publishing Pte. Ltd.: Singapore, Singapore, 2012.
38. Wyatt, R.E.; Lopreore, C.L.; Parlant, G. Electronic transitions with quantum trajectories. J. Chem. Phys. 2001, 114, 5113-5116.
39. Lopreore, C.L.; Wyatt, R.E. Electronic transitions with quantum trajectories. II. J. Chem. Phys. 2002, 116, 1228-1238.
40. Gindensperger, E.; Meier, C.; Beswick, J.; Parlant, G. Combining fixed-and moving-grid methods to study direct dissociation processes involving nonadiabatic transitions. J. Chem. Phys. 2005, 123, 214107.
41. Poirier, B.; Parlant, G. Reconciling semiclassical and Bohmian mechanics: IV. Multisurface dynamics. J. Phys. Chem. A 2007, 111, 10400-10408.
42. Garashchuk, S.; Rassolov, V.A.; Schatz, G.C. Semiclassical nonadiabatic dynamics using a mixed wave-function representation. J. Chem. Phys. 2005, 123, 174108.
43. Curchod, B.F.E.; Tavernelli, I.; Rothlisberger, U. Trajectory-based solution of the nonadiabatic quantum dynamics equations: An on-the-fly approach for molecular dynamics simulations. Phys. Chem. Chem. Phys. 2011, 13, 3231-3236.
44. Curchod, B.F.E.; Tavernelli, I. On trajectory-based nonadiabatic dynamics: Bohmian dynamics versus trajectory surface hopping. J. Chem. Phys. 2013, 138, 184112.
45. Martínez, T.J.; Ben-Nun, M.; Levine, R.D. Multi-electronic-state molecular dynamics: A wave function approach with applications. J. Phys. Chem. 1996, 100, 7884-7895.
46. Martínez, T.J.; Ben-Nun, M.; Levine, R.D. Molecular collision dynamics on several electronic states. J. Phys. Chem. A 1997, 101, 6389-6402.
47. Martínez, T.J.; Levine, R.D. Non-adiabatic molecular dynamics: Split-operator multiple spawning with applications to photodissociation. J. Chem. Soc. Faraday Trans. 1997, 93, 941-947.
48. Ben-Nun, M.; Martínez, T.J. Nonadiabatic molecular dynamics: Validation of the multiple spawning method for a multidimensional problem. J. Chem. Phys. 1998, 108, 7244-7257.
49. Born, M. Kopplung der Elektronen-und Kernbewegung in Molekeln und Kristallen (in German); Vandenhoeck & Ruprecht: Göttingen, Germany, 1951.
50. Born, M.; Huang, K. Dynamical Theory of Crystal Lattices; Clarendon: Oxford, UK, 1954.
51. The term "Born-Oppenheimer approximation" is also used to name what should be referred to as the "adiabatic BO approximation".
52. Ben-Nun, M.; Martínez, T.J. Ab Initio Quantum Molecular Dynamics. In Advances in Chemical Physics; Volume 121; Wiley: New York, NY, USA, 2002; pp. 439-512.
53. The spawning process is rather involved, and the interested reader should refer to [52] for a very detailed discussion of the algorithm.
54. Ben-Nun, M.; Quenneville, J.; Martínez, T.J. Ab initio multiple spawning: Photochemistry from first principles quantum molecular dynamics. J. Phys. Chem. A 2000, 104, 5161-5175.
55. For an in-depth discussion on Bohmian mechanics and its physical meaning, see [33].
56. Tavernelli, I. Ab initio-driven trajectory-based nuclear quantum dynamics in phase space. Phys. Rev. A 2013, 87, 042501.
57. Tully, J.C. Nonadiabatic Dynamics. In Modern Methods for Multidimensional Dynamics Computations in Chemistry; Thompson, D.L., Ed.; World Scientific: Singapore, Singapore, 1998.
58. Tavernelli, I. Electronic density response of liquid water using time-dependent density functional theory. Phys. Rev. B 2006, 73, 094204.
59. Abedi, A.; Maitra, N.; Gross, E. Exact factorization of the time-dependent electron-nuclear wave function. Phys. Rev. Lett. 2010, 105, 123002.
60. Abedi, A.; Maitra, N.T.; Gross, E. Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction. J. Chem. Phys. 2012, 137, 22A530.
61. Hunter, G. Conditional probability amplitudes in wave mechanics. Int. J. Quantum Chem. 1975, 9, 237-242.
62. Alonso, J.L.; Clemente-Gallardo, J.; Echenique-Robba, P.; Jover-Galtier, J.A. Comment on "Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction" (J. Chem. Phys.137, 22A530 (2012)). J. Chem. Phys. 2013, 139, 087101.
63. Abedi, A.; Maitra, N.T.; Gross, E.K.U. Response to: Comment on "Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction" (J. Chem. Phys. 139, 087101 (2013)). J. Chem. Phys. 2013, 139, 087102.
64. Barbatti, M.; Shepard, R.; Lischka, H. Computational and methodological elements for nonadiabatic trajectory dynamics simulations of molecules. In Conical Intersections: Theory, Computation and Experiment; Domcke, W., Yarkony, D.R., Koeppel, H., Eds.; World Scientific: Singapore, Singapore, 2011; p. 415.
65. Barbatti, M. Nonadiabatic dynamics with trajectory surface hopping method. WIREs Comput. Mol. Sci. 2011, 1, 620-633.
66. Curchod, B.F.E.; Rothlisberger, U.; Tavernelli, I. Trajectory-based nonadiabatic dynamics with time-dependent density functional theory. Chem. Phys. Chem. 2013, 14, 1314-1340.
67. Burant, J.C.; Tully, J.C. Nonadiabatic dynamics via the classical limit Schrödinger equation. J. Chem. Phys. 2000, 112, 6097.
68. Granucci, G.; Persico, M. Critical appraisal of the fewest switches algorithm for surface hopping. J. Chem. Phys. 2007, 126, 134114-11.
69. Worth, G.A.; Hunt, P.; Robb, M.A. Nonadiabatic dynamics: A comparison of surface hopping direct dynamics with quantum wave packet calculations. J. Phys. Chem. A 2003, 107, 621-631.
70. Herman, M.F.; Moody, M.P. Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations. J. Chem. Phys. 2005, 122, 094104.
71. Granucci, G.; Persico, M.; Zoccante, A. Including quantum decoherence in surface hopping. J. Chem. Phys. 2010, 133, 134111.
72. Richter, M.; Marquetand, P.; González-Vázquez, J.; Sola, I.; González, L. SHARC: Ab Initio molecular dynamics with surface hopping in the adiabatic representation including arbitrary couplings. J. Chem. Theory Comput. 2011, 7, 1253-1258.
73. Shenvi, N.; Subotnik, J.; Yang,W. Phase-corrected surface hopping: Correcting the phase evolution of the electronic wavefunction. J. Chem. Phys. 2011, 135, 024101.
74. Subotnik, J.; Shenvi, N. Decoherence and surface hopping: When can averaging over initial conditions help capture the effects of wave packet separation? J. Chem. Phys. 2011, 134, 244114.
75. Shenvi, N.; Subotnik, J.; Yang, W. Simultaneous-trajectory surface hopping: A parameter-free algorithm for implementing decoherence in nonadiabatic dynamics. J. Chem. Phys. 2011, 134, 144102.
76. Shenvi, N.; Yang, W. Achieving partial decoherence in surface hopping through phase correction. J. Chem. Phys. 2012, 137, doi:10.1063/1.4746407.