Quantum-classical path integral with self-consistent solvent-driven reference propagators

Journal of Physical Chemistry B

Volumn 117, Issue 42, 2013, Pages 13357-13366

  Banerjee, Tuseeta ^a   Makri, Nancy ^a,b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); HAMILTONIANS; SOLVENTS;

QUANTUM-CLASSICAL; RAPID CONVERGENCE; SELF-CONSISTENT FIELD; SOLVENT REORGANIZATION; STATE COUPLINGS; TIME INCREMENTS; TRANSITION PROBABILITIES; TWO-LEVEL SYSTEM;

QUANTUM THEORY;

EID: 84886655560     PISSN: 15206106     EISSN: 15205207     Source Type: Journal    
DOI: 10.1021/jp4043123     Document Type: Article

References (69)

1. Ehrenfest, P. Bemerkung Über Die Angenäherte Gültigkeit Der Klassischen Mechanik Innerhalb Der Quantenmechanik Z. Phys. 1927, 45, 455-457
2. Tully, J. C. Molecular Dynamics with Electronic Transitions J. Chem. Phys. 1990, 93, 1061-1071
3. Gerber, R. B.; Ratner, M. A. Self-Consistent-Field Methods for Vibrational Excitations in Polyatomic Systems Adv. Chem. Phys. 1988, 70, 97-132
4. Billing, G. D. Classical Path Method in Inelastic and Reactive Scattering Int. Rev. Phys. Chem. 1994, 13, 309
5. Pechukas, P. Time-Dependent Semiclassical Scattering Theory. I. Potential Scattering Phys. Rev. 1969, 181, 166-185
6. 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
7. Herman, M. F. Dynamics by Semiclassical Methods Annu. Rev. Phys. Chem. 1994, 45, 83
8. Hammes-Schiffer, S.; Tully, J. C. Proton Transfer in Solution: Molecular Dynamics with Quantum Transitions J. Chem. Phys. 1994, 101, 4657-4667
9. Hammes-Schiffer, S. Theory of Proton-Coupled Electron Transfer in Energy Conversion Processes Acc. Chem. Res. 2009, 42, 1881-1889
10. Webster, F. J.; Schnitker, J.; Friedrichs, M. S.; Friesner, R. A.; Rossky, P. J. Solvation Dynamics of the Hydrated Electron: A Nonadiabatic Quantum Simulation Phys. Rev. Lett. 1991, 66, 3172-3175
11. Webster, F.; Rossky, P. J.; Friesner, R. A. Nonadiabatic Processes in Condensed Matter: Semiclassical Theory and Implementation Comput. Phys. Commun. 1991, 63, 494-522
12. Coker, D. F.; Xiao, L. Methods for Molecular Dynamics with Nonadiabatic Transitions J. Chem. Phys. 1995, 102, 496-510
13. Prezhdo, O. V.; Rossky, P. J. Mean Field Molecular Dynamics with Surface Hopping J. Chem. Phys. 1997, 107, 825-834
14. Ben-Nun, M.; Quenneville, J.; Martinez, T. J. Ab Initio Multiple Spawning: Photochemistry from First Principles Molecular Dynamics J. Phys. Chem. 2000, 104, 5161-5175
15. Burant, J. C.; Tully, J. C. Nonadiabatic Dynamics Via the Classical Limit Schrodinger Equation J. Chem. Phys. 2000, 112, 6097-6103
16. Prezhdo, O. V.; Brooksby, C. Quantum Backreaction through the Bohmian Particle Phys. Rev. Lett. 2001, 86, 3215-3219
17. Wyatt, R. E.; Lopreore, C. L.; Parlant, G. Electronic Transitions with Quantum Trajectories J. Chem. Phys. 2001, 114, 5113-5116
18. Donoso, A.; Martens, C. C. Simulation of Coherent Nonadiabatic Dynamics Using Classical Trajectories J. Phys. Chem. A 1998, 102, 4291
19. Kapral, R.; Ciccotti, G. Mixed Quantum-Classical Dynamics J. Chem. Phys. 1999, 110, 8919-8929
20. Meyer, H.-D.; Miller, W. H. A Classical Analog for Electronic Degrees of Freedom in Nonadiabatic Collision Processes J. Chem. Phys. 1979, 70, 3214-3223
21. Stock, G.; Thoss, M. Semiclassical Description of Nonadiabatic Quantum Dynamics Phys. Rev. Lett. 1997, 78, 578-581
22. Miller, W. H. Electronically Nonadiabatic Dynamics Via Semiclassical Initial Value Methods J. Phys. Chem. 2009, 113, 1405-1415
23. Feynman, R. P. Space-Time Approach to Non-Relativistic Quantum Mechanics Rev. Mod. Phys. 1948, 20, 367-387
24. Feynman, R. P.; Hibbs, A. R. Quantum Mechanics and Path Integrals; McGraw-Hill: New York, 1965.
25. Makri, N.; Thompson, K. Semiclassical Influence Functionals for Quantum Systems in Anharmonic Environments Chem. Phys. Lett. 1998, 291, 101-109
26. Thompson, K.; Makri, N. Influence Functionals with Semiclassical Propagators in Combined Forward-Backward Time J. Chem. Phys. 1999, 110, 1343-1353
27. Makri, N. Quantum Dissipative Systems: A Numerically Exact Methodology J. Phys. Chem. 1998, 102, 4414-4427
28. Makri, N. Iterative Evaluation of the Path Integral for a System Coupled to an Anharmonic Bath J. Chem. Phys. 1999, 111, 6164-6167
29. Makri, N. Path Integral Renormalization for Quantum Dissipative Dynamics with Multiple Timescales Mol. Phys. 2012, 110, 1001-1007
30. Makri, N. Dynamics of Reduced Density Matrices: Classical Memory Vs. Quantum Nonlocality J. Chem. Phys. 1998, 109, 2994-2998
31. Lambert, R.; Makri, N. Quantum-Classical Path Integral: Classical Memory and Weak Quantum Nonlocality J. Chem. Phys. 2012, 137, 22A552
32. Lambert, R.; Makri, N. Quantum-Classical Path Integral: Numerical Formulation J. Chem. Phys. 2012, 137, 22A553
33. Makri, N.; Makarov, D. E. Tensor Multiplication for Iterative Quantum Time Evolution of Reduced Density Matrices. I. Theory J. Chem. Phys. 1995, 102, 4600-4610
34. Makri, N.; Makarov, D. E. Tensor Multiplication for Iterative Quantum Time Evolution of Reduced Density Matrices. Ii. Numerical Methodology J. Chem. Phys. 1995, 102, 4611-4618
35. Shi, Q.; Geva, E. A Relationship between Semiclassical and Centroid Correlation Functions J. Chem. Phys. 2003, 118, 8173-8183
36. Poulsen, J. A.; Nyman, G.; Rossky, P. J. Practical Evaluation of Condensed Phase Quantum Correlation Functions: A Feynman - Kleinert Variational Linearized Path Integral Method J. Chem. Phys. 2003, 119, 12179-12193
37. Wigner, E. J. Calculation of the Rate of Elementary Association Reactions Chem. Phys. 1937, 5, 720
38. Sun, X.; Miller, W. H. Mixed Semiclassical-Classical Approaches to the Dynamics of Complex Molecular Systems J. Chem. Phys. 1997, 106, 916-927
39. Thompson, K.; Makri, N. Rigorous Forward-Backward Semiclassical Formulation of Many-Body Dynamics Phys. Rev. E 1999, 59, R4729-R4732
40. Bacic, Z.; Light, J. C. Theoretical Methods for Rovibrational States of Floppy Molecules Annu. Rev. Phys. Chem. 1989, 40, 469-498
41. Topaler, M.; Makri, N. System-Specific Discrete Variable Representations for Path Integral Calculations with Quasi-Adiabatic Propagators Chem. Phys. Lett. 1993, 210, 448
42. Sim, E.; Makri, N. Filtered Propagator Functional for Iterative Dynamics of Quantum Dissipative Systems Comput. Phys. Commun. 1997, 99, 335-354
43. Sim, E. Quantum Dynamics for a System Coupled to Slow Baths: On-the-Fly Filtered Propagator Method J. Chem. Phys. 2001, 115, 4450-4456
44. Lambert, R.; Makri, N. Memory Path Propagator Matrix for Long-Time Dissipative Charge Transport Dynamics Mol. Phys. 2012, 110, 1967-1975
45. Frauenfelder, H.; Wolynes, P. G. Rate Theories and Puzzles of Heme Protein Kinetics Science 1985, 228, 337
46. Wolynes, P. G. Dissipation, Tunneling and Adiabaticity Criteria for Curve Crossing Problems in the Condensed Phase J. Chem. Phys. 1987, 86, 1957-1966
47. Makri, N. Improved Feynman Propagators on a Grid and Non-Adiabatic Corrections within the Path Integral Framework Chem. Phys. Lett. 1992, 193, 435-444
48. Ilk, G.; Makri, N. Real Time Path Integral Methods for a System Coupled to an Anharmonic Bath J. Chem. Phys. 1994, 101, 6708
49. Dirac, P. A. Note on the Exchange Phenomena in the Thomas Atom. Proc. Cambridge Philos. Soc. 1930, 26.
50. Makri, N.; Miller, W. H. Time-Dependent Self-Consistent Field Approximation for a Reaction Coordinate Coupled to a Harmonic Bath: Single and Multiple Configuration Treatments J. Chem. Phys. 1987, 87, 5781-5787
51. Wahnstrom, G.; Carmeli, B.; Metiu, H. The Calculation of the Thermal Rate Coefficient by a Method Combining Classical and Quantum Dynamics J. Chem. Phys. 1988, 88, 2478-2491
52. Haug, K.; Metiu, H. A Test of the Possibility of Calculating Absorption Spectra by Mixed Quantum-Classical Methods J. Chem. Phys. 1992, 97, 4781-4791
53. Leggett, A. J.; Chakravarty, S.; Dorsey, A. T.; Fisher, M. P. A.; Garg, A.; Zwerger, M. Dynamics of the Dissipative Two-State System Rev. Mod. Phys. 1987, 59, 1-85
54. Caldeira, A. O.; Leggett, A. J. Path Integral Approach to Quantum Brownian Motion Physica A 1983, 121, 587-616
55. Makri, N. The Linear Response Approximation and Its Lowest Order Corrections: An Influence Functional Approach J. Phys. Chem. 1999, 103, 2823-2829
56. Feynman, R. P.; Vernon, F. L. The Theory of a General Quantum System Interacting with a Linear Dissipative System Ann. Phys. 1963, 24, 118
57. Wang, H.; Sun, X.; Miller, W. H. Semiclassical Approximations for the Calculation of Thermal Rate Constants for Chemical Reactions in Complex Molecular Systems J. Chem. Phys. 1998, 108, 9726-9736
58. Shi, Q.; Geva, E. Semiclassical Theory of Vibrational Energy Relaxation in the Condensed Phase J. Phys. Chem. A 2003, 107, 9059-9069
59. Frantsuzov, P. A.; Neumaier, A.; Mandelshtam, V. A. Gaussian Resolutions for Equilibrium Density Matrices Chem. Phys. Lett. 2003, 381, 117
60. Liu, J.; Miller, W. H. Using the Thermal Gaussian Approximation for the Boltzmann Operator in Semiclassical Initial Value Time Correlation Functions J. Chem. Phys. 2006, 125, 224104
61. Liu, J.; Miller, W. H. A Simple Model for the Treatment of Imaginary Frequencies in Chemical Reaction Rates and Molecular Liquids J. Chem. Phys. 2009, 131, 074113
62. Jezek, E.; Makri, N. Finite Temperature Correlation Functions Via Forward-Backward Semiclassical Dynamics J. Phys. Chem. 2001, 105, 2851-2857
63. Makri, N. Monte Carlo Evaluation of Forward-Backward Semiclassical Correlation Functions with a Quantized Coherent State Density J. Phys. Chem. B 2002, 106, 8390-8398
64. Nakayama, A.; Makri, N. Simulation of Dynamical Properties in Normal and Superfluid Helium Proc. Natl. Acad Sci. U.S.A. 2005, 102, 4230-4234
65. Makri, N.; Miller, W. H. Coherent State Semiclassical Initial Value Representation for the Boltzmann Operator in Thermal Correlation Functions J. Chem. Phys. 2002, 116, 9207-9212
66. Jadhao, V.; Makri, N. Iterative Monte Carlo for Quantum Dynamics J. Chem. Phys. (Communication) 2008, 129, 161102
67. Jadhao, V.; Makri, N. Iterative Monte Carlo with Bead-Adapted Sampling for Complex Time Correlation Functions J. Chem. Phys. 2010, 132, 104110
68. Jadhao, V.; Makri, N. Iterative Monte Carlo Path Integral with Optimal Grids from Whole-Necklace Sampling J. Chem. Phys. 2010, 133, 114105
69. Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, H.; Teller, E. Equation of State Calculations by Fast Computing Machines J. Chem. Phys. 1953, 21, 1087-1092