Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density

The self-consistent hybrid approach [H. Wang, M. Thoss, and W. H. Miller, J. Chem. Phys. 115, 2979 (2001), preceding paper] is applied to the spin-boson problem with Debye spectral density as a model for electron-transfer reactions in a solvent exhibiting Debye dielectric relaxation. The population dynamics of the donor and acceptor states in this system is studied for a broad range of parameters, including the adiabatic (slow bath), nonadiabatic (fast bath), as well as the intermediate regime. Based on illustrative examples we discuss the transition from damped coherent dynamics to purely incoherent decay. Using the numerically exact results of the self-consistent hybrid approach as a benchmark, several approximate theories that have been widely used to describe the dynamics in the spin-boson model are tested: the noninteracting blip approximation, the Bloch–Redfield theory, the Smoluchowski-equation treatment of the reaction coordinate (Zusman equations), and the classical path approach (Ehrenfest model...

[1]  M. Schreiber,et al.  Density matrix description of ultrafast dissipative wave packet dynamics , 1993 .

[2]  A. Leggett.  Quantum tunneling in the presence of an arbitrary linear dissipation mechanism , 1984 .

[3]  G. Stock,et al.  Flow of zero-point energy and exploration of phase space in classical simulations of quantum relaxation dynamics. II. Application to nonadiabatic processes , 1999 .

[4]  K. Yoshihara,et al.  Vibrational Coherence in Electron Donor−Acceptor Complexes , 1999 .

[5]  Rudolph A. Marcus,et al.  On the Theory of Electron-Transfer Reactions. VI. Unified Treatment for Homogeneous and Electrode Reactions , 1965 .

[6]  G. Worth,et al.  Relaxation of a system with a conical intersection coupled to a bath: A benchmark 24-dimensional wave packet study treating the environment explicitly , 1998 .

[7]  Michael F. Herman.  Generalization of the geometric optical series approach for nonadiabatic scattering problems , 1982 .

[8]  C. Aslangul,et al.  Spin-boson systems: equivalence between the dilute-blip and the Born approximations , 1986 .

[9]  H. Grabert,et al.  Influence of friction and temperature on coherent quantum tunneling , 1987 .

[10]  R. Marcus,et al.  Electron transfers in chemistry and biology , 1985 .

[11]  R. Friesner,et al.  Application of a multilevel Redfield theory to electron transfer in condensed phases , 1992 .

[12]  G. Voth,et al.  The Computation of Electron Transfer Rates: The Nonadiabatic Instanton Solution. , 1995 .

[13]  Rudolph A. Marcus,et al.  Chemical and Electrochemical Electron-Transfer Theory , 1964 .

[14]  R. Egger,et al.  Quantum Monte Carlo simulation of the dynamics of the spin-boson model , 1992 .

[15]  Chandler,et al.  Coherent-incoherent transition and relaxation in condensed-phase tunneling systems. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[16]  Jianshu Cao.  An adiabatic picture for electron transfer in mixed-valence systems 1 This Letter is dedicated to Pr , 1999 .

[17]  Gerhard Stock,et al.  A semiclassical self‐consistent‐field approach to dissipative dynamics: The spin–boson problem , 1995 .

[18]  Fabrice Rappaport,et al.  Visualization of coherent nuclear motion in a membrane protein by femtosecond spectroscopy , 1993, Nature.

[19]  R. Coalson,et al.  Simulation of electron transfer in polar solvents: Effects of nonequilibrium initial state preparation , 1996 .

[20]  R. Graham,et al.  Two-state system coupled to a boson mode: Quantum dynamics and classical approximations , 1984 .

[21]  Kurt Warncke,et al.  Nature of biological electron transfer , 1992, Nature.

[22]  M. Ratner,et al.  Photoinduced electron transfer in mixed-valence compounds: Beyond the golden rule regime , 1998 .

[23]  N. Makri.  Stabilization of localized states in dissipative tunneling systems interacting with monochromatic fields , 1997 .

[24]  J. Tully,et al.  Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H+ with D2 , 1971 .

[25]  Jau Tang.  Electron transfer reactions in a non-Debye medium with frequency-dependent friction , 1996 .

[26]  Gerhard Stock,et al.  Surface-hopping modeling of photoinduced relaxation dynamics on coupled potential-energy surfaces , 1997 .

[27]  R. Silbey,et al.  Electronic Coherence in Mixed-Valence Systems: Spectral Analysis , 1999, physics/0008164.

[28]  A. Nitzan,et al.  A nonequilibrium golden rule formula for electronic state populations in nonadiabatically coupled systems , 1994 .

[29]  D. Chandler,et al.  Effective adiabatic approximation for a two level system coupled to a bath , 1985 .

[30]  DYNAMICAL SIMULATION OF CURRENT FLUCTUATIONS IN A DISSIPATIVE TWO-STATE SYSTEM , 1998, cond-mat/9802054.

[31]  U. Weiss.  Quantum Dissipative Systems , 1993 .

[32]  G. D. Billing,et al.  On the applicability of the classical trajectory equations in inelastic scattering theory , 1975 .

[33]  Haobin Wang,et al.  Basis set approach to the quantum dissipative dynamics: Application of the multiconfiguration time-dependent Hartree method to the spin-boson problem , 2000 .

[34]  J. Jortner,et al.  Dynamic solvent effects on outer‐sphere electron transfer , 1987 .

[35]  N. Scherer,et al.  Excitation Dephasing, Product Formation, and Vibrational Coherence in an Intervalence Charge-Transfer Reaction , 1995 .

[36]  G. Stock,et al.  Flow of zero-point energy and exploration of phase space in classical simulations of quantum relaxation dynamics , 1999 .

[37]  Haobin Wang,et al.  Semiclassical study of electronically nonadiabatic dynamics in the condensed-phase: Spin-boson problem with Debye spectral density , 1999 .

[38]  D. Coker,et al.  Methods for molecular dynamics with nonadiabatic transitions , 1994, chem-ph/9408002.

[39]  G. D. Billing.  Quantum corrections to the classical path theory , 1993 .

[40]  M. Beck,et al.  The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propa , 1999 .

[41]  Dynamical simulations for dissipative multi-state systems: discretized integral equation approach , 1996 .

[42]  R. Coalson.  A spin–boson model for spectroscopy involving nonadiabatically coupled potential energy surfaces , 1987 .

[43]  R. A. Kuharski,et al.  Molecular model for aqueous ferrous–ferric electron transfer , 1988 .

[44]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[45]  W. Domcke,et al.  Intramolecular electron-transfer dynamics in the inverted regime: quantum mechanical multi-mode model including dissipation , 1996 .

[46]  M. Grifoni,et al.  Dissipation, decoherence and preparation effects in the spin-boson system , 1999 .

[47]  W. Miller,et al.  Semiclassical Theory of Electronic Transitions in Low Energy Atomic and Molecular Collisions Involving Several Nuclear Degrees of Freedom , 1972 .

[48]  Richard A. Friesner,et al.  Efficient memory equation algorithm for reduced dynamics in spin-boson models , 1999 .

[49]  A. Stuchebrukhov,et al.  Quantum effects in electron transfer reactions with strong electronic coupling , 1994 .

[50]  R. Friesner,et al.  Solution of the Redfield equation for the dissipative quantum dynamics of multilevel systems , 1994 .

[51]  Is the direct observation of electronic coherence in electron transfer reactions possible , 1997, cond-mat/9709106.

[52]  G. Stock.  A semiclassical self-consistent-field approach to dissipative dynamics. II. Internal conversion processes , 1995 .

[53]  R. Feynman,et al.  The Theory of a general quantum system interacting with a linear dissipative system , 1963 .

[54]  William H. Miller,et al.  Semiclassical theory of electronically nonadiabatic dynamics: results of a linearized approximation to the initial value representation , 1998 .

[55]  Christoph Meier,et al.  Non-Markovian evolution of the density operator in the presence of strong laser fields , 1999 .

[56]  Nancy Makri,et al.  Path integrals for dissipative systems by tensor multiplication. Condensed phase quantum dynamics for arbitrarily long time , 1994 .

[57]  J. Onuchic,et al.  Effect of friction on electron transfer in biomolecules , 1985 .

[58]  William H. Miller,et al.  Systematic convergence in the dynamical hybrid approach for complex systems: A numerically exact methodology , 2001 .

[59]  David A. Micha,et al.  A self‐consistent eikonal treatment of electronic transitions in molecular collisions , 1983 .

[60]  D. Jonas,et al.  Femtosecond Wavepacket Spectroscopy: Influence of Temperature, Wavelength, and Pulse Duration , 1995 .

[61]  A dynamical theory of electron transfer: Crossover from weak to strong electronic coupling , 1996, chem-ph/9608002.

[62]  J. Tully.  Molecular dynamics with electronic transitions , 1990 .

[63]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[64]  G. Worth,et al.  Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian , 1999 .

[65]  Robert A. Harris,et al.  On the stabilization of optical isomers through tunneling friction , 1983 .

[66]  J. Skinner,et al.  ON THE THEORY OF MULTIPHONON RELAXATION RATES IN SOLIDS , 1995 .

[67]  Shaul Mukamel,et al.  Dielectric friction and the transition from adiabatic to nonadiabatic electron transfer. I. Solvation dynamics in Liouville space , 1988 .

[68]  A. Leggett,et al.  Dynamics of the dissipative two-state system , 1987 .

[69]  J. Wachtveitl,et al.  Vibrational Coherence in Photosynthetic Reaction Centers Observed in the Bacteriochlorophyll Anion Band , 1998 .

[70]  Bruce J. Berne,et al.  Vibrational energy relaxation in the condensed phases: Quantum vs classical bath for multiphonon processes , 1997 .

[71]  Weiss,et al.  Correlation functions for dissipative two-state systems: Effects of the initial preparation. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[72]  N. Makri,et al.  TENSOR PROPAGATOR FOR ITERATIVE QUANTUM TIME EVOLUTION OF REDUCED DENSITY MATRICES. I: THEORY , 1995 .

[73]  Alberto Suárez,et al.  Hydrogen tunneling in condensed media , 1991 .

[74]  N. Mott.  On the Theory of Excitation by Collision with Heavy Particles , 1931, Mathematical Proceedings of the Cambridge Philosophical Society.

[75]  U. Manthe,et al.  Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl , 1992 .

[76]  U. Manthe,et al.  The multi-configurational time-dependent Hartree approach , 1990 .

[77]  R. Cukier,et al.  The transition from nonadiabatic to solvent controlled adiabatic electron transfer: Solvent dynamical effects in the inverted regime , 1989 .

[78]  A. Magerl,et al.  Influence of the electronic state on H tunnelling in niobium , 1987 .

[79]  U. Weiss,et al.  Low-Temperature Properties of Biased Two-Level Systems: Effects of Frequency-Dependent Damping , 1989 .

[80]  Mak,et al.  Low-temperature dynamical simulation of spin-boson systems. , 1994, Physical review. B, Condensed matter.

[81]  Quantum theory for free energies of electron transfer , 1992 .

[82]  P. Hänggi,et al.  Controlling electron transfer in strong time-dependent fields: Theory beyond the Golden Rule approximation , 2000 .

[83]  A. Stuchebrukhov,et al.  Outer-sphere Electron Transfer in Polar Solvents: Quantum Scaling of Strongly Interacting Systems. , 1993 .

[84]  Richard A. Friesner,et al.  Nonadiabatic processes in condensed matter: semi-classical theory and implementation , 1991 .

[85]  R. Friesner,et al.  Reduced dynamics in spin-boson models: A method for both slow and fast bath , 2000 .

[86]  W. Zinth,et al.  Vibrational coherence in ultrafast electron-transfer dynamics of oxazine 1 in N,N-dimethylaniline: simulation of a femtosecond pump-probe experiment , 1998 .

[87]  L. D. Zusman.  Outer-sphere electron transfer in polar solvents , 1980 .