multilayer formulation of the multi-configuration time-dependent hartree theory
DESCRIPTION
Multilayer Formulation of the Multi-Configuration Time-Dependent Hartree Theory. Haobin Wang Department of Chemistry and Biochemistry New Mexico State University Las Cruces, New Mexico, USA. Collaborator: Michael Thoss Support: NSF. Outline. - PowerPoint PPT PresentationTRANSCRIPT
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Multilayer Formulation of the Multi-Configuration
Time-Dependent Hartree Theory
Haobin WangDepartment of Chemistry and
BiochemistryNew Mexico State UniversityLas Cruces, New Mexico, USA
Collaborator: Michael ThossSupport: NSF
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• Conventional brute-force approach to wave packet propagation
• Multi-configuration time-dependent Hartree (MCTDH) method
• Multilayer formulation of MCTDH (ML-MCTDH)
• Quantum simulation of time correlation functions
• Application to ultrafast electron transfer reactions
Outline
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Conventional Wave Packet Propagation
• Dirac-Frenkel variational principle
• Conventional Full CI Expansion (orthonormal basis)
• Equations of Motion
• Capability: <10 degrees of freedom (<~n10 configurations)even for separable limit
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Multi-Configuration Time-Dependent Hartree
• Multi-configuration expansion of the wave function
• Variations
• Both expansion coefficients and configurations are time-dependent
Meyer, Manthe, Cederbaum, Chem. Phys. Lett. 165 (1990) 73
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MCTDH Equations of Motion
• Some notations
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MCTDH Equations of Motion
• Reduced density matrices and mean-field operators
The “single hole” function
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Implementation of the MCTDH
• Full CI expansion of the single particle functions (mode grouping and adiabatic basis contraction)
• Only a few single particle functions are selected among the full CI space
Example: 5 single particle groups, each has 1000 basis functions
Conventional approach: 10005 = 1015 configurations MCTDH with 10 single particle functions per group: 10×1000×5 + 105 = 1.5×105 parameters
• Capability of the MCTDH theory: ~10×10 = 100 degrees of freedom
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Multi-Layer Formulation of the MCTDH Theory
• Multi-configurational expansion of the SP functions
• More complex way of expressing the wave function
• Two-layer MCTDH
Wang, Thoss, J. Chem. Phys. 119 (2003) 1289
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The Multilayer MCTDH Theory
Wang, Thoss, J. Chem. Phys. 119 (2003) 1289
…….
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The Multilayer MCTDH Theory
Wang, Thoss, J. Chem. Phys. 119 (2003) 1289
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Exploring Dynamical Simplicity Using ML-MCTDH
• Capability of the two-layer ML-MCTDH: ~10×10×10 = 1000 degrees of freedom
• Capability of the three-layer ML-MCTDH: ~10×10×10×10 = 10000 degrees of freedom
Conventional
MCTDH
ML-MCTDH
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The Scaling of the ML-MCTDH Theory
• f: the number of degrees of freedom • L: the number of layers• N: the number of (contracted) basis functions• n: the number of single-particle functions
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• The Spin-Boson Model
The Scaling of the ML-MCTDH Theory
electronic
nuclear
coupling
• Hamiltonian
• Bath spectral density
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Model Scaling of the ML-MCTDH Theory
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Model Scaling of the ML-MCTDH Theory
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Model Scaling of the ML-MCTDH Theory
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Simulating Time Correlation Functions
• Examples
• Imaginary Time Propagation and Monte Carlo Sampling
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Quantum Study of Transport Processes
Electron transfer at dye-semiconductor interfaces
Photochemical reactions
hν
e-
Electron transfer in mixed-valence compounds in solution
hν
e-
hν
cis
trans
V
Charge transport through single molecule junctions
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pumpprobe
Basic Models
|g>
|d>|k>
hν
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Intervalence Electron Transfer
• Experiment: - Back ET in ≈ 100 – 200 fs
- Coherent structure in Pump-Probe signal
hν
hν
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Photoinduced ET in Mixed-Valence Complexes
Experiment [Barbara et al., JPC A 104 (2000)
10637]: ET bimodal decay ≈ 100 fs / 2 ps
hν
Wang, Thoss, J. Phys. Chem. A 107 (2003) 2126
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Validity of Different Methods
Mean-field (Hartree)
Classical Ehrenfest
Self-consistent hybrid
Golden rule (NIBA)
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Vibrational Dynamics in Intervalence ET
Thoss, Wang, Domcke, Chem. Phys. 296 (2004) 217
Charge-Transfer State Ground state
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Electron-transfer at dye-semiconductor interfaces
Zimmermann, Willig, et al., J. Chem. Phys. B 105 (2001) 9345
hν
e-
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Example: Coumarin 343 – TiO2
hν
e-
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ET at dye-semiconductor interfaces: Coumarin 343 - TiO2
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ET at dye-semiconductor interfaces: Coumarin 343 - TiO2
Absorption spectra
Experiment: Huber et al., Chem. Phys. 285 (2002) 39
C343 in solutionC343 adsorbed on TiO2
experiment
simulation
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Experiments: electron injection 20 - 200 fs
Rehm, JCP 100 (1996) 9577 Murakoshi, Nanostr. Mat. 679 (1997) 221 Gosh, JPCB 102 (1998) 10208 Huber, Chem. Phys. 285 (2002) 39
ET at dye-semiconductor interfaces: Coumarin 343 -
TiO2
population of the donor state
|d>|k>
|g>
hν
Kondov, Thoss, Wang, J. Phys. Chem. A 110 (2006) 1364
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ET at dye-semiconductor interfaces: Coumarin 343 - TiO2
vibrational dynamics
|d>|k>
|g>
hν
donor state
acceptor statesω = 1612 cm-1
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ET at dye-semiconductor interfaces: Coumarin 343 - TiO2
vibrational dynamics
Vibrational motion induced by ultrafast ET
donor state
acceptor states
|d> |k>
|g>
hν
ω = 133 cm-1
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ET at dye-semiconductor interfaces
ML-MCTDH
Ehrenfest
Mean-Field (Hartree)
hν
|d>|k>
|g>
Electron injection dynamics - comparison of different methods
population of the donor state
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ET at dye-semiconductor interfaces: Coumarin 343 - TiO2
photoinduced electron injection dynamics
Simulation of the dynamics including the coupling to the laser field
|d>|k>
|g>
hν
laser pulse (5 fs)
donor population
acceptor population
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ET at dye-semiconductor interfaces: Coumarin 343 - TiO2
photoinduced electron injection dynamics
Simulation of the dynamics including the coupling to the laser field
|d>|k>
|g>
hν
laser pulse (20 fs)
donor population
acceptor population
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ET at dye-semiconductor interfaces: Coumarin 343 - TiO2
photoinduced electron injection dynamics
Simulation of the dynamics including the coupling to the laser field
|d>|k>
|g>
hν
laser pulse
donor population
acceptor population
(40 fs)
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Experiment: electron injection 6 fsHuber, Moser, Grätzel, Wachtveitl, J. Phys. Chem. B 106 (2002) 6494
ET at dye-semiconductor interfaces: Alizarin - TiO2
population of the donor state
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Summary of the ML-MCTDH Theory
• Powerful tool to propagate wave packet in complex systems
• Can reveal various dynamical information– population dynamics and rate constant– reduced wave packet motions – time-resolved nonlinear spectroscopy– dynamic/static properties: real and imaginary time
• Current status– Has been implemented for certain potential energy functions:
two-body, three-body, etc.– The (time-dependent) correlation DVR of Manthe
• Challenges– Implementation: somewhat difficult– Long time dynamics: “chaos”