Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

On the proper derivation of the Floquet-based quantum classical Liouville equation and surface hopping describing a molecule or material subject to an external field

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/5.0013873· OSTI ID:1656844
 [1];  [2];  [2]
  1. Univ. of Pennsylvania, Philadelphia, PA (United States); University of Pennsylvania
  2. Univ. of Pennsylvania, Philadelphia, PA (United States)
+ Show Author Affiliations
We investigate different approaches to derive the proper Floquet-based quantum–classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis and then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form that is similar to the usual QCLE with two modifications: (1) The electronic degrees of freedom are expanded to infinite dimension and (2) the nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a fictitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., [J. Chem. Phys. 140, 084104 (2014)] who found that transforming to the adiabatic representation must always be the last operation applied, although now we have extended this result to a time-dependent Hamiltonian. Finally, this paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping.
Research Organization:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
AC02-05CH11231; SC0019397
OSTI ID:
1656844
Alternate ID(s):
OSTI ID: 1643725
Journal Information:
Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 4 Vol. 153; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (55)

Nonadiabatic dynamics: The SHARC approach
  • Mai, Sebastian; Marquetand, Philipp; González, Leticia
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 6 https://doi.org/10.1002/wcms.1370
journal May 2018
Nonadiabatic processes in condensed matter: semi-classical theory and implementation journal February 1991
Surface hopping from the perspective of quantum–classical Liouville dynamics journal December 2016
Non-adiabatic couplings in Liouville description of mixed quantum-classical dynamics journal July 2002
Improved treatment of momentum at classically forbidden electronic transitions in trajectory surface hopping calculations journal February 2003
An Efficient, Augmented Surface Hopping Algorithm That Includes Decoherence for Use in Large-Scale Simulations journal October 2016
Nonadiabatic Dynamics in a Laser Field: Using Floquet Fewest Switches Surface Hopping To Calculate Electronic Populations for Slow Nuclear Velocities journal January 2020
Optical Activity from the Exciton Aharonov–Bohm Effect: A Floquet Engineering Approach journal January 2020
Control of Excitation Energy Transfer in Condensed Phase Molecular Systems by Floquet Engineering journal February 2018
Detailed Balance in Ehrenfest Mixed Quantum-Classical Dynamics journal January 2006
SHARC: ab Initio Molecular Dynamics with Surface Hopping in the Adiabatic Representation Including Arbitrary Couplings journal March 2011
All-Atom Semiclassical Dynamics Study of Quantum Coherence in Photosynthetic Fenna–Matthews–Olson Complex journal July 2012
Nonresonant Photons Catalyze Photodissociation of Phenol journal December 2018
Mixed Quantum-Classical Dynamics in the Adiabatic Representation To Simulate Molecules Driven by Strong Laser Pulses journal December 2011
Improvement of the Internal Consistency in Trajectory Surface Hopping journal November 1999
Coherent structural trapping through wave packet dispersion during photoinduced spin state switching journal May 2017
Drop-on-demand sample delivery for studying biocatalysts in action at X-ray free-electron lasers journal February 2017
Photon catalysis of deuterium iodide photodissociation journal January 2019
Introductory lecture: Nonadiabatic effects in chemical dynamics journal January 2004
A theoretical model for molecules interacting with intense laser pulses: The Floquet-based quantum-classical Liouville equation journal October 2001
Dissipative mixed quantum-classical simulation of the aqueous solvated electron system journal January 2002
Solvent-induced electronic decoherence: Configuration dependent dissipative evolution for solvated electron systems journal January 2002
Mixed quantum-classical Liouville molecular dynamics without momentum jump journal June 2003
Mixed quantum-classical equilibrium journal March 2005
Electronic decoherence time for non-Born-Oppenheimer trajectories journal August 2005
Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence journal December 2005
Mixed quantum-classical equilibrium: Surface hopping journal July 2008
Quantum decoherence in mixed quantum‐classical systems: Nonadiabatic processes journal November 1995
Quantum decoherence and the isotope effect in condensed phase nonadiabatic molecular dynamics simulations journal April 1996
A semiclassical approach to intense‐field above‐threshold dissociation in the long wavelength limit journal September 1996
How to recover Marcus theory with fewest switches surface hopping: Add just a touch of decoherence journal December 2012
Perspective: Nonadiabatic dynamics theory journal December 2012
The ultraviolet photodissociation dynamics of hydrogen bromide journal January 1999
Mixed quantum-classical dynamics journal May 1999
Orientation of pyrimidine in the gas phase using a strong electric field: Spectroscopy and relaxation dynamics journal June 1999
Nonadiabatic excited-state molecular dynamics: Treatment of electronic decoherence journal June 2013
Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics journal July 2013
Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence journal December 2013
Communication: The correct interpretation of surface hopping trajectories: How to calculate electronic properties journal December 2013
Interplay of radiative and nonradiative transitions in surface hopping with radiation-molecule interactions journal January 2014
Analysis of geometric phase effects in the quantum-classical Liouville formalism journal February 2014
How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: A simple generalization of ground-state Kubo theory journal July 2014
An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry curvature and “magnetic” forces journal March 2019
A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians journal August 2019
Laser-field-induced surface-hopping method for the simulation and control of ultrafast photodynamics journal May 2009
Simulation of laser-induced coupled electron-nuclear dynamics and time-resolved harmonic spectra in complex systems journal March 2011
Surface hopping in laser-driven molecular dynamics journal June 2017
Exact Factorization of the Time-Dependent Electron-Nuclear Wave Function journal September 2010
Self-Referenced Coherent Diffraction X-Ray Movie of Ångstrom- and Femtosecond-Scale Atomic Motion journal October 2016
Floquet surface hopping: Laser-driven dissociation and ionization dynamics of H 2 + journal May 2016
Glownia et al. Reply: journal August 2017
Relationship between Quantum Decoherence Times and Solvation Dynamics in Condensed Phase Chemical Systems journal December 1998
Light-matter interactions via the exact factorization approach journal August 2018
Understanding the Surface Hopping View of Electronic Transitions and Decoherence journal May 2016
Progress in the Theory of Mixed Quantum-Classical Dynamics journal May 2006

Similar Records

Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence
Journal Article · Fri Dec 06 23:00:00 EST 2013 · Journal of Chemical Physics · OSTI ID:22251285
Analysis of geometric phase effects in the quantum-classical Liouville formalism
Journal Article · Thu Feb 27 23:00:00 EST 2014 · Journal of Chemical Physics · OSTI ID:22255059
Laser assisted charge transfer reactions in slow ion--atom collisions: Coupled dressed quasimolecular-states approach
Journal Article · Sun Jul 15 00:00:00 EDT 1984 · J. Chem. Phys.; (United States) · OSTI ID:7098803

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY