DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems

Journal Article · · Journal of Chemical Physics
DOI: https://doi.org/10.1063/1.5005059 · OSTI ID:1498058
 [1]; ORCiD logo [1]
  1. Peking Univ., Beijing (China). Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Furthermore, its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1498058
Journal Information:
Journal of Chemical Physics, Vol. 148, Issue 10; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (58)

On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics journal August 2017
A classical analog for electronic degrees of freedom in nonadiabatic collision processes journal April 1979
Non-oscillatory flux correlation functions for efficient nonadiabatic rate theory journal August 2014
Imaginary time path integral Monte Carlo route to rate coefficients for nonadiabatic barrier crossing journal December 1987
Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities journal July 2014
A unified thermostat scheme for efficient configurational sampling for classical/quantum canonical ensembles via molecular dynamics journal July 2017
Dissipation equation of motion approach to open quantum systems journal May 2016
Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach journal November 2015
Equilibrium-reduced density matrix formulation: Influence of noise, disorder, and temperature on localization in excitonic systems journal March 2012
Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes journal April 2014
Stochastic description of quantum Brownian dynamics journal May 2016
Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions journal December 2011
Exact quantum statistics for electronically nonadiabatic systems using continuous path variables journal December 2010
Forward–backward solution of quantum-classical Liouville equation in the adiabatic mapping basis journal December 2013
Semiclassical Description of Nonadiabatic Quantum Dynamics journal January 1997
Dynamics of the dissipative two-state system journal January 1987
Iterative quantum-classical path integral with dynamically consistent state hopping journal January 2016
On the Simulation of Quantum Systems: Path Integral Methods journal January 1986
Time-dependent wavepacket diffusion method and its applications in organic semiconductors journal December 2014
Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals journal August 1993
Accelerating the convergence of path integral dynamics with a generalized Langevin equation journal February 2011
Exciton Delocalization in the B850 Light-Harvesting Complex:  Comparison of Different Measures journal June 2001
Numerically exact, time-dependent study of correlated electron transport in model molecular junctions journal April 2013
A new symmetrical quasi-classical model for electronically non-adiabatic processes: Application to the case of weak non-adiabatic coupling journal October 2016
Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only 1-electron interactions journal January 2017
Exciton Analysis in 2D Electronic Spectroscopy journal June 2005
The semiclassical calculation of nonadiabatic tunneling rates journal January 1998
Semiclassical description of electronically nonadiabatic dynamics via the initial value representation journal August 2007
A multi-state trajectory method for non-adiabatic dynamics simulations journal March 2016
Molecular dynamics simulations at constant pressure and/or temperature journal February 1980
Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations journal February 2006
Mean field ring polymer molecular dynamics for electronically nonadiabatic reaction rates journal January 2016
Path-integral simulations beyond the adiabatic approximation journal September 2007
A molecular dynamics method for simulations in the canonical ensemble journal June 1984
Nosé–Hoover chains: The canonical ensemble via continuous dynamics journal August 1992
Ab Initio Multiple Spawning:  Photochemistry from First Principles Quantum Molecular Dynamics journal June 2000
Variational path integral molecular dynamics and hybrid Monte Carlo algorithms using a fourth order propagator with applications to molecular systems journal August 2016
Multiple Exciton Coherence Sizes in Photosynthetic Antenna Complexes viewed by Pump−Probe Spectroscopy journal September 1997
The rigorous stochastic matrix multiplication scheme for the calculations of reduced equilibrium density matrices of open multilevel quantum systems journal April 2014
Efficient and general algorithms for path integral Car–Parrinello molecular dynamics journal April 1996
On path integral Monte Carlo simulations journal May 1982
Rational Construction of Stochastic Numerical Methods for Molecular Sampling journal June 2012
Efficient stochastic thermostatting of path integral molecular dynamics journal September 2010
Canonical dynamics: Equilibrium phase-space distributions journal March 1985
Extension of path integral quantum transition state theory to the case of nonadiabatic activated dynamics journal August 1999
Path integrals in the theory of condensed helium journal April 1995
An extension of stochastic hierarchy equations of motion for the equilibrium correlation functions journal June 2017
The computation of electron transfer rates: The nonadiabatic instanton solution journal July 1995
Nonadiabatic instanton calculation of multistate electron transfer reaction rate: Interference effects in three and four states systems journal June 2001
A unified theoretical framework for mapping models for the multi-state Hamiltonian journal November 2016
Study of an F center in molten KCl journal January 1984
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat journal July 2016
Molecular dynamics with electronic transitions journal July 1990
Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems journal April 2017
Quantum Dissipative Dynamics:  A Numerically Exact Methodology journal June 1998
Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets book January 2004
Iterative Calculation of Energy Eigenstates Employing the Multilayer Multiconfiguration Time-Dependent Hartree Theory journal May 2014
Path-integral simulation of finite-temperature properties of systems involving multiple, coupled electronic states journal October 2001

Cited By (5)

Preface: Special Topic on Nuclear Quantum Effects journal March 2018
A new perspective for nonadiabatic dynamics with phase space mapping models journal July 2019
Critical role of quantum dynamical effects in the Raman spectroscopy of liquid water journal November 2017
Critical role of quantum dynamical effects in the Raman spectroscopy of liquid water text January 2018
Critical role of quantum dynamical effects in the Raman spectroscopy of liquid water text January 2017

Figures / Tables (20)