Iterative quantum-classical path integral with dynamically consistent state hopping

Walters, Peter L.; Makri, Nancy

doi:10.1063/1.4939950

Title: Iterative quantum-classical path integral with dynamically consistent state hopping

Full Record
Other Related Research

Abstract

We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.

Authors:

Walters, Peter L.; Makri, Nancy ^[1]

Department of Chemistry, University of Illinois, Urbana, Illinois 61801 (United States)

Publication Date:: Thu Jan 28 00:00:00 EST 2016

OSTI Identifier:: 22493681

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 144; Journal Issue: 4; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONVERGENCE; ITERATIVE METHODS; PATH INTEGRALS; PROBABILISTIC ESTIMATION; QUANTUM MECHANICS; QUANTUM SYSTEMS; TRAJECTORIES

Citation Formats


                    Walters, Peter L., and Makri, Nancy. Iterative quantum-classical path integral with dynamically consistent state hopping.  United States: N. p., 2016. 
        Web.  doi:10.1063/1.4939950.

Copy to clipboard


                    Walters, Peter L., & Makri, Nancy. Iterative quantum-classical path integral with dynamically consistent state hopping.  United States.  https://doi.org/10.1063/1.4939950

Copy to clipboard


                    Walters, Peter L., and Makri, Nancy. 2016.  
        "Iterative quantum-classical path integral with dynamically consistent state hopping".  United States.  https://doi.org/10.1063/1.4939950.

Copy to clipboard


                    
@article{osti_22493681,

  title        = {Iterative quantum-classical path integral with dynamically consistent state hopping},

  author       = {Walters, Peter L. and Makri, Nancy},

  abstractNote = {We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.},

  doi          = {10.1063/1.4939950},

  url          = {https://www.osti.gov/biblio/22493681},
  journal      = {Journal of Chemical Physics},

  issn         = {0021-9606},

  number       = 4,

  volume       = 144,

  place        = {United States},

  year         = {Thu Jan 28 00:00:00 EST 2016},

  month        = {Thu Jan 28 00:00:00 EST 2016}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1063/1.4939950

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction

Journal Article Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa - Journal of Chemical Physics

We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the coursemore »« less
https://doi.org/10.1063/1.4933375
Numerical tests of coherence-corrected surface hopping methods using a donor-bridge-acceptor model system

Journal Article Sifain, Andrew; Wang, Linjun; Tretiak, Sergei; ... - Journal of Chemical Physics

Surface hopping (SH) is a popular mixed quantum-classical method for modeling nonadiabatic excited state processes in molecules and condensed phase materials. The method is simple, efficient, and easy to implement, but the use of classical and independent nuclear trajectories introduces an overcoherence in the electronic density matrix which, if ignored, often leads to spurious results, such as overestimated reaction rates. Several methods have been proposed to incorporate decoherence into SH simulations, but a lack of insightful benchmarks makes their relative accuracy unknown. Herein, we run numerical simulations of common coherence-corrected SH methods including Truhlar’s decay-of-mixing (DOM) and Subotnik’s augmented SHmore »« less
Cited by 16
https://doi.org/10.1063/1.5092999

Full Text Available
Communication: Proper treatment of classically forbidden electronic transitions significantly improves detailed balance in surface hopping

Journal Article Sifain, Andrew; Wang, Linjun; Prezhdo, Oleg - Journal of Chemical Physics

Surface hopping is the most popular method for nonadiabatic molecular dynamics. Many have reported that it does not rigorously attain detailed balance at thermal equilibrium, but does so approximately. We show that convergence to the Boltzmann populations is significantly improved when the nuclear velocity is reversed after a classically forbidden hop. The proposed prescription significantly reduces the total number of classically forbidden hops encountered along a trajectory, suggesting that some randomization in nuclear velocity is needed when classically forbidden hops constitute a large fraction of attempted hops. Our results are verified computationally using two- and three-level quantum subsystems, coupled tomore »« less
https://doi.org/10.1063/1.4953444
Mixed quantum–classical approach to model non-adiabatic electron–nuclear dynamics: Detailed balance and improved surface hopping method

Journal Article Stolyarov, E.; White, A.; Mozyrsky, D. - Journal of Chemical Physics

We develop a density matrix formalism to describe coupled electron–nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates inmore »« less
Cited by 1
https://doi.org/10.1063/5.0014284

Full Text Available
Ultrafast Electronic Relaxation through a Conical Intersection: Nonadiabatic Dynamics Disentangled through an Oscillator Strength-Based Diabatization Framework

Journal Article Medders, Gregory; Alguire, Ethan; Jain, Amber; ... - Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory

Here, we employ surface hopping trajectories to model the short-time dynamics of gas-phase and partially solvated 4-(N,N-dimethylamino)benzonitrile (DMABN), a dual fluorescent molecule that is known to undergo a nonadiabatic transition through a conical intersection. To compare theory vs time-resolved fluorescence measurements, we calculate the mixed quantum–classical density matrix and the ensemble averaged transition dipole moment. We introduce a diabatization scheme based on the oscillator strength to convert the TDDFT adiabatic states into diabatic states of L_a and L_b character. Somewhat surprisingly, we find that the rate of relaxation reported by emission to the ground state is almost 50% slower thanmore »« less
Cited by 14
https://doi.org/10.1021/acs.jpca.6b12120

Full Text Available

Similar Records