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Title: Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function

Abstract

In an adiabatic mixed quantum-classical simulation, the avoided crossing of weakly coupled eigenstates can lead to unphysical discontinuities in wave function dynamics, otherwise known as the trivial crossing problem. A standard solution to the trivial crossing problem eliminates spatial discontinuities in wave function dynamics by imposing changes to the eigenstate of the wave function. In this paper, we show that this solution has the side effect of introducing transient discontinuities in the nodal symmetry of the wave function. We present an alternative solution to the trivial crossing problem that preserves both the spatial and nodal structure of the adiabatic wave function. By considering a model of exciton dynamics on conjugated polymer systems, we show that failure to preserve wave function symmetry yields exciton dynamics that depends unphysically on polymer system size. We demonstrate that our symmetry-preserving solution to the trivial crossing problem yields more realistic dynamics and can thus improve the accuracy of simulations of larger systems that are prone to the trivial crossing problem.

Authors:
ORCiD logo [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Univ. of Chicago, IL (United States)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1557213
Grant/Contract Number:  
SC0001088
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 15; Journal Issue: 8; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Lee, Elizabeth M. Y., and Willard, Adam P. Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function. United States: N. p., 2019. Web. doi:10.1021/acs.jctc.9b00302.
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Lee, Elizabeth M. Y., & Willard, Adam P. Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function. United States. https://doi.org/10.1021/acs.jctc.9b00302
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Lee, Elizabeth M. Y., and Willard, Adam P. Mon . "Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function". United States. https://doi.org/10.1021/acs.jctc.9b00302. https://www.osti.gov/servlets/purl/1557213.
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@article{osti_1557213,
title = {Solving the Trivial Crossing Problem While Preserving the Nodal Symmetry of the Wave Function},
author = {Lee, Elizabeth M. Y. and Willard, Adam P.},
abstractNote = {In an adiabatic mixed quantum-classical simulation, the avoided crossing of weakly coupled eigenstates can lead to unphysical discontinuities in wave function dynamics, otherwise known as the trivial crossing problem. A standard solution to the trivial crossing problem eliminates spatial discontinuities in wave function dynamics by imposing changes to the eigenstate of the wave function. In this paper, we show that this solution has the side effect of introducing transient discontinuities in the nodal symmetry of the wave function. We present an alternative solution to the trivial crossing problem that preserves both the spatial and nodal structure of the adiabatic wave function. By considering a model of exciton dynamics on conjugated polymer systems, we show that failure to preserve wave function symmetry yields exciton dynamics that depends unphysically on polymer system size. We demonstrate that our symmetry-preserving solution to the trivial crossing problem yields more realistic dynamics and can thus improve the accuracy of simulations of larger systems that are prone to the trivial crossing problem.},
doi = {10.1021/acs.jctc.9b00302},
journal = {Journal of Chemical Theory and Computation},
number = 8,
volume = 15,
place = {United States},
year = {Mon Jul 15 00:00:00 EDT 2019},
month = {Mon Jul 15 00:00:00 EDT 2019}
}
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https://doi.org/10.1021/acs.jctc.9b00302
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Works referenced in this record:

An insight into non-emissive excited states in conjugated polymers
journal, September 2015

  • Hu, Zhongjian; Willard, Adam P.; Ono, Robert J.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms9246

Adaptive time steps in trajectory surface hopping simulations
journal, May 2016

  • Spörkel, Lasse; Thiel, Walter
  • The Journal of Chemical Physics, Vol. 144, Issue 19
  • DOI: 10.1063/1.4948956

Solution for the Trivial Crossing Problem in Surface Hopping Simulations by the Classification on Excited States
journal, March 2018

  • Sun, Zhen; Li, Sheng; Xie, Shijie
  • The Journal of Physical Chemistry C, Vol. 122, Issue 15
  • DOI: 10.1021/acs.jpcc.8b00084

Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules
journal, July 2012

  • Fernandez-Alberti, Sebastian; Roitberg, Adrian E.; Nelson, Tammie
  • The Journal of Chemical Physics, Vol. 137, Issue 1
  • DOI: 10.1063/1.4732536

Evaluation of the Time-Derivative Coupling for Accurate Electronic State Transition Probabilities from Numerical Simulations
journal, June 2014

  • Meek, Garrett A.; Levine, Benjamin G.
  • The Journal of Physical Chemistry Letters, Vol. 5, Issue 13
  • DOI: 10.1021/jz5009449

A Semi‐Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. II
journal, May 1953

  • Pariser, Rudolph; Parr, Robert G.
  • The Journal of Chemical Physics, Vol. 21, Issue 5
  • DOI: 10.1063/1.1699030

Exciton Dynamics in Disordered Poly( p -phenylenevinylene). 2. Exciton Diffusion
journal, October 2012

  • Barford, William; Bittner, Eric R.; Ward, Alec
  • The Journal of Physical Chemistry A, Vol. 116, Issue 42
  • DOI: 10.1021/jp307041n

Recent Progress in Surface Hopping: 2011–2015
journal, May 2016

  • Wang, Linjun; Akimov, Alexey; Prezhdo, Oleg V.
  • The Journal of Physical Chemistry Letters, Vol. 7, Issue 11
  • DOI: 10.1021/acs.jpclett.6b00710

Implementation of surface hopping molecular dynamics using semiempirical methods
journal, June 2008

Computer Simulation of the Excited State Dynamics of Betaine-30 in Acetonitrile
journal, November 1999

  • Lobaugh, John; Rossky, Peter J.
  • The Journal of Physical Chemistry A, Vol. 103, Issue 47
  • DOI: 10.1021/jp991604w

Intramolecular Exciton Diffusion in Poly(3-hexylthiophene)
journal, September 2013

  • Healy, Andrew T.; Boudouris, Bryan W.; Frisbie, C. Daniel
  • The Journal of Physical Chemistry Letters, Vol. 4, Issue 20
  • DOI: 10.1021/jz401694j

Molecular dynamics with electronic transitions
journal, July 1990

  • Tully, John C.
  • The Journal of Chemical Physics, Vol. 93, Issue 2
  • DOI: 10.1063/1.459170

Intrachain exciton dynamics in conjugated polymer chains in solution
journal, August 2015

  • Tozer, Oliver Robert; Barford, William
  • The Journal of Chemical Physics, Vol. 143, Issue 8
  • DOI: 10.1063/1.4929378

Molecular-Level Details of Morphology-Dependent Exciton Migration in Poly(3-hexylthiophene) Nanostructures
journal, March 2015

  • Tapping, Patrick C.; Clafton, Scott N.; Schwarz, Kyra N.
  • The Journal of Physical Chemistry C, Vol. 119, Issue 13
  • DOI: 10.1021/acs.jpcc.5b00705

Second-order integrators for Langevin equations with holonomic constraints
journal, September 2006

Ultrafast Dynamical Localization of Photoexcited States in Conformationally Disordered Poly( p -phenylenevinylene)
journal, August 2011

  • Barford, William; Boczarow, Igor; Wharram, Thomas
  • The Journal of Physical Chemistry A, Vol. 115, Issue 33
  • DOI: 10.1021/jp204822h

Flexible Surface Hopping Approach to Model the Crossover from Hopping to Band-like Transport in Organic Crystals
journal, May 2013

  • Wang, Linjun; Beljonne, David
  • The Journal of Physical Chemistry Letters, Vol. 4, Issue 11
  • DOI: 10.1021/jz400871j

Conformation and Energy Transfer in Single Conjugated Polymers
journal, March 2012

  • Bolinger, Joshua C.; Traub, Matthew C.; Brazard, Johanna
  • Accounts of Chemical Research, Vol. 45, Issue 11
  • DOI: 10.1021/ar300012k

A Semi‐Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. I.
journal, March 1953

  • Pariser, Rudolph; Parr, Robert G.
  • The Journal of Chemical Physics, Vol. 21, Issue 3
  • DOI: 10.1063/1.1698929

Perspective: Nonadiabatic dynamics theory
journal, December 2012

  • Tully, John C.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4757762

Tailored exciton diffusion in organic photovoltaic cells for enhanced power conversion efficiency
journal, November 2012

  • Menke, S. Matthew; Luhman, Wade A.; Holmes, Russell J.
  • Nature Materials, Vol. 12, Issue 2
  • DOI: 10.1038/nmat3467

Hot charge-transfer excitons set the time limit for charge separation at donor/acceptor interfaces in organic photovoltaics
journal, December 2012

  • Jailaubekov, Askat E.; Willard, Adam P.; Tritsch, John R.
  • Nature Materials, Vol. 12, Issue 1
  • DOI: 10.1038/nmat3500

A Simple Solution to the Trivial Crossing Problem in Surface Hopping
journal, January 2014

  • Wang, Linjun; Prezhdo, Oleg V.
  • The Journal of Physical Chemistry Letters, Vol. 5, Issue 4
  • DOI: 10.1021/jz500025c

Relating Chromophoric and Structural Disorder in Conjugated Polymers
journal, April 2017

Subspace Surface Hopping with Size-Independent Dynamics
journal, January 2019

The symmetrical quasi-classical approach to electronically nonadiabatic dynamics applied to ultrafast exciton migration processes in semiconducting polymers
journal, July 2018

  • Liang, Ruibin; Cotton, Stephen J.; Binder, Robert
  • The Journal of Chemical Physics, Vol. 149, Issue 4
  • DOI: 10.1063/1.5037815

The theory of molecular excitons [Теория молекулярных экситонов]
journal, January 1964

Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization
journal, August 1972

  • Warshel, A.; Karplus, M.
  • Journal of the American Chemical Society, Vol. 94, Issue 16
  • DOI: 10.1021/ja00771a014

Understanding the Surface Hopping View of Electronic Transitions and Decoherence
journal, May 2016

Conformational disorder in conjugated polymers
journal, June 1989

  • Rossi, G.; Chance, R. R.; Silbey, R.
  • The Journal of Chemical Physics, Vol. 90, Issue 12
  • DOI: 10.1063/1.456193

A scheme to interpolate potential energy surfaces and derivative coupling vectors without performing a global diabatization
journal, December 2011

  • Evenhuis, Christian; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 135, Issue 22
  • DOI: 10.1063/1.3660686

Long-range exciton transport in conjugated polymer nanofibers prepared by seeded growth.
text, January 2018

  • Jin, Xu-Hui; Price, Michael B.; Finnegan, John R.
  • Apollo - University of Cambridge Repository
  • DOI: 10.17863/cam.27709

Implementation of surface hopping molecular dynamics using semiempirical methods
journal, June 2008

Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules
journal, July 2012

  • Fernandez-Alberti, Sebastian; Roitberg, Adrian E.; Nelson, Tammie
  • The Journal of Chemical Physics, Vol. 137, Issue 1
  • DOI: 10.1063/1.4732536

A scheme to interpolate potential energy surfaces and derivative coupling vectors without performing a global diabatization
journal, December 2011

  • Evenhuis, Christian; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 135, Issue 22
  • DOI: 10.1063/1.3660686

Surface hopping dynamics using a locally diabatic formalism: Charge transfer in the ethylene dimer cation and excited state dynamics in the 2-pyridone dimer
journal, December 2012

  • Plasser, Felix; Granucci, Giovanni; Pittner, Jiri
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4738960

Evaluation of the Time-Derivative Coupling for Accurate Electronic State Transition Probabilities from Numerical Simulations
journal, June 2014

  • Meek, Garrett A.; Levine, Benjamin G.
  • The Journal of Physical Chemistry Letters, Vol. 5, Issue 13
  • DOI: 10.1021/jz5009449

A Simple Solution to the Trivial Crossing Problem in Surface Hopping
journal, January 2014

  • Wang, Linjun; Prezhdo, Oleg V.
  • The Journal of Physical Chemistry Letters, Vol. 5, Issue 4
  • DOI: 10.1021/jz500025c

Understanding the Surface Hopping View of Electronic Transitions and Decoherence
journal, May 2016

Recent Progress in Surface Hopping: 2011–2015
journal, May 2016

  • Wang, Linjun; Akimov, Alexey; Prezhdo, Oleg V.
  • The Journal of Physical Chemistry Letters, Vol. 7, Issue 11
  • DOI: 10.1021/acs.jpclett.6b00710

Artifacts due to trivial unavoided crossings in the modeling of photoinduced energy transfer dynamics in extended conjugated molecules
journal, December 2013

Intrachain exciton dynamics in conjugated polymer chains in solution
journal, August 2015

  • Tozer, Oliver Robert; Barford, William
  • The Journal of Chemical Physics, Vol. 143, Issue 8
  • DOI: 10.1063/1.4929378

Perspective: Nonadiabatic dynamics theory
journal, December 2012

  • Tully, John C.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4757762

Subspace Surface Hopping with Size-Independent Dynamics
journal, January 2019

Solution for the Trivial Crossing Problem in Surface Hopping Simulations by the Classification on Excited States
journal, March 2018

  • Sun, Zhen; Li, Sheng; Xie, Shijie
  • The Journal of Physical Chemistry C, Vol. 122, Issue 15
  • DOI: 10.1021/acs.jpcc.8b00084

Flexible Surface Hopping Approach to Model the Crossover from Hopping to Band-like Transport in Organic Crystals
journal, May 2013

  • Wang, Linjun; Beljonne, David
  • The Journal of Physical Chemistry Letters, Vol. 4, Issue 11
  • DOI: 10.1021/jz400871j

Nodes of wavefunctions
journal, March 2007

The Diabatic Picture of Electron Transfer, Reaction Barriers, and Molecular Dynamics
journal, March 2010

Chemical Dynamics in Condensed Phases
book, April 2006

Conformation and Energy Transfer in Single Conjugated Polymers
journal, March 2012

  • Bolinger, Joshua C.; Traub, Matthew C.; Brazard, Johanna
  • Accounts of Chemical Research, Vol. 45, Issue 11
  • DOI: 10.1021/ar300012k

Tailored exciton diffusion in organic photovoltaic cells for enhanced power conversion efficiency
journal, November 2012

  • Menke, S. Matthew; Luhman, Wade A.; Holmes, Russell J.
  • Nature Materials, Vol. 12, Issue 2
  • DOI: 10.1038/nmat3467

Long-range exciton transport in conjugated polymer nanofibers prepared by seeded growth
journal, May 2018

Conformational disorder in conjugated polymers
journal, June 1989

  • Rossi, G.; Chance, R. R.; Silbey, R.
  • The Journal of Chemical Physics, Vol. 90, Issue 12
  • DOI: 10.1063/1.456193

Relating Chromophoric and Structural Disorder in Conjugated Polymers
journal, April 2017

Ultrafast Dynamical Localization of Photoexcited States in Conformationally Disordered Poly( p -phenylenevinylene)
journal, August 2011

  • Barford, William; Boczarow, Igor; Wharram, Thomas
  • The Journal of Physical Chemistry A, Vol. 115, Issue 33
  • DOI: 10.1021/jp204822h

Conformational Dynamics Guides Coherent Exciton Migration in Conjugated Polymer Materials: First-Principles Quantum Dynamical Study
journal, May 2018

The symmetrical quasi-classical approach to electronically nonadiabatic dynamics applied to ultrafast exciton migration processes in semiconducting polymers
journal, July 2018

  • Liang, Ruibin; Cotton, Stephen J.; Binder, Robert
  • The Journal of Chemical Physics, Vol. 149, Issue 4
  • DOI: 10.1063/1.5037815

Molecular-Level Details of Morphology-Dependent Exciton Migration in Poly(3-hexylthiophene) Nanostructures
journal, March 2015

  • Tapping, Patrick C.; Clafton, Scott N.; Schwarz, Kyra N.
  • The Journal of Physical Chemistry C, Vol. 119, Issue 13
  • DOI: 10.1021/acs.jpcc.5b00705

Computer Simulation of the Excited State Dynamics of Betaine-30 in Acetonitrile
journal, November 1999

  • Lobaugh, John; Rossky, Peter J.
  • The Journal of Physical Chemistry A, Vol. 103, Issue 47
  • DOI: 10.1021/jp991604w

Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization
journal, August 1972

  • Warshel, A.; Karplus, M.
  • Journal of the American Chemical Society, Vol. 94, Issue 16
  • DOI: 10.1021/ja00771a014

A Semi‐Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. I.
journal, March 1953

  • Pariser, Rudolph; Parr, Robert G.
  • The Journal of Chemical Physics, Vol. 21, Issue 3
  • DOI: 10.1063/1.1698929

A Semi‐Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. II
journal, May 1953

  • Pariser, Rudolph; Parr, Robert G.
  • The Journal of Chemical Physics, Vol. 21, Issue 5
  • DOI: 10.1063/1.1699030

Electron interaction in unsaturated hydrocarbons
journal, January 1953

Hot charge-transfer excitons set the time limit for charge separation at donor/acceptor interfaces in organic photovoltaics
journal, December 2012

  • Jailaubekov, Askat E.; Willard, Adam P.; Tritsch, John R.
  • Nature Materials, Vol. 12, Issue 1
  • DOI: 10.1038/nmat3500

An insight into non-emissive excited states in conjugated polymers
journal, September 2015

  • Hu, Zhongjian; Willard, Adam P.; Ono, Robert J.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms9246

Second-order integrators for Langevin equations with holonomic constraints
journal, September 2006

Exciton Dynamics in Disordered Poly( p -phenylenevinylene). 2. Exciton Diffusion
journal, October 2012

  • Barford, William; Bittner, Eric R.; Ward, Alec
  • The Journal of Physical Chemistry A, Vol. 116, Issue 42
  • DOI: 10.1021/jp307041n

Molecular dynamics with electronic transitions
journal, July 1990

  • Tully, John C.
  • The Journal of Chemical Physics, Vol. 93, Issue 2
  • DOI: 10.1063/1.459170

Adaptive time steps in trajectory surface hopping simulations
journal, May 2016

  • Spörkel, Lasse; Thiel, Walter
  • The Journal of Chemical Physics, Vol. 144, Issue 19
  • DOI: 10.1063/1.4948956

Intramolecular Exciton Diffusion in Poly(3-hexylthiophene)
journal, September 2013

  • Healy, Andrew T.; Boudouris, Bryan W.; Frisbie, C. Daniel
  • The Journal of Physical Chemistry Letters, Vol. 4, Issue 20
  • DOI: 10.1021/jz401694j

Coarse-grained simulations of the solution-phase self-assembly of poly(3-hexylthiophene) nanostructures
journal, January 2013

  • Schwarz, Kyra N.; Kee, Tak W.; Huang, David M.
  • Nanoscale, Vol. 5, Issue 5
  • DOI: 10.1039/c3nr33324h
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    Works referencing / citing this record:

    Exciton Dynamics in Conjugated Polymers
    preprint, January 2021

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