skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules

Abstract

Here in this paper, we present a new implementation of the Ab Initio Multiple Cloning (AIMC) method, which is applied for non-adiabatic excited-state molecular dynamics simulations of photoinduced processes in conjugated molecules. Within our framework, the multidimensional wave-function is decomposed into a superposition of a number of Gaussian coherent states guided by Ehrenfest trajectories that are suited to clone and swap their electronic amplitudes throughout the simulation. New generalized cloning criteria are defined and tested. Because of sharp changes of the electronic states, which are common for conjugated polymers, the electronic parts of the Gaussian coherent states are represented in the Time Dependent Diabatic Basis (TDDB). The input to these simulations in terms of the excited-state energies, gradients and non-adiabatic couplings, is calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. As a test case, we consider the photoinduced unidirectional electronic and vibrational energy transfer between two- and three-ring linear poly(phenylene ethynylene) units linked by meta-substitution. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer between dendritic branches are discussed.

Authors:
ORCiD logo [1]; ORCiD logo [1];  [2];  [3];  [4]
  1. Universidad Nacional de Quilmes, B1876BXD Bernal, Argentina
  2. School of Chemistry, University of Leeds, Leeds LS2 9JT, UK, School of Mathematics
  3. Center for Nonlinear Studies (CNLS), and Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, USA
  4. School of Chemistry, University of Leeds, Leeds LS2 9JT, UK
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC). Basic Energy Sciences (BES) (SC-22); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1454892
Alternate Identifier(s):
OSTI ID: 1483522
Report Number(s):
LA-UR-18-23123
Journal ID: ISSN 1463-9076; PPCPFQ
Grant/Contract Number:  
AC52-06NA25396; 89233218CNA000001; EP/P021123/1; EP/N007549/1
Resource Type:
Published Article
Journal Name:
Physical Chemistry Chemical Physics. PCCP (Print)
Additional Journal Information:
Journal Name: Physical Chemistry Chemical Physics. PCCP (Print) Journal Volume: 20 Journal Issue: 26; Journal ID: ISSN 1463-9076
Publisher:
Royal Society of Chemistry
Country of Publication:
United Kingdom
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Freixas, Victor M., Fernandez-Alberti, Sebastian, Makhov, Dmitry V., Tretiak, Sergei, and Shalashilin, Dmitrii. An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules. United Kingdom: N. p., 2018. Web. doi:10.1039/C8CP02321B.
Freixas, Victor M., Fernandez-Alberti, Sebastian, Makhov, Dmitry V., Tretiak, Sergei, & Shalashilin, Dmitrii. An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules. United Kingdom. doi:10.1039/C8CP02321B.
Freixas, Victor M., Fernandez-Alberti, Sebastian, Makhov, Dmitry V., Tretiak, Sergei, and Shalashilin, Dmitrii. Mon . "An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules". United Kingdom. doi:10.1039/C8CP02321B.
@article{osti_1454892,
title = {An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules},
author = {Freixas, Victor M. and Fernandez-Alberti, Sebastian and Makhov, Dmitry V. and Tretiak, Sergei and Shalashilin, Dmitrii},
abstractNote = {Here in this paper, we present a new implementation of the Ab Initio Multiple Cloning (AIMC) method, which is applied for non-adiabatic excited-state molecular dynamics simulations of photoinduced processes in conjugated molecules. Within our framework, the multidimensional wave-function is decomposed into a superposition of a number of Gaussian coherent states guided by Ehrenfest trajectories that are suited to clone and swap their electronic amplitudes throughout the simulation. New generalized cloning criteria are defined and tested. Because of sharp changes of the electronic states, which are common for conjugated polymers, the electronic parts of the Gaussian coherent states are represented in the Time Dependent Diabatic Basis (TDDB). The input to these simulations in terms of the excited-state energies, gradients and non-adiabatic couplings, is calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. As a test case, we consider the photoinduced unidirectional electronic and vibrational energy transfer between two- and three-ring linear poly(phenylene ethynylene) units linked by meta-substitution. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer between dendritic branches are discussed.},
doi = {10.1039/C8CP02321B},
journal = {Physical Chemistry Chemical Physics. PCCP (Print)},
number = 26,
volume = 20,
place = {United Kingdom},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1039/C8CP02321B

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Solving the time-dependent Schrödinger equation for nuclear motion in one step: direct dynamics of non-adiabatic systems
journal, August 2008


Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature
journal, February 2010

  • Collini, Elisabetta; Wong, Cathy Y.; Wilk, Krystyna E.
  • Nature, Vol. 463, Issue 7281
  • DOI: 10.1038/nature08811

The PYXAID Program for Non-Adiabatic Molecular Dynamics in Condensed Matter Systems
journal, October 2013

  • Akimov, Alexey V.; Prezhdo, Oleg V.
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 11
  • DOI: 10.1021/ct400641n

Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics
journal, August 2014

  • Makhov, Dmitry V.; Glover, William J.; Martinez, Todd J.
  • The Journal of Chemical Physics, Vol. 141, Issue 5
  • DOI: 10.1063/1.4891530

Controlling the mechanism of fulvene S1/S0 decay: switching off the stepwise population transfer
journal, January 2010

  • Mendive-Tapia, David; Lasorne, Benjamin; Worth, Graham A.
  • Physical Chemistry Chemical Physics, Vol. 12, Issue 48
  • DOI: 10.1039/c0cp01757d

Singlet and Triplet Excited-State Dynamics Study of the Keto and Enol Tautomers of Cytosine
journal, July 2013

  • Mai, Sebastian; Marquetand, Philipp; Richter, Martin
  • ChemPhysChem, Vol. 14, Issue 13
  • DOI: 10.1002/cphc.201300370

Reversible fluorescence quenching in carbon nanotubes for biomolecular sensing
journal, September 2007

  • Satishkumar, B. C.; Brown, Leif O.; Gao, Yuan
  • Nature Nanotechnology, Vol. 2, Issue 9
  • DOI: 10.1038/nnano.2007.261

Proton transfer in solution: Molecular dynamics with quantum transitions
journal, September 1994

  • Hammes‐Schiffer, Sharon; Tully, John C.
  • The Journal of Chemical Physics, Vol. 101, Issue 6
  • DOI: 10.1063/1.467455

Ab Initio Multiple Spawning Photochemical Dynamics of DMABN Using GPUs
journal, December 2016

  • Curchod, Basile F. E.; Sisto, Aaron; Martínez, Todd J.
  • The Journal of Physical Chemistry A, Vol. 121, Issue 1
  • DOI: 10.1021/acs.jpca.6b09962

Excitons in poly(para phenylene vinylene): a quantum-chemical perspective based on high-level ab initio calculations
journal, January 2016

  • Mewes, Stefanie A.; Mewes, Jan-Michael; Dreuw, Andreas
  • Physical Chemistry Chemical Physics, Vol. 18, Issue 4
  • DOI: 10.1039/C5CP07077E

Ab initio multiple cloning simulations of pyrrole photodissociation: TKER spectra and velocity map imaging
journal, January 2015

  • Makhov, Dmitry V.; Saita, Kenichiro; Martinez, Todd J.
  • Physical Chemistry Chemical Physics, Vol. 17, Issue 5
  • DOI: 10.1039/C4CP04571H

Laminated fabrication of polymeric photovoltaic diodes
journal, September 1998

  • Granström, M.; Petritsch, K.; Arias, A. C.
  • Nature, Vol. 395, Issue 6699
  • DOI: 10.1038/26183

High-Resolution Inkjet Printing of All-Polymer Transistor Circuits
journal, December 2000


Computational Study of Photoexcited Dynamics in Bichromophoric Cross-Shaped Oligofluorene
journal, October 2014

  • Ondarse-Alvarez, D.; Oldani, N.; Tretiak, S.
  • The Journal of Physical Chemistry A, Vol. 118, Issue 45
  • DOI: 10.1021/jp504720n

An efficient implementation of semiempirical quantum-chemical orthogonalization-corrected methods for excited-state dynamics
journal, April 2018

  • Liu, Jie; Thiel, Walter
  • The Journal of Chemical Physics, Vol. 148, Issue 15
  • DOI: 10.1063/1.5022466

The on-the-fly surface-hopping program system Newton-X: Application to ab initio simulation of the nonadiabatic photodynamics of benchmark systems
journal, August 2007

  • Barbatti, Mario; Granucci, Giovanni; Persico, Maurizio
  • Journal of Photochemistry and Photobiology A: Chemistry, Vol. 190, Issue 2-3
  • DOI: 10.1016/j.jphotochem.2006.12.008

Atomistic non-adiabatic dynamics of the LH2 complex with a GPU-accelerated ab initio exciton model
journal, January 2017

  • Sisto, Aaron; Stross, Clem; van der Kamp, Marc W.
  • Physical Chemistry Chemical Physics, Vol. 19, Issue 23
  • DOI: 10.1039/C7CP00492C

The phase space CCS approach to quantum and semiclassical molecular dynamics for high-dimensional systems
journal, September 2004


Hexamethylcyclopentadiene: time-resolved photoelectron spectroscopy and ab initio multiple spawning simulations
journal, January 2014

  • Wolf, T. J. A.; Kuhlman, T. S.; Schalk, O.
  • Phys. Chem. Chem. Phys., Vol. 16, Issue 23
  • DOI: 10.1039/C4CP00977K

Mixed quantum–classical dynamics
journal, January 1998


Non-adiabatic excited state molecular dynamics of phenylene ethynylene dendrimer using a multiconfigurational Ehrenfest approach
journal, January 2016

  • Fernandez-Alberti, Sebastian; Makhov, Dmitry V.; Tretiak, Sergei
  • Physical Chemistry Chemical Physics, Vol. 18, Issue 15
  • DOI: 10.1039/C5CP07332D

Nonadiabatic Excited-State Molecular Dynamics Modeling of Photoinduced Dynamics in Conjugated Molecules
journal, May 2011

  • Nelson, Tammie; Fernandez-Alberti, Sebastian; Chernyak, Vladimir
  • The Journal of Physical Chemistry B, Vol. 115, Issue 18
  • DOI: 10.1021/jp109522g

Nonadiabatic Excited-State Molecular Dynamics: Modeling Photophysics in Organic Conjugated Materials
journal, February 2014

  • Nelson, Tammie; Fernandez-Alberti, Sebastian; Roitberg, Adrian E.
  • Accounts of Chemical Research, Vol. 47, Issue 4
  • DOI: 10.1021/ar400263p

Trees to trap photons
journal, July 1997


Molecular Understanding of Organic Solar Cells: The Challenges
journal, November 2009

  • Brédas, Jean-Luc; Norton, Joseph E.; Cornil, Jérôme
  • Accounts of Chemical Research, Vol. 42, Issue 11
  • DOI: 10.1021/ar900099h

Density Matrix Analysis and Simulation of Electronic Excitations in Conjugated and Aggregated Molecules
journal, September 2002

  • Tretiak, Sergei; Mukamel, Shaul
  • Chemical Reviews, Vol. 102, Issue 9
  • DOI: 10.1021/cr0101252

Two-Dimensional Real-Space Analysis of Optical Excitations in Acceptor-Substituted Carotenoids
journal, November 1997

  • Tretiak, Sergei; Chernyak, Vladimir; Mukamel, Shaul
  • Journal of the American Chemical Society, Vol. 119, Issue 47
  • DOI: 10.1021/ja9720164

Photoinduced Excited-State Energy-Transfer Dynamics of a Nitrogen-Cored Symmetric Dendrimer: From the Perspective of the Jahn–Teller Effect
journal, March 2015

  • Huang, Jing; Du, Likai; Wang, Jun
  • The Journal of Physical Chemistry C, Vol. 119, Issue 14
  • DOI: 10.1021/jp512496z

Electronic and Structural Elements That Regulate the Excited-State Dynamics in Purine Nucleobase Derivatives
journal, March 2015

  • Crespo-Hernández, Carlos E.; Martínez-Fernández, Lara; Rauer, Clemens
  • Journal of the American Chemical Society, Vol. 137, Issue 13
  • DOI: 10.1021/ja512536c

Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model
journal, June 1985

  • Dewar, Michael J. S.; Zoebisch, Eve G.; Healy, Eamonn F.
  • Journal of the American Chemical Society, Vol. 107, Issue 13
  • DOI: 10.1021/ja00299a024

Nonadiabatic Photodynamics of a Retinal Model in Polar and Nonpolar Environment
journal, February 2013

  • Ruckenbauer, Matthias; Barbatti, Mario; Müller, Thomas
  • The Journal of Physical Chemistry A, Vol. 117, Issue 13
  • DOI: 10.1021/jp400401f

Improved quantum efficiency for electroluminescence in semiconducting polymers
journal, February 1999

  • Cao, Yong; Parker, Ian D.; Yu, Gang
  • Nature, Vol. 397, Issue 6718
  • DOI: 10.1038/17087

Photodynamics of the adenine model 4-aminopyrimidine embedded within double strand of DNA
journal, January 2011

  • Zelený, Tomáš; Hobza, Pavel; Nachtigallová, Dana
  • Collection of Czechoslovak Chemical Communications, Vol. 76, Issue 6
  • DOI: 10.1135/cccc2011046

Advanced Capabilities of the PYXAID Program: Integration Schemes, Decoherence Effects, Multiexcitonic States, and Field-Matter Interaction
journal, January 2014

  • Akimov, Alexey V.; Prezhdo, Oleg V.
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 2
  • DOI: 10.1021/ct400934c

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


Shishiodoshi unidirectional energy transfer mechanism in phenylene ethynylene dendrimers
journal, December 2012

  • Fernandez-Alberti, S.; Roitberg, Adrian E.; Kleiman, Valeria D.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4745835

Nonadiabatic Molecular Dynamics Simulations of the Energy Transfer between Building Blocks in a Phenylene Ethynylene Dendrimer
journal, July 2009

  • Fernandez-Alberti, Sebastian; Kleiman, Valeria D.; Tretiak, Sergei
  • The Journal of Physical Chemistry A, Vol. 113, Issue 26
  • DOI: 10.1021/jp900904q

Photoinduced dynamics in cycloparaphenylenes: planarization, electron–phonon coupling, localization and intra-ring migration of the electronic excitation
journal, January 2017

  • Oldani, N.; Doorn, S. K.; Tretiak, S.
  • Physical Chemistry Chemical Physics, Vol. 19, Issue 45
  • DOI: 10.1039/C7CP06426H

Toward fully quantum modelling of ultrafast photodissociation imaging experiments. Treating tunnelling in the ab initio multiple cloning approach
journal, January 2016

  • Makhov, Dmitry V.; Martinez, Todd J.; Shalashilin, Dmitrii V.
  • Faraday Discussions, Vol. 194
  • DOI: 10.1039/C6FD00073H

On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei
journal, March 1979

  • Mead, C. Alden; Truhlar, Donald G.
  • The Journal of Chemical Physics, Vol. 70, Issue 5
  • DOI: 10.1063/1.437734

Nonadiabatic dynamics with the help of multiconfigurational Ehrenfest method: Improved theory and fully quantum 24D simulation of pyrazine
journal, June 2010

  • Shalashilin, Dmitrii V.
  • The Journal of Chemical Physics, Vol. 132, Issue 24
  • DOI: 10.1063/1.3442747

Dynamics of Energy Transfer in a Conjugated Dendrimer Driven by Ultrafast Localization of Excitations
journal, July 2015

  • Galindo, Johan F.; Atas, Evrim; Altan, Aysun
  • Journal of the American Chemical Society, Vol. 137, Issue 36
  • DOI: 10.1021/jacs.5b04075

Relaxation mechanisms of UV-photoexcited DNA and RNA nucleobases
journal, November 2010

  • Barbatti, M.; Aquino, A. J. A.; Szymczak, J. J.
  • Proceedings of the National Academy of Sciences, Vol. 107, Issue 50
  • DOI: 10.1073/pnas.1014982107

On-the-fly ab initio molecular dynamics with multiconfigurational Ehrenfest method
journal, December 2012

  • Saita, Kenichiro; Shalashilin, Dmitrii V.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4734313

Full quantum mechanical molecular dynamics using Gaussian wavepackets
journal, January 2003


Ab initio multiple spawning dynamics study of dimethylnitramine and dimethylnitramine-Fe complex to model their ultrafast nonadiabatic chemistry
journal, July 2017

  • Bera, Anupam; Ghosh, Jayanta; Bhattacharya, Atanu
  • The Journal of Chemical Physics, Vol. 147, Issue 4
  • DOI: 10.1063/1.4993947

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

Does Stacking Restrain the Photodynamics of Individual Nucleobases?
journal, June 2010

  • Nachtigallová, Dana; Zelený, Tomáš; Ruckenbauer, Matthias
  • Journal of the American Chemical Society, Vol. 132, Issue 24
  • DOI: 10.1021/ja1029705

Ab Initio Multiple Spawning:  Photochemistry from First Principles Quantum Molecular Dynamics
journal, June 2000

  • Ben-Nun, M.; Quenneville, Jason; Martínez, Todd J.
  • The Journal of Physical Chemistry A, Vol. 104, Issue 22
  • DOI: 10.1021/jp994174i

Dendrimer photoantenna supermolecules: energetic funnels, exciton hopping and correlated excimer formation
journal, August 1999


Non-radiative relaxation of photoexcited chlorophylls: theoretical and experimental study
journal, September 2015

  • Bricker, William P.; Shenai, Prathamesh M.; Ghosh, Avishek
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep13625

A b initio quantum direct dynamics simulations of ultrafast photochemistry with Multiconfigurational Ehrenfest approach
journal, August 2017


Excitonic couplings and electronic coherence in bridged naphthalene dimers
journal, November 1999

  • Tretiak, S.; Zhang, W. M.; Chernyak, V.
  • Proceedings of the National Academy of Sciences, Vol. 96, Issue 23
  • DOI: 10.1073/pnas.96.23.13003

Recursive density‐matrix‐spectral‐moment algorithm for molecular nonlinear polarizabilities
journal, November 1996

  • Tretiak, Sergei; Chernyak, Vladimir; Mukamel, Shaul
  • The Journal of Chemical Physics, Vol. 105, Issue 19
  • DOI: 10.1063/1.472621

Strikingly Different Effects of Hydrogen Bonding on the Photodynamics of Individual Nucleobases in DNA: Comparison of Guanine and Cytosine
journal, August 2012

  • Zelený, Tomáš; Ruckenbauer, Matthias; Aquino, Adelia J. A.
  • Journal of the American Chemical Society, Vol. 134, Issue 33
  • DOI: 10.1021/ja3028845

Nonadiabatic Dynamics of Cycloparaphenylenes with TD-DFTB Surface Hopping
journal, November 2017

  • Stojanović, Ljiljana; Aziz, Saadullah G.; Hilal, Rifaat H.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 12
  • DOI: 10.1021/acs.jctc.7b01000

Quantal Phase Factors Accompanying Adiabatic Changes
journal, March 1984

  • Berry, M. V.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 392, Issue 1802
  • DOI: 10.1098/rspa.1984.0023

Nonadiabatic molecular dynamics: Validation of the multiple spawning method for a multidimensional problem
journal, May 1998

  • Ben-Nun, M.; Martı́nez, Todd J.
  • The Journal of Chemical Physics, Vol. 108, Issue 17
  • DOI: 10.1063/1.476142

Ultrafast electronic energy relaxation in a conjugated dendrimer leading to inter-branch energy redistribution
journal, January 2016

  • Ondarse-Alvarez, D.; Kömürlü, S.; Roitberg, A. E.
  • Physical Chemistry Chemical Physics, Vol. 18, Issue 36
  • DOI: 10.1039/C6CP04448D

Quantum dynamics simulations using Gaussian wavepackets: the vMCG method
journal, April 2015


A general method to describe intersystem crossing dynamics in trajectory surface hopping
journal, March 2015

  • Mai, Sebastian; Marquetand, Philipp; González, Leticia
  • International Journal of Quantum Chemistry, Vol. 115, Issue 18
  • DOI: 10.1002/qua.24891

Electronic Coherence and Collective Optical Excitations of Conjugated Molecules
journal, August 1997


Dynamics of Light Harvesting in Photosynthesis
journal, May 2009


Nonadiabatic dynamics by mean-field and surface-hopping approaches: energy conservation considerations
journal, June 2010


Photoinduced Intra- and Intermolecular Energy Transfer in Chlorophyll a Dimer
journal, May 2017

  • Zheng, Fulu; Fernandez-Alberti, Sebastian; Tretiak, Sergei
  • The Journal of Physical Chemistry B, Vol. 121, Issue 21
  • DOI: 10.1021/acs.jpcb.7b02021

SHARC: ab Initio Molecular Dynamics with Surface Hopping in the Adiabatic Representation Including Arbitrary Couplings
journal, March 2011

  • Richter, Martin; Marquetand, Philipp; González-Vázquez, Jesús
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 5
  • DOI: 10.1021/ct1007394

Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H + with D 2
journal, July 1971

  • Tully, John C.; Preston, Richard K.
  • The Journal of Chemical Physics, Vol. 55, Issue 2
  • DOI: 10.1063/1.1675788

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

Electronic Spectra of the Nanostar Dendrimer: Theory and Experiment
journal, October 2010

  • Palma, Julio L.; Atas, Evrim; Hardison, Lindsay
  • The Journal of Physical Chemistry C, Vol. 114, Issue 48
  • DOI: 10.1021/jp1062918

Optimization of width parameters for quantum dynamics with frozen Gaussian basis sets
journal, May 2010


Self-Trapping of Excitons, Violation of Condon Approximation, and Efficient Fluorescence in Conjugated Cycloparaphenylenes
journal, October 2014

  • Adamska, Lyudmyla; Nayyar, Iffat; Chen, Hang
  • Nano Letters, Vol. 14, Issue 11
  • DOI: 10.1021/nl503133e

An On-the-Fly Surface-Hopping Program JADE for Nonadiabatic Molecular Dynamics of Polyatomic Systems: Implementation and Applications
journal, March 2015

  • Du, Likai; Lan, Zhenggang
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 4
  • DOI: 10.1021/ct501106d