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Title: The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm–Dancoff approximation

Abstract

The primary computational challenge when simulating nonadiabatic ab initio molecular dynamics is the unfavourable compute costs of electronic structure calculations with molecular size. Simple electronic structure theories, like time-dependent density functional theory within the Tamm–Dancoff approximation (TDDFT/TDA), alleviate this cost for moderately sized molecular systems simulated on realistic time scales. Although TDDFT/TDA does have some limitations in accuracy, an appealing feature is that, in addition to including electron correlation through the use of a density functional, the cost of calculating analytic nuclear gradients and nonadiabatic coupling vectors is often computationally feasible even for moderately sized basis sets. Here in this work, some of the benefits and limitations of TDDFT/TDA are discussed and analysed with regard to its applicability as a ‘back-end’ electronic structure method for the symmetric quasi-classical Meyer–Miller model (SQC/MM). In order to investigate the benefits and limitations of TDDFT/TDA, SQC/MM is employed to predict and analyse a prototypical example of excited-state hydrogen transfer in gas-phase malonaldehyde. Then, the ring-opening dynamics of selenophene are simulated, which highlight some of the deficiencies of TDDFT/TDA. Additionally, some new algorithms are proposed that speed up the calculation of analytic nuclear gradients and nonadiabatic coupling vectors for a set of excited electronic states.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]
  1. University of California, Berkeley, CA (United States)
  2. University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
OSTI Identifier:
1985499
Grant/Contract Number:  
AC02-05CH11231; CHE-1856707
Resource Type:
Accepted Manuscript
Journal Name:
Molecular Physics
Additional Journal Information:
Journal Volume: 121; Journal Issue: 7-8; Journal ID: ISSN 0026-8976
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; quasi-classical nonadiabatic dynamics; time-dependent density functional theory; molecular dynamics

Citation Formats

Talbot, Justin J., Head-Gordon, Martin, and Cotton, Stephen J. The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm–Dancoff approximation. United States: N. p., 2022. Web. doi:10.1080/00268976.2022.2153761.
Talbot, Justin J., Head-Gordon, Martin, & Cotton, Stephen J. The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm–Dancoff approximation. United States. https://doi.org/10.1080/00268976.2022.2153761
Talbot, Justin J., Head-Gordon, Martin, and Cotton, Stephen J. Fri . "The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm–Dancoff approximation". United States. https://doi.org/10.1080/00268976.2022.2153761. https://www.osti.gov/servlets/purl/1985499.
@article{osti_1985499,
title = {The symmetric quasi-classical model using on-the-fly time-dependent density functional theory within the Tamm–Dancoff approximation},
author = {Talbot, Justin J. and Head-Gordon, Martin and Cotton, Stephen J.},
abstractNote = {The primary computational challenge when simulating nonadiabatic ab initio molecular dynamics is the unfavourable compute costs of electronic structure calculations with molecular size. Simple electronic structure theories, like time-dependent density functional theory within the Tamm–Dancoff approximation (TDDFT/TDA), alleviate this cost for moderately sized molecular systems simulated on realistic time scales. Although TDDFT/TDA does have some limitations in accuracy, an appealing feature is that, in addition to including electron correlation through the use of a density functional, the cost of calculating analytic nuclear gradients and nonadiabatic coupling vectors is often computationally feasible even for moderately sized basis sets. Here in this work, some of the benefits and limitations of TDDFT/TDA are discussed and analysed with regard to its applicability as a ‘back-end’ electronic structure method for the symmetric quasi-classical Meyer–Miller model (SQC/MM). In order to investigate the benefits and limitations of TDDFT/TDA, SQC/MM is employed to predict and analyse a prototypical example of excited-state hydrogen transfer in gas-phase malonaldehyde. Then, the ring-opening dynamics of selenophene are simulated, which highlight some of the deficiencies of TDDFT/TDA. Additionally, some new algorithms are proposed that speed up the calculation of analytic nuclear gradients and nonadiabatic coupling vectors for a set of excited electronic states.},
doi = {10.1080/00268976.2022.2153761},
journal = {Molecular Physics},
number = 7-8,
volume = 121,
place = {United States},
year = {Fri Dec 09 00:00:00 EST 2022},
month = {Fri Dec 09 00:00:00 EST 2022}
}

Works referenced in this record:

On the adiabatic representation of Meyer-Miller electronic-nuclear dynamics
journal, August 2017

  • Cotton, Stephen J.; Liang, Ruibin; Miller, William H.
  • The Journal of Chemical Physics, Vol. 147, Issue 6
  • DOI: 10.1063/1.4995301

Derivative Couplings with Built-In Electron-Translation Factors: Application to Benzene
journal, July 2012

  • Fatehi, Shervin; Subotnik, Joseph E.
  • The Journal of Physical Chemistry Letters, Vol. 3, Issue 15
  • DOI: 10.1021/jz3006173

A computational study of radiationless deactivation mechanisms of furan
journal, January 2011


A classical analog for electronic degrees of freedom in nonadiabatic collision processes
journal, April 1979

  • Meyera), Hans‐Dieter; Miller, William H.
  • The Journal of Chemical Physics, Vol. 70, Issue 7
  • DOI: 10.1063/1.437910

A walk through the approximations of ab initio multiple spawning
journal, April 2018

  • Mignolet, Benoit; Curchod, Basile F. E.
  • The Journal of Chemical Physics, Vol. 148, Issue 13
  • DOI: 10.1063/1.5022877

Fast Numerical Evaluation of Time-Derivative Nonadiabatic Couplings for Mixed Quantum–Classical Methods
journal, October 2015

  • Ryabinkin, Ilya G.; Nagesh, Jayashree; Izmaylov, Artur F.
  • The Journal of Physical Chemistry Letters, Vol. 6, Issue 21
  • DOI: 10.1021/acs.jpclett.5b02062

Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiff base C5H6NH2+
journal, September 2021

  • Zhang, Xing; Herbert, John M.
  • The Journal of Chemical Physics, Vol. 155, Issue 12
  • DOI: 10.1063/5.0062757

The ring-opening channel and the influence of Rydberg states on the excited state dynamics of furan and its derivatives
journal, August 2018

  • Schalk, O.; Geng, T.; Hansson, T.
  • The Journal of Chemical Physics, Vol. 149, Issue 8
  • DOI: 10.1063/1.5024655

Ab initio quantum dynamical study of photoinduced ring opening in furan
journal, October 2011

  • Gromov, E. V.; Lévêque, C.; Gatti, F.
  • The Journal of Chemical Physics, Vol. 135, Issue 16
  • DOI: 10.1063/1.3653792

Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electronically non-adiabatic processes
journal, December 2013

  • Cotton, Stephen J.; Miller, William H.
  • The Journal of Chemical Physics, Vol. 139, Issue 23
  • DOI: 10.1063/1.4845235

Ab initio two-component Ehrenfest dynamics
journal, September 2015

  • Ding, Feizhi; Goings, Joshua J.; Liu, Hongbin
  • The Journal of Chemical Physics, Vol. 143, Issue 11
  • DOI: 10.1063/1.4930985

Ab Initio Nonadiabatic Quantum Molecular Dynamics
journal, February 2018


Highly Efficient Algorithms for CIS Type Excited State Wave Function Overlaps
journal, April 2019

  • Sapunar, Marin; Piteša, Tomislav; Davidović, Davor
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 6
  • DOI: 10.1021/acs.jctc.9b00235

Conical Intersections: Electronic Structure, Dynamics and Spectroscopy
book, July 2004

  • Domcke, Wolfgang; Yarkony, David R.; Köppel, Horst
  • Advanced Series in Physical Chemistry, Vol. 15
  • DOI: 10.1142/5406

First Principles Nonadiabatic Excited-State Molecular Dynamics in NWChem
journal, August 2020

  • Song, Huajing; Fischer, Sean A.; Zhang, Yu
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 10
  • DOI: 10.1021/acs.jctc.0c00295

Effects of heteroatom substitution in conjugated heterocyclic compounds on photovoltaic performance: from sulfur to tellurium
journal, January 2014

  • Park, Y. S.; Kale, T. S.; Nam, C. -Y.
  • Chem. Commun., Vol. 50, Issue 59
  • DOI: 10.1039/C4CC01862A

Automated Search for Minimum Energy Conical Intersection Geometries between the Lowest Two Singlet States S 0 /S 1 -MECIs by the Spin-Flip TDDFT Method
journal, August 2013

  • Harabuchi, Yu; Maeda, Satoshi; Taketsugu, Tetsuya
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 9
  • DOI: 10.1021/ct400512u

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials
journal, February 2020


Quasi-Diabatic Scheme for Nonadiabatic On-the-Fly Simulations
journal, October 2019

  • Zhou, Wanghuai; Mandal, Arkajit; Huo, Pengfei
  • The Journal of Physical Chemistry Letters, Vol. 10, Issue 22
  • DOI: 10.1021/acs.jpclett.9b02747

Deactivation via ring opening: A quantum chemical study of the excited states of furan and comparison to thiophene
journal, June 2008


Communication: GAIMS—Generalized Ab Initio Multiple Spawning for both internal conversion and intersystem crossing processes
journal, March 2016

  • Curchod, Basile F. E.; Rauer, Clemens; Marquetand, Philipp
  • The Journal of Chemical Physics, Vol. 144, Issue 10
  • DOI: 10.1063/1.4943571

Ab initio symmetric quasi-classical approach to investigate molecular Tully models
journal, August 2021

  • Weight, Braden M.; Mandal, Arkajit; Huo, Pengfei
  • The Journal of Chemical Physics, Vol. 155, Issue 8
  • DOI: 10.1063/5.0061934

Chalcogen containing heterocyclic scaffolds: New hybrids with antitumoral activity
journal, November 2016


Perspective: Nonadiabatic dynamics theory
journal, December 2012

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

Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory
journal, August 2014

  • Zhang, Xing; Herbert, John M.
  • The Journal of Chemical Physics, Vol. 141, Issue 6
  • DOI: 10.1063/1.4891984

Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance
journal, December 2011

  • Fatehi, Shervin; Alguire, Ethan; Shao, Yihan
  • The Journal of Chemical Physics, Vol. 135, Issue 23
  • DOI: 10.1063/1.3665031

Algorithms and codes for the assignment problem
journal, December 1988

  • Carpaneto, Giorgio; Martello, Silvano; Toth, Paolo
  • Annals of Operations Research, Vol. 13, Issue 1
  • DOI: 10.1007/BF02288323

Methods to Calculate Electronic Excited-State Dynamics for Molecules on Large Metal Clusters with Many States: Ensuring Fast Overlap Calculations and a Robust Choice of Phase
journal, May 2022

  • Chen, Hsing-Ta; Chen, Junhan; Cofer-Shabica, D. Vale
  • Journal of Chemical Theory and Computation, Vol. 18, Issue 6
  • DOI: 10.1021/acs.jctc.1c01304

Nonadiabatic excited-state dynamics of polar π-systems and related model compounds of biological relevance
journal, January 2008

  • Barbatti, Mario; Ruckenbauer, Matthias; Szymczak, Jaroslaw J.
  • Phys. Chem. Chem. Phys., Vol. 10, Issue 4
  • DOI: 10.1039/B709315M

Photoinduced Heterocyclic Ring Opening of Furfural: Distinct Open-Chain Product Identification by Ultrafast X-ray Transient Absorption Spectroscopy
journal, September 2018

  • Bhattacherjee, Aditi; Schnorr, Kirsten; Oesterling, Sven
  • Journal of the American Chemical Society, Vol. 140, Issue 39
  • DOI: 10.1021/jacs.8b07155

Excited state dynamics of thiophene and bithiophene: new insights into theoretically challenging systems
journal, January 2015

  • Prlj, Antonio; Curchod, Basile F. E.; Corminboeuf, Clémence
  • Physical Chemistry Chemical Physics, Vol. 17, Issue 22
  • DOI: 10.1039/C5CP01429H

Optimization of mixed quantum-classical dynamics: Time-derivative coupling terms and selected couplings
journal, February 2009


Ab Initio Molecular Dynamics of Excited-State Intramolecular Proton Transfer Using Multireference Perturbation Theory
journal, November 2007

  • Coe, Joshua D.; Levine, Benjamin G.; Martínez, Todd J.
  • The Journal of Physical Chemistry A, Vol. 111, Issue 44
  • DOI: 10.1021/jp072027b

A new symmetrical quasi-classical model for electronically non-adiabatic processes: Application to the case of weak non-adiabatic coupling
journal, October 2016

  • Cotton, Stephen J.; Miller, William H.
  • The Journal of Chemical Physics, Vol. 145, Issue 14
  • DOI: 10.1063/1.4963914

Probing competing relaxation pathways in malonaldehyde with transient X-ray absorption spectroscopy
journal, January 2020

  • List, Nanna H.; Dempwolff, Adrian L.; Dreuw, Andreas
  • Chemical Science, Vol. 11, Issue 16
  • DOI: 10.1039/D0SC00840K

A new approach to molecular dynamics with non-adiabatic and spin-orbit effects with applications to QM/MM simulations of thiophene and selenophene
journal, March 2017

  • Pederzoli, Marek; Pittner, Jiří
  • The Journal of Chemical Physics, Vol. 146, Issue 11
  • DOI: 10.1063/1.4978289

Nearest orthogonal matrix representation for face recognition
journal, March 2015


Recent Advances in Heterocyclic Nanographenes and Other Polycyclic Heteroaromatic Compounds
journal, December 2021


Trajectory-adjusted electronic zero point energy in classical Meyer-Miller vibronic dynamics: Symmetrical quasiclassical application to photodissociation
journal, May 2019

  • Cotton, Stephen J.; Miller, William H.
  • The Journal of Chemical Physics, Vol. 150, Issue 19
  • DOI: 10.1063/1.5094458

Ab initio Ehrenfest dynamics
journal, August 2005

  • Li, Xiaosong; Tully, John C.; Schlegel, H. Bernhard
  • The Journal of Chemical Physics, Vol. 123, Issue 8
  • DOI: 10.1063/1.2008258

Controlled intramolecular H-transfer in malonaldehyde in the electronic ground state mediated through the conical intersection of 1nπ* and 1ππ* excited electronic states
journal, January 2019

  • Nandipati, K. R.; Kanakati, Arun Kumar; Singh, H.
  • Physical Chemistry Chemical Physics, Vol. 21, Issue 36
  • DOI: 10.1039/C9CP03762D

Ultrafast dynamics in thiophene investigated by femtosecond pump probe photoelectron spectroscopy and theory
journal, January 2008

  • Weinkauf, R.; Lehr, L.; Schlag, E. W.
  • Phys. Chem. Chem. Phys., Vol. 10, Issue 3
  • DOI: 10.1039/B710381F

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package
journal, August 2021

  • Epifanovsky, Evgeny; Gilbert, Andrew T. B.; Feng, Xintian
  • The Journal of Chemical Physics, Vol. 155, Issue 8
  • DOI: 10.1063/5.0055522

Exploring the Dynamics of the Photoinduced Ring-Opening of Heterocyclic Molecules
journal, July 2017

  • Ashfold, Michael N. R.; Bain, Matthew; Hansen, Christopher S.
  • The Journal of Physical Chemistry Letters, Vol. 8, Issue 14
  • DOI: 10.1021/acs.jpclett.7b01219

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

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

The Position of the N Atom Plays a Significant Role for Excited-State Decay of Heterocycles
journal, February 2017


Time-dependent density functional theory Ehrenfest dynamics: Collisions between atomic oxygen and graphite clusters
journal, April 2007

  • Isborn, Christine M.; Li, Xiaosong; Tully, John C.
  • The Journal of Chemical Physics, Vol. 126, Issue 13
  • DOI: 10.1063/1.2713391

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

Simulations of the dissociation of small helium clusters with ab initio molecular dynamics in electronically excited states
journal, April 2014

  • Closser, Kristina D.; Gessner, Oliver; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 140, Issue 13
  • DOI: 10.1063/1.4869193

A parallel implementation of the analytic nuclear gradient for time-dependent density functional theory within the Tamm–Dancoff approximation
journal, October 2010


Theoretical study of photoinduced ring-opening in furan
journal, October 2010

  • Gromov, E. V.; Trofimov, A. B.; Gatti, F.
  • The Journal of Chemical Physics, Vol. 133, Issue 16
  • DOI: 10.1063/1.3493451

Efficient and Flexible Computation of Many-Electron Wave Function Overlaps
journal, February 2016

  • Plasser, Felix; Ruckenbauer, Matthias; Mai, Sebastian
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 3
  • DOI: 10.1021/acs.jctc.5b01148

On-the-Fly Symmetrical Quasi-Classical Dynamics with Meyer–Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections
journal, May 2021

  • Hu, Deping; Xie, Yu; Peng, Jiawei
  • Journal of Chemical Theory and Computation, Vol. 17, Issue 6
  • DOI: 10.1021/acs.jctc.0c01249

Modeling Non-adiabatic Dynamics in Nanoscale and Condensed Matter Systems
journal, November 2021


Competitive Decay at Two- and Three-State Conical Intersections in Excited-State Intramolecular Proton Transfer
journal, April 2005

  • Coe, Joshua D.; Martínez, Todd J.
  • Journal of the American Chemical Society, Vol. 127, Issue 13
  • DOI: 10.1021/ja043093j

Ultrafast nonradiative deactivation of photoexcited 8-oxo-hypoxanthine: a nonadiabatic molecular dynamics study
journal, January 2021

  • Jankowska, Joanna; Góra, Robert W.
  • Physical Chemistry Chemical Physics, Vol. 23, Issue 2
  • DOI: 10.1039/D0CP05271J

Photophysics of Malonaldehyde:  An ab Initio Study
journal, June 1999

  • Sobolewski, Andrzej L.; Domcke, Wolfgang
  • The Journal of Physical Chemistry A, Vol. 103, Issue 23
  • DOI: 10.1021/jp990030s

Calculation of the vibrational excited states of malonaldehyde and their tunneling splittings with the multi-configuration time-dependent Hartree method
journal, July 2014

  • Schröder, Markus; Meyer, Hans-Dieter
  • The Journal of Chemical Physics, Vol. 141, Issue 3
  • DOI: 10.1063/1.4890116

Recent progress of sulphur-containing high-efficiency organic light-emitting diodes (OLEDs)
journal, January 2022

  • Feng, Zijun; Cheng, Zhuang; Jin, Haixu
  • Journal of Materials Chemistry C, Vol. 10, Issue 12
  • DOI: 10.1039/D1TC05255A

Competition between ring-puckering and ring-opening excited state reactions exemplified on 5H-furan-2-one and derivatives
journal, February 2020

  • Schalk, Oliver; Galiana, Joachim; Geng, Ting
  • The Journal of Chemical Physics, Vol. 152, Issue 6
  • DOI: 10.1063/1.5129366

Time-dependent density functional theory within the Tamm–Dancoff approximation
journal, December 1999


Ab Initio Molecular Dynamics of Excited-State Intramolecular Proton Transfer around a Three-State Conical Intersection in Malonaldehyde
journal, January 2006

  • Coe, Joshua D.; Martínez, Todd J.
  • The Journal of Physical Chemistry A, Vol. 110, Issue 2
  • DOI: 10.1021/jp0535339

Introductory lecture: Nonadiabatic effects in chemical dynamics
journal, January 2004

  • Jasper, Ahren W.; Zhu, Chaoyuan; Nangia, Shikha
  • Faraday Discussions, Vol. 127
  • DOI: 10.1039/b405601a

Beyond Time-Dependent Density Functional Theory Using Only Single Excitations: Methods for Computational Studies of Excited States in Complex Systems
journal, April 2016


XXXIV. Notes on the molecular orbital treatment of the hydrogen molecule
journal, April 1949

  • Coulson, C. A.; Fischer, I.
  • The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 40, Issue 303
  • DOI: 10.1080/14786444908521726

Surface hopping from the perspective of quantum–classical Liouville dynamics
journal, December 2016


Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–Classical Dynamics
journal, April 2018


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

Adiabatic Molecular Orbital Tracking in Ab Initio Molecular Dynamics
journal, July 2021

  • Zhanserkeev, Asylbek A.; Talbot, Justin J.; Steele, Ryan P.
  • Journal of Chemical Theory and Computation, Vol. 17, Issue 8
  • DOI: 10.1021/acs.jctc.1c00553

An Efficient, Augmented Surface Hopping Algorithm That Includes Decoherence for Use in Large-Scale Simulations
journal, October 2016

  • Jain, Amber; Alguire, Ethan; Subotnik, Joseph E.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 11
  • DOI: 10.1021/acs.jctc.6b00673

Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations
journal, March 2013

  • Cotton, Stephen J.; Miller, William H.
  • The Journal of Physical Chemistry A, Vol. 117, Issue 32
  • DOI: 10.1021/jp401078u

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

Ab initio non-adiabatic molecular dynamics
journal, January 2013

  • Tapavicza, Enrico; Bellchambers, Gregory D.; Vincent, Jordan C.
  • Physical Chemistry Chemical Physics, Vol. 15, Issue 42
  • DOI: 10.1039/c3cp51514a

Performance of TDDFT with and without spin-flip in trajectory surface hopping dynamics: cis – trans azobenzene photoisomerization
journal, January 2018

  • Yue, Ling; Liu, Yajun; Zhu, Chaoyuan
  • Physical Chemistry Chemical Physics, Vol. 20, Issue 37
  • DOI: 10.1039/C8CP03851A