Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene

Morrison, Adrian F.; Herbert, John M.

doi:10.1063/1.4985607

Title: Analytic derivative couplings and first-principles exciton/phonon coupling constants for an ab initio Frenkel-Davydov exciton model: Theory, implementation, and application to compute triplet exciton mobility parameters for crystalline tetracene

Journal Article · Wed Jun 14 00:00:00 EDT 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4985607· OSTI ID:1604464

Morrison, Adrian F. ^[1];

^[1]

The Ohio State Univ., Columbus, OH (United States)

Recently, we introduced an ab initio version of the Frenkel-Davydov exciton model for computing excited-state properties of molecular crystals and aggregates. Within this model, supersystem excited states are approximated as linear combinations of excitations localized on molecular sites, and the electronic Hamiltonian is constructed and diagonalized in a direct-product basis of non-orthogonal configuration state functions computed for isolated fragments. In this work, we derive and implement analytic derivative couplings for this model, including nuclear derivatives of the natural transition orbital and symmetric orthogonalization transformations that are part of the approximation. Nuclear derivatives of the exciton Hamiltonian’s matrix elements, required in order to compute the nonadiabatic couplings, are equivalent to the “Holstein” and “Peierls” exciton/phonon couplings that are widely discussed in the context of model Hamiltonians for energy and charge transport in organic photovoltaics. As an example, we compute the couplings that modulate triplet exciton transport in crystalline tetracene, which is relevant in the context of carrier diffusion following singlet exciton fission.

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Research Organization:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division

Grant/Contract Number:: SC0008850; SC0008550

OSTI ID:: 1604464

Alternate ID(s):: OSTI ID: 1363833

Journal Information:: Journal of Chemical Physics, Vol. 146, Issue 22; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 20 works

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References (66)

Derivative Couplings with Built-In Electron-Translation Factors: Application to Benzene Fatehi, Shervin; Subotnik, Joseph E. The Journal of Physical Chemistry Letters, Vol. 3, Issue 15 https://doi.org/10.1021/jz3006173	journal	July 2012
First-order nonadiabatic couplings from time-dependent hybrid density functional response theory: Consistent formalism, implementation, and performance Send, Robert; Furche, Filipp The Journal of Chemical Physics, Vol. 132, Issue 4 https://doi.org/10.1063/1.3292571	journal	January 2010
Lattice theory of ultrafast excitonic and charge-transfer dynamics in DNA Bittner, Eric R. The Journal of Chemical Physics, Vol. 125, Issue 9 https://doi.org/10.1063/1.2335452	journal	September 2006
Real-time observation of multiexcitonic states in ultrafast singlet fission using coherent 2D electronic spectroscopy Bakulin, Artem A.; Morgan, Sarah E.; Kehoe, Tom B. Nature Chemistry, Vol. 8, Issue 1 https://doi.org/10.1038/nchem.2371	journal	October 2015
Ab initio theory of charge-carrier conduction in ultrapure organic crystals Hannewald, K.; Bobbert, P. A. Applied Physics Letters, Vol. 85, Issue 9 https://doi.org/10.1063/1.1776335	journal	August 2004
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
Role of Conical Intersections in Molecular Spectroscopy and Photoinduced Chemical Dynamics Domcke, Wolfgang; Yarkony, David R. Annual Review of Physical Chemistry, Vol. 63, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103522	journal	May 2012
On the Transformation of light into Heat in Solids. I Frenkel, J. Physical Review, Vol. 37, Issue 1 https://doi.org/10.1103/physrev.37.17	journal	January 1931
On the evaluation of analytic energy derivatives for correlated wave functions Handy, Nicholas C.; Schaefer, Henry F. The Journal of Chemical Physics, Vol. 81, Issue 11 https://doi.org/10.1063/1.447489	journal	December 1984
A first-principles study of the vibrational properties of crystalline tetracene under pressure Abdulla, Mayami; Refson, Keith; Friend, Richard H. Journal of Physics: Condensed Matter, Vol. 27, Issue 37 https://doi.org/10.1088/0953-8984/27/37/375402	journal	September 2015
Potential energy surface crossings in organic photochemistry Bernardi, Fernando; Olivucci, Massimo; Robb, Michael A. Chemical Society Reviews, Vol. 25, Issue 5 https://doi.org/10.1039/cs9962500321	journal	January 1996
Femtosecond Conical Intersection Dynamics of Tryptophan in Proteins and Validation of Slowdown of Hydration Layer Dynamics Yang, Jin; Zhang, Luyuan; Wang, Lijuan Journal of the American Chemical Society, Vol. 134, Issue 40 https://doi.org/10.1021/ja305283j	journal	September 2012
Dipolar coupling between electronic transitions of the DNA bases and its relevance to exciton states in double helices Bouvier, B.; Gustavsson, T.; Markovitsi, D. Chemical Physics, Vol. 275, Issue 1-3 https://doi.org/10.1016/s0301-0104(01)00523-7	journal	January 2002
Analytic derivative couplings in time-dependent density functional theory: Quadratic response theory versus pseudo-wavefunction approach Zhang, Xing; Herbert, John M. The Journal of Chemical Physics, Vol. 142, Issue 6 https://doi.org/10.1063/1.4907376	journal	February 2015
Isomerization Through Conical Intersections Levine, Benjamin G.; Martínez, Todd J. Annual Review of Physical Chemistry, Vol. 58, Issue 1 https://doi.org/10.1146/annurev.physchem.57.032905.104612	journal	May 2007
On the Nature of Nonplanarity in the [N]Phenylenes Holmes, Daniel; Kumaraswamy, Sriram; Matzger, Adam J. Chemistry - A European Journal, Vol. 5, Issue 11 https://doi.org/10.1002/(sici)1521-3765(19991105)5:11<3399::aid-chem3399>3.0.co;2-v	journal	November 1999
Explorative computational study of the singlet fission process Havenith, Remco W. A.; de Gier, Hilde D.; Broer, Ria Molecular Physics, Vol. 110, Issue 19-20 https://doi.org/10.1080/00268976.2012.695810	journal	April 2012
Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory Zhang, Xing; Herbert, John M. The Journal of Chemical Physics, Vol. 141, Issue 6 https://doi.org/10.1063/1.4891984	journal	August 2014
Corresponding Orbitals and the Nonorthogonality Problem in Molecular Quantum Mechanics King, Harry F.; Stanton, Richard E.; Kim, Hojing The Journal of Chemical Physics, Vol. 47, Issue 6 https://doi.org/10.1063/1.1712221	journal	September 1967
Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance Fatehi, Shervin; Alguire, Ethan; Shao, Yihan The Journal of Chemical Physics, Vol. 135, Issue 23 https://doi.org/10.1063/1.3665031	journal	December 2011
Ab Initio Nonadiabatic Dynamics of Multichromophore Complexes: A Scalable Graphical-Processing-Unit-Accelerated Exciton Framework Sisto, Aaron; Glowacki, David R.; Martinez, Todd J. Accounts of Chemical Research, Vol. 47, Issue 9 https://doi.org/10.1021/ar500229p	journal	July 2014
Excited-state hydrogen detachment and hydrogen transfer driven by repulsive 1πσ* states: A new paradigm for nonradiative decay in aromatic biomolecules Sobolewski, A. L.; Domcke, W.; Dedonder-Lardeux, C. Physical Chemistry Chemical Physics, Vol. 4, Issue 7 https://doi.org/10.1039/b110941n	journal	February 2002
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package Shao, Yihan; Gan, Zhengting; Epifanovsky, Evgeny Molecular Physics, Vol. 113, Issue 2 https://doi.org/10.1080/00268976.2014.952696	journal	September 2014
Influence of Conformational Dynamics on the Exciton States of DNA Oligomers Bouvier, Benjamin; Dognon, Jean-Pierre; Lavery, Richard The Journal of Physical Chemistry B, Vol. 107, Issue 48 https://doi.org/10.1021/jp036164u	journal	December 2003
Nonadiabatic Events and Conical Intersections Matsika, Spiridoula; Krause, Pascal Annual Review of Physical Chemistry, Vol. 62, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103450	journal	May 2011
On the evaluation of nonadiabatic coupling matrix elements for MCSCF/CI wave functions using analytic derivative methods. III. Second derivative terms Lengsfield, Byron H.; Yarkony, David R. The Journal of Chemical Physics, Vol. 84, Issue 1 https://doi.org/10.1063/1.450144	journal	January 1986
Low-Scaling Quantum Chemistry Approach to Excited-State Properties via an ab Initio Exciton Model: Application to Excitation Energy Transfer in a Self-Assembled Nanotube Morrison, Adrian F.; Herbert, John M. The Journal of Physical Chemistry Letters, Vol. 6, Issue 21 https://doi.org/10.1021/acs.jpclett.5b02109	journal	October 2015
First-order nonadiabatic coupling matrix elements using coupled cluster methods. I. Theory Christiansen, Ove The Journal of Chemical Physics, Vol. 110, Issue 2 https://doi.org/10.1063/1.478179	journal	January 1999
Natural transition orbitals Martin, Richard L. The Journal of Chemical Physics, Vol. 118, Issue 11 https://doi.org/10.1063/1.1558471	journal	March 2003
Charge-Transport Regime of Crystalline Organic Semiconductors: Diffusion Limited by Thermal Off-Diagonal Electronic Disorder Troisi, Alessandro; Orlandi, Giorgio Physical Review Letters, Vol. 96, Issue 8 https://doi.org/10.1103/physrevlett.96.086601	journal	March 2006
Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections Chai, Jeng-Da; Head-Gordon, Martin Physical Chemistry Chemical Physics, Vol. 10, Issue 44 https://doi.org/10.1039/b810189b	journal	January 2008
Mechanism for Singlet Fission in Pentacene and Tetracene: From Single Exciton to Two Triplets Zimmerman, Paul M.; Bell, Franziska; Casanova, David Journal of the American Chemical Society, Vol. 133, Issue 49 https://doi.org/10.1021/ja208431r	journal	December 2011
First order nonadiabatic coupling matrix elements between excited states: Implementation and application at the TD-DFT and pp-TDA levels Li, Zhendong; Suo, Bingbing; Liu, Wenjian The Journal of Chemical Physics, Vol. 141, Issue 24 https://doi.org/10.1063/1.4903986	journal	December 2014
Analytical State-Average Complete-Active-Space Self-Consistent Field Nonadiabatic Coupling Vectors: Implementation with Density-Fitted Two-Electron Integrals and Application to Conical Intersections Fdez. Galván, Ignacio; Delcey, Mickaël G.; Pedersen, Thomas Bondo Journal of Chemical Theory and Computation, Vol. 12, Issue 8 https://doi.org/10.1021/acs.jctc.6b00384	journal	July 2016
Charge Transport in Organic Semiconductors Coropceanu, Veaceslav; Cornil, Jérôme; da Silva Filho, Demetrio A. Chemical Reviews, Vol. 107, Issue 4 https://doi.org/10.1021/cr050140x	journal	April 2007
Vibronic interactions and superconductivity in acene anions and cations Kato, Takashi; Yamabe, Tokio The Journal of Chemical Physics, Vol. 115, Issue 18 https://doi.org/10.1063/1.1409539	journal	November 2001
Natural orbitals in CIS and singular-value decomposition Surján, Péter R. Chemical Physics Letters, Vol. 439, Issue 4-6 https://doi.org/10.1016/j.cplett.2007.03.094	journal	May 2007
Differential equations for the analytic singular value decomposition of a matrix Wright, K. Numerische Mathematik, Vol. 63, Issue 1 https://doi.org/10.1007/bf01385862	journal	December 1992
A parallel implementation of the analytic nuclear gradient for time-dependent density functional theory within the Tamm–Dancoff approximation Liu, Fenglai; Gan, Zhengting; Shao, Yihan Molecular Physics, Vol. 108, Issue 19-20 https://doi.org/10.1080/00268976.2010.526642	journal	October 2010
On the evaluation of nonadiabatic coupling matrix elements using SA‐MCSCF/CI wave functions and analytic gradient methods. I Lengsfield, Byron H.; Saxe, Paul; Yarkony, David R. The Journal of Chemical Physics, Vol. 81, Issue 10 https://doi.org/10.1063/1.447428	journal	November 1984
Dynamics of the Intermolecular Transfer Integral in Crystalline Organic Semiconductors Troisi, Alessandro; Orlandi, Giorgio The Journal of Physical Chemistry A, Vol. 110, Issue 11 https://doi.org/10.1021/jp055432g	journal	March 2006
Defect-Induced Conical Intersections Promote Nonradiative Recombination Shu, Yinan; Fales, B. Scott; Levine, Benjamin G. Nano Letters, Vol. 15, Issue 9 https://doi.org/10.1021/acs.nanolett.5b02848	journal	August 2015
Fission of Entangled Spins: An Electronic Structure Perspective Feng, Xintian; Luzanov, Anatoliy V.; Krylov, Anna I. The Journal of Physical Chemistry Letters, Vol. 4, Issue 22 https://doi.org/10.1021/jz402122m	journal	November 2013
First-order derivative couplings between excited states from adiabatic TDDFT response theory Ou, Qi; Bellchambers, Gregory D.; Furche, Filipp The Journal of Chemical Physics, Vol. 142, Issue 6 https://doi.org/10.1063/1.4906941	journal	February 2015
Ab Initio Implementation of the Frenkel–Davydov Exciton Model: A Naturally Parallelizable Approach to Computing Collective Excitations in Crystals and Aggregates Morrison, Adrian F.; You, Zhi-Qiang; Herbert, John M. Journal of Chemical Theory and Computation, Vol. 10, Issue 12 https://doi.org/10.1021/ct500765m	journal	November 2014
Hartree–Fock solutions as a quasidiabatic basis for nonorthogonal configuration interaction Thom, Alex J. W.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 131, Issue 12 https://doi.org/10.1063/1.3236841	journal	September 2009
Electron–molecular vibration (e–mv) coupling in charge‐transfer compounds and its consequences on the optical spectra: A theoretical framework Painelli, A.; Girlando, A. The Journal of Chemical Physics, Vol. 84, Issue 10 https://doi.org/10.1063/1.449926	journal	May 1986
New Algorithms for Optimizing and Linking Conical Intersection Points Sicilia, Fabrizio; Blancafort, Lluís; Bearpark, Michael J. Journal of Chemical Theory and Computation, Vol. 4, Issue 2 https://doi.org/10.1021/ct7002435	journal	January 2008
BEYOND BORN-OPPENHEIMER: Molecular Dynamics Through a Conical Intersection Worth, Graham A.; Cederbaum, Lorenz S. Annual Review of Physical Chemistry, Vol. 55, Issue 1 https://doi.org/10.1146/annurev.physchem.55.091602.094335	journal	June 2004
The Theory of Molecular Excitons Davydov, A. S. Soviet Physics Uspekhi, Vol. 7, Issue 2 https://doi.org/10.1070/pu1964v007n02abeh003659	journal	February 1964
On the evaluation of non-adiabatic coupling matrix elements for large scale CI wavefunctions Saxe, Paul; Lengsfield, Byron H.; Yarkony, David R. Chemical Physics Letters, Vol. 113, Issue 2 https://doi.org/10.1016/0009-2614(85)80935-0	journal	January 1985
A direct method for the location of the lowest energy point on a potential surface crossing Bearpark, Michael J.; Robb, Michael A.; Bernhard Schlegel, H. Chemical Physics Letters, Vol. 223, Issue 3 https://doi.org/10.1016/0009-2614(94)00433-1	journal	June 1994
Beyond Time-Dependent Density Functional Theory Using Only Single Excitations: Methods for Computational Studies of Excited States in Complex Systems Herbert, John M.; Zhang, Xing; Morrison, Adrian F. Accounts of Chemical Research, Vol. 49, Issue 5 https://doi.org/10.1021/acs.accounts.6b00047	journal	April 2016
Estimating the Derivative Coupling Vector Using Gradients Kammeraad, Joshua A.; Zimmerman, Paul M. The Journal of Physical Chemistry Letters, Vol. 7, Issue 24 https://doi.org/10.1021/acs.jpclett.6b02501	journal	November 2016
Analytical second derivatives for excited electronic states using the single excitation configuration interaction method: theory and application to benzo[a]pyrene and chalcone Maurice, David; Head-Gordon, Martin Molecular Physics, Vol. 96, Issue 10 https://doi.org/10.1080/00268979909483096	journal	May 1999
Using singular value decomposition for a compact presentation and improved interpretation of the CIS wave functions Mayer, I. Chemical Physics Letters, Vol. 437, Issue 4-6 https://doi.org/10.1016/j.cplett.2007.02.038	journal	April 2007
Evidence for Singlet Fission Driven by Vibronic Coherence in Crystalline Tetracene Morrison, Adrian F.; Herbert, John M. The Journal of Physical Chemistry Letters, Vol. 8, Issue 7 https://doi.org/10.1021/acs.jpclett.7b00230	journal	March 2017
Peierls and Holstein carrier-phonon coupling in crystalline rubrene Girlando, Alberto; Grisanti, Luca; Masino, Matteo Physical Review B, Vol. 82, Issue 3 https://doi.org/10.1103/physrevb.82.035208	journal	July 2010
Explorations of conical intersections and their ramifications for chemistry through the Jahn–Teller effect Applegate, Brian E.; Barckholtz, Timothy A.; Miller, Terry A. Chem. Soc. Rev., Vol. 32, Issue 1 https://doi.org/10.1039/a910269h	journal	January 2003
Single determinant wave functions Amos, A. T.; Hall, G. G. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 263, Issue 1315, p. 483-493 https://doi.org/10.1098/rspa.1961.0175	journal	October 1961
Derivative studies in hartree-fock and møller-plesset theories Pople, J. A.; Krishnan, R.; Schlegel, H. B. International Journal of Quantum Chemistry, Vol. 16, Issue S13 https://doi.org/10.1002/qua.560160825	journal	March 1979
Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism Lischka, Hans; Dallos, Michal; Szalay, Péter G. The Journal of Chemical Physics, Vol. 120, Issue 16 https://doi.org/10.1063/1.1668615	journal	April 2004
Analytic evaluation of the nonadiabatic coupling vector between excited states using equation-of-motion coupled-cluster theory Tajti, Attila; Szalay, Péter G. The Journal of Chemical Physics, Vol. 131, Issue 12 https://doi.org/10.1063/1.3232011	journal	September 2009
Microscopic theory of singlet exciton fission. II. Application to pentacene dimers and the role of superexchange Berkelbach, Timothy C.; Hybertsen, Mark S.; Reichman, David R. The Journal of Chemical Physics, Vol. 138, Issue 11 https://doi.org/10.1063/1.4794427	journal	March 2013
Prediction of the Absolute Charge Mobility of Molecular Semiconductors: the Case of Rubrene Troisi, A. Advanced Materials, Vol. 19, Issue 15 https://doi.org/10.1002/adma.200700550	journal	August 2007
Evidence for conical intersection dynamics mediating ultrafast singlet exciton fission Musser, Andrew J.; Liebel, Matz; Schnedermann, Christoph Nature Physics, Vol. 11, Issue 4 https://doi.org/10.1038/nphys3241	journal	March 2015

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