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Schubert A, Bhandari S, Geva E, Dunietz BD. A Computational Study of the Electronic Energy and Charge Transfer Rates and Pathways in the Tetraphenyldibenzoperiflanthene/Fullerene Interfacial Dyad. J Phys Chem Lett 2023; 14:9569-9583. [PMID: 37862043 DOI: 10.1021/acs.jpclett.3c01927] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2023]
Abstract
The electronic transition rates and pathways underlying interfacial charge separation in tetraphenyldibenzoperiflanthene:fullerene (DBP:C70) blends are investigated computationally. The analysis is based on a polarization-consistent framework employing screened range-separated hybrid functional in a polarizable continuum model to parametrize Fermi's golden rule rate theory. The model considers the possible transitions within the 25 lowest excited states of a DBP:C70 dyad that are accessible by photoexcitation. The different identified pathways contributing to charge carrier generation include electron and hole transfer and backtransfer, exciton transfer, and internal relaxation steps. The larger density of states of C70 appears to explain the previously observed larger efficiency for charge separation through hole transfer mechanism. We also analyze the validity of the high-temperature and short-time semiclassical approximations of the FGR theory, where both overestimated and underestimated Marcus theory based constants can be affected.
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Affiliation(s)
- Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, United States
| | - Srijana Bhandari
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Barry D Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, United States
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2
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Jang SJ, Rhee YM. Modified Fermi's golden rule rate expressions. J Chem Phys 2023; 159:014101. [PMID: 37403843 DOI: 10.1063/5.0152804] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2023] [Accepted: 06/12/2023] [Indexed: 07/06/2023] Open
Abstract
Fermi's golden rule (FGR) serves as the basis for many expressions of spectroscopic observables and quantum transition rates. The utility of FGR has been demonstrated through decades of experimental confirmation. However, there still remain important cases where the evaluation of a FGR rate is ambiguous or ill-defined. Examples are cases where the rate has divergent terms due to the sparsity in the density of final states or time dependent fluctuations of system Hamiltonians. Strictly speaking, assumptions of FGR are no longer valid for such cases. However, it is still possible to define modified FGR rate expressions that are useful as effective rates. The resulting modified FGR rate expressions resolve a long standing ambiguity often encountered in using FGR and offer more reliable ways to model general rate processes. Simple model calculations illustrate the utility and implications of new rate expressions.
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Affiliation(s)
- Seogjoo J Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and PhD Programs in Chemistry and Physics, Graduate Center of the City University of New York, New York, New York 10016, USA
- Korea Institute for Advanced Study, Seoul 02455, South Korea
- Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon 34141, South Korea
| | - Young Min Rhee
- Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon 34141, South Korea
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3
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Jang SJ. A simple generalization of the energy gap law for nonradiative processes. J Chem Phys 2021; 155:164106. [PMID: 34717346 DOI: 10.1063/5.0068868] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
For more than 50 years, an elegant energy gap (EG) law developed by Englman and Jortner [Mol. Phys. 18, 145 (1970)] has served as a key theory to understand and model the nearly exponential dependence of nonradiative transition rates on the difference of energy between the initial and final states. This work revisits the theory, clarifies the key assumptions involved in the rate expression, and provides a generalization for the cases where the effects of temperature dependence and low-frequency modes cannot be ignored. For a specific example where the low-frequency vibrational and/or solvation responses can be modeled as an Ohmic spectral density, a simple generalization of the EG law is provided. Test calculations demonstrate that this generalized EG law brings significant improvement over the original EG law. Both the original and generalized EG laws are also compared with the stationary phase approximations developed for electron transfer theory, which suggests the possibility of a simple interpolation formula valid for any value of EG.
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Affiliation(s)
- Seogjoo J Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and PhD Programs in Chemistry and Physics, and Initiative for the Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
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4
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Chen N, Devi M, Jang SJ. Computational modeling of charge hopping dynamics along a disordered one-dimensional wire with energy gradients in quantum environments. J Chem Phys 2020; 153:054109. [PMID: 32770925 DOI: 10.1063/5.0011004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This computational study investigates the effects of energy gradients on charge hopping dynamics along a one-dimensional chain of discrete sites coupled to quantum bath, which is modeled at the level of Pauli master equation (PME). This study also assesses the performance of different approximations for the hopping rates. Three different methods for solving the PME, a fourth order Runge-Kutta method, numerical diagonalization of the rate matrix followed by analytic propagation, and kinetic Monte Carlo simulation method, are tested and confirmed to produce virtually identical values of time dependent mean square displacement, diffusion constant, and mobility. Five different rate expressions, exact numerical evaluation of Fermi's Golden Rule (FGR) rate, stationary phase interpolation (SPI) approximation, semiclassical approximation, classical Marcus rate, and Miller-Abrahams rate, are tested to help understand the effects of approximations in representing quantum environments in the presence of energy gradients. The results based on direct numerical evaluation of FGR rate exhibit transition from diffusive to non-diffusive behavior with the increase in the gradient and show that the charge transport in the quantum bath is more sensitive to the magnitude of the gradient and the disorder than in the classical bath. Among all the four approximations for the hopping rates, the SPI approximation is confirmed to work best overall. A comparison of two different methods to calculate the mobility identifies drift motion of the population distribution as the major source of non-diffusive behavior and provides more reliable information on the contribution of quantum bath.
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Affiliation(s)
- Ning Chen
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA
| | - Murali Devi
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA
| | - Seogjoo J Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA
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5
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Heller ER, Richardson JO. Instanton formulation of Fermi’s golden rule in the Marcus inverted regime. J Chem Phys 2020; 152:034106. [DOI: 10.1063/1.5137823] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Eric R. Heller
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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Maiti B, Schubert A, Sarkar S, Bhandari S, Wang K, Li Z, Geva E, Twieg RJ, Dunietz BD. Enhancing charge mobilities in organic semiconductors by selective fluorination: a design approach based on a quantum mechanical perspective. Chem Sci 2017; 8:6947-6953. [PMID: 29147520 PMCID: PMC5642104 DOI: 10.1039/c7sc02491f] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2017] [Accepted: 08/12/2017] [Indexed: 11/21/2022] Open
Abstract
Selective fluorination of organic semiconducting molecules is proposed as a means to achieving enhanced hole mobility. Naphthalene is examined here as a root molecular system with fluorination performed at various sites. Our quantum chemical calculations show that selective fluorination can enhance attractive intermolecular interactions while reducing charge trapping. Those observations suggest a design principle whereby fluorination is utilized for achieving high charge mobilities in the crystalline form. The utility of this design principle is demonstrated through an application to perylene, which is an important building block of organic semiconducting materials. We also show that a quantum mechanical perspective of nuclear degrees of freedom is crucial for a reliable description of charge transport.
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Affiliation(s)
- Buddhadev Maiti
- Department of Chemistry and Biochemistry , Kent State University , Kent , OH 44242 , USA . ; ; r
| | - Alexander Schubert
- Department of Chemistry and Biochemistry , Kent State University , Kent , OH 44242 , USA . ; ; r
- Department of Chemistry , University of Michigan , Ann Arbor , MI 48109 , USA .
| | - Sunandan Sarkar
- Department of Chemistry and Biochemistry , Kent State University , Kent , OH 44242 , USA . ; ; r
| | - Srijana Bhandari
- Department of Chemistry and Biochemistry , Kent State University , Kent , OH 44242 , USA . ; ; r
| | - Kunlun Wang
- Department of Chemistry and Biochemistry , Kent State University , Kent , OH 44242 , USA . ; ; r
| | - Zhe Li
- Department of Chemistry and Biochemistry , Kent State University , Kent , OH 44242 , USA . ; ; r
| | - Eitan Geva
- Department of Chemistry , University of Michigan , Ann Arbor , MI 48109 , USA .
| | - Robert J Twieg
- Department of Chemistry and Biochemistry , Kent State University , Kent , OH 44242 , USA . ; ; r
| | - Barry D Dunietz
- Department of Chemistry and Biochemistry , Kent State University , Kent , OH 44242 , USA . ; ; r
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7
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Newton MD. Extension of Hopfield’s Electron Transfer Model To Accommodate Site–Site Correlation. J Phys Chem B 2015; 119:14728-37. [DOI: 10.1021/acs.jpcb.5b07456] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Marshall D. Newton
- Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973, United States
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8
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Sun X, Geva E. Equilibrium Fermi’s Golden Rule Charge Transfer Rate Constants in the Condensed Phase: The Linearized Semiclassical Method vs Classical Marcus Theory. J Phys Chem A 2015; 120:2976-90. [DOI: 10.1021/acs.jpca.5b08280] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
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9
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Block E, Jang S, Matsunami H, Sekharan S, Dethier B, Ertem MZ, Gundala S, Pan Y, Li S, Li Z, Lodge SN, Ozbil M, Jiang H, Penalba SF, Batista VS, Zhuang H. Implausibility of the vibrational theory of olfaction. Proc Natl Acad Sci U S A 2015; 112:E2766-74. [PMID: 25901328 PMCID: PMC4450420 DOI: 10.1073/pnas.1503054112] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
The vibrational theory of olfaction assumes that electron transfer occurs across odorants at the active sites of odorant receptors (ORs), serving as a sensitive measure of odorant vibrational frequencies, ultimately leading to olfactory perception. A previous study reported that human subjects differentiated hydrogen/deuterium isotopomers (isomers with isotopic atoms) of the musk compound cyclopentadecanone as evidence supporting the theory. Here, we find no evidence for such differentiation at the molecular level. In fact, we find that the human musk-recognizing receptor, OR5AN1, identified using a heterologous OR expression system and robustly responding to cyclopentadecanone and muscone, fails to distinguish isotopomers of these compounds in vitro. Furthermore, the mouse (methylthio)methanethiol-recognizing receptor, MOR244-3, as well as other selected human and mouse ORs, responded similarly to normal, deuterated, and (13)C isotopomers of their respective ligands, paralleling our results with the musk receptor OR5AN1. These findings suggest that the proposed vibration theory does not apply to the human musk receptor OR5AN1, mouse thiol receptor MOR244-3, or other ORs examined. Also, contrary to the vibration theory predictions, muscone-d30 lacks the 1,380- to 1,550-cm(-1) IR bands claimed to be essential for musk odor. Furthermore, our theoretical analysis shows that the proposed electron transfer mechanism of the vibrational frequencies of odorants could be easily suppressed by quantum effects of nonodorant molecular vibrational modes. These and other concerns about electron transfer at ORs, together with our extensive experimental data, argue against the plausibility of the vibration theory.
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Affiliation(s)
- Eric Block
- Department of Chemistry, University at Albany, State University of New York, Albany, NY 12222;
| | - Seogjoo Jang
- Department of Chemistry and Biochemistry, Queens College, and Graduate Center, City University of New York, Flushing, NY 11367;
| | - Hiroaki Matsunami
- Department of Molecular Genetics and Microbiology and Department of Neurobiology, Duke Institute for Brain Sciences, Duke University Medical Center, Durham, NC 27710;
| | | | - Bérénice Dethier
- Department of Chemistry, University at Albany, State University of New York, Albany, NY 12222
| | - Mehmed Z Ertem
- Department of Chemistry, Yale University, New Haven, CT 06520; Chemistry Department, Brookhaven National Laboratory, Upton, NY 11973
| | - Sivaji Gundala
- Department of Chemistry, University at Albany, State University of New York, Albany, NY 12222
| | - Yi Pan
- Department of Pathophysiology, Key Laboratory of Cell Differentiation and Apoptosis of Ministry of Education, Shanghai Jiaotong University School of Medicine, Shanghai 200025, China; and
| | - Shengju Li
- Department of Pathophysiology, Key Laboratory of Cell Differentiation and Apoptosis of Ministry of Education, Shanghai Jiaotong University School of Medicine, Shanghai 200025, China; and
| | - Zhen Li
- Department of Pathophysiology, Key Laboratory of Cell Differentiation and Apoptosis of Ministry of Education, Shanghai Jiaotong University School of Medicine, Shanghai 200025, China; and
| | - Stephene N Lodge
- Department of Chemistry, University at Albany, State University of New York, Albany, NY 12222
| | - Mehmet Ozbil
- Department of Chemistry, Yale University, New Haven, CT 06520
| | - Huihong Jiang
- Department of Pathophysiology, Key Laboratory of Cell Differentiation and Apoptosis of Ministry of Education, Shanghai Jiaotong University School of Medicine, Shanghai 200025, China; and
| | - Sonia F Penalba
- Department of Chemistry, University at Albany, State University of New York, Albany, NY 12222
| | | | - Hanyi Zhuang
- Department of Pathophysiology, Key Laboratory of Cell Differentiation and Apoptosis of Ministry of Education, Shanghai Jiaotong University School of Medicine, Shanghai 200025, China; and Institute of Health Sciences, Shanghai Jiao tong University School of Medicine/Shanghai Institutes for Biological Sciences of Chinese Academy of Sciences, Shanghai 200031, China
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10
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Jang S, Montoya-Castillo A. Charge Hopping Dynamics along a Disordered Chain in Quantum Environments: Comparative Study of Different Rate Kernels. J Phys Chem B 2015; 119:7659-65. [DOI: 10.1021/jp511933m] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Seogjoo Jang
- Department of Chemistry and
Biochemistry, Queens College
and the Graduate Center, City University of New York, 65-30 Kissena
Boulevard, Queens, New York 11367-1597, United States
| | - Andrés Montoya-Castillo
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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11
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Basilevsky MV, Odinokov AV, Titov SV, Mitina EA. Golden rule kinetics of transfer reactions in condensed phase: the microscopic model of electron transfer reactions in disordered solid matrices. J Chem Phys 2013; 139:234102. [PMID: 24359347 DOI: 10.1063/1.4838335] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ0 = ℏω0/k(B)T where ω0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ0 < 1 - 3) and for low (ξ0 ≫ 1) temperature ranges. For the first (quasi-classical) kinetic regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantum-mechanical low-temperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a non-vanishing reaction rate has been revealed when T → 0. An accurate computational methodology for the cross-over kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the kinetic regimes, which are usually postulated in the existing theories of the ET. Our alternative dynamic ET model for local modes immersed in the continuum harmonic medium is formulated for both classical and quantum regimes, and accounts explicitly for the mode∕medium interaction. The kinetics of the energy exchange between the local ET subsystem and the surrounding environment essentially determine the total ET rate. The efficient computer code for rate computations is elaborated on. The computations are available for a wide range of system parameters, such as the temperature, external field, local mode frequency, and characteristics of mode/medium interaction. The relation of the present approach to the Marcus ET theory and to the quantum-statistical reaction rate theory [V. G. Levich and R. R. Dogonadze, Dokl. Akad. Nauk SSSR, Ser. Fiz. Khim. 124, 213 (1959); J. Ulstrup, Charge Transfer in Condensed Media (Springer, Berlin, 1979); M. Bixon and J. Jortner, Adv. Chem. Phys. 106, 35 (1999)] underlying it is discussed and illustrated by the results of computations for practically important target systems.
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Affiliation(s)
- M V Basilevsky
- Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow, Russia
| | - A V Odinokov
- Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow, Russia
| | - S V Titov
- Karpov Institute of Physical Chemistry, 3-1∕12, Building 6, Obuha pereulok, Moscow, Russia
| | - E A Mitina
- Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow, Russia
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12
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Ignaczak A. Adiabatic versus non-adiabatic approach to the inner sphere vibrational effects on electrochemical reduction rates. Electrochim Acta 2008. [DOI: 10.1016/j.electacta.2007.10.052] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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