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Lindoy LP, Kloss B, Reichman DR. Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator. J Chem Phys 2021; 155:174109. [PMID: 34742222 DOI: 10.1063/5.0070043] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach can suffer from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of regularization of the EOMs. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here, we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to 106 bath modes and find that for these problems, the PSI requires roughly 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH and 2-3/1-2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to ∼1.3×109 parameters to obtain accurate dynamics.
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Affiliation(s)
- Lachlan P Lindoy
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Benedikt Kloss
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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2
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Lindoy LP, Kloss B, Reichman DR. Time evolution of ML-MCTDH wavefunctions. I. Gauge conditions, basis functions, and singularities. J Chem Phys 2021; 155:174108. [PMID: 34742180 DOI: 10.1063/5.0070042] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
We derive a family of equations-of-motion (EOMs) for evolving multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) wavefunctions that, unlike the standard ML-MCTDH EOMs, never require the evaluation of the inverse of singular matrices. All members of this family of EOMs make use of alternative static gauge conditions than those used for standard ML-MCTDH. These alternative conditions result in an expansion of the wavefunction in terms of a set of potentially arbitrary orthonormal functions, rather than in terms of a set of non-orthonormal and potentially linearly dependent functions, as is the case for standard ML-MCTDH. We show that the EOMs used in the projector splitting integrator (PSI) and the invariant EOM approaches are two special cases of this family obtained from different choices for the dynamic gauge condition, with the invariant EOMs making use of a choice that introduces potentially unbounded operators into the EOMs. As a consequence, all arguments for the existence of parallelizable integration schemes for the invariant EOMs can also be applied to the PSI EOMs.
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Affiliation(s)
- Lachlan P Lindoy
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Benedikt Kloss
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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3
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Borrelli R, Gelin MF. Finite temperature quantum dynamics of complex systems: Integrating
thermo‐field
theories and
tensor‐train
methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1539] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
| | - Maxim F. Gelin
- School of Sciences Hangzhou Dianzi University Hangzhou China
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4
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Moitra T, Karak P, Chakraborty S, Ruud K, Chakrabarti S. Behind the scenes of spin-forbidden decay pathways in transition metal complexes. Phys Chem Chem Phys 2021; 23:59-81. [PMID: 33319894 DOI: 10.1039/d0cp05108j] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The interpretation of the ultrafast photophysics of transition metal complexes following photo-absorption is quite involved as the heavy metal center leads to a complicated and entangled singlet-triplet manifold. This opens up multiple pathways for deactivation, often with competitive rates. As a result, intersystem crossing (ISC) and phosphorescence are commonly observed in transition metal complexes. A detailed understanding of such an excited-state structure and dynamics calls for state-of-the-art experimental and theoretical methodologies. In this review, we delve into the inability of non-relativistic quantum theory to describe spin-forbidden transitions, which can be overcome by taking into account spin-orbit coupling, whose importance grows with increasing atomic number. We present the quantum chemical theory of phosphorescence and ISC together with illustrative examples. Finally, a few applications are highlighted, bridging the gap between theoretical studies and experimental applications, such as photofunctional materials.
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Affiliation(s)
- Torsha Moitra
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, DK-2800 Kongens Lyngby, Denmark
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5
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Borrelli R. Theoretical study of charge-transfer processes at finite temperature using a novel thermal Schrödinger equation. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.06.005] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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6
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Parson WW. Temperature Dependence of the Rate of Intramolecular Electron Transfer. J Phys Chem B 2018; 122:8824-8833. [DOI: 10.1021/acs.jpcb.8b06497] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- William W. Parson
- Department of Biochemistry, University of Washington, Seattle, Washington 98195, United States
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7
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Cherepanov DA, Milanovsky GE, Gopta OA, Balasubramanian R, Bryant DA, Semenov AY, Golbeck JH. Electron–Phonon Coupling in Cyanobacterial Photosystem I. J Phys Chem B 2018; 122:7943-7955. [DOI: 10.1021/acs.jpcb.8b03906] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Dmitry A. Cherepanov
- A.N. Belozersky Institute of Physical-Chemical Biology, Moscow State University, Leninskye Gory,
1, Building 40, 119992 Moscow, Russia
- N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygina st., 4, 117977 Moscow, Russia
| | - Georgy E. Milanovsky
- A.N. Belozersky Institute of Physical-Chemical Biology, Moscow State University, Leninskye Gory,
1, Building 40, 119992 Moscow, Russia
| | - Oksana A. Gopta
- A.N. Belozersky Institute of Physical-Chemical Biology, Moscow State University, Leninskye Gory,
1, Building 40, 119992 Moscow, Russia
- Department of Biochemistry and Molecular Biology, The Pennsylvania State University, 328 Frear Laboratory, University Park, Pennsylvania 16802, United States
| | - Ramakrishnan Balasubramanian
- Department of Biochemistry and Molecular Biology, The Pennsylvania State University, 328 Frear Laboratory, University Park, Pennsylvania 16802, United States
| | - Donald A. Bryant
- Department of Biochemistry and Molecular Biology, The Pennsylvania State University, 328 Frear Laboratory, University Park, Pennsylvania 16802, United States
- Department of Chemistry and Biochemistry, Montana State University, 103 Chemistry and Biochemistry Building, PO Box 173400, Bozeman, Montana 59717, United States
| | - Alexey Yu. Semenov
- A.N. Belozersky Institute of Physical-Chemical Biology, Moscow State University, Leninskye Gory,
1, Building 40, 119992 Moscow, Russia
- N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygina st., 4, 117977 Moscow, Russia
| | - John H. Golbeck
- Department of Biochemistry and Molecular Biology, The Pennsylvania State University, 328 Frear Laboratory, University Park, Pennsylvania 16802, United States
- Department of Chemistry, The Pennsylvania State University, 328 Frear Laboratory, University Park, Pennsylvania 16802, United States
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8
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Parson WW. Electron-Transfer Dynamics in a Zn-Porphyrin-Quinone Cyclophane: Effects of Solvent, Vibrational Relaxations, and Conical Intersections. J Phys Chem B 2018; 122:3854-3863. [DOI: 10.1021/acs.jpcb.8b01072] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- William W. Parson
- Department of Biochemistry, University of Washington, Seattle, Washington 98195, United States
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9
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Yamamoto K, Takatsuka K. On the photocatalytic cycle of water splitting with small manganese oxides and the roles of water clusters as direct sources of oxygen molecules. Phys Chem Chem Phys 2018; 20:6708-6725. [DOI: 10.1039/c7cp07171j] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A study on the photocatalytic cycle of water splitting and coupled proton electron-wavepacket transfer (CPEWT) as key processes of the mechanism.
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Affiliation(s)
- Kentaro Yamamoto
- Fukui Institute for Fundamental Chemistry
- Kyoto University
- Kyoto 606-8103
- Japan
| | - Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry
- Kyoto University
- Kyoto 606-8103
- Japan
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10
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Borrelli R, Gelin MF. Simulation of Quantum Dynamics of Excitonic Systems at Finite Temperature: an efficient method based on Thermo Field Dynamics. Sci Rep 2017; 7:9127. [PMID: 28831074 PMCID: PMC5567225 DOI: 10.1038/s41598-017-08901-2] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2017] [Accepted: 07/18/2017] [Indexed: 11/09/2022] Open
Abstract
Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on Thermo Field Dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. The solution of Thermo Field Dynamics equations with a novel technique for the propagation of Tensor Trains (Matrix Product States) is implemented and discussed. The methodology is applied to the study of the exciton dynamics in the Fenna-Mathews-Olsen complex using a realistic structured spectral density to model the electron-phonon interaction. The results of the simulations highlight the effect of specific vibrational modes on the exciton dynamics and energy transfer process, as well as call for careful modeling of electron-phonon couplings.
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Affiliation(s)
| | - Maxim F Gelin
- Department of Theoretical Chemistry, Technische Universität München, Garching, D-85747, Germany
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11
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Manthe U. Wavepacket dynamics and the multi-configurational time-dependent Hartree approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:253001. [PMID: 28430111 DOI: 10.1088/1361-648x/aa6e96] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.
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Affiliation(s)
- Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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12
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Borrelli R, Gelin MF. Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach. J Chem Phys 2017; 145:224101. [PMID: 27984899 DOI: 10.1063/1.4971211] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.
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Affiliation(s)
| | - Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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13
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Using quantum dynamics simulations to follow the competition between charge migration and charge transfer in polyatomic molecules. Chem Phys 2017. [DOI: 10.1016/j.chemphys.2016.10.007] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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14
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High JS, Rego LGC, Jakubikova E. Quantum Dynamics Simulations of Excited State Energy Transfer in a Zinc–Free-Base Porphyrin Dyad. J Phys Chem A 2016; 120:8075-8084. [DOI: 10.1021/acs.jpca.6b05739] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Judah S. High
- Department
of Chemistry, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - Luis G. C. Rego
- Department
of Physics, Federal University of Santa Catarina, Florianopolis 88040-900, Brazil
| | - Elena Jakubikova
- Department
of Chemistry, North Carolina State University, Raleigh, North Carolina 27695, United States
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15
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Borrelli R, Peluso A. Quantum dynamics of electronic transitions with Gauss-Hermite wave packets. J Chem Phys 2016; 144:114102. [DOI: 10.1063/1.4943538] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Raffaele Borrelli
- Department of Agricultural, Forestry and Food Science, Università di Torino, I-10095 Grugliasco, TO, Italy
| | - Andrea Peluso
- Department of Chemistry and Biology, Università di Salerno, I-84081 Fisciano, SA, Italy
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16
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Nenov A, Segarra-Martí J, Giussani A, Conti I, Rivalta I, Dumont E, Jaiswal VK, Altavilla SF, Mukamel S, Garavelli M. Probing deactivation pathways of DNA nucleobases by two-dimensional electronic spectroscopy: first principles simulations. Faraday Discuss 2015; 177:345-62. [PMID: 25607949 DOI: 10.1039/c4fd00175c] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
The SOS//QM/MM [Rivalta et al., Int. J. Quant. Chem., 2014, 114, 85] method consists of an arsenal of computational tools allowing accurate simulation of one-dimensional (1D) and bi-dimensional (2D) electronic spectra of monomeric and dimeric systems with unprecedented details and accuracy. Prominent features like doubly excited local and excimer states, accessible in multi-photon processes, as well as charge-transfer states arise naturally through the fully quantum-mechanical description of the aggregates. In this contribution the SOS//QM/MM approach is extended to simulate time-resolved 2D spectra that can be used to characterize ultrafast excited state relaxation dynamics with atomistic details. We demonstrate how critical structures on the excited state potential energy surface, obtained through state-of-the-art quantum chemical computations, can be used as snapshots of the excited state relaxation dynamics to generate spectral fingerprints for different de-excitation channels. The approach is based on high-level multi-configurational wavefunction methods combined with non-linear response theory and incorporates the effects of the solvent/environment through hybrid quantum mechanics/molecular mechanics (QM/MM) techniques. Specifically, the protocol makes use of the second-order Perturbation Theory (CASPT2) on top of Complete Active Space Self Consistent Field (CASSCF) strategy to compute the high-lying excited states that can be accessed in different 2D experimental setups. As an example, the photophysics of the stacked adenine-adenine dimer in a double-stranded DNA is modeled through 2D near-ultraviolet (NUV) spectroscopy.
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Affiliation(s)
- Artur Nenov
- Dipartimento di Chimica G. Ciamician, Università di Bologna, Via F. Selmi 2, 40126 Bologna, Italy.
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17
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Li J, Kondov I, Wang H, Thoss M. Quantum dynamical simulation of photoinduced electron transfer processes in dye-semiconductor systems: theory and application to coumarin 343 at TiO₂. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:134202. [PMID: 25767089 DOI: 10.1088/0953-8984/27/13/134202] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
A recently developed methodology to simulate photoinduced electron transfer processes at dye-semiconductor interfaces is outlined. The methodology employs a first-principles-based model Hamiltonian and accurate quantum dynamics simulations using the multilayer multiconfiguration time-dependent Hartree approach. This method is applied to study electron injection in the dye-semiconductor system coumarin 343-TiO2. Specifically, the influence of electronic-vibrational coupling is analyzed. Extending previous work, we consider the influence of Dushinsky rotation of the normal modes as well as anharmonicities of the potential energy surfaces on the electron transfer dynamics.
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Affiliation(s)
- Jingrui Li
- Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, GA 30332-0400,USA. Institute of Theoretical Physics and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
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18
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Borrelli R, Peluso A. Quantum Dynamics of Radiationless Electronic Transitions Including Normal Modes Displacements and Duschinsky Rotations: A Second-Order Cumulant Approach. J Chem Theory Comput 2015; 11:415-22. [DOI: 10.1021/ct500966c] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Raffaele Borrelli
- Department
of Agricultural, Forestry and Food Science, University of Torino, I-10195 Grugliasco, Italy
| | - Andrea Peluso
- Department
of Chemistry and Biology, University of Salerno, I-84081 Fisciano, Italy
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19
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Borrelli R, Capobianco A, Landi A, Peluso A. Vibronic couplings and coherent electron transfer in bridged systems. Phys Chem Chem Phys 2015; 17:30937-45. [DOI: 10.1039/c5cp01190f] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
A computational strategy to analyze the dynamics of coherent electron transfer processes in bridged systems, involving three or more electronic states, is presented.
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Affiliation(s)
- Raffaele Borrelli
- Department of Agricultural
- Forestry and Food Science
- University of Torino
- I-10095 Grugliasco
- Italy
| | - Amedeo Capobianco
- Dipartimento di Chimica e Biologia
- Università di Salerno
- I-84084 Fisciano (SA)
- Italy
| | - Alessandro Landi
- Dipartimento di Chimica e Biologia
- Università di Salerno
- I-84084 Fisciano (SA)
- Italy
| | - Andrea Peluso
- Dipartimento di Chimica e Biologia
- Università di Salerno
- I-84084 Fisciano (SA)
- Italy
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20
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Otto F. Multi-layer Potfit: An accurate potential representation for efficient high-dimensional quantum dynamics. J Chem Phys 2014; 140:014106. [DOI: 10.1063/1.4856135] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Borrelli R, Ellena S, Barolo C. Theoretical and experimental determination of the absorption and emission spectra of a prototypical indolenine-based squaraine dye. Phys Chem Chem Phys 2014; 16:2390-8. [DOI: 10.1039/c3cp54298j] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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22
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Borrelli R, Capobianco A, Peluso A. Franck–Condon factors—Computational approaches and recent developments. CAN J CHEM 2013. [DOI: 10.1139/cjc-2012-0518] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Algorithms and methodologies for the calculation of Franck–Condon integrals are reviewed. Starting from the standard approach based on the Cartesian representation of the normal modes and the use of Duschinsky's transformation and recursion formulas, methods for treating large displacements of the equilibrium positions and anharmonic and non-Condon effects are considered. Finally, focusing attention on problems arising from the use of recurrence relations, some of the proposed solutions are critically reviewed along with new alternative approaches.
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Affiliation(s)
- Raffaele Borrelli
- Dipartimento di Scienze Agrarie, Forestali e Alimentari, Università di Torino, I-10095 Grugliasco (TO), Italy
| | - Amedeo Capobianco
- Dipartimento di Chimica e Biologia, Università di Salerno, I-84084, Fisciano (SA), Italy
| | - Andrea Peluso
- Dipartimento di Chimica e Biologia, Università di Salerno, I-84084, Fisciano (SA), Italy
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23
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Borrelli R, Peluso A. Elementary electron transfer reactions: from basic concepts to recent computational advances. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2013. [DOI: 10.1002/wcms.1147] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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24
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Li J, Wang H, Persson P, Thoss M. Photoinduced electron transfer processes in dye-semiconductor systems with different spacer groups. J Chem Phys 2012; 137:22A529. [DOI: 10.1063/1.4746768] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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