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Zhao Y. The hierarchy of Davydov's Ansätze: From guesswork to numerically "exact" many-body wave functions. J Chem Phys 2023; 158:080901. [PMID: 36859105 DOI: 10.1063/5.0140002] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
This Perspective presents an overview of the development of the hierarchy of Davydov's Ansätze and a few of their applications in many-body problems in computational chemical physics. Davydov's solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansätze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov's Ansätze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrödinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov's Ansätze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states.
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Affiliation(s)
- Yang Zhao
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
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2
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Zeng J, Yao Y. Variational Squeezed Davydov Ansatz for Realistic Chemical Systems with Nonlinear Vibronic Coupling. J Chem Theory Comput 2022; 18:1255-1263. [PMID: 35100509 DOI: 10.1021/acs.jctc.1c00859] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Chemical systems normally possess strong nonlinear vibronic couplings at both zero and finite temperature. For the lowest-order quadratic couplings, here, we introduce a squeezing operator into a variational coherent-state-based method, Davydov ansatz, to simulate the quantum dynamics and the respective spectroscopy. Two molecular systems, pyrazine and the 2-pyridone dimer, are taken as calculated model systems, both of which involve nontrivial quadratic vibronic couplings in high- and low-frequency regions, respectively. Upon a comparison with the benchmarks, the method manifests its advantage for nonlinear couplings. The squeezed bases are also proven to be applicable for the finite temperature by adapting with the thermofield dynamics.
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Affiliation(s)
- Jiarui Zeng
- Department of Physics, South China University of Technology, Guangzhou 510640, China
| | - Yao Yao
- Department of Physics, South China University of Technology, Guangzhou 510640, China.,State Key Laboratory of Luminescent Materials and Devices, South China University of Technology, Guangzhou 510640, China
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3
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Zhao Y, Sun K, Chen L, Gelin M. The hierarchy of Davydov's Ansätze and its applications. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1589] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Yang Zhao
- Division of Materials Science Nanyang Technological University Singapore Singapore
| | - Kewei Sun
- Division of Materials Science Nanyang Technological University Singapore Singapore
- School of Science, Hanghzhou Dianzi University Hangzhou China
| | - Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems Dresden Germany
| | - Maxim Gelin
- School of Science, Hanghzhou Dianzi University Hangzhou China
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Borrelli R. Density matrix dynamics in twin-formulation: An efficient methodology based on tensor-train representation of reduced equations of motion. J Chem Phys 2019; 150:234102. [PMID: 31228887 DOI: 10.1063/1.5099416] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
The twin-formulation of quantum statistical mechanics is employed to describe a new methodology for the solution of the equations of motion of the reduced density matrix in their hierarchical formulation. It is shown that the introduction of tilde operators and of their algebra in the dual space greatly simplifies the application of numerical techniques for the propagation of the density matrix. The application of tensor-train representation of a vector to solve complex quantum dynamical problems within the framework of the twin-formulation is discussed. Next, applications of the hierarchical equations of motion to a dissipative polaron model are presented showing the validity and accuracy of the new approach.
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5
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Landi A, Borrelli R, Capobianco A, Peluso A. Transient and Enduring Electronic Resonances Drive Coherent Long Distance Charge Transport in Molecular Wires. J Phys Chem Lett 2019; 10:1845-1851. [PMID: 30939015 DOI: 10.1021/acs.jpclett.9b00650] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
It is shown that the yields of oxidative damage observed in double-stranded DNA oligomers consisting of two guanines separated by adenine-thymine (A:T) n bridges of various lengths are reliably accounted for by a multistep mechanism, in which transient and nontransient electronic resonances induce charge transport and solvent relaxation stabilizes the hole transfer products. The proposed multistep mechanism leads to results in excellent agreement with the observed yield ratios for both the short and the long distance regime; the almost distance independence of yield ratios for longer bridges ( n ≥ 3) is the consequence of the significant energy decrease of the electronic levels of the bridge, which, as the bridge length increases, become quasi-degenerate with those of the acceptor and donor groups (enduring resonance). These results provide significant guidelines for the design of novel DNA sequences to be employed in organic electronics.
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Affiliation(s)
- Alessandro Landi
- Dipartimento di Chimica e Biologia , Università di Salerno , I-84084 Fisciano , Salerno , Italy
| | - Raffaele Borrelli
- Department of Agricultural, Forestry and Food Science , University of Torino , Via Leonardo da Vinci 44 , I-10095 Grugliasco , Italy
| | - Amedeo Capobianco
- Dipartimento di Chimica e Biologia , Università di Salerno , I-84084 Fisciano , Salerno , Italy
| | - Andrea Peluso
- Dipartimento di Chimica e Biologia , Università di Salerno , I-84084 Fisciano , Salerno , Italy
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6
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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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Wang L, Fujihashi Y, Chen L, Zhao Y. Finite-temperature time-dependent variation with multiple Davydov states. J Chem Phys 2018; 146:124127. [PMID: 28388128 DOI: 10.1063/1.4979017] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.
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Affiliation(s)
- Lu Wang
- Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Yuta Fujihashi
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
| | - Lipeng Chen
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
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9
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Chen L, Zhao Y. Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach. J Chem Phys 2018; 147:214102. [PMID: 29221386 DOI: 10.1063/1.5000823] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Combining the multiple Davydov D2 Ansatz with the method of thermo-field dynamics, we study finite temperature dynamics of a Holstein polaron on a lattice. It has been demonstrated, using the hierarchy equations of motion method as a benchmark, that our approach provides an efficient, robust description of finite temperature dynamics of the Holstein polaron in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. The method of thermo-field dynamics handles temperature effects in the Hilbert space with key numerical advantages over other treatments of finite-temperature dynamics based on quantum master equations in the Liouville space or wave function propagation with Monte Carlo importance sampling. While for weak to moderate diagonal coupling temperature increases inhibit polaron mobility, it is found that off-diagonal coupling induces phonon-assisted transport that dominates at high temperatures. Results on the mean square displacements show that band-like transport features dominate the diagonal coupling cases, and there exists a crossover from band-like to hopping transport with increasing temperature when including off-diagonal coupling. As a proof of concept, our theory provides a unified treatment of coherent and incoherent transport in molecular crystals and is applicable to any temperature.
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Affiliation(s)
- Lipeng Chen
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
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Landi A, Borrelli R, Capobianco A, Velardo A, Peluso A. Hole Hopping Rates in Organic Semiconductors: A Second-Order Cumulant Approach. J Chem Theory Comput 2018. [PMID: 29345937 DOI: 10.1021/acs.jpcc.8b08126] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/18/2023]
Abstract
Second-order cumulant expansion of the time dependent reduced density matrix has been employed to evaluate hole hopping rates in pentacene, tetracene, picene, and rubrene homodimers. The cumulant expansion is a full quantum mechanical approach, which enables the use of the whole set of nuclear coordinates in computations and the inclusion of both the effects of the equilibrium position displacements and of normal mode mixing upon hole transfer. The time dependent populations predicted by cumulant approach are in good agreement with those obtained by numerical solution of time dependent Schrödinger equation, even for ultrafast processes, where the Fermi Golden Rule fails.
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Affiliation(s)
- Alessandro Landi
- Dipartimento di Chimica e Biologia "A. Zambelli" , Università di Salerno , Via Giovanni Paolo II , I-84084 Fisciano (SA) , Italy
| | - Raffaele Borrelli
- Department of Agricultural, Forestry and Food Science , University of Torino , I-10195 Grugliasco , Italy
| | - Amedeo Capobianco
- Dipartimento di Chimica e Biologia "A. Zambelli" , Università di Salerno , Via Giovanni Paolo II , I-84084 Fisciano (SA) , Italy
| | - Amalia Velardo
- Dipartimento di Chimica e Biologia "A. Zambelli" , Università di Salerno , Via Giovanni Paolo II , I-84084 Fisciano (SA) , Italy
| | - Andrea Peluso
- Dipartimento di Chimica e Biologia "A. Zambelli" , Università di Salerno , Via Giovanni Paolo II , I-84084 Fisciano (SA) , Italy
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Comparison of the results of a mean-field mixed quantum/classical method with full quantum predictions for nonadiabatic dynamics: application to the $$\pi \pi ^*/n\pi ^*$$ π π ∗ / n π ∗ decay of thymine. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2218-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
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12
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Landi A, Borrelli R, Capobianco A, Velardo A, Peluso A. Hole Hopping Rates in Organic Semiconductors: A Second-Order Cumulant Approach. J Chem Theory Comput 2018; 14:1594-1601. [DOI: 10.1021/acs.jctc.7b00858] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Alessandro Landi
- Dipartimento di Chimica e Biologia “A. Zambelli”, Università di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy
| | - Raffaele Borrelli
- Department of Agricultural, Forestry and Food Science, University of Torino, I-10195 Grugliasco, Italy
| | - Amedeo Capobianco
- Dipartimento di Chimica e Biologia “A. Zambelli”, Università di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy
| | - Amalia Velardo
- Dipartimento di Chimica e Biologia “A. Zambelli”, Università di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy
| | - Andrea Peluso
- Dipartimento di Chimica e Biologia “A. Zambelli”, Università di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy
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13
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Chen L, Borrelli R, Zhao Y. Dynamics of Coupled Electron–Boson Systems with the Multiple Davydov D1 Ansatz and the Generalized Coherent State. J Phys Chem A 2017; 121:8757-8770. [DOI: 10.1021/acs.jpca.7b07069] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lipeng Chen
- Division
of Materials Science, Nanyang Technological University, 639798, Singapore
| | - Raffaele Borrelli
- Department
of Agricultural, Forestry and Food Science, Universitá di Torino, I-10095 Grugliasco, Turin, Italy
| | - Yang Zhao
- Division
of Materials Science, Nanyang Technological University, 639798, Singapore
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14
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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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15
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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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16
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Borrelli R, Gelin MF. The Generalized Coherent State ansatz: Application to quantum electron-vibrational dynamics. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.05.013] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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