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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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Chen ZH, Wang Y, Xu RX, Yan Y. Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory vs core-system hierarchy construction. J Chem Phys 2023; 158:074102. [PMID: 36813728 DOI: 10.1063/5.0134700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the λ(t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which, in turn, confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for "visualizing" the correlated solvation dynamics.
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Affiliation(s)
- Zi-Hao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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3
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Jakučionis M, Žukas A, Abramavičius D. Inspecting molecular aggregate quadratic vibronic coupling effects using squeezed coherent states. Phys Chem Chem Phys 2023; 25:1705-1716. [PMID: 36562503 DOI: 10.1039/d2cp04212f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
We present a systematic comparison of three quantum mechanical approaches describing excitation dynamics in molecular complexes using the time-dependent variational principle (TDVP) with increasing sophistication trial wavefunctions (ansatze): Davydov D2, squeezed D2 (sqD2) and a numerically exact multiple D2 (mD2) ansatz in order to characterize validity of the sqD2 ansatz. Numerical simulations of molecular aggregate absorption and fluorescence spectra with intra- and intermolecular vibrational modes, including quadratic electronic-vibrational (vibronic) coupling term, which is due to vibrational frequency shift upon pigment excitation are presented. Simulated absorption and fluorescence spectra of a J type molecular dimer with high frequency intramolecular vibrational modes obtained with D2 and sqD2 ansatze match the spectra of mD2 ansatz only in the single pigment model without quadratic vibronic coupling. In general, the use of mD2 ansatz is required to model an accurate dimer and larger aggregate's spectra. For a J dimer aggregate coupled to a low frequency intermolecular phonon bath, absorption and fluorescence spectra are qualitatively similar using all three ansatze. The quadratic vibronic coupling term in both absorption and fluorescence spectra manifests itself as a lineshape peak amplitude redistribution, static frequency shift and an additional shift, which is temperature dependent. Overall the squeezed D2 model does not result in a considerable improvement of the simulation results compared to the simplest Davydov D2 approach.
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Affiliation(s)
- Mantas Jakučionis
- Institute of Chemical Physics, Vilnius University, Sauletekio Ave. 9-III, LT-10222, Vilnius, Lithuania.
| | - Agnius Žukas
- Institute of Chemical Physics, Vilnius University, Sauletekio Ave. 9-III, LT-10222, Vilnius, Lithuania.
| | - Darius Abramavičius
- Institute of Chemical Physics, Vilnius University, Sauletekio Ave. 9-III, LT-10222, Vilnius, Lithuania.
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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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Jakučionis M, Gaižiu Nas I, Šulskus J, Abramavičius D. Simulation of Ab Initio Optical Absorption Spectrum of β-Carotene with Fully Resolved S0 and S2 Vibrational Normal Modes. J Phys Chem A 2022; 126:180-189. [PMID: 34985272 DOI: 10.1021/acs.jpca.1c06115] [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
The electronic absorption spectrum of β-carotene (β-Car) is studied using quantum chemistry and quantum dynamics simulations. Vibrational normal modes were computed in optimized geometries of the electronic ground state S0 and the optically bright excited S2 state using the time-dependent density functional theory. By expressing the S2-state normal modes in terms of the ground-state modes, we find that no one-to-one correspondence between the ground- and excited-state vibrational modes exists. Using the ab initio results, we simulated the β-Car absorption spectrum with all 282 vibrational modes in a model solvent at 300 K using the time-dependent Dirac-Frenkel variational principle and are able to qualitatively reproduce the full absorption line shape. By comparing the 282-mode model with the prominent 2-mode model, widely used to interpret carotenoid experiments, we find that the full 282-mode model better describes the high-frequency progression of carotenoid absorption spectra; hence, vibrational modes become highly mixed during the S0 → S2 optical excitation. The obtained results suggest that electronic energy dissipation is mediated by numerous vibrational modes.
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Affiliation(s)
- Mantas Jakučionis
- Institute of Chemical Physics, Vilnius University, Sauletekio Avenue 9-III, LT-10222 Vilnius, Lithuania
| | - Ignas Gaižiu Nas
- Institute of Chemical Physics, Vilnius University, Sauletekio Avenue 9-III, LT-10222 Vilnius, Lithuania
| | - Juozas Šulskus
- Institute of Chemical Physics, Vilnius University, Sauletekio Avenue 9-III, LT-10222 Vilnius, Lithuania
| | - Darius Abramavičius
- Institute of Chemical Physics, Vilnius University, Sauletekio Avenue 9-III, LT-10222 Vilnius, Lithuania
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Jakučionis M, Žukas A, Abramavicius D. Modeling Molecular J and H Aggregates using Multiple-Davydov D2 Ansatz. Phys Chem Chem Phys 2022; 24:17665-17672. [DOI: 10.1039/d2cp00819j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The linear absorption spectrum of J and H molecular aggregates is studied using the time-dependent Dirac-Frenkel variational principle (TDVP) with the multi-Davydov D2 (mD2) trial wavefunction (Ansatz). Both the electronic...
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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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Chen ZH, Wang Y, Xu RX, Yan Y. Quantum dissipation with nonlinear environment couplings: Stochastic fields dressed dissipaton equation of motion approach. J Chem Phys 2021; 155:174111. [PMID: 34742182 DOI: 10.1063/5.0067880] [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
Accurate and efficient simulation on quantum dissipation with nonlinear environment couplings remains a challenging task nowadays. In this work, we propose to incorporate the stochastic fields, which resolve just the nonlinear environment coupling terms, into the dissipaton-equation-of-motion (DEOM) construction. The stochastic fields are introduced via the Hubbard-Stratonovich transformation. After the transformation, the resulted stochastic-fields-dressed (SFD) total Hamiltonian contains only linear environment coupling terms. On the basis of that, SFD-DEOM can then be constructed. The resultant SFD-DEOM, together with the ensemble average over the stochastic fields, constitutes an exact and nonperturbative approach to quantum dissipation under nonlinear environment couplings. It is also of relatively high efficiency and stability due to the fact that only nonlinear environment coupling terms are dealt with stochastic fields, while linear couplings are still treated as the usual DEOM. Numerical performance and demonstrations are presented with a two-state model system.
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Affiliation(s)
- Zi-Hao Chen
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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Bubilaitis V, Rancova O, Abramavicius D. Vibration-mediated energy transport in bacterial reaction center: Simulation study. J Chem Phys 2021; 154:214115. [PMID: 34240965 DOI: 10.1063/5.0048815] [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
Exciton energy relaxation in a bacterial Reaction Center (bRC) pigment-protein aggregate presumably involves emission of high energy vibrational quanta to cover wide energy gaps between excitons. Here, we assess this hypothesis utilizing vibronic two-particle theory in modeling of the excitation relaxation process in bRC. Specific high frequency molecular vibrational modes are included explicitly one at a time in order to check which high frequency vibrations are involved in the excitation relaxation process. The low frequency bath modes are treated perturbatively within Redfield relaxation theory. The analysis of the population relaxation rate data indicates energy flow pathways in bRC and suggests that specific vibrations may be responsible for the excitation relaxation process.
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Affiliation(s)
- Vytautas Bubilaitis
- Institute of Chemical Physics, Vilnius University, Sauletekio al. 9-III, Vilnius 10222, Lithuania
| | - Olga Rancova
- Institute of Chemical Physics, Vilnius University, Sauletekio al. 9-III, Vilnius 10222, Lithuania
| | - Darius Abramavicius
- Institute of Chemical Physics, Vilnius University, Sauletekio al. 9-III, Vilnius 10222, Lithuania
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Jakučionis M, Mancal T, Abramavičius D. Modeling irreversible molecular internal conversion using the time-dependent variational approach with sD2 ansatz. Phys Chem Chem Phys 2020; 22:8952-8962. [DOI: 10.1039/d0cp01092h] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A model of irreversible molecular internal conversion dynamics due to molecular thermal energy dissipation to the bath is presented.
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Affiliation(s)
- Mantas Jakučionis
- Institute of Chemical Physics
- Vilnius University
- LT-10222 Vilnius
- Lithuania
| | - Tomas Mancal
- Faculty of Mathematics and Physics
- Charles University
- 121 16 Prague
- Czech Republic
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Ren J, Shuai Z, Kin-Lic Chan G. Time-Dependent Density Matrix Renormalization Group Algorithms for Nearly Exact Absorption and Fluorescence Spectra of Molecular Aggregates at Both Zero and Finite Temperature. J Chem Theory Comput 2018; 14:5027-5039. [DOI: 10.1021/acs.jctc.8b00628] [Citation(s) in RCA: 61] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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Xu RX, Liu Y, Zhang HD, Yan Y. Theories of quantum dissipation and nonlinear coupling bath descriptors. J Chem Phys 2018; 148:114103. [PMID: 29566509 DOI: 10.1063/1.4991779] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.
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Affiliation(s)
- Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yang Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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