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Gao S, Wang YC, Zhao Y. Phonon-mediated ultrafast energy- and momentum-resolved hole dynamics in monolayer black phosphorus. J Chem Phys 2024; 160:124112. [PMID: 38530009 DOI: 10.1063/5.0201776] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 03/13/2024] [Indexed: 03/27/2024] Open
Abstract
The electron-phonon scattering plays a crucial role in determining the electronic, transport, optical, and thermal properties of materials. Here, we employ a non-Markovian stochastic Schrödinger equation (NMSSE) in momentum space, together with ab initio calculations for energy bands and electron-phonon interactions, to reveal the phonon-mediated ultrafast hole relaxation dynamics in the valence bands of monolayer black phosphorus. Our numerical simulations show that the hole can initially remain in the high-energy valence bands for more than 100 fs due to the weak interband scatterings, and its energy relaxation follows single-exponential decay toward the valence band maximum after scattering into low-energy valence bands. The total relaxation time of holes is much longer than that of electrons in the conduction band. This suggests that harnessing the excess energy of holes may be more effective than that of electrons. Compared to the semiclassical Boltzmann equation based on a hopping model, the NMSSE highlights the persistence of quantum coherence for a long time, which significantly impacts the relaxation dynamics. These findings complement the understanding of hot carrier relaxation dynamics in two-dimensional materials and may offer novel insights into harnessing hole energy in photocatalysis.
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Affiliation(s)
- Siyuan Gao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iCHEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - Yu-Chen Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iCHEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iCHEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
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2
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Lian M, Wang YC, Zhao Y. Phonon-Mediated Ultrafast Electron Relaxation Dynamics in Monolayer Black Phosphorus: Instantaneous Coherent Delocalization. J Phys Chem Lett 2023; 14:6990-6997. [PMID: 37523252 DOI: 10.1021/acs.jpclett.3c01541] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/02/2023]
Abstract
Understanding carrier relaxation processes in semiconductors is crucial for designing high-performance optoelectronic and photocatalytic devices. Recent transient spectroscopic experiments on two-dimensional materials have revealed ultrafast optical responses within several tens of femtoseconds, which are usually ascribed to electron-electron scattering. Here, by conducting quantum dynamics simulations for monolayer black phosphorus, we show that electron-phonon scattering also profoundly influences the early stage of carrier dynamics. The photogenerated electron generally undergoes phonon-mediated instantaneous coherent delocalization in reciprocal space, accompanied by an entropy-driven sharp change in electronic energy. The distribution of the density of states controls the energy exchange between the electron and lattice vibrations. The phonon-induced quantum coherence significantly suspends the energy relaxation time, which is very beneficial for harvesting electron excess energy. These findings offer novel insights into the ultrafast carrier dynamics and energy flow in two-dimensional materials and may prompt new opportunities for regulation of carrier dynamic behaviors.
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Affiliation(s)
- Man Lian
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Yu-Chen Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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3
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Feng S, Zhao Y, Liang W. Substituent Effect on Vibrationally Resolved Absorption Spectra and Exciton Dynamics of Dipyrrolonaphthyridinedione Aggregates. J Phys Chem A 2022; 126:6395-6406. [PMID: 36073236 DOI: 10.1021/acs.jpca.2c03907] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Dipyrrolonaphthyridinedione (DPND) thin films exhibit interesting photophysical properties and singlet fission (SF) processes. A recent experimental work found that the alkyl substitution in the DPND skeleton has the remarkable influence on the characteristics of electronic absorption spectra and SF rates. Here, we theoretically elucidate the microscopic mechanism of the substituent effect on the optical properties and exciton dynamics of materials by combining the electronic structure calculations and the quantum dynamics simulations. The results show that the alkyl substituent has a minor effect on the single molecular properties but dramatically changes those of DPND aggregates via varying the intermolecular interactions. The aggregates of DPND with and without alkyl side chains exhibit the more likely characters of H-type aggregations. In the former (DPND6), the weak degree of mixing of intramolecular localized excited (LE) states and intermolecular charge transfer (CT) states makes the low-energy absorption band possess the predominant optical absorption, while in the latter (DPND), the CT and LE states are close in energy, together with their strong interaction, resulting in the substantial state-mixing, so that its two low-energy absorption bands have nearly equal oscillator strengths and a wide energy spacing of more than 0.5 eV. The simulation of exciton dynamics elucidates that the photoinitiated states in both aggregates cannot generate the free charge carrier because of the lack of enough driving forces. However, the population exchanges between LE and CT states in DPND aggregates are much faster than in DPND6 aggregates, indicating the different SF behaviors, consistent with the experimental observation.
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Affiliation(s)
- Shishi Feng
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
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4
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Si Q, Lian M, Zhao Y. Photo‐induced energy and charge transfer dynamics in Y6 dimers. J CHIN CHEM SOC-TAIP 2022. [DOI: 10.1002/jccs.202200288] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Qinqin Si
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering Xiamen University Xiamen PR China
| | - Man Lian
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering Xiamen University Xiamen PR China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering Xiamen University Xiamen PR China
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5
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Feng S, Wang YC, Liang W, Zhao Y. Vibrationally resolved absorption spectra and ultrafast exciton dynamics in α-phase and β-phase zinc phthalocyanine aggregates. Phys Chem Chem Phys 2022; 24:2974-2987. [PMID: 35043813 DOI: 10.1039/d1cp03600a] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The vibrationally resolved absorption spectra and ultrafast exciton dynamics in α-phase and β-phase zinc phthalocyanine (ZnPc) aggregates are theoretically investigated using a non-Markovian stochastic Schrödinger equation combined with first-principles calculations. It is found that although similar double-peak structures arise in the Q-band region of the absorption spectra in both phases, these peaks are different in nature and exhibit distinct types of behavior with respect to the aggregation length. The analysis on the basis of an effective two-state model indicates that the two absorption peaks in the α phase are from mixing between the charge-transfer (CT) state and the bright Frenkel exciton (FE) state. By contrast, in the β-phase, the low-energy peak is solely contributed by a low-lying bright FE state, whereas the high-energy peak originates from the interplay between the CT state and another high-lying bright FE state. For the relaxation processes right after photoexcitation from the Q-band region, it is found that within the first dozens of femtoseconds the ZnPc aggregates of both phases tend to temporarily fall into some intermediate states where the population distribution and average electronic energy do not obviously evolve. In addition, it is found that the optical transition of the low-lying bright FE state in the β phase is not favorable for the formation of bound CT states due to the absence of enough driving forces.
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Affiliation(s)
- Shishi Feng
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, People's Republic of China.
| | - Yu-Chen Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, People's Republic of China.
| | - WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, People's Republic of China.
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, People's Republic of China.
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6
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Feng S, Wang YC, Liang W, Zhao Y. Vibrationally Resolved Absorption Spectra and Exciton Dynamics in Zinc Phthalocyanine Aggregates: Effects of Aggregation Lengths and Remote Exciton Transfer. J Phys Chem A 2021; 125:2932-2943. [PMID: 33822626 DOI: 10.1021/acs.jpca.1c01271] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The vibrationally resolved absorption spectra and exciton dynamics in the α-zinc phthalocyanine aggregates are theoretically investigated by using a non-Markovian stochastic Schrödinger equation. The model Hamiltonian adopted for spectral and dynamic simulations explicitly includes the couplings for both nearest-neighbor and remote exciton transfer, and it is parametrized from first-principles calculations. The results indicate that aggregation lengths and remote exciton transfer significantly influence the relative energy alignment between delocalized Frenkel exciton (FE) and charge transfer (CT) states, which in turn strongly affects the relative intensities of the two absorption peaks in the Q-band region. Analytical formulas are derived to establish quantitative structure-spectra relationships in aggregates, and they offer simple patterns to extract electronic-state properties directly from absorption spectra. The dynamics simulations reveal that the light absorption can directly generate mixed states with both FE and CT features, but it is hard for the photoexcitation from the Q-band region to generate free carriers due to the high energies of charge-separated states.
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Affiliation(s)
- Shishi Feng
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - Yu-Chen Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
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7
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Wang YC, Zhao Y. The hierarchical stochastic schrödinger equations: Theory and applications. CHINESE J CHEM PHYS 2020. [DOI: 10.1063/1674-0068/cjcp2009165] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Yu-Chen Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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8
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Feng S, Wang YC, Ke Y, Liang W, Zhao Y. Effect of charge-transfer states on the vibrationally resolved absorption spectra and exciton dynamics in ZnPc aggregates: Simulations from a non-Makovian stochastic Schrödinger equation. J Chem Phys 2020; 153:034116. [DOI: 10.1063/5.0013935] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Shishi Feng
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yu-Chen Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yaling Ke
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - WanZhen Liang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
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Nematiaram T, Troisi A. Modeling charge transport in high-mobility molecular semiconductors: Balancing electronic structure and quantum dynamics methods with the help of experiments. J Chem Phys 2020; 152:190902. [DOI: 10.1063/5.0008357] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Affiliation(s)
- Tahereh Nematiaram
- Department of Chemistry and Materials Innovation Factory, University of Liverpool, Liverpool L69 7ZD, United Kingdom
| | - Alessandro Troisi
- Department of Chemistry and Materials Innovation Factory, University of Liverpool, Liverpool L69 7ZD, United Kingdom
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10
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Yan YA, Wang H, Shao J. A unified view of hierarchy approach and formula of differentiation. J Chem Phys 2019; 151:164110. [PMID: 31675858 DOI: 10.1063/1.5126341] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
The stochastic differential equation is a powerful tool for describing the dynamics of a dissipative system in which noise characterizes the influence of the environment. For the Ornstein-Uhlenbeck noise, both the formula of differentiation and the hierarchy approach provide efficient numerical simulations, with the stochastic differential equation transformed into a set of coupled, linear ordinary differential equations. We show that while these two deterministic schemes result in different sets of equations, they can be regarded as two representations of an underlying linear-dynamics. Moreover, by manipulating the involved Ornstein-Uhlenbeck noise, we propose a unified algorithm that may reduce to the hierarchy approach or the formula of differentiation in different limits. We further analyze the numerical performance of this algorithm and find that the hierarchy approach appears to be more efficient for our numerical model studies.
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Affiliation(s)
- Yun-An Yan
- School of Physics and Optoelectronic Engineering, Ludong University, Shandong 264025, China
| | - Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
| | - Jiushu Shao
- College of Chemistry and Center for Advanced Quantum Studies, Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, Beijing Normal University, Beijing 100875, China
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Lian M, Wang YC, Ke Y, Zhao Y. Non-Markovian stochastic Schrödinger equation in k-space toward the calculation of carrier dynamics in organic semiconductors. J Chem Phys 2019; 151:044115. [DOI: 10.1063/1.5096219] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Man Lian
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Yu-Chen Wang
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Yaling Ke
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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12
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Wang Y, Ke Y, Zhao Y. The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1375] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Yu‐Chen Wang
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
| | - Yaling Ke
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
| | - Yi Zhao
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
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13
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Ke Y, Zhao Y. Calculations of coherent two-dimensional electronic spectra using forward and backward stochastic wavefunctions. J Chem Phys 2018; 149:014104. [DOI: 10.1063/1.5037684] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Affiliation(s)
- Yaling Ke
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
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14
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Ke Y, Zhao Y. Quantum dynamics simulations in an ultraslow bath using hierarchy of stochastic Schrödinger equations. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1430385] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Yaling Ke
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, P. R. China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, P. R. China
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