1
|
Zhou L, Gao X, Shuai Z. A stochastic Schrödinger equation and matrix product state approach to carrier transport in organic semiconductors with nonlocal electron-phonon interaction. J Chem Phys 2024; 161:084118. [PMID: 39212211 DOI: 10.1063/5.0221143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2024] [Accepted: 08/12/2024] [Indexed: 09/04/2024] Open
Abstract
Evaluation of the charge transport property of organic semiconductors requires exact quantum dynamics simulation of large systems. We present a numerically nearly exact approach to investigate carrier transport dynamics in organic semiconductors by extending the non-Markovian stochastic Schrödinger equation with complex frequency modes to a forward-backward scheme and by solving it using the matrix product state (MPS) approach. By utilizing the forward-backward formalism for noise generation, the bath correlation function can be effectively treated as a temperature-independent imaginary part, enabling a more accurate decomposition with fewer complex frequency modes. Using this approach, we study the carrier transport and mobility in the one-dimensional Peierls model, where the nonlocal electron-phonon interaction is taken into account. The reliability of this approach was validated by comparing carrier diffusion motion with those obtained from the hierarchical equations of motion method across various parameter regimes of the phonon bath. The efficiency was demonstrated by the modest virtual bond dimensions of MPS and the low scaling of the computational time with the system size.
Collapse
Affiliation(s)
- Liqi Zhou
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, China
| | - Xing Gao
- School of Materials, Sun Yat-sen University, Shenzhen, Guangdong 518107, China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, China
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong 518172, China
| |
Collapse
|
2
|
Huang C, Bai S, Shi Q. Simulation of the Pump-Probe Spectra and Excitation Energy Relaxation of the B850 Band of the LH2 Complex in Purple Bacteria. J Phys Chem B 2024; 128:7467-7475. [PMID: 39059418 DOI: 10.1021/acs.jpcb.4c02059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2024]
Abstract
Ultrafast spectroscopic techniques have been vital in studying excitation energy transfer (EET) in photosynthetic light harvesting complexes. In this paper, we simulate the pump-probe spectra of the B850 band of the light harvesting complex 2 (LH2) of purple bacteria, by using the hierarchical equation of motion method and the optical response function approach. The ground state bleach, stimulated emission, and excited state absorption components of the pump-probe spectra are analyzed in detail. The laser pulse-induced population dynamics are also simulated to help understand the main features of the pump-probe spectra and the EET process. It is shown that the excitation energy relaxation is an ultrafast process with multiple time scales. The first 40 fs of the pump-probe spectra is dominated by the relaxation of the k = ±1 states to both the k = 0 and higher energy states. Dynamics on a longer time scale around 200 fs reflects the relaxation of higher energy states to the k = 0 state.
Collapse
Affiliation(s)
- Chenghong Huang
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun,Beijing 100190, China
- China University of Chinese Academy of Sciences, Beijing 100049, China
| | - Shuming Bai
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun,Beijing 100190, China
- China University of Chinese Academy of Sciences, Beijing 100049, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun,Beijing 100190, China
- China University of Chinese Academy of Sciences, Beijing 100049, China
| |
Collapse
|
3
|
Citty B, Lynd JK, Gera T, Varvelo L, Raccah DIGB. MesoHOPS: Size-invariant scaling calculations of multi-excitation open quantum systems. J Chem Phys 2024; 160:144118. [PMID: 38619062 DOI: 10.1063/5.0197825] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2024] [Accepted: 03/11/2024] [Indexed: 04/16/2024] Open
Abstract
The photoexcitation dynamics of molecular materials on the 10-100 nm length scale depend on complex interactions between electronic and vibrational degrees of freedom, rendering exact calculations difficult or intractable. The adaptive Hierarchy of Pure States (adHOPS) is a formally exact method that leverages the locality imposed by interactions between thermal environments and electronic excitations to achieve size-invariant scaling calculations for single-excitation processes in systems described by a Frenkel-Holstein Hamiltonian. Here, we extend adHOPS to account for arbitrary couplings between thermal environments and vertical excitation energies, enabling formally exact, size-invariant calculations that involve multiple excitations or states with shared thermal environments. In addition, we introduce a low-temperature correction and an effective integration of the noise to reduce the computational expense of including ultrafast vibrational relaxation in Hierarchy of Pure States (HOPS) simulations. We present these advances in the latest version of the open-source MesoHOPS library and use MesoHOPS to characterize charge separation at a one-dimensional organic heterojunction when both the electron and hole are mobile.
Collapse
Affiliation(s)
- Brian Citty
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| | - Jacob K Lynd
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| | - Tarun Gera
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| | - Leonel Varvelo
- Department of Chemistry, Southern Methodist University, PO Box 750314 Dallas, Texas 75205, USA
| | - Doran I G B Raccah
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| |
Collapse
|
4
|
Boettcher V, Hartmann R, Beyer K, Strunz WT. Dynamics of a strongly coupled quantum heat engine-Computing bath observables from the hierarchy of pure states. J Chem Phys 2024; 160:094108. [PMID: 38436445 DOI: 10.1063/5.0192075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 02/07/2024] [Indexed: 03/05/2024] Open
Abstract
We present a fully quantum dynamical treatment of a quantum heat engine and its baths based on the Hierarchy of Pure States (HOPS), an exact and general method for open quantum system dynamics. We show how the change of the bath energy and the interaction energy can be determined within HOPS for arbitrary coupling strength and smooth time dependence of the modulation protocol. The dynamics of all energetic contributions during the operation can be carefully examined both in its initial transient phase and, also later, in its periodic steady state. A quantum Otto engine with a qubit as an inherently nonlinear work medium is studied in a regime where the energy associated with the interaction Hamiltonian plays an important role for the global energy balance and, thus, must not be neglected when calculating its power and efficiency. We confirm that the work required to drive the coupling with the baths sensitively depends on the speed of the modulation protocol. Remarkably, departing from the conventional scheme of well-separated phases by allowing for temporal overlap, we discover that one can even gain energy from the modulation of bath interactions. We visualize these various work contributions using the analog of state change diagrams of thermodynamic cycles. We offer a concise, full presentation of HOPS with its extension to bath observables, as it serves as a universal tool for the numerically exact description of general quantum dynamical (thermodynamic) scenarios far from the weak-coupling limit.
Collapse
Affiliation(s)
- Valentin Boettcher
- Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany
- Department of Physics, McGill University, Montréal, Québec H3A 2T8, Canada
| | - Richard Hartmann
- Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany
| | - Konstantin Beyer
- Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany
- Department of Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA
| | - Walter T Strunz
- Institute of Theoretical Physics, TUD Dresden University of Technology, 01062 Dresden, Germany
| |
Collapse
|
5
|
Baiz C, Bredenbeck J, Cho M, Jansen T, Krummel A, Roberts S. Celebrating 25 years of 2D IR spectroscopy. J Chem Phys 2024; 160:010401. [PMID: 38165102 DOI: 10.1063/5.0190809] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 12/12/2023] [Indexed: 01/03/2024] Open
Affiliation(s)
- Carlos Baiz
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| | - Jens Bredenbeck
- Institute of Biophysics, Department of Physics, Goethe-University, Max von Laue-Str. 1, 60438 Frankfurt am Main, Germany
| | - Minhaeng Cho
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, Republic of Korea
- Department of Chemistry, Korea University, Seoul 02841, Republic of Korea
| | - Thomas Jansen
- University of Groningen, Zernike Institute for Advanced Materials, Nijenborgh 4, 6 9747 AG Groningen, The Netherlands
| | - Amber Krummel
- Colorado State University, Department of Chemistry, Fort Collins, Colorado 80523, USA
| | - Sean Roberts
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| |
Collapse
|
6
|
Gera T, Chen L, Eisfeld A, Reimers JR, Taffet EJ, Raccah DIGB. Simulating optical linear absorption for mesoscale molecular aggregates: An adaptive hierarchy of pure states approach. J Chem Phys 2023; 158:2887556. [PMID: 37125709 DOI: 10.1063/5.0141882] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2023] [Accepted: 03/07/2023] [Indexed: 05/02/2023] Open
Abstract
In this paper, we present dyadic adaptive HOPS (DadHOPS), a new method for calculating linear absorption spectra for large molecular aggregates. This method combines the adaptive HOPS (adHOPS) framework, which uses locality to improve computational scaling, with the dyadic HOPS method previously developed to calculate linear and nonlinear spectroscopic signals. To construct a local representation of dyadic HOPS, we introduce an initial state decomposition that reconstructs the linear absorption spectra from a sum over locally excited initial conditions. We demonstrate the sum over initial conditions can be efficiently Monte Carlo sampled and that the corresponding calculations achieve size-invariant [i.e., O(1)] scaling for sufficiently large aggregates while trivially incorporating static disorder in the Hamiltonian. We present calculations on the photosystem I core complex to explore the behavior of the initial state decomposition in complex molecular aggregates as well as proof-of-concept DadHOPS calculations on an artificial molecular aggregate inspired by perylene bis-imide to demonstrate the size-invariance of the method.
Collapse
Affiliation(s)
- Tarun Gera
- Department of Chemistry, Southern Methodist University, P.O. Box, Dallas, Texas 750314, USA
| | - Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, Dresden, Germany
| | - Alexander Eisfeld
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, Dresden, Germany
| | - Jeffrey R Reimers
- International Centre for Quantum and Molecular Structures and the School of Physics, Shanghai University, 200444 Shanghai, China
- School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney NSW 2007, Australia
| | - Elliot J Taffet
- Department of Chemistry, Southern Methodist University, P.O. Box, Dallas, Texas 750314, USA
| | - Doran I G B Raccah
- Department of Chemistry, Southern Methodist University, P.O. Box, Dallas, Texas 750314, USA
| |
Collapse
|