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Guan W, Bao P, Peng J, Lan Z, Shi Q. mpsqd: A matrix product state based Python package to simulate closed and open system quantum dynamics. J Chem Phys 2024; 161:122501. [PMID: 39324531 DOI: 10.1063/5.0226214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2024] [Accepted: 09/06/2024] [Indexed: 09/27/2024] Open
Abstract
We introduce a Python package based on matrix product states (MPS) to simulate both the time-dependent Schrödinger equation (TDSE) and the hierarchical equations of motion (HEOM). The wave function in the TDSE or the reduced density operator/auxiliary density operators in the HEOM are represented using MPS. A matrix product operator (MPO) is then constructed to represent the Hamiltonian in the TDSE or the generalized Liouvillian in the HEOM. The fourth-order Runge-Kutta method and the time-dependent variational principle are used to propagate the MPS. Several examples, including the nonadiabatic interconversion dynamics of the pyrazine molecule, excitation energy transfer dynamics in molecular aggregates and photosynthetic light-harvesting complexes, the spin-boson model, a laser driven two-state model, the Holstein model, and charge transport in the Anderson impurity model, are presented to demonstrate the capability of the package.
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Affiliation(s)
- Weizhong Guan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Peng Bao
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Jiawei Peng
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety & MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, China and School of Environment, South China Normal University, Guangzhou 510006, China
- School of Chemistry, South China Normal University, Guangzhou 510006, China
| | - Zhenggang Lan
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety & MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, China and School of Environment, South China Normal University, Guangzhou 510006, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
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2
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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.
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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
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3
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Wang YS, Zhong Manis JX, Rohan MC, Orlando TM, Kretchmer JS. Modeling Intermolecular Coulombic Decay with Non-Hermitian Real-Time Time-Dependent Density Functional Theory. J Phys Chem Lett 2024; 15:7806-7813. [PMID: 39052307 PMCID: PMC11299181 DOI: 10.1021/acs.jpclett.4c01146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2024] [Revised: 06/24/2024] [Accepted: 07/01/2024] [Indexed: 07/27/2024]
Abstract
In this work, we investigate the capability of using real-time time-dependent density functional theory (RT-TDDFT) in conjunction with a complex absorbing potential (CAP) to simulate the intermolecular Coulombic decay (ICD) processes following the ionization of an inner-valence electron. We examine the ICD dynamics in a series of noncovalent bonded dimer systems, including hydrogen-bonded and purely van der Waals (VdW)-bonded systems. In comparison to previous work, we show that RT-TDDFT simulations with a CAP correctly capture the ICD phenomenon in systems exhibiting a stronger binding energy. The calculated time scales for ICD of the studied systems are in the range of 5-50 fs, in agreement with previous studies. However, there is a breakdown in the accuracy of the methodology for the pure VdW-bonded systems. Overall, the presented RT-TDDFT/CAP methodology provides a powerful tool for differentiating between competing electronic relaxation pathways following inner-valence or core ionization without necessitating any a priori assumptions.
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Affiliation(s)
- Yi-Siang Wang
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - James X. Zhong Manis
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Matthew C. Rohan
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Thomas M. Orlando
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Joshua S. Kretchmer
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
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4
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Li T, Yan Y, Shi Q. Is there a finite mobility for the one vibrational mode Holstein model? Implications from real time simulations. J Chem Phys 2024; 160:111102. [PMID: 38501468 DOI: 10.1063/5.0198107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2024] [Accepted: 03/02/2024] [Indexed: 03/20/2024] Open
Abstract
The question of whether there exists a finite mobility in the standard Holstein model with one vibrational mode on each site remains unclear. In this Communication, we approach this problem by employing the hierarchical equation of motion method to simulate model systems where the vibrational modes are dissipative. It is found that, as the friction becomes smaller, the charge carrier mobility increases significantly and a friction-free limit cannot be obtained. The current autocorrelation functions are also calculated for the friction-free Holstein model, and converged results cannot be obtained with an increase in the number of sites. Based on these observations, we conclude that a finite mobility cannot be defined for the standard Holstein model in the parameter regime explored in this work.
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Affiliation(s)
- Tianchu Li
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, 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, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
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5
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Liu Z, Hu H, Sun X. Multistate Reaction Coordinate Model for Charge and Energy Transfer Dynamics in the Condensed Phase. J Chem Theory Comput 2023; 19:7151-7170. [PMID: 37815937 PMCID: PMC10601487 DOI: 10.1021/acs.jctc.3c00770] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Indexed: 10/12/2023]
Abstract
Constructing multistate model Hamiltonians from all-atom electronic structure calculations and molecular dynamics simulations is crucial for understanding charge and energy transfer dynamics in complex condensed phases. The most popular two-level system model is the spin-boson Hamiltonian, where the nuclear degrees of freedom are represented as shifted normal modes. Recently, we proposed the general multistate nontrivial extension of the spin-boson model, i.e., the multistate harmonic (MSH) model, which is constructed by extending the spatial dimensions of each nuclear mode so as to satisfy the all-atom reorganization energy restrictions for all pairs of electronic states. In this work, we propose the multistate reaction coordinate (MRC) model with a primary reaction coordinate and secondary bath modes as in the Caldeira-Leggett form but in extended spatial dimensions. The MRC model is proven to be equivalent to the MSH model and offers an intuitive physical picture of the nuclear-electronic feedback in nonadiabatic processes such as the inherent trajectory of the reaction coordinate. The reaction coordinate is represented in extended dimensions, carrying the entire reorganization energies and bilinearly coupled to the secondary bath modes. We demonstrate the MRC model construction for photoinduced charge transfer in an organic photovoltaic caroteniod-porphyrin-C60 molecular triad dissolved in tetrahydrofuran as well as excitation energy transfer in a photosynthetic light-harvesting Fenna-Matthews-Olson complex. The MRC model provides an effective and robust platform for investigating quantum dissipative dynamics in complex condensed-phase systems since it allows a consistent description of realistic spectral density, state-dependent system-bath couplings, and heterogeneous environments due to static disorder in reorganization energies.
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Affiliation(s)
- Zengkui Liu
- Division
of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai, 200124, China
- NYU-ECNU
Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China
- Department
of Chemistry, New York University, New York, New York, 10003, United States
| | - Haorui Hu
- Division
of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai, 200124, China
| | - Xiang Sun
- Division
of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai, 200124, China
- NYU-ECNU
Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China
- Department
of Chemistry, New York University, New York, New York, 10003, United States
- Shanghai
Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU Shanghai, 567 West Yangsi Road, Shanghai, 200124, China
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6
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Yang H, Li W, Ren J, Shuai Z. Time-Dependent Density Matrix Renormalization Group Method for Quantum Transport with Phonon Coupling in Molecular Junction. J Chem Theory Comput 2023; 19:6070-6081. [PMID: 37669099 DOI: 10.1021/acs.jctc.3c00340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/06/2023]
Abstract
Quantum transport in molecular junctions has attracted great attention. The charge motion in a molecular junction can cause geometric deformation, leading to strong electron phonon coupling, which was often overlooked. We have formulated a nearly exact method to assess the time-dependent current and occupation number in the molecular junction modeled by the electron-phonon coupled bridge state using the time-dependent density matrix renormalization group (TD-DMRG) method. The oscillation period and amplitude of the current are found to be dependent on the electron phonon coupling strength and energy level alignment with the electrodes. In an attempt to better understand these phenomena, we have devised a new approximation that explains the bistability phenomenon and the behavior of steady currents in the strong electron-phonon coupling regime. Comparisons have been made with the multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) method and the analytical result in the purely electronic limit. Furthermore, we explore the entropy of different orderings, extending to the electron phonon model problems. Regarding finite temperature, the thermal Bogoliubov transformation of both fermions and bosons is used and compared with imaginary time evolution results.
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Affiliation(s)
- Hengrui Yang
- MOE Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Weitang Li
- MOE Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Jiajun Ren
- MOE Key Laboratory of Theoretical and Computational Photochemistry, College of Chemistry, Beijing Normal University, Beijing 100875, 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
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Guangdong 518172, People's Republic of China
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7
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Willson JT, Liu W, Balzer D, Kassal I. Jumping Kinetic Monte Carlo: Fast and Accurate Simulations of Partially Delocalized Charge Transport in Organic Semiconductors. J Phys Chem Lett 2023; 14:3757-3764. [PMID: 37044057 DOI: 10.1021/acs.jpclett.3c00388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Developing devices using disordered organic semiconductors requires accurate and practical models of charge transport. In these materials, charge transport occurs through partially delocalized states in an intermediate regime between localized hopping and delocalized band conduction. Partial delocalization can increase mobilities by orders of magnitude compared to those with conventional hopping, making it important for the design of materials and devices. Although delocalization, disorder, and polaron formation can be described using delocalized kinetic Monte Carlo (dKMC), it is a computationally expensive method. Here, we develop jumping kinetic Monte Carlo (jKMC), a model that approaches the accuracy of dKMC for modest amounts of delocalization (such as those found in disordered organic semiconductors), with a computational cost comparable to that of conventional hopping. jKMC achieves its computational performance by modeling conduction using identical spherical polarons, yielding a simple delocalization correction to the Marcus hopping rate that allows polarons to jump over their nearest neighbors. jKMC can be used in regimes of partial delocalization inaccessible to dKMC to show that modest delocalization can increase mobilities by as much as 2 orders of magnitude.
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Affiliation(s)
- Jacob T Willson
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia
| | - William Liu
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia
| | - Daniel Balzer
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia
| | - Ivan Kassal
- School of Chemistry, University of Sydney, Sydney, NSW 2006, Australia
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8
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Yehorova D, Kretchmer JS. A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems. J Chem Phys 2023; 158:131102. [PMID: 37031109 DOI: 10.1063/5.0146973] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/07/2023] Open
Abstract
In this work, we derive a multi-fragment real-time extension of the projected density matrix embedding theory (pDMET) designed to treat non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static pDMET, the real time pDMET partitions the total system into many fragments; the coupling between each fragment and the rest of the system is treated through a compact representation of the environment in terms of a quantum bath. The real-time pDMET involves simultaneously propagating the wavefunctions for each separate fragment–bath embedding system along with an auxiliary mean-field wavefunction of the total system. The equations of motion are derived by (i) projecting the time-dependent Schrödinger equation in the fragment and bath space associated with each separate fragment and by (ii) enforcing the pDMET matching conditions between the global 1-particle reduced density matrix (1-RDM) obtained from the fragment calculations and the mean-field 1-RDM at all points in time. The accuracy of the method is benchmarked through comparisons to time-dependent density-matrix renormalization group and time-dependent Hartree–Fock (TDHF) theory; the methods were applied to a one- and two-dimensional single-impurity Anderson model and multi-impurity Anderson models with ordered and disordered distributions of the impurities. The results demonstrate a large improvement over TDHF and rapid convergence to the exact dynamics with an increase in fragment size. Our results demonstrate that the real-time pDMET is a promising and flexible method that balances accuracy and efficiency to simulate the non-equilibrium electron dynamics in heterogeneous systems of large size.
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Affiliation(s)
- Dariia Yehorova
- Department of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Joshua S. Kretchmer
- Department of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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9
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Rajpurohit S, Simoni J, Tan LZ. Photo-induced phase-transitions in complex solids. NANOSCALE ADVANCES 2022; 4:4997-5008. [PMID: 36504738 PMCID: PMC9680828 DOI: 10.1039/d2na00481j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
Photo-induced phase-transitions (PIPTs) driven by highly cooperative interactions are of fundamental interest as they offer a way to tune and control material properties on ultrafast timescales. Due to strong correlations and interactions, complex quantum materials host several fascinating PIPTs such as light-induced charge density waves and ferroelectricity and have become a desirable setting for studying these PIPTs. A central issue in this field is the proper understanding of the underlying mechanisms driving the PIPTs. As these PIPTs are highly nonlinear processes and often involve multiple time and length scales, different theoretical approaches are often needed to understand the underlying mechanisms. In this review, we present a brief overview of PIPTs realized in complex materials, followed by a discussion of the available theoretical methods with selected examples of recent progress in understanding of the nonequilibrium pathways of PIPTs.
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Affiliation(s)
| | - Jacopo Simoni
- Molecular Foundry, Lawrence Berkeley National Laboratory USA
| | - Liang Z Tan
- Molecular Foundry, Lawrence Berkeley National Laboratory USA
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Ge Y, Li W, Ren J, Shuai Z. Computational Method for Evaluating the Thermoelectric Power Factor for Organic Materials Modeled by the Holstein Model: A Time-Dependent Density Matrix Renormalization Group Formalism. J Chem Theory Comput 2022; 18:6437-6446. [PMID: 36174220 DOI: 10.1021/acs.jctc.2c00651] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Organic/polymeric materials are of emerging importance for thermoelectric conversion. The soft nature of these materials implies strong electron-phonon coupling, often leading to carrier localization. This poses great challenges for the conventional Boltzmann transport description based on relaxation time approximation and band structure calculations. In this work, combining the Kubo formula with the finite-temperature time-dependent density matrix renormalization group (FT-TD-DMRG) in the grand canonical ensemble, we developed a nearly exact algorithm to calculate the thermoelectric power factor PF = α2 σ, where α is the Seebeck coefficient and σ is the electrical conductivity, and apply the algorithm to Holstein Hamiltonian with electron-phonon coupling to model organic materials. Our algorithm can provide a unified description covering the weak coupling limit described by the bandlike Boltzmann transport to the strong coupling hopping limit.
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Affiliation(s)
- Yufei Ge
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084Beijing, P. R. China
| | - Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084Beijing, P. R. China
| | - Jiajun Ren
- MOE Key Laboratory of Theoretical and Computational Photochemistry, College of Chemistry, Beijing Normal University, 100875Beijing, P. R. China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084Beijing, P. R. China.,School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen518172, Guangdong, P. R. China
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11
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Xing T, Li T, Yan Y, Bai S, Shi Q. Application of the imaginary time hierarchical equations of motion method to calculate real time correlation functions. J Chem Phys 2022; 156:244102. [DOI: 10.1063/5.0095790] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
We investigate the application of the imaginary time hierarchical equations of motion method to calculate real time quantum correlation functions. By starting from the path integral expression for the correlated system–bath equilibrium state, we first derive a new set of equations that decouple the imaginary time propagation and the calculation of auxiliary density operators. The new equations, thus, greatly simplify the calculation of the equilibrium correlated initial state that is subsequently used in the real time propagation to obtain the quantum correlation functions. It is also shown that a periodic decomposition of the bath imaginary time correlation function is no longer necessary in the new equations such that different decomposition schemes can be explored. The applicability of the new method is demonstrated in several numerical examples, including the spin-Boson model, the Holstein model, and the double-well model for proton transfer reaction.
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Affiliation(s)
- Tao Xing
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Tianchu Li
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and 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, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and 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, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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12
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Wang YC, Zhao Y. Diagrammatic quantum Monte Carlo toward the calculation of transport properties in disordered semiconductors. J Chem Phys 2022; 156:204116. [DOI: 10.1063/5.0091124] [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
A new diagrammatic quantum Monte Carlo approach is proposed to deal with the imaginary time propagator involving both dynamic disorder (i.e., electron–phonon interactions) and static disorder of local or nonlocal nature in a unified and numerically exact way. The establishment of the whole framework relies on a general reciprocal-space expression and a generalized Wick’s theorem for the static disorder. Since the numerical cost is independent of the system size, various physical quantities, such as the thermally averaged coherence, Matsubara one-particle Green’s function, and current autocorrelation function, can be efficiently evaluated in the thermodynamic limit (infinite in the system size). The validity and performance of the proposed approach are systematically examined in a broad parameter regime. This approach, combined with proper numerical analytic continuation methods and first-principles calculations, is expected to be a versatile tool toward the calculation of various transport properties, such as mobilities in realistic semiconductors involving multiple electronic energy bands, high-frequency optical and low-frequency acoustic phonons, different forms of dynamic and static disorders, and anisotropy.
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Affiliation(s)
- 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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13
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Hino K, Kurashige Y. Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials. J Chem Theory Comput 2022; 18:3347-3356. [PMID: 35606892 DOI: 10.1021/acs.jctc.2c00243] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige, J. Chem. Phys. 2018, 19, 194114] is extended to realistic anharmonic potentials with n-mode representations beyond the linear vibronic coupling model. For realistic vibrational potentials, the local mode representation should give a more compact representation of the potentials, i.e., lowering the dimensionality of the entanglements, than the normal coordinates, and the MPS-MCTDH formulation should work more efficiently and maintain the accuracy with a small bond dimension of the MPS ansatz. In fact, it was confirmed that the use of the local coordinates made the interaction matrices diagonal dominant and the number of terms in the n-body expansion of the potentials was significantly reduced. The method was applied to the IR spectrum of the CH2O molecule, the zero-point energies, and the vibrational energy redistribution dynamics of polyenes C2nH2n+2. The results showed that the efficiency of the MPS-MCTDH method is significantly accelerated by the use of local coordinates even if the long-range interactions are included in the potential.
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Affiliation(s)
- Kentaro Hino
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Yuki Kurashige
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
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14
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Li W, Ren J, Yang H, Shuai Z. On the fly swapping algorithm for ordering of degrees of freedom in density matrix renormalization group. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:254003. [PMID: 35378514 DOI: 10.1088/1361-648x/ac640e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 04/04/2022] [Indexed: 06/14/2023]
Abstract
Density matrix renormalization group (DMRG) and its time-dependent variants have found widespread applications in quantum chemistry, includingab initioelectronic structure of complex bio-molecules, spectroscopy for molecular aggregates, and charge transport in bulk organic semiconductors. The underlying wavefunction ansatz for DMRG, matrix product state (MPS), requires mapping degrees of freedom (DOF) into a one-dimensional topology. DOF ordering becomes a crucial factor for DMRG accuracy. In this work, we propose swapping neighboring DOFs during the DMRG sweeps for DOF ordering, which we term 'on the fly swapping' (OFS) algorithm. We show that OFS is universal for both static and time-dependent DMRG with minimum computational overhead. Examples are given for one dimensional antiferromagnetic Heisenberg model,ab initioelectronic structure of N2molecule, and the S1/S2internal conversion dynamics of pyrazine molecule. It is found that OFS can indeed improve accuracy by finding better DOF ordering in all cases.
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Affiliation(s)
- Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Hengrui Yang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, People's Republic of China
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15
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Ren J, Li W, Jiang T, Wang Y, Shuai Z. Time‐dependent density matrix renormalization group method for quantum dynamics in complex systems. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1614] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
| | - Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
| | - Tong Jiang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
| | - Yuanheng Wang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry Tsinghua University Beijing People's Republic of China
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16
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Giannini S, Blumberger J. Charge Transport in Organic Semiconductors: The Perspective from Nonadiabatic Molecular Dynamics. Acc Chem Res 2022; 55:819-830. [PMID: 35196456 PMCID: PMC8928466 DOI: 10.1021/acs.accounts.1c00675] [Citation(s) in RCA: 32] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
![]()
Organic semiconductors (OSs) are an exciting
class of materials
that have enabled disruptive technologies in this century including
large-area electronics, flexible displays, and inexpensive solar cells.
All of these technologies rely on the motion of electrical charges
within the material and the diffusivity of these charges critically
determines their performance. In this respect, it is remarkable that
the nature of the charge transport in these materials has puzzled
the community for so many years, even for apparently simple systems
such as molecular single crystals: some experiments would better fit
an interpretation in terms of a localized particle picture, akin to
molecular or biological electron transfer, while others are in better
agreement with a wave-like interpretation, more akin to band transport
in metals. Exciting recent progress in the theory and simulation
of charge
carrier transport in OSs has now led to a unified understanding of
these disparate findings, and this Account will review one of these
tools developed in our laboratory in some detail: direct charge carrier
propagation by quantum-classical nonadiabatic molecular dynamics.
One finds that even in defect-free crystals the charge carrier can
either localize on a single molecule or substantially delocalize over
a large number of molecules depending on the relative strength of
electronic couplings between the molecules, reorganization, or charge
trapping energy of the molecule and thermal fluctuations of electronic
couplings and site energies, also known as electron–phonon
couplings. Our simulations predict that in molecular OSs exhibiting
some of
the highest measured charge mobilities to date, the charge carrier
forms “flickering” polarons, objects that are delocalized
over 10–20 molecules on average and that constantly change
their shape and extension under the influence of thermal disorder.
The flickering polarons propagate through the OS by short (≈10
fs long) bursts of the wave function that lead to an expansion of
the polaron to about twice its size, resulting in spatial displacement,
carrier diffusion, charge mobility, and electrical conductivity. Arguably
best termed “transient delocalization”, this mechanistic
scenario is very similar to the one assumed in transient localization
theory and supports its assertions. We also review recent applications
of our methodology to charge transport in disordered and nanocrystalline
samples, which allows us to understand the influence of defects and
grain boundaries on the charge propagation. Unfortunately, the
energetically favorable packing structures of
typical OSs, whether molecular or polymeric, places fundamental constraints
on charge mobilities/electronic conductivity compared to inorganic
semiconductors, which limits their range of applications. In this
Account, we review the design rules that could pave the way for new
very high-mobility OS materials and we argue that 2D covalent organic
frameworks are one of the most promising candidates to satisfy them. We conclude that our nonadiabatic dynamics method is a powerful
approach for predicting charge carrier transport in crystalline and
disordered materials. We close with a brief outlook on extensions
of the method to exciton transport, dissociation, and recombination.
This will bring us a step closer to an understanding of the birth,
survival, and annihiliation of charges at interfaces of optoelectronic
devices.
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Affiliation(s)
- Samuele Giannini
- Department of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, United Kingdom
| | - Jochen Blumberger
- Department of Physics and Astronomy and Thomas Young Centre, University College London, London WC1E 6BT, United Kingdom
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17
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Li W, Ma H, Li S, Ma J. Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning. Chem Sci 2021; 12:14987-15006. [PMID: 34909141 PMCID: PMC8612375 DOI: 10.1039/d1sc02574k] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 10/12/2021] [Indexed: 12/11/2022] Open
Abstract
Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.
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Affiliation(s)
- Wei Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
| | - Haibo Ma
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
- Jiangsu Key Laboratory of Advanced Organic Materials, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University Nanjing 210023 China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
| | - Jing Ma
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
- Jiangsu Key Laboratory of Advanced Organic Materials, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University Nanjing 210023 China
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18
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Peng R, White AF, Zhai H, Kin-Lic Chan G. Conservation laws in coupled cluster dynamics at finite temperature. J Chem Phys 2021; 155:044103. [PMID: 34340387 DOI: 10.1063/5.0059257] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We extend the finite-temperature Keldysh non-equilibrium coupled cluster theory (Keldysh-CC) [A. F. White and G. K.-L. Chan, J. Chem. Theory Comput. 15, 6137-6253 (2019)] to include a time-dependent orbital basis. When chosen to minimize the action, such a basis restores local and global conservation laws (Ehrenfest's theorem) for all one-particle properties while remaining energy conserving for time-independent Hamiltonians. We present the time-dependent Keldysh orbital-optimized coupled cluster doubles method in analogy with the formalism for zero-temperature dynamics, extended to finite temperatures through the time-dependent action on the Keldysh contour. To demonstrate the conservation property and understand the numerical performance of the method, we apply it to several problems of non-equilibrium finite-temperature dynamics: a 1D Hubbard model with a time-dependent Peierls phase, laser driving of molecular H2, driven dynamics in warm-dense silicon, and transport in the single impurity Anderson model.
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Affiliation(s)
- Ruojing Peng
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Alec F White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Huanchen Zhai
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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19
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Li W, Ren J, Shuai Z. A general charge transport picture for organic semiconductors with nonlocal electron-phonon couplings. Nat Commun 2021; 12:4260. [PMID: 34253724 PMCID: PMC8275621 DOI: 10.1038/s41467-021-24520-y] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 06/22/2021] [Indexed: 11/16/2022] Open
Abstract
The nonlocal electron-phonon couplings in organic semiconductors responsible for the fluctuation of intermolecular transfer integrals has been the center of interest recently. Several irreconcilable scenarios coexist for the description of the nonlocal electron-phonon coupling, such as phonon-assisted transport, transient localization, and band-like transport. Through a nearly exact numerical study for the carrier mobility of the Holstein-Peierls model using the matrix product states approach, we locate the phonon-assisted transport, transient localization and band-like regimes as a function of the transfer integral (V) and the nonlocal electron-phonon couplings (ΔV), and their distinct transport behaviors are analyzed by carrier mobility, mean free path, optical conductivity and one-particle spectral function. We also identify an "intermediate regime" where none of the established pictures applies, and the generally perceived hopping regime is found to be at a very limited end in the proposed regime paradigm.
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Affiliation(s)
- Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, China
| | - Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing, China.
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20
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Wang Y, Ren J, Shuai Z. Evaluating the anharmonicity contributions to the molecular excited state internal conversion rates with finite temperature TD-DMRG. J Chem Phys 2021; 154:214109. [PMID: 34240969 DOI: 10.1063/5.0052804] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we propose a new method to calculate molecular nonradiative electronic relaxation rates based on the numerically exact time-dependent density matrix renormalization group theory. This method could go beyond the existing frameworks under the harmonic approximation (HA) of the potential energy surface (PES) so that the anharmonic effect could be considered, which is of vital importance when the electronic energy gap is much larger than the vibrational frequency. We calculate the internal conversion (IC) rates in a two-mode model with Morse potential to investigate the validity of HA. We find that HA is unsatisfactory unless only the lowest several vibrational states of the lower electronic state are involved in the transition process when the adiabatic excitation energy is relatively low. As the excitation energy increases, HA first underestimates and then overestimates the IC rates when the excited state PES shifts toward the dissociative side of the ground state PES. On the contrary, HA slightly overestimates the IC rates when the excited state PES shifts toward the repulsive side. In both cases, a higher temperature enlarges the error of HA. As a real example to demonstrate the effectiveness and scalability of the method, we calculate the IC rates of azulene from S1 to S0 on the ab initio anharmonic PES approximated by the one-mode representation. The calculated IC rates of azulene under HA are consistent with the analytically exact results. The rates on the anharmonic PES are 30%-40% higher than the rates under HA.
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Affiliation(s)
- Yuanheng Wang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - 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
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21
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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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22
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Yan Y, Xing T, Shi Q. A new method to improve the numerical stability of the hierarchical equations of motion for discrete harmonic oscillator modes. J Chem Phys 2020; 153:204109. [DOI: 10.1063/5.0027962] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yaming Yan
- 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; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Tao Xing
- 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; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, 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; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
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23
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Shuai Z, Li W, Ren J, Jiang Y, Geng H. Applying Marcus theory to describe the carrier transports in organic semiconductors: Limitations and beyond. J Chem Phys 2020; 153:080902. [PMID: 32872875 DOI: 10.1063/5.0018312] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Marcus theory has been successfully applied to molecular design for organic semiconductors with the aid of quantum chemistry calculations for the molecular parameters: the intermolecular electronic coupling V and the intramolecular charge reorganization energy λ. The assumption behind this is the localized nature of the electronic state for representing the charge carriers, being holes or electrons. As far as the quantitative description of carrier mobility is concerned, the direct application of Marcus semiclassical theory usually led to underestimation of the experimental data. A number of effects going beyond such a semiclassical description will be introduced here, including the quantum nuclear effect, dynamic disorder, and delocalization effects. The recently developed quantum dynamics simulation at the time-dependent density matrix renormalization group theory is briefly discussed. The latter was shown to be a quickly emerging efficient quantum dynamics method for the complex system.
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Affiliation(s)
- Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084 Beijing, People's Republic of China
| | - Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084 Beijing, People's Republic of China
| | - Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084 Beijing, People's Republic of China
| | - Yuqian Jiang
- Laboratory for Nanosystem and Hierarchy Fabrication, National Center for Nanoscience and Technology, Chinese Academy of Sciences, 100084 Beijing, People's Republic of China
| | - Hua Geng
- Department of Chemistry, Capital Normal University, 100048 Beijing, People's Republic of China
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24
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Ren J, Li W, Jiang T, Shuai Z. A general automatic method for optimal construction of matrix product operators using bipartite graph theory. J Chem Phys 2020; 153:084118. [PMID: 32872857 DOI: 10.1063/5.0018149] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
Constructing matrix product operators (MPOs) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For the DMRG to be conveniently used in different problems described by different Hamiltonians, in this work, we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) it is automatic in that only the definition of the operator is required; (ii) it is symbolic thus free of any numerical error; (iii) the complementary operator technique can be fully employed so that the resulting MPO is globally optimal for any given order of degrees of freedom; and (iv) the symmetry of the system could be fully employed to reduce the dimension of MPO. To demonstrate the effectiveness of the new algorithm, the MPOs of Hamiltonians ranging from the prototypical spin-boson model and the Holstein model to the more complicated ab initio electronic Hamiltonian and the anharmonic vibrational Hamiltonian with the sextic force field are constructed. It is found that for the former three cases, our automatic algorithm can reproduce exactly the same MPOs as the optimally hand-crafted ones already known in the literature.
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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
| | - Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Tong Jiang
- 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
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