1
|
Gumber S, Prezhdo OV. Energy-Conserving Surface Hopping for Auger Processes. J Chem Theory Comput 2024. [PMID: 38902855 DOI: 10.1021/acs.jctc.4c00562] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/22/2024]
Abstract
Auger-type processes are ubiquitous in nanoscale materials because quantum confinement enhances Coulomb interactions, and there exist large densities of states. Modeling Auger processes requires the modification of nonadiabatic (NA) molecular dynamics algorithms to include transitions caused by both NA and Coulomb couplings. The system is split into quantum and classical subsystems, e.g., electrons and vibrations, and as a result, energy conservation becomes nontrivial. In surface hopping, an electronic transition induced by NA coupling is accompanied by a classical velocity readjustment to ensure conservation of the total quantum-classical energy. A different treatment is needed for Auger transitions driven by Coulomb interactions. We develop a nonadiabatic molecular dynamics methodology that meticulously differentiates the energy redistribution accompanying hops induced by the NA coupling and the Coulomb interaction and correctly conserves the total energy at each transition. If the transition is driven by a Coulomb interaction, the hop energy is redistributed within the quantum electronic subsystem only. If the transition is NA, the energy is redistributed between the quantum and classical subsystems. Properly maintaining energy conservation for both types of transitions is crucial to generate a correct order of events, obtain accurate transition times, maintain a proper statistical distribution of state populations, and reach thermodynamic equilibrium. We test the method with biexciton annihilation and Auger-assisted hot electron relaxation in a CdSe quantum dot. The sequence of Auger and phonon-driven processes and the calculated time scales are in excellent agreement with the experimental results. The developed approach can be coupled with any surface-hopping method and provides a crucial practical advance to study charge-carrier dynamics in the nanoscale and condensed matter systems.
Collapse
Affiliation(s)
- Shriya Gumber
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - Oleg V Prezhdo
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, United States
| |
Collapse
|
2
|
Liu J, Lu G, Zhang X. Exciton dispersion and exciton-phonon interaction in solids by time-dependent density functional theory. J Chem Phys 2023; 158:044116. [PMID: 36725491 DOI: 10.1063/5.0137326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
Understanding, predicting, and ultimately controlling exciton band structure and exciton dynamics are central to diverse chemical and materials problems. Here, we have developed a first-principles method to determine exciton dispersion and exciton-phonon interaction in semiconducting and insulating solids based on time-dependent density functional theory. The first-principles method is formulated in planewave bases and pseudopotentials and can be used to compute exciton band structures, exciton charge density, ionic forces, the non-adiabatic coupling matrix between excitonic states, and the exciton-phonon coupling matrix. Based on the spinor formulation, the method enables self-consistent noncollinear calculations to capture spin-orbital coupling. Hybrid exchange-correlation functionals are incorporated to deal with long-range electron-hole interactions in solids. A sub-Hilbert space approximation is introduced to reduce the computational cost without loss of accuracy. For validations, we have applied the method to compute the exciton band structure and exciton-phonon coupling strength in transition metal dichalcogenide monolayers; both agree very well with the previous GW-Bethe-Salpeter equation and experimental results. This development paves the way for accurate determinations of exciton dynamics in a wide range of solid-state materials.
Collapse
Affiliation(s)
- Junyi Liu
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA
| | - Gang Lu
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA
| | - Xu Zhang
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, USA
| |
Collapse
|
3
|
Liu J, Hu W, Yang J. Accelerating Linear-Response Time-Dependent Hybrid Density Functional Theory with Low-Rank Decomposition Techniques in the Plane-Wave Basis. J Chem Theory Comput 2022; 18:6713-6721. [PMID: 36242561 DOI: 10.1021/acs.jctc.2c00763] [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
We present an efficient low-rank implementation of linear-response time-dependent density functional theory for hybrid functionals (hybrid-LR-TDDFT) within the plane-wave pseudopotential framework. The adaptively compressed exchange (ACE) operator and the natural transition orbitals (NTOs) are introduced to build the low-rank representation of the nonlocal exchange operator in the hybrid-LR-TDDFT Hamiltonian. Numerical tests demonstrate that the ACE approximation significantly reduces the computational cost of applying the nonlocal exchange operator without loss of accuracy, and the NTO approximation can further accelerate the hybrid-LR-TDDFT calculations by introducing an NTO cutoff parameter. This new method enables us to effectively study the excitonic properties of two-dimensional MoS2 consisting of 216 atoms and ∼1900 electrons with range-separated hybrid functionals on a single graphics processing unit.
Collapse
Affiliation(s)
- Jie Liu
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Wei Hu
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| | - Jinlong Yang
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China.,Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui230026, China
| |
Collapse
|
4
|
Wang Z, Wu C, Liu W. NAC-TDDFT: Time-Dependent Density Functional Theory for Nonadiabatic Couplings. Acc Chem Res 2021; 54:3288-3297. [PMID: 34448566 DOI: 10.1021/acs.accounts.1c00312] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
First-order nonadiabatic coupling (NAC) matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of systems of chemical interests, time-dependent density functional theory (TDDFT) is usually the first choice of methods. However, the lack of many-electron wave functions in TDDFT renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. Because of this, various variants of NAC-TDDFT have been proposed in the literature from different standing points, including the Hellmann-Feynman-like expression and auxiliary/pseudo-wave function (AWF)-, equation-of-motion (EOM)-, and time-dependent perturbation theory (TDPT)-based formulations. Based on critical analyses, the following conclusions are made here: (1) The Hellmann-Feynman-like expression, which is rooted in exact wave function theory, is hardly useful due to huge demand on basis sets. (2) Although most popular, the AWF variants of NAC-TDDFT are not theoretically founded and become ambiguous particularly for the fo-NACMEs between two excited states, although they do agree with the EOM and TDPT variants under the Tamm-Dancoff approximation. (3) The TDPT variant of NAC-TDDFT is theoretically most rigorous but suffers from numerical instabilities on the one hand and does not differ to a significant extent from the EOM variant on the other hand. (4) As such, the EOM variant of NAC-TDDFT for the fo-NACMEs between the ground and excited states and between two excited states is solely the right choice in practice. These formal analyses are fully supported by numerical experimentations, taking azulene as a showcase. The proper implementation of the EOM variant of NAC-TDDFT is also highlighted, showing that the fo-NACMEs between the ground and excited states and between two excited states are computationally very much the same as the analytic energy gradients of DFT and TDDFT, respectively. Possible future developments of the EOM variant of NAC-TDDFT are also highlighted. Its extensions to spin-adapted open-shell TDDFT and proper treatment of spin-orbit couplings (which are another source of force for electronically nonadiabatic processes) are particularly warranted in the near future.
Collapse
Affiliation(s)
- Zikuan Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Chenyu Wu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| |
Collapse
|
5
|
Zhou G, Lu G, Prezhdo OV. Modeling Auger Processes with Nonadiabatic Molecular Dynamics. NANO LETTERS 2021; 21:756-761. [PMID: 33320680 DOI: 10.1021/acs.nanolett.0c04442] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Auger-type energy exchange plays key roles in the carrier dynamics in nanomaterials due to strong carrier-carrier interactions. However, theoretical descriptions are limited to perturbative calculations of scattering rates on static structures. We develop an accurate and efficient ab initio technique to model Auger scattering with nonadiabatic molecular dynamics. We incorporate the many-body Coulomb matrix into several surface hopping methods and describe simultaneously charge-charge and charge-phonon scattering in the time-domain and in a nonperturbative, configuration-dependent manner. The approach is illustrated with a CdSe quantum dot. Auger scattering between electrons and holes breaks the phonon bottleneck to electron relaxation. The bottleneck is recovered when electrons and holes are decoupled. The simulations correctly reproduce all experimental processes and time scales, including Auger- and phonon-assisted cooling of hot electrons, intraband carrier relaxation, and carrier recombination. Providing detailed insights into the energy flow, the developed method allows studies of carrier dynamics in nanomaterials with strong carrier-carrier interactions.
Collapse
Affiliation(s)
- Guoqing Zhou
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, United States
| | - Gang Lu
- Department of Physics and Astronomy, California State University, Northridge, California 91330, United States
| | - Oleg V Prezhdo
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, United States
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| |
Collapse
|
6
|
Zhang X, Lu G, Baer R, Rabani E, Neuhauser D. Linear-Response Time-Dependent Density Functional Theory with Stochastic Range-Separated Hybrids. J Chem Theory Comput 2020; 16:1064-1072. [DOI: 10.1021/acs.jctc.9b01121] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xu Zhang
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, United States
| | - Gang Lu
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, United States
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, United States
| |
Collapse
|
7
|
Zhang L, Chu W, Zheng Q, Benderskii AV, Prezhdo OV, Zhao J. Suppression of Electron-Hole Recombination by Intrinsic Defects in 2D Monoelemental Material. J Phys Chem Lett 2019; 10:6151-6158. [PMID: 31553184 DOI: 10.1021/acs.jpclett.9b02620] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
The Shockley-Read-Hall (SRH) model, in which the deep trap defect states in the band gap are proposed as nonradiative electron-hole (e-h) recombination centers, has been widely used to describe the nonradiative e-h recombination through the defects in semiconductor. By using the ab initio nonadiabatic molecular dynamics method, we find that the SRH model fails to describe the e-h recombination behavior for defects in 2D monoelemental material such as monolayer black phosphorus (BP). Through the investigation of three intrinsic defects with shallow and deep defect states in monolayer BP, it is found that, surprisingly, none of these defects significantly accelerates the e-h recombination. Further analysis shows that because monolayer BP is a monoelemental material, the distinct impurity phonon, which often induces fast e-h recombination, is not formed. Moreover, because of the flexibility of 2D material, the defects scatter the phonons present in pristine BP, generating multiple modes with lower frequencies compared with the pristine BP, which further suppresses the e-h recombination. We propose that the conclusion can be extended to other monoelemental 2D materials, which is important guidance for the future design of functional semiconductors.
Collapse
Affiliation(s)
- Lili Zhang
- ICQD/Hefei National Laboratory for Physical Sciences at Microscale, and Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, and Department of Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Department of Chemistry , University of Southern California , Los Angeles , California 90089 , United States
| | - Weibin Chu
- ICQD/Hefei National Laboratory for Physical Sciences at Microscale, and Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, and Department of Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Department of Chemistry , University of Southern California , Los Angeles , California 90089 , United States
| | - Qijing Zheng
- ICQD/Hefei National Laboratory for Physical Sciences at Microscale, and Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, and Department of Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Synergetic Innovation Center of Quantum Information & Quantum Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
| | - Alexander V Benderskii
- Department of Chemistry , University of Southern California , Los Angeles , California 90089 , United States
| | - Oleg V Prezhdo
- Department of Chemistry , University of Southern California , Los Angeles , California 90089 , United States
| | - Jin Zhao
- ICQD/Hefei National Laboratory for Physical Sciences at Microscale, and Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, and Department of Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
- Synergetic Innovation Center of Quantum Information & Quantum Physics , University of Science and Technology of China , Hefei , Anhui 230026 , China
| |
Collapse
|