1
|
Liu Z, Brian D, Sun X. PyCTRAMER: A Python package for charge transfer rate constant of condensed-phase systems from Marcus theory to Fermi's golden rule. J Chem Phys 2024; 161:064101. [PMID: 39120028 DOI: 10.1063/5.0224524] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2024] [Accepted: 07/24/2024] [Indexed: 08/10/2024] Open
Abstract
In this work, we introduce PyCTRAMER, a comprehensive Python package designed for calculating charge transfer (CT) rate constants in disordered condensed-phase systems at finite temperatures, such as organic photovoltaic (OPV) materials. PyCTRAMER is a restructured and enriched version of the CTRAMER (Charge-Transfer RAtes from Molecular dynamics, Electronic structure, and Rate theory) package [Tinnin et al. J. Chem. Phys. 154, 214108 (2021)], enabling the computation of the Marcus CT rate constant and the six levels of the linearized semiclassical approximations of Fermi's golden rule (FGR) rate constant. It supports various types of intramolecular and intermolecular CT transitions from the excitonic states to CT state. Integrating quantum chemistry calculations, all-atom molecular dynamics (MD) simulations, spin-boson model construction, and rate constant calculations, PyCTRAMER offers an automatic workflow for handling photoinduced CT processes in explicit solvent environments and interfacial CT in amorphous donor/acceptor blends. The package also provides versatile tools for individual workflow steps, including electronic state analysis, state-specific force field construction, MD simulations, and spin-boson model construction from energy trajectories. We demonstrate the software's capabilities through two examples, highlighting both intramolecular and intermolecular CT processes in prototypical OPV systems.
Collapse
Affiliation(s)
- Zengkui Liu
- Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- 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, USA
| | - Dominikus Brian
- 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, USA
| | - Xiang Sun
- Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- 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, USA
| |
Collapse
|
2
|
Liu Z, Song Z, Sun X. All-Atom Photoinduced Charge Transfer Dynamics in Condensed Phase via Multistate Nonlinear-Response Instantaneous Marcus Theory. J Chem Theory Comput 2024; 20:3993-4006. [PMID: 38657208 PMCID: PMC11099976 DOI: 10.1021/acs.jctc.4c00010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2024] [Revised: 03/30/2024] [Accepted: 04/08/2024] [Indexed: 04/26/2024]
Abstract
Photoinduced charge transfer (CT) in the condensed phase is an essential component in solar energy conversion, but it is challenging to simulate such a process on the all-atom level. The traditional Marcus theory has been utilized for obtaining CT rate constants between pairs of electronic states but cannot account for the nonequilibrium effects due to the initial nuclear preparation. The recently proposed instantaneous Marcus theory (IMT) and its nonlinear-response formulation allow for incorporating the nonequilibrium nuclear relaxation to electronic transition between two states after the photoexcitation from the equilibrium ground state and provide the time-dependent rate coefficient. In this work, we extend the nonlinear-response IMT method for treating photoinduced CT among general multiple electronic states and demonstrate it in the organic photovoltaic carotenoid-porphyrin-fullerene triad dissolved in explicit tetrahydrofuran solvent. All-atom molecular dynamics simulations were employed to obtain the time correlation functions of energy gaps, which were used to generate the IMT-required time-dependent averages and variances of the relevant energy gaps. Our calculations show that the multistate IMT could capture the significant nonequilibrium effects due to the initial nuclear state preparation, and this is corroborated by the substantial differences between the population dynamics predicted by the multistate IMT and the Marcus theory, where the Marcus theory underestimates the population transfer. The population dynamics by multistate IMT is also shown to have a better agreement with the all-atom nonadiabatic mapping dynamics than the Marcus theory does. Because the multistate nonlinear-response IMT is straightforward and cost-effective in implementation and accounts for the nonequilibrium nuclear effects, we believe this method offers a practical strategy for studying charge transfer dynamics in complex condensed-phase systems.
Collapse
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
| | - Zailing Song
- 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
| |
Collapse
|
3
|
Lin HH, Wang CI, Yang CH, Secario MK, Hsu CP. Two-Step Machine Learning Approach for Charge-Transfer Coupling with Structurally Diverse Data. J Phys Chem A 2024; 128:271-280. [PMID: 38157315 DOI: 10.1021/acs.jpca.3c04524] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2024]
Abstract
Electronic coupling is important in determining charge-transfer rates and dynamics. Coupling strength is sensitive to both intermolecular, e.g., orientation or distance, and intramolecular degrees of freedom. Hence, it is challenging to build an accurate machine learning model to predict electronic coupling of molecular pairs, especially for those derived from the amorphous phase, for which intermolecular configurations are much more diverse than those derived from crystals. In this work, we devise a new prediction algorithm that employs two consecutive KRR models. The first model predicts molecular orbitals (MOs) from structural variation for each fragment, and coupling is further predicted by using the overlap integral included in a second model. With our two-step procedure, we achieved mean absolute errors of 0.27 meV for an ethylene dimer and 1.99 meV for a naphthalene pair, much improved accuracy amounting to 14-fold and 3-fold error reductions, respectively. In addition, MOs from the first model can also be the starting point to obtain other quantum chemical properties from atomistic structures. This approach is also compatible with a MO predictor with sufficient accuracy.
Collapse
Affiliation(s)
- Hung-Hsuan Lin
- Institute of Chemistry, Academia Sinica, 128 Section 2 Academia Road, Nankang, Taipei 115, Taiwan
- Molecular Science and Digital Innovation Center, Genetics Generation Advancement Corp, No. 28, Ln. 36, Xinhu First Rd., Neihu, Taipei 114, Taiwan
| | - Chun-I Wang
- Institute of Chemistry, Academia Sinica, 128 Section 2 Academia Road, Nankang, Taipei 115, Taiwan
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Chou-Hsun Yang
- Institute of Chemistry, Academia Sinica, 128 Section 2 Academia Road, Nankang, Taipei 115, Taiwan
| | - Muhammad Khari Secario
- Institute of Chemistry, Academia Sinica, 128 Section 2 Academia Road, Nankang, Taipei 115, Taiwan
- Taiwan International Graduate Program on Sustainable Chemical Science & Technology, Academia Sinica Institute of Chemistry, 128 Academia Road Sec.2, Nankang, Taipei 115, Taiwan
- Department of Applied Chemistry, National Yang Ming Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan
| | - Chao-Ping Hsu
- Institute of Chemistry, Academia Sinica, 128 Section 2 Academia Road, Nankang, Taipei 115, Taiwan
- Division of Physics, National Center for Theoretical Sciences, 1, Section 4, Roosevelt Road, Taipei 106, Taiwan
| |
Collapse
|
4
|
Raza A, Mehmood RF, Rashid EU, Nasr S, Yahia IS, Iqbal J, Alatawi NS, Khera RA. Amplifying the photovoltaic properties of phenylene dithiophene core based non-fused ring by engineering the terminal acceptors modification to enhance the efficiency of organic solar cells. J Mol Graph Model 2023; 124:108563. [PMID: 37480831 DOI: 10.1016/j.jmgm.2023.108563] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 07/05/2023] [Accepted: 07/07/2023] [Indexed: 07/24/2023]
Abstract
In this study, a series of eight non-fused rings-based semiconducting acceptors (AR1-AR8) were computationally developed by making modifications to the parent molecule (PTICO). In this study, a DFT analysis was conducted at an accurately chosen level of theory to gather a comprehensive inventory of the optoelectronic characteristics of AR1-AR8 and PTICO. The findings indicate that all recently developed molecules exhibit a bathochromic shift in their maximum UV-visible absorbance (λmax) with a smaller band gap (Eg). AR1 has demonstrated the most significant red shift in UV-visible absorbance and possesses the smallest Eg when compared to other recently developed acceptors. AR2 acceptor has shown the best results both as electron and hole-transporting materials owing to its smallest value of reorganization energy for electrons and holes. J61 donor was engaged to calculate the open-circuit voltage (VOC) and the highest VOC with maximum FF % value was observed in AR4. The investigation of charge transfer was also conducted utilizing J61 in conjunction with the AR4 acceptor. Natural transition orbitals (NTO) have also been inspected to recognize the percentage electron transport contribution (% ETC) from the ground state to the first excites state (S0 to S1). The findings of this research suggest that the modified acceptors exhibit potential for practical implementation in the development of organic solar cells that possess improved photovoltaic performance.
Collapse
Affiliation(s)
- Ahmad Raza
- Department of Chemistry, University of Agriculture, Faisalabad, 38000, Pakistan
| | - Rana Farhat Mehmood
- Department of Chemistry, University of Education, Township, Lahore, 54770, Pakistan D Research, Pakistan
| | - Ehsan Ullah Rashid
- Department of Chemistry, University of Agriculture, Faisalabad, 38000, Pakistan
| | - Samia Nasr
- Research Center for Advanced Materials Science (RCAMS), King Khalid University, Abha, 61413, P.O. Box 9004, Saudi Arabia; Chemistry Department, Faculty of Science, King Khalid University, Abha, 61413, P.O. Box 9004, Saudi Arabia
| | - I S Yahia
- Research Center for Advanced Materials Science (RCAMS), King Khalid University, Abha, 61413, P.O. Box 9004, Saudi Arabia; Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia; Center of Medical and Bio-Allied Health Sciences Research (CMBHSR), Ajman University, Ajman, P.O. Box 346, United Arab Emirates
| | - Javed Iqbal
- Department of Chemistry, University of Agriculture, Faisalabad, 38000, Pakistan.
| | - Naifa S Alatawi
- Physics Department, Faculty of Science, University of Tabuk, Tabuk, 71421, Saudi Arabia
| | - Rasheed Ahmad Khera
- Department of Chemistry, University of Agriculture, Faisalabad, 38000, Pakistan.
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
Deffner M, Weise MP, Zhang H, Mücke M, Proppe J, Franco I, Herrmann C. Learning Conductance: Gaussian Process Regression for Molecular Electronics. J Chem Theory Comput 2023; 19:992-1002. [PMID: 36692968 DOI: 10.1021/acs.jctc.2c00648] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Experimental studies of charge transport through single molecules often rely on break junction setups, where molecular junctions are repeatedly formed and broken while measuring the conductance, leading to a statistical distribution of conductance values. Modeling this experimental situation and the resulting conductance histograms is challenging for theoretical methods, as computations need to capture structural changes in experiments, including the statistics of junction formation and rupture. This type of extensive structural sampling implies that even when evaluating conductance from computationally efficient electronic structure methods, which typically are of reduced accuracy, the evaluation of conductance histograms is too expensive to be a routine task. Highly accurate quantum transport computations are only computationally feasible for a few selected conformations and thus necessarily ignore the rich conformational space probed in experiments. To overcome these limitations, we investigate the potential of machine learning for modeling conductance histograms, in particular by Gaussian process regression. We show that by selecting specific structural parameters as features, Gaussian process regression can be used to efficiently predict the zero-bias conductance from molecular structures, reducing the computational cost of simulating conductance histograms by an order of magnitude. This enables the efficient calculation of conductance histograms even on the basis of computationally expensive first-principles approaches by effectively reducing the number of necessary charge transport calculations, paving the way toward their routine evaluation.
Collapse
Affiliation(s)
- Michael Deffner
- Institute of Inorganic and Applied Chemistry, University of Hamburg, Hamburg22761, Germany.,The Hamburg Centre for Ultrafast Imaging, Hamburg22761, Germany
| | - Marc Philipp Weise
- Institute of Inorganic and Applied Chemistry, University of Hamburg, Hamburg22761, Germany
| | - Haitao Zhang
- Institute of Inorganic and Applied Chemistry, University of Hamburg, Hamburg22761, Germany
| | - Maike Mücke
- Institute of Physical Chemistry, Georg-August University, Göttingen37077, Germany
| | - Jonny Proppe
- Institute of Physical and Theoretical Chemistry, TU Braunschweig, Braunschweig38106, Germany
| | - Ignacio Franco
- Departments of Chemistry and Physics, University of Rochester, Rochester, New York14627-0216, United States
| | - Carmen Herrmann
- Institute of Inorganic and Applied Chemistry, University of Hamburg, Hamburg22761, Germany.,The Hamburg Centre for Ultrafast Imaging, Hamburg22761, Germany
| |
Collapse
|
7
|
Hu Z, Sun X. All-Atom Nonadiabatic Semiclassical Mapping Dynamics for Photoinduced Charge Transfer of Organic Photovoltaic Molecules in Explicit Solvents. J Chem Theory Comput 2022; 18:5819-5836. [PMID: 36073792 DOI: 10.1021/acs.jctc.2c00631] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Direct all-atom simulation of nonadiabatic dynamics in disordered condensed phases like liquid solutions and amorphous solids has been challenging. The first all-atom simulation of the photoinduced charge-transfer dynamics of a prototypical organic photovoltaic carotenoid-porphyrin-C60 molecular triad in explicit tetrahydrofuran is presented. Based on the Meyer-Miller mapping Hamiltonian, various semiclassical and mixed quantum-classical dynamics are employed, including the linearized semiclassical, symmetrical quasiclassical, mean-field Ehrenfest, classical mapping model, and spin-mapping model approaches. The all-atom nonadiabatic dynamics were compared to multi-state harmonic models with a globally shared bath, and the models built using the ensemble averages on the initial electronic state could reproduce the all-atom results. The solvent effect was found to be critical for the photoinduced charge transfer, and the time-dependent solute-solvent radial distribution functions revealed that only the nonadiabatic dynamics started with the effective forces on the initial electronic state could capture the correct nuclear dynamics. The proposed strategy for modeling condensed-phase nonadiabatic dynamics with atomistic details is readily applied to complex condensed-phase systems.
Collapse
Affiliation(s)
- Zhubin Hu
- Division of Arts and Sciences, New York University Shanghai, 1555 Century Avenue, Shanghai 200122, China.,NYU-ECNU Center for Computational Chemistry, New York University Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China.,State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Xiang Sun
- Division of Arts and Sciences, New York University Shanghai, 1555 Century Avenue, Shanghai 200122, China.,NYU-ECNU Center for Computational Chemistry, New York University Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China.,State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China.,Department of Chemistry, New York University, New York, New York 10003, United States
| |
Collapse
|
8
|
Liu Z, Xu W, Tuckerman ME, Sun X. Imaginary-Time Open-Chain Path-Integral Approach for Two-State Time Correlation Functions and Applications in Charge Transfer. J Chem Phys 2022; 157:114111. [DOI: 10.1063/5.0098162] [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
Quantum time correlation functions (TCFs) involving two states are important for describing nonadiabatic dynamical processes such as charge transfer. Based on a previous single-state method, we propose an imaginary-time open-chain path-integral (OCPI) approach for evaluating the two-state symmetrized TCFs. Expressing the forward and backward propagation on different electronic potential energy surfaces as a complex-time path integral, we then transform the path variables to average and difference variables such that the integration over the difference variables up to the second order can be performed analytically. The resulting expression for the symmetrized TCF is equivalent to sampling the open-chain configurations in an effective potential that corresponds to the average surface. Using importance sampling over the extended OCPI space via open path integral molecular dynamics, we tested the resulting path-integral approximation by calculating the Fermi's golden rule charge transfer rate constant within a widely-used spin-boson model. Comparing with the real-time linearized semiclassical method and analytical result, we show that the imaginary-time OCPI provides an accurate two-state symmetrized TCF and rate constant in the typical turnover region. It is shown that the first bead of the open chain corresponds to physical zero-time, and the endpoint bead corresponds to final time t; oscillations of the end-to-end distance perfectly match the nuclear mode frequency. The two-state OCPI scheme is seen to capture the tested model's electronic quantum coherence and nuclear quantum effects accurately.
Collapse
Affiliation(s)
- Zengkui Liu
- Division of Arts and Sciences, New York University Shanghai, China
| | - Wen Xu
- New York University Shanghai, China
| | - Mark E. Tuckerman
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, United States of America
| | - Xiang Sun
- Division of Arts and Sciences, New York University Shanghai, China
| |
Collapse
|
9
|
Tinnin J, Bhandari S, Zhang P, Geva E, Dunietz BD, Sun X, Cheung MS. Correlating Interfacial Charge Transfer Rates with Interfacial Molecular Structure in the Tetraphenyldibenzoperiflanthene/C 70 Organic Photovoltaic System. J Phys Chem Lett 2022; 13:763-769. [PMID: 35040657 DOI: 10.1021/acs.jpclett.1c03618] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Organic photovoltaics (OPV) is an emerging solar cell technology that offers vast advantages such as low-cost manufacturing, transparency, and solution processability. However, because the performance of OPV devices is still disappointing compared to their inorganic counterparts, better understanding of how controlling the molecular-level morphology can impact performance is needed. To this end, one has to overcome significant challenges that stem from the complexity and heterogeneity of the underlying electronic structure and molecular morphology. In this Letter, we address this challenge in the context of the DBP/C70 OPV system by employing a modular workflow that combines recent advances in electronic structure, molecular dynamics, and rate theory. We show how the wide range of interfacial pairs can be classified into four types of interfacial donor-acceptor geometries and find that the least populated interfacial geometry gives rise to the fastest charge transfer (CT) rates.
Collapse
Affiliation(s)
- Jacob Tinnin
- Department of Physics, University of Houston, 617 Science & Research Building 1, Houston, Texas 77204, United States
- Center for Theoretical Biological Physics, Rice University, 6500 Main St., BioScience Research Collaborative, Suite 1005G, Houston, Texas 77030-1402, United States
| | - Srijana Bhandari
- Department of Chemistry and Biochemistry, Kent State University, 1175 Risman Drive, Kent, Ohio 44242, United States
- Department of Chemistry, Case Western Reserve University, 10800 Euclid Avenue, Cleveland, Ohio 44106, United States
| | - Pengzhi Zhang
- Department of Physics, University of Houston, 617 Science & Research Building 1, Houston, Texas 77204, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109, United States
| | - Barry D Dunietz
- Department of Chemistry and Biochemistry, Kent State University, 1175 Risman Drive, Kent, Ohio 44242, United States
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, 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
| | - Margaret S Cheung
- Department of Physics, University of Houston, 617 Science & Research Building 1, Houston, Texas 77204, United States
- Center for Theoretical Biological Physics, Rice University, 6500 Main St., BioScience Research Collaborative, Suite 1005G, Houston, Texas 77030-1402, United States
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, 902 Battelle Blvd, Richland, Washington 99354, United States
| |
Collapse
|