1
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Ivander F, Lindoy LP, Lee J. Unified framework for open quantum dynamics with memory. Nat Commun 2024; 15:8087. [PMID: 39278965 PMCID: PMC11402990 DOI: 10.1038/s41467-024-52081-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Accepted: 08/23/2024] [Indexed: 09/18/2024] Open
Abstract
The dynamics of quantum systems coupled to baths are typically studied using the Nakajima-Zwanzig memory kernel ( K ) or the influence functions (I), particularly when memory effects are present. Despite their significance, formal connections between the two have not been explicitly known. We establish their connections by examining the system propagator for a N-level system linearly coupled to Gaussian baths with various types of system-bath coupling. For a certain class of problems, we devised a non-perturbative, diagrammatic approach to construct K from I for (driven) systems interacting with Gaussian baths, bypassing conventional projection-free dynamics inputs. Our work provides a way to interpret approximate path integral methods in terms of approximate memory kernels. Moreover, it offers a Hamiltonian learning procedure to extract the bath spectral density from reduced system trajectories, opening new avenues in quantum sensing and engineering. The insights we provide advance our understanding of non-Markovian dynamics and will serve as a stepping stone for future theoretical and experimental developments in this area.
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Affiliation(s)
- Felix Ivander
- Quantum Science and Engineering, Harvard University, Cambridge, MA, USA
| | - Lachlan P Lindoy
- National Physical Laboratory, Teddington, TW11 0LW, United Kingdom
| | - Joonho Lee
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA.
- Google Quantum AI, Venice, CA, USA.
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2
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Malpathak S, Ananth N. Semiclassical dynamics in Wigner phase space II: Nonadiabatic hybrid Wigner dynamics. J Chem Phys 2024; 161:094110. [PMID: 39234964 DOI: 10.1063/5.0223187] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2024] [Accepted: 08/12/2024] [Indexed: 09/06/2024] Open
Abstract
We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman-Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects.
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Affiliation(s)
- Shreyas Malpathak
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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3
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Liu L, Ren J, Fang W. Improved memory truncation scheme for quasi-adiabatic propagator path integral via influence functional renormalization. J Chem Phys 2024; 161:084101. [PMID: 39171703 DOI: 10.1063/5.0221916] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2024] [Accepted: 08/05/2024] [Indexed: 08/23/2024] Open
Abstract
Accurately simulating non-Markovian quantum dynamics in system-bath coupled problems remains challenging. In this work, we present a novel memory truncation scheme for the iterative quasi-adiabatic propagator path integral (iQuAPI) method to improve accuracy. Conventional memory truncation in iQuAPI discards all influence functional beyond a certain time interval, which is not effective for problems with a long memory time. Our proposed scheme selectively retains the most significant parts of the influence functional using the density matrix renormalization group algorithm. We validate the effectiveness of our scheme through simulations of the spin-boson model across various parameter sets, demonstrating faster convergence and improved accuracy compared to the conventional scheme. Our findings suggest that the new memory truncation scheme significantly advances the capabilities of iQuAPI for problems with a long memory time.
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Affiliation(s)
- Limin Liu
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875 Beijing, People's Republic of China
| | - Jiajun Ren
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875 Beijing, People's Republic of China
| | - Weihai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, 100875 Beijing, People's Republic of China
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4
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Dutta R, Cabral DGA, Lyu N, Vu NP, Wang Y, Allen B, Dan X, Cortiñas RG, Khazaei P, Schäfer M, Albornoz ACCD, Smart SE, Nie S, Devoret MH, Mazziotti DA, Narang P, Wang C, Whitfield JD, Wilson AK, Hendrickson HP, Lidar DA, Pérez-Bernal F, Santos LF, Kais S, Geva E, Batista VS. Simulating Chemistry on Bosonic Quantum Devices. J Chem Theory Comput 2024. [PMID: 39068594 DOI: 10.1021/acs.jctc.4c00544] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/30/2024]
Abstract
Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this Perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure.
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Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Delmar G A Cabral
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Nam P Vu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
- Department of Chemistry, Lafayette College, Easton, Pennsylvania 18042, United States
| | - Yuchen Wang
- Department of Chemistry, Department of Physics, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Brandon Allen
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Xiaohan Dan
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Rodrigo G Cortiñas
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Pouya Khazaei
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Max Schäfer
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Alejandro C C D Albornoz
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - Scott E Smart
- Division of Physical Sciences, College of Letters and Science and Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Scott Nie
- Division of Physical Sciences, College of Letters and Science and Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Michel H Devoret
- Department of Applied Physics and Department of Physics, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
| | - David A Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States
| | - Prineha Narang
- Division of Physical Sciences, College of Letters and Science and Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, California 90095, United States
| | - Chen Wang
- Department of Physics, University of Massachusetts - Amherst, Amherst, Massachusetts 01003, United States
| | - James D Whitfield
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 01003, United States
| | - Angela K Wilson
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48864, United States
| | - Heidi P Hendrickson
- Department of Chemistry, Lafayette College, Easton, Pennsylvania 18042, United States
| | - Daniel A Lidar
- Department of Electrical & Computer Engineering, Department of Chemistry, Department of Physics & Astronomy, and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, United States
| | - Francisco Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain
| | - Lea F Santos
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269, United States
| | - Sabre Kais
- Department of Chemistry, Department of Physics, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
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5
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Liu Z, Lyu N, Hu Z, Zeng H, Batista VS, Sun X. Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics. J Chem Phys 2024; 161:024102. [PMID: 38980091 DOI: 10.1063/5.0208708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2024] [Accepted: 06/20/2024] [Indexed: 07/10/2024] Open
Abstract
Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.
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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, USA
| | - Ningyi Lyu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Zhubin Hu
- 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
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Hao Zeng
- 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
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - 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, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
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6
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Fay TP. Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime. J Chem Phys 2024; 161:014101. [PMID: 38949594 DOI: 10.1063/5.0218653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane-anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes.
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Affiliation(s)
- Thomas P Fay
- Institut de Chimie Radicalaire, Aix-Marseille Université, Campus de Saint-Jérôme, Av. Esc. Normandie Niemen, 13397 Marseille, France
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7
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Kim CW, Franco I. General framework for quantifying dissipation pathways in open quantum systems. I. Theoretical formulation. J Chem Phys 2024; 160:214111. [PMID: 38833366 DOI: 10.1063/5.0202860] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Accepted: 05/13/2024] [Indexed: 06/06/2024] Open
Abstract
We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is performed by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima-Zwanzig projection operator technique, which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillators or spin baths and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic baths [Kim and Franco, J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems.
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Affiliation(s)
- Chang Woo Kim
- Department of Chemistry, Chonnam National University, Gwangju 61186, South Korea
| | - Ignacio Franco
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
- Department of Physics, University of Rochester, Rochester, New York 14627, USA
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8
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Fay TP, Limmer DT. Unraveling the mechanisms of triplet state formation in a heavy-atom free photosensitizer. Chem Sci 2024; 15:6726-6737. [PMID: 38725521 PMCID: PMC11077524 DOI: 10.1039/d4sc01369g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 03/29/2024] [Indexed: 05/12/2024] Open
Abstract
Triplet excited state generation plays a pivotal role in photosensitizers, however the reliance on transition metals and heavy atoms can limit the utility of these systems. In this study, we demonstrate that an interplay of competing quantum effects controls the high triplet quantum yield in a prototypical boron dipyrromethene-anthracene (BD-An) donor-acceptor dyad photosensitizer, which is only captured by an accurate treatment of both inner and outer sphere reorganization energies. Our ab initio-derived model provides excellent agreement with experimentally measured spectra, triplet yields and excited state kinetic data, including the triplet lifetime. We find that rapid triplet state formation occurs primarily via high-energy triplet states through both spin-orbit coupled charge transfer and El-Sayed's rule breaking intersystem crossing, rather than direct spin-orbit coupled charge transfer to the lowest lying triplet state. Our calculations also reveal that competing effects of nuclear tunneling, electronic state recrossing, and electronic polarizability dictate the rate of non-productive ground state recombination. This study sheds light on the quantum effects driving efficient triplet formation in the BD-An system, and offers a promising simulation methodology for diverse photochemical systems.
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Affiliation(s)
- Thomas P Fay
- Department of Chemistry, University of California Berkeley CA 94720 USA
| | - David T Limmer
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Kavli Energy Nanoscience Institute Berkeley CA 94720 USA
- Chemical Science Division Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
- Material Science Division Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
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9
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Sayer T, Montoya-Castillo A. Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra. J Chem Phys 2024; 160:044108. [PMID: 38270238 DOI: 10.1063/5.0185578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 12/26/2023] [Indexed: 01/26/2024] Open
Abstract
Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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10
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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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11
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Dominic AJ, Cao S, Montoya-Castillo A, Huang X. Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently. J Am Chem Soc 2023; 145:9916-9927. [PMID: 37104720 DOI: 10.1021/jacs.3c01095] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
Conformational changes underpin function and encode complex biomolecular mechanisms. Gaining atomic-level detail of how such changes occur has the potential to reveal these mechanisms and is of critical importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resolution than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomolecular systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the molecular dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.
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Affiliation(s)
- Anthony J Dominic
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Siqin Cao
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | | | - Xuhui Huang
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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12
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Montoya-Castillo A, Markland TE. A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics. J Chem Phys 2023; 158:094112. [PMID: 36889969 DOI: 10.1063/5.0138664] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023] Open
Abstract
The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces to transport through nanojunctions and offer a prime target for quantum computing applications. Here, we derive the set of conditions under which fermionic operators can be exactly replaced by bosonic operators that render the problem amenable to a large toolbox of dynamical methods while still capturing the correct dynamics of n-body operators. Importantly, our analysis offers a simple guide on how one can exploit these simple maps to calculate nonequilibrium and equilibrium single- and multi-time correlation functions essential in describing transport and spectroscopy. We use this to rigorously analyze and delineate the applicability of simple yet effective Cartesian maps that have been shown to correctly capture the correct fermionic dynamics in select models of nanoscopic transport. We illustrate our analytical results with exact simulations of the resonant level model. Our work provides new insights as to when one can leverage the simplicity of bosonic maps to simulate the dynamics of many-electron systems, especially those where an atomistic representation of nuclear interactions becomes essential.
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Affiliation(s)
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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13
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Lyu N, Mulvihill E, Soley MB, Geva E, Batista VS. Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations. J Chem Theory Comput 2023; 19:1111-1129. [PMID: 36719350 DOI: 10.1021/acs.jctc.2c00892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion and dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a spin-boson model system described by various types of GQMEs. Exact memory kernels and inhomogeneous terms are obtained from short-time quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) simulations and are compared with those obtained from an approximate linearized semiclassical method, allowing for assessment of the accuracy of these approximate memory kernels and inhomogeneous terms. Moreover, we have analyzed the computational cost of the full and reduced-dimensionality GQMEs. The scaling of the computational cost is dependent on several factors, sometimes with opposite scaling trends. The TT-TFD memory kernels can provide insights on the main sources of inaccuracies of GQME approaches when combined with approximate input methods and pave the road for the development of quantum circuits that implement GQMEs on digital quantum computers.
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Affiliation(s)
- Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Ellen Mulvihill
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Micheline B Soley
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.,Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States.,Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.,Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
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14
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Sayer T, Montoya-Castillo A. Compact and complete description of non-Markovian dynamics. J Chem Phys 2023; 158:014105. [PMID: 36610963 DOI: 10.1063/5.0132614] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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15
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Amati G, Saller MAC, Kelly A, Richardson JO. Quasiclassical approaches to the generalized quantum master equation. J Chem Phys 2022; 157:234103. [PMID: 36550031 DOI: 10.1063/5.0124028] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels that are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper, we study the approximate solution of the GQME, obtained by calculating the kernels with two methods: Ehrenfest mean-field theory and spin-mapping. We test the approaches on a range of spin-boson models with increasing energy bias between the two electronic levels and place a particular focus on the long-time limits of the populations. We find that the accuracy of the predictions of the GQME depends strongly on the specific technique used to calculate the kernels. In particular, spin-mapping outperforms Ehrenfest for all the systems studied. The problem of unphysical negative electronic populations affecting spin-mapping is resolved by coupling the method with the master equation. Conversely, Ehrenfest in conjunction with the GQME can predict negative populations, despite the fact that the populations calculated from direct dynamics are positive definite.
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Affiliation(s)
- Graziano Amati
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | | | - Aaron Kelly
- The Hamburg Center for Ultrafast Imaging, Universität Hamburg, Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, Germany
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16
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Lai Y, Geva E. Electronic Absorption Spectra from Off-Diagonal Quantum Master Equations. J Chem Phys 2022; 157:104115. [DOI: 10.1063/5.0106888] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Quantum master equations (QMEs) provide a general framework for describing electronic dynamics within a complex molecular system. Off-diagonal QMEs (OD-QMEs) correspond to a family of QMEs that describe the electronic dynamics in the interaction picture based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. The fact that OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrodinger picture electronic coherences from them. A key experimental quantity that relies on the ability to obtain accurate Schrodinger picture electronic coherences is the absorption spectrum. In this paper, we propose using a recently introduced procedure for extracting Schrodinger picture electronic coherences from interaction picture inputs to calculate electronic absorption spectra from electronic dynamics generated by OD-QMEs. The accuracy of the absorption spectra obtained in this way is studied in the context of a biexciton benchmark model, by comparing spectra calculated based on time-local and time-nonlocal OD-QMEs to spectra calculated based on a Redfield-type QME and the non-perturbative and quantum-mechanically exact hierarchical equations of motion (HEOM) method.
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Affiliation(s)
- Yifan Lai
- Chemistry, University of Michigan, United States of America
| | - Eitan Geva
- Department of Chemistry, University of Michigan Department of Chemistry, United States of America
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17
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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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18
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Mulvihill E, Geva E. Simulating the dynamics of electronic observables via reduced-dimensionality generalized quantum master equations. J Chem Phys 2022; 156:044119. [DOI: 10.1063/5.0078040] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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19
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Brian D, Sun X. Generalized quantum master equation: A tutorial review and recent advances. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2109157] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Dominikus Brian
- Division of Arts and Sciences, NYU Shanghai, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York 10003, USA
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York 10003, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200241, China
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