1
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Lawrence JE, Mannouch JR, Richardson JO. A size-consistent multi-state mapping approach to surface hopping. J Chem Phys 2024; 160:244112. [PMID: 38940540 DOI: 10.1063/5.0208575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 06/05/2024] [Indexed: 06/29/2024] Open
Abstract
We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.
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Affiliation(s)
- Joseph E Lawrence
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
- Simons Center for Computational Physical Chemistry, New York University, New York, New York 10003, USA
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Jonathan R Mannouch
- Hamburg Center for Ultrafast Imaging, Universität Hamburg and the Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
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2
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Han D, Akimov AV. Nonadiabatic Dynamics with Exact Factorization: Implementation and Assessment. J Chem Theory Comput 2024; 20:5022-5042. [PMID: 38837952 DOI: 10.1021/acs.jctc.4c00343] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
In this work, we report our implementation of several independent-trajectory mixed-quantum-classical (ITMQC) nonadiabatic dynamics methods based on exact factorization (XF) in the Libra package for nonadiabatic and excited-state dynamics. Namely, the exact factorization surface hopping (SHXF), mixed quantum-classical dynamics (MQCXF), and mean-field (MFXF) are introduced. Performance of these methods is compared to that of several traditional surface hopping schemes, such as the fewest-switches surface hopping (FSSH), branching-corrected surface hopping (BCSH), and the simplified decay of mixing (SDM), as well as conventional Ehrenfest (mean-field, MF) method. Based on a comprehensive set of 1D model Hamiltonians, we find the ranking SHXF ≈ MQCXF > BCSH > SDM > FSSH ≫ MF, with the BCSH sometimes outperforming the XF methods in terms of describing coherences. Although the MFXF method can yield reasonable populations and coherences for some cases, it does not conserve the total energy and is therefore not recommended. We also find that the branching correction for auxiliary trajectories is important for the XF methods to yield accurate populations and coherences. However, the branching correction can worsen the quality of the energy conservation in the MQCXF. Finally, we find that using the time-dependent Gaussian width approximation used in the XF methods for computing decoherence correction can improve the quality of energy conservation in the MQCXF dynamics. The parameter-free scheme of Subotnik for computing the Gaussian widths is found to deliver the best performance in situations where such widths are not known a priori.
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Affiliation(s)
- Daeho Han
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States
| | - Alexey V Akimov
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States
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3
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Shu Y, Truhlar DG. Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients. J Chem Theory Comput 2024; 20:4396-4426. [PMID: 38819014 DOI: 10.1021/acs.jctc.4c00424] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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4
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Mannouch JR, Kelly A. Quantum Quality with Classical Cost: Ab Initio Nonadiabatic Dynamics Simulations Using the Mapping Approach to Surface Hopping. J Phys Chem Lett 2024; 15:5814-5823. [PMID: 38781480 PMCID: PMC11163471 DOI: 10.1021/acs.jpclett.4c00535] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Revised: 05/07/2024] [Accepted: 05/09/2024] [Indexed: 05/25/2024]
Abstract
Nonadiabatic dynamics methods are an essential tool for investigating photochemical processes. In the context of employing first-principles electronic structure techniques, such simulations can be carried out in a practical manner using semiclassical trajectory-based methods or wave packet approaches. While all approaches applicable to first-principles simulations are necessarily approximate, it is commonly thought that wave packet approaches offer inherent advantages over their semiclassical counterparts in terms of accuracy and that this trait simply comes at a higher computational cost. Here we demonstrate that the mapping approach to surface hopping (MASH), a recently introduced trajectory-based nonadiabatic dynamics method, can be efficiently applied in tandem with ab initio electronic structure. Our results even suggest that MASH may provide more accurate results than on-the-fly wave packet techniques, all at a much lower computational cost.
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Affiliation(s)
- Jonathan R. Mannouch
- Hamburg Center for Ultrafast
Imaging, Universität Hamburg and
the Max Planck Institute
for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Aaron Kelly
- Hamburg Center for Ultrafast
Imaging, Universität Hamburg and
the Max Planck Institute
for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
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5
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Lawrence JE, Mannouch JR, Richardson JO. Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping. J Phys Chem Lett 2024; 15:707-716. [PMID: 38214476 PMCID: PMC10823533 DOI: 10.1021/acs.jpclett.3c03197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 12/22/2023] [Accepted: 01/05/2024] [Indexed: 01/13/2024]
Abstract
It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.
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Affiliation(s)
- Joseph E. Lawrence
- Department
of Chemistry and Applied Biosciences, ETH
Zurich, 8093 Zurich, Switzerland
| | - Jonathan R. Mannouch
- Hamburg
Center for Ultrafast Imaging, Universität
Hamburg and Max Planck Institute for the Structure and Dynamics of
Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jeremy O. Richardson
- Department
of Chemistry and Applied Biosciences, ETH
Zurich, 8093 Zurich, Switzerland
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6
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Gustin I, Kim CW, McCamant DW, Franco I. Mapping electronic decoherence pathways in molecules. Proc Natl Acad Sci U S A 2023; 120:e2309987120. [PMID: 38015846 PMCID: PMC10710033 DOI: 10.1073/pnas.2309987120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 10/25/2023] [Indexed: 11/30/2023] Open
Abstract
Establishing the fundamental chemical principles that govern molecular electronic quantum decoherence has remained an outstanding challenge. Fundamental questions such as how solvent and intramolecular vibrations or chemical functionalization contribute to the decoherence remain unanswered and are beyond the reach of state-of-the-art theoretical and experimental approaches. Here we address this challenge by developing a strategy to isolate electronic decoherence pathways for molecular chromophores immersed in condensed phase environments that enables elucidating how electronic quantum coherence is lost. For this, we first identify resonance Raman spectroscopy as a general experimental method to reconstruct molecular spectral densities with full chemical complexity at room temperature, in solvent, and for fluorescent and non-fluorescent molecules. We then show how to quantitatively capture the decoherence dynamics from the spectral density and identify decoherence pathways by decomposing the overall coherence loss into contributions due to individual molecular vibrations and solvent modes. We illustrate the utility of the strategy by analyzing the electronic decoherence pathways of the DNA base thymine in water. Its electronic coherences decay in [Formula: see text]30 fs. The early-time decoherence is determined by intramolecular vibrations while the overall decay by solvent. Chemical substitution of thymine modulates the decoherence with hydrogen-bond interactions of the thymine ring with water leading to the fastest decoherence. Increasing temperature leads to faster decoherence as it enhances the importance of solvent contributions but leaves the early-time decoherence dynamics intact. The developed strategy opens key opportunities to establish the connection between molecular structure and quantum decoherence as needed to develop chemical strategies to rationally modulate it.
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Affiliation(s)
- Ignacio Gustin
- Department of Chemistry, University of Rochester, Rochester, NY14627
| | - Chang Woo Kim
- Department of Chemistry, Chonnam National University, Gwangju61186, South Korea
| | - David W. McCamant
- Department of Chemistry, University of Rochester, Rochester, NY14627
| | - Ignacio Franco
- Department of Chemistry, University of Rochester, Rochester, NY14627
- Department of Physics, University of Rochester, Rochester, NY14627
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7
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Dergachev ID, Dergachev VD, Rooein M, Mirzanejad A, Varganov SA. Predicting Kinetics and Dynamics of Spin-Dependent Processes. Acc Chem Res 2023; 56:856-866. [PMID: 36926853 DOI: 10.1021/acs.accounts.2c00843] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/18/2023]
Abstract
ConspectusPredicting mechanisms and rates of nonadiabatic spin-dependent processes including photoinduced intersystem crossings, thermally activated spin-forbidden reactions, and spin crossovers in metal centers is a very active field of research. These processes play critical roles in transition-metal-based and metalloenzymatic catalysis, molecular magnets, light-harvesting materials, organic light-emitting diodes, photosensitizers for photodynamic therapy, and many other applications. Therefore, accurate modeling of spin-dependent processes in complex systems and on different time scales is important for many problems in chemistry, biochemistry, and materials sciences.Nonadiabatic statistical theory (NAST) and nonadiabatic molecular dynamics (NAMD) are two complementary approaches to modeling the kinetics and dynamics of spin-dependent processes. NAST predicts the probabilities and rate constants of nonradiative transitions between electronic states with different spin multiplicities using molecular properties at only few critical points on the potential energy surfaces (PESs), including the reactant minimum and the minimum energy crossing point (MECP) between two spin states. This makes it possible to obtain molecular properties for NAST calculations using accurate but often computationally expensive electronic structure methods, which is critical for predicting the rate constants of spin-dependent processes. Alternatively, NAST can be used to study spin-dependent processes in very large complex molecular systems using less computationally expensive electronic structure methods. The nuclear quantum effects, such as zero-point vibrational energy, tunneling, and interference between reaction paths can be easily incorporated. However, the statistical and local nature of NAST makes it more suitable for large systems and slow kinetics. In contrast, NAMD explores entire PESs of interacting electronic states, making it ideal for modeling fast barrierless spin-dependent processes. Because the knowledge of large portions of PESs is often needed, the simulations require a very large number of electronic structure calculations, which limits the NAMD applicability to relatively small molecular systems and ultrafast kinetics.In this Account, we discuss our contribution to the development of the NAST and NAMD approaches for predicting the rates and mechanism of spin-dependent processes. First, we briefly describe our NAST and NAMD implementations. The NAST implementation is an extension of the transition state theory to the processes involving two crossing potential energy surfaces of different spin multiplicities. The NAMD approach includes the trajectory surface hopping (TSH) and ab initio multiple spawning (AIMS) methods. Second, we discuss several applications of NAST and NAMD to model spin-dependent processes in different systems. The NAST applicability to large complex systems is demonstrated by the studies of the spin-forbidden isomerization of the active sites of metal-sulfur proteins. Our implementation of the MECP search algorithm within the fully ab initio fragment molecular orbital method allows applying NAST to systems with thousands of atoms, such as the solvated protein rubredoxin. Applications of NAMD to ultrafast spin-dependent processes are represented by the generalized AIMS simulations utilizing the fast GPU-based TeraChem electronic structure program to gain insight into the complex photoexcited state relaxation in 2-cyclopentenone.
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Affiliation(s)
- Ilya D Dergachev
- Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, United States
| | - Vsevolod D Dergachev
- Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, United States
| | - Mitra Rooein
- Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, United States
| | - Amir Mirzanejad
- Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, United States
| | - Sergey A Varganov
- Department of Chemistry, University of Nevada, Reno, 1664 N. Virginia Street, Reno, Nevada 89557-0216, United States
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8
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Abstract
We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, such as in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can, in principle, be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost.
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9
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Zhou Z, Wu Y, Bian X, Subotnik JE. Nonadiabatic Dynamics in a Continuous Circularly Polarized Laser Field with Floquet Phase-Space Surface Hopping. J Chem Theory Comput 2023; 19:718-732. [PMID: 36655857 DOI: 10.1021/acs.jctc.2c00948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Nonadiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (where the electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase-space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Thus, the F-PSSH algorithm sets the stage for future modeling of nonadiabatic dynamics under strong externally pumped circular polarization.
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Affiliation(s)
- Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph Eli Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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10
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Wu Y, Subotnik JE. A quantum-classical Liouville formalism in a preconditioned basis and its connection with phase-space surface hopping. J Chem Phys 2023; 158:024115. [PMID: 36641414 DOI: 10.1063/5.0124835] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
We revisit a recent proposal to model nonadiabatic problems with a complex-valued Hamiltonian through a phase-space surface hopping (PSSH) algorithm employing a pseudo-diabatic basis. Here, we show that such a pseudo-diabatic PSSH (PD-PSSH) ansatz is consistent with a quantum-classical Liouville equation (QCLE) that can be derived following a preconditioning process, and we demonstrate that a proper PD-PSSH algorithm is able to capture some geometric magnetic effects (whereas the standard fewest switches surface hopping approach cannot capture such effects). We also find that a preconditioned QCLE can outperform the standard QCLE in certain cases, highlighting the fact that there is no unique QCLE. Finally, we also point out that one can construct a mean-field Ehrenfest algorithm using a phase-space representation similar to what is done for PSSH. These findings would appear extremely helpful as far as understanding and simulating nonadiabatic dynamics with complex-valued Hamiltonians and/or spin degeneracy.
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Affiliation(s)
- Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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11
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Shu Y, Truhlar DG. Decoherence and Its Role in Electronically Nonadiabatic Dynamics. J Chem Theory Comput 2023; 19:380-395. [PMID: 36622843 PMCID: PMC9878713 DOI: 10.1021/acs.jctc.2c00988] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Indexed: 01/10/2023]
Abstract
Decoherence is the tendency of a time-evolved reduced density matrix for a subsystem to assume a form corresponding to a statistical ensemble of states rather than a coherent combination of pure-state wave functions. When a molecular process involves changes in the electronic state and the coordinates of the nuclei, as in ultraviolet or visible light photochemistry or electronically inelastic collisions, the reduced density matrix of the electronic subsystem suffers decoherence, due to its interaction with the nuclear subsystem. We present the background necessary to conceptualize this decoherence; in particular, we discuss the density matrix description of pure states and mixed states, and we discuss pointer states and decoherence time. We then discuss how decoherence is treated in the coherent switching with decay of mixing algorithm and the trajectory surface hopping method for semiclassical calculations of electronically nonadiabatic processes.
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Affiliation(s)
- Yinan Shu
- Department of Chemistry,
Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota55455-0431, United States
| | - Donald G. Truhlar
- Department of Chemistry,
Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota55455-0431, United States
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12
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Jain A, Sindhu A. Pedagogical Overview of the Fewest Switches Surface Hopping Method. ACS OMEGA 2022; 7:45810-45824. [PMID: 36570264 PMCID: PMC9773185 DOI: 10.1021/acsomega.2c04843] [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: 07/31/2022] [Accepted: 11/18/2022] [Indexed: 06/17/2023]
Abstract
The fewest switches surface hopping method continues to grow in popularity to capture electronic nonadiabaticity and quantum nuclear effects due to its simplicity and accuracy. Knowing the basics of the method is essential for the correct implementation and interpretation of results. This review covers the fundamentals of the fewest switches surface hopping method with a detailed discussion of the nuances such as decoherence schemes and frustrated hops and the correct approach to calculating populations. The consequences of incorrect implementation are further discussed toward calculating kinetic and thermodynamic properties. Some tips for practitioners and a step-by-step algorithm for developers are provided. Finally, some of the finer technicalities of the fewest switches surface hopping method that are buried deep in the literature are pointed out to help graduate students better appreciate this method.
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13
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Barbatti M, Bondanza M, Crespo-Otero R, Demoulin B, Dral PO, Granucci G, Kossoski F, Lischka H, Mennucci B, Mukherjee S, Pederzoli M, Persico M, Pinheiro Jr M, Pittner J, Plasser F, Sangiogo Gil E, Stojanovic L. Newton-X Platform: New Software Developments for Surface Hopping and Nuclear Ensembles. J Chem Theory Comput 2022; 18:6851-6865. [PMID: 36194696 PMCID: PMC9648185 DOI: 10.1021/acs.jctc.2c00804] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Indexed: 12/01/2022]
Abstract
Newton-X is an open-source computational platform to perform nonadiabatic molecular dynamics based on surface hopping and spectrum simulations using the nuclear ensemble approach. Both are among the most common methodologies in computational chemistry for photophysical and photochemical investigations. This paper describes the main features of these methods and how they are implemented in Newton-X. It emphasizes the newest developments, including zero-point-energy leakage correction, dynamics on complex-valued potential energy surfaces, dynamics induced by incoherent light, dynamics based on machine-learning potentials, exciton dynamics of multiple chromophores, and supervised and unsupervised machine learning techniques. Newton-X is interfaced with several third-party quantum-chemistry programs, spanning a broad spectrum of electronic structure methods.
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Affiliation(s)
- Mario Barbatti
- Aix
Marseille University, CNRS, ICR, 13013Marseille, France
- Institut
Universitaire de France, 75231Paris, France
| | - Mattia Bondanza
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, via Moruzzi
13, 56124Pisa, Italy
| | - Rachel Crespo-Otero
- Department
of Chemistry, Queen Mary University of London, Mile End Road, E1 4NSLondon, U.K.
| | | | - Pavlo O. Dral
- State
Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial
Key Laboratory of Theoretical and Computational Chemistry, Department
of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, 361005Xiamen, China
| | - Giovanni Granucci
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, via Moruzzi
13, 56124Pisa, Italy
| | - Fábris Kossoski
- Laboratoire
de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31000Toulouse, France
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas79409, United States
| | - Benedetta Mennucci
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, via Moruzzi
13, 56124Pisa, Italy
| | | | - Marek Pederzoli
- J.
Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223Prague 8, Czech Republic
| | - Maurizio Persico
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, via Moruzzi
13, 56124Pisa, Italy
| | | | - Jiří Pittner
- J.
Heyrovsky Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223Prague 8, Czech Republic
| | - Felix Plasser
- Department
of Chemistry, Loughborough University, LE11 3TULoughborough, U.K.
| | - Eduarda Sangiogo Gil
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, via Moruzzi
13, 56124Pisa, Italy
| | - Ljiljana Stojanovic
- Department
of Physics and Astronomy, University College
London, Gower Street, WC1E 6BTLondon, U.K.
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14
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Bian X, Wu Y, Teh HH, Subotnik JE. Incorporating Berry Force Effects into the Fewest Switches Surface-Hopping Algorithm: Intersystem Crossing and the Case of Electronic Degeneracy. J Chem Theory Comput 2022; 18:2075-2090. [PMID: 35263116 DOI: 10.1021/acs.jctc.1c01103] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a preliminary surface-hopping approach for modeling intersystem crossing (ISC) dynamics between four electronic states: one singlet and one (triply degenerate) triplet. In order to incorporate all Berry force effects, the algorithm requires that, when moving along an adiabatic surface associated with the triplet manifold, one must also keep track of a quasi-diabatic index (akin to a "ms" quantum number) for each trajectory. For a simple model problem, we find that a great deal of new physics can be captured by our algorithm, setting the stage for larger, more realistic (or perhaps even ab initio) simulations in the future.
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Affiliation(s)
- Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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15
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Ab initio Nonadiabatic Dynamics of Semiconductor Nanomaterials via Surface Hopping Method. CHINESE J CHEM PHYS 2022. [DOI: 10.1063/1674-0068/cjcp2111247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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16
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de la Lande A, Denisov S, Mostafavi M. The mystery of sub-picosecond charge transfer following irradiation of hydrated uridine monophosphate. Phys Chem Chem Phys 2021; 23:21148-21162. [PMID: 34528029 DOI: 10.1039/d0cp06482c] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The early mechanisms by which ionizing rays damage biological structures by so-called direct effects are largely elusive. In a recent picosecond pulse radiolysis study of concentrated uridine monophosphate solutions [J. Ma, S. A. Denisov, J.-L. Marignier, P. Pernot, A. Adhikary, S. Seki and M. Mostafavi, J. Phys. Chem. Lett., 2018, 9, 5105], unexpected results were found regarding the oxidation of the nucleobase. The signature of the oxidized nucleobase could not be detected 5 ps after the electron pulse, but only the oxidized phosphate, raising intriguing questions about the identity of charge-transfer mechanisms that could explain the absence of U+. We address here this question by means of advanced first-principles atomistic simulations of solvated uridine monophosphate, combining Density Functional Theory (DFT) with polarizable embedding schemes. We contrast three very distinct mechanisms of charge transfer covering the atto-, femto- and pico-second timescales. We first investigate the ionization mechanism and subsequent hole/charge migrations on a timescale of attoseconds to a few femtoseconds under the frozen nuclei approximation. We then consider a nuclear-driven phosphate-to-oxidized-nucleobase electron transfer, showing that it is an uncompetitive reaction channel on the sub-picosecond timescale, despite its high exothermicity and significant electronic coupling. Finally, we show that non-adiabatic charge transfer is enabled by femtosecond nuclear relaxation after ionization. We show that electronic decoherence and the electronic coupling strength are the key parameters that determine the hopping probabilities. Our results provide important insight into the interplay between electronics and nuclear motions in the early stages of the multiscale responses of biological matter subjected to ionizing radiation.
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Affiliation(s)
- Aurélien de la Lande
- Institut de Chimie Physique, CNRS, Université Paris Saclay (UMR 8000), 15 Avenue Jean Perrin, 91405, France.
| | - Sergey Denisov
- Institut de Chimie Physique, CNRS, Université Paris Saclay (UMR 8000), 15 Avenue Jean Perrin, 91405, France.
| | - Mehran Mostafavi
- Institut de Chimie Physique, CNRS, Université Paris Saclay (UMR 8000), 15 Avenue Jean Perrin, 91405, France.
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17
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Wu Y, Subotnik JE. Semiclassical description of nuclear dynamics moving through complex-valued single avoided crossings of two electronic states. J Chem Phys 2021; 154:234101. [PMID: 34241259 DOI: 10.1063/5.0054014] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The standard fewest-switches surface hopping (FSSH) approach fails to model nonadiabatic dynamics when the electronic Hamiltonian is complex-valued and there are multiple nuclear dimensions; FSSH does not include geometric magnetic effects and does not have access to a gauge independent direction for momentum rescaling. In this paper, for the case of a Hamiltonian with two electronic states, we propose an extension of Tully's FSSH algorithm, which includes geometric magnetic forces and, through diabatization, establishes a well-defined rescaling direction. When combined with a decoherence correction, our new algorithm shows satisfying results for a model set of two-dimensional single avoided crossings.
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Affiliation(s)
- Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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18
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Abstract
In this article, we review nonadiabatic molecular dynamics (NAMD) methods for modeling spin-crossover transitions. First, we discuss different representations of electronic states employed in the grid-based and direct NAMD simulations. The nature of interstate couplings in different representations is highlighted, with the main focus on nonadiabatic and spin-orbit couplings. Second, we describe three NAMD methods that have been used to simulate spin-crossover dynamics, including trajectory surface hopping, ab initio multiple spawning, and multiconfiguration time-dependent Hartree. Some aspects of employing different electronic structure methods to obtain information about potential energy surfaces and interstate couplings for NAMD simulations are also discussed. Third, representative applications of NAMD to spin crossovers in molecular systems of different sizes and complexities are highlighted. Finally, we pose several fundamental questions related to spin-dependent processes. These questions should be possible to address with future methodological developments in NAMD.
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Affiliation(s)
- Saikat Mukherjee
- Institut de Chimie Radicalaire, CNRS 7273, Aix-Marseille University, 13013 Marseille, France;
| | - Dmitry A Fedorov
- Oak Ridge Associated Universities, Oak Ridge, Tennessee 37830, USA;
| | - Sergey A Varganov
- Department of Chemistry, University of Nevada, Reno, Nevada 89557-0216, USA;
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19
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Bian X, Wu Y, Teh HH, Zhou Z, Chen HT, Subotnik JE. Modeling nonadiabatic dynamics with degenerate electronic states, intersystem crossing, and spin separation: A key goal for chemical physics. J Chem Phys 2021; 154:110901. [DOI: 10.1063/5.0039371] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
- Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Hsing-Ta Chen
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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20
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Miao G, Bian X, Zhou Z, Subotnik J. A "backtracking" correction for the fewest switches surface hopping algorithm. J Chem Phys 2020; 153:111101. [PMID: 32962370 DOI: 10.1063/5.0022436] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a "backtracking" mechanism within Tully's fewest switches surface hopping (FSSH) algorithm, whereby whenever one detects consecutive (double) hops during a short period of time, one simply rewinds the dynamics backward in time. In doing so, one reduces the number of hopping events and comes closer to a truly fewest switches surface hopping approach with independent trajectories. With this algorithmic change, we demonstrate that surface hopping can be reasonably accurate for nuclear dynamics in a multidimensional configuration space with a complex-valued (i.e., not real-valued) electronic Hamiltonian; without this adjustment, surface hopping often fails. The added computational cost is marginal. Future research will be needed to assess whether or not this backtracking correction can improve the accuracy of a typical FSSH calculation with a real-valued electronic Hamiltonian (that ignores spin).
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Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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21
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Chen HT, Zhou Z, Subotnik JE. On the proper derivation of the Floquet-based quantum classical Liouville equation and surface hopping describing a molecule or material subject to an external field. J Chem Phys 2020; 153:044116. [PMID: 32752688 DOI: 10.1063/5.0013873] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate different approaches to derive the proper Floquet-based quantum-classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis and then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form that is similar to the usual QCLE with two modifications: (1) The electronic degrees of freedom are expanded to infinite dimension and (2) the nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a fictitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., [J. Chem. Phys. 140, 084104 (2014)] who found that transforming to the adiabatic representation must always be the last operation applied, although now we have extended this result to a time-dependent Hamiltonian. This paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping.
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Affiliation(s)
- Hsing-Ta Chen
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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22
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Shu Y, Zhang L, Mai S, Sun S, González L, Truhlar DG. Implementation of Coherent Switching with Decay of Mixing into the SHARC Program. J Chem Theory Comput 2020; 16:3464-3475. [DOI: 10.1021/acs.jctc.0c00112] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Yinan Shu
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Linyao Zhang
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
| | - Sebastian Mai
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090, Vienna, Austria
| | - Shaozeng Sun
- School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
| | - Leticia González
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090, Vienna, Austria
| | - Donald G. Truhlar
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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23
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Zhou Z, Chen HT, Nitzan A, Subotnik JE. Nonadiabatic Dynamics in a Laser Field: Using Floquet Fewest Switches Surface Hopping To Calculate Electronic Populations for Slow Nuclear Velocities. J Chem Theory Comput 2020; 16:821-834. [PMID: 31951404 DOI: 10.1021/acs.jctc.9b00950] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism, especially for slow nuclear velocities. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between wavepackets on different Floquet states. Our results should be of interest to all those interested in laser-induced molecular dynamics.
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Affiliation(s)
- Zeyu Zhou
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
| | - Hsing-Ta Chen
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
| | - Abraham Nitzan
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
| | - Joseph Eli Subotnik
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
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24
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Subotnik J, Miao G, Bellonzi N, Teh HH, Dou W. A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians. J Chem Phys 2019; 151:074113. [DOI: 10.1063/1.5116210] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Wenjie Dou
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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25
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Fedorov DA, Levine BG. Nonadiabatic Quantum Molecular Dynamics in Dense Manifolds of Electronic States. J Phys Chem Lett 2019; 10:4542-4548. [PMID: 31342748 DOI: 10.1021/acs.jpclett.9b01902] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Most nonadiabatic molecular dynamics methods require the determination of a basis of adiabatic or diabatic electronic states at every time step, but in dense manifolds of electronic states, such approaches become intractable. A notable exception is Ehrenfest molecular dynamics, which can be implemented without explicit determination of such a basis but suffers from unphysical behavior when propagation on a mean-field potential energy surface (PES) does not accurately reflect the true dynamics on multiple electronic states. Here we introduce the multiple cloning for dense manifolds of states (MCDMS) method, a systematically improvable approximation to the multiple cloning method. MCDMS avoids both the mean-field PES problem and the need to compute the full electronic spectrum. This is achieved by reformulating multiple cloning to use a subspace of approximate eigenstates constructed from the time-dependent Ehrenfest electronic wave function. By application to model systems, we show that this approach allows a substantial reduction in the size of the required electronic basis without significant loss in accuracy.
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Affiliation(s)
- Dmitry A Fedorov
- Department of Chemistry , Michigan State University , East Lansing , Michigan 48824 , United States
| | - Benjamin G Levine
- Department of Chemistry , Michigan State University , East Lansing , Michigan 48824 , United States
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26
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Miao G, Subotnik J. Revisiting the Recoherence Problem in the Fewest Switches Surface Hopping Algorithm. J Phys Chem A 2019; 123:5428-5435. [DOI: 10.1021/acs.jpca.9b03188] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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27
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Miao G, Bellonzi N, Subotnik J. An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry curvature and “magnetic” forces. J Chem Phys 2019; 150:124101. [DOI: 10.1063/1.5088770] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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28
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Miao G, Ouyang W, Subotnik J. A comparison of surface hopping approaches for capturing metal-molecule electron transfer: A broadened classical master equation versus independent electron surface hopping. J Chem Phys 2019; 150:041711. [PMID: 30709317 DOI: 10.1063/1.5050235] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within a generalized Anderson-Holstein model, we investigate electron transfer rates using two different surface hopping algorithms: a broadened classical master equation (BCME) and independent electron surface hopping (IESH). We find that for large enough bandwidth and density of one electron states, and in the presence of external friction, the IESH results converge to the BCME results for impurity-bath model systems, recovering both relaxation rates and equilibrium populations. Without external friction, however, the BCME and IESH results can strongly disagree, and preliminary evidence suggests that IESH does not always recover the correct equilibrium state. Finally, we also demonstrate that adding an electronic thermostat to IESH does help drive the metallic substrate to the correct equilibrium state, but this improvement can sometimes come at the cost of worse short time dynamics. Overall, our results should be of use for all computational chemists looking to model either gas phase scattering or electrochemical dynamics at a metal interface.
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Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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29
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Dawes R, Quintas‐Sánchez E. THE CONSTRUCTION OF AB INITIO‐BASED POTENTIAL ENERGY SURFACES. REVIEWS IN COMPUTATIONAL CHEMISTRY 2018. [DOI: 10.1002/9781119518068.ch5] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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30
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Gu B, Franco I. Electronic interactions do not affect electronic decoherence in the pure-dephasing limit. J Chem Phys 2018; 149:174115. [PMID: 30408977 DOI: 10.1063/1.5049710] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
The relationship between electronic interactions and electronic decoherence is a fundamental problem in chemistry. Here we show that varying the electron-electron interactions does not affect the electronic decoherence in the pure-dephasing limit. In this limit, the effect of varying the electronic interactions is to rigidly shift in energy the diabatic potential energy surfaces without changing their shape, thus keeping the nuclear dynamics in these surfaces that leads to the electronic decoherence intact. This analysis offers a simple and intuitive understanding of previous theoretical and computational efforts to characterize the influence of electronic interactions on the decoherence and opens opportunities to study exact electronic decoherence with approximate electronic structure theories.
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Affiliation(s)
- Bing Gu
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Ignacio Franco
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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31
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Tempelaar R, Reichman DR. Generalization of fewest-switches surface hopping for coherences. J Chem Phys 2018; 148:102309. [DOI: 10.1063/1.5000843] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roel Tempelaar
- Department of Chemistry, Columbia University, 3000 Broadway,
New York, New York 10027, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, 3000 Broadway,
New York, New York 10027, USA
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32
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Gao LH, Xie BB, Fang WH. Theories and Applications of Mixed Quantum-Classical Non-adiabatic Dynamics. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1712234] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Liang-hui Gao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Bin-bin Xie
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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33
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Gu B, Franco I. Generalized Theory for the Timescale of Molecular Electronic Decoherence in the Condensed Phase. J Phys Chem Lett 2018; 9:773-778. [PMID: 29343064 DOI: 10.1021/acs.jpclett.7b03322] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We introduce a general theory of electronic decoherence for molecules in the condensed phase that captures contributions coming from pure dephasing effects, electronic transitions among diabatic states, and their interference. The theory is constructed by taking advantage of a recently developed [ J. Phys. Chem. Lett. 2017 , 8 , 4289 - 4294 ] general expression for decoherence times that is based on an early time expansion of the purity dynamics and extends early electronic decoherence models based on pure dephasing ideas. Using this theory, we construct the decoherence time for the displaced harmonic oscillator model amended with constant and linear diabatic couplings, which is a widely used model of the photoexcited dynamics of molecules. The validity of the short-time expansion is demonstrated by the quantitative agreement of the theory with exact numerical computations of the decoherence dynamics obtained using the hierarchical equation of motion method. These developments offer a rigorous understanding of early time electronic decoherence processes that accompany basic molecular events and demonstrate that electronic transitions among diabatic states play a major role in the decoherence dynamics.
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Affiliation(s)
- Bing Gu
- Department of Chemistry, University of Rochester , Rochester, New York 14627, United States
| | - Ignacio Franco
- Department of Chemistry, University of Rochester , Rochester, New York 14627, United States
- Department of Physics, University of Rochester , Rochester, New York 14627, United States
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34
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Mallus MI, Schallwig M, Kleinekathöfer U. Relation between Vibrational Dephasing Time and Energy Gap Fluctuations. J Phys Chem B 2017. [PMID: 28625060 DOI: 10.1021/acs.jpcb.7b02693] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Dephasing processes are present in basically all applications in which quantum mechanics plays a role. These applications certainly include excitation energy and charge transfer in biological systems. In a previous study, we have analyzed the vibrational dephasing time as a function of energy gap fluctuation for a large set of molecular simulations. In that investigation, individual molecular subunits were the focus of the calculations. The set of studied molecules included bacteriochlorophylls in Fenna-Matthews-Olson and light-harvesting system 2 complexes as well as bilins in PE545 aggregates. The present work extends this study to entire complexes, including the respective intermolecular couplings. Again, it can be concluded that a universal and inverse proportionality exists between dephasing time and variance of the excitonic energy gap fluctuations, whereas the respective proportionality constants can be rationalized using the energy gap autocorrelation functions. Furthermore, these findings can be extended to the gaps between higher-lying neighboring excitonic states.
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Affiliation(s)
- Maria Ilaria Mallus
- Department of Physics and Earth Sciences, Jacobs University Bremen , Campus Ring 1, 28759 Bremen, Germany
| | - Maximilian Schallwig
- Department of Physics and Earth Sciences, Jacobs University Bremen , Campus Ring 1, 28759 Bremen, Germany
| | - Ulrich Kleinekathöfer
- Department of Physics and Earth Sciences, Jacobs University Bremen , Campus Ring 1, 28759 Bremen, Germany
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35
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Wüster S. Quantum Zeno Suppression of Intramolecular Forces. PHYSICAL REVIEW LETTERS 2017; 119:013001. [PMID: 28731744 DOI: 10.1103/physrevlett.119.013001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2016] [Indexed: 06/07/2023]
Abstract
We show that Born-Oppenheimer surfaces can intrinsically decohere, implying loss of coherence among constituent electronic basis states. We consider the example of interatomic forces due to resonant dipole-dipole interactions within a dimer of highly excited Rydberg atoms, embedded in an ultracold gas. These forces rely on a coherent superposition of two-atom electronic states, which is destroyed by continuous monitoring of the dimer state through a detection scheme utilizing the background gas atoms. We show that this intrinsic decoherence of the molecular energy surface can gradually deteriorate a repulsive dimer state, causing a mixing of attractive and repulsive character. For sufficiently strong decoherence, a Zeno-like effect causes a complete cessation of interatomic forces. We finally show how short decohering pulses can controllably redistribute population between the different molecular energy surfaces.
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Affiliation(s)
- S Wüster
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany, Department of Physics, Bilkent University, 06800 Çankaya, Ankara, Turkey and Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462 023, India
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36
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Long R, Prezhdo OV, Fang W. Nonadiabatic charge dynamics in novel solar cell materials. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1305] [Citation(s) in RCA: 50] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Run Long
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education Beijing Normal University Beijing P.R. China
| | - Oleg V. Prezhdo
- Department of Chemistry University of Southern California Los Angeles CA USA
| | - Weihai Fang
- College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education Beijing Normal University Beijing P.R. China
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37
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Abstract
We present a generalized non-Hermitian equation of motion (nH-EOM) to go beyond standard trajectory surface hopping dynamics. The derivation is based on the Born-Huang expansion of the total wave function and the polar representation of the nuclear factor. The nH-EOM contains two additional terms, a skew symmetry term iΓ with dissipation operator Γ to account for decoherence, and a kinetic-energy renormalization term to account for phase shifts, without destroying the invariance to the choice of representation. Numerically, the nH-EOM can still be solved efficiently using a semiclassical approximation in the framework of Tully's fewest-switches surface hopping (FSSH) algorithm. Applications to model Hamiltonians demonstrate improved performance over the standard FSSH approach, through comparison to exact quantum results.
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Affiliation(s)
- Xing Gao
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz, D-45470, Mülheim an der Ruhr, Germany
| | - Walter Thiel
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz, D-45470, Mülheim an der Ruhr, Germany
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38
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Subotnik JE, Jain A, Landry B, Petit A, Ouyang W, Bellonzi N. Understanding the Surface Hopping View of Electronic Transitions and Decoherence. Annu Rev Phys Chem 2016; 67:387-417. [DOI: 10.1146/annurev-physchem-040215-112245] [Citation(s) in RCA: 234] [Impact Index Per Article: 29.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Amber Jain
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Brian Landry
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Andrew Petit
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
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39
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Mallus MI, Aghtar M, Chandrasekaran S, Lüdemann G, Elstner M, Kleinekathöfer U. Relation between Dephasing Time and Energy Gap Fluctuations in Biomolecular Systems. J Phys Chem Lett 2016; 7:1102-1108. [PMID: 26950038 DOI: 10.1021/acs.jpclett.6b00134] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Excitation energy and charge transfer are fundamental processes in biological systems. Because of their quantum nature, the effect of dephasing on these processes is of interest especially when trying to understand their efficiency. Moreover, recent experiments have shown quantum coherences in such systems. As a first step toward a better understanding, we studied the relationship between dephasing time and energy gap fluctuations of the individual molecular subunits. A larger set of molecular simulations has been investigated to shed light on this dependence. This set includes bacterio-chlorophylls in Fenna-Matthews-Olson complexes, the PE545 aggregate, the LH2 complexes, DNA, photolyase, and cryptochromes. For the individual molecular subunits of these aggregates it has been confirmed quantitatively that an inverse proportionality exists between dephasing time and average gap energy fluctuation. However, for entire complexes including the respective intermolecular couplings, such a relation still needs to be verified.
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Affiliation(s)
- Maria Ilaria Mallus
- Department of Physics and Earth Sciences, Jacobs University Bremen , Campus Ring 1, 28759 Bremen, Germany
| | - Mortaza Aghtar
- Department of Physics and Earth Sciences, Jacobs University Bremen , Campus Ring 1, 28759 Bremen, Germany
| | | | - Gesa Lüdemann
- Institute of Physical Chemistry, Karlsruhe Institute of Technology , 76131 Karlsruhe, Germany
| | - Marcus Elstner
- Institute of Physical Chemistry, Karlsruhe Institute of Technology , 76131 Karlsruhe, Germany
| | - Ulrich Kleinekathöfer
- Department of Physics and Earth Sciences, Jacobs University Bremen , Campus Ring 1, 28759 Bremen, Germany
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40
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Chen HT, Reichman DR. On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems. J Chem Phys 2016; 144:094104. [DOI: 10.1063/1.4942867] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hsing-Ta Chen
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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41
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Jain A, Subotnik JE. Does Nonadiabatic Transition State Theory Make Sense Without Decoherence? J Phys Chem Lett 2015; 6:4809-4814. [PMID: 26631360 DOI: 10.1021/acs.jpclett.5b02148] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We analyze thermal rate constants as computed with surface hopping dynamics and resolve certain inconsistencies that have permeated the literature. On one hand, according to Landry and Subotnik (J. Chem. Phys. 2012, 137, 22A513), without decoherence, direct dynamics with surface hopping overestimates the rate of relaxation for the spin-boson Hamiltonian. On the other hand, according to Jain and Subotnik (J. Chem. Phys. 2015, 143, 134107), without decoherence, a transition state theory with surface hopping underestimates spin-boson rate constants. In this Letter, we resolve this apparent contradiction. We show that, without decoherence, direct dynamics and transition state theory should not agree; agreement is guaranteed only with decoherence. We also show that, even though the effects of decoherence may be hidden for isoenergetic reactions, these decoherence failures are exposed for exothermic reactions. We believe these lessons are essential when interpreting surface hopping papers published in the literature without any decoherence corrections.
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Affiliation(s)
- Amber Jain
- Department of Chemistry, University of Pennsylvania , 231 South 34th Street, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania , 231 South 34th Street, Philadelphia, Pennsylvania 19104, United States
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42
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Ouyang W, Dou W, Subotnik JE. Surface hopping with a manifold of electronic states. I. Incorporating surface-leaking to capture lifetimes. J Chem Phys 2015; 142:084109. [PMID: 25725714 DOI: 10.1063/1.4908032] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the incorporation of the surface-leaking (SL) algorithm into Tully's fewest-switches surface hopping (FSSH) algorithm to simulate some electronic relaxation induced by an electronic bath in conjunction with some electronic transitions between discrete states. The resulting SL-FSSH algorithm is benchmarked against exact quantum scattering calculations for three one-dimensional model problems. The results show excellent agreement between SL-FSSH and exact quantum dynamics in the wide band limit, suggesting the potential for a SL-FSSH algorithm. Discrepancies and failures are investigated in detail to understand the factors that will limit the reliability of SL-FSSH, especially the wide band approximation. Considering the easiness of implementation and the low computational cost, we expect this method to be useful in studying processes involving both a continuum of electronic states (where electronic dynamics are probabilistic) and processes involving only a few electronic states (where non-adiabatic processes cannot ignore short-time coherence).
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Affiliation(s)
- Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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43
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Jasper AW. Multidimensional Effects in Nonadiabatic Statistical Theories of Spin-Forbidden Kinetics: A Case Study of 3O + CO → CO2. J Phys Chem A 2015; 119:7339-51. [DOI: 10.1021/jp512942w] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ahren W. Jasper
- Combustion
Research Facility, Sandia National Laboratories, Livermore, California 94551, United States
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Landry BR, Subotnik JE. Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical). J Chem Phys 2015; 142:104102. [PMID: 25770523 DOI: 10.1063/1.4913494] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
We evaluate the accuracy of Tully's surface hopping algorithm for the spin-boson model in the limit of small to moderate reorganization energy. We calculate transition rates between diabatic surfaces in the exciton basis and compare against exact results from the hierarchical equations of motion; we also compare against approximate rates from the secular Redfield equation and Ehrenfest dynamics. We show that decoherence-corrected surface hopping performs very well in this regime, agreeing with secular Redfield theory for very weak system-bath coupling and outperforming secular Redfield theory for moderate system-bath coupling. Surface hopping can also be extended beyond the Markovian limits of standard Redfield theory. Given previous work [B. R. Landry and J. E. Subotnik, J. Chem. Phys. 137, 22A513 (2012)] that establishes the accuracy of decoherence-corrected surface-hopping in the Marcus regime, this work suggests that surface hopping may well have a very wide range of applicability.
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Affiliation(s)
- Brian R Landry
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
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Dou W, Nitzan A, Subotnik JE. Surface hopping with a manifold of electronic states. II. Application to the many-body Anderson-Holstein model. J Chem Phys 2015; 142:084110. [DOI: 10.1063/1.4908034] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Abraham Nitzan
- School of Chemistry, The Sackler Faculty of Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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46
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Abstract
While individual Tully-style fewest switches surface hopping (FSSH) trajectories are stochastic and cannot be inverted in time, it is possible to reverse in time the dynamics of a swarm of FSSH trajectories. Here we show exactly how to invert such dynamics, and we investigate the stability of such time-reversed surface hopping dynamics. We demonstrate that FSSH trajectories can be inverted successfully for short time periods, but the time-reversed dynamics become unstable for long times with multiple hopping events. We argue that this instability of FSSH going backward in time can be correlated with the stability of the FSSH algorithm going forward in time.
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Affiliation(s)
- Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania , Philadelphia, Pennsylvania 19104, United States
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Reimers JR, McKemmish LK, McKenzie RH, Hush NS. Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: the general importance of all three Born–Oppenheimer breakdown corrections. Phys Chem Chem Phys 2015. [DOI: 10.1039/c5cp02238j] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Analytical and numerical solutions describing Born–Oppenheimer breakdown in a simple, widely applicable, model depict shortcomings in modern computational methods.
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Affiliation(s)
- Jeffrey R. Reimers
- International Centre for Quantum and Molecular Structure
- College of Sciences, Shanghai University
- Shanghai 200444
- China
- School of Mathematical and Physical Sciences
| | - Laura K. McKemmish
- Department of Physics and Astronomy
- University College London
- London
- UK
- School of Chemistry
| | - Ross H. McKenzie
- School of Mathematics and Physics
- The University of Queensland
- Australia
| | - Noel S. Hush
- School of Chemistry
- The University of Sydney
- Sydney
- Australia
- School of Molecular Biosciences
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Petit AS, Subotnik JE. Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories. J Chem Phys 2014; 141:154108. [DOI: 10.1063/1.4897258] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Andrew S. Petit
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, USA
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49
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Landry BR, Subotnik JE. Quantifying the Lifetime of Triplet Energy Transfer Processes in Organic Chromophores: A Case Study of 4-(2-Naphthylmethyl)benzaldehyde. J Chem Theory Comput 2014; 10:4253-63. [DOI: 10.1021/ct500583d] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Brian R. Landry
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, 231 S. 34th Street, Philadelphia, Pennsylvania 19104, United States
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50
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Subotnik JE, Ouyang W, Landry BR. Can we derive Tully's surface-hopping algorithm from the semiclassical quantum Liouville equation? Almost, but only with decoherence. J Chem Phys 2014; 139:214107. [PMID: 24320364 DOI: 10.1063/1.4829856] [Citation(s) in RCA: 133] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied--some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly.
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Affiliation(s)
- Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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