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  • 1
    Online Resource
    Online Resource
    AIP Publishing ; 2020
    In:  The Journal of Chemical Physics Vol. 153, No. 1 ( 2020-07-07)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 153, No. 1 ( 2020-07-07)
    Abstract: Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called “lag time”). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5–10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2020
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 2
    Online Resource
    Online Resource
    AIP Publishing ; 2017
    In:  The Journal of Chemical Physics Vol. 146, No. 2 ( 2017-01-14)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 146, No. 2 ( 2017-01-14)
    Abstract: We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2017
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 3
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 151, No. 7 ( 2019-08-21)
    Abstract: Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here, we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclear-electronic time scale separation; the Franck-Condon method, which includes dynamical effects but generally only at the harmonic level; and the recently introduced ensemble zero-temperature Franck-Condon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2019
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 4
    Online Resource
    Online Resource
    AIP Publishing ; 2020
    In:  The Journal of Chemical Physics Vol. 153, No. 24 ( 2020-12-28)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 153, No. 24 ( 2020-12-28)
    Abstract: Excited state electron and hole transfer underpin fundamental steps in processes such as exciton dissociation at photovoltaic heterojunctions, photoinduced charge transfer at electrodes, and electron transfer in photosynthetic reaction centers. Diabatic states corresponding to charge or excitation localized species, such as locally excited and charge transfer states, provide a physically intuitive framework to simulate and understand these processes. However, obtaining accurate diabatic states and their couplings from adiabatic electronic states generally leads to inaccurate results when combined with low-tier electronic structure methods, such as time-dependent density functional theory, and exorbitant computational cost when combined with high-level wavefunction-based methods. Here, we introduce a density functional theory (DFT)-based diabatization scheme that directly constructs the diabatic states using absolutely localized molecular orbitals (ALMOs), which we denote as Δ-ALMO(MSDFT2). We demonstrate that our method, which combines ALMO calculations with the ΔSCF technique to construct electronically excited diabatic states and obtains their couplings with charge-transfer states using our MSDFT2 scheme, gives accurate results for excited state electron and hole transfer in both charged and uncharged systems that underlie DNA repair, charge separation in donor–acceptor dyads, chromophore-to-solvent electron transfer, and singlet fission. This framework for the accurate and efficient construction of excited state diabats and evaluation of their couplings directly from DFT thus offers a route to simulate and elucidate photoinduced electron and hole transfer in large disordered systems, such as those encountered in the condensed phase.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2020
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 5
    Online Resource
    Online Resource
    AIP Publishing ; 2016
    In:  The Journal of Chemical Physics Vol. 144, No. 18 ( 2016-05-14)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 144, No. 18 ( 2016-05-14)
    Abstract: We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion to circumvent the difficulty of projected dynamics, we obtain a self-consistent equation for the memory kernel which requires only knowledge of normally evolved auxiliary kernels. To illustrate the properties of the current approach, we focus on the spin-boson model and limit our attention to the use of a simple and inexpensive quasi-classical dynamics, given by the Ehrenfest method, for the calculation of the auxiliary kernels. For the first time, we provide a detailed analysis of the dependence of the properties of the memory kernels obtained via different projection operators, namely, the thermal (Redfield-type) and population based (NIBA-type) projection operators. We further elucidate the conditions that lead to short-lived memory kernels and the regions of parameter space to which this program is best suited. Via a thorough analysis of the different closures available for the auxiliary kernels and the convergence properties of the self-consistently extracted memory kernel, we identify the mechanisms whereby the current approach leads to a significant improvement over the direct usage of standard semi- and quasi-classical dynamics.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2016
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 6
    Online Resource
    Online Resource
    AIP Publishing ; 2017
    In:  The Journal of Chemical Physics Vol. 146, No. 8 ( 2017-02-28)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 146, No. 8 ( 2017-02-28)
    Abstract: The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2017
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 7
    Online Resource
    Online Resource
    AIP Publishing ; 2023
    In:  The Journal of Chemical Physics Vol. 158, No. 1 ( 2023-01-07)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 158, No. 1 ( 2023-01-07)
    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.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2023
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 8
    Online Resource
    Online Resource
    AIP Publishing ; 2016
    In:  The Journal of Chemical Physics Vol. 144, No. 18 ( 2016-05-14)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 144, No. 18 ( 2016-05-14)
    Abstract: Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2016
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 9
    Online Resource
    Online Resource
    AIP Publishing ; 2015
    In:  The Journal of Chemical Physics Vol. 143, No. 19 ( 2015-11-21)
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 143, No. 19 ( 2015-11-21)
    Abstract: We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high-frequency bath degrees of freedom only, while the low-frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. We further generalize the method to multi-site models and compare with exact results for a model of the Fenna–Matthews–Olson complex. The results from the method are found to dramatically improve Redfield dynamics in highly non-Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low-frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2015
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
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  • 10
    In: The Journal of Chemical Physics, AIP Publishing, Vol. 150, No. 24 ( 2019-06-28)
    Abstract: Methods derived from the generalized quantum master equation (GQME) framework have provided the basis for elucidating energy and charge transfer in systems ranging from molecular solids to photosynthetic complexes. Recently, the nonperturbative combination of the GQME with quantum-classical methods has resulted in approaches whose accuracy and efficiency exceed those of the original quantum-classical schemes while offering significant accuracy improvements over perturbative expansions of the GQME. Here, we show that, while the non-Markovian memory kernel required to propagate the GQME scales quartically with the number of subsystem states, the number of trajectories required scales at most quadratically when using quantum-classical methods to construct the kernel. We then present an algorithm that allows further acceleration of the quantum-classical GQME by providing a way to selectively sample the kernel matrix elements that are most important to the process of interest. We demonstrate the utility of these advances by applying the combination of Ehrenfest mean field theory with the GQME (MF-GQME) to models of the Fenna-Matthews-Olson (FMO) complex and the light harvesting complex II (LHCII), with 7 and 14 states, respectively. This allows us to show that the MF-GQME is able to accurately capture all the relevant dynamical time scales in LHCII: the initial nonequilibrium population transfer on the femtosecond time scale, the steady state-type trapping on the picosecond time scale, and the long time population relaxation. Remarkably, all of these physical effects spanning tens of picoseconds can be encoded in a memory kernel that decays only after ∼65 fs.
    Type of Medium: Online Resource
    ISSN: 0021-9606 , 1089-7690
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2019
    detail.hit.zdb_id: 3113-6
    detail.hit.zdb_id: 1473050-9
    Location Call Number Limitation Availability
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