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Bhattacharyya S, Sayer T, Montoya-Castillo A. Anomalous Transport of Small Polarons Arises from Transient Lattice Relaxation or Immovable Boundaries. J Phys Chem Lett 2024; 15:1382-1389. [PMID: 38288689 DOI: 10.1021/acs.jpclett.3c03380] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2024]
Abstract
Elucidating transport mechanisms is crucial for advancing material design, yet state-of-the-art theory is restricted to exact simulations of small lattices with severe finite-size effects or approximate ones that assume the nature of transport. We leverage algorithmic advances to tame finite-size effects and exactly simulate small polaron formation and transport in the Holstein model. We further analyze the applicability of the ubiquitously used equilibrium-based Green-Kubo relations and nonequilibrium methods to predict charge mobility. We find that these methods can converge to different values and track this disparity to finite-size dependence and the sensitivity of Green-Kubo relations to the system's topology. Contrary to standard perturbative calculations, our results demonstrate that small polarons exhibit anomalous transport that manifests transiently due to nonequilibrium lattice relaxation or permanently as a signature of immovable boundaries. These findings can offer new interpretations of transport experiments on polymers and transition metal oxides.
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Affiliation(s)
- Srijan Bhattacharyya
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States
| | - Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States
| | - Andrés Montoya-Castillo
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, United States
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2
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Sayer T, Montoya-Castillo A. Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra. J Chem Phys 2024; 160:044108. [PMID: 38270238 DOI: 10.1063/5.0185578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 12/26/2023] [Indexed: 01/26/2024] Open
Abstract
Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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3
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Wiethorn ZR, Hunter KE, Zuehlsdorff TJ, Montoya-Castillo A. Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations. J Chem Phys 2023; 159:244114. [PMID: 38153146 DOI: 10.1063/5.0180405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 12/06/2023] [Indexed: 12/29/2023] Open
Abstract
While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.
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Affiliation(s)
- Zachary R Wiethorn
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Kye E Hunter
- Department of Chemistry, Oregon State University, Corvallis, Oregon 97331, USA
| | - Tim J Zuehlsdorff
- Department of Chemistry, Oregon State University, Corvallis, Oregon 97331, USA
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4
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Chen MS, Mao Y, Snider A, Gupta P, Montoya-Castillo A, Zuehlsdorff TJ, Isborn CM, Markland TE. Elucidating the Role of Hydrogen Bonding in the Optical Spectroscopy of the Solvated Green Fluorescent Protein Chromophore: Using Machine Learning to Establish the Importance of High-Level Electronic Structure. J Phys Chem Lett 2023; 14:6610-6619. [PMID: 37459252 DOI: 10.1021/acs.jpclett.3c01444] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/28/2023]
Abstract
Hydrogen bonding interactions with chromophores in chemical and biological environments play a key role in determining their electronic absorption and relaxation processes, which are manifested in their linear and multidimensional optical spectra. For chromophores in the condensed phase, the large number of atoms needed to simulate the environment has traditionally prohibited the use of high-level excited-state electronic structure methods. By leveraging transfer learning, we show how to construct machine-learned models to accurately predict the high-level excitation energies of a chromophore in solution from only 400 high-level calculations. We show that when the electronic excitations of the green fluorescent protein chromophore in water are treated using EOM-CCSD embedded in a DFT description of the solvent the optical spectrum is correctly captured and that this improvement arises from correctly treating the coupling of the electronic transition to electric fields, which leads to a larger response upon hydrogen bonding between the chromophore and water.
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Affiliation(s)
- Michael S Chen
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - Yuezhi Mao
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - Andrew Snider
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Prachi Gupta
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Andrés Montoya-Castillo
- Department of Chemistry, University of Colorado, Boulder, Boulder, Colorado 80309, United States
| | - Tim J Zuehlsdorff
- Department of Chemistry, Oregon State University, Corvallis, Oregon 97331, United States
| | - Christine M Isborn
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
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5
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Sayer T, Farah YR, Austin R, Sambur J, Krummel AT, Montoya-Castillo A. Trion Formation Resolves Observed Peak Shifts in the Optical Spectra of Transition-Metal Dichalcogenides. Nano Lett 2023. [PMID: 37311112 DOI: 10.1021/acs.nanolett.3c01342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Monolayer transition-metal dichalcogenides (ML-TMDs) have the potential to unlock novel photonic and chemical technologies if their optoelectronic properties can be understood and controlled. Yet, recent work has offered contradictory explanations for how TMD absorption spectra change with carrier concentration, fluence, and time. Here, we test our hypothesis that the large broadening and shifting of the strong band-edge features observed in optical spectra arise from the formation of negative trions. We do this by fitting an ab initio based, many-body model to our experimental electrochemical data. Our approach provides an excellent, global description of the potential-dependent linear absorption data. We further leverage our model to demonstrate that trion formation explains the nonmonotonic potential dependence of the transient absorption spectra, including through photoinduced derivative line shapes for the trion peak. Our results motivate the continued development of theoretical methods to describe cutting-edge experiments in a physically transparent way.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder 80309, Colorado, United States
| | - Yusef R Farah
- Department of Chemistry, Colorado State University, Fort Collins 80523, Colorado, United States
| | - Rachelle Austin
- Department of Chemistry, Colorado State University, Fort Collins 80523, Colorado, United States
| | - Justin Sambur
- Department of Chemistry, Colorado State University, Fort Collins 80523, Colorado, United States
- School of Advanced Materials Discovery, Colorado State University, Fort Collins 80524, Colorado, United States
| | - Amber T Krummel
- Department of Chemistry, Colorado State University, Fort Collins 80523, Colorado, United States
| | - Andrés Montoya-Castillo
- Department of Chemistry, University of Colorado Boulder, Boulder 80309, Colorado, United States
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6
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Dominic AJ, Cao S, Montoya-Castillo A, Huang X. Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently. J Am Chem Soc 2023; 145:9916-9927. [PMID: 37104720 DOI: 10.1021/jacs.3c01095] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
Conformational changes underpin function and encode complex biomolecular mechanisms. Gaining atomic-level detail of how such changes occur has the potential to reveal these mechanisms and is of critical importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resolution than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomolecular systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the molecular dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.
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Affiliation(s)
- Anthony J Dominic
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Siqin Cao
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | | | - Xuhui Huang
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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7
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Austin R, Farah Y, Sayer T, Luther B, Montoya-Castillo A, Krummel A, Sambur J. Hot carrier extraction from 2D semiconductor photoelectrodes. Proc Natl Acad Sci U S A 2023; 120:e2220333120. [PMID: 37011201 PMCID: PMC10104502 DOI: 10.1073/pnas.2220333120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/07/2023] [Indexed: 04/05/2023] Open
Abstract
Hot carrier-based energy conversion systems could double the efficiency of conventional solar energy technology or drive photochemical reactions that would not be possible using fully thermalized, "cool" carriers, but current strategies require expensive multijunction architectures. Using an unprecedented combination of photoelectrochemical and in situ transient absorption spectroscopy measurements, we demonstrate ultrafast (<50 fs) hot exciton and free carrier extraction under applied bias in a proof-of-concept photoelectrochemical solar cell made from earth-abundant and potentially inexpensive monolayer (ML) MoS2. Our approach facilitates ultrathin 7 Å charge transport distances over 1 cm2 areas by intimately coupling ML-MoS2 to an electron-selective solid contact and a hole-selective electrolyte contact. Our theoretical investigations of the spatial distribution of exciton states suggest greater electronic coupling between hot exciton states located on peripheral S atoms and neighboring contacts likely facilitates ultrafast charge transfer. Our work delineates future two-dimensional (2D) semiconductor design strategies for practical implementation in ultrathin photovoltaic and solar fuel applications.
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Affiliation(s)
- Rachelle Austin
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
| | - Yusef R. Farah
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
| | - Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, CO80309
| | - Bradley M. Luther
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
| | | | - Amber T. Krummel
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
| | - Justin B. Sambur
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
- School of Advanced Materials Discovery, Colorado State University, Fort Collins, CO80523
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8
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Dominic AJ, Sayer T, Cao S, Markland TE, Huang X, Montoya-Castillo A. Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations. Proc Natl Acad Sci U S A 2023; 120:e2221048120. [PMID: 36920924 PMCID: PMC10041170 DOI: 10.1073/pnas.2221048120] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 02/21/2023] [Indexed: 03/16/2023] Open
Abstract
The ability to predict and understand complex molecular motions occurring over diverse timescales ranging from picoseconds to seconds and even hours in biological systems remains one of the largest challenges to chemical theory. Markov state models (MSMs), which provide a memoryless description of the transitions between different states of a biochemical system, have provided numerous important physically transparent insights into biological function. However, constructing these models often necessitates performing extremely long molecular simulations to converge the rates. Here, we show that by incorporating memory via the time-convolutionless generalized master equation (TCL-GME) one can build a theoretically transparent and physically intuitive memory-enriched model of biochemical processes with up to a three order of magnitude reduction in the simulation data required while also providing a higher temporal resolution. We derive the conditions under which the TCL-GME provides a more efficient means to capture slow dynamics than MSMs and rigorously prove when the two provide equally valid and efficient descriptions of the slow configurational dynamics. We further introduce a simple averaging procedure that enables our TCL-GME approach to quickly converge and accurately predict long-time dynamics even when parameterized with noisy reference data arising from short trajectories. We illustrate the advantages of the TCL-GME using alanine dipeptide, the human argonaute complex, and FiP35 WW domain.
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Affiliation(s)
| | - Thomas Sayer
- Department of Chemistry, University of Colorado, Boulder, CO80309
| | - Siqin Cao
- Department of Chemistry, University of Wisconsin-Madison, Madison, WI53706
| | | | - Xuhui Huang
- Department of Chemistry, University of Wisconsin-Madison, Madison, WI53706
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9
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Montoya-Castillo A, Markland TE. A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics. J Chem Phys 2023; 158:094112. [PMID: 36889969 DOI: 10.1063/5.0138664] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023] Open
Abstract
The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces to transport through nanojunctions and offer a prime target for quantum computing applications. Here, we derive the set of conditions under which fermionic operators can be exactly replaced by bosonic operators that render the problem amenable to a large toolbox of dynamical methods while still capturing the correct dynamics of n-body operators. Importantly, our analysis offers a simple guide on how one can exploit these simple maps to calculate nonequilibrium and equilibrium single- and multi-time correlation functions essential in describing transport and spectroscopy. We use this to rigorously analyze and delineate the applicability of simple yet effective Cartesian maps that have been shown to correctly capture the correct fermionic dynamics in select models of nanoscopic transport. We illustrate our analytical results with exact simulations of the resonant level model. Our work provides new insights as to when one can leverage the simplicity of bosonic maps to simulate the dynamics of many-electron systems, especially those where an atomistic representation of nuclear interactions becomes essential.
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Affiliation(s)
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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10
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Atsango AO, Montoya-Castillo A, Markland TE. An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra. J Chem Phys 2023; 158:074107. [PMID: 36813724 DOI: 10.1063/5.0138671] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Linear and nonlinear electronic spectra provide an important tool to probe the absorption and transfer of electronic energy. Here, we introduce a pure state Ehrenfest approach to obtain accurate linear and nonlinear spectra that is applicable to systems with large numbers of excited states and complex chemical environments. We achieve this by representing the initial conditions as sums of pure states and unfolding multi-time correlation functions into the Schrödinger picture. By doing this, we show that one can obtain significant improvements in accuracy over the previously used projected Ehrenfest approach and that these benefits are particularly pronounced in cases where the initial condition is a coherence between excited states. While such initial conditions do not arise when calculating linear electronic spectra, they play a vital role in capturing multidimensional spectroscopies. We demonstrate the performance of our method by showing that it is able to quantitatively capture the exact linear, 2D electronic spectroscopy, and pump-probe spectra for a Frenkel exciton model in slow bath regimes and is even able to reproduce the main spectral features in fast bath regimes.
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Affiliation(s)
- Austin O Atsango
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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11
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Abstract
Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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12
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Montoya-Castillo A, Chen MS, Raj SL, Jung KA, Kjaer KS, Morawietz T, Gaffney KJ, van Driel TB, Markland TE. Optically Induced Anisotropy in Time-Resolved Scattering: Imaging Molecular-Scale Structure and Dynamics in Disordered Media with Experiment and Theory. Phys Rev Lett 2022; 129:056001. [PMID: 35960558 DOI: 10.1103/physrevlett.129.056001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Accepted: 06/29/2022] [Indexed: 06/15/2023]
Abstract
Time-resolved scattering experiments enable imaging of materials at the molecular scale with femtosecond time resolution. However, in disordered media they provide access to just one radial dimension thus limiting the study of orientational structure and dynamics. Here we introduce a rigorous and practical theoretical framework for predicting and interpreting experiments combining optically induced anisotropy and time-resolved scattering. Using impulsive nuclear Raman and ultrafast x-ray scattering experiments of chloroform and simulations, we demonstrate that this framework can accurately predict and elucidate both the spatial and temporal features of these experiments.
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Affiliation(s)
| | - Michael S Chen
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Sumana L Raj
- Stanford PULSE Institute, SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, USA
| | - Kenneth A Jung
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Kasper S Kjaer
- Stanford PULSE Institute, SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, USA
| | - Tobias Morawietz
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Kelly J Gaffney
- Stanford PULSE Institute, SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, USA
| | - Tim B van Driel
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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13
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Cao S, Montoya-Castillo A, Wang W, Markland TE, Huang X. On the advantages of exploiting memory in Markov state models for biomolecular dynamics. J Chem Phys 2021; 153:014105. [PMID: 32640825 DOI: 10.1063/5.0010787] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
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.
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Affiliation(s)
- Siqin Cao
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | | | - Wei Wang
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Xuhui Huang
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
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14
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Mao Y, Montoya-Castillo A, Markland TE. Excited state diabatization on the cheap using DFT: Photoinduced electron and hole transfer. J Chem Phys 2020; 153:244111. [PMID: 33380087 DOI: 10.1063/5.0035593] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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.
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Affiliation(s)
- Yuezhi Mao
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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15
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Mao Y, Montoya-Castillo A, Markland TE. Accurate and efficient DFT-based diabatization for hole and electron transfer using absolutely localized molecular orbitals. J Chem Phys 2019; 151:164114. [DOI: 10.1063/1.5125275] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Affiliation(s)
- Yuezhi Mao
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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16
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Zuehlsdorff TJ, Montoya-Castillo A, Napoli JA, Markland TE, Isborn CM. Optical spectra in the condensed phase: Capturing anharmonic and vibronic features using dynamic and static approaches. J Chem Phys 2019; 151:074111. [PMID: 31438704 DOI: 10.1063/1.5114818] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
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.
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Affiliation(s)
- Tim J Zuehlsdorff
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | | | - Joseph A Napoli
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Christine M Isborn
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
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Pfalzgraff WC, Montoya-Castillo A, Kelly A, Markland TE. Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics. J Chem Phys 2019; 150:244109. [DOI: 10.1063/1.5095715] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- William C. Pfalzgraff
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
- Department of Chemistry, Chatham University, Pittsburgh, Pennsylvania 15232, USA
| | | | - Aaron Kelly
- Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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18
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Abstract
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to map a general many-fermion Hamiltonian and then consider two specific models that encode the fundamental physics of many fermionic systems, the Anderson impurity and Hubbard models. We use these models to demonstrate how efficient mappings of these Hamiltonians can be constructed using a judicious choice of index ordering of the fermions. This development provides an alternative exact route to calculate the static and dynamical properties of fermionic systems and sets the stage to exploit the quantum-classical and semiclassical hierarchies to systematically derive methods offering a range of accuracies, thus enabling the study of problems where the fermionic degrees of freedom are coupled to complex anharmonic nuclear motion and spins which lie beyond the reach of most currently available methods.
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Affiliation(s)
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California, 94305, USA.
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Montoya-Castillo A, Reichman DR. Approximate but accurate quantum dynamics from the Mori formalism. II. Equilibrium time correlation functions. J Chem Phys 2017; 146:084110. [DOI: 10.1063/1.4975388] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Montoya-Castillo A, Reichman DR. Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths. J Chem Phys 2017; 146:024107. [DOI: 10.1063/1.4973646] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Montoya-Castillo A, Reichman DR. Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics. J Chem Phys 2016; 144:184104. [DOI: 10.1063/1.4948408] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Kelly A, Montoya-Castillo A, Wang L, Markland TE. Generalized quantum master equations in and out of equilibrium: When can one win? J Chem Phys 2016; 144:184105. [DOI: 10.1063/1.4948612] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Aaron Kelly
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Lu Wang
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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Montoya-Castillo A, Berkelbach TC, Reichman DR. Extending the applicability of Redfield theories into highly non-Markovian regimes. J Chem Phys 2015; 143:194108. [DOI: 10.1063/1.4935443] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Timothy C. Berkelbach
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Jang S, Montoya-Castillo A. Charge Hopping Dynamics along a Disordered Chain in Quantum Environments: Comparative Study of Different Rate Kernels. J Phys Chem B 2015; 119:7659-65. [DOI: 10.1021/jp511933m] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Seogjoo Jang
- Department of Chemistry and
Biochemistry, Queens College
and the Graduate Center, City University of New York, 65-30 Kissena
Boulevard, Queens, New York 11367-1597, United States
| | - Andrés Montoya-Castillo
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, United States
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