Dynamics Of Complex Molecular Systems Research Articles

Optical Measurement of Photorecombination Time Delays

Recollision physics and attosecond pulse generation meld the precision of optics with collision physics. As a follow-up to our previous work, we reveal a new direction for the study of electronic structure and multielectron dynamics by exploiting the collision-physics nature of recollision. We show experimentally that, by perturbing recollision trajectories with an infrared field, photorecombination time delays can be measured entirely optically using the Cooper minimum in argon as an example. In doing so, we demonstrate the relationship between recollision trajectories and the transition moment coupling the ground and continuum states. In particular, we show that recollision trajectories are influenced by their parent ion, while it is commonly assumed they are not. Our work paves the way for the entirely optical measurement of ultrafast electron dynamics and photorecombination delays due to electronic structure, multielectron interaction, and strong-field-driven dynamics in complex molecular systems and correlated solid-state systems.

Design principles of Markov state models and variational string method for protein-protein interactions

The characterization of the thermodynamics and time-dependent kinetics is of particular interest in protein-protein association and dissociation. Markov State Models (MSMs) provide a powerful framework to characterize the dynamics of complex molecular systems by constructing a reduced stochastic model of the full system and defining a set of conformational featured microstates to determine the matrix of transition probabilities between them. Here, a systematic examination of a variety of MSMs methodologies is conducted using different combinations of input featurization and simulation methods to study how the robustness and the quality of the information generated from MSMs for protein association is affected.

Real-space subfemtosecond imaging of quantum electronic coherences in molecules

Tracking electron motion in molecules is the key to understanding and controlling chemical transformations. Contemporary techniques in attosecond science are able to generate and trace the consequences of this motion in real time, but not in real space. Scanning tunnelling microscopy, on the other hand, can locally probe the valence electron density in molecules, but cannot alone provide dynamical information at this ultrafast timescale. Here we show that, by combining scanning tunnelling microscopy and attosecond technologies, quantum electronic coherences induced in molecules by <6-fs-long carrier-envelope-phase-stable near-infrared laser pulses can be directly visualized at ångström-scale spatial and subfemtosecond temporal resolutions. We demonstrate concurrent real-space and -time imaging of coherences involving the valence orbitals of perylenetetracarboxylic dianhydride molecules, and full control over the population of the involved orbitals. This approach opens the way to the unambiguous observation and manipulation of electron dynamics in complex molecular systems.

Ultrafast Photon-Induced Tunneling Microscopy.

Unification of the techniques of ultrafast science and scanning tunneling microscopy (STM) has the potential of tracking electronic motion in molecules simultaneously in real space and real time. Laser pulses can couple to an STM junction either in the weak-field or in the strong-field interaction regime. The strong-field regime entails significant modification (dressing) of the tunneling barrier of the STM junction, whereas the weak-field or the photon-driven regime entails perturbative interaction. Here, we describe how photons carried in an ultrashort pulse interact with an STM junction, defining the basic fundamental framework of ultrafast photon-induced tunneling microscopy. Selective dipole coupling of electronic states by photons is shown to be controllable by adjusting the DC bias at the STM junction. An ultrafast tunneling microscopy involving photons is established. Consolidation of the technique calls for innovative approaches to detect photon-induced tunneling currents at the STM junction. We introduce and characterize here three techniques involving dispersion, polarization, and frequency modulation of the laser pulses to lock-in detect the laser-induced tunneling current. We show that photon-induced tunneling currents can simultaneously achieve angstrom scale spatial resolution and sub-femtosecond temporal resolution. Ultrafast photon-induced tunneling microscopy will be able to directly probe electron dynamics in complex molecular systems, without the need of reconstruction techniques.

Efficient quantum dynamics simulations of complex molecular systems: A unified treatment of dynamic and static disorder.

We present a unified and highly numerically efficient formalism for the simulation of quantum dynamics of complex molecular systems, which takes into account both temperature effects and static disorder. The methodology is based on the thermo-field dynamics formalism, and Gaussian static disorder is included into simulations via auxiliary bosonic operators. This approach, combined with the tensor-train/matrix-product state representation of the thermalized stochastic wave function, is applied to study the effect of dynamic and static disorders in charge-transfer processes in model organic semiconductor chains employing the Su-Schrieffer-Heeger (Holstein-Peierls) model Hamiltonian.

Electronic Currents and Magnetic Fields in H2+ Induced by Coherent Resonant Bichromatic Circularly Polarized Laser Pulses: Effects of Orientation, Phase, and Helicity

We theoretically study pulse phase and helicity effects on ultrafast magnetic field generation in intense bichromatic circularly polarized laser fields. Simulations are performed on the aligned molecular ion H2+ from numerical solutions of corresponding time-dependent Schrödinger equations. We demonstrate how electron coherent resonant excitation influences the phase and helicity of the optically induced magnetic field generation. The dependence of the generated magnetic field on the pulse phase arises from the interference effect between multiple excitation and ionization pathways, and is shown to be sensitive to molecular alignment and laser polarization. Molecular resonant excitation induces coherent ring electron currents, giving enhancement or suppression of the phase dependence. Pulse helicity effects control laser-induced electron dynamics in bichromatic circular polarization excitation. These phenomena are demonstrated by a molecular attosecond photoionization model and coherent electron current theory. The results offer a guiding principle for generating ultrafast magnetic fields and for studying coherent electron dynamics in complex molecular systems.

Tracking Ultrafast Structural Dynamics by Time-Domain Raman Spectroscopy.

In traditional Raman spectroscopy, narrow-band light is irradiated on a sample, and its inelastic scattering, i.e., Raman scattering, is detected. The energy difference between the Raman scattering and the incident light corresponds to the vibrational energy of the molecule, providing the Raman spectrum that contains rich information about the molecular-level properties of the materials. On the other hand, by using ultrashort optical pulses, it is possible to induce Raman-active coherent nuclear motion of the molecule and to observe the molecular vibration in real time. Moreover, this time-domain Raman measurement can be combined with femtosecond photoexcitation, triggering chemical changes, which enables tracking ultrafast structural dynamics in a form of “time-resolved” time-domain Raman spectroscopy, also known as time-resolved impulsive stimulated Raman spectroscopy. With the advent of stable, ultrashort laser pulse sources, time-resolved impulsive stimulated Raman spectroscopy now realizes high sensitivity and a wide detection frequency window from THz to 3000 cm–1, and has seen success in unveiling the molecular mechanisms underlying the efficient functions of complex molecular systems. In this Perspective, we overview the present status of time-domain Raman spectroscopy, particularly focusing on its application to the study of femtosecond structural dynamics. We first explain the principle and a brief history of time-domain Raman spectroscopy and then describe the apparatus and recent applications to the femtosecond dynamics of complex molecular systems, including proteins, molecular assemblies, and functional materials. We also discuss future directions for time-domain Raman spectroscopy, which has reached a status allowing a wide range of applications.

Simulating energy transfer dynamics in the Fenna-Matthews-Olson complex via the modified generalized quantum master equation.

The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna-Matthews-Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model.

An Ab Initio Multiple Cloning Method for Non-Adiabatic Excited-State Molecular Dynamics in NWChem.

The recently developed ab initio multiple cloning (AIMC) approach based on the multiconfigurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to nonadiabatic dynamics with a particular strength in the proper description of decoherence effects because of the branching of vibrational wavepackets at a level crossing. Here, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-field theory to determine the equations of motion for classical trajectories. The multidimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based nonadiabatic coupling approach within the AIMC method, all observables are calculated on-the-fly in the nonadiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level nonadiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.

Expanding the Range of Hierarchical Equations of Motion by Tensor-Train Implementation.

The non-equilibrium thermo-field dynamics formulation of the hierarchical equations of motion combined with the tensor-train representation of the density matrix is discussed, and a new numerical integration scheme is introduced. The numerical methodology is based on an adaptive low-rank Galerkin reduction scheme and can preserve linear invariants (such as the trace of the density matrix). The method is applied to the study of the charge transfer dynamics in model pentacene molecular aggregates. The combined effect of a discrete set of molecular vibrational modes and a thermal bath is investigated, paying special attention to the coherent-incoherent transition of the charge transport. The new computational framework is shown to be a very promising methodology for the study of the quantum dynamics of complex molecular systems in the condensed phase.

A critical perspective on Markov state model treatments of protein-protein association using coarse-grained simulations.

Atomic-level information is essential to explain the specific interactions governing protein–protein recognition in terms of structure and dynamics. Of particular interest is a characterization of the time-dependent kinetic aspects of protein–protein association and dissociation. A powerful framework to characterize the dynamics of complex molecular systems is provided by Markov State Models (MSMs). The central idea is to construct a reduced stochastic model of the full system by defining a set of conformational featured microstates and determining the matrix of transition probabilities between them. While a MSM framework can sometimes be very effective, different combinations of input featurization and simulation methods can significantly affect the robustness and the quality of the information generated from MSMs in the context of protein association. Here, a systematic examination of a variety of MSMs methodologies is undertaken to clarify these issues. To circumvent the uncertainties caused by sampling issues, we use a simplified coarse-grained model of the barnase–barstar protein complex. A sensitivity analysis is proposed to identify the microstates of an MSM that contribute most to the error in conjunction with the transition-based reweighting analysis method for a more efficient and accurate MSM construction.

Femtosecond Structural Dynamics of Complex Molecular Systems Studied by Time-Domain Raman Spectroscopy Using Few-Cycle Pulses

Femtosecond Structural Dynamics of Complex Molecular Systems Studied by Time-Domain Raman Spectroscopy Using Few-Cycle Pulses

A Primer on Temperature-Controlled Entangled-Photon Virtual-State Spectroscopy

Entangled two-photon absorption spectroscopy has been widely recognized as a promising tool for revealing important information about the structure and dynamics of complex molecular systems. In this contribution, we present the basics of the theory behind this technique and describe a novel experimental scheme known as temperature-controlled entangled-photon absorption spectroscopy, which constitutes the first, realistic proposal for the experimental implementation of nonlinear spectroscopy with quantum light.

Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach.

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.

Nonadiabatic Molecular Dynamics with Tight-Binding Fragment Molecular Orbitals.

This work presents a nonadiabatic molecular dynamics methodology that relies on the use of fragment molecular orbitals computed using tight-binding Hamiltonians. The approach aims to model charge and energy transfer in large systems via quantum-classical trajectory-based approaches. The technique relies on a chemically motivated fragmentation of the overall system into arbitrary fragments. Several types of fragment molecular orbitals (FMO) can be constructed and used in nonadiabatic simulations, comprising quasidiabatic, adiabatic, and Löwdin-transformed ones. The adiabatic FMOs are found to be most suitable for modeling nonadiabatic dynamics in complex molecular systems. The overall algorithm shows advantageous scaling properties, making it possible to model long time scale charge transfer processes in large systems with many hundreds of atoms. The approach is applied to study charge transfer in subphtalocyanine(SubPc)/C60 heterojunction. The computational results emphasize the importance of decoherence and details of interfacial structure for obtaining accurate charge transfer time scales in SubPc/C60 herejunctions.

Markov state modeling and dynamical coarse-graining via discrete relaxation path sampling.

A method is derived to coarse-grain the dynamics of complex molecular systems to a Markov jump process (MJP) describing how the system jumps between cells that fully partition its state space. The main inputs are relaxation times for each pair of cells, which are shown to be robust with respect to positioning of the cell boundaries. These relaxation times can be calculated via molecular dynamics simulations performed in each cell separately and are used in an efficient estimator for the rate matrix of the MJP. The method is illustrated through applications to Sinai billiards and a cluster of Lennard-Jones discs.

Signatures of conical intersections in two-dimensional electronic spectra

Femtosecond two-dimensional (2D) electronic spectroscopy is a versatile technique for the exploration of ultrafast photoinduced dynamics in complex molecular systems. We have performed the first computational simulation of a femtosecond 2D electronic spectrum for a model system with a conical intersection, using the wave-function version of the equation-of-motion phase-matching approach. It is shown that the 2D electronic spectrum of a two-state two-mode conical intersection simultaneously provides information on the complicated energy-level structure of the vibronically coupled states as well as on the time-dependent electronic population decay. The challenges and prospects of future simulations of 2D spectra of multi-mode conical intersections are briefly discussed.

Criteria for the accuracy of small polaron quantum master equation in simulating excitation energy transfer dynamics

The small polaron quantum master equation (SPQME) proposed by Jang et al. [J. Chem. Phys. 129, 101104 (2008)] is a promising approach to describe coherent excitation energy transfer dynamics in complex molecular systems. To determine the applicable regime of the SPQME approach, we perform a comprehensive investigation of its accuracy by comparing its simulated population dynamics with numerically exact quasi-adiabatic path integral calculations. We demonstrate that the SPQME method yields accurate dynamics in a wide parameter range. Furthermore, our results show that the accuracy of polaron theory depends strongly upon the degree of exciton delocalization and timescale of polaron formation. Finally, we propose a simple criterion to assess the applicability of the SPQME theory that ensures the reliability of practical simulations of energy transfer dynamics with SPQME in light-harvesting systems.

Two-Dimensional Fluorescence Lifetime Correlation Spectroscopy. 1. Principle

Fluorescence correlation spectroscopy (FCS) is a unique tool for investigating microsecond molecular dynamics of complex molecules in equilibrium. However, application of FCS in the study of molecular dynamics has been limited, owing to the complexity in the extraction of physically meaningful information. In this work, we develop a new method that combines FCS and time-correlated single photon counting (TCPSC) to extract unambiguous information about equilibrium dynamics of complex molecular systems. In this method, which we name two-dimensional fluorescence lifetime correlation spectroscopy (2D FLCS), we analyze the correlation of the fluorescence photon pairs, referring to the fluorescence lifetime. We first obtain the correlations of the photon pairs with respect to the excitation-emission delay times in the form of a two-dimensional (2D) map. Then, the 2D map is converted to the correlations between different species that have distinct fluorescence lifetimes using inverse Laplace transformation. This 2D FLCS is capable of visualizing the equilibration dynamics of complex molecules with microsecond time resolution at the single-molecule level. We performed a kinetic Monte Carlo simulation of a TCPSC-FCS experiment as a proof-of-principle example. The result clearly shows the validity of the proposed method and its high potential in analyzing the photon data of dynamic systems.

Electronically Nonadiabatic Dynamics in Complex Molecular Systems: An Efficient and Accurate Semiclassical Solution

Chemical reaction dynamics is always a central theme in chemistry research. In many important chemical processes, reaction dynamics is electronically nonadiabatic, i.e., dynamics involves coupled multiple electronic states. We demonstrate in this paper that a semiclassical (SC) treatment based on an initial value representation methodology and a classical mapping formalism for the electronic degrees of freedom is now able to provide a rigorous and practical solution to electronically nonadiabatic dynamics in complex molecular systems. The key component of this treatment is to incorporate a correlated importance sampling protocol in nonadiabatic SC calculations, which results in a speedup factor of 100 or more in comparison with that using the standard sampling approach. This is illustrated by application to a two-state model coupled with up to 10 nuclear bath modes for a benchmark nonadiabatic excitation energy transfer problem. This work provides great opportunities for the effectively theoretical investigations on reaction mechanisms in complex molecular systems, in which electronically nonadiabatic dynamics plays an importance role.