Three-point frequency fluctuation correlation functions of the OH stretch in liquid water

Characterizing the dynamics of the OH stretch in isotopically substituted liquid water (HOD in D(2)O) in terms of three-point frequency fluctuation correlation functions and joint probability densities shows that dynamics during hydrogen bond rearrangements occur primarily along a coordinate which is perpendicular to the spectroscopic coordinate. Molecular dynamics simulations show that three-point correlation functions are sensitive to this motion, unlike two-point correlation functions, and can select sets of trajectories which linger in the area of the transition state. Three-dimensional-infrared correlation spectroscopy could potentially measure these dynamics, though motional narrowing significantly changes the shape of the resulting spectra.     

Coherence transfer processes in vibrational relaxation of polyatomic molecules in condensed media

The vibrational relaxation of a polyatomic molecule in a condensed host is studied by a consideration of two molecular vibrations. Relaxation processes, intermode coupling terms and vibrational frequency fluctuation contributions are retained. Population decay (T₁), dephasing (T₂), and coherence transfer rates are evaluated through second order in the limit where the host bath dynamics are rapid compared to these molecular timescales. The rates are expressed in terms of temperature and frequency dependent bath correlation functions. For the special case of a three level system (the ground state and ones where one of the two vibrational modes is excited) the important effects of anharmonicity are incorporated. It is shown that certain coherence transfer terms involve zero frequency bath correlation functions, so they should be larger than the high frequency ones which obey modified energy gap laws. A discussion is presented of the types of interactions which may contribute to these coherence transfer processes.     

Revealing time bunching effect in single-molecule enzyme conformational dynamics

In this perspective, we focus our discussion on how the single-molecule spectroscopy and statistical analysis are able to reveal enzyme hidden properties, taking the study of T4 lysozyme as an example. Protein conformational fluctuations and dynamics play a crucial role in biomolecular functions, such as in enzymatic reactions. Single-molecule spectroscopy is a powerful approach to analyze protein conformational dynamics under physiological conditions, providing dynamic perspectives on a molecular-level understanding of protein structure-function mechanisms. Using single-molecule fluorescence spectroscopy, we have probed T4 lysozyme conformational motions under the hydrolysis reaction of a polysaccharide of E. coli B cell walls by monitoring the fluorescence resonant energy transfer (FRET) between a donor-acceptor probe pair tethered to T4 lysozyme domains involving open-close hinge-bending motions. Based on the single-molecule spectroscopic results, molecular dynamics simulation, a random walk model analysis, and a novel 2D statistical correlation analysis, we have revealed a time bunching effect in protein conformational motion dynamics that is critical to enzymatic functions. Bunching effect implies that conformational motion times tend to bunch in a finite and narrow time window. We show that convoluted multiple Poisson rate processes give rise to the bunching effect in the enzymatic reaction dynamics. Evidently, the bunching effect is likely common in protein conformational dynamics involving in conformation-gated protein functions. In this perspective, we will also discuss a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anti-correlated fluctuations under a non-correlated noise background. Using this new method, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anti-correlated, or non-correlated; after which, a cross correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis.     

Hydrodynamic correlation functions for molten salts

Abstract

The linearized hydrodynamic equations for a binary ionic fluid, with specific reference to a dissociated molten salt, are used to evaluate correlation functions of local fluctuation variables and the corresponding response functions. Previous results for the instantaneous correlation functions are extended and connected with thermodynamic fluctuation theory. Different dynamical behaviours, depending on the relative magnitude of the relaxation frequency for charge fluctuations and the sound wave frequency, are demonstrated. When 4πσ/? > ck, charge fluctuations are uncoupled from mass fluctuations, the latter being isomorphous to those of a one-component neutral fluid. Kubo relations for the transport coefficients are derived in this regime. When 4πσ/? < ck, the behaviour of the ionic fluid becomes isomorphous to that of a neutral mixture, with electrical conduction playing a role analogous to interdiffusion and contributing, in particular, to the damping of sound waves. An interpolation formula between these two limiting behaviours of the relaxation frequencies is also derived. The consequences of these results for the light scattering spectrum of an ionic fluid are briefly discussed     

Measuring Ultrafast Spectral Diffusion and Correlation Dynamics by Two‐Dimensional Electronic Spectroscopy

The frequency fluctuation correlation function (FFCF) measures the spectral diffusion of a state's transition while the frequency fluctuation cross‐correlation function (FXCF) measures the correlation dynamics between the transitions of two separate states. These quantities contain a wealth of information on how the chromophores or excitonic states interact and couple with its environment and with each other. We summarize the experimental implementations and theoretical considerations of using two‐dimensional electronic spectroscopy to characterize FFCFs and FXCFs. Applications can be found in systems such as the chlorophyll pigment molecules in light‐harvesting complexes and CdSe nanomaterials.     

Hydrodynamic fluctuations and spinodal decomposition in ternary systems

Time correlation functions of concentration fluctuations are obtained from hydrodynamic fluctuation theory extended to ternary systems. The coupling between the concentrations of the different species is accounted for and leads naturally to symmetric correlation functions unlike those previously reported. The time correlation functions of concentration fluctuations incorporating the effect of thermal noise are used to obtain the initial scattering intensity of ternary polymer-polymer-solvent systems undergoing spinodal decomposition. It is shown that the scattering function is represented by a sum of three exponentials. Single exponential growth is predicted under certain conditions which appear to have been met in the limited experimental data available. © 1994 John Wiley & Sons, Inc.     

Ultrafast Structural Fluctuations of Myoglobin‐Bound Thiocyanate and Selenocyanate Ions Measured with Two‐Dimensional Infrared Photon Echo Spectroscopy

Structural dynamics within the distal cavity of myoglobin protein is investigated using 2D‐IR and IR pump–probe spectroscopy of the N≡C stretch modes of heme‐bound thiocyanate and selenocyanate ions. Although myoglobin‐bound thiocyanate group shows a doublet in its IR absorption spectrum, no cross peaks originating from chemical exchange between the two components are observed in the time‐resolved 2D IR spectra within the experimental time window. Frequency–frequency correlation functions of the two studied anionic ligands are obtained by means of a few different analysis approaches; these functions were then used to elucidate the differences in structural fluctuation around ligand, ligand–protein interactions, and the degree of structural heterogeneity within the hydrophobic pocket of these myoglobin complexes.     

A time correlation function theory describing static field enhanced third order optical effects at interfaces

Sum vibrational frequency spectroscopy, a second order optical process, is interface specific in the dipole approximation. At charged interfaces, there exists a static field, and as a direct consequence, the experimentally detected signal is a combination of enhanced second and static field induced third order contributions. There is significant evidence in the literature of the importance/relative magnitude of this third order contribution, but no previous molecularly detailed approach existed to separately calculate the second and third order contributions. Thus, for the first time, a molecularly detailed time correlation function theory is derived here that allows for the second and third order contributions to sum frequency vibrational spectra to be individually determined. Further, a practical, molecular dynamics based, implementation procedure for the derived correlation functions that describe the third order phenomenon is also presented. This approach includes a novel generalization of point atomic polarizability models to calculate the hyperpolarizability of a molecular system. The full system hyperpolarizability appears in the time correlation functions responsible for third order contributions in the presence of a static field.     

Tunneling dynamics of a double‐well oscillator: Effects of barrier fluctuation and thermal modulation

The tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier is studied. For barriers fluctuating randomly in time we show by exact numerical calculation the significant effect of barrier fluctuation on the tunneling behavior of the particle. At nonzero temperatures the computed tunneling rate constant passes through a maximum when plotted against fluctuation frequency. The resonant frequency (at which the maximum appears) slowly decreases with increase in temperature and attains a constant value at higher temperature and it increases linearly with increase in barrier height of the potential. Another important observation is that in presence of barrier fluctuation the dependence of tunneling rate constant on temperature is strongly guided by the barrier fluctuation frequency. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 280–285, 2003     

Centroid molecular dynamics: comparison with exact results for model systems

The relation between the accuracy of centroid molecular dynamics correlation functions, and the geometry of the centroid potential is investigated. It is shown that, depending on the temperature, there exist several regimes, and in each of them certain features of the exact Kubo correlation functions are reproduced. The change of regimes is related to the emergence of barriers in the centroid potential. In order to clarify how the above described picture of regimes is modified in real systems when dissipation is important, a methodology is developed to test the accuracy of centroid correlation functions for the model of a particle coupled to a harmonic heat bath. A modification of the centroid molecular dynamics method to include the influence of the heat bath is introduced. Preliminary results of comparison of centroid molecular dynamics with the numerically exact results of filtered propagator functional method are presented.     

Effects of the DNA state fluctuation on single-cell dynamics of self-regulating gene

A dynamical mean-field theory is developed to analyze stochastic single-cell dynamics of gene expression. By explicitly taking account of nonequilibrium and nonadiabatic features of the DNA state fluctuation, two-time correlation functions and response functions of single-cell dynamics are derived. The method is applied to a self-regulating gene to predict a rich variety of dynamical phenomena such as an anomalous increase of relaxation time and oscillatory decay of correlations. The effective "temperature" defined as the ratio of the correlation to the response in the protein number is small when the DNA state change is frequent, while it grows large when the DNA state change is infrequent, indicating the strong enhancement of noise in the latter case.     

Temporal asymmetry of fluctuations in nonequilibrium steady states: links with correlation functions and nonlinear response

The presence of temporal asymmetries in fluctuation paths of nonequilibrium systems has recently been confirmed numerically in nonequilibrium molecular dynamics simulations of particular deterministic systems. Here we show that this is a common feature of homogeneously driven and thermostatted, reversible, deterministic, chaotic, nonequilibrium systems of interacting particles. This is done by expressing fluctuation paths as correlation functions. The theoretical arguments look rather general, and we expect them to easily extend to other forms of driving and thermostats. The emergence of asymmetry is also justified using the transient time correlation function expression of nonlinear response theory. Numerical simulations are used to verify our arguments.     

A guide to accurate measurement of diffusion using fluorescence correlation techniques with blinking quantum dot nanoparticle labels

Fluctuation-based fluorescence correlation techniques are widely used to study dynamics of fluorophore labeled biomolecules in cells. Semiconductor quantum dots (QDs) have been developed as bright and photostable fluorescent probes for various biological applications. However, the fluorescence intermittency of QDs, commonly referred to as "blinking", is believed to complicate quantitative correlation spectroscopy measurements of transport properties, as it is an additional source of fluctuations that contribute on a wide range of time scales. The QD blinking fluctuations obey power-law distributions so there is no single characteristic fluctuation time for this phenomenon. Consequently, it is highly challenging to separate fluorescence blinking fluctuations from those due to transport dynamics. Here, we quantify the bias introduced by QD blinking in transport measurements made using fluctuation methods. Using computer simulated image time series of diffusing point emitters with set "on" and "off" time emission characteristics, we show that blinking results in a systematic overestimation of the diffusion coefficients measured with correlation analysis when a simple diffusion model is used to fit the time correlation decays. The relative error depends on the inherent blinking power-law statistics, the sampling rate relative to the characteristic diffusion time and blinking times, and the total number of images in the time series. This systematic error can be significant; moreover, it can often go unnoticed in common transport model fits of experimental data. We propose an alternative fitting model that incorporates blinking and improves the accuracy of the recovered diffusion coefficients. We also show how to completely eliminate the bias by applying k-space image correlation spectroscopy, which completely separates the diffusion and blinking dynamics, and allows the simultaneous recovery of accurate diffusion coefficients and QD blinking probability distribution function exponents.     

Vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to harmonic bath

The vibrational spectroscopy and relaxation of an anharmonic oscillator coupled to a harmonic bath are examined to assess the applicability of the time correlation function (TCF), the response function, and the semiclassical frequency modulation (SFM) model to the calculation of infrared (IR) spectra. These three approaches are often used in connection with the molecular dynamics simulations but have not been compared in detail. We also analyze the vibrational energy relaxation (VER), which determines the line shape and is itself a pivotal process in energy transport. The IR spectra and VER are calculated using the generalized Langevin equation (GLE), the Gaussian wavepacket (GWP) method, and the quantum master equation (QME). By calculating the vibrational frequency TCF, a detailed analysis of the frequency fluctuation and correlation time of the model is provided. The peak amplitude and width in the IR spectra calculated by the GLE with the harmonic quantum correction are shown to agree well with those by the QME though the vibrational frequency is generally overestimated. The GWP method improves the peak position by considering the zero-point energy and the anharmonicity although the red-shift slightly overshoots the QME reference. The GWP also yields an extra peak in the higher-frequency region than the fundamental transition arising from the difference frequency of the center and width oscillations of a wavepacket. The SFM approach underestimates the peak amplitude of the IR spectra but well reproduces the peak width. Further, the dependence of the VER rate on the strength of an excitation pulse is discussed.     

Amide I vibrational dynamics of N-methylacetamide in polar solvents: the role of electrostatic interactions

The vibrational frequency of the amide I transition of peptides is known to be sensitive to the strength of its hydrogen bonding interactions. In an effort to account for interactions with hydrogen bonding solvents in terms of electrostatics, we study the vibrational dynamics of the amide I coordinate of N-methylacetamide in prototypical polar solvents: D2O, CDCl3, and DMSO-d6. These three solvents have varying hydrogen bonding strengths, and provide three distinct solvent environments for the amide group. The frequency-frequency correlation function, the orientational correlation function, and the vibrational relaxation rate of the amide I vibration in each solvent are retrieved by using three-pulse vibrational photon echoes, two-dimensional infrared spectroscopy, and pump-probe spectroscopy. Direct comparisons are made to molecular dynamics simulations. We find good quantitative agreement between the experimentally retrieved and simulated correlation functions over all time scales when the solute-solvent interactions are determined from the electrostatic potential between the solvent and the atomic sites of the amide group.     

Combined electronic structure/molecular dynamics approach for ultrafast infrared spectroscopy of dilute HOD in liquid H2O and D2O

We present a new approach that combines electronic structure methods and molecular dynamics simulations to investigate the infrared spectroscopy of condensed phase systems. This approach is applied to the OH stretch band of dilute HOD in liquid D2O and the OD stretch band of dilute HOD in liquid H2O for two commonly employed models of water, TIP4P and SPC/E. Ab initio OH and OD anharmonic transition frequencies are calculated for 100 HOD x (D2O)n and HOD x(H2O)n (n = 4-9) clusters randomly selected from liquid water simulations. A linear empirical relationship between the ab initio frequencies and the component of the electric field from the solvent along the bond of interest is developed. This relationship is used in a molecular dynamics simulation to compute frequency fluctuation time-correlation functions and infrared absorption line shapes. The normalized frequency fluctuation time-correlation functions are in good agreement with the results of previous theoretical approaches. Their long-time decay times are 0.5 ps for the TIP4P model and 0.9 ps for the SPC/E model, both of which appear to be somewhat too fast compared to recent experiments. The calculated line shapes are in good agreement with experiment, and improve upon the results of previous theoretical approaches. The methods presented are simple, and transferable to more complicated systems.     

Constancy maximization based weight optimization in high dimensional model representation for multivariate functions

High Dimensional Model Representation (HDMR) method is a technique that represents a multivariate function in terms of less-variate functions. Even though the method has a finite expansion, to determine the components of this expansion is very expensive due to integration based natures of the components. Hence, the HDMR expansion is generally truncated at certain multivariance level and such approximations are produced to represent the given multivariate function approximately. The weight function selection becomes an important issue for the HDMR based applications when it is desired to give different importances to function values at different points. An appropriately chosen weight function may increase the quality of the approximation incredibly. This work aims at a multivariate weight function optimization to obtain high quality approximations through the HDMR method to represent multivariate functions. The proposed optimization considers constancy measurer maximization which produces a quadratic vector equation to be solved. Another contribution of this work is to use a recently developed method, fluctuation free integration, with HDMR, to solve this equation easily. This work is an extension of a previous work about weight optimization in HDMR for univariate functions.     

Local hydrogen bonding dynamics and collective reorganization in water: ultrafast infrared spectroscopy of HOD/D(2)O

We present an investigation into hydrogen bonding dynamics and kinetics in water using femtosecond infrared spectroscopy of the OH stretching vibration of HOD in D(2)O. Infrared vibrational echo peak shift and polarization-selective pump-probe experiments were performed with mid-IR pulses short enough to capture all relevant dynamical processes. The experiments are self-consistently analyzed with a nonlinear response function expressed in terms of three dynamical parameters for the OH stretching vibration: the frequency correlation function, the lifetime, and the second Legendre polynomial dipole reorientation correlation function. It also accounts for vibrational-relaxation-induced excitation of intermolecular motion that appears as heating. The long time, picosecond behavior is consistent with previous work, but new dynamics are revealed on the sub-200 fs time scale. The frequency correlation function is characterized by a 50 fs decay and 180 fs beat associated with underdamped intermolecular vibrations of hydrogen bonding partners prior to 1.4 ps exponential relaxation. The reorientational correlation function observes a 50 fs librational decay prior to 3 ps diffusive reorientation. Both of these correlation functions compare favorably with the predictions from classical molecular dynamics simulations. The time-dependent behavior can be separated into short and long time scales by the 340 fs correlation time for OH frequency shifts. The fast time scales arise from dynamics that are mainly local: fluctuations in hydrogen bond distances and angles within relatively fixed intermolecular configurations. On time scales longer than the correlation time, dephasing and reorientations reflect collective reorganization of the liquid structure. Since the OH transition frequency and dipole are only weakly sensitive to these collective coordinates, this is a kinetic regime which gives an effective rate for exchange of intermolecular structures.     

Structure and Dynamics of Water/Methanol Mixtures at Hydroxylated Silica Interfaces Relevant to Chromatography

The spectroscopy and dynamics of water/methanol (MeOH) mixtures at hydroxylated silica surfaces is investigated from atomistic simulations. The particular focus is on how the structural dynamics of MeOH changes when comparing surface‐bound and MeOH in the bulk. From analyzing the frequency frequency correlation functions it is found that the dynamics on the picosecond time scale differs by almost a factor of two. While the relaxation time is 2.0 ps for MeOH in the bulk solvent it is considerably slowed‐down to 3.5 ps for surface‐bound MeOH. Surface‐adsorbed MeOH molecules reside there for several nanoseconds and their H‐bonds are strongly oriented towards the surface‐OH groups. These results are of particular relevance for chromatographic systems where the solvent may play a central role in their function. The present simulations suggest that surface‐sensitive spectroscopic techniques should be useful in better characterizing such heterogeneous systems and provide detailed insight into solvent dynamics and structure relevant in chromatographic applications.     

Dynamic two-dimensional fluorescence correlation spectroscopy. Generalized correlation and experimental factors

Dynamic two-dimensional fluorescence correlation spectroscopy (2D FCS) is presented in the general form. Dynamic 2D FCS evaluates the time correlation function between two wavelength axes when an external perturbation is applied to the sample. It displays the vibronic features with similar time response functions in the synchronous correlation spectrum and the features with different time responses in the asynchronous correlation spectrum. The correlation analysis allows detailed assignments of the vibronic spectra of multicomponent samples. The emission-emission 2D FCS has proven to be able to resolve spectra with substantial overlaps, of species in equilibrium with each other, and of reacting species whose kinetic constants are linked and multiexponential. Similarly, the correlation analysis between excitation wavelengths allows the assignment of the excitation bands to fluorescent components. When a sinusoidal light source is used to excite the sample, the excitation-emission correlation requires the collection of only four spectra, two in-phase and two quadrature. The two-dimensional excitation-emission correlation analysis uncovers the association between the excitation and the emission vibronic features, enabling the complete assignment of the component spectra. The band associations and spectral assignments are facilitated by the two-dimensional phase map that is constructed from the synchronous and asynchronous correlation spectra. Spectral resolution can be optimized by varying the frequency of excitation and is not influenced by the detector phase angle used to collect the spectra. The resolution power of the 2D FCS is demonstrated with the retrieval of the anthracene emission spectrum from a pyrene-anthracene mixture when it contributes only 4% to the total fluorescence intensity.