Ultrafast electron-transfer and solvent adiabaticity effects in viologen charge-transfer complexes

We report ultrafast electron transfer (ET) in charge-transfer complexes that shows solvent relaxation effects consistent with adiabatic crossover models of nonadiabatic ET. The complexes of either dimethyl viologen (MV) or diheptyl viologen (HV) with 4,4'-biphenol (BP) (MVBP or HVBP complexes) have identical charge-transfer spectra and kinetics in ethylene glycol with approximately 900 fs ET decay. We assign this decay time as largely due to adiabatic control of a predicted approximately 40 fs nonadiabatic ET. The MVBP decay in methanol of 470 fs is reduced in mixtures having low (2-20%) concentrations of acetonitrile to as short as 330 fs; these effects are associated with faster relaxation time in methanol and its mixtures. In contrast, HVBP has much longer ET decay in methanol (730 fs) and mixture effects that only reduce its decay to 550 fs. We identify the heptyl substituent as creating major perturbations to solvent relaxation times in the methanol solvation shell of HVBP. These charge-transfer systems have reasonably well-defined geometry with weak electronic coupling where the electronic transitions are not dependent on intramolecular motions. We used a nonadiabatic ET model with several models for adiabatic crossover predictions to discuss the small variation of energy gap with solvent and the ET rates derived from adiabatic solvent control. A time correlation model of solvent relaxation was used to define the solvent relaxation times for this case of approximately zero-barrier ET.     

Site-Resolved Measurement of Microsecond-to-Millisecond Conformational-Exchange Processes in Proteins by Solid-State NMR Spectroscopy

We demonstrate that conformational exchange processes in proteins on microsecond-to-millisecond time scales can be detected and quantified by solid-state NMR spectroscopy. We show two independent approaches that measure the effect of conformational exchange on transverse relaxation parameters, namely Carr-Purcell-Meiboom-Gill relaxation-dispersion experiments and measurement of differential multiple-quantum coherence decay. Long coherence lifetimes, as required for these experiments, are achieved by the use of highly deuterated samples and fast magic-angle spinning. The usefulness of the approaches is demonstrated by application to microcrystalline ubiquitin. We detect a conformational exchange process in a region of the protein for which dynamics have also been observed in solution. Interestingly, quantitative analysis of the data reveals that the exchange process is more than 1 order of magnitude slower than in solution, and this points to the impact of the crystalline environment on free energy barriers.     

Coherent averaging of electron spins by rotary echoes in excited triplet states

A theoretical treatment of rotary echoes derived from average hamiltonian formalism in photoexcited triplet states is presented. From a general relaxation matrix, it is shown that relaxation fields perpendicular to the driving field H_eff are completely averaged, whereas relaxation fields parallel to H_eff are not. Rotary echoes are found to differ from other coherence techniques only in the geometry of the experiment and not in the averaging properties per se. Off-resonance driving field conditions are shown to impair the efficiency of the averaging and to cause beats in the observed echo decay. Finally, inhomogenous line broadening is shown to produce a damped echo decay with beats even when the field is on-resonance.     

On spectral relaxation in proteins

During the past several years there has been debate about the origins of nonexponential intensity decays of intrinsic tryptophan (trp) fluorescence of proteins, especially for single tryptophan proteins (STP). In this review we summarize the data from diverse sources suggesting that time-dependent spectral relaxation is a ubiquitous feature of protein fluorescence. For most proteins, the observations from numerous laboratories have shown that for trp residues in proteins (1) the mean decay times increase with increasing observation wavelength; (2) decay associated spectra generally show longer decay times for the longer wavelength components; and (3) collisional quenching of proteins usually results in emission spectral shifts to shorter wavelengths. Additional evidence for spectral relaxation comes from the time-resolved emission spectra that usually shows time-dependent shifts to longer wavelengths. These overall observations are consistent with spectral relaxation in proteins occurring on a subnanosecond timescale. These results suggest that spectral relaxation is a significant if not dominant source of nonexponential decay in STP, and should be considered in any interpretation of nonexponential decay of intrinsic protein fluorescence.     

Time-resolved fluorescence of the bacteriophage T4 capsid protein gp23

The time-resolved fluorescence properties of the bacteriophage T4 capsid protein gp23 are investigated. The structural characteristics of this protein are largely unknown and can be probed by recording time-resolved and decay-associated fluorescence spectra and intensity decay curves using a 200 ps-gated intensified CCD-camera. Spectral and decay data are recorded simultaneously, which makes data acquisition fast compared to time-correlated single-photon counting. A red-shift of the emission maximum within the first nanosecond of decay is observed, which can be explained by the different decay-associated spectra of fluorescence lifetimes of the protein in combination with dipolar relaxation. In addition, iodide quenching experiments are performed, to study the degree of exposure of the various tryptophan residues. A model for the origin of the observed lifetimes of 0.032 +/- 0.003, 0.39 +/- 0.06, 2.1 +/- 0.1 and 6.8 +/- 0.8 ns is presented: the 32 ps lifetime can be assigned to the emission of a buried tryptophan residue, the 0.4 and 2.1 ns lifetimes to two partly buried residues, and the 6.8 ns lifetime to a single tryptophan outside the bulk of the folded gp23.     

Quantitative measurement of differential 15N-H(alpha/beta)T2 relaxation rates in a perdeuterated protein by MAS solid-state NMR spectroscopy

Dynamic parameters become more and more accessible in the study of uniformly isotopically enriched proteins by MAS solid-state NMR. We demonstrate that T(2)-related relaxation properties can quantitatively be determined in a sample of a perdeuterated microcrystalline protein by the measurement of (15)N,(1)H dipole, (15)N CSA cross-correlated relaxation rates. We find that the measured cross-correlated relaxation rates are independent of the MAS rotation frequency, and therefore reflect local dynamic fluctuations of the protein structure.     

Evaluation of protein 15N relaxation times by inverse Laplace transformation

Relaxation times (T1, T2, T1rho) are usually evaluated from exponential decay data by least-squares fitting methods. For this procedure, the integrals or amplitudes of signals must be determined, which can be laborious with large data sets. Moreover, the fitting requires a priori knowledge of the number of exponential components responsible for the decay. We have adapted inverse Laplace transformation (ILT) for the analysis of relaxation data. Exponential components are resolved with ILT to reciprocal space on their corresponding relaxation rate values. The ILT approach was applied to 3D linewidth-resolved 15N HSQC experiments to evaluate 15N T1 and T2 relaxation times of ubiquitin. The resulting spectrum is a true 3D spectrum, where the signals are separated by their 1H and 15N chemical shifts (HSQC correlations) and by their relaxation rate values (R1 or R2). From this spectrum, the relaxation times can be obtained directly with a simple peak-picking procedure.     

Spatial regimes in the dynamics of polyolefins: collective motion

Molecular simulation is used to characterize the spatial dependence of collective motion in four saturated hydrocarbon polymers. The observable is the distinct intermediate scattering function, as measured in coherent quasielastic neutron scattering experiments. Ranges of 0.01-1000 ps in time and 2-14 A in spatial scale are covered. In this time range, a two-step relaxation, consisting of a fast exponential decay and a slower stretched decay, is observed for all spatial scales. The relaxation times for the fast process are very similar to those obtained by following self motion, with a small modulation of relaxation times near the peak in the static structure factor which is well described by the narrowing picture suggested by de Gennes. For the slow process, self and collective relaxation times have larger numerical differences and follow different scaling with spatial scale. The modulation of slow relaxation times is larger than that observed for the fast process, but is overestimated by the de Gennes prediction, which only works qualitatively.     

从静态应力松弛实验求材料准松弛时间谱的一种数值计算方法

避开繁琐困难的函数求解过程，采用数值计算方法，从常规的静态应力松弛实验，直接求被测材料的松弛单元的表现松弛强度．主松弛时间τ０由单－ＭＡＸＷＥＬＬ模型求得，其他松弛时间分别约取为１０（－２）·τ０，１０（－１）·τ０，１０１·τ０，１０３·τ０。应力松弛万程取５参数模型，记为谱的强度ａｉ（或Ａｉ）通过多元线性回归，由最小二乘法确定．对一种天然橡胶试样在不同温度下的松弛曲线进行处理，回归值与原始实验值吻合良好，不同温度下的松弛单元对总松弛的贡献，反映出温度对松弛过程的活化作用．     

Transient electric birefringence of wormlike macromolecules in electric fields of arbitrary strength: a computer simulation study

We have studied the birefringence decay of linear models of macromolecules for two different types of flexibility, the broken-rod chain and the wormlike chain, using a computer simulation of a transient electric birefringence experiment. We have paid particular attention to the influence of the intensity of the orienting field, including two orienting mechanisms, the induced dipole, and the permanent dipole. We have compared wormlike and broken-rod models of the same radius of gyration, finding that they present a different decay curve under the influence of the same intensity of the field. We have seen that these differences are due to the faster relaxation times (smaller in the wormlike chain model) and amplitudes, because, regardless of the type of flexibility, the overall size of a molecule (measured by the radius of gyration) essentially determines the longest relaxation time. We have also analyzed how the relaxation process is affected by the degree of flexibility, the orientation mechanisms, and the intensity of the field. Studying a different aspect, we have paid attention to the deformation of a molecule in a transient electric birefringence experiment as a source of information. In this work we have developed equations to characterize this deformation in terms of one of the components of the gyration tensor, if a dynamic light scattering experiment under the influence of an electric field could be performed. To develop this work we have simulated the Brownian dynamics of the different models, relaxing after the removal of an orienting external electric field of arbitrary strength. A comparison with other methods such a the rigid body treatment or the correlation analysis of Brownian trajectories has also been included. We have seen that differences between the two Brownian dynamics methods are small and that the rigid-body treatment is only an acceptable approximation to obtain the longest relaxation time.     

Quantitative analysis of protein backbone dynamics in microcrystalline ubiquitin by solid-state NMR spectroscopy

Characterization of protein dynamics by solid-state NMR spectroscopy requires robust and accurate measurement protocols, which are not yet fully developed. In this study, we investigate the backbone dynamics of microcrystalline ubiquitin using different approaches. A rotational-echo double-resonance type (REDOR-type) methodology allows one to accurately measure (1)H-(15)N order parameters in highly deuterated samples. We show that the systematic errors in the REDOR experiment are as low as 1% or even less, giving access to accurate data for the amplitudes of backbone mobility. Combining such dipolar-coupling-derived order parameters with autocorrelated and cross-correlated (15)N relaxation rates, we are able to quantitate amplitudes and correlation times of backbone dynamics on picosecond and nanosecond time scales in a residue-resolved manner. While the mobility on picosecond time scales appears to have rather uniform amplitude throughout the protein, we unambiguously identify and quantitate nanosecond mobility with order parameters S(2) as low as 0.8 in some regions of the protein, where nanosecond dynamics has also been revealed in solution state. The methodology used here, a combination of accurate dipolar-coupling measurements and different relaxation parameters, yields details about dynamics on different time scales and can be applied to solid protein samples such as amyloid fibrils or membrane proteins.     

Structural relaxation in complex liquids: non-Markovian dynamics in a bistable potential

The time correlation function C(t) identical with of the distance fluctuations of a particle moving in a bistable potential under the action of fractional Gaussian noise (fGn) is calculated from a Smoluchowski-type equation derived from a generalized Langevin equation (GLE). The time derivative of this function, dC(t)dt, is compared with data from optical Kerr effect measurements of liquid crystal dynamics in the vicinity of the isotropic-to-nematic transition, which are related to the time derivative of an orientational correlation function. A number of characteristic features of the experimental decay curves, including short and intermediate time power law behavior and long time exponential relaxation, are qualitatively reproduced by the analytical calculations, even though the latter do not explicitly treat orientational degrees of freedom. The GLE formalism with fGn was, in fact, originally proposed as a model of protein conformational fluctuations, so the present results suggest that it may also serve more generally as a model of structural relaxation in complex condensed phase media.     

What is the time scale for α-helix nucleation?

Helix formation is an elementary process in protein folding, influencing both the rate and mechanism of the global folding reaction. Yet, because helix formation is less cooperative than protein folding, the kinetics are often multiexponential, and the observed relaxation times are not straightforwardly related to the microscopic rates for helix nucleation and elongation. Recent ultrafast spectroscopic measurements on the peptide Ac-WAAAH(+)-NH(2) were best fit by two relaxation modes on the ～0.1-1 ns time scale, (1) apparently much faster than had previously been experimentally inferred for helix nucleation. Here, we use replica-exchange molecular dynamics simulations with an optimized all-atom protein force field (Amber ff03w) and an accurate water model (TIP4P/2005) to study the kinetics of helix formation in this peptide. We calculate temperature-dependent microscopic rate coefficients from the simulations by treating the dynamics between helical states as a Markov process using a recently developed formalism. The fluorescence relaxation curves obtained from simulated temperature jumps are in excellent agreement with the experimentally determined results. We find that the kinetics are multiphasic but can be approximated well by a double-exponential function. The major processes contributing to the relaxation are the shrinking of helical states at the C-terminal end and a faster re-equilibration among coil states. Despite the fast observed relaxation, the helix nucleation time is estimated from our model to be 20-70 ns at 300 K, with a dependence on temperature well described by Arrhenius kinetics.     

Measurement of NMR cross-polarization (CP) rate constants in the slow CP regime: relevance to structure determinations of zeolite-sorbate and other complexes by cp magic-angle spinning NMR

When analyzing I --> S variable contact time cross-polarization (CP) curves, the spin dynamics are usually assumed to be describable in the "fast CP regime" in which the growth of the S spin magnetization is governed by the rate of cross polarization while its decay is governed by the rate of I spin T1rho relaxation. However, in the investigation of the structures of zeolite-sorbate and other complexes by polarization transfer this will not necessarily be the case. We discuss the measurement of I --> S CP rate constants under the "slow CP regime" in which the rate of T1rho relaxation is fast compared to the rate of cross polarization, leading to a reversal of the usual assumptions such that the rate or growth is governed by the rate of I spin T1rho relaxation while the decay is governed by the rate of cross polarization (and the S spin T1rho relaxation). It is very important to recognize when a system is in the slow CP regime, as an analysis assuming the normal fast CP will lead to erroneous data. However, even when the slow CP regime is recognized, it is difficult to obtain absolute values for the CP rate constants from fits to standard CP curves, since the CP rate constant is correlated to the scaling factor, the contribution from 29Si T1rho relaxation is ignored, and it is difficult to obtain reliable data at very long contact times. The use of a 29Si{1H} CP "drain" or "depolarization" experiment, which measures absolute values of the CP rate constants, is therefore proposed as being most appropriate for theses situations. To illustrate the importance of these observations, measurements of the 1H-29Si CP rate constants in the p-dichlorobenzene/ZSM-5 sorbate-zeolite complex by 29Si{1H} CP and CP drain magic-angle spinning (MAS) NMR experiments are presented and compared and used to determine the location of the guest sorbate molecules in the cavities of the host zeolite framework.     

Dynamics in supercooled ionic organic liquids and mode coupling theory analysis

Optically heterodyne-detected optical Kerr effect experiments are applied to study the orientational dynamics of the supercooled ionic organic liquids N-propyl-3-methylpyridinium bis(trifluoromethylsulfonyl)imide (PMPIm) and 1-ethyl-3-methylimidazolium tosylate (EMImTOS). The orientational dynamics are complex with relaxation involving several power law decays followed by a final exponential decay. A mode coupling theory (MCT) schematic model, the Sj?gren model, was able to reproduce the PMPIm data very successfully over a wide range of times from 1 ps to hundreds of ns for all temperatures studied. Over the temperature range from room temperature down to the critical temperature Tc of 231 K, the OHD-OKE signal of PMPIm is characterized by the intermediate power law t(-1.00+/-0.04) at short times, a von Schweidler power law t(-0.51+/-0.03) at intermediate times, and a highly temperature-dependent exponential (alpha relaxation) at long times. This form of the decay is identical to the form observed previously for a large number of organic van der Waals liquids. MCT analysis indicates that the theory can explain the experimental data very well for a range of temperatures above Tc, but as might be expected, there are some deviations from the theoretical modeling at temperatures close to Tc. For EMImTOS, the orientational dynamics were studied on the ps time scale in the deeply supercooled region near its glass transition temperature. The orientational relaxation of EMImTOS clearly displays the feature associated with the boson peak at approximately 2 ps, which is the first time domain evidence of the boson peak in ionic organic liquids. Overall, all the dynamical features observed earlier for organic van der Waals liquids using the same experimental technique are also observed for organic ionic liquids.     

Elastoviscous properties of polyisobutylene. IV. Relaxation time spectrum and calculation of bulk viscosity

The elastoviscous behavior of polyisobutylene may be interpreted in terms of a mechanical model consisting of a distribution of Maxwell elements connected in parallel. The structure of this “generalized Maxwell model” is specified by the distribution of relaxation times of the component elements. The relaxation of stress curve of the material is directly related to the distribution of relaxation times, and general expressions for the bulk viscosities (tensile and shear) of such a system in terms of the distribution of relaxation times are readily obtained. A simple “box distribution” of relaxation times is described which can be used to approximate the relaxation behavior of polyisobutylene at the long-time end of the relaxation time spectrum, and in terms of which the expressions for bulk viscosity reduce to very simple form. The parameters specifying this distribution may be determined from experimental relaxation curves by a simple graphical method. Values of these parameters as a functions of molecular weight and temperature are computed, by use of these data. It is shown that bulk viscosity values calculated from relaxation data by this method are in good agreement with experimental values for both tensile and shear deformations, and for both unfractionated and fractionated polymers. Measurements of viscosity and of relaxation of stress can thus be directly correlated, and could be used in combination to characterize elastoviscous properties over wide ranges of molecular weight and temperature.     

Heterogeneous dynamics and dynamic heterogeneities at the glass transition probed with single molecule spectroscopy

We studied the temperature dependence of the structural relaxation in poly(vinyl acetate) near the glass transition temperature with single molecule spectroscopy from Tg-1 K to Tg+12 K. The temperature dependence of the observed relaxation times matches results from bulk experiments; the observed relaxation times are, however, 80-fold slower than those from bulk experiments at the same temperature. We attribute this factor to the size of the probe molecule. The individual relaxation times of the single molecule environments are distributed normally on a logarithmic time scale, confirming that the dynamics in poly(vinyl acetate) is heterogeneous. The width of the distribution of individual relaxation times is essentially independent of temperature. The observed full width at half maximum (FWHM) on a logarithmic time axis is approximately 0.7, corresponding to a factor of about 5-fold, significantly narrower than the dielectric spectrum of the same material with a FWHM of about 2.0 on a logarithmic time axis, corresponding to a factor of about 100-fold. We explain this narrow width as the effect of temporal averaging of single molecule fluorescence signals over numerous environments due to a limited lifetime of the probed heterogeneities, indicating that heterogeneities are dynamic. We determine a loose upper limit for the ratio of the structural relaxation time to the lifetime of the heterogeneities (the rate memory parameter) of Q<80 for the range of investigated temperatures.     

Short‐time stretch relaxation of entangled polymer solutions investigated using full Rouse model predictions

We conduct a systematical investigation into the short‐time stretch relaxation behavior (i.e., shorter than the Rouse time but sufficiently longer than the glassy time) of entangled polymer liquid in single‐step strain flows, on the basis of theory/data comparisons for a broad series of type‐A entangled polymer solutions. First, within existing normal‐mode formulations, the Rouse model predictions on a full‐chain stretch relaxation in single‐step strain flows are derived for a popular 1‐D model proposed within the Doi–Edwards tube model, as well as for the original 3‐D model for nonentangled systems. In addition, an existing formula for the aforementioned 1‐D model that, however, rested upon a consistent‐averaging or the so‐called uniform‐chain‐stretch approximation is simultaneously examined. Subsequently, the previously derived formulas on chain stretch relaxation are directly incorporated into a reliable mean‐field tube model that utilizes the linear relaxation spectrum and the Rouse time constant consistently determined from linear viscoelastic data. It is found that the predictions of the 1‐D model differ substantially from that of the original 3‐D model at short times. Theory/data comparisons further indicate that the 1‐D model without approximations seems able to describe fairly well the nonlinear relaxation data under investigation. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1199–1211, 2006     

Quantum two-state dynamics driven by stationary non-Markovian discrete noise: Exact results

We consider the problem of stochastic averaging of a quantum two-state dynamics driven by non-Markovian, discrete noises of the continuous time random walk type (multistate renewal processes). The emphasis is put on the proper averaging over the stationary noise realizations corresponding, e.g., to a stationary environment. A two-state non-Markovian process with an arbitrary non-exponential distribution of residence times (RTDs) in its states with a finite mean residence time provides a paradigm. For the case of a two-state quantum relaxation caused by such a classical stochastic field we obtain the explicit exact, analytical expression for the averaged Laplace-transformed relaxation dynamics. In the limit of Markovian noise (implying an exponential RTD), all previously known results are recovered. We exemplify new more general results for the case of non-Markovian noise with a biexponential RTD. The averaged, real-time relaxation dynamics is obtained in this case by numerically exact solving of a resulting algebraic polynomial problem. Moreover, the case of manifest non-Markovian noise with an infinite range of temporal autocorrelation (which in principle is not accessible to any kind of perturbative treatment) is studied, both analytically (asymptotic long-time dynamics) and numerically (by a precise numerical inversion of the Laplace-transformed averaged quantum relaxation).