Ultrafast electron diffraction: oriented molecular structures in space and time.

The technique of ultrafast electron diffraction allows direct measurement of changes which occur in the molecular structures of isolated molecules upon excitation by femtosecond laser pulses. The vectorial nature of the molecule-radiation interaction also ensures that the orientation of the transient populations created by the laser excitation is not isotropic. Here, we examine the influence on electron diffraction measurements--on the femtosecond and picosecond timescales--of this induced initial anisotropy and subsequent inertial (collision-free) molecular reorientation, accounting for the geometry and dynamics of a laser-induced reaction (dissociation). The orientations of both the residual ground-state population and the excited- or product-state populations evolve in time, with different characteristic rotational dephasing and recurrence times due to differing moments of inertia. This purely orientational evolution imposes a corresponding evolution on the electron scattering pattern, which we show may be similar to evolution due to intrinsic structural changes in the molecule, and thus potentially subject to misinterpretation. The contribution of each internuclear separation is shown to depend on its orientation in the molecular frame relative to the transition dipole for the photoexcitation; thus not only bond lengths, but also bond angles leave a characteristic imprint on the diffraction. Of particular note is the fact that the influence of anisotropy persists at all times, producing distinct differences between the asymptotic "static" diffraction image and the predictions of isotropic diffraction theory.     

Anisotropic Picosecond X-ray Solution Scattering from Photo-selectively Aligned Protein Molecules

Anisotropic X-ray scattering patterns of transiently aligned protein molecules in solution are measured by using pump-probe X-ray solution scattering. When a linearly polarized laser pulse interacts with an ensemble of molecules, the population of excited molecules is created with their transition dipoles preferentially aligned along the laser polarization direction. We measured the X-ray scattering from the myoglobin protein molecules excited by a linearly polarized, short laser pulse and obtained anisotropic scattering patterns on 100 ps time scale. An anisotropic scattering pattern contains higher structural information content than a typical isotropic pattern available from randomly oriented molecules. In addition, multiple independent diffraction patterns measured by using various laser polarization orientations will give substantially increased amount of structural information compared with a single isotropic pattern. By monitoring the temporal change of the anisotropic scattering pattern from 100 ps to 1 μs, we observed the orientational dynamics of photo-generated myoglobin with the rotational diffusion time of ～15 ns.     

Ultrafast electron diffraction: dynamical structures on complex energy landscapes.

In this contribution, we report studies in ultrafast electron diffraction (UED), with the aim of exploring new directions. The main focus is on the determination of complex structures and their dynamics with spatial and temporal resolutions sufficient to give an atomic-scale picture for the evolution in chemical or biological change. We also provide the theoretical framework for UED, and compare the experimental findings of UED to those predicted by density functional and charge density calculations. Selected applications are given in order to highlight phenomena related to concepts such as bifurcation of trajectories in dynamics, far-from-equilibrium coherent structures, and conformational robustness in biological structures. For the former two cases, we consider chemical systems, and, for the latter, we examine proteins of 200 atoms (angiotensin I) or more.     

Classical differential cross sections and rotational energy transfer distributions for realistic ion—molecule potentials in the CPST limit

Classical differential cross sections, rotational energy transfer distributions at specified scattering angles and the first moments of the rotational energy transfer distributions are calculated for two ion—molecule systems: K⁺ ?CSCl and Li⁺ ?CO. The deflection angles and change in angular momentum are calculated using classical perturbation scattering theory (CPST). Monte Carlo techniques are then used to calculate the orientation averaged total differential cross sections and the rotational energy transfer distributions. Results are compared with experiment and agreement is found to be satisfactory. These two systems represent two extremes in anisotropy. For Li⁺ ?CO a strong classical rainbow peak is still seen in the differential cross section, while in the K⁺ ?CSCl system the rainbow is complete quenched. In the rotational energy transfer distributions of both systems, rotational rainbow peaks are clearly observed. The calculations also predict a leveling off of the first moment of the rotational energy transfer distribution at high angles, corresponding to the transition to repulsive scattering. On the basis of these results some comments are made on the nature of classical rainbow scattering for anisotropic systems.     

On the shape of the Q-branch of Raman scattering spectra in dense media. Theory

A nonadiabatic quasi-classical impact theory of the Q-band shape for isotropic and anisotropic Raman scattering by linear rotors has been developed. With our previous results this allows us to obtain upper and lower estimates of the contribution of collisional rotational relaxation to the Raman line broadening.     

Molecular structure and vibrational raman and infrared spectra of bromochlorofluoromethane and its silicon and germanium analogs: quantum-mechanical DFT and MP2 calculations

DFT(B3LYP) and MP2 calculations with the 6-311G(2d, 2p)-type basis set have been carried out for the prediction of molecular parameters (bond distances, bond angles, rotational constants, and dipole moments) and vibrational Raman and infrared spectra (harmonic wavenumbers, absolute intensities, Raman scattering activities, and depolarization ratios) of bromochlorofluoromethane (HCBrCIF) and its silicon and germanium analogs (HSiBrClF and HGeBrCIF). The predicted geometry and vibrational Raman and infrared spectra of HCBrClF agree well with the available experimental data for this molecule and their deuterated derivatives. This agreement allows one to believe that the predicted molecular parameters and vibrational spectra of HSiBrClF, HGeBrClF, and their deuterated derivatives will guide their future experimental studies.     

Dynamics of ferrocene in AlPO4-5 single crystals probed by nuclear forward scattering

We have investigated the dynamics of ferrocene in the channels of single crystals of AlPO(4)-5, using nuclear forward scattering. Around 150 K, rotational dynamics sets in, which is strongly anisotropic up to 235 K. Assuming planar rotation of the ferrocene molecules within the channels we obtained an activation energy of (8.2+/-1.0) kJ mol(-1). Between 235 K and room temperature, the rotation becomes isotropic.     

The most stable tautomer of 3-amino-1,2,4-triazin-5-one and its structural geometry

With the purpose of finding predominant tautomer among five possible isomers of 3-amino-1,2,4-triazin-5-one and to refine some unreasonable structural parameters previously reported from X-ray diffraction measurements, a series of ab initio calculations were carried out. In agreement with previous results, our calculations show that 3-amino-1,2,4-triazin-5(2H)-one tautomer is the most stable one. Concerning the predominant tautomer, comparisons were made between structural parameters calculated and those obtained by X-ray crystallographic analysis. The structural geometry of the main skeleton of the molecule calculated by the B3LYP/6-311++G** density functional method are generally in good agreement with the experimental values, and those predicted by Pauling's method. Bond distance values calculated are in excellent agreement with the conventionally accepted bond lengths in similar molecules. All bond distances, bond angles, dihedral angles, dipole moments and rotational constants are presented.     

Explanation of spin-lattice relaxation rates of spin labels obtained with multifrequency saturation recovery EPR

Electron paramagnetic resonance (EPR) pulsed saturation recovery (pSR) measurements of spin-lattice relaxation rates have been made on nitroxide-containing fatty acids embedded in lipid bilayers by Hyde and co-workers. The data have been collected for a number of spin-labeled fatty acids at several microwave spectrometer frequencies (from 2 to 35 GHz). We compare these spin-lattice relaxation rates to those predicted by the Redfield theory incorporating several mechanisms. The dominant relaxation mechanism at low spectrometer frequencies is the electron-nuclear dipolar (END) process, with spin rotation (SR), chemical shift anisotropy (CSA), and a generalized spin diffusion (GSD) mechanism all contributing. The use of a wide range of spectrometer frequencies makes clear that the dynamics cannot be modeled adequately by rigid-body isotropic rotational motion. The dynamics of rigid-body anisotropic rotational motion is sufficient to explain the experimental relaxation rates within the experimental error. More refined models of the motion could have been considered, and our analysis does not rule them out. However, the results demonstrate that measurements at only two suitably chosen spectrometer frequencies are sufficient to distinguish anisotropic from isotropic motion. The results presented demonstrate that the principal mechanisms responsible for anisotropically driven spin-lattice relaxation are well understood in the liquids regime.     

Orientational and interaction induced dynamics in the isotropic phase of a liquid crystal: polarization resolved ultrafast optical Kerr effect spectroscopy

The ultrafast dynamics of the isotropic phase of a liquid crystal 4'-pentyl-4-p-biphenylcarbonitrile (5CB) have been investigated using polarization resolved optical Kerr effect spectroscopy. Measurements were made as a function of both temperature and dilution in nonpolar solvents. To separate single molecule and interaction induced components to the relaxation of the induced birefringence, measurements of both the anisotropic and isotropic response were made. The isotropic response was found to be dominated by a damped low-frequency mode of intramolecular origin. There is a minor additional component assigned to an interaction induced contribution. There is at most an extremely weak isotropic signal beyond 1 ps, showing that the picosecond time scale dynamics of 5CB are dominated by orientational relaxation. The isotropic response is independent of temperature in the range studied (0.2-50 K above the nematic to isotropic phase-transition temperature). The anisotropic response exhibits relaxation dynamics on time scales spanning subpicosecond to several hundred picoseconds and beyond. The fastest components are dominated by a librational response, but there are smaller contributions from three low-frequency intramolecular modes, and a contribution from interaction induced effects. The low-frequency spectral density extracted from these data are independent of temperature in the range studied, 0.2-30 K above the phase-transition temperature, but shift to lower frequency on dilution in alkane solvents. In neat 5CB the picosecond time scale orientational dynamics are dominated by temperature-independent reorientation within the pseudonematic domains, while in solution these are disrupted, and the orientational response becomes faster and temperature dependent.     

Subdiffusive dynamics of a liquid crystal in the isotropic phase

The isotropic phase dynamics of a system of 4-n-hexyl-4'-cyano-biphenyl (6CB) molecules has been studied by molecular dynamics computer simulations. We have explored the range of 275-330 K keeping the system isotropic, although supercooled under its nematic transition temperature. The weak rototranslational coupling allowed us to separately evaluate translational (TDOF) and orientational degrees of freedom (ODOF). Evidences of subdiffusive dynamics, more apparent at the lowest temperatures, are found in translational and orientational dynamics. Mean square displacement as well as self-intermediate center of mass and rotational scattering functions show a plateau, also visible in the orientational correlation function. According to the mode coupling theory (MCT), this plateau is the signature of the beta-relaxation regime. Three-time intermediate scattering functions reveal that the plateau is related to a homogeneous dynamics, more extended in time for the orientational degrees of freedom (up to 1 ns). The time-temperature superposition principle and the factorization property predicted by the idealized version of MCT hold, again for both kinds of dynamics. The temperature dependence of diffusion coefficient and orientational relaxation time is well described by a power law. Critical temperatures Tc are 244+/-6 and 258+/-6 K, respectively, the latter is some 10 K below the corresponding experimental values. The different values of Tc we obtained indicate that ODOF freezes earlier than TDOF. This appears due to the strongly anisotropic environment that surrounds a 6CB molecule, even in the isotropic phase. The lifetime of these "cages," estimated by time dependent conditional probability functions, is strongly temperature dependent, ranging from some hundreds of picoseconds at 320 K to a few nanoseconds at 275 K.     

Small-angle scattering of polarized light. I. comparison of theoretical predictions for isotropic and anisotropic spheres

This paper describes small angle light scattering (SALS) calculations and compares the results for isotropic and anisotropic spheres. For isotropic spheres the exact Mie theory is compared with the Rayleigh-Gans-Debye (RGD) and the anomalous diffraction (AD) approximations in order to study the validity of the approximations. For anisotropic spheres the RGD is compared with the AD approximation. A study of SALS in the RGD approximation shows that the first-order intensity maximum corresponding to a lobe of the four-leaf clover pattern is not only a function of the sphere diameter but also depends on the isotropic and the anisotropic refractive index of the sphere. The practical implications of this are discussed.     

Correlated angular and quantum state-resolved CO2 scattering dynamics at the gas-liquid interface

Molecular beam scattering dynamics at the gas-liquid interface are investigated for CO2 (E(inc) = 10.6(8) kcal/mol) impinging on liquid perfluoropolyether (PFPE), with quantum state (v, J) populations measured as a function of incident (theta(inc)) and final (theta(scat)) scattering angles. The internal state distributions are well-characterized for both normal and grazing incident angles by a two-component Boltzmann model for trapping desorption (TD) and impulsive scattering (IS) at rotational temperatures T(rot)(TD/IS), where the fractional TD probability for CO2 on the perfluorinated surface is denoted by TD and IS densities (rho) as alpha = rhoTD/(rhoTD + rhoIS). On the basis of an assumed cos(theta(scat)) scattering behavior for the TD flux component, the angular dependence of the IS flux at normal incidence (theta(inc) = 0 degrees) is surprisingly well-modeled by a simple cos(n)(theta(scat)) distribution with n = 1.0 +/- 0.2, while glancing incident angles (theta(inc) = 30 degrees, 45 degrees, and 60 degrees) result in lobular angular IS distributions scattered preferentially in the forward direction. This trend is also corroborated in the TD fraction alpha, which decreases rapidly under non-normal incident conditions as a function of backward versus forward scattering direction. Furthermore, the extent of rotational excitation in the IS channel increases dramatically with increasing angle of incidence, consistent with an increasing rotational torque due to surface roughness at the gas-liquid interface.     

Statistical approach to light scattering from deformed textured heterogeneous polymer materials

A statistical theory of light scattering from deformed isotropic and textured heterogeneous polymer materials is formulated. Two types of textured structures are analyzed: assemblies of optically isotropic and anisotropic rods and a spatially anisotropic distribution of isotropic spherical inclusion centers. The small-angle H_v light-scattering patterns are calculated. The appearance of scattering from isotropic rods and spheres in deformed materials has been demonstrated. The changes of the H_v scattering patterns as a function of elongation and strucuture parameters are discussed. © 1993 John Wiley & Sons, Inc.     

Solvent and lipid dynamics of hydrated lipid bilayers by incoherent quasielastic neutron scattering

The microscopic dynamics of the planar, multilamellar lipid bilayer system 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) has been investigated using quasielastic neutron scattering. The DMPC was hydrated to a level corresponding to approximately nine water molecules per lipid molecule. Selective deuteration has been used to separately extract the dynamics of the water, the acyl chains, and the polar head groups from the strong incoherent scattering of the remaining hydrogen atoms. Furthermore, the motions parallel and perpendicular to the bilayers were probed by using two different sample orientations relative to the incident neutron beam. For both sample orientations, the results showed an onset of water motions at 260 K on the experimental time scale of about 100 ps. From lack of wave-vector dependence of the onset temperature for water motions, it is evident that the observed water dynamics is of mainly rotational character at such low temperatures. At 290 K, i.e., slightly below the gel-to-liquid transition around 295 K, the nature of the water dynamics had changed to a more translational character, well described by a jump-diffusion model. On the limited experimental time and length (about 10 A) scales, this jump-diffusion process was isotropic, despite the very anisotropic system. The acyl chains exhibited a weak onset of anharmonic motions already at 120 K, probably due to conformational changes (trans-gauche and/or syn-anti) in the plane of the lipid bilayers. Other anharmonic motions were not observed on the experimental time scale until temperature had been reached above the gel-to-liquid transition around 295 K, where the acyl chains start to show more substantial motions.     

Anisotropic rotations in 1-naphthylamine. Existence of a red-edge transition moment normal to the ring plane

The rotational motions of 1-naphthylamine in propylene glycol are investigated by means of steady-state flourescence polarization measurements and differential polarized phase flourometry, on excitation at various wavelengths. For excitation at 370 nm the average rotational rate is faster than for excitation at shorter wavelength and the rotations are clearly anisotropic. On excitation from 370nm to the red edge of the spectrum (390 nm) the average rotational rate slows down by a factor of two and the rotations become nearly isotropic. The results reveal the possible existence of an excited state generated preferentially by excitation at the edge of the absorption, in which the transition moments in both absorption and emission are prependicular to the plane of the aromatic rings.     

Structural dynamics of free proteins in diffraction

Among the macromolecular patterns of biological significance, right-handed α-helices are perhaps the most abundant structural motifs. Here, guided by experimental findings, we discuss both ultrafast initial steps and longer-time-scale structural dynamics of helix-coil transitions induced by a range of temperature jumps in large, isolated macromolecular ensembles of an α-helical protein segment thymosin β(9) (Tβ(9)), and elucidate the comprehensive picture of (un)folding. In continuation of an earlier theoretical work from this laboratory that utilized a simplistic structure-scrambling algorithm combined with a variety of self-avoidance thresholds to approximately model helix-coil transitions in Tβ(9), in the present contribution we focus on the actual dynamics of unfolding as obtained from massively distributed ensemble-convergent MD simulations which provide an unprecedented scope of information on the nature of transient macromolecular structures, and with atomic-scale spatiotemporal resolution. In addition to the use of radial distribution functions of ultrafast electron diffraction (UED) simulations in gaining an insight into the elementary steps of conformational interconversions, we also investigate the structural dynamics of the protein via the native (α-helical) hydrogen bonding contact metric which is an intuitive coarse graining approach. Importantly, the decay of α-helical motifs and the (globular) conformational annealing in Tβ(9) occur consecutively or competitively, depending on the magnitude of temperature jump.     

Configurational studies on amylose. I. Scattering functions

Scattering functions for amylose chains have been calculated as a statistical mechanical average over eligible configurations based on the rotational isomeric state approximation. Main emphasis has been placed on an intermediate-angle range (0.1 < h = (4π/γ)sinθ < 1.0 Å^?1) where the scattering function is sensitive to local chain configurations. In order to avoid overestimation of the regularity of chain configurations, the rotational isomeric states for each glycosidic bond have been defined by a set of discrete torsion angles at intervals of 5°. Pair correlation functions for atoms separated by sequences shorter than 31 glucose units are evaluated by the Monte Carlo method, while the interference for longer sequences is calculated by a series expansion in the even moments of the chain. All carbons and all skeletal oxygens are treated as point scatterers in order to incorporate all the interferences between atoms in unit pairs in the calculations. The calculated scattering function shows appreciable oscillation at intermediate angles, reflecting the characteristic helical tendency of the configurations. The Debye function is found to be inadequate in the intermediate-angle region owing to the non-Gaussian character of the distribution function and to breakdown of the assumption that the mean-square distance between a pair of atoms is proportional to the number of bonds between them, because of the bulkiness of the glucose unit.     

Mobility of molecules and diagram of the state of a glyceryl monooleate-water system according to NMR data

Transverse relaxation and self-diffusion of molecules in a glyceryl monooleate (monoolein)-D₂O system was studied using pulsed ¹H NMR in a range of water concentrations from 10 to 30 wt % and a range of temperatures from 20 to 90°C. It was noted that self-diffusion is described by one or two self-diffusion coefficients, depending on the temperature and concentration of water, while NMR-relaxation has a complex form. It was determined that with a reduction in the transverse magnetization, a component that has a form similar to Gaussian and relaxation times of 70 to 250 μs is observed at certain temperatures and concentrations of water, confirming the formation of structures in which glyceryl monooleate molecules (GM) are characterized by anisotropic rotational mobility. It was demonstrated that the ranges of the concentrations of water and temperature in which this component is observed correspond to liquid-crystalline phase for lamellar and inverse hexagonal structural organizations of lipids, according to the state diagram obtained by X-ray diffraction. In the state diagram areas corresponding to micellar and cubic structures (characterized by the isotropic rotation of GM molecules in the time scale of NMR), multiexponential decays of magnetization with average relaxation times were noted in the range of 10 to 200 ms. A number of features were discovered with the use of NMR: specimens always contain structures with isotropic rotational mobility in the presence of structures characterized by anisotropic rotational mobility; a change in the fraction of the structures with anisotropic rotational mobility takes place slowly over 5–15 K, not abruptly. Our conclusions regarding the polymorphism of a GM-D₂O system in the presence of anisotropic structures was confirmed by an analysis of the transverse NMR relaxation in an egg phosphatidylcholine-D₂O system, for which the presence of only lamellar liquid-crystalline structure is confirmed by ³¹P NMR.     

Si(111) Electrode/Electrolyte Interracial Studied by in-situ Second Harmonic Generation

Si(111) electrode has been widely used in electrochemical and photoelectrochemical studies. The potential dependent measurements of the second harmonic generation (SHG) were performed to study Si(111) electrode interface. At different azimuthal angles of the Si(111) and under different polarization combinations, the curve of the intensity of SHG with extern potential has a different form of line or parabola. Quantitative analysis showed that these differences in the potential-dependence can be explained by the isotropic and anisotropic contribution of the Si(111) electrode. The change in the isotropic and anisotropic contribution of the Si(111) electrode may be attributed to the increase in the doping concentration of Si(111) electrodes.