Reorientational Correlation Functions Research Articles

Molecular dynamics simulations and solid-state nuclear magnetic resonance spectroscopy measurements of C-H bond order parameters and effective correlation times in a POPC-GM3 bilayer.

Glycolipids such as gangliosides affect the properties of lipid membranes and in extension the interactions between membranes and other biomolecules like proteins. To better understand how the properties of individual lipid molecules can contribute to shape the functional aspects of a membrane, the spatial restriction and dynamics of C-H bond segments can be measured using nuclear magnetic resonance (NMR) spectroscopy. We combine solid-state NMR spectroscopy with all-atom molecular dynamics (MD) simulations to investigate how ganglioside GM3 affects the bilayer structure and dynamics of C-H bond segments. These two methods yield reorientational correlation functions, molecular profiles of C-H bond order parameters |SCH| and effective correlation times τe, which we compare for lipids in POPC bilayers with and without 30 mol% GM3. Our results revealed that all C-H segments of POPC reorient slower in the presence of GM3 and that the defining features of the GM3-POPC bilayer lie in the GM3 headgroup; it gives the bilayer an extended headgroup layer with high order (|SCH| up to 0.3-0.4) and slow dynamics (τe up to 100 ns), a character that may be mechanistically important in ganglioside interactions with other biomolecules.

Structure and dynamics of water plastic crystals from computer simulations.

Water has a rich phase diagram with several crystals, as confirmed by experiments. High-pressure and high-temperature water is of interest for Earth's mantle and exoplanetary investigations. It is in this region of the phase diagram of water that new plastic crystal phases of water have been revealed via computer simulations by both classical forcefields and ab initio calculations. However, these plastic phases still remain elusive in experiments. Here, we present a complete characterization of the structure, dynamics, and thermodynamics of the computational plastic crystal phases of water using molecular dynamics and the two-phase thermodynamic method and uncover the interplay between them. The relaxation times of different reorientational correlation functions are obtained for the hypothetical body-centered-cubic and face-centered-cubic plastic crystal phases of water at T = 440 K and P = 8 GPa. Results are compared to a high pressure liquid and ice VII phases to improve the understanding of the plastic crystal phases. Entropy results indicate that the fcc crystal is more stable compared to the bcc structure under the studied conditions.

The effect of polymorphism on the structural, dynamic and dielectric properties of plastic crystal water: A molecular dynamics simulation perspective.

We have employed molecular dynamics simulations based on the TIP4P/2005 water model to investigate the local structural, dynamical, and dielectric properties of the two recently reported body-centered-cubic and face-centered-cubic plastic crystal phases of water. Our results reveal significant differences in the local orientational structure and rotational dynamics of water molecules for the two polymorphs. The probability distributions of trigonal and tetrahedral order parameters exhibit a multi-modal structure, implying the existence of significant local orientational heterogeneities, particularly in the face-centered-cubic phase. The calculated hydrogen bond statistics and dynamics provide further indications of the existence of a strongly heterogeneous and rapidly interconverting local orientational structural network in both polymorphs. We have observed a hindered molecular rotation, much more pronounced in the body-centered-cubic phase, which is reflected by the decay of the fourth-order Legendre reorientational correlation functions and angular Van Hove functions. Molecular rotation, however, is additionally hindered in the high-pressure liquid compared to the plastic crystal phase. The results obtained also reveal significant differences in the dielectric properties of the polymorphs due to the different dipolar orientational correlation characterizing each phase.

Dielectric relaxation in acetamide + urea deep eutectics and neat molten urea: Origin of time scales via temperature dependent measurements and computer simulations.

Dielectric relaxation (DR) measurements in the frequency window 0.2 ≤ ν(GHz) ≤ 50 for deep eutectic solvents (DESs) made of acetamide (CH3CONH2) and urea (NH2CONH2) with the general composition, [f CH3CONH2 + (1 - f) NH2CONH2] at f = 0.6 and 0.7, reveal three distinct relaxation time scales-τ1 ∼ 120 ps, τ2 ∼ 40 ps, and τ3 ∼ 5 ps. Qualitatively similar time scales have been observed for DR of neat molten urea, whereas the reported DR for neat molten acetamide in the same frequency window reflects two relaxation processes with no trace of ∼100 ps time scale. This slowest DR time scale (τ1) resembles closely to the long-time constant of the simulated structural H-bond relaxation (CHB(t)) involving urea pairs. Similarity in activation energies estimated from the temperature dependent DR measurements (335 ≤ T/K ≤ 363) and structural H-bond relaxations indicates that the structural H-bond relaxation overwhelmingly dominates the slowest DR relaxation in these DESs. Simulated collective reorientational correlation functions (C ℓ (t)), on the other hand, suggest that the second slower time scale (∼40 ps) derives contributions from both the single particle orientation dynamics and structural H-bond relaxation, leaving no role for hydrodynamic molecular rotations. The sub-10 ps DR time scale has been found to be connected to the fast reorientation dynamics of the component molecules (acetamide or urea). Fractional viscosity dependence for the longest DR times, , has been observed for these DESs with the fraction power p = 0.7. Subsequently, the temporal heterogeneity aspects of these media have been investigated by examining the simulated particle motion characteristics and substantiated by estimating the dynamically correlated time scales and length-scales through simulations of four-point susceptibilities and density correlations. These estimated dynamical time scales and length-scales assist in explaining the different inferences regarding solution heterogeneity drawn from different measurements on these DESs.

Peculiar Molecular Shape and Size Dependence of the Dynamics of Fluids Confined in a Small-Pore Metal–Organic Framework

Force-field-based molecular dynamics simulations were deployed to systematically explore the dynamics of confined molecules of different shapes and sizes, that is, linear (CO2 and N2) and spherical (CH4) fluids, in a model small pore system, that is, the metal-organic framework SIFSIX-2-Cu-i. These computations unveil an unprecedented molecular symmetry dependence of the translational and rotational dynamics of fluids confined in channel-like nanoporous materials. In particular, this peculiar behavior is reflected by the extremely slow decay of the Legendre reorientational correlation functions of even-parity order for the linear fluids, which is associated with jump-like orientation flips, while the spherical fluid shows a very fast decay taking place on a subpicosecond time scale. Such a fundamental understanding is relevant to diverse disciplines such as in chemistry, physics, biology, and materials science, where diatomic or polyatomic molecules of different shapes/sizes diffuse through nanopores.

Communication: Heterogeneous water dynamics on a clathrate hydrate lattice detected by multidimensional oxygen nuclear magnetic resonance

Previous deuteron nuclear magnetic resonance studies revealed conflicting evidence regarding the possible motional heterogeneity of the water dynamics on the hydrate lattice of an ice-like crystal. Using oxygen-17 nuclei as a sensitive quadrupolar probe, the reorientational two-time correlation function displays a clear nonexponentiality. To check whether this dispersive behavior is a consequence of dynamic heterogeneity or rather of an intrinsic nonexponentiality, a multidimensional, four-time magnetic resonance experiment was devised that is generally applicable to strongly quadrupolarly perturbed half-integer nuclei such as oxygen-17. Measurements of an appropriate four-time function demonstrate that it is possible to select a subensemble of slow water molecules. Its mean time scale is compared to theoretical predictions and evidence for significant motional heterogeneity is found.

Perspectives of Deuteron Field-Cycling NMR Relaxometry for Probing Molecular Dynamics in Soft Matter.

Due to the single-particle character of the quadrupolar interaction in molecular systems, (2)H NMR poses a unique method for probing reorientational dynamics. Spin-lattice relaxation gives access to the spectral density, and its frequency dependency can be monitored by field-cycling (FC) techniques. However, most FC NMR studies employ (1)H; the use of (2)H is still rare. We report on the application of (2)H FC NMR for investigating the dynamics in molecular liquids and polymers. Commercial as well as home-built relaxometers are employed accessing a frequency range from 30 Hz to 6 MHz. Due to low gyromagnetic ratio, high coupling constants, and finite FC switching times, current (2)H FC NMR does not reach the dispersion region in liquids (toluene and glycerol), yet good agreement with the results from conventional high-field (HF) relaxation studies is demonstrated. The pronounced difference at low frequencies between (2)H and (1)H FC NMR data shows the relevance of intermolecular relaxation in the case of (1)H NMR. In the case of the polymers polybutadiene and poly(ethylene-alt-propylene), very similar relaxation dispersion is observed and attributed to Rouse and entanglement dynamics. Combination with HF (2)H relaxation data via applying frequency-temperature superposition allows the reconstruction of the full spectral density reflecting both polymer as well as glassy dynamics. Transformation into the time domain yields the reorientational correlation function C2(t) extending over nine decades in time with a long-time power law, C2(t) ∝ t(-0.45±0.05), which does not conform to the prediction of the tube-reptation model, for which ∝ t(-0.25) is expected. Entanglement sets in below C2(t = τe) ≅ S(2) = 0.001, where τe is the entanglement time and S the corresponding order parameter. Finally, we discuss the future prospects of the (2)H FC NMR technique.

Raman band shape analysis of cyanate-anion ionic liquids

Raman band shape analysis of the C≡N stretching mode was carried out for ionic liquids based on [SCN]−, [N(CN)2]−, [C(CN)3]−, and [B(CN)4]−, with a common cation, 1-ethyl-3-methylimidazolium, [C2C1im]+. Vibrational and reorientational time correlation functions were obtained by Fourier transforming isotropic and anisotropic Raman spectra. Comparison is provided between results for [C2C1im][SCN] and literature data available for molten alkali thiocyanates. Vibrational dephasing of the ωCN mode in [C2C1im][SCN] belongs to the regime of inhomogeneous broadening as it is determined by the distribution of vibrational frequencies, <Δω2>. Vibrational dephasing in [N(CN)2]−, [C(CN)3]−, and [B(CN)4]−, depends on both the <Δω2> and the correlation time of frequency fluctuation. Decay rates of reorientational time correlation functions within the range of 1.0ps do not correlate with the viscosity of these ionic liquids. Molecular dynamics simulations of these ionic liquids provide support to the experimental finding that the reorientational time correlation function of [SCN]− decays faster than the other anions. The Raman band shape analysis suggests that the short-time dynamics of these ionic liquids is structure-limited because of steric hindrance.

Water around fullerene shape amphiphiles: A molecular dynamics simulation study of hydrophobic hydration.

Fullerene C60 sub-colloidal particle with diameter ∼1 nm represents a boundary case between small and large hydrophobic solutes on the length scale of hydrophobic hydration. In the present paper, a molecular dynamics simulation is performed to investigate this complex phenomenon for bare C60 fullerene and its amphiphilic/charged derivatives, so called shape amphiphiles. Since most of the unique properties of water originate from the pattern of hydrogen bond network and its dynamics, spatial, and orientational aspects of water in solvation shells around the solute surface having hydrophilic and hydrophobic regions are analyzed. Dynamical properties such as translational-rotational mobility, reorientational correlation and occupation time correlation functions of water molecules, and diffusion coefficients are also calculated. Slower dynamics of solvent molecules—water retardation—in the vicinity of the solutes is observed. Both the topological properties of hydrogen bond pattern and the "dangling" -OH groups that represent surface defects in water network are monitored. The fraction of such defect structures is increased near the hydrophobic cap of fullerenes. Some "dry" regions of C60 are observed which can be considered as signatures of surface dewetting. In an effort to provide molecular level insight into the thermodynamics of hydration, the free energy of solvation is determined for a family of fullerene particles using thermodynamic integration technique.

Boundary condition effects on the dynamic and electric properties of hydration layers.

Water solvation has a central role in several biochemical processes ranging from protein folding to biomolecular recognition and enzyme catalysis. Because of its importance, the structure and dynamics of hydration layers around biological macromolecules have been the targets of a great number of experimental and computational studies. In the present contribution, we have investigated the effects of periodic boundary conditions (PBCs), as used in conjunction with molecular dynamics (MD) simulations, on the dynamic and electric properties of water layers. In particular, we have systematically performed MD simulations of neat water and biomolecules in aqueous solutions by imposing a different external dielectric constant, a generally overlooked parameter in PBC simulations. The effect of the system size has also been addressed. Overall, our results consistently indicate that the dipole moment properties of water layers, and specifically the dipole moment fluctuations and the reorientational correlation functions, can be sensitive to the choice of the external boundary conditions, whereas other molecular properties, such as the self-diffusion coefficient and the reorientational relaxation times, are not affected. We think that our investigation may help to assess appropriate simulation conditions for modeling the aqueous environment of relevant biochemical systems and processes.

Second-order quadrupole interaction based detection of ultra-slow motions: Tensor operator framework for central-transition spectroscopy and the dynamics in hexagonal ice as an experimental example

The second-order quadrupolar broadening of the central transition of nuclear probes with half-integer spins I is demonstrated to be useful to detect ultraslow molecular motions. On the basis of density matrix calculations explicit expressions are derived for quadrupolarly modulated sin–sin and cos–cos signals of selectively excited nuclei with I=3/2, 5/2, 7/2, and 9/2. These correlation functions are suitable for implementation in two-dimensional exchange spectroscopy as well as for stimulated-echo experiments. As an application, 17O measurements of the reorientational correlation function of water molecules in hexagonal ice are presented.

Relaxation stretching, fast dynamics, and activation energy: a comparison of molecular and ionic liquids as revealed by depolarized light scattering.

Depolarized light scattering (DLS) spectra of a series of 16 molecular and 6 room temperature ionic liquids are investigated by applying tandem-Fabry-Pérot interferometry, double monochromator, and photon correlation spectroscopy. Temperatures up to well above the melting point, in some cases, even up to the boiling point, are covered, and all liquids can be supercooled. The accessed time constants are between 1 ps and 10 ns; in some cases, even longer times are reached. The susceptibility spectra and likewise the corresponding reorientational correlation functions are characterized by stretching parameter β(CD) (0.32-0.80) for the long-time decay (α-process), strength of fast dynamics 1 - f, and time scale at shortest times expressed by k(B)T/I* with the apparent quantity I* reflecting essentially inertia effects. An additional (intermediate) power-law regime (or excess wing in the frequency domain) between fast dynamics and the α-process has to be taken into account. For a given system the spectral parameters are virtually temperature independent up to the boiling point, i.e., frequency-temperature superposition applies for the α-process. Among the liquids, the quantity I* correlates with molecular mass, and the larger 1 - f, the smaller the inertial quantity I*. No correlation among 1 - f and β(CD) is revealed. Testing for correlation of β(CD) or 1 - f with parameters describing the temperature dependence of the correlation time τ(α), namely, high-temperature activation energy E(∞), fragility m, or glass transition temperature T(g), no significant correlation is found. Regarding molecular vs ionic liquids, no relevant difference in the evolution of their DLS spectra is observed.

Reorientation Dynamics of Nanoconfined Acetonitrile: A Critical Examination of Two-State Models

Molecular dynamics simulations are used to investigate the reorientation dynamics of liquid acetonitrile confined within a nanoscale, hydrophilic silica pore. The dynamics are strongly modified relative to the bulk liquid-the time scale for reorientation is increased by orders-of-magnitude and the dynamics become nonexponential-and these effects are examined at the molecular level. In particular, commonly invoked two-state (or core-shell) models, with and without consideration of exchange of molecules between the states, are applied and discussed. A rigorous decomposition of the acetonitrile reorientational correlation function is introduced that permits the approximations implicit in the two-state models to be identified and tested systematically. The results show that exchange is an important component of the nanoconfined acetonitrile reorientation dynamics and a two-state model with exchange can accurately describe the correlation. However, the faithfulness of the model is related to the separation of time scales in the two states, which exists for a wide range of definitions of the two states. This suggests that caution should be exercised when inferring molecular-level details from application of two-state models.

Ultrafast 2DIR probe of a host-guest inclusion complex: Structural and dynamical constraints of nanoconfinement

Two-dimensional infrared (2DIR) spectroscopy is used to study the influence of nanoconfinement on the spectral diffusion dynamics of cyclopentadienyl manganese tricarbonyl (CpMn(CO)3, CMT) free in solution and confined in the cavity of β-cyclodextrin. Contrary to the reorientation correlation function of the solvent molecules, determined through molecular dynamics simulations, measurements in three different solvents indicate that CMT confined in β-cyclodextrin undergoes spectral diffusion that is faster than free CMT. To account for this discrepancy, we propose that spectral diffusion time scales contain a dynamical contribution that is dependent on the effective size of the conformational space presented by the solvation environment. This solvation state space size is related to the number of participating solvent molecules, which in turn is proportional to the solvent accessible surface area (SASA). We test the role of the number of participating solvent molecules using a simple Gaussian-Markov simulation and find that an increase in the number of participating solvent molecules indeed slows the time required to search the available conformational space. Finally, we test this dependence by comparing the spectral diffusion of a previously studied manganese carbonyl, dimanganese decacarbonyl (Mn2(CO)10, DMDC), to CMT and find that DMDC, which has a larger SASA, exhibits slower spectral diffusion. The experimental observations and the supporting simplistic solvation model suggest that vibrational probe molecules, such as CMT, might be able to function as sensors of conformational entropy.

Effect of heavy hydrogen isotopes on the vibrational line shape for supercritical water through rotational couplings

The rotational couplings, which determine the infrared spectral line shape in the low-density supercritical water, were analyzed as functions of the density and the temperature by applying molecular dynamics simulation to a flexible water model, SPC∕Fw and by varying the moment of inertia of the water through substitution for the H atom in H2O by heavy hydrogen isotopes. The differences in the frequency and the relative intensity between the sharp center peak and the rotational broad side-bands were analyzed for the O-H, O-D, and O-T stretch spectra. The frequency differences between the sharp center peak and the rotational broad side-bands are linearly correlated with the inverse of the moment of inertia of the isotope-substituted water species. The intensity of the sharp peak is associated with the long-time component of the reorientational time correlation function for the stretching bond vector. At 400 °C, where a substantial amount of hydrogen bonds are dynamically persisting, an intensity decrease in the rotational broad side-bands was observed with increasing density from 0.01 to 0.40 g cm(-3), respectively, corresponding to 0.56 and 22.2 M (=mol dm(-3)), orders of magnitude higher than the ideal gas densities. This arises from the decrease in the correlation time of the angular velocity and the rotational couplings due to an increase in the hydrogen-bonding perturbation. The intensity decrease of the rotational side-bands with increasing density is more significant for the water isotopes with heavier hydrogens. At a high temperature of 1200 °C, the rotational side-bands at 0.01 to 0.05 g cm(-3) were more distinct than those at 400 °C, and even at a medium density of 0.40 g cm(-3) a significant signal broadening due to the rotational couplings was clearly observed because of the accelerated rotational momentum. The vibrational spectrum cannot be decomposed into definite chemical clusters for the thermodynamic and kinetic analysis because of the dynamic origin.

Rank-dependent orientational relaxation in an ionic liquid: an all-atom simulation study

We have employed all-atom molecular dynamics simulation to investigate the heterogeneity effects on reorientation correlation time in the ionic liquid (IL), 1-butyl-3-methylimidazolium hexafluorophosphate ([Bmim][PF6]), at 298 and 450 K. Our simulated density, radial distribution functions, viscosity, and self-diffusion coefficients compare well with the existing literature data. Even though the room temperature (298 K) simulations could not probe the entire decay of the reorientation correlation function (C l (t)) due to the inherent slow diffusional timescale in this IL and limited computational resources available, the simulated C l (t) at high temperature (450 K) captures the entire decay. The ratio between the simulated reorientation time constants, $$ R = \frac{{\int_{0}^{\infty } {{\text{d}}tC_{1} (t )} }}{{\int_{0}^{\infty } {{\text{d}}tC_{2} (t )} }} = \frac{{\left\langle {\tau_{1} } \right\rangle }}{{\left\langle {\tau_{2} } \right\rangle }} $$ , differs considerably from 3 at 450 K, indicating the presence of significant heterogeneity effects even at this high temperature. This observation corroborates well with the simulated non-Gaussian parameter at this temperature.

Reorientational Dynamics of Organophosphate Glass Formers – a Joint Study by 31P NMR, Dielectric Spectroscopy and Light Scattering

Abstract We study molecular reorientation in the glass formers triethyl-, tripropyl-, and m-tricresyl phosphate by measuring 31P NMR spectra, relaxation (T 1 and T 2), stimulated echo decays and two-dimensional spectra over a large temperature range (130–370 K). The results are compared to those from dielectric spectroscopy (DS) and depolarized light scattering (LS). While the time constants τ α of the primary (α-) process in the range × 10−11–100 s well agree, the stretching of the reorientational correlation function is probe dependent, i.e., the rank-two functions (NMR and LS) essentially agree whereas the rank-one function (DS) is less stretched. The very similar 2D spectra recorded as a function of mixing time demonstrate that the reorientational mechanism does not significantly vary among the super-cooled liquids. A model of combining large- and small-angle reorientation allows for reproducing the 2D spectra and may be taken as generic for the dynamics in viscous molecular liquids. Pronounced secondary (β-) processes do not only effect the NMR relaxation but can be identified directly in the time domain by the stimulated echo technique. This becomes possible due to its broad time window (10 μs–100 s). Thus, applying the different 1D and 2D techniques makes 31P NMR well suited to probe molecular reorientation over a wide dynamic range.

Mean Square Displacement and Reorientational Correlation Function in Entangled Polymer Melts Revealed by Field Cycling1H and2H NMR Relaxometry

Mixtures of protonated and deuterated polybutadiene and polydimethylsiloxane are studied by means of field-cycling (FC) 1H NMR relaxometry in order to analyze the intra- and intermolecular contributions to spin–lattice relaxation. They reflect reorientational and translational dynamics,respectively. Master curves in the susceptibility representation χ″(ωτs) are constructed by employing frequency–temperature superposition with τs denoting the segmental correlation time. The intermolecular contribution is dominating at low frequencies and allows extracting the segmental mean square displacement ⟨R2(t)⟩, which reveals two power-law regimes. The one at short times agrees with t0.5 predicted for the free Rouse regime and at long times a lower exponent is observed in fair agreement with t0.25 expected for the constrained Rouse regime of the tube-reptation model. Concomitantly the reorientational rank-two correlation function C2(t/τs) is obtained from the intramolecular part. Again two power-law regimes t–ε are identified for polybutadiene. The first agrees with t–1 of free Rouse dynamics whereas at long times ε = 0.49 is obtained. The latter is corroborated by the 2H relaxation of deuterated polybutadiene, yet, it does not agree with ε = 0.25 predicted for constrained Rouse dynamics. Thus, the relation C2(t) ∝ ⟨R2(t)⟩–1 as assumed by the tube-reptation model is not confirmed.

Rotational Dynamics of Plastic Ice

A plastic phase predicted to exist between crystalline ice VII and liquid water has been investigated. The present work focuses on the dynamics of the water molecules in the phases at high temperature and pressure, i.e., ice VII, plastic ice, and liquid water. The hydrogen-bond correlation function providing the lifetime of hydrogen bonds is compared to the reorientational correlation function to examine a relation between a rotation of an individual molecule and an energetic relaxation process. The hydrogen-bond correlation function of plastic ice decays in a way similar to liquid but it converges to a finite value as seen in ice VII, reflecting the rotational motion of the water molecule at the fixed location. In addition, the relaxation times of the two correlation functions for plastic ice resemble one another, confirming the fact that only the rotational motion invokes the hydrogen-bond rearrangements in plastic ice.

Effect of the local hydrogen bonding network on the reorientational and translational dynamics in supercritical water

Molecular dynamics simulations have been performed in a wide range of densities along a near critical isotherm of supercritical water in order to reveal the interconnection between the local hydrogen bonding (HB) network and several related dynamic properties. The results obtained have revealed a significant slowing down of reorientational dynamics of the water molecules as the value of the number of hydrogen bond per molecule increases and this is reflected on the increase in the reorientational correlation times. The calculated reorientational times exhibit also an increasing trend by increasing the bulk density, and this effect is more pronounced in the case of the first-order Legendre reorientational correlation functions. A clear nonlinear dependence of the librational mode frequencies of the water molecules on the augmented local density around them has also been revealed. This result could be regarded as an additional support of experimental observations suggesting the use of a nonlinear relation when analyzing the density dependence of spectroscopic peak frequencies in order to extract information about local density augmentation in supercritical fluids. The HB dynamics have been also investigated, revealing a plateau in the calculated HB lifetimes at intermediate and higher liquidlike densities and a small increase at low, gaslike densities.