Large Angular Jumps Research Articles

The collective burst mechanism of angular jumps in liquid water

Understanding the microscopic origins of collective reorientational motions in aqueous systems requires techniques that allow us to reach beyond our chemical imagination. Herein, we elucidate a mechanism using a protocol that automatically detects abrupt motions in reorientational dynamics, showing that large angular jumps in liquid water involve highly cooperative orchestrated motions. Our automatized detection of angular fluctuations, unravels a heterogeneity in the type of angular jumps occurring concertedly in the system. We show that large orientational motions require a highly collective dynamical process involving correlated motion of many water molecules in the hydrogen-bond network that form spatially connected clusters going beyond the local angular jump mechanism. This phenomenon is rooted in the collective fluctuations of the network topology which results in the creation of defects in waves on the THz timescale. The mechanism we propose involves a cascade of hydrogen-bond fluctuations underlying angular jumps and provides new insights into the current localized picture of angular jumps, and its wide use in the interpretations of numerous spectroscopies as well in reorientational dynamics of water near biological and inorganic systems. The role of finite size effects, as well as of the chosen water model, on the collective reorientation is also elucidated.

Ionic Dynamics and Vibrational Spectral Diffusion of a Protic Alkylammonium Ionic Salt through Intrinsic Cationic N-H Vibrational Probe from FPMD Simulations.

We employed density functional theory (DFT)-based molecular dynamics simulations to explore the structure, dynamics, and spectral properties of the protic ionic entity trimethylammonium chloride (TMACl). Structural investigations include calculating the site-site radial distribution functions (RDFs), the distribution of constituent cations and anions in three-dimensional space, and combined distribution functions of the hydrogen-bonded pair RDF versus angle, revealing the structural characteristics of the ionic solvation and the intermolecular interactions within ions. Further, we determined the instantaneous vibrational stretching frequencies of the intrinsic N-H stretch probe modes by applying the time-series wavelet method. The associated ionic dynamics within the protic ionic compound were investigated by calculating the time-evolution of the fluctuating frequencies and the frequency-time correlation functions (FFCFs). The time scale related to the local structural relaxation process and the average hydrogen bond lifetime, ion cage dynamics, and mean squared displacement were investigated. The faster decay component of the FFCFs, depicting the intermolecular motion of intact hydrogen bonds in TMACl, is 0.07 ps for the Perdew-Burke-Ernzerhof (PBE)-based simulation and 0.06 ps for the PBE-D2 representation. The slower time scale of the longer picosecond decay time component of PBE and PBE-D2 representations are 3.13 and 2.87 ps, respectively. These picosecond time scales represent more significant fluctuations of the hydrogen-bonding partners in the ionic entity and hydrogen-bond jump events accompanied by large angular jumps. The longest picosecond time scales represent structural relaxation, including large angular jumps and ion-pair dynamics. Also, ion cage lifetimes correlate with the slowest time scale of the associated dynamics of vibrational spectral diffusion despite the type of DFT functional. This study benchmarks DFT treatments of the exchange-correlation functional with and without the van der Waals (vdW) dispersion correction scheme. The inclusion of vdW interactions to the PBE functional represents a less structured state of the ionic entity and faster dynamics of the molecular motions relative to the one predicted by the PBE system. All the results illustrate the necessity of accurately describing the Coulomb interactions, vdW dispersive interactive forces, and localized hydrogen bonds required to sustain the energetic balance in this ionic salt.

Reorientational dynamics of molecules in liquid methane: A molecular dynamics simulation study

Rotational motion of molecules in liquids plays an important role in determining the liquids' Nuclear Magnetic Resonance (NMR) spin-relaxation properties. The traditional theory of NMR spin relaxation assumes that the reorientational dynamics of molecules in liquids can be described by a continuous-time rotational-diffusion random walk with a single rotational-diffusion coefficient. However, recent experimental and theoretical studies have demonstrated that the simple rotational-diffusion model does not fully capture the rotational dynamics of molecules in liquids: for example, the reorientation of molecules in liquid water occurs through a combination of continuous-time rotational diffusion and discrete, large angular jumps resulting from collective rearrangements of the hydrogen-bond network of water.In order to obtain further insights into the origin of large angular jumps in the rotational motion of liquid water, we studied the rotational dynamics of methane - an apolar, non‑hydrogen-bonding liquid with a spherically symmetric molecule. The reorientational propagator and the ensemble-averaged Legendre polynomial reorientational functions of liquid methane were analysed using molecular dynamics simulations. On the femtosecond timescale, the reorientational motion of methane molecules was found to be characterised by free-rotation gas-like Gaussian decay of the reorientational Legendre polynomials, a result consistent with the available experimental data for liquid methane. On the long timescale (picoseconds) the decay of the reorientational Legendre polynomials was exponential, suggestive of a Debye-like continuous-time rotational diffusion behaviour. However, the ratios of the exponential time constants for different orders of the Legendre polynomials failed to match the rotational-diffusion model. We discuss the implications of these findings for the understanding of rotational motion of molecules in hydrogen-bonding and non‑hydrogen-bonding liquids.

Non-monotonic dynamics of water in its binary mixture with 1,2-dimethoxy ethane: A combined THz spectroscopic and MD simulation study.

A combined experimental (mid- and far-infrared FTIR spectroscopy and THz time domain spectroscopy (TTDS) (0.3-1.6 THz)) and molecular dynamics (MD) simulation technique are used to understand the evolution of the structure and dynamics of water in its binary mixture with 1,2-dimethoxy ethane (DME) over the entire concentration range. The cooperative hydrogen bond dynamics of water obtained from Debye relaxation of TTDS data reveals a non-monotonous behaviour in which the collective dynamics is much faster in the low Xw region (where Xw is the mole fraction of water in the mixture), whereas in Xw ∼ 0.8 region, the dynamics gets slower than that of pure water. The concentration dependence of the reorientation times of water, calculated from the MD simulations, also captures this non-monotonous character. The MD simulation trajectories reveal presence of large amplitude angular jumps, which dominate the orientational relaxation. We rationalize the non-monotonous, concentration dependent orientational dynamics by identifying two different physical mechanisms which operate at high and low water concentration regimes.

Pressure Dependence of Hydrogen-Bond Dynamics in Liquid Water Probed by Ultrafast Infrared Spectroscopy.

Clarifying the structure/dynamics relation of water hydrogen-bond network has been the aim of extensive research over many decades. By joining anvil cell high-pressure technology, femtosecond 2D infrared spectroscopy, and molecular dynamics simulations, we studied, for the first time, the spectral diffusion of the stretching frequency of an HOD impurity in liquid water as a function of pressure. Our experimental and simulation results concordantly demonstrate that the rate of spectral diffusion is almost insensitive to the applied pressure. This behavior is in contrast with the previously reported pressure-induced speed up of the orientational dynamics, which can be rationalized in terms of large angular jumps involving sudden switching between two hydrogen-bonded configurations. The different trend of the spectral diffusion can be, instead, inferred considering that the first solvation shell preserves the tetrahedral structure with pressure and the OD stretching frequency is only slight perturbed.

Microscopic origin of temporal heterogeneities in translational dynamics of liquid water.

Liquid water is known to reorient via a combination of large angular jumps (due to exchange of hydrogen bonding (H-bond) partners) and diffusive orientations. Translation of the molecule undergoing the orientational jump and its initial and final H-bond acceptors plays a key role in the microscopic reorientation process. Here, we partition the translational dynamics into those occurring during intervals when rotating water molecules (and their initial and final H-bonding partners) undergo orientational jump and those arising when molecules wait between consecutive orientational jumps. These intervals are chosen in such a way that none of the four possible H-bonds involving the chosen water molecule undergo an exchange process within its duration. Translational dynamics is analysed in terms of the distribution of particle displacements, van Hove functions, and its moments. We observe that the translational dynamics, calculated from molecular dynamics simulations of liquid water, is fastest during the orientational jumps and slowest during periods of waiting. The translational dynamics during all temporal intervals shows an intermediate behaviour. This is the microscopic origin of temporal dynamic heterogeneity in liquid water, which is mild at 300 K and systematically increases with supercooling. Study of such partitioned dynamics in supercooled water shows increased disparity in dynamics occurring in the two different types of intervals. Nature of the distribution of particle displacements in supercooled water is investigated and it reveals signatures non-Gaussian behaviour.

Primary and secondary relaxation process in plastically crystalline cyanocyclohexane studied by 2H nuclear magnetic resonance. I

We study the main (α-) and secondary (β-) relaxation in the plastically crystalline (PC) phase of cyanocyclohexane by various 2H nuclear magnetic resonance (NMR) methods (line-shape, spin-lattice relaxation, stimulated echo, and two-dimensional spectra) above and below the glass transition temperature T(g) = 134 K. Our results regarding the α-process demonstrate that molecular motion is not governed by the symmetry of the lattice. Rather it is similar to the one reported for structural glass formers and can be modeled by a reorientation proceeding via a distribution of small and large angular jumps. A solid-echo line-shape analysis regarding the β-process below T(g) yields again very similar results when compared to those of the structural glass formers ethanol and toluene. Hence we cannot confirm an intramolecular origin for the β-process in cyanocyclohexane. The fast β-process in the PC phase allows for the first time a detailed 2H NMR study of the process also at T > T(g): an additional minimum in the spin-lattice relaxation time reflecting the β-process is found. Furthermore the solid-echo spectra show a distinct deviation from the rigid limit Pake pattern, which allows a direct determination of the temperature dependent spatial restriction of the process. In Part II of this work, a quantitative analysis is carried out, where we demonstrate that within the model of a "wobbling in a cone" the mean cone angle increases above T(g) and the corresponding relaxation strength is compared to dielectric results.

Hydrogen-Bond Dynamics in a Protic Ionic Liquid: Evidence of Large-Angle Jumps.

We study the molecular rotation of the protic room-temperature ionic liquid ethylammonium nitrate with dielectric relaxation spectroscopy and femtosecond-infrared spectroscopy (fs-IR) of the ammonium N-H vibrations. The results suggest that the rotation of ethylammonium ion takes place via large angular jumps. Such nondiffusive reorientational dynamics is unique to strongly hydrogen-bonded liquids such as water and indicates that the intermolecular interaction is highly directional in this class of ionic liquids.

Water-Assisted Vibrational Relaxation of a Metal Carbonyl Complex Studied with Ultrafast 2D-IR

Water is capable of assisting exceptionally rapid vibrational relaxation within dissolved solute species. Although ultrafast dynamics of metal carbonyl complexes have long served as models for vibrational relaxation, all reports to-date have investigated nonaqueous solutions due to the insolubility of the vast majority of metal carbonyl complexes in water. Using the water-soluble complex [RuCl(2)(CO)(3)](2), which belongs to a class known as "carbon monoxide (CO) releasing molecules" (CORM), we report the first ultrafast vibrational relaxation measurements of a metal carbonyl complex in water and compare this relaxation with polar organic solvents, namely, methanol. The vibrational relaxation, measured by two-dimensional IR (2D-IR) spectroscopy, is an order of magnitude faster in H(2)O (3.12 ± 0.29 ps) than in methanol (42.25 ± 3 ps). The accelerated relaxation times of the coupled CO units in H(2)O and D(2)O is interpreted as resulting from the enhancement of intramolecular relaxation pathways through additional coupling induced by the solvent. In addition, the vibrational lifetime shows a significant isotope dependence: in D(2)O the relaxation time is 4.27 ± 0.27 ps, a difference of roughly 30%. We interpret these measurements in terms of a nonresonant channel primarily arising from water's reorientational dynamics, which occur primarily through large angular jumps, as well as a resonant transfer of vibrational energy from the carbonyl bands to the libration-bend combination band. These measurements indicate that metal carbonyls, which are among the strongest IR transitions, are exquisitely sensitive to the presence of water and hold promise as IR analogs of EPR spin labels.

Magnitude and Molecular Origin of Water Slowdown Next to a Protein

Hydration shell dynamics plays a critical role in protein folding and biochemical activity and has thus been actively studied through a broad range of techniques. While all observations concur with a slowdown of water dynamics relative to the bulk, the magnitude and molecular origin of this retardation remain unclear. Via numerical simulations and theoretical modeling, we establish a molecular description of protein hydration dynamics and identify the key protein features that govern it. Through detailed microscopic mapping of the water reorientation and hydrogen-bond (HB) dynamics around lysozyme, we first determine that 80% of the hydration layer waters experience a moderate slowdown factor of ~2-3, while the slower residual population is distributed along a power-law tail, in quantitative agreement with recent NMR results. We then establish that the water reorientation mechanism at the protein interface is dominated by large angular jumps similar to the bulk situation. A theoretical extended jump model is shown to provide the first rigorous determination of the two key contributions to the observed slowdown: a topological excluded-volume factor resulting from the local protein geometry, which governs the dynamics of the fastest 80% of the waters, and a free energetic factor arising from the water-protein HB strength, which is especially important for the remaining waters in confined sites at the protein interface. These simple local factors are shown to provide a nearly quantitative description of the hydration shell dynamics.

Flickering dipoles in the gas phase: Structures, internal dynamics, and dipole moments of β-naphthol-H2O in its ground and excited electronic states

Described here are the rotationally resolved S(1)-S(0) electronic spectra of the acid-base complex cis-β-naphthol-H(2)O in the gas phase, both in the presence and absence of an applied electric field. The data show that the complex has a trans-linear O-H⋅⋅⋅O hydrogen bond configuration involving the -OH group of cis-β-naphthol and the oxygen lone pairs of the attached water molecule in both electronic states. The measured permanent electric dipole moments of the complex are 4.00 and 4.66 D in the S(0) and S(1) states, respectively. These reveal a small amount of photoinduced charge transfer between solute and solvent, as supported by density functional theory calculations and an energy decomposition analysis. The water molecule also was found to tunnel through a barrier to internal motion nearly equal in energy to kT at room temperature. The resulting large angular jumps in solvent orientation produce "flickering dipoles" that are recognized as being important to the dynamics of bulk water.

How Biomolecules Influence Water Structure and Dynamics

Interactions between solutes and water impact both water structure and structural dynamics as well as solute properties (e.g. conformational fluctuations of proteins). To understand these interactions we investigate water near disaccharides using classical atomistic molecular dynamics simulations. Disaccharides show topological and chemical complexity characteristic of larger biomolecules but are sufficiently small to permit detailed study. We observe that increases in hydrophobicity precisely map slow down in water translation and rotation of local water populations. In line with recent studies of proteins, we find that chemically similar functional groups may interact differently with water depending on neighboring functional groups.To explain these observations we examine the mechanism of hydrogen bond exchange for waters hydrogen bonded to other waters but within the sugar first solvation shell, as well as waters hydrogen bonded to the sugar. Recent work showed that water in bulk rotates through large angular jumps that pass through bifurcated hydrogen bond intermediates and that rotation rates can be rationalized through transition state theory. Previous reports found that the rotational slow down of water near small solutes can be predicted from changes in the accessible transition state volume or the enthalpy of the hydrogen bonds. For our larger solutes we find that accounting for the transition state volume alone overestimates water rotational slow down. Differences in hydrogen bond enthalpy are also insufficient to predict rotational slowdown. Water slowdown can only be understood by additionally accounting for subtle changes in the free energy landscape associated with water rotation - reduction in the number of available reactant states and broadening of the transition state barriers. The presence of solutes of even moderate size thus affects water dynamics in ways difficult to predict using simple scaling considerations from bulk, making water response system dependent.

Water reorientation in the hydration shells of hydrophilic and hydrophobic solutes

We discuss some key aspects of our recent theoretical work on water reorientation dynamics, which is important in a wide range of phenomena, including aqueous phase chemical reactions, protein folding, and drug binding to proteins and DNA. It is shown that, contrary to the standard conception that these dynamics are diffusional, the reorientation of a water molecule occurs by sudden, large amplitude angular jumps. The mechanism involves the exchange of one hydrogen bond for another by the reorienting water, and the process can be fruitfully viewed as a chemical reaction. The results for reorientation times, which can be well described analytically, are discussed in the context of the molecular level interpretation of recent ultrafast infrared spectroscopic results, focusing on the concepts of structure making/breaking and solvent ‘icebergs’.

Direct Evidence of Angular Jumps During Water Reorientation Through Two-Dimensional Infrared Anisotropy

Water reorientation was recently suggested via simulations to proceed through large angular jumps, but direct experimental evidence has so far remained elusive. Here we show that both infrared pump−probe and photon echo spectroscopies can provide such evidence through the measurement of the two-dimensional anisotropy decay. We calculate these two-dimensional anisotropies from simulations and show they can be interpreted as a vibrational frequency-resolved orientation time-correlation function. We develop a frequency-dependent extended jump model to predict the nature of the angular jump signature in these anisotropies. This model provides a rigorous and unambiguous connection between ultrafast infrared experimental results and the presence of angular jumps in bulk water, and calls for new experiments.

Reorientation of Water Inside Carbon Nanorings by Large Angular Jumps

Molecular dynamics simulations of the orientational dynamics of water molecules confined inside narrow carbon nanorings reveal that reorientational relaxation is mediated by large amplitude angular jumps. The distribution of waiting time between jumps peaks at about 60 fs, and has a slowly decaying exponential tail with a timescale of about 440 fs. These time scales are much faster than the mean waiting time between jumps of the water molecules in bulk.

Reinterpretation of the Liquid Water Quasi-Elastic Neutron Scattering Spectra Based on a Nondiffusive Jump Reorientation Mechanism

We show that previous interpretations of the liquid water quasielastic neutron scattering spectra have largely underestimated the water reorientation time. Through molecular dynamics simulations and an extended jump model, we reconcile these results with the times obtained via other techniques such as NMR and ultrafast infrared spectroscopies. This reinterpretation provides the first experimental confirmation that water reorientation is not a diffusive process, and occurs through large angular jumps.

Orientational relaxation in a dispersive dynamic medium: Generalization of the Kubo-Ivanov-Anderson jump-diffusion model to include fractional environmental dynamics

The Ivanov-Anderson model (and an earlier treatment by Kubo) envisages a decay of the orientational correlation by random but large amplitude molecular jumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion. Recent computer simulation studies on water and viscous liquids have shown that large amplitude motions may indeed be more of a rule than exception. Existing theoretical studies on jump diffusion mostly assume an exponential (Poissonian) waiting time distribution for jumps, thereby again leading to an exponential decay. Here we extend the existing formalism of Ivanov and Anderson to include an algebraic waiting time distribution between two jumps. As a result, the first (l=1) and second (l=2) rank orientational time correlation functions show the same long time power law, but their short time decay behavior is quite different. The predicted Cole-Cole plot of dielectric relaxation reproduces various features of non-Debye behavior observed experimentally. We also developed a theory where both unrestricted small jumps and large angular jumps coexist simultaneously. The small jumps are shown to have a large effect on the long time decay, particularly in mitigating the effects of algebraic waiting time distribution, and in giving rise to an exponential-like decay, with a time constant, surprisingly, less than the time constant that arises from small amplitude decay alone.

Vibrational phase relaxation of O–H stretch in bulk water: Role of large amplitude angular jumps and negative cross-correlations among the forces on the O–H bond

The ultrafast vibrational phase relaxation of O–H stretch in bulk water is investigated in molecular dynamics simulations. The dephasing time ( T 2) of the O–H stretch in bulk water calculated from the frequency fluctuation time correlation function ( C ω ( t)) is in the range of 70–80 femtosecond (fs), which is comparable to the characteristic timescale obtained from the vibrational echo peak shift measurements using infrared photon echo [W.P. de Boeij, M.S. Pshenichnikov, D.A. Wiersma, Ann. Rev. Phys. Chem. 49 (1998) 99]. The ultrafast decay of C ω ( t) is found to be responsible for the ultrashort T 2 in bulk water. Careful analysis reveals the following two interesting reasons for the ultrafast decay of C ω ( t). (A) The large amplitude angular jumps of water molecules (within 30–40 fs time duration) provide a large scale contribution to the mean square vibrational frequency fluctuation and gives rise to the rapid spectral diffusion on 100 fs time scale. (B) The projected force, due to all the atoms of the solvent molecules on the oxygen ( F O( t)) and hydrogen ( F H( t)) atom of the O–H bond exhibit a large negative cross-correlation (NCC). We further find that this NCC is partly responsible for a weak, non-Arrhenius temperature dependence of the dephasing rate.

Giant-block twist grain boundary smectic phases

Study of a diverse set of chiral smectic materials, each of which has twist grain boundary (TGB) phases over a broad temperature range and exhibits grid patterns in the Grandjean textures of the TGB helix, shows that these features arise from a common structure: "giant" smectic blocks of planar layers of thickness l(b) > 200 nm terminated by GBs that are sharp, mediating large angular jumps in layer orientation between blocks (60 degrees < Delta < 90 degrees ), and lubricating the thermal contraction of the smectic layers within the blocks. This phenomenology is well described by basic theoretical models applicable in the limit that the ratio of molecular tilt penetration length-to-layer coherence length is large, and featuring GBs in which smectic ordering is weak, approaching thin, melted (nematic-like) walls. In this limit the energy cost of change of the block size is small, leading to a wide variation of block dimension, depending on preparation conditions. The models also account for the temperature dependence of the TGB helix pitch.

Translational and reorientational heterogeneity in the glass-forming liquid Ca0.4K0.6(NO3)1.4

Molecular dynamics (MD) simulations were performed in order to reveal dynamical heterogeneity in the glass-forming liquid Ca0.4K0.6(NO3)1.4 (CKN). A polarizable model for the nitrate anion has been used in a 10.0 ns simulation of 996 ions at 450 K, which is close to the previously estimated glass transition temperature for this model (Tg ∼ 380 K). Mobile and immobile ions within 500.0 ps time windows were identified, and short-range spatial correlations between them were analysed. Mobile ions are strongly correlated, but they are much less correlated with immobile ones. In the case of the NO3− species, the sub-ensemble of translationally mobile ions also results in a rapidly decaying reorientational correlation function. Thus, if one probes spatial heterogeneity of rotational degrees of freedom in CKN, one will be also probing spatial heterogeneity of translational degrees of freedom, and vice-versa. By using a reorientation analogous of the van Hove correlation function, small angle rotational diffusion in the dynamics of mobile anions, and large angular jumps in the dynamics of immobile ones were observed.