Rotational Correlation Functions Research Articles

Invariant dynamics in a united-atom model of an ionic liquid.

We study a united-atom model of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethyl)sulfonylamide to determine to what extent there exist curves in the phase diagram along which the microscopic dynamics are invariant when expressed in dimensionless, or reduced, form. The initial identification of these curves, termed isodynes, is made by noting that contours of reduced shear viscosity and reduced self-diffusion coefficient coincide to a good approximation. Choosing specifically the contours of reduced viscosity as nominal isodynes, further simulations were carried out for state points on these, and other aspects of dynamics were investigated to study their degree of invariance. These include the mean-squared displacement, shear-stress autocorrelation function, and various rotational correlation functions. These were invariant to a good approximation, with the main exception being rotations of the anion about its long axis. The dynamical features that are invariant have in common that they are aspects that would be relevant for a coarse-grained description of the system; specifically, removing the most microscopic degrees of freedom in principle leads to a simplification of the potential energy landscape, which allows for the existence of isodynes.

Utilizing correlation functions to develop a multistate model of P. denitrificans F1-ATPase and enhance single-molecule imaging resolution

F1-ATPase enzyme is a biological motor which hydrolyzes ATP. The enzyme has been observed via single-molecule imaging experiments wherein the enzyme is allowed to rotate freely while being recorded using a gold nanoparticle. During hydrolysis, the enzyme causes Brownian noise when rotating to new chemical states because of a size difference between the 4 nm enzyme and 40 nm probe. The unconvoluted rotary movement has been revealed using techniques including rotational correction, correlation functions, and comparison of average rotational jumps which contribute to developing a multistate model.

Structure and dynamics of liquid linear and cyclic alkanes: A molecular dynamics study

Small linear alkanes, pentane and hexane, and their cyclic counterparts, cyclopentane and cyclohexane, have been examined via molecular dynamics simulations. We assess the thermodynamic, structural and dynamic behavior of said liquids, paying particular attention to dynamic properties such as diffusion coefficients, vibrational spectra, rotational correlation functions and relaxation times. The study gives an insight into the overall behavior of small alkanes, accentuating the nuances imposed by the difference in molecular shape. This is particularly relevant when considering the widespread use of these liquids as solvents.

Heterogeneous Structures of Ionic Liquids as Probed by CO Rotation with Nuclear Magnetic Resonance Relaxation Analysis and Molecular Dynamics Simulations.

The rotational dynamics of carbon monoxide (CO) in ionic liquids (ILs) was investigated by nuclear magnetic resonance (NMR) relaxation measurements and molecular dynamics (MD) simulations. NMR spin-lattice relaxation time measurements were performed for 17O-enriched CO in 10 ILs (four imidazolium-cation-based, four phosphonium-cation-based, and two ammonium-cation-based ILs, all paired with the bis(trifluorosulfonylmethane)imide anion). In combination with previously reported data for five ILs and viscosity data, our results indicated that the obtained rotational relaxation times (τ2R) were much smaller than those predicted using the Stokes-Einstein-Debye (SED) theory. For the same viscosity/temperature values, the τ2R-1 value increased linearly with increasing carbon number of the alkyl group in the cation. The deviation from the SED equation was due to the insensitivity of τ2R to the carbon number, even though a higher carbon number generally leads to higher viscosity values for ILs. To investigate the unique rotational properties of CO in the ILs, MD simulations were performed on five representative ILs (two imidazolium, two phosphonium, and one ammonium) containing CO solutes. From rotational correlation function analyses, the CO rotation mainly occurred in a free rotation-like manner within 1 ps, which explained the relative insensitivity of CO rotation to viscosity. In the subsequent time scale (>1 ps), the minor component of the CO rotation was discriminated among different ILs. It was strongly suggested that, because CO preferably locates in the outer part of the alkyl groups in the cation, the slow CO rotation is correlated with the outer alkyl dynamics, which are decoupled from the whole cation rotation.

Thermodynamic, structural and dynamic properties of selected non-associative neat liquids

Non-associative neat liquids benzene, acetone and carbon tetrachloride have been examined via molecular dynamics simulations. Several models of each neat liquid have been simulated, and selected thermodynamic and structural results are presented. However, the models have been compared mainly in terms of their dynamic quantities. Since models are rarely parametrized with the dynamic properties in mind, the principal goal of this work is to present quantities such as the power spectra, rotational correlation functions and relaxation times, diffusion coefficients and self and distinct parts of the van Hove functions in relation to available experimental data. The general trends of the calculated data provide a benchmark for the behavior of neat simple liquids which will be built upon in the cases of mixtures with associative liquids.

NMR Relaxometry: The Canonical Case Glycerol.

We present a quantitative description of the proton spin-lattice relaxation rate R1(T,ω) of glycerol including temperatures from 191 to 360 K and a frequency range 10 kHz < ω/2π < 20 MHz covered by the field-cycling technique. The analysis encompasses the data compiled by Noack and co-workers in 1971, so far, the most complete data set (10 kHz > ω/2π < 117 MHz). Applying frequency-temperature superposition, master curves are constructed extending over 15 decades in frequency/time. They are described by contributions reflecting translational and rotational dynamics mediated by inter- and intramolecular relaxation pathways. The rotational part of the spectral density/susceptibility shows high similarity with those reported by dielectric spectroscopy or photon correlation spectroscopy (PCS). In addition to a Cole-Davidson-like peak, a high-frequency "excess wing" has to be accounted for. Quantitative agreement with the PCS susceptibility is found which probes the same order of the rotational correlation function. The translational contribution is reproduced by applying the force-free hard sphere model, describing diffusion of dipolarly coupled spin systems. Rotational and translational time constants are compared to those from other techniques. Our approach is paradigmatic for the analysis of spin relaxation in glass-forming liquids. It also solves long-standing deficiencies regarding the analyses of deuteron relaxation. Moreover, the case of glycerol is special as its large separation of translation and rotation dynamics, probably because of its hydrogen bond network, is not found in nonassociated liquids.

Structure, transport properties, and dielectric properties of lactic acid/pyruvic acid aqueous solution in a biofuel cell: A molecular simulation study

Molecular dynamics (MD) simulation of lactic acid (L‐acid) and pyruvic acid (P‐acid) in a physiological salt solution has been performed, which is used as the electrolyte in a sort of biofuel cell working on a human skin. The structure, frequency distribution of molecules, dielectric properties, rotational correlation functions, and diffusion coefficients have been calculated. The anomalous behavior of dielectric constants for the lower concentration of L‐acid and P‐acid has been obtained from MD. The anomalous dielectric constant is discussed in relation with the various physical properties of the solution including the life time of the interaction in the solution. MD results suggest that the anomalous behavior is supposed to be attributed to the difference of interactions between ions in the lower and higher concentration region. POLYM. ENG. SCI., 59:2474–2478, 2019. © 2019 Society of Plastics Engineers

Classification of mobile- and immobile-molecule timescales for the Stokes–Einstein and Stokes–Einstein–Debye relations in supercooled water

Molecular dynamics simulations have been performed on TIP4P/2005 supercooled water to investigate the molecular diffusion and shear viscosity at various timescales and assess the Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations. For this purpose, we calculated various time correlation functions, such as the mean-squared displacement, stress relaxation function, density correlation function, hydrogen-bond correlation function, rotational correlation function of molecular orientation, non-Gaussian parameter, and four-point correlation function. Our study of the SE and SED relations indicates that the transport coefficients and timescales obtained using these time correlation functions may be classified into two distinct classes: those governed by either mobile or immobile molecules, due to dynamical heterogeneity. In particular, we show that the stress relaxation time, hydrogen-bond lifetime, and large-angle rotational relaxation time are coupled with translational diffusion, and are characterized by mobile molecules. In contrast, the structural -relaxation time, small-angle rotational relaxation time, and characteristic timescales of four-point correlation functions are decoupled with translational diffusion, and are governed by immobile molecules. This decoupling results in a violation of the SE relation. These results indicate that the identification of timescales that appropriately characterize transport coefficients, such as translational diffusion constant and shear viscosity, provides a deep insight into the violation of the SE and SED relations in glass-forming liquids.

Universality classes of topological phase transitions with higher-order band crossing

In topological insulators and topological superconductors, the discrete jump of the topological invariant upon tuning a certain system parameter defines a topological phase transition. A unified framework is employed to address the quantum criticality of the topological phase transitions in one to three spatial dimensions, which simultaneously incorporates the symmetry classification, order of band crossing, m-fold rotational symmetry, correlation functions, critical exponents, scaling laws, and renormalization group approach. We first classify higher-order Dirac models according to the time-reversal, particle-hole, and chiral symmetries, and determine the even–oddness of the order of band crossing in each symmetry class. The even–oddness further constrains the rotational symmetry m permitted in a symmetry class. Expressing the topological invariant in terms of a momentum space integration over a curvature function, the order of band crossing determines the critical exponent of the curvature function, as well as that of the Wannier state correlation function introduced through the Fourier transform of the curvature function. The conservation of topological invariant further yields a scaling law between critical exponents. In addition, a renormalization group approach based on deforming the curvature function is demonstrated for all dimensions and symmetry classes. Through clarification of how the critical quantities, including the jump of the topological invariant and critical exponents, depend on the nonspatial and the rotational symmetry, our work introduces the notion of universality class into the description of topological phase transitions.

Dynamics of heroin molecule inside the lipid membrane: a molecular dynamics study.

Heroin, or diamorphine (C21H23NO5), is an opium product used for various pharmaceutical and euphoric purposes. In this work, the molecular dynamics simulation study of the heroin inside the two lipid bilayers, dipalmitoylphosphatidylcholine (DMPC) and dipalmitoylphosphatidylcholine (DPPC) are presented. The whole study was conducted at three different temperatures. The location of the heroin drug, the nature of the diffusion, rotational correlation function and structural variation inside both lipid bilayers is studied. Moreover, the free energy of the solvation of the drug inside both lipid bilayers is calculated. It is found that during the whole molecular dynamics study, the drug locates at the center of both lipid membranes. The effect of the temperature is not seen at the drug location. The nature of the diffusion of the heroin drug is anomalous. The radius of gyration is calculated to study the structural variations of the heroin molecule inside both lipid bilayers. It is found that the heroin molecule does not change its structure at three temperatures. From the rotational correlation function, it is seen that the drug is more hindered for rotation inside the DPPC lipid bilayer as compared to the DMPC lipid bilayer. It is applicable for all three temperatures. The rotational correlation time of the drug is decreased while the temperature of the system is increased. In the case of DMPC, there is an abrupt change in rotational correlation time while the phase is changed.

How proteins modify water dynamics.

Much of biology happens at the protein-water interface, so all dynamical processes in this region are of fundamental importance. Local structural fluctuations in the hydration layer can be probed by 17O magnetic relaxation dispersion (MRD), which, at high frequencies, measures the integral of a biaxial rotational time correlation function (TCF)-the integral rotational correlation time. Numerous 17O MRD studies have demonstrated that this correlation time, when averaged over the first hydration shell, is longer than in bulk water by a factor 3-5. This rotational perturbation factor (RPF) has been corroborated by molecular dynamics simulations, which can also reveal the underlying molecular mechanisms. Here, we address several outstanding problems in this area by analyzing an extensive set of molecular dynamics data, including four globular proteins and three water models. The vexed issue of polarity versus topography as the primary determinant of hydration water dynamics is resolved by establishing a protein-invariant exponential dependence of the RPF on a simple confinement index. We conclude that the previously observed correlation of the RPF with surface polarity is a secondary effect of the correlation between polarity and confinement. Water rotation interpolates between a perturbed but bulk-like collective mechanism at low confinement and an exchange-mediated orientational randomization (EMOR) mechanism at high confinement. The EMOR process, which accounts for about half of the RPF, was not recognized in previous simulation studies, where only the early part of the TCF was examined. Based on the analysis of the experimentally relevant TCF over its full time course, we compare simulated and measured RPFs, finding a 30% discrepancy attributable to force field imperfections. We also compute the full 17O MRD profile, including the low-frequency dispersion produced by buried water molecules. Computing a local RPF for each hydration shell, we find that the perturbation decays exponentially with a decay "length" of 0.3 shells and that the second and higher shells account for a mere 3% of the total perturbation measured by 17O MRD. The only long-range effect is a weak water alignment in the electric field produced by an electroneutral protein (not screened by counterions), but this effect is negligibly small for 17O MRD. By contrast, we find that the 17O TCF is significantly more sensitive to the important short-range perturbations than the other two TCFs examined here.

Orientational order and dynamics of interfacial water near a hexagonal boron-nitride sheet: An ab initio molecular dynamics study.

Structural and dynamical properties of interfacial water molecules near a hexagonal boron nitride sheet (h-BN) are investigated by means of Born-Oppenheimer molecular dynamics simulations. Orientational profiles in the interfacial regions reveal two distinct types of water molecules near the BN surface. Depending on the positions of the water molecules, on top of either N or B atoms, one type contains water molecules that are oriented with one OH bond pointing toward the N atoms and the other type contains water molecules that remain parallel to the BN sheet. Distinct hydrogen bonding and stabilization energies of these two types of water molecules are found from our calculations. In order to see the effects of dispersion interactions, simulations are performed with the BLYP (Becke-Lee-Yang-Parr) functional and also BLYP with Grimme's D3 corrections (BLYP-D3). An enhancement of water ordering near the surface is observed with the inclusion of dispersion corrections. Further analysis of the diffusion coefficients, rotational time correlation functions, and hydrogen bond dynamics shows that water molecules near the h-BN sheet move faster compared to bulk water molecules both translationally and rotationally. The water molecules in the first layer are found to show substantial lateral diffusion. The escape dynamics of water from the solvation layer at the BN surface is also looked at in the current study. We have also investigated some of the electronic properties of interfacial water such as the charge density and dipole moment. It is found that the water molecules at the surface of the BN sheet have a lower dipole moment than bulk molecules.

Numerical Simulation of Brownian Motion of Multiple Particles Via a Fluctuating Lattice Boltzmann Model

In this work the fluctuating lattice Boltzmann model was adopted to simulate the Brownian motion of multiple particles in two dimensions. The thermal equilibrium between the particles and the fluctuating fluid was evaluated. More importantly, both the translational and rotational velocity correlation functions (VCFs) were studied for different number of particles. It has been shown that the translational and rotational VCFs decay at t-1 and t-2 at long times, respectively, which the long time tails of Brownian particles are moving randomly in a fluid.

Solute Rotation in Ionic Liquids: Size, Shape, and Electrostatic Effects.

Herein are reported temperature-dependent measurements and molecular dynamics simulations designed to investigate the effects of molecular size, shape, and electrostatics on rotational dynamics in ionic liquids. Experiments were performed in the representative ionic liquid 1-butyl-3-methylimadazolium tetrafluoroborate ([Im41][BF4]) and simulations in the generic ionic liquid model ILM2 as well as a more detailed representation of [Im41][BF4]. 2H longitudinal spin relaxation times (T1) were measured for deuterated versions of 1,4-dimethylbenzene, 1-cyano-4-methylbenzene, and 1,4-dimethylpyridinium between 296 and 337 K. Fluorescence anisotropy measurements were made on the larger solutes 9,10-dimethylanthracene, 9-cyano-10-methylanthracence, and 9,10-dimethylacridnium between 240 and 292 K. Both experiment and simulation showed the nonpolar solutes rotate ∼2-fold faster than their dipolar and charged counterparts. The rotational correlation functions measured in fluorescence experiments are significantly nonexponential and can be fit to stretched exponential functions having stretching exponents 0.4 ≤ β ≤ 0.8, with β decreasing with decreasing temperature. Rotational correlation times in both the NMR and fluorescence experiments conform approximately to the hydrodynamic expectation τrot ∝ (η/T)p with p ≅ 1, and observed times are reasonably close to slip hydrodynamic predictions. Simulations, even with the idealized ILM2 solvent model, are in semiquantitative agreement with experiment when compared on the basis of equal values of ηT-1. When rotational diffusion coefficients (Di) rather than correlation times were considered, much larger departures from hydrodynamic predictions are found in many cases (p ∼ 0.5 and Di ≫ slip predictions). Rotational van Hove functions and trajectory analyses reveal the importance of large-angle jumps about some axes, even in the larger solutes.

Structure-Activity Relationship in TLR4 Mutations: Atomistic Molecular Dynamics Simulations and Residue Interaction Network Analysis

Toll-like receptor 4 (TLR4), a vital innate immune receptor present on cell surfaces, initiates a signaling cascade during danger and bacterial intrusion. TLR4 needs to form a stable hexamer complex, which is necessary to dimerize the cytoplasmic domain. However, D299G and T399I polymorphism may abrogate the stability of the complex, leading to compromised TLR4 signaling. Crystallography provides valuable insights into the structural aspects of the TLR4 ectodomain; however, the dynamic behavior of polymorphic TLR4 is still unclear. Here, we employed molecular dynamics simulations (MDS), as well as principal component and residue network analyses, to decipher the structural aspects and signaling propagation associated with mutations in TLR4. The mutated complexes were less cohesive, displayed local and global variation in the secondary structure, and anomalous decay in rotational correlation function. Principal component analysis indicated that the mutated complexes also exhibited distinct low-frequency motions, which may be correlated to the differential behaviors of these TLR4 variants. Moreover, residue interaction networks (RIN) revealed that the mutated TLR4/myeloid differentiation factor (MD) 2 complex may perpetuate abnormal signaling pathways. Cumulatively, the MDS and RIN analyses elucidated the mutant-specific conformational alterations, which may help in deciphering the mechanism of loss-of-function mutations.

Effect of glycosylation on hydration behavior at the ice-binding surface of the Ocean Pout type III antifreeze protein: a molecular dynamics simulation

Antifreeze proteins (AFPs), found in certain vertebrates, plants, fungi and bacteria have the ability to permit their survival in subzero environments by thermal hysteresis mechanism. However, the exact mechanism of ice growth inhibition is still not clearly understood. Here, four long explicit molecular dynamics (MD) simulations have been carried out at two different temperatures (277 and 298 K) with and without glycan to study the conformational rigidity of the Ocean pout type III antifreeze protein in aqueous medium and the structural arrangements of water molecules hydrating its ice-binding surface. It is found that irrespective of the temperature the ice-binding surface (IBS) of the protein is relatively more rigid than its non ice-binding surface (NonIBS) in its native and glycosylated form. Hydrophilic residues N14, T18 and Q44 are essential to antifreeze activity. Radial distribution, density distribution function and nearest neighbor orientation plots with respect to individual two surfaces confirm that density of water molecule near these binding surface in native and glycosylated form are relatively more than the nonbinding surface. The glycosylated form shows a strong peak than the native one. From rotational auto correlation function of water molecules around ice-binding sites, it is prominent that with increase in temperature, strong interaction between the water oxygen and the hydrogen bond acceptor group on the protein-binding surface decreases. This provides a possible molecular reason behind the ice-binding activity of ocean pout at the prism plane of ice.

Effect of sulfate anion on the structure and transport properties of seawater: A molecular simulation study

A molecular dynamics simulation has been performed in the sodium sulfate dissolved sodium chloride aqueous solution, as a simple model of seawater. The structure has been analyzed to determine the configuration of a sulfate anion and a neighboring water molecule. The complex formation between sulfate anion and water molecule has been discussed by the diffusion coefficient, the conductivity and the rotational correlation function.

Rotational Dynamics in Ionic Liquids from NMR Relaxation Experiments and Simulations: Benzene and 1-Ethyl-3-Methylimidazolium.

Temperature-dependent (2)H longitudinal spin relaxation times (T1) of dilute benzene-d6 in 1-butyl-3-methylimidazolium tetrafluoroborate ([Im41][BF4]) and two deuterated variants of the 1-ethyl-3-methylimidazolium cation (Im21(+)-d1 and Im21(+)-d6) in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Im21][Tf2N]), measured at multiple Larmor frequencies, were used to probe rotational dynamics in ionic liquids. Rotational correlation times significantly faster than predicted by slip hydrodynamic calculations were observed for both solutes. Molecular dynamics simulations of these systems enabled extraction of more information about the rotational dynamics from the NMR data than rotation times alone. The multifrequency (2)H T1(T) data could be fit to within uncertainties over a broad region about the T1 minimum using models of the relevant rotational time correlation functions and their viscosity/temperature dependence derived from simulation. Such simulation-guided fitting provided confidence in the semiquantitative accuracy of the simulation models and enabled interpretation of NMR measurements to higher viscosities than previously possible. Simulations of the benzene system were therefore used to explore the nature of solute rotation in ionic liquids and how it might differ from rotation in conventional solvents. Whereas "spinning" about the C6 axis of benzene senses similarly weak solvent friction in both types of solvents, "tumbling" (rotations about in-plane axes) differs significantly in conventional solvents and ionic liquids. In the sluggish environment provided by ionic liquids, orientational caging and the presence of rare but influential large-amplitude (180°) jumps about in-plane axes lead to rotations being markedly nondiffusive, especially below room temperature.

Dilute or Concentrated Electrolyte Solutions? Insight from Ionic Liquid/Water Electrolytes

When room-temperature ionic liquids (IL) are used as an electrolyte, their transport behaviors are still under heavy debate due to their complicated ion-associations. In this article, we conducted molecular dynamics simulations to study the molecular scale ion associations from the very dilute 1-butyl-3-methylimidazolium iodide/water solution to the pure IL. It revealed that ions are localized in a multicoordinated ion cage structure with nanoseconds in concentrated IL solutions. Dynamics analyses indicate that the transport of this solution can be depicted by the Debye-Hückel model only in dilute IL/water electrolyte. The velocity and rotational correlation functions showed that the lifetime of translational and rotational motions are at the level of picoseconds and nanoseconds, respectively, because of the ion cage effect. The lifetime of ion association demonstrated that the recombination of association ions was prevalent in IL solutions. It means that the dipolar or stable contact ion-pairs model may not be suitable for depicting the IL transport.

Theoretical vibrational sum-frequency generation spectroscopy of water near lipid and surfactant monolayer interfaces. II. Two-dimensional spectra.

The structural stability and function of biomolecules is strongly influenced by the dynamics and hydrogen bonding of interfacial water. Understanding and characterizing the dynamics of these water molecules require a surface-sensitive technique such as two-dimensional vibrational sum-frequency generation (2DSFG) spectroscopy. We have combined theoretical 2DSFG calculations with molecular dynamics simulations in order to investigate the dynamics of water near different lipid and surfactant monolayer surfaces. We show that 2DSFG can distinguish the dynamics of interfacial water as a function of the lipid charge and headgroup chemistry. The dynamics of water is slow compared to the bulk near water-zwitterionic and water-anionic interfaces due to conformational constraints on interfacial water imposed by strong phosphate-water hydrogen bonding. The dynamics of water is somewhat faster near water-cationic lipid interfaces as no such constraint is present. Using hydrogen bonding and rotational correlation functions, we characterize the dynamics of water as a function of the distance from the interface between water and zwitterionic lipids. We find that there is a transition from bulk-like to interface-like dynamics approximately 7 Å away from a zwitterionic phosphatidylcholine monolayer surface.