Orientational Correlation Times Research Articles

MD Simulation and Analysis of the Pair Correlation Functions, Self-Diffusion Coefficients and Orientational Correlation Times in Aqueous KCl Solutions at Different Temperatures and Concentrations

MD Simulation and Analysis of the Pair Correlation Functions, Self-Diffusion Coefficients and Orientational Correlation Times in Aqueous KCl Solutions at Different Temperatures and Concentrations

Fractional Extended Diffusion Theory to capture anomalous relaxation from biased/accelerated molecular simulations.

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586-599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head-tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes.

How Far Is "Bulk Water" from Interfaces? Depends on the Nature of the Surface and What We Measure.

Using systematic molecular dynamics (MD) simulations, we revisit the question: At what distance from an interface do the properties of "bulk water" get recovered? We have considered three different kinds of interfaces: nonpolar (hydrophobic; isooctane-water interface), charged (negative; AOT bilayer), and polar (zwitterionic; POPC bilayer). In order to interrogate the extent of perturbation of the interfacial water molecules as a function of the distance from the interface, we utilize a diverse range of structural and dynamical parameters. To capture the structural perturbations, we look into local density (translational order), local tetrahedral order parameter, and dipolar orientation of the water molecules. We also explore the anisotropic diffusion of the water molecules in the direction perpendicular to the interface as well as the planar diffusion parallel to the interface in a distance dependent manner. In addition, the orientational time correlation functions have been computed to understand the extent of slowdown in the rotational dynamics. As expected, the electrostatic field emanating from the charged AOT interface seems to have the highest long-range effect on the orientational order and dynamics of the water molecules, whereas specific interactions like hydrogen bonding and electrostatic interaction lead to significant trapping and kinetic slowdown for both AOT and POPC (zwitterionic) very close to the interface. Our analysis highlights that not only the length-scale of perturbation depends on the nature of the interfaces and specific interactions but also the type of water property that we measure/calculate. Different water properties seem to have widely different length-scale of perturbation. Orientational order parameters seem to be perturbed to a much longer length-scale as compared to translational order parameters. The global orientational order of water can be perturbed even up to ∼4-5 nm near the negatively charged AOT surface in the absence of any extra electrolyte. This observation has significant implication toward the interpretation of experimental measurements as well since different spectroscopic techniques would probe different parameters or water properties with possible mutual disagreement and inconsistency between different types of measurements. Thus, our study provides a broader and unifying perspective toward the aspect of "context dependent" structural and dynamical perturbation of "interfacial water".

Structure and Dynamics of the Hydration Shell: Spatially Decomposed Time Correlation Approach.

Molecular simulations provide insight into solvation structures and dynamics with unparalleled spatial and temporal resolution. Here, we take advantage of this fact and develop a set of generally applicable computational tools for a detailed analysis of the hydration shell around an ionic or molecular solute. These tools allow us to quantify and visualize orientationally resolved radial distribution functions as well as distance-resolved orientational time-correlation functions of water molecules surrounding the solute. Such a detailed view of the hydration shells allows us to unravel important structural and dynamical features, which are not accessible when employing standard analysis techniques.

Dynamics of a binary mixture of non-spherical molecules: Test of hydrodynamic predictions.

We consider a new class of model systems to study systematically the role of molecular shape in the transport properties of dense liquids. Our model is a liquid binary mixture where both the molecules are non-spherical and characterized by a collection of parameters. Although in the real world most of the molecules are non-spherical, only a limited number of theoretical studies exist on the effects of molecular shapes and hardly any have addressed the validity of the hydrodynamic predictions of rotational and translational diffusion of these shapes in liquids. In this work, we study a model liquid consisting of a mixture of prolate and oblate (80:20 mixture) ellipsoids with interactions governed by a modified Gay-Berne potential for a particular aspect ratio (ratio of the length and diameter of the ellipsoids), at various temperature and pressure conditions. We report calculations of transport properties of this binary mixture by varying temperature over a wide range at a fixed pressure. We find that for the pressure-density conditions studied, there is no signature of any phase separation, except transitions to the crystalline phase at low temperatures and relatively low pressure (the reason we largely confined our studies to high pressure). We find that for our model binary mixture, both stick and slip hydrodynamic predictions break down in a major fashion, for both prolates and oblates and particularly so for rotation. Moreover, prolates and oblates themselves display different dynamical features in the mean square displacement and in orientational time correlation functions.

Reorientation of OH-group connecting bifurcated H-bond acceptors in liquid water

The OH-group connecting bifurcated H-bond (HB) acceptors is one case of the three-centered HBs found in physical and biological systems. An example is the transition state of molecular reorientation jump mechanism in liquid water, ionic solutions, and hydration shells of biomolecules. In this Letter, the orientational time correlation functions of these special OH-groups in water were studied by performing molecular dynamics simulations and using the normal-mode approach developed recently. The reorientation angle of the OH-group before entering the diffusive regime can be estimated through the plateau in the mean-square rotational displacement calculated by several methods.

Applicability of effective pair potentials for active Brownian particles.

We have performed a case study investigating a recently proposed scheme to obtain an effective pair potential for active Brownian particles (Farage et al., Phys. Rev. E 91, 042310 (2015)). Applying this scheme to the Lennard-Jones potential, numerical simulations of active Brownian particles are compared to simulations of passive Brownian particles interacting by the effective pair potential. Analyzing the static pair correlations, our results indicate a limited range of activity parameters (speed and orientational correlation time) for which we obtain quantitative, or even qualitative, agreement. Moreover, we find a qualitatively different behavior for the virial pressure even for small propulsion speeds. Combining these findings we conclude that beyond linear response active particles exhibit genuine non-equilibrium properties that cannot be captured by effective pair interaction alone.

The Anion Effect on Li(+) Ion Coordination Structure in Ethylene Carbonate Solutions.

Rechargeable lithium ion batteries are an attractive alternative power source for a wide variety of applications. To optimize their performances, a complete description of the solvation properties of the ion in the electrolyte is crucial. A comprehensive understanding at the nanoscale of the solvation structure of lithium ions in nonaqueous carbonate electrolytes is, however, still unclear. We have measured by femtosecond vibrational spectroscopy the orientational correlation time of the CO stretching mode of Li(+)-bound and Li(+)-unbound ethylene carbonate molecules, in LiBF4, LiPF6, and LiClO4 ethylene carbonate solutions with different concentrations. Surprisingly, we have found that the coordination number of ethylene carbonate in the first solvation shell of Li(+) is only two, in all solutions with concentrations higher than 0.5 M. Density functional theory calculations indicate that the presence of anions in the first coordination shell modifies the generally accepted tetrahedral structure of the complex, allowing only two EC molecules to coordinate to Li(+) directly. Our results demonstrate for the first time, to the best of our knowledge, the anion influence on the overall structure of the first solvation shell of the Li(+) ion. The formation of such a cation/solvent/anion complex provides a rational explanation for the ionic conductivity drop of lithium/carbonate electrolyte solutions at high concentrations.

Orientational dynamics in nematic liquid crystals

We examine the behaviour of single-particle orientational time correlation functions in nematic liquid crystals. As well as the expected dynamics involving oscillation in a mean-field potential, and occasional jumps between orientations parallel and antiparallel to the director, we provide the first simulation evidence of long-time tails characteristic of coupling to director fluctuations.

Orientational Time Correlation Functions for Vibrational Sum-Frequency Generation. 3. Methanol

Molecular dynamics simulations have been used to study the orientational dynamics of methanol at the liquid/vapor and liquid/silica interfaces. Orientational time-correlation functions for the symmetric and asymmetric methyl stretches of methanol have been calculated to assess the role of reorientation in the vibrational sum-frequency generation (VSFG) spectroscopy of these modes at the two interfaces. We find that internal methyl rotation plays a significant role in suppressing the intensity of the asymmetric methyl stretches at the liquid/vapor interface. The broad orientational distribution of the methyl groups and the properties of the Raman spectra of the asymmetric stretches are also major contributors to the low intensity of these modes in VSFG spectra at this interface. We find that after an initial rapid, inertial decay, there is little coupling among the orientational degrees of freedom of the methyl group, which suggests that time-dependent VSFG spectroscopy may be used to probe interfacial ori...

Local structural effects on orientational relaxation of OH-bond in liquid water over short to intermediate timescales.

By simulating the rigid simple point charge extended model at temperature T = 300 K, the orientational relaxation of the OH-bond in water was investigated over short to intermediate timescales, within which molecules undergo inertial rotation and libration and then enter the rotational diffusion regime. According to the second-cumulant approximation, the orientational time correlation function (TCF) of each axis that is parallel or perpendicular to an OH-bond is related to an effective rotational density of states (DOS), which is determined using the power spectra of angular velocity autocorrelation functions (AVAFs) of the other two axes. In addition, the AVAF power spectrum of an axis was approximated as the rotational stable instantaneous normal mode (INM) spectrum of the axis. As described in a previous study [S. L. Chang, T. M. Wu, and C. Y. Mou, J. Chem. Phys. 121, 3605 (2004)], simulated molecules were classified into subensembles, according to either the local structures or the H-bond configurations of the molecules. For global molecules and the classified subensembles, the simulation results for the first- and second-rank orientational TCFs were compared with the second-cumulant predictions obtained using the effective rotational DOSs and the rotational stable-INM spectra. On short timescales, the OH-bond in water behaves similar to an inertial rotor and its anisotropy is lower than that of a water molecule. For molecules with three or more H-bonds, the OH-bond orientational TCFs are characterized by a recurrence, which is an indication for libration of the OH-bond. The recurrence can generally be described by the second-cumulant prediction obtained using the rotational stable-INM spectra; however, the orientational TCFs after the recurrence switch to a behavior similar to that predicted using the AVAF power spectra. By contrast, the OH-bond orientational TCFs of molecules initially connected with one or two H-bonds decay monotonically or exhibit a weak recurrence, indicating rapid relaxation into the rotational diffusion regime after the initial Gaussian decay. In addition to accurately describing the Gaussian decay, the second-cumulant predictions formulated using the rotational stable-INM spectra and the AVAF power spectra serve as the upper and lower limits, respectively, for the OH-bond orientational TCFs of these molecules after the Gaussian decay.

Role of hydrophilicity and length of diblock arms for determining star polymer physical properties.

We present a molecular simulation study of star polymers consisting of 16 diblock copolymer arms bound to a small adamantane core by varying both arm length and the outer hydrophilic block when attached to the same hydrophobic block of poly-δ-valerolactone. Here we consider two biocompatible star polymers in which the hydrophilic block is composed of polyethylene glycol (PEG) or polymethyloxazoline (POXA) in addition to a polycarbonate-based polymer with a pendant hydrophilic group (PC1). We find that the different hydrophilic blocks of the star polymers show qualitatively different trends in their interactions with aqueous solvent, orientational time correlation functions, and orientational correlation between pairs of monomers of their polymeric arms in solution, in which we find that the PEG polymers are more thermosensitive compared with the POXA and PC1 star polymers over the physiological temperature range we have investigated.

Mixed classical quantum dynamical simulation of mid-infrared Q branch of HCl diluted in Ar

We have developed a mixed classical quantum dynamical simulation technique which has been applied to the study of fundamental bands of HCl diluted in dense Ar at different thermodynamic conditions. This technique is an improvement of the stochastic simulation method developed in a previous work, in which the stochastic treatment of the diatomic neighborhood has been replaced by a molecular dynamics description. Like the previous stochastic method, the technique introduced in this work explains the presence in the spectral bands of a triplet P–Q–R branch structure, similar to that observed in the experimental vibro-rotational profiles. We have studied the quantum effects on the diatomic line shapes, the spectral repercussion of the P2 symmetry terms of the solute–solvent anisotropic potential, and the spectral modifications due to the alternative description of a diatomic environment with a stochastic or a dynamical model. Also, we have determined the orientational correlation times and the statistical parameters associated to the anisotropic interaction.

Orientational time correlation functions for vibrational sum-frequency generation. 2. Propionitrile.

Molecular dynamics (MD) simulations of propionitrile have been performed to assess the influence of reorientation on vibrational sum-frequency-generation (VSFG) spectra at the liquid/vapor (LV) and liquid/silica (LS) interfaces. Orientational time-correlation functions (TCFs) are derived for the VSFG spectroscopy of the symmetric and asymmetric stretches of functional groups such as methylene groups and rotationally hindered methyl groups. The MD simulations are used to compute VSFG orientational TCFs for the methyl, methylene, and cyanide groups of propionitrile at the LV and LS interfaces. Although propionitrile exhibits relatively fast reorientation in the bulk liquid, we find that for symmetric stretching modes at these interfaces, reorientation only plays a significant role in VSFG spectra under SPS polarization conditions. For asymmetric stretches, reorientation affects the VSFG spectra significantly under all polarization conditions. Azimuthal dynamics tend to dominate the orientational TCFs.

Simulations of solid-liquid friction at ice-Ih/water interfaces

We have investigated the structural and dynamic properties of the basal and prismatic facets of the ice Ih/water interface when the solid phase is drawn through the liquid (i.e., sheared relative to the fluid phase). To impose the shear, we utilized a velocity-shearing and scaling approach to reverse non-equilibrium molecular dynamics. This method can create simultaneous temperature and velocity gradients and allow the measurement of transport properties at interfaces. The interfacial width was found to be independent of the relative velocity of the ice and liquid layers over a wide range of shear rates. Decays of molecular orientational time correlation functions gave similar estimates for the width of the interfaces, although the short- and longer-time decay components behave differently closer to the interface. Although both facets of ice are in "stick" boundary conditions in liquid water, the solid-liquid friction coefficients were found to be significantly different for the basal and prismatic facets of ice.

Langevin dynamics simulation of DNA ejection from a phage

We have performed Langevin dynamics simulations of a coarse-grained model of ejection of dsDNA from Φ29 phage. Our simulation results show significant variations in the local ejection speed, consistent with experimental observations reported in the literature for both in vivo and in vitro systems. In efforts to understand the origin of such variations in the local speed of ejection, we have investigated the correlations between the local ejection kinetics and the packaged structures created at various motor forces and chain flexibility. At lower motor forces, the packaged DNA length is shorter with better organization. On the other hand, at higher motor forces typical of realistic situations, the DNA organization inside the capsid suffers from significant orientational disorder, but yet with long orientational correlation times. This in turn leads to lack of registry between the direction of the DNA segments just to be ejected and the direction of exit. As a result, a significant amount of momentum transfer is required locally for successful exit. Consequently, the DNA ejection temporarily slows down exhibiting pauses. This slowing down occurs at random times during the ejection process, completely determined by the particular starting conformation created by prescribed motor forces. In order to augment our inference, we have additionally investigated the ejection of chains with deliberately changed persistence length. For less inflexible chains, the demand on the occurrence of large momentum transfer for successful ejection is weaker, resulting in more uniform ejection kinetics. While being consistent with experimental observations, our results show the nonergodic nature of the ejection kinetics and call for better theoretical models to portray the kinetics of genome ejection from phages.

Are rare, long waiting times between rearrangement events responsible for the slowdown of the dynamics at the glass transition?

The dramatic slowdown of the structural relaxation at the glass transition is one of the most puzzling features of glass dynamics. Single molecule orientational correlation times show this strong Vogel-Fulcher-Tammann temperature dependence typical for glasses. Through statistical analysis of single molecule trajectories, we can identify individual glass rearrangement events in the vicinity of a probe molecule in the glass former poly(vinyl acetate) from 8 K below to 6 K above the glass transition temperature. We find that changes in the distribution of waiting times between individual glass rearrangement events are much less dramatic with temperature, the main difference being a small, but decisive number of increasingly long waiting times at lower temperatures. We notice similar individual, local relaxation events in molecular dynamics trajectories for a variety of glassy systems further from the glass transition, leading to waiting time distributions with similar features as those observed in the single molecule experiments. We show that these rare long waiting times are responsible for the dramatic increase in correlation time upon cooling.

Orientational Time Correlation Functions for Vibrational Sum-Frequency Generation. 1. Acetonitrile

Orientational time correlation functions (TCFs) are derived for vibrational sum-frequency generation (VSFG) spectroscopy of the symmetric and asymmetric stretches of high-symmetry oscillators such as freely rotating methyl groups, acetylenic C-H groups, and cyanide groups. Molecular dynamics simulations are used to calculate these TCFs and the corresponding elements of the second-order response for acetonitrile at the liquid/vapor and liquid/silica interfaces. We find that the influence of reorientation depends significantly on both the functional group in question and the polarization conditions used. Additionally, under some circumstances, reorientation can cause the VSFG response function to grow with time, partially counteracting the effects of other dephasing mechanisms.

Liquid-to-glass transition of tetrahydrofuran and 2-methyltetrahydrofuran

Both tetrahydrofuran (THF) and 2-methyltetrahydrofuran (MTHF) are studied systematically at desired temperatures using molecular dynamics simulations. The results show that the calculated densities are well consistent with experiment. Their glass transition temperatures are obtained: 115 K ∼ 130 K for THF and 131 K ∼ 142 K for MTHF. The calculated results from the dipolar orientational time correlation functions indicate that the “long time" behavior is often associated with a glass transition. From the radial and spatial distributions, we also find that the methyl has a direct impact on the structural symmetry of molecules, which leads to the differences of physical properties between THF and MTHF.

Comparison of Various Correlation Times in Polymer Melts by Molecular Dynamics Simulation

This investigation presents data from prolonged molecular dynamics simulations of dense monodisperse polymer melts of linear polymer chains of length between N = 3 and N = 255. Hear N is number of chain coarse-grained segments. The study aim is to observe the crossover from Rouse-like dynamics for short chains to reptation-like dynamics for long chains and its influence on various translational and orientational correlation times. To address the problem, we calculate a variety of different quantities: standard mean-square displacement of inner monomer and of the chain mass centre, autocorrelation function of chain end-to-end vector, orientational autocorrelation functions of segment and chain end-to-end vector. The last two functions define NMR relaxation in polymer melts. The chain length dependences of all large-scale correlation times reveals clear crossover from non-entangled to entangled dynamics near NC ≈ 35. Additional primitive path analysis of the same data gives statistically consistent entanglement value NE ≈ 14, i.e., the longest chain investigated is well entangled and displays explicit motional anisotropy. The full data assembly explains qualitatively strong dependence of NMR transverse relaxation time for Rouse-like regime and weak one in reptation regime.