On the Rotational Diffusion of Molecules

Rotationally-Resolved Two-Dimensional Infrared Spectroscopy of CO2(g): Rotational Wavepackets and Angular Momentum Transfer

Angular momentum transfer and wavepacket dynamics of CO₂(g) were measured on the picosecond time scale using polarization-resolved two-dimensional infrared (2D-IR) spectroscopy. The dynamics of rotational levels up to J_max ≈ 50 are observed simultaneously at room temperature. Rotational wavepackets launched by the pump pulses cause oscillations in the intensity of individual peaks and beating patterns in the 2D-IR spectra. The structure of the rotationally resolved 2D-IR spectrum is explained using nonlinear response function theory. Spectral diffusion of the rotationally resolved 2D-IR peaks reveals information about angular momentum transfer. We demonstrate the ability to directly measure inelastic angular momentum dynamics simultaneously across the ∼50 thermally excited rotational levels over several hundred picoseconds.

Diffusion of confined fluids in microporous zeolites and clay materials

Fluids exhibit remarkable variation in their structural and dynamic properties when they are confined at the nanoscopic scale. Various factors, including geometric restriction, the size and shape of the guest molecules, the topology of the host, and guest-host interactions, are responsible for the alterations in these properties. Due to their porous structures, aluminosilicates provide a suitable host system for studying the diffusion of sorbates in confinement. Zeolites and clays are two classes of the aluminosilicate family, comprising very ordered porous or layered structures. Zeolitic materials are important due to their high catalytic activity and molecular sieving properties. Guest molecules adsorbed by zeolites display many interesting features including unidimensional diffusion, non-isotropic rotation, preferred orientation and levitation effects, depending on the guest and host characteristics. These are useful for the separation of hydrocarbons which commonly exist as mixtures in nature. Similarly, clay materials have found application in catalysis, desalination, enhanced oil recovery, and isolation barriers used in radioactive waste disposal. It has been shown that the bonding interactions, level of hydration, interlayer spacing, and number of charge-balancing cations are the important factors that determine the nature of diffusion of water molecules in clays. Here, we present a review of the current status of the diffusion mechanisms of various adsorbed species in different microporous zeolites and clays, as investigated using quasielastic neutron scattering and classical molecular dynamics simulation techniques. It is impossible to write an exhaustive review of the subject matter, as it has been explored over several decades and involves many research topics. However, an effort is made to cover the relevant issues specific to the dynamics of different molecules in microporous zeolites and clay materials and to highlight a variety of interesting features that are important for both practical applications and fundamental aspects.

Effects of Hydrogen Bonding on the Rotational Dynamics of Water-Like Molecules in Liquids: Insights from Molecular Dynamics Simulations

Rotational motion of molecules plays an important role in determining NMR spin relaxation properties of liquids. The textbook theory of NMR spin relaxation predominantly uses the assumption that the reorientational dynamics of molecules is described by a continuous time rotational diffusion random walk with a single rotational diffusion coefficient. Previously we and others have shown that reorientation of water molecules on the timescales of picoseconds is not consistent with the Debye rotational-diffusion model. In particular, multiple timescales of molecular reorientation were observed in liquid water. This was attributed to the hydrogen bonding network in water and the consequent presence of collective rearrangements of the molecular network. In order to better understand the origins of the complex reorientational behaviour of water molecules, we carried out molecular dynamics (MD) simulations of a liquid that has a similar molecular geometry to water but does not form hydrogen bonds: hydrogen sulfide. These simulations were carried out at T=208K and p=1 atm (~5K below the boiling point). Ensemble-averaged Legendre polynomial functions of hydrogen sulfide exhibited a Gaussian decay on the sub-picosecond timescale but, unlike water, did not exhibit oscillatory behaviour. We attribute these differences to hydrogen sulfide’s absence of hydrogen bonding.

Orientational relaxation of a quantum linear rotor in a dissipative environment: Simulations with the hierarchical equations-of-motion method

We study the effect of a dissipative environment on the orientational relaxation of a three-dimensional quantum linear rotor. We provide a derivation of the Hamiltonian of a linear rotor coupled to a harmonic bath from first principles, confirming earlier conjectures. The dynamics generated by this Hamiltonian is investigated by the hierarchical equations-of-motion method assuming a Drude spectral density of the bath. We perform numerically accurate simulations and analyze the behavior of orientational correlation functions and the rotational structures of infrared absorption and Raman scattering spectra. We explore the features of orientational correlation functions and their spectra for a wide range of system-bath couplings, bath memory times, and temperatures. We discuss the signatures of the orientational relaxation in the underdamped regime, the strongly damped regime, and the librational regime. We show that the behavior of orientational correlation functions and their spectra can conveniently be analyzed in terms of three characteristic times, which are explicitly expressed in terms of the parameters of the Hamiltonian.

Translational and rotational diffusion of rod shaped molecules by molecular dynamics simulations

The results of molecular dynamics simulations of the dynamical evolution of assemblies of linear rigid rods of variable aspect ratio, a, and number density, ρ, in the isotropic phase are reported. The rods consist of m equally spaced sites interacting with the Weeks-Chandler-Andersen repulsive pair potential, where 2 < m < 16. With increasing m, features specific to long rods, such as anisotropic self-diffusion, become apparent. There is also an increasing separation between the characteristic relaxation times of the torque, angular velocity, and reorientational time correlation functions with increasing density. The latter is exponential at high densities even for dimers. The isotropic translational diffusion coefficient, D_i, and rotational diffusion coefficient, D_r, are reported as a function of m and ρ or volume fraction, ξ. The mD_i data scale with ξ throughout much of the simulated range, while the rotational diffusion coefficients scale approximately as m³D_r against ρ at low densities but as ∼m⁶D_r at high ρ, consistent with theories of colloidal and noncolloidal rod-containing liquids. The crossover density between the two regimes is parameterized in analytic form. The probability distribution functions for displacements and angular jumps in a given time show evidence of non-Gaussian behavior with increasing density. The shear viscosity and D_i scale approximately as m and m^-1, respectively, in the semidilute regime, which is consistent with a Stokes-Einstein-like relationship. At high concentrations, a frustrated or glassy structure formed in which the rods were randomly oriented.

Molecular Dynamics Simulations of Membrane Permeability

This Review illustrates the evaluation of permeability of lipid membranes from molecular dynamics (MD) simulation primarily using water and oxygen as examples. Membrane entrance, translocation, and exit of these simple permeants (one hydrophilic and one hydrophobic) can be simulated by conventional MD, and permeabilities can be evaluated directly by Fick's First Law, transition rates, and a global Bayesian analysis of the inhomogeneous solubility-diffusion model. The assorted results, many of which are applicable to simulations of nonbiological membranes, highlight the limitations of the homogeneous solubility diffusion model; support the utility of inhomogeneous solubility diffusion and compartmental models; underscore the need for comparison with experiment for both simple solvent systems (such as water/hexadecane) and well-characterized membranes; and demonstrate the need for microsecond simulations for even simple permeants like water and oxygen. Undulations, subdiffusion, fractional viscosity dependence, periodic boundary conditions, and recent developments in the field are also discussed. Last, while enhanced sampling methods and increasingly sophisticated treatments of diffusion add substantially to the repertoire of simulation-based approaches, they do not address directly the critical need for force fields with polarizability and multipoles, and constant pH methods.

Influence of aluminates on the structure and dynamics of water and ions in the nanometer channel of calcium silicate hydrate (C–S–H) gel

Al species incorporated in silicate chains enhance hydrophilicity and cation immobilization ability of the C–S–H gel.

Three-dimensional telegrapher's equation and its fractional generalization

We derive the three-dimensional telegrapher's equation out of a random walk model. The model is a three-dimensional version of the multistate random walk where the number of different states form a continuum representing the spatial directions that the walker can take. We set the general equations and solve them for isotropic and uniform walks which finally allows us to obtain the telegrapher's equation in three dimensions. We generalize the isotropic model and the telegrapher's equation to include fractional anomalous transport in three dimensions.

A new potential for methylammonium lead iodide

A new force field for MALI designed to model the material and the reactants predicts experimental properties and demonstrates the short and long range ordering present in the material.

Multipolar force fields and their effects on solvent dynamics around simple solutes

The performance of multipole (MTP) and point charge (PC) force fields in classical molecular dynamics (MD) simulations of condensed-phase systems for both equilibrium and dynamical quantities is compared. MTP electrostatics provides an improved description of the anisotropic electrostatic potential, which is especially important to describe key, challenging interactions, such as lone pairs, π-interactions, and hydrogen bonds. These chemical environments are probed by focusing on the hydration properties of two molecules: N-methylacetamide and phenyl bromide. Both, equilibrium and dynamical, quantities are affected by the quality of the electrostatic model. The alteration of the first solvation shell in MTP simulations is validated by comparing with lifetimes and correlation times of solute-solvent interactions from experiment. The improved dynamical behavior found in the MTP simulations—observed for molecules parametrized using very different protocols—suggests that a systematic improvement of both equilibrium and dynamical quantities when using MTP electrostatics is possible.

2D IR spectra of cyanide in water investigated by molecular dynamics simulations

Using classical molecular dynamics simulations, the 2D infrared (IR) spectroscopy of CN(-) solvated in D2O is investigated. Depending on the force field parametrizations, most of which are based on multipolar interactions for the CN(-) molecule, the frequency-frequency correlation function and observables computed from it differ. Most notably, models based on multipoles for CN(-) and TIP3P for water yield quantitatively correct results when compared with experiments. Furthermore, the recent finding that T1 times are sensitive to the van der Waals ranges on the CN(-) is confirmed in the present study. For the linear IR spectrum, the best model reproduces the full widths at half maximum almost quantitatively (13.0 cm(-1) vs. 14.9 cm(-1)) if the rotational contribution to the linewidth is included. Without the rotational contribution, the lines are too narrow by about a factor of two, which agrees with Raman and IR experiments. The computed and experimental tilt angles (or nodal slopes) α as a function of the 2D IR waiting time compare favorably with the measured ones and the frequency fluctuation correlation function is invariably found to contain three time scales: a sub-ps, 1 ps, and one on the 10-ps time scale. These time scales are discussed in terms of the structural dynamics of the surrounding solvent and it is found that the longest time scale (≈10 ps) most likely corresponds to solvent exchange between the first and second solvation shell, in agreement with interpretations from nuclear magnetic resonance measurements.

Rotational dynamics of a dipolar supercooled liquid

We study the rotational dynamics of a supercooled molecular liquid by means of molecular dynamics simulations. The system under investigation is composed of rigid diatomic molecules with an associate dipole moment. At room temperature, orientational correlations decrease rapidly with increasing distances. Upon cooling, angles between dipole moments of molecules within the first coordination shell decrease. As for the dynamical properties, rotational diffusion coefficients decrease with temperature at a smaller rate than translational diffusion coefficients do, and the critical temperature associated with the former is lower than the one corresponding to their translational counterparts. Translation and rotation about an inertial axis are uncorrelated, whereas some coupling between translation and dipole reorientation is obtained.

Diagonalization-free implementation of spin relaxation theory for large spin systems

The Liouville space spin relaxation theory equations are reformulated in such a way as to avoid the computationally expensive Hamiltonian diagonalization step, replacing it by numerical evaluation of the integrals in the generalized cumulant expansion. The resulting algorithm is particularly useful in the cases where the static part of the Hamiltonian is dominated by interactions other than Zeeman (e.g. in quadrupolar resonance, low-field EPR and Spin Chemistry). When used together with state space restriction tools, the algorithm reported is capable of computing full relaxation superoperators for NMR systems with more than 15 spins.

Comparative NMR properties of H2 and HD in toluene-d8 and in H2/HD@C60

Spin-lattice relaxation times, T(1), have been measured from 200-340 K for the protons in H(2) and HD molecules dissolved in toluene-d(8) and incarcerated in C(60). It is found that HD relaxes more slowly than H(2) in both environments and at all temperatures, as expected from the smaller values of the spin-rotation and dipole-dipole coupling in HD compared to H(2). More detailed analysis using models developed to describe relaxation in both condensed media and the gas phase indicates that transitions among the rotational states of H(2) occur at a rate similar to those of HD in both toluene-d(8) solution and in C(60), in contrast to the situation in gas phase collisions between hydrogen and He or Ar, where the lifetimes of rotational states of HD are markedly shorter than those for H(2). Measurements of the relative (1)H chemical shifts of H(2) and HD, the coupling constant J(HD), and the widths of the HD peaks at various temperatures revealed only small effects with insufficient accuracy to warrant more detailed interpretation.

Water/hydrocarbon interfaces: effect of hydrocarbon branching on single-molecule relaxation

Water/hydrocarbon interfaces are studied using molecular dynamics simulations in order to understand the effect of hydrocarbon branching on the dynamics of the system at and away from the interface. A recently proposed procedure for studying the intrinsic structure of the interface in such systems is utilized, and dynamics are probed in the usual laboratory frame as well as the intrinsic frame. The use of these two frames of reference leads to insight into the effect of capillary waves at the interface on dynamics. The systems were partitioned into zones with a width of 5 A, and a number of quantities of dynamical relevance, namely, the residence times, mean squared displacements, the velocity auto correlation functions, and orientational time correlations for molecules of both phases, were calculated in the laboratory and intrinsic frames at and away from the interface. For the aqueous phase, translational motion is found to be (a) diffusive at long times and not anomalous as in proteins or micelles, (b) faster at the interface than in the bulk, and (c) faster upon reduction of the effect of capillary waves. The rotational motion of water is (a) more anisotropic at the interface than in the bulk and (b) dependent on the orientation of the covalent O-H bond with respect to the plane of the interface. The effect of hydrocarbon branching on aqueous dynamics was found to be small, a result similar to the effect on the interfacial water structure. The hydrocarbon phase shows a larger variation for all dynamical probes, a trend consistent with their interfacial structure.

Angular momentum dependent friction slows down rotational relaxation under nonequilibrium conditions

It has recently been shown that relaxation of the rotational energy of hot nonequilibrium photofragments (i) slows down significantly with the increase of their initial rotational temperature and (ii) differs dramatically from the relaxation of the equilibrium rotational energy correlation function, manifesting thereby the breakdown of the linear response description [A. C. Moskun et al., Science 311, 1907 (2006)]. We demonstrate that this phenomenon may be caused by the angular momentum dependence of rotational friction. We have developed the generalized Fokker-Planck equation whose rotational friction depends upon angular momentum algebraically. The calculated rotational correlation functions correspond well to their counterparts obtained via molecular dynamics simulations in a broad range of initial nonequilibrium conditions. It is suggested that the angular momentum dependence of friction should be taken into account while describing rotational relaxation far from equilibrium.

Water Dynamics in Nafion Fuel Cell Membranes: the Effects of Confinement and Structural Changes on the Hydrogen Bond Network

The complex environments experienced by water molecules in the hydrophilic channels of Nafion membranes are studied by ultrafast infrared pump-probe spectroscopy. A wavelength dependent study of the vibrational lifetime of the O-D stretch of dilute HOD in H(2)O confined in Nafion membranes provides evidence of two distinct ensembles of water molecules. While only two ensembles are present at each level of membrane hydration studied, the characteristics of the two ensembles change as the water content of the membrane changes. Time dependent anisotropy measurements show that the orientational motions of water molecules in Nafion membranes are significantly slower than in bulk water and that lower hydration levels result in slower orientational relaxation. Initial wavelength dependent results for the anisotropy show no clear variation in the time scale for orientational motion across a broad range of frequencies. The anisotropy decay is analyzed using a model based on restricted orientational diffusion within a hydrogen bond configuration followed by total reorientation through jump diffusion.