Generalized Langevin theory on the dynamics of simple fluids under external fields

A theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solute-solvent-solvent three-body correlation function is taken into account through the hypernetted-chain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of molecular-dynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the short-time part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the short-time expansion of the theoretical solvation correlation function is exact up to t(2) with the exact three-body correlation function. A quantitative improvement is found in the long-time region, too. Our theory is also applied to the force-force time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the mode-coupling theory on the solute diffusion.     

Liquid crystal optical response dynamics of the flexoelectric effect in a spatially inhomogeneous electric field

An investigation of the flexoelectric effect in a spatially inhomogeneous field revealed the two specific features of the liquid crystal optical response. First the optical response occurs at frequencies up to 500 Hz testifying to possible response time for flexoelectric effect-devices from 2 to 5 ms. Secondly in a photosensitive structure a flexoelectric effect application allows the implementation of an optical analogue of synchronous detection as well as the subtraction of images.     

The dynamics of high Rydberg states in the presence of time-dependent inhomogeneous fields

This paper presents calculations of the evolution of an optically prepared Rydberg wavepacket in the presence of time-dependent inhomogeneous electric fields and the results have relevance to the stabilization of Rydberg states as appropriate to ZEKE spectroscopy. The field is considered to arise from the combination of an applied field, which may be ramped in time, and the presence of microscopic charges, e.g., a pseudo-random distribution of ions, whose positions may also change with time. The results of the calculations lead to a clearer definition of the conditions under which Rydberg stabilization is achieved, such as in field switching experiments (Baranov et al., Chem. Phys. Lett., 1998, 291, 311), and also confirm the mechanisms by which the randomization of population between blue-shifted and red-shifted Stark states occurs in the presence of micro-fields due to ions (Palm et al., Philos. Trans. R. Soc. London, Ser. A, 1997, 355, 1551). The motion of the ions is found to have a significant m-locking effect in the calculations, providing a possible mechanism for the commonly observed long-lifetime tail in the population decay of high-n Rydberg states.     

Structure formation and dynamics of water in strong external electric fields

We have performed molecular dynamics computer simulations of water in homogeneous external electric fields which were varied in a wide range of field strengths. The dielectric response is found to be linear up to fields E₀≈0.01 V/Å from where dielectric saturation effects become important. At fields of E₀≈3 V/Å a phase transition into an ordered, ice-like structure is observed, which is stabilized through hydrogen-bonds. With an increasing external electric field, the frequency spectrum of the water dynamics shows a remarkable red shift of the intramolecular modes and a blue shift of the librational motions, where the frequency varies quadratically with the field strength. A simple analytical model is discussed which reproduces the observed behavior.     

Surface anchoring and the saturation behaviour of a NLC cell under external electric and magnetic fields

Based on the modified Rapini-Papoular formula for surface anchoring energy, the saturation behaviour of a weak anchoring nematic liquid crystal cell under electric and magnetic fields has been studied by the methods of analytical derivation and numerical calculation. The results show that the transition at saturation point may be second order, as many authors have predicted. However, it may also be first order. The condition for the first order transition is deduced; it is related to the anchoring parameters. The influence of anchoring on the saturation field strength is also discussed, both for second and for first orders; the results are shown by graphically.     

Analytical solution for restricted diffusion in circular and spherical layers under inhomogeneous magnetic fields

We propose an analytical solution for restricted diffusion of spin-bearing particles in circular and spherical layers in inhomogeneous magnetic fields. More precisely, we derive exact and explicit formulas for the matrix representing an applied magnetic field in the Laplacian eigenbasis and governing the magnetization evolution. For thin layers, a significant difference between two geometrical length scales (thickness and overall size) allows for accurate perturbative calculations. In these two-scale geometries, apparent diffusion coefficient (ADC) as a function of diffusion time exhibits a new region with a reduced but constant value. The emergence of this intermediate diffusion regime, which is analogous to the tortuosity regime in porous media, is explained in terms of the underlying Laplace operator eigenvalues. In general, regions with constant ADCs would be reminiscent of multiscale geometries, and their observation can potentially be used in experiments to detect the length scales by varying diffusion time.     

Polymer dynamics and topology: Extension of stars and dendrimers in external fields

We study the influence of topology on the extension of branched polymers subjected to external forces. Such forces can be applied mechanically (by micromanipulation techniques such as laser tweezers) or electrically (in the case of charged polymers). We focus on the unfold dynamics of star and dendrimer type structures. Some of the dynamical quantities of interest are: (i) the structural average of the mean monomer displacement, (ii) the elastic and the loss moduli and (iii) the mean displacement of a specified monomer. In a Gaussian‐type approach, (i) and (ii) depend only on the eigenvalues of the adjacency matrix whereas (iii) also requires the knowledge of the eigenvectors. Thus one can sometimes dispense with a full diagonalisation and use efficient recursion procedures. We highlight how the dynamic properties depend on topology: the number of branches and their length for stars and the number of generations for dendrimers. The intermediate time (crossover) behavior turns out to be most revealing of the underlying structure. We compare our results to those for fractal structures in external fields.     

DMC: A multifunctional hybrid dynamics/Monte Carlo simulation algorithm for the evaluation of conformational space

A hybrid conformational search algorithm (DMC) is described that combines a modified form of molecular dynamics with Metropolis Monte Carlo sampling, using the COSMIC(90) force field. Trial configurations are generated by short bursts of high-temperature dynamics in which the initial kinetic energy is focused into single bond rotations or alternatively into “corner-flapping” motions in ring systems. Constant temperature and simulated annealing search protocols have been applied to the conformational analysis of several model hydrocarbons (cyclopentane, cyclohexane, cycloheptane, cyclooctane, cycloheptadecane, decane, and tetradecane), and the performance compared with conventional molecular dynamics and Monte Carlo sampling methods. Optimum Metropolis sampling temperatures have been determined and range from 1000–2000 K for acyclic molecules to 3000 K for cyclic systems. Simulated annealing runs are most successful at locating the global minimum when cooling slowing from these optimum temperatures.     

Comparative study of insulin chain-B in isolated and monomeric environments under external stress

We have conducted a series of theoretical simulations of insulin chain-B under different electric field conditions. This work extends our previous studies of the isolated chain-B by including chain-A and revealing the effects of chemical stress. For this complete protein, we observed increased stability under ambient conditions and under the application of thermal stress, compared to isolated chain-B. On the other hand, the presence of chain-A enhanced the effects of the applied electric field. Under the static field, the presence of chain-A lowered the strength of the field necessary to stretch the protein. Under the oscillating fields, there was relatively less stretching due to the competitive alignment process of the three helical regions with respect to the field. At high field strengths, we observed that the high frequency oscillating field caused less secondary structure disruption than a lower frequency field of the same strength.     

A string model for the chemical reaction coordinate in static external fields

A theoretical method for estimating the effects of a static external field upon a reaction path is proposed. The reaction path is defined as the intrinsic reaction coordinate (IRC) which is treated as a string. The string is deformed by the external static force field. We project the external force onto the normal modes orthogonal and parallel to the string. The string is dragged along each direction of the normal mode. The cell structure [10b] attached to the string is also deformed; the transition state (TS) is shifted, and the internal structure of the reaction system is expanded or compressed in configuration space. A min-max relationship of the external effect on the string is found: the smaller the magnitude of the force constant of the normal mode orthogonal to the string, the larger the deformation of the string in the direction of the normal mode. As an example, the effects of one water molecule for hydrogen-migrating isomerization of formaldehyde and fluoroformaldehyde are considered.     

Multistage ab initio quantum wavepacket dynamics for electronic structure and dynamics in open systems: momentum representation, coupled electron-nuclear dynamics, and external fields

We recently proposed a multistage ab initio wavepacket dynamics (MS-AIWD) treatment for the study of delocalized electronic systems as well as electron transport through donor-bridge-acceptor systems such as those found in molecular-wire/electrode networks. In this method, the full donor-bridge-acceptor open system is treated through a rigorous partitioning scheme that utilizes judiciously placed offsetting absorbing and emitting boundary conditions. In this manner, the electronic coupling between the bridge molecule and surrounding electrodes is accounted. Here, we extend MS-AIWD to include the dynamics of open-electronic systems in conjunction with (a) simultaneous treatment of nuclear dynamics and (b) external electromagnetic fields. This generalization is benchmarked through an analysis of wavepackets propagated on a potential modeled on an Al(27) - C(7) - Al(27) nanowire. The wavepacket results are inspected in the momentum representation and the dependence of momentum of the wavepacket as well as its transmission probabilities on the magnitude of external bias are analyzed.     

Recent applications and developments of charge equilibration force fields for modeling dynamical charges in classical molecular dynamics simulations

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, in our hands those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for small molecules, proteins, lipids, and lipid bilayers and recently have begun work on carbohydrate force fields. The latter area has been relatively untouched by force field developers with particular focus on polarizable, non-additive interaction potential models. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration method for phase-dependent polarizable force fields, lipid molecules, and small-molecule carbohydrates. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields.     

Conformational analysis of diphenylacetylene under the influence of an external electric field

Theoretical investigation of the torsional potentials of a molecular wire, diphenylacetylene, was carried out at the B3LYP/6-311+G** level by considering the influence of the external electric field (EF). It demonstrates that many molecular features are sensitive to the EF applied. In particular, the torsional barrier increases and the LUMO-HOMO gap decreases with the increase of EF. Quantitative correlations between these features and the external EF were revealed. The current-voltage behavior corresponding to different conformers was studied as well by non-equilibrium Green's function method combined with the density functional theory. Further, the evolution of the LUMO-HOMO gap and the spatial distribution of molecular orbital were used to analyze these structure-property relationships.     

Cubic phases of block copolymers under shear and electric fields by cell dynamics simulation. I. Spherical phase

Cell dynamics simulation is used to investigate pathways of sphere-to-cylinder transition in block copolymer melt under applied simple shear flow and electric field. Both fields can induce the transition when their strength is above some critical value. At weak fields the spherical phase is preserved, with spheres being deformed into ellipsoids. Weak shear flow is found to improve order in the spherical phase. Observed sliding of layers of spheres under shear is very similar to the experimental finding by Hamley et al. [J. Chem. Phys. 108, 6929 (1998)]. The kinetic pathways are sensitive to the degree of microphase separation in the system and hence affected by temperature. The details of the pathways are described by means of Minkowski functionals.     

Spatial encoding and the acquisition of high-resolution NMR spectra in inhomogeneous magnetic fields

A scheme enabling the acquisition of high-resolution nuclear magnetic resonance (NMR) spectra within inhomogeneous magnetic fields is introduced and exemplified. The scheme is based on the spatial encoding protocol recently introduced for collecting multidimensional NMR data within a single scan, which retrieves spectral information via interference phenomena between spin packets located at distinct positions within the sample. This in turn enables compensating for field inhomogeneities over the sample as a whole by shifting the phases of the radio-frequency pulses involved in the spatial encoding, rather than by demanding an extreme uniformity in the employed magnetic field. The upper tolerable field inhomogeneity limit thus becomes orders of magnitude higher than that in conventional time-domain acquisitions. No particular spatial dependencies are demanded by the new scheme, which can yield its high-resolution results on a single-scan basis.     

Deflection and deceleration of hydrogen Rydberg molecules in inhomogeneous electric fields

Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17-18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 micros after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.     

A hybrid genetic algorithm for estimating the equilibrium potential of an ion-selective electrode

Non-linear equations can be used to model the measured potential of ion-selective electrodes (ISEs) as a function of time. This can be done by using non-linear least squares regression to fit parameters of non-linear equations to an ISE response curve. In iterative non-linear least squares regression (which can be considered as local optimisers), the determination of starting parameter estimates that yield convergence to the global optimum can be difficult. Starting values away from the global optimum can lead to either abortive divergence or convergence to a local optimum. To address this issue, a global optimisation technique was used to find initial parameter estimates near the global optimum for subsequent further refinement to the absolute optimum. A genetic algorithm has been applied to two non-linear equations relating the measured potential from selected ISEs to time. The parameter estimates found from the genetic algorithm were used as starting values for non-linear least squares regression, and subsequent refinement to the absolute optimum. This approach was successfully used for both expressions with measured data from three different ISEs; namely, calcium, chloride and lead ISEs.     

Molecular and supramolecular dynamics of hybrid organic-inorganic interfaces for the rational construction of advanced hybrid nanomaterials

Today the capability to rationally design and construct hybrid materials utilizing a performance-property driven methodology is strongly dependent on our ability to control the structure and the dynamics of hybrid interfaces. This control needs a deep knowledge of their molecular and supramolecular dynamics that must be evaluated in situ, in the soft matter or colloidal states. For this purpose the use of modern methodologies of characterization such as time resolved synchrotron experiments and advanced pulsed field gradient NMR methods (DOSY) is particularly relevant. In this critical review, two important examples are discussed. They concern, first, the study of surface capping organic components' affinity towards nanoparticle surfaces by DOSY NMR. The knowledge and therefore the tuning of this affinity is paramount because it controls solubility, transferability and stability of colloidal dispersions of nanoparticles (NPs). In the second part, the mechanism of micellar templated formation of hybrid mesophases will be discussed in the frame of the main results obtained via in situ SAXS (107 references).     

A generalized Born formalism for heterogeneous dielectric environments: application to the implicit modeling of biological membranes

Reliable computer simulations of complex biological environments such as integral membrane proteins with explicit water and lipid molecules remain a challenging task. We propose a modification of the standard generalized Born theory of homogeneous solvent for modeling the heterogeneous dielectric environments such as lipid/water interfaces. Our model allows the representation of biological membranes in the form of multiple layered dielectric regions with dielectric constants that are different from the solute cavity. The proposed new formalism is shown to predict the electrostatic component of solvation free energy with a relative error of 0.17% compared to exact finite-difference solutions of the Poisson equation for a transmembrane helix test system. Molecular dynamics simulations of melittin and bacteriorhodopsin are carried out and performed over 10 ns and 7 ns of simulation time, respectively. The center of melittin along the membrane normal in these stable simulations is in excellent agreement with the relevant experimental data. Simulations of bacteriorhodopsin started from the experimental structure remained stable and in close agreement with experiment. We also examined the free energy profiles of water and amino acid side chain analogs upon membrane insertion. The results with our implicit membrane model agree well with the experimental transfer free energy data from cyclohexane to water as well as explicit solvent simulations of water and selected side chain analogs.     

Long-range influence of carbohydrates on the solvation dynamics of water--answers from terahertz absorption measurements and molecular modeling simulations

We present new terahertz (THz) spectroscopic measurements of solvated sugars and compare the effect of two disaccharides (trehalose and lactose) and one monosaccharide (glucose) with respect to the solute-induced changes in the sub-picosecond network dynamics of the hydration water. We found that the solute affects the fast collective network motions of the solvent, even beyond the first solvation layer. For all three carbohydrates, we find an increase of 2-4% in the THz absorption coefficient of the hydration water in comparison to bulk water. Concentration-dependent changes in the THz absorption between 2.1 and 2.8 THz of the solute-water mixture were measured with a precision better than 1% and were used to deduce a dynamical hydration shell, which extends from the surface up to 5.7 +/- 0.4 and 6.5 +/- 0.9 A for the disaccharides lactose and trehalose, respectively, and 3.7 +/- 0.9 A for the glucose. This exceeds the values for the static hydration shell as determined, for example, by scattering, where the long-range structure was found to be not significantly affected by the solute beyond the first hydration shell. When comparing all three carbohydrates, we found that the solute-induced change in the THz absorption depends on the product of molar concentration of the solute and the number of hydrogen bonds between the carbohydrate and water molecules. We can conclude that the long-range influence on the sub-picosecond collective water network motions of the hydration water is directly correlated with the average number of hydrogen bonds between the molecule and adjacent water molecules for carbohydrates. This implies that monosaccharides have a smaller influence on the surrounding water molecules than disaccharides. This could explain the bioprotection mechanism of sugar-water mixtures, which has been found to be more effective for disaccharides than for monosaccharides.