NVU dynamics. II. Comparing to four other dynamics

In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schr?der, and J. C. Dyre, "NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface," J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here, simulations of NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Lennard-Jones Gaussian liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular, to leading order in 1∕N these two dynamics give identical time-autocorrelation functions. In the final part of the paper, NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nose?-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make single-particle diffusion constants identical to that of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.     

Fluctuating charge normal modes: An algorithm for implementing molecular dynamics simulations with polarizable potentials

A new method for performing molecular dynamics simulations with fluctuating charge polarizable potentials is introduced. In fluctuating charge models, polarizability is treated by allowing the partial charges to be variables, with values that are coupled to charges on the same molecule as well as those on other molecules. The charges can be efficiently propagated in a molecular dynamics simulation using extended Lagrangian dynamics. By making a coordinate change from the charge variables to a set of normal mode charge coordinates for each molecule, a new method is constructed in which the normal mode charge variables uncouple from those on the same molecule. The method is applied to the TIP4P-FQ model of water and compared to other methods for implementing the dynamics. The methods are compared using different molecular dynamics time steps.     

Ab initio Ehrenfest dynamics

We present an ab initio direct Ehrenfest dynamics scheme using a three time-step integrator. The three different time steps are implemented with nuclear velocity Verlet, nuclear-position-coupled midpoint Fock integrator, and time-dependent Hartree-Fock with a modified midpoint and unitary transformation algorithm. The computational cost of the ab initio direct Ehrenfest dynamics presented here is found to be only a factor of 2-4 larger than that of Born-Oppenheimer (BO) dynamics. As an example, we compute the vibration of the NaCl molecule and the intramolecular torsional motion of H2C=NH2+ by Ehrenfest dynamics compared with BO dynamics. For the vibration of NaCl with an initial kinetic energy of 1.16 eV, Ehrenfest dynamics converges to BO dynamics with the same vibrational frequency. The intramolecular rotation of H2C=NH2+ produces significant electronic excitation in the Ehrenfest trajectory. The amount of nonadiabaticity, suggested by the amplitude of the coherent progression of the excited and ground electronic states, is observed to be directly related to the strength of the electron-nuclear coupling. Such nonadiabaticity is seen to have a significant effect on the dynamics compared with the adiabatic approximation.     

A centroid molecular dynamics study of liquid para-hydrogen and ortho-deuterium

Centroid molecular dynamics (CMD) is applied to the study of collective and single-particle dynamics in liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The CMD results are compared with the results of classical molecular dynamics, quantum mode coupling theory, a maximum entropy analytic continuation approach, pair-product forward- backward semiclassical dynamics, and available experimental results. The self-diffusion constants are in excellent agreement with the experimental measurements for all systems studied. Furthermore, it is shown that the method is able to adequately describe both the single-particle and collective dynamics of quantum liquids.     

Towards an assessment of the accuracy of density functional theory for first principles simulations of water. II

A series of 20 ps ab initio molecular dynamics simulations of water at ambient density and temperatures ranging from 300 to 450 K are presented. Car-Parrinello (CP) and Born-Oppenheimer (BO) molecular dynamics techniques are compared for systems containing 54 and 64 water molecules. At 300 K, an excellent agreement is found between radial distribution functions (RDFs) obtained with BO and CP dynamics, provided an appropriately small value of the fictitious mass parameter is used in the CP simulation. However, we find that the diffusion coefficients computed from CP dynamics are approximately two times larger than those obtained with BO simulations for T>400 K, where statistically meaningful comparisons can be made. Overall, both BO and CP dynamics at 300 K yield overstructured RDFs and slow diffusion as compared to experiment. In order to understand these discrepancies, the effect of proton quantum motion is investigated with the use of empirical interaction potentials. We find that proton quantum effects may have a larger impact than previously thought on structure and diffusion of the liquid.     

Solid film versus solution-phase charge-recombination dynamics of exTTF-bridge-C60 dyads

The charge-recombination dynamics of two exTTF-C60 dyads (exTTF = 9,10-bis(1,3-dithiol-2-ylidene)-9,10-dihydroanthracene), observed after photoinduced charge separation, are compared in solution and in the solid state. The dyads differ only in the degree of conjugation of the bridge between the donor (exTTF) and the acceptor (C60) moieties. In solution, photoexcitation of the nonconjugated dyad C60-BN-exTTF (1) (BN = 1,1'-binaphthyl) shows slower charge-recombination dynamics compared with the conjugated dyad C60-TVB-exTTF (2) (TVB = bisthienylvinylenebenzene) (lifetimes of 24 and 0.6 micros, respectively), consistent with the expected stronger electronic coupling in the conjugated dyad. However, in solid films, the dynamics are remarkably different, with dyad 2 showing slower recombination dynamics than 1. For dyad 1, recombination dynamics for the solid films are observed to be tenfold faster than in solution, with this acceleration attributed to enhanced electronic coupling between the geminate radical pair in the solid film. In contrast, for dyad 2, the recombination dynamics in the solid film exhibit a lifetime of 7 micros, tenfold slower than that observed for this dyad in solution. These slow recombination dynamics are assigned to the dissociation of the initially formed geminate radical pair to free carriers. Subsequent trapping of the free carriers at film defects results in the observed slow recombination dynamics. It is thus apparent that consideration of solution-phase recombination data is of only limited value in predicting the solid-film behaviour. These results are discussed with reference to the development of organic solar cells based upon molecular donor-acceptor structures.     

Algorithms for sampling a quantum microcanonical ensemble of harmonic oscillators at potential minima and conical intersections

Algorithms are presented for sampling quantum microcanonical ensembles for a potential energy minimum and for the conical intersection at the minimum energy crossing point of two coupled electronic states. These ensembles may be used to initialize trajectories for chemical dynamics simulations. The unimolecular dynamics of a microcanonical ensemble about a potential energy minimum may be compared with the dynamics predicted by quantum Rice-Ramsperger-Kassel-Marcus (RRKM) theory. If the dynamics is non-RRKM, it will be of particular interest to determine which states have particularly long lifetimes. Initializing a microcanonical ensemble for the electronically excited state at a conical intersection is a model for electronic nonadiabatic dynamics. The trajectory surface-hopping approach may be used to study the ensuing chemical dynamics. A strength of the model is that zero-point energy conditions are included for the initial nonadiabatic dynamics at the conical intersection.     

Brownian dynamics simulations of polyelectrolyte molecules traveling through an entropic trap array during electrophoresis

Using Brownian dynamics simulations of wormlike chain bead-spring models, the dynamics of linear and star-branched polyelectrolyte molecules traveling through an array of entropic traps during electrophoresis have been investigated. First, the effectiveness of using coarse-grained bead-spring systems for linear molecules to model the electrophoretic process was demonstrated and compared to previous bead-rod (Kramers) chain simulations by Panwar and Kumar [Macromolecules 39, 1297 (2006)]. Second, the coarse-grained bead-spring model has been extended to investigate the effect of branching on the dynamics of molecules through the entropic trap array. Initial studies indicate the reduced mobility of star-branched molecules as compared to equivalent linear molecules. The radius of gyration of the polymer molecule appears to be the dominating factor governing the time scales encountered during traversal of the entropic trapping array.     

Quantum tunneling effect in entanglement dynamics

Quantum tunneling effect in entanglement dynamics between two coupled particles with separable Gaussian initial state is investigated using entangled trajectory molecular dynamics method in terms of the reduced‐density linear entropy. It has been presented through showing distinguish contribution of single trajectory to linear entropy between classical trajectory and entangled trajectory with same initial state. We find that quantum tunneling effect makes single trajectory's contribution remarkably decrease under quantum dynamics compared to classical dynamics. The nonlocality of quantum entanglement is presented, and the energy transfer between two coupled particles through quantum correlations and classical ones is also discussed in the end. © 2015 Wiley Periodicals, Inc.     

Reorientation dynamics of nanoconfined water: power-law decay, hydrogen-bond jumps, and test of a two-state model

The reorientation dynamics of water confined within nanoscale, hydrophilic silica pores are investigated using molecular dynamics simulations. The effect of surface hydrogen-bonding and electrostatic interactions are examined by comparing with both a silica pore with no charges (representing hydrophobic confinement) and bulk water. The OH reorientation in water is found to slow significantly in hydrophilic confinement compared to bulk water, and is well-described by a power-law decay extending beyond one nanosecond. In contrast, the dynamics of water in the hydrophobic pore are more modestly affected. A two-state model, commonly used to interpret confined liquid properties, is tested by analysis of the position-dependence of the water dynamics. While the two-state model provides a good fit of the orientational decay, our molecular-level analysis evidences that it relies on an over-simplified picture of water dynamics. In contrast with the two-state model assumptions, the interface dynamics is markedly heterogeneous, especially in the hydrophilic pore and there is no single interfacial state with a common dynamics.     

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Dynamics of nanoscopic water: vibrational echo and infrared pump-probe studies of reverse micelles

The dynamics of water in nanoscopic pools 1.7-4.0 nm in diameter in AOT reverse micelles were studied with ultrafast infrared spectrally resolved stimulated vibrational echo and pump-probe spectroscopies. The experiments were conducted on the OD hydroxyl stretch of low-concentration HOD in the H2O, providing a direct examination of the hydrogen-bond network dynamics. Pump-probe experiments show that the vibrational lifetime of the OD stretch mode increases as the size of the reverse micelle decreases. These experiments are also sensitive to hydrogen-bond dissociation and reformation dynamics, which are observed to change with reverse micelle size. Spectrally resolved vibrational echo data were obtained at several frequencies. The vibrational echo data are compared to data taken on bulk water and on a 6 M NaCl solution, which is used to examine the role of ionic strength on the water dynamics in reverse micelles. Two types of vibrational echo measurements are presented: the vibrational echo decays and the vibrational echo peak shifts. As the water nanopool size decreases, the vibrational echo decays become slower. Even the largest nanopool (4 nm, approximately 1000 water molecules) has dynamics that are substantially slower than bulk water. It is demonstrated that the slow dynamics in the reverse micelle water nanopools are a result of confinement rather than ionic strength. The data are fit using time-dependent diagrammatic perturbation theory to obtain the frequency-frequency correlation function (FFCF) for each reverse micelle. The results are compared to the FFCF of water and show that the largest differences are in the slowest time scale dynamics. In bulk water, the slowest time scale dynamics are caused by hydrogen-bond network equilibration, i.e., the making and breaking of hydrogen bonds. For the smallest nanopools, the longest time scale component of the water dynamics is approximately 10 times longer than the dynamics in bulk water. The vibrational echo data for the smallest reverse micelle displays a dependence on the detection wavelength, which may indicate that multiple ensembles of water molecules are being observed.     

Dynamics imaging of lipid phases and lipid-marker interactions in model biomembranes

Biomembranes are complex systems that regulate numerous biological processes. Lipid phases that constitute these membranes influence their properties and transport characteristics. Here, we demonstrate the potential of short-range dynamics imaging (excited-state lifetime, rotational diffusion, and order parameter) as a sensitive probe of lipid phases in giant unilamellar vesicles (GUVs). Liquid-disordered and gel phases were labeled with Bodipy-PC at room temperature. Two-photon fluorescence lifetime imaging microscopy of single-phase GUVs reveals more heterogeneity in fluorescence lifetimes of Bodipy in the gel phase (DPPC: 3.8+/-0.6 ns) as compared with the fluid phase (DOPC: 5.2+/-0.2 ns). The phase-specificity of excited-state lifetime of Bodipy-PC is attributed to the stacking of ordered lipid molecules that possibly enhances homo-FRET. Fluorescence polarization anisotropy imaging also reveals distinctive molecular order that is phase specific. The results are compared with DiI-C12-labeled fluid GUVs to investigate the sensitivity of our fluorescence dynamics assay to different lipid-marker interactions. Our results provide a molecular perspective of lipid phase dynamics and the nature of their microenvironments that will ultimately help our understanding of the structure-function relationship of biomembranes in vivo. Furthermore, these ultrafast excited-state dynamics will be used for molecular dynamics simulation of lipid-lipid, lipid-marker and lipid-protein interactions.     

Calculation of diffusion coefficients for carbon dioxide + solute system near the critical conditions by non-equilibrium molecular dynamics simulation

A non-equilibrium molecular dynamics simulation was adopted to calculate the diffusion coefficients for a pseudo-binary system of carbon dioxide and for a carbon dioxide + solute system at 308.2 and 318.2 K. The calculated results were compared with the self- and tracer diffusion coefficients calculated by an equilibrium molecular dynamics simulation. The simulated results for the pseudo-binary system of carbon dioxide by the non-equilibrium molecular dynamics simulation are in good agreement with the results of self diffusion coefficients for pure carbon dioxide by the equilibrium molecular dynamics simulation. The simulated results of mutual diffusion coefficients for the carbon dioxide + solute system by the non-equilibrium molecular dynamics simulation are slightly lower than the results of the tracer diffusion coefficients by the equilibrium molecular dynamics simulation. The anomalous behavior of diffusion coefficients near the critical concentration was represented by the results of the non-equilibrium molecular dynamics simulation.     

Adiabatic—sudden transition in chemical reactions: Study of a model for H + H2 (ν =1)

Classical and quantal total reaction probabilities are compared with adiabatic and sudden predictions for a model of the H + H₂ (ν = 1) reaction. Near the adiabatic threshold, a distinct transition is found from dominately adiabatic dynamics to dominately sudden dynamics.     

High-resolution neutron-scattering study of slow dynamics of surface water molecules in zirconium oxide

We have performed a quasielastic neutron-scattering experiment on backscattering spectrometer with sub-mueV resolution to investigate the slow dynamics of surface water in zirconium oxide using the sample studied previously with a time-of-flight neutron spectrometer [E. Mamontov, J. Chem. Phys. 121, 9087 (2004)]. The backscattering measurements in the temperature range of 240-300 K have revealed a translational dynamics slower by another order of magnitude compared to the translational dynamics of the outer hydration layer observed in the time-of-flight experiment. The relaxation function of this slow motion is described by a stretched exponential with the stretch factors between 0.8 and 0.9, indicating a distribution of the relaxation times. The temperature dependence of the average residence time is non-Arrhenius, suggesting that the translational motion studied in this work is more complex than surface jump diffusion previously observed for the molecules of the outer hydration layer. The observed slow dynamics is ascribed to the molecules of the inner hydration layer that form more hydrogen bonds compared to the molecules of the outer hydration layer. Despite being slower by two orders of magnitude, the translational motion of the molecules of the inner hydration layer may have more in common with bulk water compared to the outer hydration layer, the dynamics of which is slower than that of bulk water by just one order of magnitude.     

Effect of surface modification on back electron transfer dynamics of dibromo fluorescein sensitized TiO2 nanoparticles

Electron injection and back electron transfer (BET) dynamics have been carried out for dibromo fluorescein (DBF) sensitized TiO2 nanoparticles capped (modified) with sodium dodecyl benzene sulfonate using transient absorption techniques in picosecond and microsecond time domain. BET dynamics have been compared with bare (unmodified) nanoparticles for the same DBF/TiO2 system. It has been observed that BET reaction is slow on the modified surface compared to a bare surface in earlier time domain (picosecond). This observation has been explained by the fact that on surface modification the energy levels of the semiconductor nanoparticles are pushed up in energy. As a result, the free energy of reaction (-deltaG zero) for BET reaction of a dye/SM-TiO2 system increases as compared to the dye/bare TiO2 system. High exoergic BET reaction in dye-sensitized TiO2 nanoparticles surfaces fall in the Marcus inverted regime, so with increasing free energy of reaction, BET rate decreases on the modified surface. However, a reversible trend in BET dynamics has been observed for the above systems in the longer time domain (microsecond). In microsecond time domain BET reaction is faster on the modified surface as compared to on the bare surface. Modification of this surface reduces the density of deep trap states. Recombination dynamics between deep-trapped electron and parent cation is slow due to low coupling strength of BET reaction. As the density of deep-trapped electrons is high in bare particles, BET reaction is slow in longer time domain.     

On the microscopic theory of polar solvation dynamics

A microscopic model of the time-resolved Stokes shift is developed. The model calculates the solvation dynamics by combining the atomic resolution of the solute structure with dipolar dynamics from the polarization structure factors of the homogeneous solvent. Calculations are made for coumarin 153 and quinoxaline optical dyes with atomic geometries and charge distributions taken from quantum calculations. Stokes shift dynamics is calculated and compared to experiment in high-temperature acetonitrile and methanol and in low-temperature 2-methyl-tetrahydrofurane using dielectric relaxation data from experiment.     

Thermodynamic properties calculation for MgO-SiO2 liquids using both empirical and first-principles molecular simulations

Both classical molecular dynamics simulations and first-principles molecular simulations were carried out to investigate the thermodynamic properties of MgO-SiO(2) melts at 4000 K and 0 GPa. After equilibrating both the mini-sized and large-sized systems using classical molecular dynamics simulations, several properties and structures were calculated and compared. Consistencies were found between results from mini-sized systems and those from large-sized systems. The first-principles molecular dynamics simulations were continued for 6 ps from several independent configurations output from the mini-sized systems. The enthalpy of mixing was calculated, and results were compared with those from empirical molecular simulations. We found that first-principles simulation modified the thermodynamic properties of silicate melts, and led to positive enthalpy of mixing at high SiO(2) concentrations and negative ones at low SiO(2) concentrations. Regressing data using the Margules equation led to results consistent with available references.     

How does the urea dynamics differ from water dynamics inside the reverse micelle?

In this study, the urea dynamics inside AOT reverse micelle (RM) has been monitored without intervention of water using time-resolved fluorescence techniques from the picosecond to nanosecond time regime. It has been observed that urea dynamics inside the reverse micelle is severely retarded compared to water RM due to the formation of highly networked urea cluster inside the RM. Time-resolved fluorescence anisotropy study also confirms the existence of a confined environment around the dye at higher concentrations of urea inside the reverse micelle. The dynamics of urea-water mixtures inside AOT reverse micelle has also been monitored with increasing urea concentration to get insight about the effect of urea on the overall solvation dynamics feature. It has been observed that with the increase in urea concentration, the overall dynamics becomes slower, and it infers the presence of few water or urea molecules, those strongly associated with surrounding urea and (or) water by hydrogen bonds.