Application of molecular dynamics simulations in molecular property prediction II: diffusion coefficient

In this work, we have evaluated how well the general assisted model building with energy refinement (AMBER) force field performs in studying the dynamic properties of liquids. Diffusion coefficients (D) have been predicted for 17 solvents, five organic compounds in aqueous solutions, four proteins in aqueous solutions, and nine organic compounds in nonaqueous solutions. An efficient sampling strategy has been proposed and tested in the calculation of the diffusion coefficients of solutes in solutions. There are two major findings of this study. First of all, the diffusion coefficients of organic solutes in aqueous solution can be well predicted: the average unsigned errors and the root mean square errors are 0.137 and 0.171 × 10(-5) cm(-2) s(-1), respectively. Second, although the absolute values of D cannot be predicted, good correlations have been achieved for eight organic solvents with experimental data (R(2) = 0.784), four proteins in aqueous solutions (R(2) = 0.996), and nine organic compounds in nonaqueous solutions (R(2) = 0.834). The temperature dependent behaviors of three solvents, namely, TIP3P water, dimethyl sulfoxide, and cyclohexane have been studied. The major molecular dynamics (MD) settings, such as the sizes of simulation boxes and with/without wrapping the coordinates of MD snapshots into the primary simulation boxes have been explored. We have concluded that our sampling strategy that averaging the mean square displacement collected in multiple short-MD simulations is efficient in predicting diffusion coefficients of solutes at infinite dilution.     

In situ study on molecular diffusion phenomena in nanoporous catalytic solids

As an omnipresent phenomenon in nature, diffusion is among the rate-determining processes in many technological processes. This is in particular true for catalytic conversion in nanoporous materials. We provide a critical review of the possibilities of exploring diffusion phenomena over microscopic dimensions in such media by direct experimental observation. By monitoring the probability distribution of molecular displacements as a function of time, the pulsed field gradient technique of NMR (PFG NMR) records the rate of molecular re-distribution. By varying the observation time, PFG NMR is thus able to trace even hierarchies of transport resistances as occurring, e.g., in catalyst particles in the form of binder-compacted assemblages of zeolite crystallites. Alternatively, and complementary to this information, interference microscopy (IFM) and IR microscopy (IRM) are able to follow the evolution of intracrystalline concentration profiles during uptake and release. This allows, in particular, an accurate quantification of the transport resistances on the surface of the individual crystallites and of the probability that reactant molecules from the gas phase, upon colliding with the external surface, are able to penetrate through such "surface barriers" into the crystal bulk phase. Being able to distinguish between different molecular species, IRM is able to record the evolution of intracrystalline concentration profiles even during multi-component adsorption and catalytic reactions (169 references).     

Langevin dynamics simulations of the diffusion of molecular knots in tensioned polymer chains

Motivated by recent experiments, in which knots have been tied in individual biopolymer molecules, we use Langevin dynamics simulations to study the diffusion of a knot along a tensioned polymer chain. We find that the dependence of the knot diffusion coefficient on the tension can be non-monotonic. This behavior can be explained by the model, in which the motion of the knot involves cooperative displacement of a local knot region. At low tension, the overall viscous drag force that acts on the knot region is proportional to the number N of monomers that participate in the knot, which decreases as the tension is increased, leading to faster diffusion. At high tension the knot becomes tight and its dynamics are dominated by the chain's internal friction, which increases with the increasing tension, thereby slowing down the knot diffusion. This model is further supported by the observation that the knot diffusion coefficient measured across a set of different knot types is inversely proportional to N. We propose that the lack of tension dependence of the knot diffusion coefficients measured in recent experiments is due to the fact that the experimental values of the tension are close to the turnover between the high- and low-force regimes.     

Elementary reaction kinetics in molecular solids. Free volume model of the diffusion limited processes

The main peculiarities of free radical reaction kinetics in organic solids are discussed from the point of view of a slightly modified free volume model of molecular mobility. The reaction and diffusion acts are supposed to occur predominantly in “diluted” microzones, the probability of “dilution” depending on the minimal volume needed for reaction or diffusion, and on the energy of a local molecular displacement. It is shown that even far separated radical pairs may react in a “static” way via the long range microdilution of the structure. The model explains the separation-dependent annealing of radical pairs as well as the stepwise annealing of large fractions of quasi-isolated centres and large capture radii for the diffusion limited reaction of the remaining species. Preliminary results concerning the pressure and plastification dependence of the rate constant are also in reasonable agreement with the proposed concept.     

Molecular simulations of water in hydrophobic microporous solids

This work reports Grand Canonical Monte-Carlo molecular simulation (GCMC) results of water adsorption in a priori hydrophobic microporous solids such as silicalite, a purely siliceous zeolite (Ø_pore～5 Å) and C-Y, a pure carbon replica of zeolite Y (Ø_pore～1 nm). At a first step, in both cases, the water-water interactions are described with the SPC model (calibrated for bulk liquid water) while water-substrate interactions are calculated within the framework of the PN-TrAZ model. This adsorbate-zeolite potential decomposes into short range (repulsive, inductive and dispersive) interaction terms with transferable parameters plus, in the case of silicalite, an electrostatic interaction term based on SPC partial charges for water and ab initio charges for silicalite. With such a standard approach, we found that water fills the microporous volume in both materials at pressure value well below P ₀; hence does not show a strong hydrophobic behaviour at variance with reference experiments (V. Eroshenko et al. in C. R. Phys. 3:111, 2002). This indicates that common models used to describe confined polar molecules are far from being operative. We show on the basis of periodic ab initio calculations that confined water molecules in silicate have a dipole value ～10% smaller than that in the 3D liquid phase indicating that the environment felt by a confined water molecule in silicalite pores is not equivalent to that in the bulk liquid. This implies that classical simulations of polar molecules in ultra confining environment should rely on polarizable potentials (K.S. Smirnov, D. Bougeard in Chem. Phys. 292:53, 2003) if one wishes to capture the underlying physics. Reducing the SPC water dipole moment by 5% in GCMC calculations does allow reproducing experimental data.     

The accuracy of diffusion quantum Monte Carlo simulations in the determination of molecular equilibrium structures

For a test set of 17 first-row small molecules, the equilibrium structures are calculated with Ornstein-Uhlenbeck diffusion quantum Monte Carlo simulations guiding by trial wave functions constructed from floating spherical Gaussian orbitals and spherical Gaussian geminals. To measure performance of the Monte Carlo calculations, the mean deviation, the mean absolute deviation, the maximum absolute deviation, and the standard deviation of Monte Carlo calculated equilibrium structures with respect to empirical equilibrium structures are given. This approach is found to yield results having a uniformly high quality, being consistent with empirical equilibrium structures and surpassing calculated values from the coupled cluster model with single, double, and noniterative triple excitations [CCSD(T)] with the basis sets of cc-pCVQZ and cc-pVQZ. The nonrelativistic equilibrium atomization energies are also presented to assess performance of the calculated methods. The mean absolute deviations regarding experimental atomization energy are 0.16 and 0.21 kcal/mol for the Monte Carlo and CCSD(T)/cc-pCV(56)Z calculations, respectively.     

Comparison of kinetic Monte Carlo and molecular dynamics simulations of diffusion in a model glass former

We present results from kinetic Monte Carlo (KMC) simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the "inherent structure entropy." The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.     

Grand canonical-like molecular dynamics simulations: application to anisotropic mass diffusion in a nanoporous medium

In this work, we describe two grand canonical-like molecular dynamics approaches to investigate mass diffusion phenomenon of a simple Lennard-Jones fluid confined between solid surfaces and in direct contact with reservoirs. In the first method, the density is used as the control variable in the reservoir whereas it is the pressure in the second method. Both methods provide consistent results, however, the constant density approach is the most efficient with respect to the computational time and implementation. Then, employing the constant density approach, we have studied the transient behavior of the diffusion process associated with the migration of one fluid into another one confined between parallel solid walls. Results have shown that the evolution of molar fraction of the invading fluid follows roughly a 1D diffusion model when the solid phase is weakly or moderately adsorbent with a characteristic time increasing when the pore width decreases. However, when the adsorption is high and the pore width small (i.e., below ten molecular sizes), the apparent mass diffusion in the adsorbed layer is reduced compared to that in the center of the slit pore. Hence, this mass diffusion process becomes a two-dimension phenomenon that must take into account an effective mass diffusion coefficient varying locally.     

Self-diffusion and transport diffusion of light gases in metal-organic framework materials assessed using molecular dynamics simulations

Metal-organic framework (MOF) materials pose an interesting alternative to more traditional nanoporous materials for a variety of separation processes. Separation processes involving nanoporous materials can be controlled by either adsorption equilibrium, diffusive transport rates, or a combination of these factors. Adsorption equilibrium has been studied for a variety of gases in MOFs, but almost nothing is currently known about molecular diffusion rates in MOFs. We have used equilibrium molecular dynamics (MD) to probe the self-diffusion and transport diffusion of a number of small gas species in several MOFs as a function of pore loading at room temperature. Specifically, we have studied Ar, CH4, CO2, N2, and H2 diffusion in MOF-5. The diffusion of Ar in MOF-2, MOF-3, and Cu-BTC has been assessed in a similar manner. Our results greatly expand the range of MOFs for which data describing molecular diffusion is available. We discuss the prospects for exploiting molecular transport properties in MOFs in practical separation processes and the future role of MD simulations in screening families of MOFs for these processes.     

Mass spectrometry of molecular solids

Summary Positive and negative ion spectra of various industrially important polymers were recorded using the Laser Microprobe Mass Analysis (LAMMA) technique. Using methods developed in earlier work [1] we interpret the ions as being generated from the polymer backbone or pendant sidechain functional groups. Results are given for polypropylene, polyacrylamide, polystyrene, polycaprolactam (Nylon 6) and polydimethylsiloxane. Mass patterns are analyzed and compared to the previous work.Part I: see [1]     

Temperature control algorithms in dual control volume grand canonical molecular dynamics simulations of hydrogen diffusion in palladium

The effectiveness of five temperature control algorithms for dual control volume grand canonical molecular dynamics is investigated in the study of hydrogen atom diffusion in a palladium bulk. The five algorithms, namely, Gaussian, generalized Gaussian moment thermostat (GGMT), velocity scaling, Nosé-Hoover (NH), and its enhanced version Nosé-Hoover chain (NHC) are examined in both equilibrium and nonequilibrium simulation studies. Our numerical results show that Gaussian yields the most inaccurate solutions for the hydrogen-palladium system due to the high friction coefficient generated from the large velocity fluctuation of hydrogen, while NHC, NH, and GGMT produce the most accurate temperature and density profiles in both equilibrium and nonequilibrium cases with their feedback control mechanisms. However, this feedback control also overestimates the self-diffusion coefficients in equilibrium systems and the diffusion coefficient in nonequilibrium systems. Velocity scaling thermostat produces slight inhomogeneities in the temperature and density profiles, but due to the dissipated heat accumulated in the control volumes it still yields accurate self-diffusion coefficients that are in good agreement with the experimental data at a wide range of temperatures while others tend to deviate.     

The effect of corrugation of pore wall on the thermal diffusion in nanopores by molecular dynamics simulations

In this work we have studied the effect of corrugation on the thermal diffusion (soret effect) in isotopic and non-isotopic fluid mixtures confined in a slit pore. We used a boundary driven non-equilibrium molecular dynamics to simulate thermal diffusion in Lennard–Jones (LJ) binary mixtures confined in structureless Steele 10-4-3 and atomistic Lennard–Jones pore walls. The results showed that for the isotopic mixture thermal diffusion factor for both wall types agrees and the corrugation of the LJ wall has no effect in isotopic mixture. However, for non-isotopic mixture confined in atomistic LJ pore the component with stronger attraction adsorbs more to the wall than the structureless Steele wall. The effect of corrugation of pore wall on the thermal diffusion is noticeable in narrow slit pore and mixture with large difference in molecular attraction parameter of components.     

Viscosity of heavy n-alkanes and diffusion of gases therein based on molecular dynamics simulations and empirical correlations

The viscosity of pure n-alkanes and n-alkane mixtures was studied by molecular dynamics (MD) simulations using the Green–Kubo method. n-Alkane molecules were modeled based on the Transferable Potential for Phase Equilibria (TraPPE) united atom force field. MD simulations at constant number of molecules or particles, volume and temperature (NVT) were performed for n-C₈ up to n-C₉₆ at different temperatures as well as for binary and six-component n-alkane mixtures which are considered as prototypes for the hydrocarbon wax produced during the Gas-To-Liquid (GTL) Fischer–Tropsch process. For the pure n-alkanes, good agreement between our simulated viscosities and existing experimental data was observed. In the case of the n-alkane mixtures, the composition dependence of viscosity was examined. The simulated viscosity results were compared with literature empirical correlations. Moreover, a new macroscopic empirical correlation for the calculation of self-diffusion coefficients of hydrogen, carbon monoxide, and water in n-alkanes and mixtures of n-alkanes was developed by combining viscosity and self-diffusion coefficient values in n-alkanes. The correlation was compared with the simulation data and an average absolute deviation (AAD) of 11.3% for pure n-alkanes and 14.3% for n-alkane mixtures was obtained.     

Unification of box shapes in molecular simulations

In molecular simulations with periodic boundary conditions the computational box may have five different shapes: triclinic; the hexagonal prism; two types of dodecahedrons; and the truncated octahedron. In this article, we show that every molecular simulation, formulated in one of these boxes, can be transformed into a simulation in one of the other ones. The transformation can be done in a preprocessing phase. The simulation in the new box is exactly identical to the simulation in the original one. This means that every molecular simulation may be done in the same type of box. Because the triclinic box is the easiest one to implement, we pay special attention to how to transform the other four box types into triclinic boxes. As a consequence, simulations in the often used truncated octahedron are superfluous; they may be done in a much simpler way in a triclinic box. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1930–1942, 1997     

Direct measurements of molecular attraction of solids

Beam balances were constructed with a photoelectromagnetic negative feedback coupling which made it possible to measure directly the resulting force of molecular attraction between plane and spherical surfaces of two plates separated by a narrow gap, as a function of the width of this gap. The width of the gap was determined from the diameter of Newton's rings. Using a simple equation, it was then possible to determine the energy of interaction per unit area of infinite plane surfaces of the same nature as a function of the width of the gap.

Measurements were made for the pairs: quartz-quartz, mixed thallium halide-mixed thallium halide, and chromium-quartz in a range of gap widths from 0·07 to 0·3 microns. In all cases, within the limits of experimental error, the results agree with the values derived from the equations of the theory of molecular attraction of macro bodies developed by E. M. . At the same time, the equation, which assumes the additivity of molecular interaction, is shown to be inapplicable.

In the measurements, special attention was paid to the removal of surface electrical charges by means of ionization of the air, and also to the removal of dust particles and to decreasing the effect of vibrations and the viscosity of the air on the measurements.

The discrepancy between the present results for quartz and those of and , who obtained forces 5000 times greater than the values corresponding to the equations, is apparently explained by the incomplete removal of surface charges in their measurements.     

Evaluating rotational diffusion from protein MD simulations

It is now feasible to carry out molecular dynamics simulations of proteins in water that are long compared to the overall tumbling of the molecule. Here, we examine rotational diffusion in four small, globular proteins (ubiquitin, binase, lysozyme, and fragment B3 of protein G) with the TIP3P, TIP4P/EW, and SPC/E water models, in simulations that are 6 to 60 times as long as the mean rotational tumbling time. We describe a method for extracting diffusion tensors from such simulations and compare the results to experimental values extracted from NMR relaxation measurements. The simulation results accurately follow a diffusion equation, even for spherical harmonic correlation functions with l as large as 8. However, the best-fit tensors are significantly different from experiment, especially for the commonly used TIP3P water model. Simulations that are 20 to 100 times longer than the rotational tumbling times are needed for good statistics. A number of residues exhibit internal motions on the nanosecond time scale, but in all cases examined here, a product of internal and overall time-correlation functions matches the total time-correlation function well.     

Coarse-grained protein molecular dynamics simulations

A limiting factor in biological science is the time-scale gap between experimental and computational trajectories. At this point, all-atom explicit solvent molecular dynamics (MD) are clearly too expensive to explore long-range protein motions and extract accurate thermodynamics of proteins in isolated or multimeric forms. To reach the appropriate time scale, we must then resort to coarse graining. Here we couple the coarse-grained OPEP model, which has already been used with activated methods, to MD simulations. Two test cases are studied: the stability of three proteins around their experimental structures and the aggregation mechanisms of the Alzheimer's Abeta16-22 peptides. We find that coarse-grained isolated proteins are stable at room temperature within 50 ns time scale. Based on two 220 ns trajectories starting from disordered chains, we find that four Abeta16-22 peptides can form a three-stranded beta sheet. We also demonstrate that the reptation move of one chain over the others, first observed using the activation-relaxation technique, is a kinetically important mechanism during aggregation. These results show that MD-OPEP is a particularly appropriate tool to study qualitatively the dynamics of long biological processes and the thermodynamics of molecular assemblies.     

Multibaric-multithermal ensemble molecular dynamics simulations

We present new generalized-ensemble molecular dynamics simulation algorithms, which we refer to as the multibaric-multithermal molecular dynamics. We describe three algorithms based on (1) the Nosé thermostat and the Andersen barostat, (2) the Nosé-Poincaré thermostat and the Andersen barostat, and (3) the Gaussian thermostat and the Andersen barostat. The multibaric-multithermal simulations perform random walks widely both in the potential-energy space and in the volume space. Therefore, one can calculate isobaric-isothermal ensemble averages in wide ranges of temperature and pressure from only one simulation run. We test the effectiveness of the multibaric-multithermal algorithm by applying it to a Lennard-Jones 12-6 potential system.     

Comparison of the hydration and diffusion of protons in perfluorosulfonic acid membranes with molecular dynamics simulations. scui@utk.edu

Classical molecular dynamics (MD) simulations were performed to determine the hydrated morphology and hydronium ion diffusion coefficients in two different perfluorosulfonic acid (PFSA) membranes as functions of water content. The structural and transport properties of 1143 equivalent weight (EW) Nafion, with its relatively long perfluoroether side chains, are compared to the short-side-chain (SSC) PFSA ionomer at an EW of 977. The separation of the side chains was kept uniform in both ionomers consisting of -(CF 2) 15- units in the backbone, and the degree of hydration was varied from 5 to 20 weight % water. The MD simulations indicated that the distribution of water clusters is more dispersed in the SSC ionomer, which leads to a more connected water-channel network at the low water contents. This suggests that the SSC ionomer may be more inclined to form sample-spanning aqueous domains through which transport of water and protons may occur. The diffusion coefficients for both hydronium ions and water molecules were calculated at hydration levels of 4.4, 6.4, 9.6, and 12.8 H 2O/SO 3H for each ionomer. When compared to experimental proton diffusion coefficients, this suggests that as the water content is increased the contribution of proton hopping to the overall proton diffusion increases.     

Spin dephasing in impurity induced states in molecular solids

Spin coherence experiments are used to determine the energy level structure, physical geometry, and exciton dynamics of a series of impurity-induced traps in 1,2,4,5-tetrachlorobenzene. The trap, a pertubed host molecule, is shown to be caused by an adjacent, translationally equivalent chemical impurity whose triplet energy may lie above or below the host exciton, but above the trap. The slow rates of thermal processes within the trap are interpreted as weak coupling between the lattice phonons and localized phonons induced at the trap by the impurity.