Dynamic evolution in coarse-grained molecular dynamics simulations of polyethylene melts

We test a coarse-grained model assigned based on united atom simulations of C50 polyethylene to seven chain lengths ranging from C76 to C300. The prior model accurately reproduced static and dynamic properties. For the dynamics, the coarse-grained time evolution was scaled by a constant value [t=alphatCG] predictable based on the difference in intermolecular interactions. In this contribution, we show that both static and dynamic observables have continued accuracy when using the C50 coarse-grained force field for chains representing up to 300 united atoms. Pair distribution functions for the longer chain systems are unaltered, and the chain dimensions present the expected N0.5 scaling. To assess dynamic properties, we compare diffusion coefficients to experimental values and united atom simulations, assign the entanglement length using various methods, examine the applicability of the Rouse model as a function of N, and compare tube diameters extracted using a primitive path analysis to experimental values. These results show that the coarse-grained model accurately reproduces dynamic properties over a range of chain lengths, including systems that are entangled.     

Molecular dynamics simulation study on the phase behavior of the Gay-Berne model with a terminal dipole and a flexible tail

To study the effect of the alkyl tail and the terminal dipole on the stability of the liquid crystalline phase of mesogens, we have carried out molecular dynamics simulations for 1CB(4-methyl-4'-cyanobiphenyl) and 5CB(4-n-pentyl-4'-cyanobiphenyl) by using a coarse-grained model. In the coarse-grained model, a 5CB molecule is divided into the rigid part of 1CB moiety, which is represented by an ellipsoid, and the remaining flexible part which is represented by a chain of united atoms. The nonbonded potential between coarse-grained segments is represented by the generalized Gay-Berne (GB) potential and the potential parameters are determined by directly comparing the GB potential with the atomistic potentials averaged over the rotation of the mesogen around its axis. In addition, a dipole moment is placed at one end of the ellipsoid opposite to the flexible tail. The ordered state obtained in the polar 5CB model was assigned as the nematic phase, and the experimental static and dynamical properties were reproduced well by using this coarse-grained model. Both the dipole-dipole interactions and the thermal fluctuation of the flexible tail increase the positional disorder in the director direction, and stabilize the nematic phase. Thus, the nematic phase in the polar 5CB is induced by a cooperative effect of the flexible tail and the terminal dipole. It is noted that a local bilayer structure with head-to-head association is formed in the nematic phase, as experimentally observed by x-ray diffraction measurements.     

Coarse-grained rigid blob model for soft matter simulations

We have developed a coarse-grained multiscale molecular simulation method for soft matter systems that directly incorporates stereochemical information. We divide the material into disjoint groups of atoms or particles that move as separate rigid bodies; we call these groups "rigid blobs," hence the name coarse-grained rigid blob model. The method is enabled by the construction of transferable interblob potentials that approximate the net intermolecular interactions, as obtained from ab initio electronic structure calculations, other all-atom empirical potentials, experimental data, or any combination of the above. We utilize a multipolar expansion to obtain the interblob potential-energy functions. The series, which contains controllable approximations that allow us to estimate the errors, approaches the original intermolecular potential as the number of terms increases. Using a novel numerical algorithm, we can calculate the interblob potentials very efficiently in terms of a few interaction moment tensors. This reduces the labor well beyond what is required in standard molecular-dynamics calculations and allows large-scale simulations for temporal scales commensurate with characteristic times of nano- and mesoscale systems. A detailed derivation of the formulas is presented, followed by illustrative applications to several systems showing that the method can effectively capture realistic microscopic details and can easily extend to large-scale simulations.     

Coarse-grained force field for simulating polymer-tethered silsesquioxane self-assembly in solution

A coarse-grained model has been developed for simulating the self-assembly of nonyl-tethered polyhedral oligomeric silsesquioxane (POSS) nanoparticles in solution. A mapping scheme for groups of atoms in the atomistic molecule onto beads in the coarse-grained model was established. The coarse-grained force field consists of solvent-mediated effective interaction potentials that were derived via a structural-based coarse-graining numerical iteration scheme. The force field was obtained from initial guesses that were refined through two different iteration algorithms. The coarse-graining scheme was validated by comparing the aggregation of POSS molecules observed in simulations of the coarse-grained model to that observed in all-atom simulations containing explicit solvent. At 300 K the effective coarse-grained potentials obtained from different initial guesses are comparable to each other. At 400 K the differences between the force fields obtained from different initial guesses, although small, are noticeable. The use of a different iteration algorithm employing identical initial guesses resulted in the same overall effective potentials for bare cube corner bead sites. In both the coarse-grained and all-atom simulations, small aggregates of POSS molecules were observed with similar local packings of the silsesquioxane cages and tether conformations. The coarse-grained model afforded a savings in computing time of roughly two orders of magnitude. Further comparisons were made between the coarse-grained monotethered POSS model developed here and a minimal model developed in earlier work. The results suggest that the interactions between POSS cages are long ranged and are captured by the coarse-grained model developed here. The minimal model is suitable for capturing the local intermolecular packing of POSS cubes at short separation distances.     

Modeling real dynamics in the coarse-grained representation of condensed phase systems

This work presents a systematic multiscale methodology to provide a more faithful representation of real dynamics in coarse-grained molecular simulation models. The theoretical formalism is based on the recently developed multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B. 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] and relies on the generalized Langevin equation approach and its simpler Langevin equation limit. The friction coefficients are determined in multiscale fashion from the underlying all-atom molecular dynamics simulations using force-velocity and velocity-velocity correlation functions for the coarse-grained sites. The diffusion properties in the resulting CG Brownian dynamics simulations are shown to be quite accurate. The time dependence of the velocity autocorrelation function is also well-reproduced relative to the all-atom model if sufficient resolution of the CG sites is implemented.     

Anisotropic united atom model including the electrostatic interactions of benzene

An optimization including electrostatic interactions has been performed for the parameters of an anisotropic united atoms intermolecular potential for benzene for thermodynamic and transport property prediction using Gibbs ensemble, isothermal-isobaric (NPT) Monte Carlo, and molecular dynamic simulations. The optimization procedure is based on the minimization of a dimensionless error criterion incorporating various thermodynamic data (saturation pressure, vaporization enthalpy, and liquid density) at ambient conditions and at 350 and 450 K. A comprehensive comparison of the new model is given with other intermolecular potentials taken from the literature. Overall thermodynamic, structural, reorientational, and translational dynamic properties of our optimized model are in very good agreement with experimental data. The new model also provides a good representation of the liquid structure, as revealed by three-dimensional spatial density functions and carbon-carbon radial distribution function. Shear viscosity variations with temperature and pressure are very well reproduced, revealing a significant improvement with respect to nonpolar models.     

Importance of van der Waals Interactions in QM/MM Simulations

The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen-bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.     

The multiscale coarse-graining method. VIII. Multiresolution hierarchical basis functions and basis function selection in the construction of coarse-grained force fields

The multiscale coarse-graining (MS-CG) method is a method for determining the effective potential energy function for a coarse-grained (CG) model of a molecular system using data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The coarse-grained potential obtained using the MS-CG method is a variational approximation for the exact many-body potential of mean force for the coarse-grained sites. Here we propose a new numerical algorithm with noise suppression capabilities and enhanced numerical stability for the solution of the MS-CG variational problem. The new method, which is a variant of the elastic net method [Friedman et al., Ann. Appl. Stat. 1, 302 (2007)], allows us to construct a large basis set, and for each value of a so-called "penalty parameter" the method automatically chooses a subset of the basis that is most important for representing the MS-CG potential. The size of the subset increases as the penalty parameter is decreased. The appropriate value to choose for the penalty parameter is the one that gives a basis set that is large enough to fit the data in the simulation data set without fitting the noise. This procedure provides regularization to mitigate potential numerical problems in the associated linear least squares calculation, and it provides a way to avoid fitting statistical error. We also develop new basis functions that are similar to multiresolution Haar functions and that have the differentiability properties that are appropriate for representing CG potentials. We demonstrate the feasibility of the combined use of the elastic net method and the multiresolution basis functions by performing a variational calculation of the CG potential for a relatively simple system. We develop a method to choose the appropriate value of the penalty parameter to give the optimal basis set. The combined effect of the new basis functions and the regularization provided by the elastic net method opens the possibility of using very large basis sets for complicated CG systems with many interaction potentials without encountering numerical problems in the variational calculation.     

银电极上4-氨基安替比林原位表面增强拉曼光谱电化学

在银电极表面4-氨基安替比林(4-AAP)分子自组装,形成单分子膜层.应用表面增强拉曼散射(SERS)光谱原位考察不同电位下4-AAP在电极表面的吸附机理及其组装液pH值对组装分子与银作用方式的影响.依据密度泛函数(DFT)理论预测4-AAP分子振动模式及其SERS光谱归属.结果表明:在开路电位下,组装层中的4-AAP分子以N15和O3为位点,由苯环倾斜和比林环垂直的方式吸附在银表面;但随着外加电位负移,4-AAP分子的苯环趋于垂直吸附而比林环则逐渐以平行方式靠近银表面.在-0.8V电位下,4-AAP分子从银表面脱附.酸性溶液中组装,形成的4-AAP膜层以N15和O3为位点吸附于银表面,比林环倾斜而苯环直立;碱性条件下,分子的吸附位点不变,比林环呈平行取向,而苯环倾斜于银表面.     

Multiscale coarse-graining of monosaccharides

A systematic multiscale coarse-graining (MS-CG) algorithm is applied to build coarse-grained models for monosaccharides in aqueous solution. The methodology is demonstrated for the example of alpha-D-glucopyranose. The nonbonded interactions are directly derived from the force-matching approach, whereas the bonded interactions are obtained through Boltzmann statistical analyses of the underlying atomistic trajectory. The MS-CG model is shown to reproduce many structural and thermodynamic properties in the constant NPT ensemble. Although the model is derived at a single temperature, pressure, and concentration, it is shown to be reasonably transferable to other thermodynamic states. In this model, long-range interactions are effectively mapped into short-range forces with a moderate cutoff and are evaluated by table look-up. As a result, molecular dynamics employing the MS-CG model is approximately 3 orders of magnitude more efficient than its atomistic counterpart. Consequently, the model is particularly suitable for simulating carbohydrate systems at large length and long time scales. Results for an alpha-(1-->4)-d-glucan with 14 glucose units are also presented, demonstrating that the MS-CG algorithm is also applicable to the coarse-graining of other saccharide systems.     

Coarse grained protein-lipid model with application to lipoprotein particles

A coarse-grained model for molecular dynamics simulations is extended from lipids to proteins. In the framework of such models pioneered by Klein, atoms are described group-wise by beads, with the interactions between beads governed by effective potentials. The extension developed here is based on a coarse-grained lipid model developed previously by Marrink et al., although future versions will reconcile the approach taken with the systematic approach of Klein and other authors. Each amino acid of the protein is represented by two coarse-grained beads, one for the backbone (identical for all residues) and one for the side-chain (which differs depending on the residue type). The coarse-graining reduces the system size about 10-fold and allows integration time steps of 25-50 fs. The model is applied to simulations of discoidal high-density lipoprotein particles involving water, lipids, and two primarily helical proteins. These particles are an ideal test system for the extension of coarse-grained models. Our model proved to be reliable in maintaining the shape of preassembled particles and in reproducing the overall structural features of high-density lipoproteins accurately. Microsecond simulations of lipoprotein assembly revealed the formation of a protein-lipid complex in which two proteins are attached to either side of a discoidal lipid bilayer.     

Mixed atomistic and coarse-grained molecular dynamics: simulation of a membrane-bound ion channel

The recently developed multiscale coarse-graining (MS-CG) method (Izvekov, S.; Voth, G. A. J. Phys. Chem. B 2005, 109, 2469; J. Chem. Phys. 2005, 123, 134105) is used to build a mixed all-atom and coarse-grained (AA-CG) model of the gramicidin A (gA) ion channel embedded in a dimyristoylphosphatidylcholine (DMPC) lipid bilayer and water environment. In this model, the gA peptide was described in full atomistic detail, while the lipid and water molecules were described using coarse-grained representations. The atom-CG and CG-CG interactions in the mixed AA-CG model were determined using the MS-CG method. Molecular dynamics (MD) simulations were performed using the resulting AA-CG model. The results from simulations of the AA-CG model compare very favorably to those from all-atom MD simulations of the entire system. Since the MS-CG method employs a general and systematic approach to obtain effective interactions from the underlying all-atom models, the present approach to rigorously develop mixed AA-CG models has the potential to be extended to many other systems.     

Intermolecular interactions in solid benzene

The lattice dynamics and molecular vibrations of benzene and deuterated benzene crystals are calculated from force constants derived from density-functional theory (DFT) calculations and compared with measured inelastic neutron-scattering spectra. A very small change (0.5%) in lattice parameter is required to obtain real lattice-mode frequencies across the Brillouin zone. There is a strong coupling between wagging and breathing modes away from the zone center. This coupling and sensitivity to cell size arises from two basic interactions. Firstly, comparatively strong interactions that hold the benzene molecules together in layers. These include an intermolecular interaction in which H atoms of one molecule link to the center of the aromatic ring of a neighboring molecule. The layers are held to each other by weaker interactions, which also have components that hold molecules together within a layer. Small changes in the lattice parameters change this second type of interaction and account for the changes to the lattice dynamics. The calculations also reveal a small auxetic effect in that elongation of the crystal along the b axis leads to an increase in internal pressure in the ac plane, that is, elongation in the b direction induces expansion in the a and c directions.     

Stacking interactions between nitrogen-containing six-membered heterocyclic aromatic rings and substituted benzene: studies in solution and in the solid state

The stacking interactions between an aromatic ring and a pyridine or a pyrimidine ring are studied by using a series of triptycene-derived scaffolds. The indicative ratios of the syn and anti conformers were determined by variable-temperature NMR spectroscopy. The syn conformer aligns the attached aromatic ring and the heterocycle in a parallel-displaced orientation while the anti conformer sets the two rings apart from each other. Comparing to the corresponding control compounds where a benzene ring is in the position of the heterocycle, higher attractive interactions are observed as indicated by the higher syn/anti ratios. In general, the attractive interactions are much less sensitive to the substituent effects than the corresponding nonheterocycles. The greatest attractive interactions were observed between a pyrimidine ring and a N,N-dimethylaminobenzene, consistent with a predominant donor-acceptor interaction. The interactions between a pyridine ring and a substituted benzene ring show that the pyridine is comparable to that of a NO2- or a CN-substituted benzene ring except for the unpredictable substituent effects.     

Coarse-grained force field for the nucleosome from self-consistent multiscaling

A coarse-grained simulation model for the nucleosome is developed, using a methodology modified from previous work on the ribosome. Protein residues and DNA nucleotides are represented as beads, interacting through harmonic (for neighboring) or Morse (for nonbonded) potentials. Force-field parameters were estimated by Boltzmann inversion of the corresponding radial distribution functions obtained from a 5-ns all-atom molecular dynamics (MD) simulation, and were refined to produce agreement with the all-atom MD simulation. This self-consistent multiscale approach yields a coarse-grained model that is capable of reproducing equilibrium structural properties calculated from a 50-ns all-atom MD simulation. This coarse-grained model speeds up nucleosome simulations by a factor of 10(3) and is expected to be useful in examining biologically relevant dynamical nucleosome phenomena on the microsecond timescale and beyond.     

Bottom-up coarse-graining of a simple graphene model: the blob picture

The coarse-graining of a simple all-atom 2D microscopic model of graphene, in terms of "blobs" described by center of mass variables, is presented. The equations of motion of the coarse-grained variables take the form of dissipative particle dynamics (DPD). The coarse-grained conservative forces and the friction of the DPD model are obtained via a bottom-up procedure from molecular dynamics (MD) simulations. The separation of timescales for blobs of 24 and 96 carbon atoms is sufficiently pronounced for the Markovian assumption, inherent to the DPD model, to provide satisfactory results. In particular, the MD velocity autocorrelation function of the blobs is well reproduced by the DPD model, provided that the effect of friction and noise is taken into account. However, DPD cross-correlations between neighbor blobs show appreciable discrepancies with respect to the MD results. Possible extensions to mend these discrepancies are briefly outlined.     

A transferable coarse-grained model for hydrogen-bonding liquids

We present here a recent development of a generalized coarse-grained model for use in molecular simulations. In this model, interactions between coarse-grained particles consist of both van der Waals and explicit electrostatic components. As a result, the coarse-grained model offers the transferability that is lacked by most current effective-potential based approaches. The previous center-of-mass framework (P. A. Golubkov and P. Ren, J. Chem. Phys., 2006, 125, 64103) is generalized here to include arbitrary off-center interaction sites for both Gay-Berne and multipoles. The new model has been applied to molecular dynamic simulations of neat methanol liquid. By placing a single point multipole at the oxygen atom rather than at the center of mass of methanol, there is a significant improvement in the ability to capture hydrogen-bonding. The critical issue of transferability of the coarse-grained model is verified on methanol-water mixtures, using parameters derived from neat liquids without any modification. The mixture density and internal energy from coarse-grained molecular dynamics simulations show good agreement with experimental measurements, on a par with what has been obtained from more detailed atomic models. By mapping the dynamics trajectory from the coarse-grained simulation into the all-atom counterpart, we are able to investigate atomic-level structure and interaction. Atomic radial distribution functions of neat methanol, neat water and mixtures compare favorably to experimental measurements. Furthermore, hydrogen-bonded 6- and 7-molecule chains of water and methanol observed in the mixture are in agreement with previous atomic simulations.     

Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide

Monte Carlo simulations are presented for a coarse-grained model of real quadrupolar fluids. Molecules are represented by particles interacting with Lennard-Jones forces plus the thermally averaged quadrupole-quadrupole interaction. The properties discussed include the vapor-liquid coexistence curve, the vapor pressure along coexistence, and the surface tension. The full isotherms are also accessible over a wide range of temperatures and densities. It is shown that the critical parameters (critical temperature, density, and pressure) depend almost linearly on a quadrupolar parameter q=Q(*4)T*, where Q* is the reduced quadrupole moment of the molecule and T* the reduced temperature. The model can be applied to a variety of small quadrupolar molecules. We focus on carbon dioxide as a test case, but consider nitrogen and benzene, too. Experimental critical temperature, density, and quadrupolar moment are sufficient to fix the parameters of the model. The resulting agreement with experiments is excellent and marks a significant improvement over approaches which neglect quadrupolar effects. The same coarse-grained model was also applied in the framework of perturbation theory in the mean spherical approximation. As expected, the latter deviates from the Monte Carlo results in the critical region, but is reasonably accurate at lower temperatures.