Molecular Simulation Data Research Articles

Optimization of a thin film deposition process using a dynamic model extracted from molecular simulations

This study presents and demonstrates an algorithm for computing a dynamic model for a thin film deposition process. The proposed algorithm is used on high dimensional Kinetic Monte Carlo (KMC) simulations and consists of applying principal component analysis (PCA) for reducing the state dimension, a self organizing map (SOM) for grouping similar surface configurations and simple cell mapping (SCM) for identifying the transitions between different surface configuration groups. The error associated with this model reduction approach is characterized by running more than 1000 test simulations with highly dynamic and random input profiles. The global error, which is the normalized Euclidean distance between the simulated and predicted states, is found to be less than 1% on average relative to the test simulation results. This indicates that our reduced order dynamic model, which was developed using a rather small simulation set, was able to accurately predict the evolution of the film microstructure for much larger simulation sets and a wide range of process conditions. Minimization of the deposition time to reach a desired film structure has also been achieved using this model. Hence, our study showed that the proposed algorithm is useful for extracting dynamic models from high dimensional and noisy molecular simulation data.

Molecular Dynamics Simulation of the Escherichia coli NikR Protein: Equilibrium Conformational Fluctuations Reveal Interdomain Allosteric Communication Pathways

Escherichia coli NikR is a homotetrameric Ni 2+- and DNA-binding protein that functions as a transcriptional repressor of the NikABCDE nickel permease. The protein is composed of two distinct domains. The N-terminal 50 amino acids of each chain forms part of the dimeric ribbon–helix–helix (RHH) domains, a well-studied DNA-binding fold. The 83-residue C-terminal nickel-binding domain forms an ACT (aspartokinase, chorismate mutase, and TyrA) fold and contains the tetrameric interface. In this study, we have utilized an equilibrium molecular dynamics simulation in order to explore the conformational dynamics of the NikR tetramer and determine important residue interactions within and between the RHH and ACT domains to gain insight into the effects of Ni 2+ on DNA-binding activity. The molecular simulation data were analyzed using two different correlation measures based on fluctuations in atomic position and noncovalent contacts together with a clustering algorithm to define groups of residues with similar correlation patterns for both types of correlation measure. Based on these analyses, we have defined a series of residue interrelationships that describe an allosteric communication pathway between the Ni 2+- and DNA-binding sites, which are separated by 40 Å. Several of the residues identified by our analyses have been previously shown experimentally to be important for NikR function. An additional subset of the identified residues structurally connects the experimentally implicated residues and may help coordinate the allosteric communication between the ACT and RHH domains.

A new analytical perturbed equation of state for hard chain fluids with attractive potentials of variable range

A completely analytical perturbation theory equation of state for hard chain fluids is derived. The derived equation of state can represent the thermodynamic properties of many kinds of hard chain fluids such as the square-well chain and Yukawa chain fluid, by varying of its parameters. The predicted results are in good agreement with both the molecular simulation data and the well-known equations of state. In this paper the hard chain molecules are modelled as a pearl necklace of freely jointed spheres that interact via site–site intermolecular potential. Our first- and second-order perturbation terms are based on the Barker–Henderson local compressibility approximation and Gulati–Hall’s perturbation theory, respectively. To obtain the perturbation terms, we do not require knowledge of site–site radial distribution function of the reference hard chain fluid, which is obtained from molecular dynamic simulation, or any explicit mathematical form of it. This perturbation method yields a simple and general analytical expression for each thermodynamic property of hard chain fluids. The most important feature of this equation of state is that it has no adjustable parameters and in some regions in which there is no simulation data for such fluids, such equation may be used to predict the needed data.

Mutant bovine odorant‐binding protein: Temperature affects the protein stability and dynamics as revealed by infrared spectroscopy and molecular dynamics simulations

Bovine odorant-binding protein (bOBP), a member of the lipocalin family, presents the so-called 3D "domain-swapped" protein structure. In fact, in solution, it appears as a dimer in which each monomer is composed by the classical lipocalin fold, with a central beta-barrel followed by a stretch of residues and the alpha-helix domain protruding out of the barrel and crossing the dimer interface. Recently, a deswapped mutant form of bOBP was obtained, in which a Gly residue was inserted after position 121 and the two residues in position 64 and 156 were replaced by Cys residues for restoring the disulfide bridge common to the lipocalin family. In this work, we used Fourier transform infrared spectroscopy and molecular dynamics simulations to investigate the effect of temperature on the structural stability and conformational dynamics of the mutant bOBP. The spectroscopic and molecular simulation data pointed out that the hydrophobic regions of the protein matrix appear to be an important factor for the protein stability and integrity. In addition, it was also found that the mutant bOBP is significantly stabilized by the binding of the ligand, which may have an impact on the biological function of bOBP. The obtained results will allow for a better use of this protein as probe for the design of advanced protein-based biosensors for the detection of compounds used in the fabrication of explosive powders.

Hydrogen-bonding athermal lattice chains compared with associating hard-sphere chains

With its flexibility and simplicity in derivation, the Veytsman statistics is proved to provide a powerful tool for representing association contributions to Helmholtz free energy of lattice fluids. However, based on a heuristic argument the probability function in the statistics is in need of a critical review as to its accuracy and parameter characteristics. For these purposes different probability functions were compared with molecular simulation data of associating hard-sphere chains in this work. Association energy of lattice fluids was found to be equal to the square-well depth of off-lattice fluids. The form and parameter value for probability functions were reviewed and a new probability function was proposed for the best agreements with molecular simulation data. The proposed probability function with optimized parameter yielded the average absolute deviations of monomer fractions and compressibility factors less than 0.04 and 7%, respectively.

Equation of state for the Lennard–Jones fluid based on the perturbation theory

An easy-to-use equation of state for the Lennard–Jones fluid based on the Barker and Henderson perturbation theory is presented. The model uses the hard sphere as the reference fluid, with its properties described using the Carnahan–Starling equation of state and a shell approach to describe the radial distribution function. The contributions of first and second order terms in the perturbation series were calculated using molecular simulation and are compared with the proposed EoS. The equation presented is in good agreement with the molecular simulation data for the pressure and internal energy of the Lennard–Jones fluid. As the equation is based on the perturbation theory it over predicts the critical temperature found from molecular simulation.

Virial Coefficients of Polarizable Water: Applications to Thermodynamic Properties and Molecular Clustering

We determine the second and third virial coefficients B2 and B3 for the Gaussian charge polarizable model (GCPM) as a function of temperature over the range 210−723 K. The overlap sampling implementation of Mayer sampling molecular simulation is applied to calculate the values, obtaining results to a precision that ranges from 0.1% for B2 to an average of 1% for B3. These calculated values compare very well with known values of B2 and B3 for real water and outperform both pairwise models and other polarizable models in describing experimental virial-coefficient data. We examine these coefficients in the context of the equation of state and molecular clustering. Comparisons are made to established molecular simulation data, quantum chemical calculations, and experimental data for real water. Under both saturated-vapor and supercritical conditions, the virial series up to B3 describes the equation of state quite well. The virial coefficients are used to characterize molecular clusters (dimers and trimers) in GCPM water under supercritical, saturated vapor, and atmospheric conditions between 210−673 K. The analysis shows that the extent of clustering in polarizable water is diminished relative to that from a pairwise water model.

Higher-Order Virial Coefficients of Water Models

We use the Mayer sampling method, with both direct and overlap sampling, to calculate and compare classical virial coefficients up to B6 for various water models (SPC, SPC/E, MSPC/E, TIP3P, and TIP4P). The precision of the computed values ranges from 0.1% for B2 to an average of 25% for B6. When expressed in a form scaled by the critical properties, the values of the coefficients for SPC water are observed to greatly exceed the magnitude of corresponding coefficients for the simple Lennard-Jones model. We examine the coefficients in the context of the equation of state and the Joule-Thomson coefficient. Comparisons of these properties are made both to established molecular simulation data for each respective model and to real water. For all models, the virial series up to B5 describes the equation of state along the saturated vapor line better than the series that includes B6. At supercritical temperatures, however, the sixth-order series often describes pressure-volume-temperature behavior better than the fifth-order series. For example, the sixth-order virial equation of state for SPC/E water predicts the 673 K isotherm within 8% of published molecular simulation values up to a density of 9 mol/L (roughly half the critical density of SPC/E water).

How short-range attractions impact the structural order, self-diffusivity, and viscosity of a fluid

We present molecular simulation data for viscosity, self-diffusivity, and the local structural ordering of (i) a hard-sphere fluid and (ii) a square-well fluid with short-range attractions. The latter fluid exhibits a region of dynamic anomalies in its phase diagram, where its mobility increases upon isochoric cooling, which is found to be a subset of a larger region of structural anomalies, in which its pair correlations strengthen upon isochoric heating. This "cascade of anomalies" qualitatively resembles that found in recent simulations of liquid water. The results for the hard-sphere and square-well systems also show that the breakdown of the Stokes-Einstein relation upon supercooling occurs for conditions where viscosity and self-diffusivity develop different couplings to the degree of pairwise structural ordering of the liquid. We discuss how these couplings reflect dynamic heterogeneities. Finally, we note that the simulation data suggest how repulsive and attractive glasses may generally be characterized by two distinct levels of short-range structural order.

Improved estimation of ligand–macromolecule binding affinities by linear response approach using a combination of multi-mode MD simulation and QM/MM methods

Structure-based predictions of binding affinities of ligands binding to proteins by coordination bonds with transition metals, covalent bonds, and bonds involving charge re-distributions are hindered by the absence of proper force fields. This shortcoming affects all methods which use force-field-based molecular simulation data on complex formation for affinity predictions. One of the most frequently used methods in this category is the Linear Response (LR) approach of Aquist, correlating binding affinities with van der Waals and electrostatic energies, as extended by Jorgensen's inclusion of solvent-accessible surface areas. All these terms represent the differences, upon binding, in the ensemble averages of pertinent quantities, obtained from molecular dynamics (MD) or Monte Carlo simulations of the complex and of single components. Here we report a modification of the LR approach by: (1) the replacement of the two energy terms through the single-point QM/MM energy of the time-averaged complex structure from an MD simulation; and (2) a rigorous consideration of multiple modes (mm) of binding. The first extension alleviates the force-field related problems, while the second extension deals with the ligands exhibiting large-scale motions in the course of an MD simulation. The second modification results in the correlation equation that is nonlinear in optimized coefficients, but does not lead to an increase in the number of optimized coefficients. The application of the resulting mm QM/MM LR approach to the inhibition of zinc-dependent gelatinase B (matrix metalloproteinase 9) by 28 hydroxamate ligands indicates a significant improvement of descriptive and predictive abilities.

Athermal lattice chains compared with hard-sphere chains

The Guggenheim–Huggins–Miller approximation of athermal lattice fluids has been a basis for lattice fluid equations of state. For better understanding of GHM solution, it was compared with molecular simulation data of hard-sphere chains. Relations were developed between parameters of lattice and off-lattice chain fluids for the comparison. The Guggenheim–Huggins–Miller approximation was found in good agreements with molecular simulation data of fused-hard-spheres when compared using the developed relations. But the agreements of GHM solution with tangent-hard-sphere chain data were found less satisfactory and deviations increased as segment number increased. Average deviations of GHM solution from mixed tangent-hard-sphere chain data were found similar to those of pure components. Real fluid parameters fitted to a GHM-based lattice fluid equation of state and the first order thermodynamic perturbation theory-based SAFT were found optimized to give similar repulsive contributions.

Description of self-diffusion coefficients of gases, liquids and fluids at high pressure based on molecular simulation data

The purpose of this work is to evaluate the potential of modeling the self-diffusion coefficient (SDC) of real fluids in all fluid states based on Lennard–Jones analytical relationships involving the SDC, the temperature, the density and the pressure. For that, we generated an equation of state (EOS) that interrelates the self-diffusion coefficient, the temperature and the density of the Lennard–Jones (LJ) fluid. We fit the parameters of such LJ–SDC–EOS using recent wide ranging molecular simulation data for the LJ fluid. We also used in this work a LJ pressure–density–temperature EOS that we combined with the LJ–SDC–EOS to make possible the calculation of LJ–SDC values from given temperature and pressure. Both EOSs are written in terms of LJ dimensionless variables, which are defined in terms of the LJ parameters ɛ and σ. These parameters are meaningful at molecular level. By combining both EOSs, we generated LJ corresponding states charts which make possible to conclude that the LJ fluid captures the observed behavioral patterns of the self-diffusion coefficient of real fluids over a wide range of conditions. In this work, we also performed predictions of the SDC of real fluids in all fluid states. For that, we assumed that a given real fluid behaves as a Lennard–Jones fluid which exactly matches the experimental critical temperature T c and the experimental critical pressure P c of the real fluid. Such an assumption implies average true prediction errors of the order of 10% for vapors, light supercritical fluids, some dense supercritical fluids and some liquids. These results make possible to conclude that it is worthwhile to use the LJ fluid reference as a basis to model the self-diffusion coefficient of real fluids, over a wide range of conditions, without resorting to non-LJ correlations for the density–temperature–pressure relationship. The database considered here contains more than 1000 experimental data points. The database practical reduced temperature range is from 0.53 to 2.4, and the practical reduced pressure range is from 0 to 68.4.

Gas-Phase Molecular Clustering of TIP4P and SPC/E Water Models from Higher-Order Virial Coefficients

Higher-order virial coefficients (up to B6) for TIP4P and SPC/E water models are used to characterize molecular clusters (up to hexamers) formed by water at various gas-phase thermodynamic state points between 298 and 773 K. Comparison of cluster statistics with available molecular simulation data for the same models indicates that the virial approach is effective at characterizing the clustering behavior. Significant deviations from experimentally confirmed ab initio results from the literature at 298 K are ascribed to inadequacies in the TIP4P model and to differences in the treatment of “physical” versus “chemical” association in the two approaches. At two conditions where an analysis could be made, the concentration of clusters that are only physically associated was found to be ∼30% of the concentration of those that are chemically associated (hydrogen bonded).

Developing predictive models for polycyanurates through a comparative study of molecular simulation and empirical thermo-mechanical data

Using a parameter set (RDA-DR2.21_Inv) previously published by our group, both the atom-to-atom connectivities and geometries and the physical and mechanical properties of poly[bis-4-(4-cyanatophenoxy)phenyl sulphone] have been simulated with remarkable accuracy. Molecular dynamics simulation, carried out on the polymer structure at a variety of experimental temperatures, yields a transition temperature of ca. 510–520 K, which can be equated with the empirical glass transition temperature ( T g) for the polycyanurate. The same dicyanate was prepared experimentally and characterised using dynamic mechanical analysis (yielding an empirical T g of ca. 519 K) and thermo-mechanical analysis (yielding an empirical T g of 508–528 K). The effect of incomplete cure of the monomer or development of structural defects in the network on the thermo-mechanical properties is also examined using molecular simulation.

Thermodynamic modeling of melts in the system Na 2O-NaAlO 2-SiO 2-F 2O −1

Fluorine is a common volatile element in magmatic-hydrothermal systems, but its solution mechanisms and thermodynamic description in highly polymerized silicate melts are poorly known. We have developed a thermodynamic model for fluorosilicate liquids that links experimentally determined phase equilibria and spectroscopic information on melt structure. The model is applicable to crystallization of fluoride minerals, fluoride-silicate immiscibility in natural felsic melts, and metallurgical processes. Configurational properties of fluorosilicate melts are described by mixing on three site levels (sublattices): (1) alkali fluoride, polyhedral aluminofluoride and silicofluoride species and nonbridging terminations of the aluminosilicate network, (2) alkali-aluminate and silicate tetrahedra within the network and (3) bridging oxygen, nonbridging oxygen and terminal fluorine atoms on tetrahedral apices of the network. Abundances of individual chemical species are described by a homogeneous equilibrium representing melt depolymerization: F − (free) + O 0 (bridging) = F 0 (terminal) + O − (nonbridging) which corresponds to a replacement of an oxygen bridging two tetrahedra by a pair of terminations, one with F and the other with an O and a charge-balancing Na. In cryolite-bearing systems two additional interaction mechanisms occur: (1) the self-dissociation of octahedral aluminofluoride complexes: [AlF 6] = [AlF 4] + 2 [F], and (2) the short-range order between (O,F)-corners and (Si,NaAl)-centers of tetrahedra: Si-O-Si + 2 [NaAl]-F = [NaAl]-O-[NaAl] + 2 Si-F. Portrayal of these equilibria in ternary Thompson reaction space allows for the decrease in the number of interaction mechanisms by linearly combining melt depolymerization with tetrahedral short-range order. In this formulation, the nonideal thermodynamic properties are represented by reaction energies of homogeneous equilibria, thus defining directly individual chemical species concentrations and configurational properties. Thermodynamic expressions for the activity-composition relationships are simplified if all entities are expressed using symbolic molecular notation (e.g., SiO 2, SiF 4, [NaAl]O 2, [NaAl]F 4, NaF etc.) with corresponding nonfractional site multiplicities (1, 2 or 4). The model has been applied to three subsystems of the Na 2O-NaAlO 2-SiO 2-F 2O −1 compositional space. Activity-composition relationships in the villiaumite-sodium silicate binaries require clustering of silicate tetrahedra and only negligible interaction between fluoride species and silicate polymer. Phase equilibria in the cryolite-albite system with a large depression of albite liquidus are interpreted via complete substitution of O 0 by O − and F 0 in the silicate framework. With increasing fluorine content, initial Al-F and Si-O short-range order evolves into the partial O-F disorder. The present model provides a useful relationship between experimental equilibria, macroscopic thermodynamics and melt speciation, thus it facilitates comparisons with, and interpretations of, spectroscopic and molecular simulation data.

An equation‐of‐state contribution for polar components: Dipolar molecules

AbstractAccounting for dipolar interactions in a physically based equation of state (EOS) can substantially improve the modeling of phase equilibria of real mixtures. An EOS contribution for dipolar interactions of nonspherical molecules is developed based on a third‐order perturbation theory. Molecular simulation data for vapor–liquid equilibria of the two‐center Lennard–Jones (2CLJ) plus pointdipole fluid is used to determine model constants of the EOS. The resulting model is compared to simulation data of pure dipolar nonspherical molecules and their mixtures and an excellent agreement is found. The proposed dipole term is applied to real substances with the perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS and it is confirmed that accounting for dipolar interactions not only reduces the binary interaction parameter, but also improves the description of pure component and mixture phase equilibria. Literature values for the dipole moment can thereby be used and no further dipole‐related pure component parameter has to be adjusted. This constitutes an advantage over earlier approaches, where dipole‐related parameters were fitted to pure component data or to mixture data. © 2005 American Institute of Chemical Engineers AIChE J, 2006

Comparison of different cubic equations of state and combination rules for predicting residual chemical potential of binary and ternary Lennard–Jones mixtures: Solid-supercritical fluid phase equilibria

Molecular simulation data of binary and ternary mixtures were used to study the capability of cubic equations of state (CEOS), Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), and Peng–Robinson (PR), to predict the residual chemical potential of a heavy solid compound in a supercritical fluid when molecules interact each other with a simple Lennard–Jones (LJ) potential. The chemical potential of the solid compound is calculated directly from the Lennard–Jones parameters of the involved molecules. It was found that if appropriate combination rules are used, van der Waals one fluid theory (vdW-1f) allows CEOS to reproduce accurately the molecular simulation data without any adjustable parameter, even if asymmetries in molecular size and energy are considerable. For the supercritical binary systems analyzed in this work, it was observed that the relation of the parameters of energy influences more the performance of vdW-1f theory (and as a consequence the performance of the CEOS), than the relation of the parameters of size.

Viscosity of pure supercritical fluids

In this work, we propose a model for representing the viscosity of supercritical pure fluids over a wide range of conditions. A given pure real fluid is represented as a Lennard–Jones (LJ) fluid having effective values of the LJ intermolecular potential parameters. The LJ fluid is actually a corresponding states fluid where the dimensionless variables have, as a distinguishing feature, a dependency on parameters meaningful at molecular level. We have paid special attention to the qualitative behavior of the model when used beyond the conditions of the supporting molecular LJ simulation data. The model is able to correlate the pure compound viscosity of real supercritical fluids over a wide range of conditions with average absolute-value relative deviations less than or equal to 7% in most cases. The correlation needs two adjustable parameters per pure compound.

A modified free-volume-based model for predicting vapor–liquid and solid–liquid equilibria for size asymmetric systems

The main purpose of this work is to present a free-volume combinatorial term in predicting vapor–liquid equilibrium (VLE) and solid–liquid equilibrium (SLE) of polymer/solvent and light and heavy hydrocarbon/hydrocarbon mixtures. The proposed term is based on a modification of the original Freed Flory–Huggins model, replacing the molar volume with a free-volume (FV) term. Using an extensive database for athermal polymer solutions at finite dilution, the single parameter of the model has been well adjusted. The results obtained from the model proposed in this work were favorably compared with those obtained from the well-established entropic-FV based models, i.e., the original entropic-FV (EFV) and the modified entropic-FV (MEFV) models. The results were also compared with those of the original UNIFAC-FV model as well as a modified UNIFAC-FV model, Kannan-FV, recently proposed model by Kannan et al. The results obtained from the proposed model showed that better improvement can be attained for the polymer systems with energetic interactions as well as for VLE and SLE study of heavy alkane solutes in light alkane solvents. This observation can be further verified by comparison of the results obtained from the proposed model with those of the molecular simulation data.

An equation‐of‐state contribution for polar components: Quadrupolar molecules

AbstractAn equation‐of‐state (EOS) contribution for quadrupolar interactions is developed based on a third‐order perturbation theory. Model constants are adjusted to comprehensive molecular simulation data for vapor–liquid equilibria of the two‐center Lennard–Jones (2CLJ) plus pointquadrupole fluid from the literature. Molecular elongations L* from 0 (spherical) to 0.8 are covered by the simulation data. The EOS is suited for both, the 2CLJ fluid and the tangent‐sphere Lennard–Jones framework. It is applied to pure components and mixtures of real substances with the perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. It is possible to use tabulated values of quadrupolar moments (independently determined) directly in the EOS, so that no additional pure component parameter is introduced. Compared with the case where quadrupolar interactions are not specifically accounted for, the proposed model gives a systematic improvement of pure component properties and of mixture phase equilibria of strong quadrupolar components, such as carbon dioxide, and the absolute value of the required binary interaction parameter is significantly reduced. © 2005 American Institute of Chemical Engineers AIChE J, 2005