An improved statistical analysis for predicting the critical temperature and critical density with Gibbs ensemble Monte Carlo simulation.

A rigorous statistical analysis is presented for Gibbs ensemble Monte Carlo simulations. This analysis reduces the uncertainty in the critical point estimate when compared with traditional methods found in the literature. Two different improvements are recommended due to the following results. First, the traditional propagation of error approach for estimating the standard deviations used in regression improperly weighs the terms in the objective function due to the inherent interdependence of the vapor and liquid densities. For this reason, an error model is developed to predict the standard deviations. Second, and most importantly, a rigorous algorithm for nonlinear regression is compared to the traditional approach of linearizing the equations and propagating the error in the slope and the intercept. The traditional regression approach can yield nonphysical confidence intervals for the critical constants. By contrast, the rigorous algorithm restricts the confidence regions to values that are physically sensible. To demonstrate the effect of these conclusions, a case study is performed to enhance the reliability of molecular simulations to resolve the n-alkane family trend for the critical temperature and critical density.

The use of two-phase molecular dynamics simulations to determine the phase behavior and critical point of propane molecular models.

Molecular dynamics simulations were performed to determine two-phase configurations of model propane molecules below the critical point and in the near-critical, two-phase region. A postprocessor that uses a Monte Carlo method for determination of volumes attributable to each molecule was used to obtain density histograms of the particles from which the bulk coexisting equilibrium vapor and liquid densities were determined. This method of analyzing coexisting densities in a two-phase simulation is straightforward and can be easily implemented for complex, multisite models. Various degrees of internal flexibility in the propane models have little effect on the coexisting densities at temperatures 40 K or more below the critical point, but internal flexibility (angle bending and bond vibrations) does affect the saturated liquid densities in the near-critical region, changing the critical temperature by approximately 20 K. Shorter cutoffs were also found to affect the phase dome and the location of the critical point.

Transient molecular dynamics simulations of liquid viscosity for nonpolar and polar fluids.

A transient molecular dynamics (TMD) method for obtaining fluid viscosity is extended to multisite, force-field models of both nonpolar and polar liquids. The method overlays a sinusoidal velocity profile over the peculiar particle velocities and then records the transient decay of the velocity profile. The viscosity is obtained by regression of the solution of the momentum equation with an appropriate constitutive equation and initial and boundary conditions corresponding to those used in the simulation. The transient velocity decays observed appeared to include both relaxation and retardation effects. The Jeffreys viscoelastic model was found to model accurately the transient responses obtained for multisite models for n-butane, isobutane, n-hexane, water, methanol, and 1-hexanol. TMD viscosities obtained for saturated liquids over a wide range of densities agreed well for the polar fluids, both with nonequilibrium molecular dynamics (NEMD) results using the same force-field models and with correlations based on experimental data. Viscosities obtained for the nonpolar fluids agreed well with the experimental and NEMD results at low to moderate densities, but underpredicted experimental values at higher densities where shear-thinning effects and viscous heating may impact the TMD simulations.

Critical and phase-equilibrium properties of an ab initio based potential model of methanol and 1-propanol using two-phase molecular dynamics simulations.

Two-phase molecular dynamics simulations employing a Monte Carlo volume sampling method were performed using an ab initio based force field model parameterized to reproduce quantum-mechanical dimer energies for methanol and 1-propanol at temperatures approaching the critical temperature. The intermolecular potential models were used to obtain the binodal vapor-liquid phase dome at temperatures to within about 10 K of the critical temperature. The efficacy of two all-atom, site-site pair potential models, developed solely from the energy landscape obtained from high-level ab initio pair interactions, was tested for the first time. The first model was regressed from the ab initio landscape without point charges using a modified Morse potential to model the complete interactions; the second model included point charges to separate Coulombic and dispersion interactions. Both models produced equivalent phase domes and critical loci. The model results for the critical temperature, density, and pressure, in addition to the sub-critical equilibrium vapor and liquid densities and vapor pressures, are compared to experimental data. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here.

Ab initio study on adsorption of hydrated Na+ and Cu+ cations on the Cu(111) surface.

The interactions of Na+ and Cu+ cations with a Cu(111) surface in the presence and absence of water molecules were investigated using cluster models and ab initio methods. Adsorption in aqueous solution was modeled with one to five water molecules around the adsorbing cation. The Cu surface was described with Cu10 and Cu18 cluster models and the computational method was MP2/RECP/6-31+G. The effect of the basis set superposition error (BSSE) was taken into account with counterpoise (CP) correction, and the accuracy of HF-level results was examined. The interactions between Na+ and the Cu surface were found to be primarily electrostatic, and the energy differences among the different adsorption sites were small. The largest CP-corrected MP2 adsorption energy for the Cu18 cluster was -188 kJ/mol. When water molecules were added around it, Na+ receded from the Cu surface and finally was surrounded totally by the water molecules. The interactions between Cu+ and the Cu surface were dominated by orbital interactions, and Cu+ preferred to adsorb on sites where it could bind to more than one surface atom. The largest CP-corrected MP2 adsorption energy for the Cu18 cluster was -447 kJ/mol. Adding water molecules around it did not cause Cu+ to draw away from the surface, but instead the water molecules began to form hydrogen bonds with one another. The magnitude of BSSE was substantial in most cases. CP corrections did not, however, have a significant impact on the relative trends among the interaction energies.

MPSA effects on copper electrodeposition investigated by molecular dynamics simulations.

In superconformal filling of copper-chip interconnects, organic additives are used to fill high-aspect-ratio trenches or vias from the bottom up. In this study we report on the development of intermolecular potentials and use molecular dynamics simulations to provide insight into the molecular function of an organic additive (3-mercaptopropanesulfonic acid or MPSA) important in superconformal electrodeposition. We also investigate how the presence of sodium chloride affects the surface adsorption and surface action of MPSA as well as the charge distribution in the system. We find that NaCl addition decreases the adsorption strength of MPSA at a simulated copper surface and attenuates the copper-ion association with MPSA. The model also was used to simulate induced-charge effects and adsorption on a nonplanar electrode surface.

Transient molecular dynamics simulations of viscosity for simple fluids.

A transient molecular dynamics (TMD) method has been developed for simulation of fluid viscosity. In this method a sinusoidal velocity profile is instantaneously overlaid onto equilibrated molecular velocities, and the subsequent decay of that velocity profile is observed. The viscosity is obtained by matching in a least-squares sense the analytical solution of the corresponding momentum transport boundary-value problem to the simulated decay of the initial velocity profile. The method was benchmarked by comparing results obtained from the TMD method for a Lennard-Jones fluid with those previously obtained using equilibrium molecular dynamics (EMD) simulations. Two different constitutive models were used in the macroscopic equations to relate the shear rate to the stress. Results using a Newtonian fluid model agree with EMD results at moderate densities but exhibit an increasingly positive error with increasing density at high densities. With the initial velocity profiles used in this study, simulated transient velocities displayed clear viscoelastic behavior at dimensionless densities above 0.7. However, the use of a linear viscoelastic model reproduces the simulated transient velocity behavior well and removes the high-density bias observed in the results obtained under the assumption of Newtonian behavior. The viscosity values obtained using the viscoelastic model are in excellent agreement with the EMD results over virtually the entire fluid domain. For simplicity, the Newtonian fluid model can be used at lower densities and the viscoelastic model at higher densities; the two models give equivalent results at intermediate densities.

Potential energy surfaces for small alcohol dimers. II. Propanol, isopropanol, t-butanol, and sec-butanol.

Potential energy landscapes for homogeneous dimers of propanol, isopropanol, tert-butanol, and sec-butanol were obtained using 735 counterpoise-corrected energies at the MP2/6-311+G(2df,2pd) level. The landscapes were sampled at 15 dimer separation distances for different relative monomer geometries, or routes, given in terms of the yaw, pitch, and roll of one monomer relative to the other and the spherical angles between the two monomer centers (taken as the C atom attached to the O). The resultant individual energy surfaces and their complex topographies were also regressed using a site-site pair potential model using a modified Morse potential that provides a mathematically simple representation of the landscapes suitable for use in molecular simulations. Generalized Morse parameters were also obtained for this model from a composite regression of these energy landscapes and those previously reported for methanol and ethanol. The quality of fit for all these energy landscapes suggests that these site parameters have transferability for possible use on other alcohols.

Potential energy surfaces for small alcohol dimers I: methanol and ethanol.

Potential energy landscapes for homogeneous dimers of methanol and ethanol were calculated using counterpoise (CP) corrected energies at the MP26-311+G(2df,2pd) level. The landscapes were sampled at approximately 15 dimer separation distances for different relative monomer geometries, or routes, given in terms of a relative monomer yaw, pitch, and roll and the spherical angles between the monomer centers (taken as the C atom attached to the O). The 19 different routes studied for methanol and the 22 routes examined for ethanol include 607 CP corrected energies. Both landscapes can be adequately represented by site-site, pairwise-additive models, suitable for use in molecular simulations. A modified Morse potential is used for the individual pair interactions either with or without point charges to represent the monomer charge distribution. A slightly better representation of the methanol landscape is obtained using point charges, while the potential energy landscape of ethanol is slightly better without point charges. This latter representation may be computationally advantageous for molecular simulations because it avoids difficulties associated with long-range effects of point-charge-type models.

Quantum chemical interaction energy surfaces of ethylene and propene dimers.

Ab initio studies of nonbonding interactions for ethylene and propene dimers were conducted at the MP2/6-311+G(2df,2pd) level. The dimers were attractive in all of the orientations studied; however, the attraction was <0.1 kcal/mol for ethylene D2h and C2h dimers, for which the pi-electron clouds or H atoms interact closely. A previously introduced transferable potential model, NIPE [Jalkanen, J.-P.; Pakkanen, T. A.; Yang, Y.; Rowley, R. L. J. Chem. Phys. 2003, 118, 5474], which is based on quantum chemical calculations of small alkane molecules, was tested against the propene and ethylene dimer data. Comparisons of results showed that interaction energies for orientations dominated by interactions between the propene methyl groups or two hydrogens were accurately predicted with the NIPE model. Interactions involving the double bond were not predicted as well, because the original NIPE regression data set did not contain any information about pi-electron systems. An extension of the NIPE model to include pi-electron interactions is proposed. Additional interaction sites are used with the same energy function as atomic interactions. This addition provides a more accurate description of the interaction energies of both ethylene and propene and extends the transferability of the NIPE model to alkenes.

Mapping the interaction energy surfaces of cyclic alkanes: evaluating the transferability of an ab initio based potential model.

Detailed interaction energy maps are computed for symmetric cyclopropane and tetrahedrane dimer systems using ab initio methods. Interaction energies of cubane and cyclohexane dimers are also reported. The global minimum energy structures of cyclopropane and tetrahedrane systems are both D(3d) structures with energies of -1.850 and -2.171 kcal mol(-1). The ability of NIPE potential model, based on ab initio nonbonding data of neopentane (N), isobutane (I), propane (P), ethane (E) and all their combinations to predict the pair interaction energies of these strained cyclic hydrocarbons is also investigated. The difference between the energies predicted by NIPE and those obtained from the ab initio calculations increases with ring strain In general, NIPE values are in close agreement with the ab initio results for alkane ring structures having low ring strain.

Molecular-dynamics simulation of the effect of ions on a liquid-liquid interface for a partially miscible mixture.

Molecular-dynamics simulations were performed to model the effect of added salt ions on the liquid-liquid interface in a partially miscible system. Simulations of the interface between saturated phases of a model 1-hexanol+water system show a bilayer structure of 1-hexanol molecules at the interface with -OH heads of the first layer directed into the water phase and the opposite orientation for the second layer. The alignment of the polar -OH groups at the interface stabilizes a charge separation of sodium and chloride ions when salt is introduced into the aqueous phase, producing an electrical double layer. Chloride ions aggregate nearer the interface and sodium ions move toward the bulk water phase, consistent with the explanation that the -OH alignment presents a region of partial positive charges to which the hydrated chloride atoms are attracted. Ions near the interface were found to be less solvated than those in the bulk phase. An electric field was also applied to drive ions through the interface. Ions crossing the interface tended to shed water molecules as they entered the hexanol bilayer, leaving a trail of water molecules. Stabilization and facilitated transport of the ion by interactions with the second layer of hexanol molecules appeared to be an important step in the mechanism of sodium ion transport.