J. Ilja Siepmann, Fellow

Simulating Complex Chemical Systems

Ternary phase diagram for CO2/N2/propane at 270 K and 60 bar. Squares and diamonds depict the experimental data (Yucelen and Kidnay, J. Chem. Eng. Data, 44, 926 [1999]) and the simulation data for the TraPPE-EH force field, respectively.

The efforts of this research group were driven by the desire to learn about complex chemical systems on the microscopic level and to predict accurate thermodynamic data for these systems. The research performed by the group helped in the understanding of how molecular architecture and composition influence structure, phase behavior, and function of the resulting complex systems. The main research tool of this group is particle-based computer simulation, and the in-house development of efficient simulation algorithms and transferable force fields allows this group to address complex chemical systems, which are not amenable to conventional simulation approaches and for which experimental data are not readily accessible.

Algorithm Development—This group proceeded on the development of three novel Monte Carlo algorithms that target the efficient sampling polymer systems, strongly associating fluids, and polarizable force fields. First, the self-adapting fixed-endpoint configurational- bias Monte Carlo (SAFE-CBMC) method enabled this group to carry out conformational changes for interior segments of chain molecules with strong intramolecular interactions. This CBMC method allowed for the efficient simulation of cyclic alkanes (or other ring structures), and was also instrumental for the sampling of polymeric molecules (with more than, for example, 20 repeat units) where conventional CBMC would allow only for conformational changes close to the chain ends.

Second, the aggregation volume bias Monte Carlo (AVBMC) method greatly increased the sampling efficiency for strongly associating fluids. These fluids exhibit large deviations from the ideal-gas or ideal-solution behavior and pose a special challenge for molecular simulation because aggregate formation leads to traps in phase space, i.e., configurations that have a very large Boltzmann weight associated with the large favorable energies of cluster formation. However, these “bonded” configurations represent only a small fraction of the total phase space compared to the large amount of non-bonded configurations.

Third, the adiabatic nuclear and electronic sampling Monte Carlo (ANES-MC) method allows simulations using polarizable force fields. In close analogy to the revolutionary Car-Parrinello molecular dynamics method, the ANES-MC algorithm for polarizable force fields treats the molecular charge distributions as additional variables. While the Car- Parrinello molecular dynamics method is able to exploit an extended Lagrangian formalism and benefits from the faster motion of the electronic degrees of freedom, the ANES-MC algorithm allows for the sampling of nuclear and electronic degrees of freedom with different temperatures by sandwiching a sequence of electronic moves in between the nuclear trial displacement.

Force Field Development—The success of molecular simulation in predicting thermophysical properties depends on the availability of accurate force fields. This group made progress in the devlopment of a multi-level force field, called “transferable potentials for phase equilibria” (TraPPE). The first-level force field, TraPPE-UA (united atom), employs the united-atom representation for alkyl segments and simple Lennard-Jones and Coulombic terms. In the second level, TraPPE-EH (explicit hydrogen), all atoms including alkyl group hydrogens and some lone-pair electron and bond-center sites are treated explicitly. In the third-level, TraPPEpol (polarizable), both the van der Waals and electrostatic interactions can respond to changes in the environment. Whereas the first level is designed for simplicity and computational efficiency with good accuracy, the second level is aimed at improved accuracy for mixtures of non-polar or apolar non-hydrogenbonding compounds. The third level is directed solely at the highest possible level of accuracy and transferability.

Extensions were made to the TraPPE force fields as follows. TraPPE-UA models for alkenes, aromatics, alcohols, ethers, ketones, and aldehydes; TraPPE-EH model for dinitrogen, carbon dioxide, and linear alkanes (see figure); and TraPPE-pol models for water.

Applications—This group investigated the binary mixture of n-heptane and supercritical ethane. Pressure-composition and temperaturecomposition phase diagrams were computed using four different molecular models of increasing complexity. In the supercritical phase, preferential solvation of heptane by ethane is not observed. Analysis of the contributions of the liquid and the supercritical phase to the decrease of the Gibbs free energy of transfer of heptane with increasing pressure suggest that the enhanced solubility of heptane in high-pressure supercritical ethane can be attributed to two causes of roughly equal importance: “pulling” of heptane into the supercritical phase by an increased density of ethane that acts as a non-specific solvent, and “pushing” heptane out of the liquid phase by an increased concentration of ethane.

Octanol-water partition coefficients are extraordinarily successful for correlating and predicting numerous processes of pharmacological and environmental importance. However, the structural details of the octanol phase, and the reason why this phase can mimic the complexities of many different environments ranging from biomembranes to soil, are controversial. This group investigated the partitioning of normal alkane and primary alcohol solutes between water and (dry or wet) 1- octanol phases using the OPLS-UA and TraPPE-UA force fields. It was found that the TraPPE-UA model yields superior results (e.g., a dramatic increase in the mutual solubility of water in octanol). Comparison of the partitioning between a helium vapor phase and dry and wet 1-octanol established that water saturation affects mostly the partitioning of polar solutes, while differences for alkane partitioning were found to be negligible. Analysis of the microscopic- level structure of the wet 1-octanol phase shows preferential partitioning of short alcohols (methanol and ethanol) into the waterrich regions of the microheterogeneous solvent mixture, whereas 1-butanol solutes are found preferentially at the boundary of hydrogenbonded clusters. These simulations demonstrate that a diverse spectrum of hydrogenbonded aggregates exists in neat and wet 1- octanol, and that water saturation substantially alters the 1-octanol environment. The simulation results are able to reconcile the conflicting views of the 1-octanol structure inferred from thermodynamic arguments, spectroscopic measurements, and diffraction experiments.

Configurational-bias Monte Carlo simulations in the grand canonical ensemble with histogram reweighting were used to determine the vapor-liquid coexistence curves and critical parameters for a few linear and branched alkanes physisorbed on a flat gold substrate. Examination of the critical ordering operator distributions confirms that these systems exhibit critical behavior consistent with the twodimensional Ising universality class. It was shown that a principle of corresponding states does not hold true between bulk fluids and adsorbed monolayers. The ratio of the twodimensional to three-dimensional critical temperatures was found to decrease with chain length for n-alkanes (from about 0.38 for methane to 0.30 for n-hexane). In contrast to typical bulk fluid behavior, the branched isomers were found to have higher critical temperatures than their linear counterparts.

Gas-liquid and reversed-phase liquid chromatography are the principal methods for the analysis and separation of organic and pharmaceutical molecules. Due to the complexity of chromatographic systems and the lack of microscopic-level information, however, many fundamental questions on the retention mechanisms remain unanswered. Accurate predictions of retention times, retention indices, and partition constants are a long sought-after goal for theoretical studies in chromatography. This group studied the retention of linear and branched alkanes and of alkylbenzenes in helium- squalane gas-liquid chromatography. Configurational-bias Monte Carlo (CBMC) simulations in the Gibbs ensemble using the TraPPE-UA force field were carried out to obtain a microscopic picture of the partitioning of 10 alkane isomers and of benzene, toluene, o-, m-, and p-xylene between a helium vapor phase and a squalane liquid phase, a prototypical gas-liquid chromatography system. The alkane solutes include some topological isomers that differ only in the arrangement of their building blocks (e.g., 2,5-dimethylhexane and 3,4-dimethylhexane or the xylene isomers), for which the prediction of the retention order is particularly difficult. The Kovats retention indices, a measure of the relative retention times, were calculated directly from the partition constants and are in good agreement with experimental values. The calculated Gibbs free energies of transfer for the normal alkanes were shown to conform to Martin’s equation, which is the basis of linear free energy relationships used in many process modeling packages. Analysis of radial distribution functions and the corresponding energy integrals did not yield evidence for specific retention structures and showed that the internal energy of solvation is not the main driving force for the separation of topological isomers. This work was highlighted in “Analytical Currents” (Analytical Chemistry, p. 185 A [March 1, 2000]) and described in terms of climbing “the Mt. Everest of separation science.”

Research Group and Collaborators

Bin Chen, Graduate Student Researcher
Dylan Drake-Wilhelm, Undergraduate Student Researcher
Rebecca M. Eden, Undergraduate Student Researcher
Brandon Hoekstra, Undergraduate Student Researcher
Junseok Lee, Graduate Student Researcher
Martin Marcus, Graduate Student Researcher
Kristi McDonald, Undergraduate Student Researcher
Jeffrey J. Potoff, Supercomputing Institute Research Scholar
John M. Stubbs, Graduate Student Researcher
Li Sun, Graduate Student Researcher
Collin D. Wick, Graduate Student Researcher (DOE Computational Science Graduate Fellow)
Ling Zhang, Graduate Student Researcher
Xin (Sophia) Zhao, Graduate Student Researcher
Nikolaj D. Zhuravlev, Graduate Student Researcher