Transferable Potentials for Phase Equilibria

About the TraPPE Force Field

The Transferable Potentials for Phase Equilibria family of force fields is a collection of functional forms and interaction parameters useful for modeling complex chemical systems with molecular mechanics simulation techniques. TraPPE maintains a high degree of accuracy in the prediction of thermophysical properties when applied to a range of different compounds, different state points, different compositions, and different properties. This makes TraPPE one of the few force fields generally suitable for materials and industrial applications.

The development of TraPPE models prioritizes transferability (maximizing the ability to build new chemical compounds by minimizing the number of (pseudo-) atoms needed) and accuracy (quantitative prediction of phase equilibria and other thermophysical properties over a wide range of physical conditions). Starting with “bonded” 1–2 (bond length), 1–3 (bond angle) and 1–4 (dihedral angle) interactions, TraPPE relies on experimental data or electronic structure calculations to provide equilibrium bond lengths and angles, the corresponding force constants, and the dihedral potentials for new models. For nonbonded interactions, parameters for representative simple molecules are found by empirical fitting procedures that reproduce experimental phase equilibrium data, typically the vapor-liquid coexistence curve (VLCC) but also binary mixtures and vapor-solid equilibria. Fitting to phase equilibrium data provides accurate benchmarks against multiple phases, temperatures, and densities. Transferability between compounds is achieved by reusing interaction sites as building blocks for new molecules. Thus, some of the TraPPE models are used for parameterization and others are used to verify the transferability. For example, ethane is used to fit the nonbonded interactions for a methyl group (-CH3) and butane is used to verify that those parameters are transferable to a different compound.

The TraPPE family of force fields now includes four levels of sophistication. TraPPE-United Atom is the most commonly used TraPPE force field and relies on united-atom representations for alkyl groups (i.e., hydrogen atoms are modeled implicitly along with the carbon atoms they are bonded to in a single pseudoatom type). TraPPE-Explicit Hydrogen is a more complex representation that uses independent interaction sites for all hydrogen atoms as well as some lone pair electrons and bond centers. TraPPE-polarizable provides models that are capable of responding to their electronic environment (in this case, both the van der Waals and electrostatic interactions are able to adjust). TraPPE-Coarse Grain minimizes the number of interaction sites by merging neighboring atoms into one large pseudoatom segment and extends the range of applicability to large systems.

Overview of Functional Forms

Nonbonded Interactions

A simple pairwise-additive potential consisting of Lennard-Jones (LJ) 12-6 and Coulombic terms is used to model the nonbonded interactions. (show more)

Bond Stretching and Angle Bending

With the exception of rigid aromatic rings, all alkyl groups and functional groups are treated as semiflexible with fixed bond lengths but bending and torsional degrees of freedom. (show more)

Dihedral Interactions

To calculate torsional potentials, TraPPE uses several different functional forms—most based on a cosine series—and determines the zero point of the dihedral angle by one of two standard conventions. In general, the dihderal interaction is parameterized to include intramolecular nonbonded 1-4 interactions, but for those special cases where this is not done, separate inclusion of these interactions is necessary. (show more)

Thanks to Our Supporters

This work is generously supported through continuing grants from the National Science Foundation - Chemical, Bioengineering, Environmental, and Transport Systems with additional support from Merck & Co., Inc., 3M Co., Procter and Gamble Co., and Abu Dhabi National Oil Co. Part of the computer resources are provided by the Minnesota Supercomputing Institute.

TraPPE– United Atom

The United Atom force field is the most widely used and most extensive force field in the TraPPE family. In the united atom approach, computational efficiency is an important consideration. To reduce computational cost, the number of interaction sites in a united-atom force field is kept as small as possible without sacrificing too much accuracy. This is done by using single interaction sites (pseudo-atoms) to represent a carbon atom together with all of its bonded hydrogen atoms. Typical psuedo-atoms in TraPPE–UA include CH4, CH3, CH2, CH and C. However, polar atoms, such as oxygen, nitrogen and sulfur, and any hydrogen atoms bonded to them, are treated as explicit interaction sites.

The total potential energy in TraPPE–UA is divided into bonded and nonbonded contributions. As is customary for united atom force fields, the nonbonded potentials are used only for the interactions of pseudo-atoms belonging to different molecules (intermolecular) or belonging to the same molecule but not accounted for by any of the intramolecular bonded potentials. TraPPE–UA includes intramolecular bonded potentials for bonds (1-2 interactions), angles (1-3 interactions) and torsions (1-4 interactions) so only those nonbonded interactions between pseudo-atoms separated by more than four bonds need to be included. Exceptions to this general approach are noted on the parameter page for individual TraPPE models.

TraPPE– Explicit Hydrogen

For systems or properties where united atom models are known to have difficulty, TraPPE provides explicit hydrogen models that can achieve a higher level of accuracy. Caution is warranted in implementing TraPPE-EH models, however, particularly for those more familiar with biomolecular force fields. Users of TraPPE-EH models should be especially attentive to the following:

  • There are important differences between TraPPE-EH for simple alkanes and TraPPE-EH for aromatic compounds.
  • For TraPPE-EH alkane models, interaction sites for hydrogen are shifted from the atomic nuclei out to the C-H bond center where the electron density is largest. For TraPPE-EH aromatic compounds, interaction sites are centered on atomic nuclei to facilitate the inclusion of partial charges.
  • For TraPPE-EH alkane models, torsional potentials are implemented so that they implicitly include 1-4 nonbonded interactions as well as 1-5 nonbonded interactions involving one hydrogen and 1-6 interactions between two hydrogen atoms. These interactions are thus neglected, resulting in a semi-flexible (but computationally efficient) model. For aromatic compounds, there are no bonded interactions because all TraPPE-EH aromatic models are rigid.
  • TraPPE-EH aromatic compounds require specific determination of partical charge parameters. The charge density of aromatic compounds is diffuse and delocalized such that all partial charges must be updated for any changes to the molecule (like the addition of an -F or -Cl atom). Partial charges for TraPPE-EH aromatic models are therefore not transferable. Mixing and matching TraPPE building blocks in the usual way will not work for TraPPE-EH, and users interested in novel molecules should contact us directly.

Once parameters are in hand, the explicit hydrogen models, like TraPPE–UA, use standard pairwise-additive Lennard-Jones and Coulomb potentials for nonbonded interactions.

TraPPE-EH development has focused on molecules for which the system or structural complexity may warrant a higher level of sophistication (e.g., solid or high-density liquid phases, aromatic rings) and includes models for simple alkanes, benzene, five- and six-membered aromatic compounds containing N, O, and S heteroatoms, aniline, nitrobenzene, and 1,3,5-triamino-2,4,6-trinitrobenzene. More recent work has extended TraPPE-EH to substituted benzenes (through the parameterization of -F, -Cl, -Br, -C≡N, and -OH) and to polycyclic aromatic hydrocarbons through the parameterization of the aromatic linker carbon for multiple rings.

TraPPE– Coarse Grain

Coarse-grain force fields have become increasingly popular over the past decade, largely because they allow one to extend molecular simulations to length and time scales beyond those accessible through common atomistic representations. Generally it is assumed that due to the limited number of interaction sites, coarse-grain potentials are not transferable to different systems or state points. It is the goal of TraPPE–CG to challenge this assumption and create a systematic procedure for parameterization of transferable coarse-grain potentials.

Our first CG models are developed for linear alkanes where C3C7 end segments and C3C6 middle segments represent the various molecules. Our parameterization approach uses the TraPPE-UA model to generate psuedo-experimental data and leads to encouraging results for the simple alkanes. Next, we plan to use our parameterization philosophy to extend TraPPE-CG to alchols and ethers.

TraPPE– Polarizable

The TraPPE-pol force field use an approach that couples the LJ parameters to the size of the fluctating charge; both van der Waals and electrostatic interactions can respond to changes in the environment. Currently TraPPE-pol models are only available for water, based on two common fluctuating charge models, but developed to allow the LJ paramters to fluctuate as well. The new TraPPE-pol models are: TIP4P-pol1, -pol2, -pol3; SPCE-pol1, pol2, pol3.

TraPPE– Small Molecules

The TraPPE force field includes models for several important small molecules. These molecules all have rigid structures (i.e., no bonded potentials) and do not otherwise fit into another TraPPE family. For example, methane, though also a small molecule, can be found with the other alkanes in TraPPE-UA or TraPPE-EH.

  • carbon dioxide
  • nitrogen
  • helium
  • oxygen
  • ethylene oxide
  • ammonia

About the Validation Effort

The development of the TraPPE force field began in the mid 1990’s with Ilja Siepmann’s move to the University of Minnesota. The initial target was a united-atom model for linear alkanes (TraPPE 1). Since that time, TraPPE has been extended to include several different families, ranging from the widely used TraPPE-United Atom force field to newer extensions like TraPPE-Coarse Grain. During the same time span, simulation methods and computing power have progressively improved. We believe it is of interest to the TraPPE user community to validate the accuracy of early TraPPE models and to provide more precise simulation data using optimized simulation protocols, larger system sizes, and additional temperatures.

Toward that end, the TraPPE validation effort consists of creating a database of new simulation data (vapor-liquid coexistence densities, vapor pressures, and critical properties) for each model developed prior to 2011. The validation simulations adhere to the following standards:

  • Several (8 or more) separate simulations will span state points along the vapor-liquid coexistence curve for a given molecule.
  • Data for each state point will be calculated using coupled-decoupled configurational-bias Monte Carlo simulations in the NVT-Gibbs ensemble with the averages and standard errors of the mean estimated from 8-16 independent trajectories.
  • At least four simulations will be carried out at temperatures higher than 0.9 Tcrit, which will then be used to estimate the critical point.
  • The lowest-temperature simulation will fall below the normal boiling point.
  • The number of particles, N, will be set to maintain a liquid-phase box length larger than 32 Å, though a larger number of particles may be used for T > 0.9 Tcrit. (A strict minimum of N = 200 will also be enforced.)
  • The system volume will be adjusted to yield on average about 10-20% of the molecules in the vapor phase for T < 0.9 Tcrit and approach an even phase ratio as Tcrit is approached.
  • The length of the simulations will be adjusted with the goal of achieving relative standard errors of the mean (RSEM) less than the following target values:
    • liquid densities, RSEM < 0.5% for T < 0.9 Tcrit
    • vapor pressures, RSEM < 2% for N < 0.9 Tcrit
    • critical temperature, RSEM < 1%
    • critical pressure, RSEM < 5%
  • Density histogram analysis will be used to determine liquid and vapor densities at temperatures near the critical point where box identity switches may occur. For more details see: M. Dinpajooh, P. Bai, D. A. Allan, and J. I. Siepmann 'Accurate and precise determination of critical properties from Gibbs ensemble Monte Carlo simulations,' J. Chem. Phys., 143, 114113 (2015).
  • Best practices will be used for setting move probabilities for optimal efficiency. For more details, please see: A. D. Cortes-Morales, I. G. Economou, C. J. Peters, and J. I. Siepmann 'Influence of simulation protocols on the efficiency of Gibbs ensemble Monte Carlo simulations,' Molecular Simulation, 39, 1135-1142 (2013).

As TraPPE models are validated, the results and specific details about the simulation set-up will appear as part of the regular TraPPE webpage, in the Simulation Data section for a given model. To see the current results from the validation effort, please choose from the list of validated models in the search box above.

The United Atom TraPPE Force Field

The United Atom TraPPE Force Field includes many valid TraPPE models for molecules not previously simulated. The only requirement is that the molecule can be constructed from exisiting TraPPE building blocks. To build such a model, begin by drawing the target molecule using the Sketcher molecular drawing tool below. The Sketcher tool accepts two forms of input: (1) draw the molecule using the menus provided or (2) click on the folder icon and copy/paste a MOLfile (V2000 format) into the provided textbox. Once the molecule is correctly represented, click on the submit button and follow the instructions for subsequent steps.

Drawing Tips:

  • The Sketcher tool above is the standard molecule builder provided with the Chem Doodle Web Components API, used here under Version 3 of the GNU General Public License. For usage documentation, please see the Sketcher Demo on the Chem Doodle webpage.
  • As a standard molecule builider, all hydrogen atoms are normally rendered implicitly, including, for example, the hydrogen in an alcohol functional group. In contrast, all TraPPE United Atom models have explicit interaction sites on hydrogen atoms attached to non-carbon atoms. Thus, to properly build a molecule for the United Atom TraPPE Force Field, hydrogen atoms bound to non-carbon atoms must be included in the drawing before submission. To draw an explicit H atom, first draw a new bond and then change the default atom at the end of the bond to hydrogen.

The United Atom TraPPE Force Field

To complete the parameter search for this built molecule, click on each pseudoatom image. A dropdown menu of options for nonbonded atom types will display. Highlight and click on the option that makes the most sense in the context of this molecule. When each atom shows just one selected nonbonded atom type ("selected" types will appear with a green background), click the button to Get Parameters. Alternativley, click Reset Sketcher to start over with a new molecule.

   

Selection Tips:

  • Click as close to the center of the atom as possible to change the dropdown menu display. The display will toggle through three different views: (1) display all the atom type options, (2) display the selected atom type, or (3) remove the menu display entirely.
  • For large molecules, the dropdown menus may overlap or partially block each other. Click on the atom for the topmost overlapping menus until they disappear, then make the selections for the atoms that were previously hidden, and finally, re-select the top menu(s). Do this as needed until all atoms display a green highlighted (i.e., selected) atom type.

Functional Forms and Parameters

Nonbonded Interactions

Please note the following:

    1-2 Bonded Interactions

    ( TraPPE uses fixed bond lengths)

    1-3 Bonded Interactions

    Simulation Data

    Liquid and Critical Properties

    Vapor-Liquid Coexistence Curve

    Clausius-Clapeyron Plot

    All TraPPE Publications from the Siepmann Group:

    TraPPE Publications from Affliated Groups:

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    Citation List

    Downloads

    Parameters Properties Structures
    There are no structures available for download at this time.