TraPPE force field

Graph of TraPPE force field accuracy relative to critical temperatures.

Transferable Potentials for Phase Equilibria (TraPPE) is a family of molecular mechanics force fields developed mainly by the research group of J. Ilja Siepmann at the University of Minnesota. The force field is parametrized against fluid-phase equilibria data with a strong emphasis on transferability. The term transferable implies that the same force field parameters are used to describe a given interaction site in different molecules (e.g., identical parameters should be used for the methyl group in n-pentane, 1-pentene, and 1-pentanol) and that the force field is applicable to predict different properties (e.g., thermodynamic, structural, or transport) across a wide range of state points (e.g., pressure, temperature, or composition).

Four major versions of the force fields exist for (mostly) organic molecules. They differ in sophistication: TraPPE-CG (coarse grain), TraPPE-UA (united-atom), TraPPE-EH (explicit-hydrogen), and TraPPE-pol (polarizable). Further, TraPPE-SM (small molecule) and TraPPE-zeo (zeolites) covers CO₂, N₂, O₂, NH₃, zeolites, etc. As of 2016, parts of the TraPPE force field are implemented in several software packages including Towhee, Materials Design, Culgi, and Scinomics.

Functional form

The basic functional form of the TraPPE force field is (for the united-atom version):

[math]\displaystyle{ U(r^N)=\sum_{j=1} ^{N-1} \sum_{i=j+1} ^N \biggl\{4\epsilon_{ij}\biggl[\left(\frac{\sigma_{ij}}{r_{ij}} \right)^{12} - \left(\frac{\sigma_{ij}}{r_{ij}} \right)^{6} \biggr]+ \frac{q_iq_j}{4\pi \epsilon_0 r_{ij}}\biggr\} \ +\ \sum_\text{angles} \frac{{k_\text{a} (\theta - \theta_0)^2}}2 \ +\ \ U_\text{torsion}\ }[/math]

Some considerations regarding the model:

• In the united-atom model, a CH_x group is treated as one interaction site or pseudo atom located on the carbon center.
• TraPPE typically uses fixed bond lengths and thus does not include a bond stretching term in the potential. However, the molecule is still semi-flexible due to the bending and torsional degrees of freedom.
• The double summation over site indices i and j represents nonbonded interactions between two pseudo atoms of different molecules or of the same molecule but separated by (usually) at least four bonds.
• Lennard-Jones potential (first term of summation) is used to describe repulsion and dispersion. [math]\displaystyle{ \sigma_{ij} }[/math] is related to the equilibrium distance, [math]\displaystyle{ R_{0,ij} }[/math], by: [math]\displaystyle{ \sigma_{ij} = R_{0,ij}/2^{1/6} }[/math] and [math]\displaystyle{ \epsilon_{ij} }[/math] is the well depth. For unlike Lennard-Jones interactions, standard Lorentz–Berthelot combining rules are used.
• Coulomb or electric potential (second term of summation) is used to describe first-order electrostatic interactions.
• The parameters for the Lennard-Jones and Coulomb potentials reflect effective values that account in a mean-field manner for higher-order and many-body dispersion and induction effects. In general, the parameters used in the TraPPE force field are fit to the vapor liquid coexistence curves of a few selected target compounds, but are found to reproduce transport properties also.

Parameter set

The parameters for the TraPPE force field can be obtained from the TraPPE website.