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.[1] 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).[1]

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.[1] As of 2016, parts of the TraPPE force field are implemented in several software packages including Towhee, Materials Design, Culgi, and Scinomics.

## Contents

* 1 Functional form
* 2 Parameter set
* 3 See also
* 4 References
* 5 External links

## Functional form

The basic functional form of the TraPPE force field is (for the united-atom version):[2]

[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 CHx 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.[1]

## See also

## References

1. ↑ 1.0 1.1 1.2 1.3 "TraPPE: Transferable Potentials for Phase Equilibria". The Siepmann Group. University of Minnesota. http://chem-siepmann.oit.umn.edu/siepmann/trappe/index.html. Retrieved February 4, 2016.
2. ↑ "TraPPE– United Atom". The Siepmann Group. University of Minnesota. http://chem-siepmann.oit.umn.edu/siepmann/trappe/index.html. Retrieved February 4, 2017.

## External links

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