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 Siepmann group 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.

Functional form

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

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_{i}q_{j}}{4\pi \epsilon _{0}r_{{ij}}}}{\biggr \}}\ +\ \sum _{{\text{angles}}}{\frac {{k_{{\text{a}}}(\theta -\theta _{0})^{2}}}2}\ +\ \ U_{{\text{torsion}}}\

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. $\sigma _{ij}$ is related to the equilibrium distance, $R_{{0,ij}}$ , by: $\sigma _{{ij}}=R_{{0,ij}}/2^{{1/6}}$ and $\epsilon _{{ij}}$ is the well depth. For unlike Lennard-Jones interactions, standard Lorentz–Berthelot combining rules are used.
Coulomb 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] or the TraPPE force field papers.^[3] Below is a list of the different types of molecules that are currently available.

TraPPE-CG

K.A. Maerzke, and J.I. Siepmann, 'Transferable potentials for phase equilibria – Coarse-grain description for linear alkanes,' J. Phys. Chem. B, 115, 3452–3465 (2011).

TraPPE-UA

M.G. Martin, and J.I. Siepmann, 'Transferable potentials for phase equilibria. 1. United-atom description of n-alkanes,' J. Phys. Chem. B, 102, 2569–2577 (1998).
M.G. Martin, and J.I. Siepmann, 'Novel configurational-bias Monte Carlo method for branched molecules. Transferable potentials for phase equilibria. 2. United-atom description of branched alkanes,' J. Phys. Chem. B, 103, 4508–4517 (1999).
C.D. Wick, M.G. Martin, and J.I. Siepmann, 'Transferable potentials for phase equilibria. 4. United-atom description of linear and branched alkenes and of alkylbenzenes,' J. Phys. Chem. B, 104, 8008-8016 (2000).
- Ethene, propene, 1-butene, trans- and cis-2-butene, 2-methylpropene, 1,5-hexadiene, 1-octene, benzene, toluene, ethylbenzene, propylbenzene, isopropylbenzene, o-, m-, and p-xylene, naphthalene
B. Chen, J.J. Potoff, and J.I. Siepmann, 'Monte Carlo calculations for alcohols and their mixtures with alkanes. Transferable potentials for phase equilibria. 5. United-atom description of primary, secondary and tertiary alcohols,' J. Phys. Chem. B, 105, 3093–3104 (2001).
J.M. Stubbs, J.J. Potoff, and J.I. Siepmann, 'Transferable potentials for phase equilibria. 6. United-atom description for ethers, glycols, ketones and aldehydes,' J. Phys. Chem. B, 108, 17596–17605 (2004).
X.S. Zhao, B. Chen, S. Karaborni, and J.I. Siepmann, 'Vapor-liquid and vapor-solid phase equilibria for united-atom benzene models near their triple points: The importance of quadrupolar interactions,' J. Phys. Chem. B 109, 5368–5374 (2005).
- 6-site model: 6 x CH placed at carbon sites
- 9-site model: 6 x CH placed at carbon sites, three more charge sites
  - +0.242 e on benzene plane, −0.121 e at ±0.785 A from benzene plane
  - Q = −23.9 x 10⁻⁴⁰ C m²
C.D. Wick, J.M. Stubbs, N. Rai, and J.I. Siepmann, 'Transferable potentials for phase equilibria. 7. United-atom description for nitrogen, amines, amides, nitriles, pyridine and pyrimidine,' J. Phys. Chem. B, 109, 18974–18982 (2005).
N. Lubna, G. Kamath, J.J. Potoff, N. Rai, and J.I. Siepmann, 'Transferable potentials for phase equilibria. 8. United-atom description for thiols, sulfides, disulfides, and thiophene,' J. Phys. Chem. B, 109, 24100–24107 (2005).
K.A. Maerzke, N.E. Schultz, R.B. Ross, and J.I. Siepmann, 'TraPPE-UA force field for acrylates and Monte Carlo simulations for their mixtures with alkanes and alcohols,' J. Phys. Chem. B 113, 6415–6425 (2009).
S.J. Keasler, S.M. Charan, C.D. Wick, I.G. Econonmou, and J.I. Siepmann, 'Transferable potentials for phase equilibria-United atom description of five- and six-membered cyclic alkanes and ethers,' J. Phys. Chem. B, 116, 11234–11246 (2012).
- Cyclopentane, tetrahydrofuran, 1,3-dioxolane, cyclohexane, oxane, 1,4-dioxane, 1,3-dioxane, 1,3,5-trioxane

TraPPE-EH

B. Chen, and J. I. Siepmann, 'Transferable potentials for phase equilibria. 3. Explicit-hydrogen description of n-alkanes,' J. Phys. Chem. B, 103, 5370–5379 (1999).
N. Rai, and J.I. Siepmann, 'Transferable potentials for phase equilibria. 9. Explicit-hydrogen description of benzene and 5-membered and 6-membered heterocyclic aromatic compounds,' J. Phys. Chem. B, 111, 10790–10799 (2007).
- Benzene, pyridine, pyrimidine, pyrazine, pyridazine, thiophene, furan, pyrrole, thiazole, oxazole, isoxazole, imidazole, pyrazole
N. Rai, D. Bhatt, J.I. Siepmann, and L.E. Fried, 'Monte Carlo simulations of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB): Pressure and temperature effects for the solid phase and vapor-liquid phase equilibria,' J. Chem. Phys. 129, art. no. 194510/8 pages (2008).
N. Rai, and J.I. Siepmann, 'Transferable potentials for phase equilibria. 10. Explicit-hydrogen description of substituted benzenes and polycyclic aromatic compounds,' J. Phys. Chem. B, 117, 273–288 (2013).

TraPPE-pol

B. Chen, J.J. Potoff, and J.I. Siepmann, 'Adiabatic nuclear and electronic sampling Monte Carlo simulations in the Gibbs ensemble: Application to polarizable force fields for water,' J. Phys. Chem. B 104, 2378-2390 (2000).

TraPPE-small

J.J. Potoff and J.I. Siepmann, 'Vapor-liquid equilibria of mixtures containing alkanes, carbon dioxide and nitrogen,' AIChE J. 47, 1676–1682 (2001).
L. Zhang and J.I. Siepmann, 'Direct calculation of Henry's law constants from Gibbs ensemble Monte Carlo simulations: Nitrogen, oxygen, carbon dioxide, and methane in ethanol,' Theor. Chem. Acc. 115, 391–397 (2006).
M.-B.H. Ketko, J.L. Rafferty, J.I. Siepmann, and J.J. Potoff, 'Development of the TraPPE-UA force field for ethylene oxide,' Fluid Phase Equil. 274, 44–49 (2008).
L. Zhang and J.I. Siepmann, 'Development of the TraPPE force field for ammonia,' Collect. Czech. Chem. Commun. 75, 577–591 (2010).

Perfluoroalkanes

S.T. Cui, J.I. Siepmann, H.D. Cochran, and P.T. Cummings, 'Intermolecular potentials and vapor-liquid phase equilibria of perfluorinated alkanes,' Fluid Phase Equil. 146, 51–61 (1998).
L. Zhang and J.I. Siepmann, 'Pressure dependence of the vapor-liquid-liquid phase behavior of ternary mixtures consisting of n-alkanes, n-perfluoroalkanes and carbon dioxide,' J. Phys. Chem. B 109, 2911–2919 (2005).

TraPPE-zeo

P. Bai, M. Tsapatsis, and J.I. Siepmann, 'TraPPE-zeo: Transferable potentials for phase equilibria force field for all-silica zeolites,' J. Phys. Chem. C 117, 24375–24387 (2013).
- Adsorption and diffusion of any types of molecules on all-silica zeolites of any framework type. Tested: non-polar: methane, ethane, n-heptane, 2-methylpropane, 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane adsorption in MFI; propane adsorption in TON; quadrupolar: carbon dioxide adsorption in MFI; polar and hydrogen-bonding: methanol, ethanol, water adsorption in MFI; methanol adsorption in FAU; diffusion: methane, water in MFI.
An ad-hoc extension to Ca2+-exchanged aluminosilicates: P. Bai, P. Ghosh, J. Sung, D. Kohen, J.I. Siepmann, and R.Q. Snurr, 'A computational study of the adsorption of n-perfluorohexane in zeolite BCR-704,' Fluid Phase Equil. 360, online (2013).

References

1 2 3 4 "The Transferable Potentials for Phase Equilibria Family of Force Fields". The Siepmann Group. University of Minnesota. Retrieved August 27, 2014.
↑ "Transferable Potentials for Phase Equilibria –United Atom". The Siepmann Group. University of Minnesota. July 9, 2013. Retrieved August 27, 2014.
↑ TraPPE force field papers

External links

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