TraPPE: Transferable Potentials for Phase Equilibria Force Field

The quantitative molecular modeling of thermophysical properties requires the availability of highly accurate and transferable force fields. The term ‘transferable’ implies that the force field parameters for a given interaction site should be transferable between different molecules (e.g., identical parameters should be used for the methyl group in, say, n-butane, 1-butene, or 1-butanol) and that the force field should be transferable to different state points (pressure, temperature, or composition) and to different properties (thermodynamic, structural, or transport).

Considering the wide range of required accuracies for different applications, the different complexities of the chemical system to be investigated, and differences in computational resources available to different users, it becomes obvious that a single force field cannot satisfy all demands. Thus it is advantageous to create a family of force fields that can cover a spectrum of accuracy requirements and system complexities. The TraPPE family of force fields is built upon three levels of sophistication for describing non-bonded interactions. The first-level force field, called TraPPE–UA (united-atom), employs the united-atom representation for alkyl segments and simple Lennard-Jones and Coulombic terms. In the second level, called 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, called TraPPE-pol (polarizable), both the vdW 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-hydrogen-bonding compounds. The third level is directed solely at the highest level of accuracy and transferability.

The general intermolecular potential function for the TraPPE model is similar to those used in other popular molecular mechanics force fields and is as follows:

Different functional forms can be used for the vdW and dihedral terms. u_pol and u_gp are the many-body polarization energy and the corresponding gas-phase groundstate energy, respectively. The vdW parameters used in the TraPPE-pol force field are connected to fluctuations of the partial charges.

The TraPPE-UA force field utilizes pseudo-atoms located at carbon centers for alkyl groups (CH₄, CH₃, CH₂, CH, and C). The total potential energy is divided into a bonded and a nonbonded part. As is customary, the nonbonded potentials are used only for the interactions of pseudo-atoms belonging to different molecules or belonging to the same molecule but not accounted for by any of the intramolecular bonded potentials. The intramolecular bonded potentials include: fixed bond lengths for neighboring pseudo-atoms (1-2 interactions), harmonic bond bending potentials for pseudo-atoms separated by two bonds (1-3 interactions), and dihedral potentials for pseudo-atoms separated by three bonds (1-4 interactions).

For the LJ interactions, a site-site based spherical potential truncation at either 12 or 14 Å should be used together with analytical tail corrections for the energy, pressure, and the chemical potential.

Electrostatic interactions should be computed using the Ewald summation technique, with k x L = 5, K_max = 5, and tin-foil boundary conditions where k, L, and K_max are the width of the Ewald charge distribution, the box length, and the upper bound for the summation over reciprocal vectors.

With the exception of rigid aromatic rings, all alkyl groups and functional groups are treated as semiflexible with fixed bondlengths but bending and torsional degrees of freedom.

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. and 3M Co.

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