10.3. Force Field

10.3.1. Universal Force Field

The Universal Force Field (UFF) available in Winmostar’s molecular dynamics calculations (Gromacs, LAMMPS) is implemented as follows.

First, use OpenBabel’s UFF parameter assignment function to assign parameters to the molecule of interest. Then, for atoms that do not correspond to the atom type described in the original UFF paper [Rappe1992], the Coordination is automatically changed and a closer atom type is assigned. See the OpenBabel source code for more information.

The functional form of UFF cannot be fully reproduced by the functions available in Gromacs and LAMMPS. Therefore, we have converted the coefficients for the functions available in Gromacs and LAMMPS by way of OBGMX [Garberoglio2012].

In addition, fourth-order function is used in Winmostar because the Angle potential in the square planar and octahedral structures does not give a proper stable structure due to the fact that there is only one minuscule point int OBGMX method. The coefficients of the quadratic function were determined by the following policy.

  • Reproducing the position (angle, energy) of two potential minimum points
  • Reproducing the energy of a maximum point between two potential minima
  • In the case of LAMMPS, however, the coefficient of zero order cannot be set, so only the energy is shifted by a constant amount (the force, which is a derivative of the energy, is the same for Gromacs and LAMMPS, so there is no practical effect).

Because of the above policy, the resulting equilibrium structure and distribution is expected to remain largely unchanged from the case using the UFF original potential. Note that the widely used OpenBabel also adds its own penalty function to the Angle potential, which strictly deviates from the UFF original potential.

In Winmostar, the coefficients of Angle for square planer and octahedral are as follows. C_{i, \mathrm{gro}} is the coefficient of Gromacs’ fourth-order function, k_{a, \mathrm{uff}} is the coefficient of UFF; in LAMMPS, only C_{2, \mathrm{gro}} and C_{4, \mathrm{gro}} are used.

C_{\mathrm{0,gro}} &= \frac{1}{4}(2-\sqrt{2})k_{a,\mathrm{uff}} \\
C_{\mathrm{1,gro}} &= 0\\
C_{\mathrm{2,gro}} &= - \frac{8 }{\pi^2} (2-\sqrt{2})k_{a,\mathrm{uff}}\\
C_{\mathrm{3,gro}} &= 0\\
C_{\mathrm{4,gro}} &= \frac{64 }{\pi^4}(2-\sqrt{2})k_{a,\mathrm{uff}} \\
\theta_{0,\mathrm{gro}} &= \frac{3}{4}\pi\\

[Rappe1992]A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard III and W.M. Skiff, J. Am. Chem. Soc., 114 (1992), 10024–10035.
[Garberoglio2012]
  1. Garberoglio, J. Comp. Chem., 33 (2012), 2204-8.