Forcefields for inorganic materials

1.  The Universal Force field (UFF)

\[ E_\text{total} = (E_\text{bond}+E_\text{angle}+E_\text{tor}+E_\text{inv})+(E_\text{vdw}+E_\text{elec}) \]

The parameters of UFF therefore do not directly contain forcefield parameters needed to do simulations with any combination of the 126 atom types covered, but essentially:

• Parameters for the individual atom types: bond radii as a function of hybridization, preferred angles, vdW parameters, torsion- and inversion energy barriers, effective nuclear charges

• Rules: for the calculation of the required forcefield parameters for atom pairs, triples etc. From the stored parameters for individual atoms.

Energy terms in UFF:

bond stretching: \(E_\text{bond}=\frac{1}{2}(r_{ij}-r_0)^2\), or L-J, Morse, etc.

\[ r_{ij}=r_i+r_j+r_\text{BO}+r_\text{EN} \]

• \(r_i,r_j\) are the bond radius of the individual atom types \(i\) and \(j\)

• \(r_\text{BO}\) is the bond order correction term, \(r_\text{BO}=-\lambda(r_i+r_j).\ln(n)\), n =1 for single bond, n=1.5 for aromatic ring, n=2 for double bond etc. \(\lambda\) is proportional constant, set to \(\lambda =0.1332\) based on optimization for propane, propene, propyne.

• \(r_\text{EN}\) is the correction term for electronegativity differences, \(r_\text{EN}= r_ir_j\frac{(\sqrt{\chi_i}-\sqrt{\chi_j})^2}{(\chi_ir_i+\chi_jr_j)}\)