where εij = (εi εj) 1/2 and Rij = (Ri + Rj)/2; Ri and Rj are the van der Waals radius; εi and εj are the characteristic energy. Equations ( ) and ( ) require three force field parameters, charge (q), van der Waals radius (R), and characteristic energy (ε). The derivation of the parameters for MM atoms in MOF clusters is discussed in the following section. For the atoms of the adsorbates, UFF parameters were used to avoid the need for reparameterization for atoms in new substrates.