The functional form of angular forces around transition metal ions in biomolecules

A method for generating angular forces around a-bonded transition metal ion s is generalized to treat pi -bonded configurations. The theoretical approa ch is based on an analysis of ligand-field and small-cluster Hamiltonians b ased on the moments of the electron state distribution. The functional form s that are obtained involve a modification of the usual expression of the b inding energy as a sum of ligand-ligand interactions, which, however, requi res very little increase in CPU time. The angular interactions have simple forms involving sin and cos functions, whose relative weights depend on whe ther the ligands are sigma- or pi -bonded. They describe the ligand-field s tabilization energy to an accuracy of about 10%, and the interaction energy of covalently bonded systems to an accuracy of better than 4%. The resulti ng functional forms for the force field are used to model the structure of small clusters, including fragments of the copper blue protein structure. L arge deviations from the typical square copper coordination are found when pi -bonded ligands are present.