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

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