Numerical integration of overlap and ligand contributions to the electric field gradient

The total electric field gradient (EFG) tensor V _pq is calculated by numerical integration of threedimensional integrals. Each of them is solved a) by integrating over one dimension analytically and b) by integrating over the remaining two dimensions on the basis of a Gauss-type integration rule. The use of 100 abscissas in the twodimensional numerical integration scheme yields satisfactory accuracy which was checked by evaluating overlap integrals; an increase to 400 abscissas does not increase the result drastically. Calculating quadrupole splittings E _Q from numerically integrated electric field gradient tensors V _pq we observe that depending a) on the amount of covalency and b) on the amount of deviation from octahedral or tetrahedral symmetry, involved in a molecular system, overlap and ligand contributions to V _pq play an important role. Especially for the sandwich compound ferrocene, Fe(C₅H₅)₂, we find a significant difference between E _Q ^{num. int.} which follows from the numerical integration method, and E _Q ^conventional which is derived from effective charges.Supported by Deutsche Forschungsgemeinschaft