Using artificial neural networks to develop molecular mechanics parameters for the modelling of metalloporphyrins. III. Five coordinate Zn(II) porphyrins and the metalloprophyrins of the early 3d metals

Artificial neural networks (ANNs) are used as an aid in developing force field parameters for modelling, using molecular mechanics methods and the MM2 force field, the porphyrins of the early transition metals, Sc(III), Ti(II), Ti(III), Ti(IV), V(II), V(III), V(IV), Cr(III), Cr(IV) and Cr(V), in which the metal is either five- or six-coordinate. The porphyrin ring itself was modelled with previously derived parameters and attention was focussed on deriving parameters to model the coordination sphere of the metal. By modelling five-coordinate Zn(II) porphyrins with an axial pyridine ligand, for which there are many structures, we demonstrate that the length of the metal-Nporph bond is relatively insensitive to the length of the metal-Naxial bond, and vice versa. There are relatively few crystal structures of the early 3d metalloporphyrins available and very few which contain the same axial ligand. Hence, preliminary parameters for modelling a wide variety of axial ligands are reported; these were typically derived by initially setting the strain free bond length and bond angles involving the metal and the axial donor atom to the crystallographically observed value, and varying the bond stretching and angle bending parameter, or the strain free bond length and bond angles iteratively, until the bond length and angles were reproduced to within 0.01 Å and 2.5°, respectively. Since the modelling of the [Zn(porphyrin)(pyridine)] complexes demonstrated the relative insensitivity of the equatorial metal-ligand parameters to the axial metal-ligand parameters and vice-versa, the paucity of structures and hence the necessarily preliminary values of the parameters for the modelling of the axial ligands did not preclude the development of parameters for the equatorial ligands. The strain free bond length lo, and the stretching force constant ks for the metal-Nporph bond length was varied in a grid-like pattern. The mean difference between the metal-Nporph bond length observed experimentally and determined by MM was defined as the error function. The minimum value of the error function was found using ANNs. Modelling the structures with the values of ks and lo that correspond to the minimum of the error function gave mean metal-Nporph bonds that differed from crystallographically observed values by at most 0.008 Å, within the experimental standard deviation of this parameter. The deviations from planarity found in many of the modelled structures were usually well reproduced in the modelling. Where significant differences were noted, these could sometimes (but not always) be shown to be due to packing forces in the crystal lattice. As expected, the orientation of axial ligands and substituents on the periphery of the porphyrin ring was often significantly different in the modelled and the solid-state structure because of the conformational freedom of these groups.