Using artificial neural networks to develop molecular mechanics parameters for the modelling of metalloporphyrins: Part IV. Five-, six-coordinate metalloporphyrins of Mn, Co, Ni and Cu

With the aid of artificial neural network (ANNs), MM2 force field parameters were derived for the molecular mechanics modelling of the metalloporphyrins of five- and six-coordinate Mn(II), Mn(III), Mn(IV), Mn(V), Co(I), Co(II), Co(III), Ni(II) and Cu(II). The previously-derived parameters for modelling the porphyrin ring itself reproduced, on average, bond lengths to within 0.003 Å, angles to within 0.3° and torsions to within 2.4° of the mean crystallographic values. As these compounds have a wide variety of axial ligands, and there are relatively few structures available which contain the same metal in the same oxidation state and with the same axial ligands, only preliminary parameters are reported for the modelling of the axial ligands. These were typically derived by 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, we have previously shown the relative insensitivity of the equatorial metal–ligand parameters to the axial metal–ligand parameters and vice-versa, the necessarily preliminary values of the parameters for the modelling of the axial ligands did not preclude the development of parameters for the modelling of the metal–Nporph bond. To develop these, the strain free bond length lo, and the stretching force constant ks for the bond length was varied in a grid-like pattern and the absolute mean difference between the metal–Nporph bond length observed experimentally and determined by MM was defined as the error function, the minimum of which was found using ANNs. When the structures were modelled with the values of ks and lo that correspond to the minimum of the error function, the mean metal–Nporph bonds differed from crystallographically observed values by at most 0.008 Å, which is comfortably within the experimental standard deviation of this metric. The deviations of the porphyrin ring from planarity were often, but not always, reproduced in the modelling. We show that where significant differences were found, these could be due to packing effects in the solid state.