Molecular mechanics modelling of porphyrins. Using artificial neural networks to develop metal parameters for four-coordinate metalloporphyrins

The development of parameters for the modelling of four coordinate Cu(II), Co(II), Ni(II), Pd(II) and Zn(II) porphyrins is described. The approach used was to reproduce as closely as possible the solid state structures of representative compounds. The previously-reported parameters for the modelling of iron porphyrins were revised so as to reproduce as closely as possible the average structure of the porphyrin core. Attention was then focussed on developing the appropriate M–L parameters (the strain free bond length, l0, and the bond stretching force constant, ks). The mean difference between the modelled and experimentally observed M–L bond lengths (the “error”) was plotted simultaneously against l0 and ks, which were varied in a grid-like pattern using experimental design principles, to generate results in the form of an error response surface. The minimum on the surface represents the optimum values of the two parameters l0 and ks. Artificial neural networks were used to generate the error response surface from relatively few input data points in search for the minimum error. This principle was successful in modelling both planar and distorted structures of Cu(II), Co(II), Ni(II), and Pd(II). However, the minimum on the error response surface for Zn(II) resulted in three of nine structures minimising into structures with conformations different from those found crystallographically. Alternative parameters, which gave a marginally greater error, were used and resulted in the correct modelling of the crystal structures used in this study.