Molecular mechanics parameters for the modelling of four-coordinate Zn(ii) porphyrins

Abstract

The development of Zn–N parameters for the molecular mechanics (MM) modelling of four-coordinate Zn(II) porphyrins using the MM2 force field is described. The approach adopted was to attempt to reproduce a wide range of four-coordinate Zn(II) porphyrins whose crystal structures have been reported, ranging from those that are essentially planar to those that are significantly distorted from planarity. The mean difference between the Zn–N bond lengths as observed experimentally and as determined by MM was defined as the error function. The error function was plotted against the Zn–N strain free bond length (l_o) and the stretching force constant for that bond (k_s). The minimum on the error response surface was determined using artificial neural networks (ANNs) from relatively few input data points. It was found that the optimum parameters, l_o = 2.007 Å and k_s = 1.59 mdyn Å⁻¹, together with the force field parameters previously described for modelling the porphyrin moiety, adequately model planar and distorted four-coordinate Zn(II) porphyrin structures. Zn–N bond lengths are reproduced on average to within 0.012 Å; other bond lengths, bond angles, torsions and improper torsions within the porphyrin are reproduced to within 0.015 Å, 2.1°, 3.0° and 2.9°, respectively. The validity of the force field parameters was demonstrated by correctly predicting the structures of four-coordinate Zn(II) porphyrins that were not used in the training of the ANNs, and predicting the structure a priori of a recently reported four-coordinate Zn(II) porphyrin. The force field was then used to undertake a brief investigation of the conformational space available to Zn(II) tetraphenylporphyrin ([Zn(TPP)]) using molecular dynamics, quenched dynamics and simulated annealing procedures. The results show that the favoured structure of [Zn(TPP)] has a planar porphyrin core; this is in agreement with available structural data, since all except one structure of [Zn(TPP)] that has been reported have planar porphyrins. Modelling of the lattice of a planar and the distorted [Zn(TPP)] structure demonstrated that the distortion of the porphyrin is a response to steric interactions with the nearest neighbours in the lattice.