The shape of porphyrins

Porphyrin molecules are a widely exploited biochemical moiety, with uses in medicinal chemistry, sensing and materials science. The shape of porphyrins, as an aromatic unit, is reductively imagined to be approximately flat, with regular, rigid shape, owing to the popular depiction as a simplified skeletal model. While this regular conformation does exist, the array of substitution patterns in synthetic porphyrins or interactions with the apoprotein in biochemical moieties often induce distortions both in-plane and out-of-plane. Structural deviation reduces symmetry from the ideal D4h and can introduce changes in the physical and electronic structure; physical changes can introduce pockets for favorable intermolecular interactions, and electronic distortion can introduce new electronic transitions and properties. A quantification of porphyrin distortion is presented based on the Normal-coordinate Structural Decomposition method (NSD) pioneered by Shelnutt. NSD transforms crystallographically-determined atomic positions of each porphyrin into a summation of common concerted atom vectors, allowing for quantification of porphyrin anisotropy by symmetry. This method has been used previously for comparison of small data sets of synthetic and biological porphyrins. In the twenty-five years since the method was pioneered, the volume and variety of available crystal structure data has ballooned, and data analysis tools available have become more sophisticated, while the method has languished. Using modern data-science methods, clusters of porphyrin distortions are grouped to show the average effect that a substitution pattern has on porphyrin shape. Aiming to provide an overview on the shape and conformation of these key macrocycles we here provide context to the strategies employed for introducing porphyrin distortion and to provide a quantitative comparative basis for analysis of novel structures. This is achieved by demonstrating that porphyrin molecules often have a predictable NSD pattern, and therefore solid-state conformation, based on chemical arguments. This quantification allows for assessment of predicted structures and forms the basis of a symmetry-by-design motif for a range of porphyrinoids. A modernized computer program used in this structural determination is provided for analysis, with this treatise acting as a guide to the interpretation of results in new structure determinations. New features include simple report generation, prediction of symmetry and assessment of cluster behavior for a range of porphyrin moieties, as well as convenient plotting functions and data reductions