Theoretical Analysis of the Porphyrin−Porphyrin Exciton Interaction in Circular Dichroism Spectra of Dimeric Tetraarylporphyrins

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Abstract
Chiral bis-porphyrins are currently the subject of intense interest as chiral receptors and as probes in the determination of structure and stereochemistry. To provide an improved framework for interpreting the circular dichroism (CD) spectra of bis-porphyrins, we have calculated the CD spectra of chiral bis-porphyrins from three classes: I, where porphyrins can adopt a relatively wide range of orientations relative to each other; II, porphyrins have a fixed relative orientation; III, porphyrins undergo π-stacking. The calculations primarily utilized the classical polarizability theory of DeVoe, but were supplemented by the quantum mechanical matrix method. Class I was represented by three isomers of the diester of 5α-cholestane-3,17-diol with 5-(4‘-carboxyphenyl)-10,15,20-triphenylporphin (2-αβ, 2-βα, 2-ββ). Careful analysis of the torsional degrees of freedom led to two to four minimum-energy conformers for each isomer, in each of which the phenyl−porphyrin bonds had torsional angles near 90°. Libration about these bonds is relatively unrestricted over a range of ±45°. CD spectra in the Soret region were calculated as Boltzmann-weighted averages over the low-energy conformers for each isomer. Three models were used: the effective transition moment model, in which only one of the degenerate Soret components is considered, along the 5-15 direction; the circular oscillator model, in which both Soret components are given equal weight; and the hybrid model, in which the 10-20 oscillator is given half the weight of the 5-15 oscillator, to mimic the effect of extensive librational averaging about the 5-15 direction. All three models predict Soret exciton couplets with signs in agreement with experiment. Quantitatively, the best results are given by the hybrid and circular oscillator models. These results validate the widely used effective transition moment model for qualitative assignments of bis-porphyrin chirality and thus permit application of the exciton chirality model. However, for quantitative studies, the circular oscillator or hybrid models should be used. The simplified effective transition moment and hybrid models are justified by the librational averaging in the class I bis-porphyrins and should only be used with such systems. Two class II bis-porphyrins were also studied by DeVoe method calculations in the circular oscillator model, which yielded good agreement with experiment. Class III bis-porphyrins were represented by 2-αα, for which the calculations gave qualitative agreement. However, limitations in the conformational analysis with the close contacts and dynamic effects in these π-stacked systems preclude quantitative results.

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