A theoretical evaluation of the vinyl torsional potential in protoporphyrins

Abstract

The potential surfaces for the vinyl torsion in 2,4-divinyl porphyrins are calculated by using semiempirical [INDO (intermediate neglect of differential overlap) and INDO-PSDCI (partial single and double excitation configuration interaction)] molecular orbital theory. Calculations are carried out on the two pyrrole hydrogen tautomers of the free base porphyrin as well as on the porphyrin dianion. The calculated potential surfaces are predicted to have energy maxima at 0° and 180° due to steric hindrance. A third maximum near 70° (approximately perpendicular) is predicted due to electronic destabilization associated with the loss of conjugation and a decrease in dispersive stabilization energy. The torsional surface associated with the porphyrin dianion is qualitatively different from that calculated for the free base porphyrin due primarily to more effective conjugation of the vinyl group into the porphyrin macrocycle in the dianion. Neither pyrrole hydrogen tautomerization nor internal rotation of the second vinyl group have any significant effect on the torsional potential surface of the first vinyl group. The latter result indicates that the vinyl groups are effectively ‘‘uncoupled’’ in 2,4-divinyl porphyrins. A complete vibronic analysis is carried out by calculating the torsional energy levels using a free internal rotor basis set containing 201 basis functions. A Boltzmann analysis of level occupation and numerical evaluation of the individual torsional expectation values are used in conjunction to calculate average dihedral angles as a function of temperature. We predict that the average torsional angle of the vinyl group is 114.2° in the free base porphyrin and 121.2° in the porphyrin dianion at ambient temperature. In order to compare these results with NMR studies, we also calculate the average angle by evaluating the expectation value of sin2 Φ. This expectation function, when transformed into an angular measurement (〈Φ*〉=sin−1〈sin2 Φ〉), restricts angular expectation values to lie within the first quadrant. Calculations of 〈Φ*〉 yield average angles of 46.3° for the free base porphyrin and 47.5° for the porphyrin dianion. These values are in good agreement with the NMR experimental value of 51° which is based on a 〈sin2 Φ〉 measurement. The origins of the nonplanarity of the vinyl substituents are analyzed in terms of repulsive, dispersive, and electrostatic nonbonding interactions as well as bonding and electron correlation effects. We demonstrate that many of the predictive limitations associated with the use of INDO semiempirical procedures to calculate potential surfaces are improved by the inclusion of electron correlation embodied in double excitation configuration interaction.