The inner-hydrogen migration in free base porphyrin

We present the results of a comprehensive study on the inner-hydrogen migration in free base porphyrin, using density functional theory with the hybrid B3-LYP exchange-correlation functional, and both the 6-31G(d) and a triple-zeta double-polarization (TZ2P) basis set. The latter computations, involving 726 contracted functions, are the largest calculations on this system to date. Full geometry optimization was carried out for the cis and trans minima, the transition state for trans-cis isomerization, and the symmetric stationary point for the synchronous trans-trans isomerization. All stationary points were characterized by vibrational analysis. Our results strongly support the conclusion, reached by earlier workers, that trans-trans hydrogen transfer occurs in a two-step process via a cis intermediate. With the TZ2P basis and including zero-point effects for the -h(2) isotopomer, the trans-cis barrier height is 13.1 kcal/mol, the cis-trans energy difference is 8.1 kcal/mol and the reverse cis-trans barrier height is 5.0 kcal/mol. The trans-cis barrier height agrees well with the value of Braun et al. (J Am Chem Soc (1996) 118:7231) obtained from NMR line shapes and a modified Bell tunneling model, but our cis-trans energy difference is higher, and the reverse barrier is lower, than the values of Braun et al. Tunneling precludes the existence of -h(2) cis-porphyrin as an observable species, but the -d(2) and, especially, -t(2) isotopomers might be observable at low temperatures if the reverse barrier is higher than our calculated value. We predict the theoretical vibrational spectrum of cis-porphyrin and suggest that IR active modes at 566 cm(-1) and 2333 cm(-1) in the -d(2) isotopomer may be used to detect the presence of the cis intermediate.