Vibronic coupling. VII. Magnetic circular dichroism of trimers, aromatic hydrocarbons, and porphyrins

Vibronic wavefunctions for trimers are used to calculate the A and B parameters characteristic of MCD spectra. In the weak-coupling limit both the A and the B parameters are zero for s = 0 states and nonzero for s = ±1 states. In the strong-coupling limit, the vibrationally induced 0–1 transition has nonzero A and B parameters, but the spectrum is dominated by the B term. Vibronic wavefunctions for cyclic polyenes are used to calculate the A and B parameters for the electronically forbidden, vibronically allowed 0–1 transitions in closed-shell aromatics and porphyrins. In 4n +2-atomic systems, the 0–1 transition for the B1u state has a small A term, vibronic in nature, and a B term that dominates the spectrum. The parameters are calculated for benzene, 18-annulene, coronene, and triphenylene. In the E2n−1 electronic state of a 4n-atomic system with 4n+2 electrons, there are two vibronic states that are made allowed by excitation of one quantum of either of two nontotally symmetric vibrations. There is a novel magnetic interaction between these two vibronic states. A model 16-membered polyene is used to calculate the A and B parameters for the metal and free-base porphyrins. In the metal porphyrins, the two A parameters are of opposite sign and each is of opposite sign to its corresponding B parameter. The MCD spectrum for each of the two 0–1 transitions in the Q state of the metal porphyrins is dominated by the A term. The free-base spectrum is also discussed. This simple and intuitive model gives calculated values that compare well with the experimental ones.