DFT calculations at the B3LYP/6-31G(d) level were carried out for the ground and excited triplet states of
free base meso-tetraphenylporphyrin, H2TPP, and its d
2, d
8, d
10, d
20, d
22, and 13C4 isotopomers. The agreement
between experimental and calculated (scaled with a single factor of 0.973) band positions for the ground
state was acceptable (rms = 9.9 cm-1). In addition, although the shifts on isotopic substitution were frequently
of the same order as this rms error in the absolute positions, it was found that the cancellation of errors in the
calculations meant that the direction and magnitude of even small isotope shifts < 10 cm-1 were also calculated
correctly. In the D
2 symmetry of the calculations the lowest lying triplet state corresponded to a one-electron
transition from the b1 HOMO to a b3 LUMO. It was found that the calculated changes in cm-1 of the vibrational
modes on excitation to this triplet (ΔS
-
T) reproduced the ΔS
-
T values of the seven bands found in the
experimental spectra. Three of these bands (ν2, ν1
2, and ν15) moved to lower cm-1 on excitation, two were
essentially unchanged (φ4 and ν1), and two moved to higher cm-1 ( ν4 and ν6). Since the ΔS
-
T values are
typically small (≤10's of cm-1), the correct prediction of the pattern of small shifts associated with population
of an excited state with a particular electronic configuration is impressive. As before, this improved accuracy
presumably arises because errors in the calculations of absolute positions cancel when values for the same
modes in different electronic states are subtracted to give shifts on excitation. This level of accuracy is necessary
if ΔS
-
T values are to be used to assign orbital parentage. Surprisingly, for several of the modes the calculated
ΔS
-
T shifts differed dramatically between isotopomers. For example, for ν2: ΔS
-
T(calc), d
0 = −5 cm-1, d
8 =
−30 cm-1; Δ
S
-
T(obs), d
0 = −15 cm-1, d
8 = −26 cm-1. These differences were found to reflect not only the
changes in force constants due to promotion to the triplet state (which are the same irrespective of which
isotopomer is under consideration) but also changes in the mode composition on excitation which alters the
isotope sensitivity. In the case of H2TPP, the mode compositions change because excitation from b1 → b3
orbitals accentuates the difference in bonding between the pairs of protonated and unprotonated pyrrole rings.
In effect, excitation increases the rectangular distortion that is already present in the ground state of free base
porphyrins and which distinguishes them from more regular D
4
h
(square) metalloporphyrins. The further
distortion causes modes that in the more regular systems involve all four of the pyrrole rings to become
increasingly localized on just the protonated or unprotonated pyrroles. More generally, the success of the
DFT calculations at this level of theory in predicting frequency shifts on excitation for an extensive series of
isotopomers clearly validates the approach. Interpretation of the resonance Raman spectra of t...