Group Theoretical Analysis

In order to assign the vibrational spectra of [Fe(TPP)Cl], an effective D_4h symmetry was applied. The analysis of the polarized data (see below) shows that this approach is justified even for five-coordinate compounds such as [M(TPP)Cl] (M = Fe, Mn, Co). D_4h symmetry is obtained for a planar porphyrin core with the metal being located in the plane and no axial ligand present. The phenyl rings of TPP are exactly perpendicular to the porphyrin plane. In this D_4h model system [M(TPP)] (idealized metalloporphyrin), the planar porphyrin core has 71 in-plane modes [1]:

Γ_{in plane} = 9 A_1g(R) + 8 A_2g(RR) + 9 B_1g(R) + 9 B_2g(R) + 18 E_u(IR)

In the NR Raman spectrum, 27 in-plane vibrations are therefore expected, 9 of them polarized (A_1g) and 18 depolarized (B_1g and B_2g). The infrared spectrum shows a maximum of 18 modes with E_u symmetry. In addition, the porphyrin core of the D_4h model system has 34 out-of-plane vibrations [1]:

Γ_{out of plane} = 3 A_1u + 6 A_2u(IR) + 4 B_2u + 5 B_1u + 8 E_g(R)

The 8 E_g modes are Raman active and the 6 A_2u modes are infrared active. Therefore, based on purely statistical consideration, much more in-plane than out-of-plane modes can be expected in the NR Raman and IR spectra of metalloporphyrins.

Besides the porphyrin core modes, a large number of phenyl vibrations are also present in TPP complexes. Different approaches are possible for the classification of these vibrations. In order to give an intuitive assignment of the phenyl modes of TPP, we use bromobenzene as a model. The TPP ligand itself has four phenyl groups, which are bound to the meso carbon atoms of the porphyrin core. Hence, for every local phenyl coordinate there are four symmetry-adapted combinations in TPP. Since the interactions of the local vibrations of different phenyl rings are small, the obtained splittings between the resulting four combinations are also small (usually 5-10 cm^-1). Hence, the four resulting symmetry adapted linear combinations are also designated as a 'symmetry block', since they are close in energy. Since there are four different irreducible representations in C_2v (the point group of bromobenzene), four different symmetry blocks exist:

out-of-plane B₁ leads to: B_1g(R) + A_2g(RR) + E_u(IR)
out-of-plane A₂ leads to: A_1u + B_2u(RR) + E_g(R)
in-plane B₂ leads to: B_1u + A_2u(IR) + E_g(R)
in-plane A₁ leads to: A_1g(R) + B_2g(R) + E_u(IR)

In order to classify the different porphyrin core and phenyl modes in D_4h symmetry, we used the idealized model [Zn(TPP)] and calculated the vibrations of this model in D_4h symmetry. [Zn(TPP)] has 169 normal modes (56 of them are degenerate), where 44 % are Raman and 27 % are IR active.

The experimental and calculated NR Raman spectra of [Fe(TPP)Cl] are shown in the top panel of Figure 1. Corresponding polarized data are also included in the lower panel. The calculated spectrum is in general shifted to somewhat higher energy (the average deviation in vibrational energies is about 2-3 %) compared to experiment. Besides the good agreement in vibrational frequencies, very good agreement with experiment is obtained for the calculated NR Raman intensities. This allows for a detailed assignment of the data. Importantly, additional information to support the Raman assignments is available from polarization measurements. The depolarization ratio ρ is defined as:

ρ = I_{perpendicular} / I_parallel

In D_4h symmetry, one obtains [1]:

(a) 0 < ρ < 0.75: polarized bands (p) (A_1g symmetry)
(b) ρ = 0.75: depolarized bands (dp) (B_1g and B_2g symmetry)
(c) ρ > 0.75: anomalous polarized bands (ap) (A_2g symmetry; only RR active)

Hence, the polarized measurements allow for a determination of the symmetry of a mode. The complete assignments obtained this way are collected in Table 3 in the reference given below.