Four-orbital model

TPP (45, 46), as well as data for octaalkyl and octathioalkyl porphyrazines. As with the phthalocyanines and porphyrins, the electronic spectra of porphyrazines can be rationalized using Gouterman s four-orbital model, shown in Fig. 5 (47, 48). All of these macrocycles, when symmetrically substituted and with a metal ion incorporated in the central hole, for example, the M[pz(A4)] or B4, have D4h symmetry, with a doubly degenerate lowest unoccupied molecular orbital (LUMO) (eg) and two highest lying highest occupied molecular orbitals (HOMOs) that complete the four Gouterman orbitals with alM and a2u symmetry. 

Figure 5. Gouterman s four-orbital model. [Adapted from (47) and (48).]...

The four-orbital model of the porphyrin spectra as applied by Gouterman (49-50) also serves to explain the mechanism of metal-to-porphyrin backbonding in metalloporphyrins of the spectral hypso type. This backbonding has been invoked for these complexes by Williams (45) and Falk (20). 

The four-orbital model implies that the a- and Soret bands are caused by transitions from the two top filled 7r-orbitals (alu, a2u) to the lowest empty 7r -orbitals (eg) of the porphyrin jr-electron system. Fig. 3 shows these four molecular orbitals (49, 65) and Fig. 4 a schematic energy level diagram with the unperturbed porphyrin levels and the energy of the normal a-band on the left (66). If the metal possesses filled d-orbitals, d,-electron donation from the dxz and dyz (d -) orbitals to the empty eg-ir -orbitals of the porphyrin may occur, thus raising the eg-7r -orbitals and lowering the d -orbitals which have now become bonding (Fig. 4). The consequence is the hypsochromic shift of the a-band observed in the d8 metalloporphyrins (Fig. 2 and Table 3). 

Up to now the four-orbital model-based theory of porphyrin absorption electronic spectra ( ) has not taken into account the influence of NH-tautomerism in non-symmetrical porphyrins on the positions and intensities of electronic transitions in the visible region. The theoretical consideration of this problem involves solving the fundamental question of the absolute orientation of electronic transition oscillators for each tautomer. First of all. 

In this paper, we present the detailed spectral information obtained for individual NH-tautomers and straightforward experimental arguments which permit us to relate the real position of the H-H axis to the molecular oscillator axes determined by substituents of different types (isocycle or alkyl groups) in two NH-tautomers. Then we used this structural information as a basis for analyzing the inversion of electronic Qx(0,0) and Qy(0,0) band intensities using the four-orbital model. 

In the four-orbital model (1 ), low-lying ir-ir states of free-base porphyrins (symmetry D2h) are considered as resulting from single electron excitation from a pair of nondegenerate highest occupied molecular orbitals (bi, bo) to a pair of nondegenerate lowest unoccupied molecular orbitals (ci, cg). In the case of symmetry D2h mutually perpendicular electric transition dipoles X and Y are not equivalent and, therefore, in the visible absorption spectra of free-base porphyrins two different electronic bands Qx(0>0) and Qy(0,0) are observed (Table 1 and Fig. 10). 

The results of these calculations follow a similar pattern to the earlier studies of the absorption spectra (146). In the case of the Q bands, the more sophisticated MCD calculation utilizing TDDFT is only a refinement of the four-orbital model. A single A term is predicted with small overall MCD intensity but significant Aj/Dj ratio. This provides further evidence that the more complicated series of bands observed in the Q band of the absorption and MCD spectra is due to vibronic effects. In the cases of NiTPP and... 

Finally, a third dithiolene ligand model has been utilized with success in order to understand the electronic structure and spectroscopy of a number of oxo-molybdenum mono- and bis(dithiolenes) (23). This dithiolene ligand bonding description utilizes the symmetric and antisymmetric out-of-plane Sop p 7t orbitals, in addition to the corresponding in-plane symmetric and antisymmetric S p p orbitals. Ab initio and density functional theory (DFT) calculations have been performed on the simple dithiolene dianion, [S2C2H2]2 (23), in order to illustrate the details of this four orbital model and electron density contours of the four MOs are presented in Fig. 4. These calculations result in an isolated set of four filled dithiolene orbitals, and these are the ligand... 

The effects of substituents at the pyrrole carbon atoms on the spectrum can be explained in terms of the four-orbital model. However, in all these calculations the metal is simply regarded as a positive charge whose magnitude affects the charges on the pyrrole nitrogen atoms only the inductive effect of the metal is considered. The "mesomeric effect of -interaction between metal and porphyrin on the spectrum has been discussed qualitatively (44), and it was noted that the transitions... 

Braterman, Davies and Williams (44) considered the possibility of configuration interaction between the porphyrin n states and the charge transfer states. According to the four-orbital model of Gouterman, discussed in Section IIB, the Soret and a— excited states are of Eu symmetry. The only allowed charge transfer transitions are from the porphyrin a u and aexcited states, and from the porphyrin a2u orbital to the metal... 

Scheme 4.2 Frontier orbitals of the porphyrins according to the Gouterman four-orbital model for D4h point group (top). In the presence of a perturbation (substituents or ligand distortion) the degeneracy might be lifted (bottom). With permission from Wiley, ref 7a.

Gouterman M, Wagniere GH, Snyder LC (1963) Spectra of porphyrins Part II four orbital model. J Mol Spectrosc 11 108-127... 

Gouterman s theory is called the four-orbital model, because it considers only the two highest occupied (with electrons) molecular orbitals (HOMOs) of a porphyrin, and the two lowest unoccupied molecular orbitals... 

LUMOs). Other, more sophisticated models have now superseded it (in particular, models that can include the effects on the spectra of complexed metal ions, and vibrations within the macrocycle), but the four-orbital approach still serves as the best introduction to the theoretical complexities of porph)nrin UV-visible spectra. First, and to put the four-orbital model in context, it will be interesting to look at some of its antecedents. 

Fig. 3.30 Porphyrin HOMOs b], >2 and LUMOs Cj and Cj showing their original (Hiickel) group theoretical notation and their modified notation as used on the four-orbital model. The original coefficients are proportional to the size of the circles. SoUd or dashed circles indicate sign. Symmetry nodes are drawn in heavy lines.

B and Q bands, but did provide qualitative data on how skeletal variations affect porphyrin absorption spectra. The stage was now set for the strengths of all these theories to be unified. Martin Gouterman did this by using configuration interaction, a technique vital in free electron and cyclic polyene theories, to describe the porphyrin excited states generated by Hiickel theory. He called this new synthesis the four-orbital model. ... 

In the T7-orbital, because of the higher electronegativity of the oxygen atom, the electron spends more time near it. Consequently, the molecule exhibits an electric dipole along the C=0 eixis. However, when electronic excitation takes place, the Tr -orbital is occupied and now the excited elec-tron spends more time near the carbon atom. Therefore, in the excited state, the polarity of the C=0 bond is reduced. In undergoing the electronic transition, the C=0 bond experiences a strong transition dipole which can be resolved into two components whose directions are perpendicular to each other. Now, back to the four orbital model. 

The four-orbital model, therefore, accounts for the number, multiplicity, and relative intensity of the Q bands. It also accounts correctly for how the intensity of the Q bands varies when the porphyrin complexes with a metal cation or picks up two further protons to become a dication. 

Thus, the four-orbital model predicts an intense band at long wavelength, and is so able to explain the green colour of chlorins. The heart of chlorophyll is a metaUochlorin macrocycle, so that we are now in a position to... 

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