Martin Gouterman

Spectra of porphyrins

Abstract The review opens by presenting the absorption spectra for three series of porphyrins derived from the basic skeleton: (a) compounds obtained by simple substitution; (b) compounds obtained by reduction of one or more pyrrole rings; and (c) compounds obtained from fusion of aromatic rings onto the basic skeleton. The spectra are discussed in terms of a four orbital model—that is intensity changes and energy shifts are related to the properties of two top filled and two lowest empty pi orbitals. Emission spectra of metal porphyrins are then discussed, three metal series being distinguished: (1) In closed shell metals, the continuous enhancement of phosphorescence at the expense of fluorescence is attributed to spin-orbit coupling. (2) In paramagnetic metals, observed effects are attributed to the existence of a state at the same energy as the usual triplet but with multiplicity the same as the ground state; its intensity is ascribed to exchange interactions. (3) In diamagnetic metals with unfilled d shells, peculiar emission properties are attributed to enhanced spin orbit coupling due to low lying metal triplets. The review closes by discussing n-π transitions and triplet-triplet spectra.

Spectra of porphyrins: Part II. Four orbital model

Abstract Porphyrin molecules are treated by combining an LCAO-MO (Huckel) calculation with a simplified treatment of configuration interaction. The Huckel calculation requires special parameters α N = α C + 2 β CC and β CN = 0.5 β CC for certain internal porphyrin nitrogen atoms. The configuration interaction parameters are determined on Zn tetraphenylporphin. Calculations are carried out for reduced porphyrins, azaporphins, and benzporphins. Spectra are predicted, and chemical and magnetic properties are discussed.

Vibronic Coupling. I. Mathematical Treatment for Two Electronic States

A general mathematical treatment of vibronic coupling of two electronic states in molecules and dimers is presented. The 2×2 matrix Hamiltonian which is derived is shown to reduce to two one‐dimensional Hamiltonians provided a certain minimum amount of symmetry is present. Some general selection rules governing electronic transitions to these states from the ground state are obtained, showing that the spectral distribution in hot bands may differ considerably from that in normal bands when vibronic coupling occurs. A special model which considers the coupling to arise from a single mode of vibration is presented. Two limiting cases which can be treated approximately by perturbation theory are considered in detail. These are shown to give rise to a ``pseudo Jahn‐Teller effect and to vibrational borrowing in the two different limits.

Spectra of porphyrins: Part III. Self-consistent molecular orbital calculations of porphyrin and related ring systems

Abstract Self-consistent molecular orbital calculations on the porphin ring by the method of Pariser, Parr, and Pople (SCMO-PPP) confirm earlier conclusions of Gouterman and Platt that the visible and Soret bands of the porphin absorption spectrum can be explained by a four-orbital model. According to this model, the lowest two pairs of excited configurations are accidentally degenerate, and the extensive interaction between them accounts for the great intensity of the Soret and the relative weakness of the visible bands; interaction with higher configurations is negligible. The four-orbital model is extended to give a successful account of the absorption spectra of tetrabenzporphin, and of reduced and aza-porphyrins. It also accounts for the “cyclic polyene perturbation” which splits the visible but not the Soret bands of free base porphin. More elaborate calculations using extensive configuration interaction give remarkable qualitative agreement with the porphin triplet-triplet absorption spectrum, and makes possible the reassignment of the ultraviolet bands of tetrazaporphin and phthalocyanine. Unfortunately, configuration interaction is consistently overestimated, and hence the calculated splitting of visible and Soret bands is too large. Further, singlet-triplet splitting is similarly overestimated.

Vibronic Coupling. II. Spectra of Dimers

We consider a model dimer composed of units with one allowed excited state and one symmetric vibration. The vibrational mode has the same force constant in the ground and excited states, but the excited state is assumed to have its equilibrium position shifted by an amount measured by λ. The dimer possesses a symmetry operation that exchanges the units and has an exciton coupling e. Spectra for various λ and e values are derived by computer. It is shown that the absorption intensity of the two polarizations rigorously satisfies two theorems: the center of gravity is at ±e for all λ; the bandwidth is | λ | for all e.

Fluorescence Polarization of Some Porphyrins

Fluorescence‐polarization data on porphyrins are reported. The results can be readily interpreted in terms of the theory of polarization spectroscopy and the theory of the electronic and vibrational structure of these molecules. It is shown how these two theories combine to interpret most of the data, but some anomalies remain. The results hint at the richness of data that may be expected from fluorescence‐polarization experiments when techniques are developed further.

Vibronic Coupling. IV. Trimers and Trigonal Molecules

The mathematical treatment of vibronic coupling in trimers and in benzene is presented. The vibronic matrix is diagonalized by computer methods for weak, intermediate, and strong coupling limits. Perturbation solutions in the two cases, e≫1≫λ2 and e≪1≪λ2 are presented. The first case is shown to be analogous to the Jahn—Teller case. Calculated spectra and vibronic probability densities are presented. The values of e and λ for the real systems, barrelene, triquinacene, and benzene are estimated, and the systems are classified as strong, weak, and intermediate coupling, respectively. This method gives qualitative agreement with the observed benzene spectrum.

Radiationless Transitions: A Semiclassical Model

Radiationless transitions of a solute molecule embedded in a crystalline solvent are treated in close analogy to radiative transitions. A semiclassical interaction Hamiltonian employing empirically determined coupling constants connects solute particles to a force field amplitude set up by the phonons of the solvent. By relating this amplitude to phonon energy density an Einstein B coefficient is derived. Debyes formula for the phonon energy density combined with thermodynamic arguments yield Einstein A coefficients. It is shown that the theory (1) explains the fast rates of radiationless transitions, (2) provides for temperature dependence, (3) has a cutoff frequency for radiationless transition, (4) provides for the Franck—Condon principle, and (5) explains the lack of selection rules. A value is derived for the empirical coupling constants.

Theory for Zero‐Field Splittings in Aromatic Hydrocarbons. III

The assumptions underlying a calculation of the zero‐field splitting parameters D and E are stated in order of increasing severity. Under these assumptions, a number of molecules are calculated and the results compared with experiment. The sensitivity of the calculations to changes in some of the assumptions is examined. The present theory is shown to be in excellent agreement with experiment for the molecules benzene, naphthalene, and anthracene; in fair agreement for phenanthrene; and in poor agreement for triphenylene and coronene.

Spectra of porphyrins: Part VII. Vapor absorption and emission of phthalocyanines

Abstract Absorption spectra and fluorescence spectra excited by the Heue5f8Ne laser line at 633 mμ are reported for H 2 Pc, MgPc, and ZnPc in the vapor. CuPc showed no vapor emission. The yields of fluorescence are temperature dependent but relatively independent of the presence of the foreign gases Ar, N 2 , CF 2 Cl 2 . There is no evidence for resonance fluorescence. The implication of the observations for the theory of radiationless transitions is discussed.