Spectroscopic and Theoretical Aspects

BY D. PHILLIPS

1 Introduction

The format for this chapter is as in previous years, with the exception that phosphorescence–microwave resonance experiments are also discussed here. For reasons of economy of space, only scant attention is paid to the early section on energy-level calculations. As before, discussion in this chapter is confined exclusively to organic molecules.

2 Molecular Orbital Calculations

Several methods continue to be developed for the estimation of excited- state energy levels and geometries, and the oscillator strengths of transitions. Improved basis functions for ab initio calculations on large molecules have been given, and the use of unrestricted Hartree–Fock (HF) theory in considering orbital energy crossing has been commented upon. Extended HF theory applied to excited electronic states has been described. The greatest single source of error in calculations on systems containing two or more electrons is the systematic neglect of correlation between electrons having antiparallel spins. Methods by which electron correlation can be included in calculations on large molecules have been discussed, and the method has been applied to benzene and linear polyenes. The effects of electron correlations on radiative transition-matrix elements have been investigated, and calculations show that use of a modified HF operator drastically reduces the number of effective electronic configurations. Electron-correlation effects on electron-density calculations in excited electronic states of molecular species have also been described. The inclusion of electron correlation in calculations corrects for the inadequacies of the independent-particle approximation. Because of the basic importance of electron pairs in chemical binding, it is appealing to attempt to incorporate correlation effects by replacing single-electron orbitals in the independent-particle approach by electronic pair functions, termed 'geminals'. The theory of the geminal approach has been given, and applications have been mentioned.

Theoretical studies of the kind outlined in this section, in which molecular excitation energies and oscillator strengths are determined, can be of great value in assisting the interpretation of experimentally observed spectra and in predicting the photophysical and photochemical behaviour of molecules not yet studied experimentally. A recent paper has pointed out that since it is excitation energies and oscillator strengths which are of principal interest to those studying photoeffects, the conventional theoretical approach utilizing the calculation of wavefunctions and of energies of individual states is wasteful in that much of the information contained in the individual wavefunctions is of no interest. Moreover, the excitation energy in this procedure is derived as the relatively small difference between energies of two states, and large errors can be introduced. To overcome these difficulties, an energy-shift theory 7 has been developed which permits direct calculation of molecular electronic excitation spectra. The formalism for this approach has been presented, but it has not yet been applied to particular molecules.

Electrostatic force theory has been used to predict the shape of ground- and excited-state molecules, and the use of molecular symmetry in SCF calculations has been discussed. Valence-electron-only calculations of electronic structures have been outlined and basic formulae given for the one-electron perturbation calculation of molecular Rydberg excited states. A method for the characterization of excited stationary states has been described, and a theoretical study of transitions from the first excited singlet states of molecules to higher singlet states has been made. These were semi-empirical PPP calculations on benzene, naphthalene, phenanthrene, pyrene, benzanthracene, benzpyrene, triphenylene, and azulene. In all cases the most intense transition, the 1Lb ->1Kb, was found to be near to the 3La ->3Ka transition in the triplet spectrum. Since excited singlet state absorption spectroscopy has become possible recently, these results are of great interest. Table 1 shows selected data from this paper compared with experimental values.

It has been shown recently that SCF MO calculations with limited configuration interaction can yield good descriptions of the equilibrium geometries of low-lying excited states of molecular species. Molecules studied in this way include acetylene, HCN, FCN, formaldehyde, F2CO, HCF, HNO, and FNO.

The dipole moments of excited states of molecules are important indicators of chemical behaviour, and attention has been focused recently on differences in dipole moments in excited singlet and triplet states of several molecules. Three principles were outlined which permit rationalization of the magnitudes of the singlet (μS) and triplet (μT) dipole moments:

(1) The two active electrons are more separated in the triplet state than in the singlet.

(2) If the two active MOs (singly occupied and normalized) are designated u and v, where possible the more tightly bound orbital (u) will differ least in singlet and triplet states, so that differences in μ are revealed by differences in (v) rather than in (u).

(3) If the shapes of singlet and triplet states differ, a proper comparison must allow for an appropriate change in valence angles.

The principles above were applied to the radical NH and the molecules CO, formaldehyde, methylene, azulene, BeO, and CaO. With the exception of the last two molecules, the guiding principles provided an adequate explanation of results, although difficulties arise with the larger molecules. In the cases of BeO and CaO the extensive configuration interaction in these molecules prevents the use of the simple rules outlined above. A theoretical study of pK values of excited states using a pair-density matrix has been reported.

Theoretical calculations on energy levels, oscillator strengths, etc. of individual species will now be briefly outlined. The binding...