Spectroscopic and Theoretical Aspects

BY R. DEVONSHIRE

1 Introduction

This Chapter covers the two-year period July 1975 to June 1977 inclusive. The format is broadly similar to that followed by David Phillips in previous years. My aim has been to make papers relatively easy to find, given that Specialist Periodical Reports do not contain a subject index. The selection of papers for the areas covered in this section is of necessity a very limited one; a simple listing of relevant papers would more than fill the available space. The end result is somewhere between being a telephone directory and a personal scrapbook.

A number of areas have developed significantly since this section last appeared and coverage of these is reasonably complete, viz. optoacoustic and related studies, single vibronic level studies, especially of the simple dicarbonyls, magnetic field effects, and laser photochemistry in general. No attempt has been made to report on the extensive literature on the photolysis of atomic or crystalline systems.

My overriding impression having completed this report of current work in a number of areas in photochemistry is of the subject's tremendous vitality at the present time.

2 Calculations of Electronically Excited States

The papers reported in this section are concerned with developments in the methods of calculation of spectroscopic and other related excited-state properties of atoms and molecules of interest in photochemistry. Although the coverage of calculations on particular systems is concentrated in this section, a number of papers containing extensive calculations appear in later sections.

An inequality formulation of the well known Hund's rules has been investigated numerically. Restricted Hartree–Fock SCF energies of various states of atoms and ions of the He, C, N, and O isoelectronic series were used to examine the behaviour of ΔE, Δ. the differences in total energy, electron–electron repulsion, and electron-nuclear repulsion respectively, in going from a singlet to a triplet state. ΔE was found to be positive in all cases because Δ was always positive and large enough to more than compensate for occasional negative values for Δ found, in particular, for the neutral atom cases. Viewed as a two-step process, the change from singlet to triplet involves firstly a conversion with frozen orbitals to an approximate triplet state which will certainly be at lower energy because of the smaller Vee. followed by a contraction of the wavefunction which results both in an increase in Vee, thus making it possible for an overall change in Vee, Δ, that is negative, and in a large decrease in Ven which makes Δ always positive.

A recent SCF theory of excited states has been used to calculate hole states of free atoms. In the method each shell is specified by a subset of orbitals and an occupation number. A suitable choice of starting orbital exponents is found from the equivalent core (EC) approximation. The results of calculations on various hole states of Ne, Na, Mg, and S are in excellent agreement with experimental measurements, and the method should prove to be particularly valuable in the interpretation of Auger and shake-up processes as it is successful for any number of open shells. The use of the one-Hamiltonian and sequential orthogonalization methods in the calculation of particle and hole states has been discussed and a number of SCF methods used in the calculation of excited states are compared in a paper which extends recent restricted Hartree–Fock calculations in high-spin open shells to singly excited states. The concept of localization in molecular excited states is critically examined in an interesting paper which proposes the use of localized molecular orbitals to describe delocalization phenomena. It is demonstrated how such a change from the usual discussion in terms of delocalized molecular orbitals can give a valuable insight into configuration interaction processes.

An algorithm has been suggested to solve the divergence problem of the quadratically convergent SCF method, and the CNDO/2 method with configuration interaction has been successfully applied to the problem of excited-state geometries in a study of the lowest excited singlet state of a number of small molecules. An algorithm for the calculation of electronic structure and spectra using the CNDO/2 CI method has also been published.

The energies of the alternant molecular orbitals, AMO's, for any alternant homonuclear molecule having a singlet ground state have been shown to be related to the conventional Hartree–Fock MO energies by a simple expression involving the correlation correction. A combined AMO and generator–co-ordinate method has been used to study excitations in the electron-gas. Ab initio SCF–LCAO calculations of a number of simple molecules, mainly diatomic species, were found to be sufficiently accurate to give the general character of the electron distribution. A theoretical approach which combines the ideas of the valence-electron and Thomas–Fermi–Dirac theories differs from earlier related treatments in that the core potential is completely non-empirical and is the same for all valence levels. The effects of many-electron rearrangements in excited states on the expressions for the electronic excitation energy have been discussed, and model calculations of transition energies for Be indicate that relaxation corrections are substantial for core excitations, but are small for valence transitions.

The use of Green's functions in the calculation of energy levels from spectral properties is featured in a general review of the application of Green's functions in quantum mechanics. Perturbation treatments based on Green's functions have been used in the calculation of excitation energies in π-electron systems and excited state lifetimes in -atomic systems. The calculation of excited states using the natural transition orbital (NTO) method has been proposed for systems...