Part I

PHYSICAL ASPECTS OF PHOTOCHEMISTRY

1 Introduction

The format of this report is similar to that of my last contribution. In general, emphasis is placed on intramolecular photophysical processes. Several aspects of photochemical excited-state decay processes are covered in later chapters of this volume.

In the two-year period covered in this report there have been a number of significant developments, amongst which are the following: (i) the relentless progress of ab initio methods of calculating excited-state properties as exemplified by calculations on a model of the active site in the iron-sulphur protein rubredoxin, (ii) fresh impetus and progress towards methods of calculation which avoid the Bom-Oppenheimer separation, (iii) a major study of cyclic π-electron systems that uses magnetic circular dichroism, which should advance the wider application of this technique, (iv) the development of the concept of a proximity effect to interpret the photophysical properties of N-heterocyclics, (v) the remarkable observations of mode-to-mode vibrational-energy flow in the first excited singlet states of benzene and aniline, and (vi) the probing of homogeneous linewidths in fluid solutions in studies of the anti-Kasha fluorescence of aromatic hydrocarbons.

2 Calculations of Electronically Excited States

Methods. — The application of ab initio quantum-mechanical calculations to problems of interest to experimental photochemists has been discussed briefly. The effect of the choice of basis set, including the addition to the basis of so-called 'polarization functions', and of the extent of configuration interaction on calculations of electronic spectra, the effect of substituents and geometry upon the relative energies of states, and of potential surfaces for chemical reactions of excited states are all illustrated by examples taken from the recent literature. A new restricted self-consistent field (RSCF) method has been proposed for the calculation of excited states. The excited-state wavefunction obtained from RSCF guarantees the orthogonality with the Hartree–Fock (HF) ground state and satisfies a number of Brillouin-type theorems. Cluster expansion is a technique for obtaining exact wavefunctions from approximate ones. When applied to open-shell systems it takes the form of the symmetry-adapted cluster (SAC) expansion method. The ground state ψg of a given spin-space symmetry is given in equation (1), where ηg is the normalization factor, θ the symmetry projector, CI, the

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

coefficients obtained from variational equations, SI+, the symmetry-adapted excitation operator, and Θ0 a reference wavefunction. It has been shown that the set of functions {ΘK}, where Θ0 = ηkPΘSk+ψ'g (P = 1 - |ψg x ψg|), forms a basis for the excited states of the same symmetry as the ψg and can lead to exact excited states. The method can be extended to excited states having symmetries different from the ground-state symmetry. A new method for calculating SCF wavefunctions for the excited states of atoms and molecules has been proposed in which for every iteration a number of diagonalizations of matrices representative of different operators are undertaken. The procedure results in a rapid convergence to the correct SCF limit. The variational bounds to excited states calculated from a generalized Brillouin-Wigner equation and from a projection operator method have been investigated.

A much improved scheme for the calculation of multiconfiguration self-consistent field (MCSCF) wavefunctions has been published recently. The authors assert that their scheme is a superior one for constructing computer programs for the MCSCF method and that it leads to programs with maximum efficiency. The authors introduce an exponential transformation for the trial state functions in a manner similar to an exponential spin–orbital transformation previously used in the method and which is intended to improve the convergence properties.

A modified Rydberg formula for atomic states has been suggested that gives accurate energies of [core] (ns21S) terms for a wide variety of atoms. The method can also be applied to [core] (nlnl' 2s+1L)] terms and extended to include configurations of the type [core] npN (N = 1 — 6). In HF calculations the core orbitals are frequently replaced by an effective potential or pseudopotential. An analysis of the use of pseudopotentials in local-density (LD) formalism calculations shows that their application there may be more appropriate than in HF calculations where more approximations are involved. An LD pseudopotential treatment of several excited and ionic states of first-row atoms showed errors due to the frozen core to be less than 10-3 hartree. The first-order HF equations of the 1s2p3s4P0 state of three-electron atomic systems have been solved exactly using the nuclear charge expansion method. There is only limited experimental information available at the present time on...