The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE^ac with the UHF-energy shows thatE_UHF<E^ac in each case revealing some kind of an upper bound nature ofE^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.

Radiationless transitions in lanthanide ions embedded in glassy and crystalline hosts have been briefly reviewed. The correlations of multiphonon relaxation rates with energy gaps, vibrational frequencies, temperatures and electronic symmetries have been discussed. The essence of various theories, such as Nth order methods, non-adiabatic Hamiltonian method, dynamic coupling model has also been presented.

It has been shown that circular dichroism (CD) and two-photon absorption (TPA) spectroscopies are capable of throwing new light on fⁿ ⇒ fⁿ optical transitions. High-resolution circular dichroism of single crystals can provide information on the chiral environment as well as on the magnetic and electric quadrupolar transition moments of lanthanide ions, and thus can be exploited for the purpose of assignment of bands. TPA, on the other hand, although capable of resolving crystal-field components better than one-photon absorption, exhibits puzzling intensity features, which need to be sorted out before it can be generally used as a diagnostic tool.

The application of supersonic jet spectroscopy to the study of low-frequency, large-amplitude, anharmonic motions in the excited states of floppy molecules has been discussed. In particular, our work on inversion and torsional vibrations of 9, 10-dihydroanthracene and dihydrophenanthrene by laser-induced fluorescence excitation technique has been reviewed. The inversion of dihydroanthracene is nicely fitted with a quadratic Gaussian type potential function and the height of the barrier in the S₁ state is calculated to be 94 cm₋₁. The inter-ring torsional frequencies of dihydrophenanthrene appear as a prominent progression and Frank-Condon analysis shows that the S₁ state of the molecule is planar in contrast to a skew configuration in the ground state. A peculiar alternation of band gaps has been noticed.

Cold isolated molecules produced in seeded supersonic jets are ideal systems for obtaining information on the nature of potential energy surfaces of excited states. The power of the technique is illustrated with examples of molecules having one or two out-of-plane low-frequency vibrations.