It is shown that if the ‘mean excitation energy’ assumption is introduced in the Brillouin-Wigner perturbation series, then the resulting series can be exactly summed. The implications of the result for calculating energy shift and for constructing trial functions are examined with special reference to the ground state of the helium atom.

The Hartree-Fock procedure is used to study the behaviour of the ground state of a system ofM spinless electrons distributed overN equivalent and equidistant sites (M ⩽N) as a function of the strength of the mutual repulsion between the electrons. Below a critical strength, all initial configurations are seen, after repeated iterations, to converge to a unique solution. Above this critical strength, in addition to the initial configurations which lead to a unique solution, there exist configurations which on repeated iterations give rise to stable two-period solutions. Although the number of independent stable two-period solutions depends on the coupling strength, for no value of the coupling are stable solutions of periodicity higher than two seen.

The vibrational overtone spectra of aryl and alkyl C-H stretch vibrations in benzaldehyde have been studied using conventional IR and thermal lensing technique at room temperature. The stretching vibrational frequencyω_e, anharmonicity constantω_ex_e and the dissociation energies of the two C-H bonds have been calculated. The bond length of C-H bond in aryl position has been estimated.