The application of the molecular model to describe inelastic electronic transitions in atom-atom collisions is reviewed. The removal of defects of the model by the introduction of electron translation factors is discussed with reference to some specific examples. A brief survey is given of the difficulties associated with the transformation from an adiabatic to adiabatic representation for complex systems. The advent of collision spe.ctroscopy with the development of new experimental techniques in the past two decades produced an unprecedented wealth of new experimental data on energy loss spectra in ion-and atom-atom collisions [ 111. On the basis of these data, it became possible to test the validity of the molecular model.Although the model has proved to be remarkably successful in providing a qualitative interpretation of both inner-and outer-shell processes [ 121, the lack of Galilean invariance when a finite molecular basis set is used, leads to many problems in quantitative applications. For example, the existence of certain nonvanishing off-diagonal matrix elements in the limit of large interatomic separations makes it formally impossible to obtain a well-defined scattering matrix. As a consequence, the total cross section may even diverge in some cases. Of course, in many, but not all, practical applications udhoc prescriptions are often successful in circumventing these problems [lo]. However, from the theoretical standpoint these procedures are imperfect.The basic problem, which stems from the inability of a finite molecular basis set to represent the correct boundary conditions, can be solved formally by the introduction of electron translation factors (ETFS) [9]. However, except in the asymptotic region, where the ETFS are well defined, their particular form in the interaction region is arbitrary [13], being governed either by physical intuition [ 141, or by some variationally based optimization procedure [15][16][17]. Indeed, the only real criteria to justify any given ETF is completeness of the basis set lnlcmatid