Calculations for C+3, C3 and C–3 show that MO (molecular orbital) and NPSO (non-paired spatial orbital) functions provide the best simple description of the electronic structure of these species. The problem of the best a priori method of generating simple, unique NPSO spin eigenfunctions has been considered. Two methods were investigated; the first emphasizes the most favourable spin distribution by means of a spin projection operator, while the second excludes completely the least favourable spin distribution. In applying these methods, the double-quartet scheme permits the necessary qualitative ordering of the spin distributions. A summary of all relevant NPSO calculations done shows the exclusion method to be generally more successful.