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This work extends the concept of seniority number, which has been widely used for classifying  N-electron Slater determinants, to wave functions of N electrons and spin S, as well as to N-electron  spin-adapted Hilbert spaces. We propose a spin-free formulation of the seniority number operator  and perform a study on the behavior of the expectation values of this operator under transformations  of the molecular basis sets. This study leads to propose a quantitative evaluation for the convergence  of the expansions of the wave functions in terms of Slater determinants. The non-invariant character  of the seniority number operator expectation value of a wave function with respect to a unitary  transformation of the molecular orbital basis set, allows us to search for a change of basis which  minimizes that expectation value. The results found in the description of wave functions of selected  atoms and molecules show that the expansions expressed in these bases exhibit a more rapid convergence  than those formulated in the canonical molecular orbital bases and even in the natural orbital  ones.Fil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Torre, Alicia. Universidad del País Vasco. Facultad de Ciencia y Tecnología. Departamento de Química Física; España;Fil: Lain, Luis. Universidad del País Vasco. Facultad de Ciencia y Tecnología. Departamento de Química Física; España;Fil: Massaccesi, Gustavo Ernesto. Universidad de Buenos Aires. Ciclo Básico Común; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Oña, Ofelia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin

Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions