We study the generalized Pauli constraints using full configuration interaction (exact diagonalization) method. These constraints go beyond the Pauli exclusion implied by antisymmetry and yield inequalities on the natural orbital occupation numbers of the one-body reduced density matrix. In this contribution, the basis set dependence of the one-body reduced density matrix is studied in small systems. We utilize standardized Gaussian basis sets including Pople-style, Ahlrich-style and Dunning-style basis set. We focus on small atoms and diatomic systems and present preliminary results concerning the basis set error in the 1-RDM eigenvalues.