First-principle calculations of 5*f*^{n} (*n*=0-7) electronic configurations are performed with several density functional theory (DFT) methods to describe the localized/delocalized states and obtain the precise population of the 5*f* manifold in delta-plutonium (*δ*-Pu). The results show that spin polarization clearly reduces the cohesive energies of each electronic configuration, and enhances the cohesion properties. For 5*f*^{0}, 5*f*^{1}, 5*f*^{3}, 5*f*^{4}, and 5*f*^{6} electronic configurations, the cohesive energies obtained by the spin- polarized local density approximation (SP-LDA)+*U* method are markedly smaller than that by the SP-LDA method when the lattice constant of *δ*-Pu exceeds 0.475 nm. The cohesive energies calculated with the spin-polarized generalized gradient approximation (SP-GGA)+U method are smaller than that by SP-GGAmethod, except for 5*f*^{4} and 5*f*^{6} electronic configurations, and the former trend to coincide with SP-LDA results when the lattice constants are larger than 0.570 nm. For the SP-LDA(GGA)+Umethod, the cohesive energies of 5f0, 5f1, 5f3, 5f4, and 5f6 (5f0, 5*f*^{1}, 5*f*^{2}, 5*f*^{3}, 5*f*^{5}, and 5*f*^{7}) electronic configurations are all equal, while the cohesive energies of 5*f*^{2}, 5*f*^{5} (5*f*^{4}) electronic configurations are the same as that of the 5*f*^{7} (5*f*^{6}) electronic configuration. The cohesive energies of 5fn electronic configurations calculated using the other methods are equal. 5*f* projected densities of states show that spin polarization results in the exchange split behavior of 5*f* orbitals. Several 5*f* states are removed from the Fermi level, which lowers the contribution of 5*f* states to chemical bonding, and enhances the lattice constant, indicating that strong spin polarization induces partial localization of 5*f* orbitals. The optimized lattice constants obtained by the SP-LDA method are in good agreement with the experimental values, but the SP-GGA+*U* method sharply overestimates the lattice constant (by up to about 20%).