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We formulated the density equation theory (DET) using the spin-dependent density matrix (SDM) as a basic variable and calculated the density matrices of the open-shell systems and excited states, as well as those of the closed-shell systems, without any use of the wave function. We calculated the open-shell systems, Be(3S), Be−(2S), B+(3S), B(2S), C2+(3S), C+(2S), N3+(3S), and N2+(2S), and the closed-shell systems, Be, Be2−, B+, B−, C2+, N3+, H2O, and HF. The new properties calculated are the transition energies and the spin densities at the nuclei. Generally speaking, the accuracy of the present results is slightly worse than that of the previous one using the spin-independent density matrix.

Direct determination of second-order density matrix using density equation: Open-shell system and excited state