The developed UMRSF method was benchmarked against three different systems, covering a wide range of problems including atomic multiplets, bond breaking, and Jahn-Teller distortion. The test calculations employed the BH&HLYP density functional in conjunction with the 6-31G 69 or 6-31G(d) basis set, as noted below. The UMRSF-TDDFT and U-SF-TDDFT calculations with a collinear exchange-correlation (XC) kernel were performed using a local development version of the GAMESS-US program. It should be emphasized that both SF-TDDFT and MRSF-TDDFT can obtain the ground singlet state as one of their response states, unlike TDDFT. This is because the ground singlet state can be obtained by a single excitation from their reference triplet state. The ground 1 S state of Be has the electron configuration of 1s 2 2s 2 . The low-lying excited states of Be include the triplet 3 P x,y,z and singlet 1 P x,y,z , corresponding to the electron configuration of 1s 2 2s 2 p 1 k , where k = x, y, z. As it is mostly described by a single closed-shell configuration, the energies obtained by the two theories are nearly identical to each other However, the 3 Px, y and 1 Px, y components are completely mixed with each other in SF variants, resulting in a state energy of 3.676 and 3.688 eV with ⟨S 2 ⟩ = 1.0 (half-half mixture of singlet and triplet). As a result, it is not possible to assign their spin states.