where 𝐴𝐴 ̂ is the antisymmetrizer, and 𝜒𝜒 𝑗𝑗 𝑈𝑈 is the jth block-localized spinorbital of fragment U (𝑈𝑈 = 𝑋𝑋, 𝑌𝑌), and 𝑁𝑁 𝑈𝑈 is the number of electrons. For the four singly excited states in the MAS, one of the two highest occupied orbitals is replaced by one of the two lowest unoccupied orbitals, and Ξ 𝐴𝐴 is optimized individually using the BLE method for the non-aufbau configurations. Note that "state" in this Letter refers to a spin-adapted wave function representing the exact density by incorporating dynamic correlation with BLKS-DFT; it is different from a determinant configuration.