Variational Selection with tPBE. The above steps are repeated for N trial values of λ, resulting in the generation of N trial trial active spaces. Wave functions are computed using each of the N trial active spaces with CASCI calculations carried out by DMRG. We then select the active space that has the lowest average tPBE energies between the ground state and the excited state of interest. This concludes the description of λAPC-tPBE.