Variational Active Space Selection with MC-PDFT

The selection of a good set of active orbitals for modeling strongly correlated quantum states is difficult to automate as it is highly dependent on the state and molecule of interest. As such, although many approaches have been proposed with some success, no single approach has worked in all cases. Here, we propose an improved framework for automated selection in which (i) multiple wave functions based on different active-spaces are generated, and (ii) the resulting wave functions are chosen between by some means of facile evaluation. Using this framework, we propose a method in which (i) we construct different active space orbitals through diagonalization of a parameterized operator, and (ii) we choose the state with the lowest tPBE absolute energy from multiconfigurational pair density functional theory (MC-PDFT) averaged over the targeted states of interest. We test the method using density matrix renormalization group (DMRG) wave functions with 40 active orbitals and bond index of 700, with no further orbital optimization following the active space selection. We find that with only four values of the parameter (i.e., with only four trial wave functions), we can obtain a mean unsigned error of only 0.19 eV for 199 vertical excitation energies in the QUESTDB database. Furthermore, the tPBE absolute energy proves robust in selecting between active spaces of very different sizes, over and above the wave function (CASCI/DMRG-CASCI) absolute energy. We believe this new framework is promising for the application of active space methods to chemical problems in a high-throughput fashion.