We propose an effective quantum information-assisted complete active space optimization scheme (QICAS). What sets QICAS apart from other correlation-based selection schemes is (i) the use of unique measures from quantum information that assess the correlation in electronic structures in an unambiguous and predictive manner and (ii) an orbital optimization step that minimizes the correlation discarded by the active space approximation. Equipped with these features, QICAS yields, for smaller correlated molecule, sets of optimized orbitals with respect to which the complete active space configuration interaction energy reaches the corresponding complete active space self-consistent field (CASSCF) energy within chemical accuracy. For more challenging systems such as the chromium dimer, QICAS offers an excellent starting point for CASSCF by greatly reducing the number of iterations required for numerical convergence. Accordingly, our study validates a profound empirical conjecture: the energetically optimal nonactive spaces are predominantly those that contain the least entanglement.

Full configuration interaction (FCI) solvers are limited to small basis sets due to their expensive computational costs. An optimal orbital selection for FCI (OptOrbFCI) is proposed to boost the power of existing FCI solvers to pursue the basis set limit under computational budget. The optimization problem coincides with that of the complete active space SCF method (CASSCF), while OptOrbFCI is algorithmically quite different. OptOrbFCI effectively finds an optimal rotation matrix via solving a constrained optimization problem directly to compress the orbitals of large basis sets to one with a manageable size, conducts FCI calculations only on rotated orbital sets, and produces a variational ground-state energy and its wave function. Coupled with coordinate descent full configuration interaction (CDFCI), we demonstrate the efficiency and accuracy of the method on carbon dimer and nitrogen dimer under basis sets up to cc-pV5Z. We also benchmark the binding curve of nitrogen dimer under cc-pVQZ basis set with 28 selected orbitals, which provide consistently lower ground-state energies than the FCI results under cc-pVDZ basis set. The dissociation energy in this case is found to be of higher accuracy.

The convolution of the excitation energies, computed by the complete active space self-consistent field (CASSCF) or other CAS-based methods, of an ensemble of geometries generated by molecular dynamic simulations is a usual recipe to obtain the absorption spectrum or the density of states of a chromophore. This approach requires that all the considered geometries have the same molecular orbitals within the active space. However, the different geometrical features and/or the different influence of the solvent or biological environments along the sample geometries makes the preservation of the active space a challenging task, which is usually ignored. In this work, we present an algorithm to correct for the active space of geometry ensembles in CASSCF calculations. The algorithm is based on the calculation of the molecular orbital overlap matrix between a previously selected reference geometry, with the desired active space, and each of the sampled geometries. Depending on the value of the overlap matrix elements, the algorithm determines whether one or more pairs of molecular orbitals of the sampled geometry have to be swapped for a subsequent CASSCF calculation. We have applied the developed algorithm to quantum mechanics/molecular mechanics CASSCF/MM and CASPT2/MM calculations for sets of geometries of the five canonical nucleobases in aqueous solution obtained from classical molecular dynamics simulations. The algorithm shows a very good efficacy since it recovered the correct active space for 76\% of the geometries which presented undesired molecular orbitals in the active space after the first CASSCF wavefunction optimization. In addition, the importance of having the same orbitals within the active space for all the geometries is discussed based on the computed density of states for the solvated nucleobases.