  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 a 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 the carbon dimer and nitrogen dimer under basis
sets up to cc-pV5Z. We also benchmark the binding curve of the nitrogen dimer
under the cc-pVQZ basis set with 28 selected orbitals, which provide
consistently lower ground-state energies than the FCI results under the cc-pVDZ
basis set. The dissociation energy in this case is found to be of higher
accuracy.
