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In a previous work (arXiv:2010.02027) we showed how the full configurationinteraction (FCI) ground state energy can be obtained as a functional of anarbitrary reference wavefunction by means of a gradient descent or quasi-Newtonalgorithm. Here, we extend this approach and consider the optimization of thelow-energy subspace of the Hamiltonian from an arbitrary reference subspace.The energies along the optimization path are obtained in terms of transitionmatrix elements among the states in the reference subspace. We show anapplication of the algorithm with a reference subspace constructed from anon-orthogonal configuration interaction (NOCI) formalism to describe theavoided crossing in LiF and the low-lying singlet and triplet spectrum offormaldehyde.

Approaching the Full Configuration Interaction Low-Energy Spectrum from an Arbitrary Reference Subspace