I am excited to share a new paper that I have co-authored with my esteemed colleagues, Edward F. Valeev, Robert J. Harrison, and Deborah A. Penchoff.
In this work, we present a method for determining nearly numerically exact orthonormal orbitals that are optimal for evaluating the energy of arbitrary (correlated) states of atoms and molecules by minimizing the energy Lagrangian. The orbitals are expressed in real space using a multiresolution spectral element basis that is adaptively refined to achieve the user-specified target precision while avoiding the ill-conditioning issues typically associated with AO basis set expansions in traditional correlated models of molecular electronic structure.
Our orbital solver, combined with a variational electronic structure model (selected Configuration Interaction or CI), provides energies of comparable precision to a state-of-the-art atomic CI solver for light atoms. The calculated electronic energies of atoms and molecules are significantly more accurate than those obtained with Gaussian AO bases of the same rank. Furthermore, our method can determine these energies even when linear dependence issues preclude the use of AO bases.