Implementation of Occupied and Virtual Edmiston–Ruedenberg Orbitals Using Cholesky Decomposed Integrals

[Image: see text] We present a trust-region optimization of the Edmiston–Ruedenberg orbital localization function. The approach is used to localize both the occupied and the virtual orbitals and is the first demonstration of general virtual orbital localization using the Edmiston–Ruedenberg localization function. In the Edmiston–Ruedenberg approach, the sum of the orbital self-repulsion energies is maximized to obtain the localized orbitals. The Cholesky decomposition reduces the cost of transforming the electron repulsion integrals, and the overall scaling of our implementation is [Image: see text]. The optimization is performed with all quantities in the molecular orbital basis, and the localization of the occupied orbitals is often less expensive than the corresponding self-consistent field (SCF) optimization. Furthermore, the occupied orbital localization scales linearly with the basis set. For the virtual space, the cost is significantly higher than the SCF optimization. The orbital spreads of the resulting virtual Edmiston–Ruedenberg orbitals are larger than for other, less expensive, orbital localization functions. This indicates that other localization procedures are more suitable for applications such as local post-Hartree–Fock calculations.