Mayer's Effective Minimal Localized Molecular Orbitals

About 30 years ago, Mayer presented a theory leading to the concept of an effective minimal atomic basis. A set of a posteriori-defined, fragment-localized molecular orbitals (LMOs) was obtained as a byproduct. In this work, a new set of LMOs, termed Mayer's effective minimal LMOs, is derived from this byproduct; it can be viewed as arising from a compactification of atomic orbitals projected onto the occupied space. The procedure is fully self-contained, requiring no input beyond that of the underlying quantum chemical calculation. The resulting LMOs are orientation invariant, computationally economical, and can be partitioned into disjoint subsets assigned to atoms or multiatomic fragments. Mayer's effective minimal LMOs span the occupied space, but their number exceeds its dimension; they therefore form a frame rather than a basis in the strict sense. The size of the set does not grow with the original AO basis but remains at a value prescribed by the user, a prudent choice being the minimal atomic orbital basis dimension.