Chemical Concepts from Molecular Orbital Theory
This chapter provides an overview of the history and application of molecular orbital theory, with a focus on the localization of molecular orbitals (MOs) and its connection to chemical concepts and algorithms in computational chemistry. Two main strategies for obtaining localized molecular orbitals (LMOs), namely, orthogonal localized molecular orbitals (OLMOs) and non-orthogonal localized molecular orbitals (NOLMOs), are discussed in detail. There are several different spatial localization schemes available for obtaining OLMOs, including Boys, Edmiston-Ruedenberg, and Pipek-Mezey methods. Furthermore, a specialized approach for regional LMOs has been developed for the elongation method. Two recently developed novel localization approaches are highlighted. Both consider a balance between localization in physical space and some additional features in energy space. The regulated localization approach involves minimizing a localization cost function that combines the spatial spread function (as in Boys method) and kinetic energy (to limit NOLMO oscillation). The resulting regularized NOLMOs offer enhanced smoothness and better transferability for linear scaling calculations, due to their reduced kinetic energies. In the second approach, a localization cost function that combines the spatial spread function and the energy spread function is used, so that the resulting OLMOs, called molecular orbitalets, are localized both in physical and energy spaces. Frontier molecular orbitalets, key for the localized orbital scaling correction to density functional approximation, extend the role of frontier molecular orbitals for small systems and describe the chemical reactivity of large systems with energy and locality insight, with potentially broad applications.
