Localization of molecular orbitals on fragments

• Published in: Journal of computational chemistry 2012-06, Vol.33 (17), p.1495-1510
• Main Author: Sax, Alexander F.
• Format: Article
• Language: English
• Subjects: Algorithms; Chemical reactions; fragment; localized; Mathematical functions; Mathematical problems; Molecular chemistry; non-iterative algorithm; orbitals; orthogonal Procrustes problem
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.22980

A non‐iterative algorithm for the localization of molecular orbitals (MOs) from complete active space self consistent field (CASSCF) and for single‐determinantal wave functions on predefined moieties is given. The localized fragment orbitals can be used to analyze chemical reactions between fragments and also the binding of fragments in the product molecule with a fragments‐in‐molecules approach by using a valence bond expansion of the CASSCF wave function. The algorithm is an example of the orthogonal Procrustes problem, which is a matrix optimization problem using the singular value decomposition. It is based on the similarity of the set of MOs for the moieties to the localized MOs of the molecule; the similarity is expressed by overlap matrices between the original fragment MOs and the localized MOs. For CASSCF wave functions, localization is done independently in the space of occupied orbitals and active orbitals, whereas, the space of virtual orbitals is mostly uninteresting. Localization of Hartree–Fock or Kohn–Sham density functional theory orbitals is not straightforward; rather, it needs careful consideration, because in this case some virtual orbitals are needed but the space of virtual orbitals depends on the basis sets used and causes considerable problems due to the diffuse character of most virtual orbitals. © 2012 Wiley Periodicals, Inc. The reliability of localized fragment orbitals depends on the quality of the molecular orbitals used in the localization process; it is important that orbitals that describe different bonding situations, such as CH‐bonding and CC‐bonding, are not mixed. Also mixing of occupied and virtual orbitals deteriorates the reliability of the localized fragment orbitals and should be avoided. CAS‐SCF orbitals fulfill these requirements much better than HF orbitals.