Fragment Aligned Molecular Orbital Analysis: An Innovative Tool for Analyzing Atypical Chemical Bonding

In chemical research, it is a common practice to carry out quantum chemical calculations and analyze the canonical molecular orbitals (CMOs) obtained to study electronic structures of chemical systems. However, extensive orbital mixing of CMOs especially in molecular clusters significantly complicates our understanding of the electronic structures. In this paper, we have developed an innovative tool called fragment aligned molecular orbital (FAMO) analysis, which reconstructs our modular chemical picture by making use of the Procrustes analysis in statistical theory to align the occupied molecular orbitals of a molecular species against the occupied (molecular) orbitals of the constituting fragments of the cluster, and results in a set of chemically intuitive semilocalized orbitals. This alignment technique minimizes the extensive orbital mixing, thus allowing precise observation of bonding interactions in complex chemical systems. A few representative clusters have been selected as showcase examples to demonstrate the advantage of FAMO analysis in deciphering the distinct bonding interactions in cluster compounds.