Modified participation ratio approach: application to edge-localized states in carbon nanoclusters

Abstract

For nanoclusters and solids, the localization analysis of one-electron states, or MOs (molecular orbitals), is frequently provided by using the so-called participation ratio (PR) index. To this conventional PR approach, we add for each MO the new index σIPR which we define as an average fluctuation of the inverse PR (IPR) value. Typically, the σIPR index displays a significant sensitivity to any spatial irregularity in the MO distribution over molecule. We apply the thus extended PR analysis to the graphene nanoflakes of different types, and small nanodiamond structures including NV color centers as well. The proposed scheme has the virtue of being quite simple, and in case of huge clusters it allows one to rapidly detect orbitals with unusual non-uniform distribution. In particular, the localization of edge states in graphene molecules is examined in this way.