Exploration of the eigenvectors of the localization delocalization matrices for rutile TiO2 finite unit cells and solids: from resonance to QTAIM

The newly introduced eigenvectors of the localization-delocalization matrices (LDM) are used to characterize the distinct functional groups in the TiO2 rutile solid material. The 1 × 1 × 1 finite unit cell and the 1 × 1 × 1 finite unit cell with the appropriate edge and corner atoms due to periodicity are included, which are neglected in a standard unit cell, as well as the solid (periodic) material are examined. The LDMs are constructed using all atoms in the two finite unit cells (for the periodic cases the corresponding atoms are used, and all other atoms are neglected). The eigenvectors and the corresponding localization/delocalization modes are used to indicate the functional groups and the resonance structures.