Structural origin of specific eigenvalues in chemical graphs of planar molecules molecular orbital functional groups

Within the framework of a functional group-like approach, the structural origin of eigenvalues ± 2, ± 1, ± √ 3, ± √ 2, and 0 are detailed. Methods for recognizing their occurrence in molecular graphs without evaluating the complete eigenspectrum are given. A graph theoretical method for evaluating the corresponding eigenvectors for these eigenvalues is elaborated. Collections of subspectral structures are tabulated. Construction of whole series of structurally related molecular graphs having the same eigenvalue can be frequently be accomplished once a given eigenvector pattern is recognized.