Electronic structures of hexane isomers studied using quantum mechanics and graph theory

Abstract

Electronic and topological properties of hexane ( C 6 H 14) and its five geometric isomers are systematically studied quantum mechanically using several techniques such as positron–electron annihilation gamma-ray spectra, C1s binding energy spectra and carbon nuclear magnetic resonance (NMR) spectra, as well as information derived from graph theory. It is revealed that the Doppler-shift in the gamma-ray spectra of the hexane isomers is in the vicinity of the n-hexane molecule with small structural dependency, in agreement with the fact that the measured Doppler-shifts of other linear alkanes are in the vicinity of hexane. The present study further reveals the electronic structures of hexane isomers, which are deeply rooted into the carbon core electrons, more than mere properties in the valence space. The calculations show that the highest occupied molecular orbitals (HOMOs) of the isomers exhibit less important roles in gamma-ray spectra; whereas the electron–positron annihilation is dominated by the electrons of the lowest occupied valence orbitals (LOVOs) and other valence electrons underneath the HOMO electrons, in agreement with previous findings. The present study further reveals that the C1s binding energies of the isomers exhibit association with the nodes of the isomers using graph theory. That is, more branched carbons likely engage with larger chemical shift, which is indicated by the largest eigenvalues (LEVs) of the adjacency matrix (AM) from graph theory. The chemical shift of the carbon NMR spectra is revealed by the LEVs of the Laplacian matrix (LM) obtained from chemical graph theory.