Next-generation quantum theory of atoms in molecules for the ground and excited states of fulvene

Abstract

A vector-based representation of the chemical bond is introduced, which we refer to as the bond-path framework set B ={p, q, r}, where p, q, and r represent 3 eigenvector-following paths with corresponding lengths H-*, H, and the familiar quantum theory of atoms in molecules (QTAIM) bond-path length (BPL). The intended application of B is for molecules subjected to various types of reactions and distortions, including photoisomerization reactions, applied torsions , or normal modes of vibration. The lengths H-* and H of the eigenvector-following paths are constructed using the (2) Hessian eigenvectors, respectively, along the bond path, these corresponding to the least and most preferred directions of charge density accumulation. In particular, the paths p and q provide a vector representation of the scalar QTAIM ellipticity epsilon. The bond-path framework set B is applied to the excited state deactivation of fulvene that involves distortions along various intramolecular degrees of freedom, such as the bond stretching/compression of bond-length alternation and bond torsion distortions. We find that the H-* and H lengths can differentiate between the ground and excited electronic states, in contrast to the QTAIM BPL. Five unique paths were presented for B= {(p(0),p(1)), (q(0),q(1)), r} for the ground and first excited states where the profile of the scaling factor, the ellipticity epsilon, reveals a large unexpected asymmetry for the excited state.