Circuit Resonance Energy:  A Key Quantity That Links Energetic and Magnetic Criteria of Aromaticity

Abstract

Energetic and magnetic criteria of aromaticity are different in nature and sometimes make different predictions as to the aromaticity of a polycyclic pi-system. Thus, some charged polycyclic pi-systems are aromatic but paratropic. We derived the individual circuit contributions to aromaticity from the magnetic response of a polycyclic pi-system and named them circuit resonance energies (CREs). Each CRE has the same sign and essentially the same magnitude as the corresponding cyclic conjugation energy (CCE) defined by Bosanac and Gutman. Such CREs were found to play a crucial role in associating the energetic criteria for determining the degree of aromaticity with the magnetic ones. We can now interpret both energetic and magnetic criteria of aromaticity consistently in terms of CREs. Ring-current diamagnetism proved to be the tendency of a cyclic pi-system to retain aromatic stabilization energy (ASE) at the level of individual circuits.

Multidimensionality of delocalization indices and nucleus‐independent chemical shifts in polycyclic aromatic hydrocarbons II: Proof of further nonlocality

“…Since the total ring current can be considered as composed of contributons from different circuits [24][25][26] (equation 1) and as the contribution from a given N-centre circuit (NC) to the current density (J Z (r; N C)) is proportional to the MCBI for the circuit NC , J Z (AB; N C) can be approximated by the MCBI projected as a vector in a diatropic manner on the bond between atoms A and B (MCBI(AB; N C)), thus:…”

“…The model reconciling magnetic and MCBI data relies on the fact that one can consider the total ring current as composed of different circuitcontributons [24][25][26] . For example, Anthracene contains six different aromatic circuits, three benzenoid circuits, two naphthalene like circuits and one circuit that follows the edge of the entire molecule.…”

Graph Theory of Aromatic Stabilization

“…In fact, the main origin of aromaticity in 3 is two length-six circuits and one length-ten circuit, all of which are conjugation circuits. 33,34 In general, inner π-bonds in PAHs, shared by two length-six conjugation circuits, have very large BREs. In marked contrast, two π-bonds that link two naphthalene nuclei in perylene (14) exhibit very small BREs, which must be attributed to the fact that the central ring is empty in Clar's sense.…”

Graph Theory of Ring-Current Diamagnetism

“…3133 We then derived a kind of ASE analytically from the ringcurrent diamagnetic susceptibility to unify energetic and magnetic criteria of aromaticity. 30,34,35 In this review article, we discuss the global aromaticity of polycyclic π-systems and related phenomena in conjunction with our graph theory of ringcurrent diamagnetism 3035 but without referring to any hypothetical polyene-like reference structure.…”