# Theoretical Elucidation of Aromaticity in Cyclic π-Conjugated Systems

Aromaticity is a molecular property inherent in cyclic conjugated systems. It had long been impossible to unambiguously decide whether or not a given cyclic conjugated system is aromatic. Thus, aromaticity has been a challenge to theoretical and experimental chemists. Dr. Jun-ichi Aihara established the criterion of aromaticity within the framework of Huckel molecular orbital theory and elucidated every aspect of aromatic character. He succeeded in interpreting aromaticity and ring-current diamagnetism consistently. His way of reasoning can be applied to all neutral and charged cyclic conjugated systems. His work is summarized below:

**1. Topological Resonance Energy and Aromaticity**

In 1975 Aihara graph-theoretically constructed a characteristic polynomial expected when a cyclic conjugated system is hypothetically deprived of aromaticity. He then defined topological resonance energy (TRE), a kind of aromatic stabilization energy (ASE), with reference to the energy derived from this polynomial. TRE was found to be the first general measure of aromaticity, being highly correlative with Dewar resonance energy (DRE), a semi-empirical ASE definable only for neutral π-systems. On the basis of this correlation, Aihara classified cyclic π-systems with positive and negative TREs as aromatics and antiaromatics, respectively.

TRE can be calculated not only for all possible planar π-systems but also for three-dimensional conjugated systems, such as polyhedral boranes and olefin-metal complexes. Hence, he is known as a chemist who established the concept of three-dimensional aromaticity. He systematically analyzed the aromaticity of fullerenes.

**2. Bond Resonance Energy and Kinetic Stability**

According to graph-theoretical analysis, TRE is a stabilization energy arising from the motion of π-electrons along various circuits in a conjugated system. Aihara then devised the method for estimating the destabilization energy expected when the cyclic motion of π-electrons through a given ?-bond is artificially interrupted. This destabilization energy is nothing other than the contribution of the π?-bond to TRE. He called it bond resonance energy (BRE).

BRE can be calculated for any π-bond in any cyclic conjugated system. Aihara found that the smallest or minimum BRE in a conjugated system represents properly the degree of kinetic stability for the π-system. When a fullerene molecule has ?-bonds shared by two pentagonal rings, they always exhibit large negative BREs. This must be why the isolated pentagon rule holds for fullerenes. The terms TRE and BRE were included in the Glossary of Terms Used in Theoretical Organic Chemistry, compiled in 1999 by the International Union of Pure and Applied Chemistry (IUPAC).

As an extension of the BRE concept, Aihara proposed a method for estimating the degree of superaromaticiry, i.e., the extra ASE of such π-systems as kekulene and cyclacenes due to macrocyclic conjugation. However, no π-systems were found to be superaromatic in this sense.

**3. Derivation of Magnetic Resonance Energy**

Aihara succeeded in interpreting aromaticity and ring-current diamagnetism in the same theoretical terms. He noted that the magnetic susceptibility due to induced ring currents can be formulated as a sum of the contributions from individual circuits and that each circuit contribution is proportional to the circuit resonance energy (CRE) multiplied by the circuit area squared. Here, CRE represents the ASE assignable to each circuit. He then defined magnetic resonance energy (MRE) as a sum of the CREs over all circuits; MRE means an ASE experienced by the external magnetic field. A good correlation was really found between MRE and TRE. This indicates that MRE can be used as a novel indicator of aromatic stabilization. MRE has an advantage in that no reference system is necessary to evaluate it.

**4. Limited Utility of Magnetic Criteria of Aromaticity**

Using the MRE concept, Aihara pointed out that magnetic criteria of aromaticity, such as the distribution of ring currents and magnetic susceptibility due to ring currents, are of limited utility. Since aromaticity is a state of energy in nature, it should be estimated using stabilization energy due to cyclic conjugation. TRE and MRE represent this kind of ASEs and can be estimated by summing CREs over all circuits. In contrast, not only ring-current magnetic susceptibility but also the distribution of ring currents is highly dependent on molecular geometry although they reflect the magnitude of CREs. Therefore, these magnetic quantities must be obscure as criteria for determining the degree of aromaticity. As the widely used NICS is closely related to the distribution of ring currents, it cannot be used safely as a criterion of aromaticity, either.

As has been seen above, Aihara successfully elucidated the essence of aromaticity, an enigma since the age of Kekule. He resolved the interrelation between aromaticity and ring-current diamagnetism. These achievements have been highly appreciated not only in Japan but around the world. We hereby honor Aihara's achievements to be worthy of the Chemical Society of Japan Award.