Structural index of (anti)aromaticity for fused polycyclic hydrocarbons in the triplet and singlet states: HOMA or HOMER?

The harmonic oscillator model of aromaticity (HOMA) has recently been reparametrized for assessing (anti)aromaticity of excited states. The derived HOMER has been tested on monocycles. In polycyclic compounds, the spin density (SD) per ring can span a wide range, and the question arises whether HOMER describes the (anti)aromaticity of all rings equally well. The purpose of this paper is to provide some information on this. The molecules studied are polybenzenoids and fused polycyclic systems composed of benzene ring(s) and one cyclobutadiene (CBD), cyclooctatetraene (COT) or pentalene unit. The results show that HOMA can be used for benzene subunits covering the entire SD range, while HOMER could be used with caution only for benzene rings adopting the main part of the SD. The aromaticity of CBD and the five-membered rings of the pentalene subunit is well described by HOMER and HOMA when their SD > 1, but the aromaticity of the COT subunits is better described by HOMA. For the perimeter of the pentalene subunit, HOMA can be used for the entire SD range, and HOMER when SD > 1.4. Interestingly, both HOMA and HOMER work very well for the 4n π-electron subunits and five-membered rings of the studied polycycles in their singlet state, while HOMA is preferable for the benzene subunits.