Original Research

Structural Chemistry

, Volume 24, Issue 4, pp 1171-1184

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Avoiding pitfalls of a theoretical approach: the harmonic oscillator measure of aromaticity index from quantum chemistry calculations

  • Marcin AndrzejakAffiliated withK. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University Email author 
  • , Piotr KubisiakAffiliated withK. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University
  • , Krzysztof K. ZborowskiAffiliated withDepartment of Chemical Physics, Faculty of Chemistry, Jagiellonian University


The concept of the harmonic oscillator measure of aromaticity (HOMA) is based on comparing the geometrical parameters of a studied molecule with the parameters for an ideal aromatic system derived from bond lengths of the reference molecules. Nowadays, HOMA is routinely computed combining the geometries from quantum chemistry calculations with the experimentally based parameterization. Thus, obtained values of HOMA, however, are bound to suffer from inaccuracies of the theoretical methods and strongly depend on computational details. This could be avoided by obtaining both the input geometries and the parameters with the same theoretical method, but efficiency of the error compensation achieved in this way has not yet been probed. In our work, we have prepared a benchmark set of HOMA values for 25 cyclic hydrocarbons, based on the all core CCSD(T)/cc-pCVQ(T)Z geometries, and used it to investigate the impact of different choices of the exchange–correlation functionals and basis sets on HOMA, calculated against the experimentally based (HOMAEP) or the consistently calculated (HOMACCP) parameters. We show that using HOMAEP leads to large and unsystematic errors, and strong sensitivity to the choice of XC functional, basis set, and the experimental data for the reference geometry. This sensitivity is largely, although not completely attenuated in the consistent approach. We recommend the most suitable functionals for calculating HOMA in both approaches (HOMAEP and HOMACCP), and provide the HOMA parameters for 25 studied exchange–correlation functionals and two popular basis sets.


Aromaticity HOMA Geometry optimization DFT Exchange–correlation functionals Coupled clusters