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

Abstract

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 exchangecorrelation functionals and basis sets on HOMA, calculated against the experimentally based (HOMA EP ) or the consistently calculated (HOMA CCP ) parameters. We show that using HOMA EP 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 (HOMA EP and HOMA CCP ), and provide the HOMA parameters for 25 studied exchange-correlation functionals and two popular basis sets.

The electron density of delocalized bonds (EDDB) applied for quantifying aromaticity

“…Test set T1, partially based on the set proposed by Andrzejak et al 13 and presented in Fig. 2, contains both Hückel's aromatic and antiaromatic systems (including the polycyclic aromatic hydrocarbons of different topology) that rely on cyclic conjugation of 2p orbitals and involve only carbon atoms.…”

“…5,6 Indeed, the precise relation between energy and delocalization indices, originally proposed by Rafat and Popelier, 7 has been shown to be very useful for measuring the aromatic stabilization energy of aromatic molecules; 8,9 very recently the exact algebraic relationship between DI and the interatomic exchange-correlation energies has also been established. 10 Among all the ways to quantify aromaticity through the ''ground-state'' criteria (energetic, structural, and electronic), there are descriptors that have gained enormous recognition and wide acceptance: the aromatic stabilization energy (ASE), 2 harmonic oscillator model of aromaticity (HOMA), [11][12][13] and different types of the multicenter delocalization indices (MCDI). [14][15][16][17][18] In turn, one of the most popular aromaticity descriptors based on the response properties is the nucleusindependent chemical shift (NICS) and its various derivatives.…”

“…3 Furthermore, the parametrization of HOMA should be performed using the same quantum-chemical method as used in a K. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, calculations of equilibrium geometries of the molecule under study, since routinely computed HOMA with the experimentally determined parameters is bound to suffer from large and unsystematic errors. 13 The magnetic-based measures of aromaticity, like NICS, have also been criticised for their complexity (NICS relies on the condensation of potentially complicated patterns of induced currents to a single number, especially in the case of fused aromatic rings), [21][22][23][24][25][26] methodological shortcomings (aromaticity evaluation using NICS is limited mainly to planar units of similar size), 6,20,27 and interpretative mistiness (quoting Prof. P. Bultinck, ''. .…”

Structural and electronic properties of alumaphosphinine complexes with metal ions: A theoretical study

“…Also, the Natural Bonding Orbital (NBO) [12] is used to obtain the charge transfer values. On the other hand, the aromaticity of the alumaphosphinine ring and its complexes is measured using several well-established indices of aromaticity such as the Nucleus-Independent Chemical Shift (NICS) [15,16], the Harmonic Oscillator Model of Aromaticity (HOMA) [17,18], the Para-Delocalization Index (PDI) [19], the electron Localization-Delocalization Matrices (LDMs) [20,21], and the aromatic uctuation index (FLU) [22] Figure 2. The distances between metal cations and the coordinating sites of alumaphosphinine ring in the complexes are also shown in Figure 2.…”

“…The Harmonic-Oscillator Model of Aromaticity (HOMA) index is found to be among the most widespread and e ective indices of aromaticity founded on structural criteria. As a structural criterion, the HOMA index [17,18] …”