An approximation of the Cioslowski–Mixon bond order indexes using the AlteQ approach.

Fast and reliable prediction of bond orders in organic systems based upon experimentally measured quantities can be performed using electron density features at bond critical points (J Am Chem Soc 105:5061–5068, 1983; J Phys Org Chem 16:133–141, 2003; Acta Cryst B 61:418–428, 2005; Acta Cryst B 63:142–150, 2007). These features are outcomes of low-temperature high-resolution X-ray diffraction experiments. However, a time-consuming procedure of gaining these quantities makes the prediction limited. In the present work we have employed an empirical approach AlteQ (J Comput Aided Mol Des 22:489–505, 2008) for evaluation of electron density properties. This approach uses a simple exponential function derived from comparison of electron density, gained from high-resolution X-ray crystallography, and distance to atomic nucleus what allows calculating density distribution in time-saving manner and gives results which are very close to experimental ones. As input data AlteQ accepts atomic coordinates of isolated molecules or molecular ensembles (for instance, protein–protein complexes or complexes of small molecules with proteins, etc.). Using AlteQ characteristics we have developed regression models predicting Cioslowski–Mixon bond order (CMBO) indexes (J Am Chem Soc 113(42):4142–4145, 1991). The models are characterized by high correlation coefficients lying in the range from 0.844 to 0.988 dependently on the type of covalent bond, thereby providing a bonding quantification that is in reasonable agreement with that obtained by orbital theory. Comparative analysis of CMBOs approximated using topological properties of AlteQ and experimental electron densities has shown that the models can be used for fast determination of bond orders directly from X-ray crystallography data and confirmed that AlteQ characteristics can replace experimental ones with satisfactory extent of accuracy.