Novel atom-type AI indices for QSPR studies of alcohols

The novel vertex degree v^m for heteroatom in molecular graph is derived on the basis of the valence connectivity δ^v of Kier–Hall. The newly proposed atom-type AI indices and previously proposed Xu index, are further modified for compounds with heteroatoms by replacing the vertex-degree of heteroatom by the proposed v^m. The multiple linear regression using the modified Xu index and AI indices can provide high-quality QSPR models for the normal boiling points (BP), molar volumes (MV), molar refractions (MR), and molecular total surface areas (TSA) of alcohols with up to 17 non-hydrogen atoms. The results imply that these physical properties may be expressed as a linear combination of the individual indices related to molecular size and atom-types. For each of the four properties, the correlation coefficient r is greater than 0.996 and particularly the decrease in the standard error is within the range of 61–83% compared with the simple linear models based on the modified Xu index, and the standard errors are 3.814, 0.939, 0.187, and 3.348 for BP, MV, MR, and TSA, respectively. The final models correspond to a fit error of 2.33, 0.70, 0.53, and 0.95% for BP, MV, MR, and TSA, respectively. The more general leave-n-out method is used to do the cross-validation. The cross-validation demonstrates the outstanding predictive power of the final models. The contributions of individual indices are used to illustrate the role of the molecular size and individual groups in molecules. The results indicate that physical properties of alcohols are dominated by the molecular size. On the other hand, although the hydrogen-bonding interactions caused by the OH group play an important role in determining the normal BPs, the branching seems to be a more important factor influencing the MVs, MRs, and TSAs than the hydrogen-bonding interaction. The contribution of individual atom type or group to properties is not a constant and depends on its structural environment in a molecule.