Lattice Energy Estimation for Complex Inorganic Ionic Crystal

A novel connectivity index ^mG based on adjacency matrix of molecular graphs was proposed as follows: ^mG=Σ(g_i·g_j·g_k···)^0.5. The element g_i of adjacency matrix was defined as g_i= (1+Z_i^1.4)/(1+r_i^1.4), where Z_i and r_i are the charge number and the thermochemical radius of ion i respectively, and the radii r_ifor metal ions are taken to be the Goldschmidt radius. The regression analysis by the connectivity index ¹G can provide a high-quality QSPR model for the lattice energies of 245 complex inorganic ionic crystal samples. The results imply that the lattice energies may be expressed as a linear model of the connectivity index ¹G. For the linear model the correlation coefficient r and the standard error s are 0.9998 and 228.72 kJ/mol, respectively. The cross-validation by the leave-one-out method demonstrates that the model is highly reliable from the point of view of statistics.