Multidimensional QSPR Model for Calculating the Critical Pressure of Substituted Naphthalenes in First-Order Phase Transitions

A multivariate QSPR model is proposed for predicting the critical pressure of substituted naphthalenes through combinations of topological molecular graph descriptors. Fifty-nine naphthalene derivatives are examined that are randomly divided into base and test sets. In considering naphthalene molecules, it was assumed the critical pressure is determined by descriptors that characterize the branching of the structure (the Wiener index) and the Hückel spectrum, which considers only the interaction between neighboring atoms (functions of the eigenvalues of the topological matrix). The energy of intermolecular interactions depends largely on the specific size of the molecules and their degree of branching. Multiple bonds are considered in calculating the Wiener index. The sum of the squares of the eigenvalues of the topological matrix describes deviations of the Hückel energy of electronic states from its average value in a molecule. The choice of the squares of the eigenvalues of the molecular graph is due to a consequence of the Horst Sachs theorem. The descriptors used in this work are calculated using the Maple 13 and PascalABCNet software. To verify the prognostic capabilities of the proposed model, critical pressures were calculated for compounds not included in the base series. The QSPR model adequately describes the critical pressure of naphthalenes in liquid–vapor phase transitions, as is confirmed by experimental data and statistical data processing. The results can be recommended for estimating the critical pressure of known and newly synthesized naphthalenes, and used in scientific and engineering calculations in petrochemistry and supercritical fluid technology.