Introducing phase transitions to quantum chemistry: from Trouton's rule to first principles vaporization entropies

In the present study, we employ quantum cluster equilibrium calculations on a small water cluster set in order to derive thermochemical equilibrium properties of the liquid phase as well as the liquid-vapor phase transition. The focus is set on the calculation of liquid phase entropies, from which entropies of vaporization at the normal boiling point of water are derived. Different electronic structure methods are compared and the influences of basis set size and of cooperative effects are discussed. In line with a previous study on the subject [B. Kirchner, J. Chem. Phys. 123, 204116 (2005)], we find that the neglect of cooperativity leads to large errors in the equilibrium cluster populations as well as in the obtained entropy values. In contrast, a correct treatment of the intermolecular many-body interaction yields liquid phase entropies and phase transition entropies being in very good agreement with the experimental reference, thus demonstrating that the quantum cluster equilibrium partition function intrinsically accounts for the shortcomings of the ideal gas partition function often employed in first principles entropy calculations. Comparing the calculated vaporization entropies to the value predicted by Trouton's rule, it is observed that for entropy calculations the consideration of intracluster cooperative effects is more important than the explicit treatment of the intercluster association even in a highly associated liquid such as water. The decomposition of entropy into contributions due to different degrees of freedom implies the need for the accurate treatment of particle indistinguishability and free volume of translation, whereas minor influences should be expected from the vibrational and rotational degrees of freedom and none from the electronic degrees of freedom.