Hybrid QTAIM and electrostatic potential-based quantum topology phase diagrams for water clusters

The topological diversity of sets of isomers of water clusters (W = H2O)(n), 7 <= n <= 10, is analyzed employing the scalar fields of total electronic charge density rho(r) and the molecular electrostatic potential (MESP). The features uncovered by the MESP are shown to be complementary to those revealed by the theory of atoms in molecules (QTAIM) analysis. The MESP is known to exhibit the electron localizations such as lone pairs that are central to water cluster behavior. Therefore, a 'hybrid' QTAIM and MESP quantum topology phase diagram (QTPD) for W-n, 7 <= n <= 10, is introduced in addition to the QTPD. The 'spanning' QTPD with upper and lower bounds is constructed from the solutions of the Poincare-Hopf relation involving the non-degenerate critical points. The changing subtle balance between the planar and three dimensional character of the growing water clusters W-n, 4 <= n <= 10, is revealed. Characterization of the structure of the QTPDs, possible with new tools, demonstrated the migration of the position of the global minimum on the spanning QTPD from the lower bound to upper bound as the W-n, 4 <= n <= 10, cluster grows in size. Differences in the structure of the QTPD are found between the clusters containing even versus odd monomers for W-n, n = 7-10. The energetic stability of the clusters which possess even number of monomers viz. n = 8, 10 is higher than that of the n = 7, 9 clusters due to relatively higher numbers of hydrogen-bond BCPs in the n = 8, 10 clusters, in agreement with energetic results reported in the literature. A 'hybrid' QTPD is created from a new chemical relation b(HB) + l >= 2n for W-n that relates the number of hydrogen-bond bond critical points (b(HB)) with the number of oxygen lone pairs exclusively specified by the negative valued MESP (3,+ 3) critical points (l). The topologies of the subset b(HB) + l = 2n for W-n, point the way to the discovery of unknown 'missing' lower energy isomers. A discussion of the relative merits and range of applicability of the QTAIM and hybrid-QTPD analyses is included and concludes that the hybrid-QTPD analysis for W-n, is more useful for the association with the energy minima on the potential energy surface.