Flip rearrangement in the water pentamer: Analysis of electronic structure

Tunneling pathways of the flip rearrangement between permutation-inversion isomers corresponding to the energetically degenerate global energy minima of (H₂O)₅ are analyzed in terms of the electronic structure. We demonstrate that charge density-based scalar measures quantify the responses of the bonding to the flip rearrangement and we discovered a high degree of continuity of the values that depend on the presence of the sliding motion of the bond critical point relative to the oxygen atom. The scalar measures can distinguish the pairs of permutation-inversion isomers everywhere except at the transition state due to the asymmetrical energy barrier; however, they cannot determine the most and least facile directions of the flip rearrangement. The vector or directional character of the two sides of the pathway is captured by the stress tensor trajectories constructed in a non-Cartesian space, defined by the variation of the position of the bond critical point. The stress tensor trajectories are presented in terms that enable bond-flexing, bond-twist, and bond-anharmonicity of the flip rearrangement between permutation-inversion isomers to be quantified. The stress tensor trajectories can distinguish the isomers at the transition state and demonstrate that the clockwise and counter-clockwise directions of the flip rearrangement are the most and least facile respectively.