On the topology of the electron density of ${\mathrm {H}}_{3}^{+}$

The topology of the electron density ρ(r) of \({\mathrm {H}}_{3}^{+}\) is revisited by series of ultra fine tuned geometry optimizations within Hartree-Fock self-consistent virial scaling (SCVS) approach in combination with correlation consistent cc-pVXZ basis sets. The calculations are extended to approach the Hartree-Fock complete basis set (CBS) limit. It is discussed that within such tuned ab initio calculations, the sources of errors that are mapped to the final density matrix in normal calculations are essentially eliminated. The results of electron density analysis on such error-free ρ(r) function via the quantum theory of atoms in molecules (QTAIM) confirm unambiguously the non-nuclear attractor (NNA) as the fundamental topological building block (together with three H atomic basins) to describe the bonding in \({\mathrm {H}}_{3}^{+}\) ion-molecule. The convergence patterns of the values of different density-dependent properties toward CBS limit are also explored. It is reported that the cc-pVXZ sets are not only energy-consistent but also density-consistent. Therefore, on the basis of this important density consistency behavior, the CBS limit values of different atomic and bonding indexes are estimated and ultimately the structure and bonding pattern of \({\mathrm {H}}_{3}^{+}\) are concluded.