Ion induced dipole clusters H(n)- (3 ≤ n-odd ≤ 13): density functional theory calculations of structure and energy

We investigate anew the possible equilibrium geometries of ion induced dipole clusters of hydrogen molecular ions, of molecular formula H(n)(-) (3 ≤ n-odd ≤ 13). Our previous publications [Sapse, A. M.; et al. Nature 1979, 278, 332; Rayez, J. C.; et al., J. Chem. Phys. 1981, 75, 5393] indicated these molecules would have a shallow minimum and adopt symmetrical geometries that accord with the valence shell electron pair repulsion (VSEPR) rules for geometries defined by electron pairs surrounding a central point of attraction. These earlier calculations were all based upon Hartree-Fock (HF) calculations with a fairly small basis of atomic functions, except for the H3(-) ion for which configuration interaction (CI) calculations were carried out. A related paper [Hirao, K.; et al., Chem. Phys. 1983, 80, 237] carried out similar calculations on the same clusters, finding geometries similar to our earlier calculations. However, although that paper argued that the stabilization energy of negative ion clusters H(n)(-) is small, vibration frequencies for the whole set of clusters was not reported, and so a definitive assertion of a true equilibrium was not present. In this paper we recalculate the energetics of the ion induced dipole clusters using density function theory (DFT) B3LYP method calculations in a basis of functions (6-311++G(d,p)). By calculating the vibration frequencies of the VSEPR geometries, we prove that in general they are not true minima because not all the resulting frequencies correspond to real values. By searching the energy surface of the B3LYP calculations, we find the true minimum geometries, which are surprising configurations and are perhaps counterintuitive. We calculate the total energy and binding energy of the new geometries. We also calculate the bond paths associated with the quantum theory of atoms in molecules (QTAIM). The B3LYP/6-311++G(d,p) results, for each molecule, deliver bond paths that radiate between each polarized H2 molecule and the polarizing H(-) ion.