Theoretical Studies of the Binding Energy and Geometry of the H5+ Molecular Ion

The geometry and binding energy of the ${\mathrm{H}}_5^{+}$ molecular ion have been examined by two different ab initio quantum mechanical variational methods. In the first a CI wavefunction was made from the 10 covalent valence‐bond structures which could be constructed from 1s orbitals at the nuclei, each 1s orbital being represented by a five‐term Gaussian expansion and having a variable scale factor. For geometries identical or similar to the D_2d geometry previously predicted from analogous calculations with cruder basis sets, we found no stability with respect to ${\mathrm{H}}_3^{+}+{\mathrm{H}}_2$ . Other geometries were examined, especially those arising naturally from the approach of ${\mathrm{H}}_3^{+}$ and H₂; however, binding was never greater than a tiny 0.6 kcal/mole. We thus concluded that the method had failed adequately to describe ${\mathrm{H}}_5^{+}$ , as it had for ${\mathrm{H}}_3^{+}$ , and that it is probably unreliable for studying ions with small binding energies. The second method used the SCF MO model with a flexible basis set to account for distortion and polarization. This gave an ${\mathrm{H}}_5^{+}$ geometry corresponding to an ${\mathrm{H}}_3^{+}\mathrm{...}{\mathrm{H}}_2$ complex of over‐all C_2v symmetry, in which the H₂ sits about 3 a.u. from the ${\mathrm{H}}_3^{+}$ apex and perpendicular to the ${\mathrm{H}}_3^{+}$ plane and to a line extending from the midpoint of the base of the ${\mathrm{H}}_3^{+}$ , through the ${\mathrm{H}}_3^{+}$ apex, and through the H₂ midpoint. The calculated binding energy relative to ${\mathrm{H}}_3^{+}+{\mathrm{H}}_2$ is 4.25 kcal/mole. Because formation of such a loose molecular complex from two closed‐shell systems should produce very little extra correlation energy in the complex, and because of basis set reasons discussed in the text, these results are believed to be reliable.