Molecular clustering about a positive ion. Structures, energetics, and vibrational frequencies of the protonated hydrogen clusters H+3, H+5, H+7, and H+9

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Abstract
The positive hydrogen clusters H+(H2)n for n=1, 2, 3, 4 have been studied via nonempirical molecular electronic structure theory. Using double zeta (DZ) and double zeta plus polarization (DZ+P) basis sets, wave functions are reported at both the self‐consistent field (SCF) and configuration interaction including all single and double excitations (CISD) levels of theory. In each case analytic gradient techniques have been used to locate stationary point geometries and to predict harmonic vibrational frequencies. The effects of electron correlation are shown to be greater for these loose molecular complexes than for ordinary molecules. Although H+5 in its lowest energy conformation is not qualitatively described as H+3⋅H2, the larger molecular ions do fit the qualitative picture H+3(H2)n, with H+3 as a nucleating center. Of special interest here are the ‘‘new’’ normal modes of these clusters, i.e., those modes having no counterpart in the isolated H+3 or H2 species. There are 15 such vibrational degrees of freedom for H+9, and the resulting harmonic vibrational frequencies range from 775 cm−1 all the way down to 63 cm−1. Dissociation energies as a function of cluster size follow the pattern established experimentally by Hiraoka and Kebarle.