Relative Energies and Geometries of the <i>cis</i>- and <i>trans</i>-HO₃ Radicals from the Parametric 2‑Electron Density Matrix Method

The parametric 2-electron reduced density matrix (2-RDM) method employing the M functional [Mazziotti, D. A. Phys. Rev. Lett. 2008, 101, 253002], also known as the 2-RDM­(M) method, improves on the accuracy of coupled electron-pair theories including coupled cluster with single–double excitations at the computational cost of configuration interaction with single–double excitations. The <i>cis</i>- and <i>trans</i>-HO₃ isomers along with their isomerization transition state were examined using the recent extension of 2-RDM­(M) to nonsinglet open-shell states [Schwerdtfeger, C. A.; Mazziotti, D. A. J. Chem. Phys. 2012, 137, 034107] and several coupled cluster methods. We report the calculated energies, geometries, natural-orbital occupation numbers, and reaction barriers for the HO₃ isomers. We find that the 2-RDM­(M) method predicts that the trans isomer of HO₃ is lower in energy than the cis isomer by 1.71 kcal/mol in the correlation-consistent polarized valence quadruple-ζ (cc-pVQZ) basis set and 1.84 kcal/mol in the augmented correlation-consistent polarized valence quadruple-ζ (aug-cc-pVQZ) basis set. Results include the harmonic zero-point vibrational energies calculated in the correlation-consistent polarized valence double-ζ basis set. On the basis of the results of a geometry optimization in the augmented correlation consistent polarized valence triple-ζ basis set, the parametric 2-RDM­(M) method predicts a central oxygen–oxygen bond of 1.6187 Å. We compare these energies and geometries to those predicted by three single-reference coupled cluster methods and experimental results and find that the inclusion of multireference correlation is important to describe properly the relative energies of the <i>cis</i>- and <i>trans</i>-HO₃ isomers and improve agreement with experimental geometries