Accuracy and limitations of second-order many-body perturbation theory for predicting vertical detachment energies of solvated-electron clusters

Abstract

Vertical electron detachment energies (VDEs) are calculated for a variety of (H₂O)_n⁻ and (HF)_n⁻ isomers, using different electronic structure methodologies but focusing in particular on a comparison between second-order Møller–Plesset perturbation theory (MP2) and coupled-cluster theory with noniterative triples, CCSD(T). For the surface-bound electrons that characterize small (H₂O)_n⁻ clusters (n ≤ 7), the correlation energy associated with the unpaired electron grows linearly as a function of the VDE but is unrelated to the number of monomers, n. In every example considered here, including strongly-bound “cavity” isomers of (H₂O)₂₄⁻, the correlation energy associated with the unpaired electron is significantly smaller than that associated with typical valence electrons. As a result, the error in the MP2 detachment energy, as a fraction of the CCSD(T) value, approaches a limit of about −7% for (H₂O)_n⁻ clusters with VDEs larger than about 0.4 eV. CCSD(T) detachment energies are bounded from below by MP2 values and from above by VDEs calculated using second-order many-body perturbation theory with molecular orbitals obtained from density functional theory. For a variety of both strongly- and weakly-bound isomers of (H₂O)₂₀⁻ and (H₂O)₂₄⁻, including both surface states and cavity states, these bounds afford typical error bars of ±0.1 eV. We have found only one case where the Hartree–Fock and density functional orbitals differ qualitatively; in this case the aforementioned bounds lie 0.4 eV apart, and second-order perturbation theory may not be reliable.