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The diffusion Monte Carlo (DMC), auxiliary field quantum Monte Carlo (AFQMC),and equation-of-motion coupled cluster (EOM-CC) methods are used to calculatethe electron binding energy (EBE) of the non-valence anion state of a model(H$_2$O)$_4$ cluster. Two geometries are considered, one at which the anion isunbound and the other at which it is bound in the Hartree-Fock (HF)approximation. It is demonstrated that DMC calculations can recover from theuse of a HF trial wave function that has collapsed onto a discretized continuumsolution, although larger electron binding energies are obtained when using atrial wave function for the anion that provides a more realistic description ofthe charge distribution, and, hence, of the nodal surface. For the geometry atwhich the cluster has a non-valence correlation-bound anion, both the inclusionof triples in the EOM-CC method and the inclusion of supplemental diffuse dfunctions in the basis set are important. DMC calculations with suitable trialwave functions give EBE values in good agreement with our best estimate EOM-CCresult. AFQMC using a trial wave function for the anion with a realisticelectron density gives a value of the EBE nearly identical to the EOM-CC resultwhen using the same basis set. For the geometry at which the anion is bound inthe HF approximation, the inclusion of triple excitations in the EOM-CCcalculations is much less important. The best estimate EOM-CC EBE value is ingood agreement with the results of DMC calculations with appropriate trial wavefunctions.

The Role of High-Order Electron Correlation Effects in a Model System for Non-valence Correlation-bound Anions