Previous calculations on model systems for the cooperative binding of two NO2 molecules to carbon nanotubes using density functional theory and second order Moller-Plesset perturbation theory gave results differing by 30 kcal/mol. Quantum Monte Carlo calculations are performed to study the role of electronic correlations in these systems and resolve the discrepancy between these previous calculations. Compared to QMC binding energies, MP2 and LDA are shown to overbind, while B3LYP and BPW91 underbind. PW91 gives the best agreement with QMC with a binding energy differing by only 3 kcal/mol. Basis set effects are also shown to be important.