Accuracy of the Boys and Bernardi function counterpoise method

Abstract

The performance of the Boys and Bernardi function counterpoise (FCP) method in eliminating the basis set superposition error (BSSE) is studied for He2, at R=5.6 a.u., within the supermolecular coupled electron pair approximation (CEPA-1) method. A series of one-electron Gaussian basis sets is designed that allows a systematic approach to the basis set limit value of the interaction energy. Every basis set contains a part suitable to reproduce the atomic correlation energy and a second part optimized for the dispersion interaction in He2. BSSE-free correlated first-order interaction energies [E(1)], calculated using perturbation theory, are reported for each of these sets. Extrapolation to the basis set limit yields a new value of 33.60±0.02 μH for E(1) at R=5.6 a.u. Extending previous work, the supermolecular CEPA-1 interaction energies for each set are then compared to the total of E(1) and the BSSE-free Mo/ller–Plesset second-order dispersion energy reported previously. While for some basis sets the uncorrected ΔE values deviate up to 43 K from the perturbation estimate, the FCP-corrected results always agree within 0.4 K. A virtuals-only counterpoise procedure is considered as well, but fails badly. The remaining discrepancies in the FCP results are ascribed to a failure of the Mo/ller–Plesset approach to precisely model the dispersion energy at the CEPA level. This problem is removed in a further, more stringent test where supermolecular EintCEPA-intra results, in which only the intra-atomic correlation (at the CEPA-1 level) is taken into account, are directly compared to the BSSE-free E(1) values. In this test the FCP-corrected supermolecular results agree, for the larger sets, to within 0.001 K with the results expected on the basis of E(1). These findings demonstrate, for the first time, that at least in He2 the FCP recipe yields interaction energies that correspond precisely (to machine precision) to the basis set and correlation method at hand.