Towards the one-particle basis set limit of second-order correlation energies: MP2-R12 calculations on small Ben and Mgn clusters (n=1–4)

Abstract

A principal source of error in electronic structure calculations is the inability of conventional CI (configuration interaction) expansions to describe the electron–electron cusp. This manifests itself in the slow convergence of correlation treatments with finite basis sets which are commonly applied in traditional ab initio quantum chemistry. In this paper we describe results obtained by adding special n-particle functions, which have terms linear in the interelectronic coordinate r12, to the usual trial wave function, which is an expansion in terms of Slater determinants. A vectorized and efficient computer program has been written for putting into practice second-order Mo/ller–Plesset perturbation theory with linear r12 terms (MP2-R12): the sore program. It exploits both direct integral evaluation strategies and techniques that permit the full (also nonabelian) use of molecular point group symmetry. These two ingredients to the program allow for the use of very large Gaussian basis sets in conjunction with the linear r12 terms. As a result we are now able to press into new territories of accuracy. Calculations on Be and Mg clusters illustrate applications of the program. Binding energies are discussed with regard to basis set saturation and with some emphasis on the basis set superposition error (BSSE). The combination of our MP2 basis set limits on one hand with results from CCSD(T) and MRCI calculations with standard basis sets on the other leads to reliable estimates of the binding energies of Be3 (27 kcal/mol), Be4 (88 kcal/mol), Mg3 (8 kcal/mol), and Mg4 (28 kcal/mol). The most extensive MP2-R12 calculations have been performed with very large uncontracted Cartesian Gaussian basis sets. Also, core–core and core–valence correlation effects have been accounted for. In this work we present the results of the first real large-scale calculations employing Hylleraas-type coordinates which have been performed so far on many-electron, polyatomic molecules.