Pitfalls for the Frozen-Core Approximation: Gaussian-2 Calculations on the Sodium Cation Affinities of Diatomic Fluorides

The Gaussian-2 (G2) total energies for species having the formula Na(FX)+ [X = H, Li → F, or Na → Cl], calculated using conventional and widely used ab initio computational program suites, show serious deficiencies which are attributable to two different effects. Firstly, for the sodium-ion adducts of almost all of the covalent fluoridesnamely HF, BF, CF, NF, OF, F2, SF, and ClFthe orbital corresponding most closely to the fluorine 2s orbital possesses a more negative eigenvalue than the set of three orbitals corresponding most closely to the sodium 2px, 2py, and 2pz orbitals, so that routine selection of the “frozen-core” option (in the single-point calculations involved in determining the G2 total energy) leads to an inappropriate correlation space. Secondly, for the sodium-ion adducts of several fluoridesmost notably, but not solely, the ionic fluorides LiF, NaF, MgF, and AlFthere is very significant mixing of the fluorine 2s and sodium 2pz orbitals, with the result that the G2 frozen-core calculations yield an incorrect correlation energy. This latter problem cannot be properly compensated for in standard G2 theory. The magnitude of either effect can be quite large, with the result that “blind” implementation of G2 theory produces apparent G2 SCA values ranging from −100 to −200 kJ mol-1 for most of the covalent fluorides. Here we investigate this phenomenon and assess three different strategies for obtaining corrected G2-like results: namely, inclusion of all Na 2s and 2p orbitals among those correlated (the G2(thaw) technique); exclusion of all Na 2p and F 2s orbitals from the correlation space (the G2(F-2s) approach); and correlation of F 2s, but not Na 2px, 2py, or 2pz, in a noncontiguous correlation space (which we term G2(NCCS)). Of the three possible approaches, the G2(thaw) procedure appears the most intrinsically reliable, but is nevertheless significantly more computationally intensive than standard G2. To this end, we assess also several methods that seek to emulate G2(thaw) at reduced cost: the best such “budget” method, G2(MP2(thaw/MP2)), is the least demanding of CPU time and is generally less computationally expensive than G2 itself.