Abstract
Excerpt: Our “multipole-based integral estimates” (MBIE) from Refs. 1–4, which we refer to as I–IV, introduced the missing 1/Rn distance dependence in integral estimates for AO-MP2 theories, which had hitherto not been described by the widely used Schwarz integral estimates.5 While the numerical errors behaved systematically and appeared perfectly well-controlled in test calculations, we discuss here (as well as in Ref. 6) some problems in the initial implementation as well as some inaccuracies in the derivation. Furthermore, we emphasize that MBIE is a rather conservative estimate and we recently developed a new type of screening for combining the advantages of MBIE and Schwarz estimates that we denote as QQR screening.7 The efficiency of the new QQR approach within AO-MP2 theory will be outlined in an upcoming work.8 The new screening procedure shows essentially the same speedups and numerical errors as our original MBIE formulation, but is much easier to implement. Therefore, we now generally recommend the new QQR screening instead of our MBIE bounds. We stress that both the speedups as well as the numerical errors described earlier are mostly conserved for both SCF and MP2 results with the revised versions of our screening schemes presented here and in detail in Refs. 7,8.