Abstract
Excerpt: In an earlier publication we proposed a new type of integral screening, the “multipole-based integral estimates” (MBIE).1 The basic idea behind MBIE was to introduce a 1/R dependence on the bra-ket distance into the integral estimate, which had hitherto not been described in the widely used Schwarz integral estimates.2 The MBIE estimates as proposed in Ref. 1 incorporate the missing distance dependence such that the numerical error behaved systematically and well controlled in test calculations. The derivation of the MBIE equations was such that they were supposed to ensure rigorosity of the integral estimates. However, there were some problems in the implementation as well as some inaccuracies in the derivation in Ref. 1, which we will discuss in the following. Although we would like to stress that the corrected formulation of MBIE can be and often is a quite conservative integral estimate, we briefly mention here also a non-rigorous variation of MBIE that leads to essentially the same speedups, even smaller numerical errors, and is at the same time much easier to implement. We denote this modified screening estimate as QQR screening and generally recommend its use instead of MBIE. A full account of the screening procedures is presented in a separate publication