Abstract:
A new kind of rigorous integral bounds was derived, which are termed "Multipole
Based Integral Estimates" (MBIE). With these it is possible to exploit for the
first time rigorously the 1/R distance decay between charge distributions in
two-electron integrals in the context of SCF methods and the 1/R**4 and
stronger decay within electron correlation approaches, respectively. The bounds
are applicable to all quantum chemical methodologies that rely on (naturally or
imposedly) local orbitals. By taking the 1/R**n decay into account, the number
of numerically significant integrals that has to be calculated can be reduced
drastically, while numerical accuracy and reliability is fully preserved. This
is illustrated for applications to linear-scaling SCF approaches, geometry
optimizations, molecular dynamics simulations, as well as MP2 calculations for
isolated and interacting systems. In particular, by exploiting the 1/R**4 decay
the scaling of correlated calculations in the framework of atomic-orbital based
Møller-Plesset perturbation theory to second order (AO-MP2) is reduced for the
first time rigorously to linear. In this way, the MBIE bounds enable correlated
calculations on systems with more than 1000 atoms or 10000 basis functions,
respectively, without loss of numerical accuracy.