Integral partition bounds for fast and effective screening of general one-, two-, and many-electron integrals

and typically only rigorous for simple spherical Gaussians. We test our bounds for six different integral kernels found throughout quantum chemistry, including exponential, Gaussian, and complementary error function based forms. We compare to previously developed estimates on the basis of significant integral counts and their usage in both explicitly correlated second-order Møller-Plesset theory (MP2-F12) and density functional theory calculations employing screened Hartree-Fock exchange.