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In this document, we briefly review the two-electron integral algorithmsbased on the range-separated algorithms and Fourier transform integralalgorithms that are implement ed in the PySCF package. For each integralalgorithm, we estimate the upper bound of relevant integrals and derive thenecessary conditions for the screening parameters, including distance cutoffand energy cutoff, to reach the desired accuracy. Our numerical tests show thatthe proposed integral estimators and screening parameters can effectivelyaddress the required accuracy while computational efforts are not wasted onunintended accuracy.

Various integral estimations and screening schemes for extended systems in PySCF