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5.5 DFT Numerical Quadrature

5.5.4 Consistency Check and Cutoffs

(February 4, 2022)

Whenever Q-Chem calculates numerical density functional integrals, the electron density itself is also integrated numerically as a test of the quality of the numerical quadrature. The extent to which this numerical result differs from the number of electrons is an indication of the accuracy of the other numerical integrals. A warning message is printed whenever the relative error in the numerical electron count reaches 0.01%, indicating that the numerical XC results may not be reliable. If the warning appears on the first SCF cycle it is probably not serious, because the initial-guess density matrix is sometimes not idempotent. This is the case with the SAD guess discussed in Section 4.4, and also with a density matrix that is taken from a previous geometry optimization cycle, and in such cases the problem will likely correct itself in subsequent SCF iterations. If the warning persists, however, then one should consider either using a finer grid or else selecting an alternative initial guess.

By default, Q-Chem will estimate the magnitude of various XC contributions on the grid and eliminate those determined to be numerically insignificant. Q-Chem uses specially-developed cutoff procedures which permits evaluation of the XC energy and potential in only 𝒪(N) work for large molecules. This is a significant improvement over the formal 𝒪(N3) scaling of the XC cost, and is critical in enabling DFT calculations to be carried out on very large systems. In rare cases, however, the default cutoff scheme can be too aggressive, eliminating contributions that should be retained; this is almost always signaled by an inaccurate numerical density integral. An example of when this could occur is in calculating anions with multiple sets of diffuse functions in the basis. A remedy may be to increase the size of the quadrature grid.