Numerical accuracy on Fm(z) for molecular integral calculations Original Research Article

Large-scale SCF calculations require more accurate numerical results. We investigated numerical accuracy on various Fm(z) evaluation methods. We found that the polynomial of z, which are often used for the Taylor series expansion and the Chebyshev approximation in molecular orbital programs, contains unexpectedly large numerical errors even if a polynomial degree is cubic. The numerical accuracy is allowable for small molecules, but may be insufficient for large molecules. On the other hand, the polynomial of δ, which requires only one more calculation step than that of z, maintains sufficient numerical accuracy because round-off errors are hardly propagated in the polynomial of δ.