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An improved generator coordinate Hartree–Fock (IGCHF) method is used to generate highly accurate Gaussian basis sets (GBSs) for the atoms from H (Z = 1) through Xe (Z = 54). In this method the Griffin–Hill–Wheeler–Hartree–Fock equations are integrated using the integral discretization technique. From these basis sets the ground-state HF total energies are calculated and compared with the corresponding values obtained with GBSs of the same size, generated with the original generator coordinate Hartree–Fock method, and with a numerical HF method. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 95: 190–193, 2003 [ABSTRACT FROM AUTHOR]