Accuracy of the electrostatic theorem for high-quality Slater and Gaussian basis sets

The fulfillment of the Hellmann–Feynman electrostatic theorem is examined for the sequences of cc-pVxZ and cc-pCVxZ Gaussian basis sets as well as for the VBx and CVBx basis sets of Slater-type orbitals. The difference between the energy gradient and electrostatic forces is large in small Gaussian basis sets of the two types, but decreases quickly as the basis sets improve. In VBx Slater basis sets these differences are small but the improvement is irregular, whereas in CVBx basis sets the fulfillment of the electrostatic theorem is very satisfactory. For the high-quality basis sets (cc-pV5Z, cc-pCVQZ, cc-pCV5Z, CVB2, and CVB3) the energy gradient can be replaced by the electrostatic force in most practical applications. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004