The electron cusp condition and the virial ratio as indicators of basis set quality

Abstract

We consider two measures of the quality of one-electron basis sets for quantum-chemical calculations: The electron–electron coalescence curvature and the correlation energy virial ratio. The former is based on the Kato cusp condition that many-electron wave functions must exhibit discontinuous first derivatives with respect to $r_{12}$ as the coordinates of any two electrons coalesce. The latter is based on a simple modification of the quantum-mechanical virial theorem that makes use of only the correlation contributions to the kinetic and potential energy expectation values. The two measures are tested using coupled cluster wave functions for helium, neon, argon, calcium, and phosphorus atoms and are found to indicate good correlation with the quality of the basis set. These techniques may provide a foundation for the development of reliable basis set diagnostics for a variety of quantum-chemical applications.