Critical analysis of the Colle-Salvetti model for electron correlation in closed shell systems: pair correlations

The Colle-Salvetti functional for electron correlation in closed shell syst ems is applied to a simple two-electron problem and compared with a variati onal wavefunction. The correlation hole is found to be too short range. As a result, the model is biased towards regions of large electron density and practically neglects pair correlations that are long range. In addition, t he correlation energy per electron is found to be singular at the nucleus. The error from neglecting the single-particle operators is found to be of t he order of magnitude of the correlation energy itself. It is concluded tha t the Colle-Salvetti model predicts inaccurate pair correlations and should be used with great care.