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 systems is applied to a simple two-electron problem and compared with a variational 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, the 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 the order of magnitude of the correlation energy itself. It is concluded that the Colle-Salvetti model predicts inaccurate pair correlations and should be used with great care.