Consequences of approximating electron correlation effects

The effect of approximating electron correlation in few-electron systems is investigated using three wavefunctions: the many body wavefunction referred to as fully-correlated (FC), the Hartree Fock wavefunction (HF), and the Colle and Salvetti Jastrow-style wavefunction (CS) used in the derivation of the popular Lee, Yang and Parr (LYP) correlation functional. The electron correlation energy, static and dynamic Coulomb holes, various expectation values, and radial energy distributions (energy densities) are considered. It is shown that whilst the CS wavefunction can capture the behaviour of the wavefunction at the singularities of the Coulomb potential corresponding to the coalescence of two particles and decreases the area of the primary static Coulomb hole by nearly 30% compared to HF for He and Li+, it is unable to accurately model expectation values that depend on the whole of space and key features of the electron density behaviour in dynamic Coulomb holes and the energy density behaviour in energy distributions. These issues are amplified when considering the hydride ion and a system with the critical nuclear charge for binding.