On the computation of electronic correlation energies within the local approach

A recently developed local approach to the computation of electron-correlation energies is extended and investigated in great detail. For that purpose it is applied to the Ne atom and the CH4 molecule for which correlation-energy calculations are available. It is shown that the local approach exhausts up to a few percent the correlation energy which is obtainable within a given basis set. A detailed comparison with conventional CI methods reveals the advantages of the present approach. Only a fraction of the two-electron matrix elements Vijkl has to be calculated, and the number of required configurations is drastically reduced. Furthermore, CH4 is used as an example to demonstrate that the correlation-energy calculations for large systems can be broken up into ones for small systems.