Correcting models with long-range electron interaction using generalized cusp conditions

Sources of energy errors resulting from the replacement of the physical Coulomb interaction by its long-range $\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{c}(\mu r)\mathrm{/}r$ approximation are explored. It is demonstrated that the results can be dramatically improved and the range of $\mu$ giving energies within chemical accuracy limits significantly extended, if the generalized cusp conditions are used to represent the wave function at small $r$. The numerical results for two-electron harmonium are presented and discussed.