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

TL;DR

This paper improves energy calculations in quantum models with long-range electron interactions by applying generalized cusp conditions, significantly extending the accurate range of the interaction parameter.

Contribution

It introduces the use of generalized cusp conditions to enhance wave function representation at small distances, reducing energy errors in long-range interaction models.

Findings

Energy errors are significantly reduced using generalized cusp conditions.

The valid range of the interaction parameter μ is extended.

Numerical results for two-electron harmonium demonstrate improved accuracy.

Abstract

Sources of energy errors resulting from the replacement of the physical Coulomb interaction by its long-range $\mathrm{erfc}(\mu r)/r$ 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.