Second-order adiabatic connection: The theory and application to two electrons in a parabolic confinement.

The adiabatic connection formalism, usually based on the first-order perturbation theory, has been generalized to an arbitrary order. The generalization stems from the observation that the formalism can be derived from a properly arranged Taylor expansion. The second-order theory is developed in detail and applied to the description of two electrons in a parabolic confinement (harmonium).

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 erfc(μ)/ approximation are explored. It is demonstrated that the results can be dramatically improved and the range of μ giving energies within chemical accuracy limits significantly extended if the generalized cusp conditions are used to represent the wave function at small . The numerical results for two-electron harmonium are presented and discussed.