Relativistic Corrections to Explicitly Correlated Wavefunctions

DPT has been applied to two kinds of explicitly correlated wave functions for the He-isoelectronic series [19, 10], the H2 molecule [10], and the H3-ion [96]. These calculations give some information on the coupling between relativistic and correlation effects. Only the leading relativistic corrections of 0(c ) were considered. For higher orders in 0(c ) problems arise if one wants to account for the correct behavior near ri2 = 0 (see section 

Interesting results were found for the partial wave expansions. If one expands the wave function of the ground state of He-like ions as 

In these expressions ip ri, rs) is the exact wave function of the ground state of an He-like ion. The expressions for Z —oo are evaluated for an artificial He atom without electron interaction. 

This means, that if one truncates at some L = Imax, one makes an error 0 [L + 1] ) of the energy. The origin of this slow convergence is the correlation cusp [85], i.e. the fact that 

Here av means angular averaging. If one takes care of the cusp explicitly, one avoids this slow convergence. 

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