Single-double SD equations

To go further, we turn to so-called all-order methods. We start by considering relativistic calculations of type carried out by Lindroth [38] and Blundell et al. [39], which account for all possible single and double excitations of the ground-state helium HF wave function. These calculations have the potential of giving an exact helium ground-state energy. 

Following [30], we write the no-pair Hamiltonian in normal order with respect to the (Is) closed shell. Thus, p ) = Hq + VqVi + V2 with 

This wave function satisfies the Schrodinger equation 

Left-multiplying by J oj and assuming the intermediate-normalization condition 

If we substitute the all-order wave function j l ) into the Schrodinger equation (134), we obtain the following equations for the single- and double-excitation coefficients. 

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Single-Double (SD) Equations for Lithium-like Ions... 

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