Variation Treatments of the Lithium Ground State

We found in Section 10.5 that to satisfy the antisymmetry requirement, the ground-state configuration must be s 2s. The correct zeroth-order wave function is (10.40)  

The zeroth-order perturbation wave function (10.40) uses the full nuclear charge (Z = 3) for both the li and 2s orbitals of lithium. We expect that the 2s electron, which is partially shielded from the nucleus by the two li electrons, will see an effective nuclear charge that is much less than 3. Even the li electrons partially shield each other (recall the treatment of the helium ground state). This reasoning suggests the introduction of two variational parameters bi and 2 into (10.40). 

We might try other forms for the orbitals besides (10.52) and (10.53) to improve the trial function. However, no matter what orbital functions we try, if we restrict ourselves to a trial function of the form of (10.54), we can never reach the true ground-state energy. To do this, we can introduce ri2, r23, and ri3 into the trial function or use a linear combination of several Slater determinants corresponding to various configurations (configuration interaction). 

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