Wave function expansions radial orbitals

One technical point should be stressed here often encountered in similar work. For the wave function calculation for Li the authors employ a Is core by calculating the closed-shell Li ion yielding an Iso orbital energy of -2.79303 a.u. and the corresponding wave function V (lso)- The valence 2s function was then obtained by solution of the corresponding radial differential equation facilitating the potential of the Iso functions. Obviously there is no orbital- or spin-polarization by the valence electron included, and all these effects come into play only after addition of further terms in the perturbation expansion. This procedure is commonly termed as the method and was... 

To obtain a self consistent field solution to the MCHF problem, two optimizations need to be performed i.e., one for the variation of the one-electron radial orbitals Pni r) in the wave function and one for the expansion coefficients. This can be done by consecutively iterating, first the orbital optimization followed by the coefficient optimization. 

One of the most commonly used expansions in the theory of the electronic structure of atoms and molecules is the partial wave expansion, in which individual atomic orbitals are expressed as products of radial functions and spherical harmonics. Appropriately symmetrized sums of products of the spherical harmonics for the coordinates of each particle can be formed to yield eigenfunctions of total Lz, S, and Sz. To prevent lengthy expressions involving 3-j and 6-j symbols from obscuring the essential physics, I shall focus on the partial wave expansion for an 5-state of the helium atom ... 

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