The Cumbersome Two-Electron Terms

In many-electron calculations, the effective electrostatic potential contains two terms. 

However, this approach is useless for calculating two-electron integrals, because a back-transformation enters four times in each integral. If the back-transformation is applied four times, the computational costs will be higher than those of the corresponding four-component calculation. 

If we directly replace the four-component spinor by its corresponding 

In most calculations, the bare (untransformed) electron-electron interaction operator is employed in the two-component Fock operator 

It is known from quasi-relativistic calculations that this bare-potential approximation provides reliable results for valence electron properties. This is particularly true for the scalar-relativistic variants discussed in the next section [see, e.g.. Refs. [656,752]], but may be different for the truly two-component method including spin-orbit splitting [655]. For core-shell properties and for the spin-orbit splitting of high-angular-momentum orbitals this approximation will not be sufficient [643,659]. 

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