Term-splitting correction

If the small magnitude of the OMC shell (5/ here) relaxation is taken into account, there is another way out that can be optimal for the low-lying states. It was suggested in [19] to add the Term-Splitting (TS) correction (see also [24]) to the (G)RECP operator... 

Figure 3. Corrections to 2p Koopmans ionization energies when including (R) relaxation and gsm (Q) relaxation and qed plus nuc terms (G) relaxation and gsm plus qed, and nuc terms. Upper left 2pj/2 corrections lower left 2p3/2 corrections upper right spin-orbit splitting corrections to Koopmans values lower right spin-orbit splitting discrepancies with respect to experimental values.

The foundation for the use of DFT methods in computational chemistry was the introduction of orbitals by Kohn and Sham. 5 The main problem in Thomas-Fermi models is that the kinetic energy is represented poorly. The basic idea in the Kohn and Sham (KS) formalism is splitting the kinetic energy functional into two parts, one of which can be calculated exactly, and a small correction term. 

The use of these two semiclassical levels of description - the statistical (e.g. TFW) model and the semiclassical (e g. WKB) treatment - of the one-body motion shows that the main, global or local, properties of a quantum system can be split into two terms the first, largest one is a smoothly varying term, where shell effects are averaged out, and the second one is an oscillating correction, which contains the information on the system specificity. The question now arises of the relevance and accuracy of such a decomposition. 

In previous papers [10,11] we have formulated a procedure for splitting the ground-state energy of a multifermionic system into an averaged, structure-less part, E, and a residual, shell-structure part, 8E. The latter originates from quantum interference effects of the one-particle motion in the confining potential [12] and has the form of a shell-correction expansion 5E = It was also shown [11] that the first-order corrective term,... 

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