Breit contribution

Due to small relaxation of outer core shells in most processes of interest, these shells can be also considered as frozen when analyzing the Breit contributions and the Bed and Bev terms can be taken into account similarly to the Bfc and Bf ones. The error of this approximation will be additionally suppressed by relative weakness of the Breit interaction with the outer core electrons as compared to the inner core ones. We note... 

Different nuclear models and contributions of the Breit interaction between valence, inner and outer core shells of uranium, plutonium and superheavy elements El 12, E113, and El 14 are considered in the framework of allelectron four-component and (G)RECP methods. It is concluded on the basis of the performed calculations and theoretical analysis that the Breit contributions with inner core shells must be taken into account in calculations of actinide and SHE compounds with chemical accuracy whereas those between valence and outer core shells can be omitted. 

The transverse part can be analysed further if one separates it into a magnetic (or current-current) and a retardation component or if one restricts oneself to its weakly relativistic limit, the so-called Breit contribution [48,97],... 

Fig. 4.2. Relativistic correction factor for the LDA exchange energy density magnetic, retardation and Breit contribution (ej " from Ref [97] has been corrected for a typographical error)...

Table 4.2 Exchange-only ground-state energies from ROPM, RHF, RKLI, RLDA and RGGA(PW91) calculations for noble gas atoms. In the case of the ROPM the self-consistent (SC) treatment of die complete Ej (T) is compared with a self-consistent inclusion of only its Breit (B) limit (together with a first-order perturbative (PT) calculation of the beyond Breit contributions (T—B)) as well as a fully perturbative evaluation of Ej. The latter procedure has also been used for the RHF calculations (Dyall et aL 1989). All energies are in mHartree (Engel et al. 1998a). Reproduced with permission from Engel et al. (1998a) 1998 Kluwer Academic/Plenum Publishers.

The "cross Coulomb-Breit contribution to RSC in the equal energies case is [20] ... 

The numerical calculations for the ground state (equal energies case) of the He-like heavy ions were given in [9,10]. The Feynman gauge calculations include also the Breit-Breit contributions. Since for these contributions the Eq. (1.3) does not hold, the total RSC was nonzero. 

The Breit contribution to the Fock matrix can be treated in much the same way [97]. This requires a new type of radial integral... 

Our DKH values and the ZORA results for g values are rather close in many cases although for such large Ag shifts as for the heavy-atom radical PdH the absolute difference can become significant. In general, the accuracy of calculated g values for c -metal species, at all levels of approximations presently described in the literature, is notably lower than that of p-element compounds [35] see also Chapter 9 of this volume. Detailed reasons for this misrepresentation still have to be found. Obviously, for g tensors of (heavy) d-metal open-shell systems, one can profit from two-component methods that directly treat spin-orbit interaction which may become too large to be amenable to a perturbation treatment. One may also benefit from specially adapted xc functionals that reflect the relativistic kinematics of the electrons and the Breit contribution to the electron-electron interaction [57]. Despite of the very minor effect of these relativistic corrections on many molecular observables [66], notable changes of the very sensitive g tensor are anticipated. 

The self-energy contribution for Is electrons in heavy atoms is comparable to the Breit contribution, reducing the K-binding energy for Hg by 196 2eV. The uncertainty here reflects the various opinions on how best to treat screening corrections. 

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