Relativistic orbital energies

Introduction of negative energy (positron) states. The coupling between the electronic and positronic states introduce a small component in the eleetronic wave funetion. The result is that the shape of the orbitals change, relativistic orbitals, for example, do not have nodes. 

Table 5.1 Effect of relativity on Hartree-Eock orbital energies (in eV) for the neutral Hg and Fe atoms. Scalar relativistic effects were treated with the DKH2 approximation...

FIGURE 59. Relativistic and non-relativistic Hartree-Fock orbital energies for tin and lead... 

The term inert pair is often used for the tendency of the 6s2 electron pair to remain formally unoxidized in the compounds of Pb(n) [and also in the case of T1(I) and Bi(m) etc.]. As discussed above, this tendency can be related to relativity. Figure 59 shows the relativistic and non-relativistic valence orbital energies for Sn and Pb. The relativistic increase of the s-p gap leads to a 6s2 inert pair in the case of Pb. However, the situation is more complex if the local geometry at the heavy atom (Pb) is discussed. There are examples for both, stereochemically inactive and stereochemically active s2 lone pairs. 

Table 1 Xenon, comparison of orbital energies for numerical Dirac and ZORA and non relativistic calculations with basis set ZORA calculations in different Coulomb matrix approximations in the UGBS basis set...

Further aspects governing computational effort and accuracy are related to the explicit treatment of relativistic effects, which are pronounced for atoms with high atomic numbers, as their core electrons reach velocities that make the influence of special relativity significant. Contraction of bond lengths and a shifting of orbital energies are observed compared to the non-relativistic treatment. An efficient way to include a major fraction of these... 

Relativistic effects. The neglect of the effects of relativity on orbital energies is another common defect of SCF calculations and is particularly important for core orbital energies which can be very large. 

A relativistic Hartree-Fock (RHF) Hamiltonian was used to generate a complete set of single-electron orbitals, energy levels and Green s functions. 

Goudsmit and Uhlenbeck electron spin. Thomas spin-orbit energy. Heisenberg and Jordan relativistic correction to energy. Net result recovery of Sommerfeld energy levels, different quantum numbers. 

Fig. 7. Comparison of the valence ns Lamb shift with the orbital energy and the relativistic, Breit, and nuclear volume contributions to it for coinage metals. Reproduced from [37].

The non-relativistic (HF) and relativistic (DF) orbital energies [23] for elements 104- through 118 are shown in Figure 8. IPs, experimental in the case of the 5d elements and calculated for the 6d elements (at the CCSD and MCDF levels), are shown in Figure 9. Single IP are listed in Tables 2 and 3. 

Fig. 8. Relativistic (DF, solid lines) and non-relativistic (HF, dashed lines) orbital energies for elements 104 through 118. The data are from [23].

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