Relativistic Effects in the Electronic Structure of Atoms

Periodic trends in relativistic effects are investigated from <sub>1</sub>H through <sub>103</sub>Lr using Dirac–Hartree–Fock and nonrelativistic Hartree–Fock calculations. Except for <sub>46</sub>Pd (4d<sup>10</sup>) (5s<sup>0</sup>), all atoms have as outermost shell the ns or n’p spinors/orbitals. We have compared the relativistic spinor energies with the corresponding nonrelativistic orbital energies. Apart from <sub>24</sub>Cr (3d<sup>5</sup>) (4s<sup>1</sup>), <sub>41</sub>Nb (4d<sup>4</sup>) (5s<sup>1</sup>), and <sub>42</sub>Mo (4d<sup>5</sup>) (5s<sup>1</sup>), the ns<sub>+</sub> spinor energies are lower than the corresponding ns orbital energies for all atoms having ns spinor (ns<sub>+</sub>) as the outermost shell, as some preceding works suggested. This indicates that kinematical effects are larger than indirect relativistic effects (the shielding effects of the ionic core plus those due to electron–electron interactions among the valence electrons). For all atoms having np<sub>+</sub> spinors as their outermost shell, in contrast, the np<sub>+</sub> spinor energies are higher than the corresponding np orbital energies as again the preceding workers suggested. This implies that indirect relativistic effects are greater than kinematical effects. In the neutral light atoms, the np<sub>–</sub> spinor energies are close to the np<sub>+</sub> spinor energies, but for the neutral heavy atoms, the np<sub>–</sub> spinor energies are considerably lower than the np<sub>+</sub> spinor energies (similarly, the np<sub>–</sub> spinors are considerably tighter than the np<sub>+</sub> spinors), indicating the importance of the direct relativistic effects in np<sub>–</sub>. In the valence nd and nf shells, the spinor energies are always higher than the corresponding orbital energies, except for <sub>46</sub>Pd (4d<sup>10</sup>) (5s<sup>0</sup>). Correspondingly, the nd and nf spinors are more diffuse than the nd and nf orbitals, except for <sub>46</sub>Pd.