Relativistic orbitals

The second (indirect) relativistic effect is the expansion of outer d and f orbitals The relativistic contraction of the s and pi/2 shells results in a more efficient screening of the nuclear charge, so that the outer orbitals which never come to the core become more expanded and energetically destabilized. While the direct relativistic effect originates in the immediate vicinity of the nucleus, the indirect relativistic effect is influenced by the outer core orbitals. It should be realized that though contracted s and pi/2 core (innermore) orbitals cause indirect destabilization of the outer orbitals, relativistically expanded d and f orbitals cause the indirect stabilization of the valence s and p-orbitals. That partially explains the very large relativistic stabilization of the 6s and 7s orbitals in Au and element 112, respectively Since d shells (it is also valid for the f shells) become fully populated at the end of the nd series, there will occur a maximum of the indirect stabilization of the valence s and p orbitals [34],... 

In equations (56) and (57), one sees that the separation between the scalar and spin-orbit contributions is dependent on the chosen ansatz function /(r). This has recently been pointed out by Visscher and van Lenthe [69] who showed that the division between scalar and spin-orbit relativistic contributions is arbitrary. 

SOCI spin-orbit configuration interaction SOFT second-order perturbation theory SOREP spin-orbit relativistic effective potential TD-DFT time dependent density functional theory ZORA zero-order regular approximation... 

Introduction of negative energy (positron) states. The coupling between the electronic and positronic states introduces a small component in the electronic wave function. Ihis leads to a change in the shape of the orbitals relativistic orbitals, for example, do not have nodes. 

Fronzoni G, Stener M, Decleva P, Wang F, Ziegler T, Van Lenthe E, Baerends E (2005) Spin-orbit relativistic time dependent density functional theoiy calculations for the description of core election excitations TiCL, case study. Chem Phys Lett 416 56-63... 

Kim has formulated a relativistic Hartree-Fock-Roothaan equation for the ground states of closed-shell atoms using Slater-type orbitals. Relativistic effects in atoms have been reviewed by Grant. Malli and coworkers have formulated a relativistic SCF method for molecules. In this method, four-component spinor wavefunctions are obtained variationally in a self-consistent scheme using Gaussian basis sets. 

L. Visscher, E. van Lenthe. On the distinction between scalar and spin-orbit relativistic effects. Chem. Phys. Lett., 306 (1999) 357- 65. 

The first term is the Pauli operator regularized, which can be seen by setting V to zero in the denominator. The second term contains a spin-free and a spin-orbit relativistic correction to the operator. The spin-orbit correction is the Pauli operator regularized. There is no spin-free relativistic correction to the Pauli operator, but as before we must realize that the relativistic correction to the property is a second-order perturbation, which includes a relativistic correction to the wave function. 

This potential is also known as a spin-orbit relativistic effective potential, or SORER Finally, we can write the entire spin-dependent pseudopotential as... 

---