The origin of relativistic effects of atomic orbitals

Abstract

a(R)= integral R0 ( integral psi a psi d Omega )r2 dr curves are presented for different contributions a to the energy of atomic orbitals. While all radial shells contribute about equally to the non-relativistic kinetic and potential orbital energies, there is almost perfect cancellation of these energies in the inner shells, and the total energy of an orbital is almost solely determined by its outermost shell. In contrast to this, the first-order relativistic mass-velocity, Darwin and spin-orbit energies originate from the innermost shells only, while all radial shells contribute to the so-called indirect relativistic orbital energy correction,. The indirect effect is important also for s atomic orbitals except for the central columns of the periodic system, where the indirect destabilisation is compensated by indirect stabilisation. This explains the 'gold maximum' of relativistic corrections.

The Pseudopotential Approximation in Electronic Structure Theory

“…Core states are localized in the vicinity of the nucleus where valence states oscillate in order to maintain orthogonality with the core functions. This results in a large kinetic energy (kinetic energy pressure) for the valence electrons in the core region, which roughly cancels the large potential energy from the Coulomb interaction (this can nicely be seen in the work by Schwarz et al [2] ). Hans G. A. Hellmann [3] in 1934 therefore replaced these effects by a pseudopotential (which he called Zusatzpotential, that is, added-on potential), [4] which is repulsive in the core region and therefore keeps the electrons out of the core (Pauli repulsion).…”

“…[33] Scalar relativistic effects are included directly into V PP by the adjustment pro-cedure, [34] as relativistic perturbation operators originating, for example, from the Breit-Pauli or Douglas-Kroll Hamiltonian are short-to-medium range in nature [2] and should not be used for smooth pseudo-valence orbitals. However, this shift of relativistic effects into the valence region seems to work perfectly well (we come back to this problem in the next section).…”

Relativistic electronic structure studies on the heaviest elements

“…4) and stabilization (Eq. 3) of the hydrogen-like s and p 1/2 electrons is a direct relativistic effect and it was shown to originate from the inner K and L shell regions [15]. This effect was found to be also large for the valence region due to the direct action of the relativistic perturbation operator on the inner part of the valence density [16].…”

Perspective: Relativistic effects

“…One may speculate, as some have done, 7 that relativistic effects on the chemical properties of heavy atoms are small because their valence shells are subject to small effective (screened) nuclear charges. This turns out to be incorrect; 8 valence orbitals in heavy many-electron atoms have comparatively small orbital energies but may have very large kinetic and potential energies. As a result, in many-electron atoms and molecules the leading order of relativistic effects for valence orbitals is also Z 2 /c 2 with Z being the full charge of the heaviest nucleus.…”