Breit interaction / operator importance

The electron-electron interaction is usually supposed to be well described by the instantaneous Coulomb interaction operator l/rn. Also, all interactions with the nuclei whose internal structure is not resolved, like electron-nucleus attraction and nucleus-nucleus repulsion, are supposed to be of this type. Of course, corrections to these approximations become important in certain cases where a high accuracy is sought, especially in computing the term values and transition probabilities of atomic spectroscopy. For example, the Breit correction to the electron-electron Coulomb interaction should not be neglected in fine-structure calculations and in the case of highly charged ions. However, in general, and particularly for standard chemical purposes, these corrections become less important. 

The frozen-core (fc) approach is not restricted to spin-independent electronic interactions the spin-orbit (SO) interaction between core and valence electrons can be expressed by a sum of Coulomb- and exchange-type operators. The matrix element formulas can be derived in a similar way as the Sla-ter-Condon rules.27 Here, it is not important whether the Breit-Pauli spin-orbit operators or their no-pair analogs are employed as these are structurally equivalent. Differences with respect to the Slater-Condon rules occur due to the symmetry properties of the angular momentum operators and because of the presence of the spin-other-orbit interaction. It is easily shown by partial integration that the linear momentum operator p is antisymmetric with respect to orbital exchange, and the same applies to t = r x p. Therefore, spin-orbit... 

Because of the importance of Darwin s expression for the classical electromagnetic interaction of two moving charges (section 3.5), we are particularly interested in the frequency-independent radial form of the Breit operator. This represents the consistent interaction term to approximately include the retarded electromagnetic interaction of the electrons in our semi-classic formalism that describes only the elementary particles (electrons) quantum mechanically. In this long-wavelength limit, m —> 0, the radial operator Vv l,2) in Eq. (9.16) becomes D (l, 2) — already known from the Coulomb case in Eq. (9.9)... 

It should be noted that the two-electron term in this Dirac—Coulomb equation is based on a classical (i.e., nonrelativistic) picture of the interaction, and it is therefore not Lorentz invariant. In many applications this is a problem of minor importance, and results that are in good agreement with experiment often are obtained with the Dirac-Coulomb equation (Eqs. [71]—[74]) or with theory derived from it through further simplifications. For situations calling for a more accurate model, a relativistic picture of the electron—electron interaction is given by the Breit operator ... 

Some of the terms included in the Breit-Pauli Hamiltonian also describe small interactions that can be probed experimentally by inducing suitable excitations in the electron or nuclear spin space, giving rise to important contributions to observable NMR and ESR parameters. In particular, for molecular properties for which there are interaction mechanisms involving the electron spin, also the spin-orbit interaction (O Eqs. 11.13 and O 11.14) becomes important The Breit-Pauli Hamiltonian in O Eqs. 11.5-11.22, however, only includes molecule-external field interactions through the presence of a scalar electrostatic potential 0 (and the associated electric field F) and the appearance of the magnetic vector potential in the mechanical momentum operator (O Eq. 11.23). In order to extract in more detail the interaction between the electronic structure of a molecule and an external electromagnetic field, we need to consider in more detail the form of the scalar and vector potentials. 

---