The Breit Operator for Retarded Interactions

As in the case of the unretarded Gaunt interaction, we choose the velocity operator expression r ca (instead of the momentum operator) to obtain consistent results as before and obtain the interaction energy of Eq. (3.252) promoted to the operator calculus of quantum theory. 

With Breit s potential energy operator, the stationary quantum mechanical equation for two electrons in the central field of an atomic nucleus reads 

Although this retardation operator includes products of the Dirac matrices for the two interacting particles, ai 2, magnetic interactions mediated via the vector potential seem to be included. However, already the derivation of the classical retarded interaction in section 3.5 clearly shows that all vector potential terms inherently feature a 1/c prefactor, as in Eq. (3.214), so that the vector potential contribution and, hence, the magnetic contribution of the interaction enters these equations unretarded [178]. This is also clear from the rigorous collection of terms after a Taylor expansion around time fi in Eq. (3.233). 

Gaunt and Breit interaction operators represent potential energies due to magnetic interactions, which one would also assume to play a role in the non-relativistic many-particle theory given by the Pauli equation, Eq. (5.140). One 

Depending on the type of molecular properties, a Breit operator is often not employed in quantum chemistry. This is because of the c damping which reduces the effect of the Breit correction compared to the Coulomb interaction and which makes this term even vanish in the limit of instantaneous interactions, c — oo. Non-negligible effects may be encountered in accurate 

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