Breit radial integrals

The Breit contribution to the Fock matrix can be treated in much the same way [97]. This requires a new type of radial integral... 

The total Hamiltonian contains three types of contributions the one-electron Dirac Hamiltonion, the Coulomb repulsion and the Breit interaction. These contributions, which appear in the energy expression, give rise to radial integrals, which need to be calculated for the two component wave function. We will simply state the MCDF equations, which can be obtained by applying the variational... 

The terms etc. in (10) represent the one-body mean-field potential, which approximates the two-electron interaction in the Hamiltonian, as is the practice in SCF schemes. In the DFB equations this interaction includes the Breit term (4) in addition to the electron repulsion l/rjj. The radial functions Pn ( ) and Qn/c( ) may be obtained by mmierical integration [20,21] or by expansion in a basis (for more details see recent reviews [22,23]). Since the Dirac Hamiltonian is not bound from below, failure to observe correct boundary conditions leads to variational collapse [24,25], where admixture of negative-energy solutions may yield energies much below experimental. To avoid this failure, the basis sets used for expanding the large and small components must maintain kinetic balance [26,27]. In the nonrelativistic limit (c oo), the small component is related to the large component by [24]... 

The individual terms of the Y.nij sum correspond to the partial contributions of the nxhjx nlj transitions is sum of the contributions of the different multiplicity transitions. The detailed expressions for the Coulomb and Breit parts can be found in Refs. [22, 23, 35]. The imaginary part contains the radial Rx and angular Sx integrals. It can be written as follows ... 

---