The many-electron equation to be solved is the Dirac-Coulomb-(Breit) equation for N electrons
The inner product is taken between the vector of three Pauli spin matrices and the momentum operator p (px,py,pz), acting on the coordinates of electron i. In our notation 12 is used for a 2x2 unit matrix. The scalar potential arises in this approximation from the fixed nuclear framework. The program package uses atomic units in which the speed of light, c, is taken to be 137.0359895. In these units m, the mass of the electron, e, the elementary charge are set to 1.
To define a many-electron Hamiltonian one needs a two-electron operator gij. A correct relativistic two-electron operator cannot be written down in closed form. From the theory of Quantum Electro Dynamics one can derive a series expansion of the complete interaction . The first term is the Coulomb interaction