Energies of atomic terms

The electronic Hamiltonian of an atom is written in the form of a sum of the one-electron and two-electron parts 

Therefore the electronic energy with a configurational function PU(ML, Ms)) constructed of orthogonal spin-orbitals is 

The above three types of integrals in atoms can be expressed through a limited number of more fundamental quantities. 

In evaluating the one-electron integral the radial R(r) and the angular T( , p) parts of the wave function are specified. As the angular functions are orthonormal, viz. 

Such an integral does not depend on the magnetic quantum number m, which means that there are five integrals with the same value for the 3d orbitals, for instance. 

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Table 50 Energies of atomic terms for equivalent d-electrons...

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