Quantum mechanics polyelectronic atoms

The electron correlation problem occurs with all polyelectronic atoms. To treat these systems using the quantum mechanical model, we must make approximations. The simplest approximation involves treating each electron as if it were moving in a field of charge that is the net result of the nuclear attraction and the average repulsions of all the other electrons. To see how this is done, let s compare the neutral helium atom and the He+ ion ... 

Spin-orbit coupling is an addition to the Schrodinger equation but it is a natural feature in Dirac s theory which associates relativity theory with quantum mechanics. There are, however, other relativistic effects in the electronic structure of polyelectronic atoms which can be related to changes in the electron mass with velocity (for a review on relativistic effects in structural chemistry, see ref. 62). 

If the electron is in the Is state, the hydrogen atom is in its lowest state of energy. In a polyelectronic atom such as carbon (six electrons) or sodium (eleven electrons) it would not seem unreasonable if all the electrons were in the Is level, thereby giving the atom the lowest possible energy. We might denote such a structure for carbon by the symbol Is and for sodium, ls . This result is wrong, but from what has been said so far there is no apparent reason why it should be wrong. The reason lies in an independent and fundamental postulate of the quantum mechanics, the Pauli exclusion principle no two electrons... 

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