The Orbital Approximation for Lithium

For an atom with electrons, the total wavefunction can be written approximately as the product of n one-electron wavefunctions  

These one-electron wavefunctions are similar to the hydrogen orbitals, but are contracted towards the nucleus because of the greater nuclear charge seen by the electrons. For Uthium, which has three electrons, one form of the wavefunction will be  

electrons 1 and 2 occupy the Is orbital with their spins paired. The third electron cannot enter this orbital because of the operation of the Pauli exclusion principle, and it goes into the 2s orbital. Lnlike the situation with hydrogen, the 2s orbital has a lower energy than the 2p orbital because of electron electron interaction (see Section 7.7), and it is occupied preferentially. The electronic structure of lithium can therefore be written as ls 2s. The electrons in the Is orbital are, on average, much closer to the nucleus than the electron in the 2s orbital, and they are said to occupy the K shell. 

The wavefunction given in equation (7.35) is not completely satisfactory because it assigns each electron to a particular spin orbital, whereas it is not possible to know with certainty what state an electron is in. To give all combinations equal weighting, and to make the overall wave-function antisymmetric with respect to interchange of electrons, equation (7.35) must be rewritten as a Slater determinant  

This determinant gives equal weighting to the six ways in which the three electrons can be fitted into the spin orbitals, whereas equation (7.35) includes only one arrangement. 

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