Slater Determinants and the Pauli Principle

Note that the first line in the determinant contains the two spin orbitals evaluated for the coordinates of the first electron. The second line consists of the spin orbitals listed in the 

What happens if we assume the two electrons to occupy the same atomic orbital and to have the same spin In this case j(r, s) = s), the two columns are identical, and the 

Earlier in this chapter we used the simple product (ri, r 1) = is (ri) Pis (f2) to calculate the energy of the ground state of a two-electron atom. There are two reasons why this was possible  

The atoms in Groups 2, 12 or 18, where all atomic orbitals are completely filled (or completely empty) in the ground state, are referred to as closed shell atoms. If such an atom contains N electrons, combination of N/2 atomic orbitals with a or spin functions will produce N spin-orbitals. The ground state is non-degenerate, and a wavefunction satisfying the Pauli Principle is easily obtained by writing down the Af x A Slater determinant  

The first line of the determinant consists of the N spin orbitals evaluated for the coordinates of the first electron. The second line consists of the spin orbitals listed in the same order evaluated for the coordinates of the second electron, and so on until the last line where the spin orbitals are evaluated for the coordinates of the Nth electron. /(N ) is a normalization constant. 

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