Question

In: Chemistry

1 a). Write down the Slater determinant for Lithium. Expand the determinant into linear combination of...

1 a). Write down the Slater determinant for Lithium. Expand the determinant into linear combination of products.

b). Write down the Slater determinant for Beryllium. Expand the determinant into linear combination of products.

Solutions

Expert Solution

The lithium atom, however, has three electrons. An antisymmetric spin wave function of three electrons could in principle be written as the Slater determinant,

Such Slater determinant, however, is equal to zero because two of the columns are equal to each other. This fact rules out the possibility of having a zero order wave function that is the Fock product of three hydrogenlike functions:

fOR Slater determinant of Berillium atom

WE would have a 4x4 determinant

1s(1) 1s*(1) 2s(1) 2s*(1)

1s(2) 1s*(2) 2s(2) 2s*(2)

1s(3) 1s*(3) 2s(3) 2s*(3)

1s(4) 1s*(4) 2s(4) 2s*(4)

s can be A and s* can be B.

queen_honey_blossom answered 2 years ago
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