md2011-06-note_Part_9

md2011-06-note_Part_9 - E C I The key problem in solving...

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Unformatted text preview: E C I The key problem in solving the many-body problem is that the electrons form an interacting system with a wavefunction of the form ( r ) ( r 1 , r 2 , . . . , r N ) . I In HF, all correlations except those required by the Pauli exclusion principle are neglected. The exchange term in the Hamiltonian (see eq. 32) has two roles; it introduces the exclusion principle and an electronic self-interaction (which must be canceled in the correlation term). I The effect is always towards lower energy, which can be interpreted as the interaction between the electron and a positive exchange hole around it. I One way to interpret the exchange energy is that it gives the lowering of the energy due to each electron interacting with the corresponding exchange hole. Notes I Taking the correlation effects between the electrons into account involves introducing new degrees of freedom to the wavefunction....
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md2011-06-note_Part_9 - E C I The key problem in solving...

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