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Does the Hartree approximation basically assume that electrons are independent and do not interact with each other?

Also, do Exchange integrals essentially measure the interaction between two different electrons?

Thanks.

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- Thread starter chemstudent09
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This is not a fundamental approximation, but it's a highly efficient one.In summary, the Hartree approximation does not assume that electrons are non-interacting, but rather includes exchange and electrostatic interactions. It does, however, assume that the kinetic energy of the electrons are independent, neglecting the coupling between kinetic and potential energy. Additionally, it is a single-determinant description of the system, making it highly efficient.

- #1

- 8

- 0

Does the Hartree approximation basically assume that electrons are independent and do not interact with each other?

Also, do Exchange integrals essentially measure the interaction between two different electrons?

Thanks.

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chemstudent09 said:Does the Hartree approximation basically assume that electrons are independent and do not interact with each other?

Also, do Exchange integrals essentially measure the interaction between two different electrons?

Well, the Hartree (or Hartree-Fock) method makes several approximations, but not that the electrons are non-interacting. If that were the case the resulting wave function of an atom would simply be a superposition of solutions to the hydrogen-like atom.

HF improves on that by including exchange (the effect of the Pauli principle), and the electrostatic interaction between the electrons (the Coulomb integral). So it includes two forms of electron-electron interaction. (although exchange is not, strictly speaking, an interaction, but a boundary condition placed on the solutions to the S.E.) The exchange integrals have no classical analog. They're simply a direct consequence of preserving the known boundary condition (antisymmetry).

However, HF does assume that the

The other approximation, implicit in HF, is that it's a single-determinant description of the system.

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