Hartree-Fock Questions Answers

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SUMMARY

The discussion centers on the Hartree-Fock approximation, which utilizes the ordinary electronic Hamiltonian and assumes the wave function is represented by a single Slater determinant. This approach leads to the derivation of the Hartree-Fock equations, which describe the behavior of single-particle wave functions while acknowledging their interdependence through exchange and Coulomb integrals. The limitation of this method is its inability to account for electron correlation due to the assumption of single-particle wave functions.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with electronic Hamiltonians
  • Knowledge of Slater determinants
  • Basic grasp of exchange and Coulomb integrals
NEXT STEPS
  • Study the derivation of the Hartree-Fock equations in detail
  • Explore methods to include electron correlation, such as Configuration Interaction (CI)
  • Learn about post-Hartree-Fock methods like Møller-Plesset perturbation theory
  • Investigate the limitations of the Hartree-Fock method in various chemical systems
USEFUL FOR

Students and researchers in quantum chemistry, theoretical chemists, and anyone interested in computational methods for electronic structure calculations.

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Hello,

I have posted my questions and my thoughts on this image, to make it more clear:

[PLAIN]http://img529.imageshack.us/img529/3486/naeng.jpg
http://img529.imageshack.us/img529/3486/naeng.jpg

Thank you!
 
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In the Hartree-Fock approximation, you're always using the ordinary electronic Hamiltonian.

The approximation, or ansatz, is that you assume the wave function takes a specific form, namely a (single) Slater determinant; an antisymmetrized product of single-particle wave functions. By plugging that into the full electronic Hamiltonian and using the orthonormality properties of the orbitals, you get (and it's a rather tedious derivation) the Hartree-Fock equations, which is the Hamitonian for these single-particle wave functions. These are still interdependent, but the dependency is reduced to having the wave functions of the other particles in the exchange and coulomb integrals, where you're integrating over all coordinates.

So one orbital depends on the other orbitals, but not on the coordinates of the other electrons. Since you assumed single-particle wave functions (of single coordinates) it can't depend on more than one coordinate. Which is why you don't have correlation.
 

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