What Are Integral Centers in Hartree Fock Theory?

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SUMMARY

The discussion centers on the interpretation of "centers" in Hartree Fock (HF) theory, particularly in the context of two-electron integrals. It is established that "centers" typically refer to atomic coordinates when Gaussian functions are employed, while Slater functions may not necessitate atomic coordinates. The distinction between two-center, three-center, and four-center integrals is clarified, emphasizing the relevance of the atomic origins of the electrons involved.

PREREQUISITES
  • Understanding of Hartree Fock theory
  • Familiarity with Gaussian and Slater basis functions
  • Knowledge of two-electron integrals in quantum chemistry
  • Basic concepts of atomic coordinates in molecular systems
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  • Research the role of Gaussian functions in quantum chemistry
  • Explore the mathematical formulation of two-electron integrals
  • Learn about the differences between Gaussian and Slater basis sets
  • Investigate the implications of multi-center integrals in computational chemistry
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Quantum chemists, computational chemists, and students studying electronic structure methods will benefit from this discussion, particularly those focusing on Hartree Fock theory and integral calculations.

greisen
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Hi,

I am looking at the integrals in HF - I am a little puzzled about the use of the word center.

F.ex. two electron integrals on different center - it that electron belonging to different atom A and B?

Than it mentions three- and four center - how to interpreted center?

Thanks in advance

best regards
 
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Hi,

I guess that centers are often atom coordinates when using gaussian functions but it is not necessary atomic coordinates when using Slater functions?
 

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