What Are Integral Centers in Hartree Fock Theory?

[greisen]

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

 

[greisen]

Hi,

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

 

[Blueshift5]

,

As a scientist familiar with Hartree Fock theory, I can offer some clarification on the terminology used for integral centers. In this context, "center" refers to the atomic nucleus around which the electrons are orbiting. In other words, when we talk about two electron integrals on different centers, we are referring to the interaction between two electrons located in different atomic orbitals. For example, in a molecule with atoms A and B, the two electron integral on different centers would involve one electron from atom A and one electron from atom B.

Similarly, when we talk about three- and four-center integrals, we are referring to the interaction between multiple atomic nuclei and electrons. For example, a three-center integral would involve three nuclei and one electron, while a four-center integral would involve four nuclei and one electron.

I hope this helps clarify the use of the term "center" in the context of Hartree Fock integrals. If you have any further questions, please don't hesitate to ask. Best regards,