How Do You Transform Two-Electron Integrals from Atomic to Molecular Basis?

[Aranya C]

Hello Everyone,

Can anyone tell me how to do a transformation from atomic basis to molecular basis incase of
2-electron integrals for the case of Gaussian type Orbitals?
Like in case of One electron integrals it is known that a transformation from the Gaussian type orbitals to their contracted form changes the basis from primitive to atomic basis and then doing an Unitary transformation it changes to Molecular Basis, But this is for One electron Integrals??
Any idea about 2electron integrals, as Unitary transformation won't work here !

 

[BigJDubs]

Thanks in advance !!</code>The transformation from the atomic basis to the molecular basis for two-electron integrals is done by a canonical transformation. This involves transforming the individual atomic orbitals, and then applying the two-electron integrals in the new basis. The transformation is given by:A = C*U*C^Twhere C is the coefficient matrix of the atomic orbitals, U is the unitary transformation matrix, and A is the resulting molecular orbital coefficient matrix. The two-electron integrals can then be calculated in the new basis by transforming the integrals in the atomic basis using the same transformation. Hope this helps!