Auxilliary Basis Coulomb Fit (I)

Where V is the matrix of 2-centre 2-electron repulsion integrals in the charge density basis and b are the three centre electron repulsion integrals between the wavefunction basis set and the charge density basis.

The approach is based on the expansion of the charge density in an auxiliary basis of Gaussian functions

As suggested by Dunlap, a variational choice of the fitting coefficients C can be obtained as follows:

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