Different approaches have been developed to obtain the auxiliary density matrix D and corresponding MO coefficients Ĉ, e.g. by minimizing solely the square difference between the occupied orbital and auxiliary basis functions or by adding an orthonormality constraint to the fitting procedure. We will restrict the discussion to the ADMM2 variant, which is often also dubbed non-purified wave function fitting and which can be expressed in terms of the projection matrix Û. For the sake of convenience, we will nevertheless refer to ADMM2approximated results in the following by the general acronym ADMM. Auxiliary basis functions and corresponding auxiliary matrices are indicated as μ and M. The projection matrix Û is obtained according to