Analysis of multi-configuration density functional theory methods: theory and model application to bond-breaking

We consider the extension of the standard single-determinant Kohn–Sham method to the case of a multi-configuration auxiliary wave function. By applying the rigorous Kohn–Sham method to this case, we construct the proper interacting and auxiliary energy functionals. Following the Hohenberg–Kohn theorem for both energy functionals, we derive the corresponding multi-configuration Kohn–Sham equations, based on a local effective potential. At the end of the analysis we show that, at the ground state, the auxiliary wavefunction must collapse into a single-determinant wave function, equal to the regular KS wavefunction. We also discuss the stability of the wavefunction in multi-configuration density functional theory methods where the auxiliary system is partially interacting, and the remaining (residual) correlation is evaluated as a functional of the density. As an example showing both the challenges and the possibilities, we implement such a procedure for the perfect pairing wavefunction, using a residual correlation functional that is based on the Lee–Yang–Parr functional, and present results for an elementary bond-breaking process.