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.