A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analyzed, by studying the overlap between DOCI and full configuration interaction (FCI) wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, a simulated annealing (SA) method is introduced as a global energy based optimisation procedure of the single-particle orbitals. Next, we
expand on the value of seniority number minimising orbitals from truncated configuration interaction (CI) wave functions for approximating the optimal single-particle orbitals of DOCI and related wave functions that contain predominantly seniority zero determinants. It is shown that the resulting seniority number and energy minimising orbitals are especially suitable for the description of static correlation.