The solution to the eigenproblem produces a density which does not generally minimize the functional and so an iterative process is used to generate a new set of matrices and a new solution, until convergence to self consistency is obtained. The number of SCF iterations needed for convergence is problem dependent and varies from approximately 4 to 20 or so. A number of codes are available for computing electronic structure in this way. Variational freedom can be added with second and higher zeta functions and polarization functions. The methods in the code for computing matrix elements are highly parallel and scale linearly with system size.
Forces also scale linearly.
The code computes total energy and forces, and can optimize the geometric structure of a system. The LCAO basis set used in MP-Quest determines some characteristics of the eigenproblem that needs to be solved. This is in contrast to methods based on plane-waves which are nonlocal. For small systems this is not important and the order of the scaling is the same, but as system size increases the scaling prefactor is much worse than that of a dense matrix eigensolver. Note that the large fraction of states needed precludes the use of Lanczos or other sparse methods.