This presentation will discuss ongoing work on unconstrained minimization schemes for the solution of eigenvalue problems. These schemes employ a preconditioned conjugate gradient approach that avoids an explicit reorthogonalization of the trial eigenvectors, in contrast to typical iterative eigenvalue solvers, therefore reducing communications and becoming a potential alternative for the solution of large problems on massively parallel computers. We target problems related to electronic structure calculations. We show results for a set of benchmark systems with an implementation of the unconstrained minimization in first-principles materials and chemistry codes that perform electronic structure calculations based on a density functional theory (DFT) approximation to the solution of the many-body Schrödinger equation. The results show that the unconstrained formulation, together with an appropriate preconditioner, offers good convergence properties and scales well on a large number of cores. We also show results for an implementation in the commonly used plane wave formulation of DFT.