Conjugate-gradient eigenvalue solvers in computing electronic properties of nanostructure architectures

In this article we report on our efforts to test and expand the current state-of-the-art in eigenvalue solvers applied to the field of nanotechnology. We singled out the nonlinear conjugate gradients (CG) methods as the backbone of our efforts for their previous success in predicting the electronic properties of large nanostructures and made a library of three different solvers (two recent and one new) that we integrated into the PESCAN (Parallel Energy SCAN) code [3] to perform a comparison. The methods and their implementation are tuned to the specifics of the physics problem. The main requirements are to be able to find (1) a few, approximately 4 to 10, of the (2) interior eigenstates, including (3) repeated eigenvalues, for (4) large Hermitian matrices.