Atom-projected and angular momentum resolved density of states in the ONETEP code

Local and angular momentum projected densities of states (DOS) are invaluable sources of information that can be obtained from density functional theory calculations. In this work, we describe a theoretical framework within ONETEP's linear-scaling DFT formalism that allows the calculation of local (atom-projected) and angular momentum projected density of states l-p-DOS. We describe four different bases that can be used for projecting the DOS with angular momentum resolution and perform a set of tests to compare them. We validate the results obtained with ONETEP's l-p-DOS against the plane-wave DFT code CASTEP. Comparable results between ONETEP's and CASTEP's charge spilling parameters are observed when we use pseudo-atomic orbitals as the projection basis sets. In general, the charge spilling parameters show remarkably low values for projections using non-contracted spherical waves as the angular momentum resolved basis. We also calculate the d-band and d-band centres for Pt atoms in (1 1 1) facets of cuboctahedral Pt nanoparticles of increasing size, which is an example of l-p-DOS application commonly used as an electronic descriptor in heterogeneous catalysis. Interestingly, the different projection bases lead to similar conclusions, showing the reliability of the implemented method for such studies. The implementation of these methods in a linear-scaling framework such as ONETEP provides another tool for analysing the electronic structure of complex nanostructured materials.