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To overcome the limitations of the traditional state-averaging approaches in excited state calculations, where one solves for and represents all states between the ground state and excited state of interest, we have investigated a number of new excited state algorithms. Building on the work of van der Vorst and Sleijpen (SIAM J. Matrix Anal. Appl., 17, 401 (1996)), we have implemented Harmonic Davidson and State-Averaged Harmonic Davidson algorithms within the context of the Density Matrixdoi:10.1063/1.2768360 pmid:17764231 fatcat:lkhbfdj7hzbcrlf4da72uhopwu