Trace Conserving Purification for Linear Scaling [O(N)] Methods: A First Enhancement to CP2K

: Implementation of the low-order purification method as an alternative to diagonalization for self-consistent density function theory calculations lowers the memory and time to solution for analysis of chemical systems. There is some improvement for low-sparsity systems, but the highest speed-up is seen in low band gap and highly sparse matrix problems. This work has been conducted and tested in the CP2K program.