CheSS – One of the most important tasks in electronic structure codes is the calculation of the density matrix. If not handled properly, this task can easily lead to a bottleneck that limits the performance of the code or even renders big calculations prohibitively expensive. CheSS is a library that was designed with the goal of enabling electronic structure calculations for very big systems. It is capable of working with sparse matrices, which naturally arise if big systems are treated with a localized basis. Therefore, it is possible to calculate the density matrix with O(N), i.e., the computation cost only increases linearly with the system size. The CheSS solver uses an expansion based on Chebyshev polynomials to calculate matrix functions (such as the density matrix or the inverse of the overlap matrix), thereby exploiting the sparsity of the input and output matrices. It works best for systems with a finite HOMO-LUMO gap and a small spectral width. CheSS exhibits a two-level parallelization using MPI and OpenMP and can scale to many thousands of cores. It has been converted into a stand-alone library starting from the original codebase within BigDFT. At the moment, it is coupled to the two MAX flagship codes BigDFT and SIESTA. The performance of CheSS has been benchmarked against PEXSI and (Sca)LAPACK for the calculation of the density matrix and the inverse of the overlap matrix, respectively. CheSS is the most efficient method, as it is demonstrated with more details and performance figures in the publication “Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library”.