 ONETEP therefore combines the advantages of the plane-wave approach (controllable accuracy and variational convergence of the total energy with respect to the size of the basis) with computational effort that scales linearly with the size of the system.The ONETEP approach involves simultaneous optimization of the density kernel (a generalization of occupation numbers to non-orthogonal basis, which represents the density matrix in the basis of NGWFs) and the NGWFs themselves.The optimized NGWFs then provide a minimal localized basis set, which can be considerably smaller in size, but of equal or higher accuracy, than the unoptimized basis sets used in most linear-scaling approaches.