title: "Lagrange functions": a family of powerful basis sets for real-space order-N electronic structure calculations.
abstract: Plane waves have unparalleled simplicity and systematic convergence by a single monotonic parameter, the energy cutoff, but they are limited to speriodic systems and require Fourier transforms that scale as N(2)logN, where N is the number of atoms. Real-space methods for order-N scaling are computationally complex and convergence depends on several variables. Here we introduce and demonstrate "Lagrange functions" as a family of analytical, complete, and orthonormal basis sets that are suitable for efficient, accurate, real-space, order-N electronic structure calculations. Convergence is controlled by a single monotonic parameter, the dimension of the basis set, and computational complexity is lower than that of plane waves.
authors.affiliation: Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee, USA.
authors.forename: Kálmán
authors.initials: K
authors.lastname: Varga
authors.forename: Zhenyu
authors.initials: Z
authors.lastname: Zhang
authors.forename: Sokrates T
authors.initials: ST
authors.lastname: Pantelides