Plane waves and radial polynomials: a new mixed basis

A new mixed basis for quantum-chemical calculations is presented. It consists of plane waves and functions strictly localized within disjoint spheres around the nuclei. The additional functions are products of spherical harmonics with radial polynomials defined using a radial grid. Nearly linear scaling is achieved by projecting the plane-wave components onto the localized basis in mixed products. The required one- and two-electron integrals are calculated, and an energy optimization scheme using preconditioned conjugate-gradient search is derived. Results of Hartree-Fock calculations on small and medium-sized molecules are presented. The total energy is shown to converge exponentially with respect to the cut-off parameters of the basis. A corresponding extrapolation yields total energies with micro-Hartree accuracy. The Hartree-Fock geometry of the water molecule is calculated to femtometre accuracy.