A Novel Gaussian-\textit{Sinc} mixed Basis Set for Electronic Structure Calculations

A Gaussian-Sinc mixed basis set for the computation of the electronic structure atoms and molecules is presented. Excellent bases functions are known ``core'' and ``valence'' separately, such as Gaussians for the ``core'' wave and Plane-waves for ``valance'' wave functions, but as yet no is known that can accurately deal with both regimes in a single basis. A Sinc mixed basis can do both. This method resolves several issues such : i) the Sincs basis spans the same space as the plane-waves basis, yet are local enough to define all interaction elements including Exchange; ii) Gaussians span the spherically symmetric core states and can be mixed with Sinc functions in a computationally efficient methodology; iii) together, mixed basis set is a flexible, computationally efficient and a highly method for solving atomic and molecular problems. This methodology has implemented within the Hartree-Fock level of theory within ultra-strong fields. To demonstrate the utility of this new method, we calculated ground state Hartree-Fock energies to five digits accuracy in ultra strong fields for Helium to Neon, Molecular Hydrogen, Water, Carbon dioxide Benzene.