A Novel Gaussian-Sinc mixed Basis Set for Electronic Structure calculations

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