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Center for Nonlinear Studies |
Gaussian-Sinc integrals allow for translationally invariant grid solutions of electronic structure. Information regarding functions is represented by the Cardinal Sine ( Sinc ), which is more practical than plane-waves. In a natural integration with Gaussians, the Gaussian-Sinc algorithm is used to calculate atomics, diatomics, and benzene. These calculations are translationally invariant, independent of lattice spacing. Convergence of Gaussian-Sinc with Torsional Spin waves is demonstrated for molecular hydrogen. Fine structure and high magnetism is considered for molecular hydrogen in a Hartree Fock theory. Calculation of several angular scattering potentials show d-wave resonance and s-wave spin frustration. Concurrently, Hartree Fock theory in the Sinc basis is calculated as a canonical tensor. A Gaussian-Quadrature of the Gaussian-Sinc integrals canonically represents the Hamiltonian. Canonical density can be polyadically decomposed from a spectral projection, thus avoiding the need to reduce space directly. Extreme single-core timings are observed for various known systems where tens of thousands of basis elements require only tens of minutes to solve for an energy. In conclusion, Gaussian-Sinc has achieved foundational results in electronic structure calculations.
Host: Sue Mniszewski & Anders Niklasson