Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction.

We present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix-vector product formation enables calculations with configuration spaces as large as 30 electrons in 30 orbitals, corresponding to an FCI calculation with over 2.

Pseudo-fivefold diffraction symmetries in tetrahedral packing.

We review the way in which atomic tetrahedra composed of metallic elements pack naturally into fused icosahedra. Orthorhombic, hexagonal, and cubic intermetallic crystals based on this packing are all shown to be united in having pseudo-fivefold rotational diffraction symmetry. A unified geometric model involving the 600-cell is presented: the model accounts for the observed pseudo-fivefold symmetries among the different Bravais lattice types.