System-Specific Separable Basis Based on Tucker Decomposition:Application to Density Functional Calculations

For fast density functional calculations, a suitablebasis that can accurately represent the orbitals within a reasonablenumber of dimensions is essential. Here, we propose a new type ofbasis constructed from Tucker decomposition of afinite-difference(FD) Hamiltonian matrix, which is intended to reflect the systeminformation implied in the Hamiltonian matrix and satisfiesorthonormality and separability conditions. By introducing thesystem-specific separable basis, the computation time for FD densityfunctional calculations for seven two- and three-dimensionalperiodic systems was reduced by a factor of 2-71 times, whilethe errors in both the atomization energy per atom and the band gap were limited to less than 0.1 eV. The accuracy and speed of thedensity functional calculations with the proposed basis can be systematically controlled by adjusting the rank size of Tuckerdecomposition.