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

For fast density functional calculations, a suitable basis that can accurately represent the orbitals within a reasonable number of dimensions is essential. Here, we propose a new type of basis constructed from Tucker decomposition of a finite-difference (FD) Hamiltonian matrix, which is intended to reflect the system information implied in the Hamiltonian matrix and satisfies orthonormality and separability conditions. By introducing the system-specific separable basis, the computation time for FD density functional calculations for seven two- and three-dimensional periodic systems was reduced by a factor of 2-71 times, while the 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 the density functional calculations with the proposed basis can be systematically controlled by adjusting the rank size of Tucker decomposition.