Large-scale DFT calculations for materials with complex structures

Utilizing the interaction between nanoscale systems is important to create new material functionality. First-principles density functional theory (DFT) calculation is a powerful tool to investigate the correlation between the atomic and electronic structures which cause materials properties. To describe complex nanoscale structures such as interfaces, defect complexes and disordered systems, large-scale structural models consisting of several thousands of atoms or more are required. However, conventional DFT calculations are limited to be typically less than a thousand atoms because the computational cost scales cubically to the number of atoms N. To overcome the limitation, we have developed a large-scale DFT code CONQUEST 1,2. CONQUEST can treat large systems by using local orbitals to express density matrices and a linear-scaling (O(N)) method based on the density matrix minimization. The computational cost scales cubically to the number of the support functions, both in the O(N) and the conventional diagonalization calculations. Therefore, to reduce the number of support functions without losing accuracy, we have introduced multi-site support functions (MSSF) 3,4. MSSFs are the linear combinations of pseudo-atomic orbitals from a target atom and its neighbor atoms in a cutoff region. MSSFs correspond to local molecular orbitals so that the number of required support functions can be the minimal. We have also proposed an efficient and comprehensive method to find out the atoms with characteristic electronic structures in large-scale systems by using statistical methods. We have investigated supported metallic nanoparticles in which the interaction between the nanoparticle and the support base plays an important role for catalytic reactivity. By our large-scale DFT calculation and the statistical analysis, the size- and site-dependence of atomic and electronic structures have been investigated for isolated and supported nanoparticles.