A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based Tight Binding

Anthony Scemama (1) , Nicolas Renon (2) , Mathias Rapacioli (3)

1 GMO - Groupe THEO (LCPQ)
2 CALMIP - Calcul en Midi-Pyrénée
3 MAD - Modélisation, Agrégats, Dynamique (LCPQ)

We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density functional based tight binding method, for which most of the computational time is spent in the linear algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that with this algorithm (i) single point calculations on very large systems (millions of atoms) can be performed on large SMP machines (ii) calculations involving intermediate size systems (1 000-100 000 atoms) are also strongly accelerated and can run efficiently on standard servers (iii) the error on the total energy due to the use of a cutoff in the molecular orbital coefficients can be controlled such that it remains smaller than the SCF convergence criterion.

Domaines: Chimie théorique et/ou physique

Anthony Scemama, Nicolas Renon, Mathias Rapacioli. A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based Tight Binding. Journal of Chemical Theory and Computation, 2014, 10, pp.2344-2354. ⟨10.1021/ct500115v⟩. ⟨hal-00992187⟩