Anastasia Kruchinina: Linear scaling techniques in electronic structure calculations

Abstract: 

In large-scale electronic structure calculations based on Hartree-Fock and Density functional theory one of the key problems is computation of the density matrix. Recursive density matrix polynomial expansion is an ecient approach which scales linearly in terms of the computational time and memory usage [1,2]. In our approach, we take advantage of eigenvalue estimates that can be extracted from the recursive expansion by a simple and robust procedure at a negligible computational cost [3].

Linear scaling approaches do not provide eigenvectors of the Fock/Kohn-Sham matrix explicitly. The computation of inner eigenpairs, in particular homo and lumo eigenpairs, can be facilitated by the recursive polynomial expansion [4]. We propose a method where eigenpairs are calculated "on the fly" adding only a small overhead to the polynomial expansion [5]. The proposed algorithms are implemented in the quantum chemistry program Ergo (www.ergoscf.org).

References

1. A. Kruchinina, E. Rudberg, E. H. Rubensson, Parameterless stopping criteria for recursive density matrix expansions, J. Chem. Theory Comput., 2016, 12 (12), pp 57885802

2. E. Rudberg, E. H. Rubensson, and P. Sa lek, Kohn-Sham density functional theory electronic structure calculations with linearly scaling computational time and memory usage, J. Chem. Theory Comput., 7 (2011), pp. 340350.

3. E. H. Rubensson and A. M. N. Niklasson, Interior eigenvalues from density matrix expansions in quantum mechanical molecular dynamics, SIAM J. Sci. Comput., 36 (2014), pp. B147B170.

4. E. H. Rubensson and S. Zahedi, Computation of interior eigenvalues in electronic structure calculations facilitated by density matrix purication, J. Chem. Phys., 128 (2008), 176101.

5. A. Kruchinina, E. Rudberg, E. H. Rubensson, Computation of frontal orbitals in the recursive density matrix expansion, in preparation