Sparse matrix diagonalization in the NRLMOL electronic structure code
Density functional theory (DFT) based simulations are playing a major role in quantum mechanical studies of materials ranging from molecules, nanoparticles to the biological systems as they offer insights that are not directly accessible from experiments and also due to their ability to make sufficiently accurate predictions. The DFT implementation in the NRLMOL electronic structure code employs Gaussian basis sets to express the Kohn-Sham orbitals. A major computationally demanding task in the electronic structure calculations is solution of the generalized eigenvalue problem, that is the determination of nontrivial solutions (λ, c) of Hc = λOc where H and O are the Hamiltonian and Overlap matrices, respectively. These steps are currently performed in the NRLMOL code using the algorithms from the LAPACK and ScaLAPACK libraries. As the system size increases, the H and O matrices become sparse due to the localized nature of the basis sets. In the present thesis we explore the possibility of using the sparse matrix diagonalization techniques from the SLEPc library. An interface between the NRLMOL and SLEPC is developed and tested for a serial version of the NRLMOL. The stand-alone version of the interface is tested on the various system sizes with different number of processors. The scalability of the interface for various slicing of eigenvalue spectrum is examined. We also performed scaling test for different condition of slicing. Another small component of the thesis is devoted to design a web-based interface for NRLMOL to handle inputs and some specific calculations.^
Hassan, Md Mahmudulla, "Sparse matrix diagonalization in the NRLMOL electronic structure code" (2016). ETD Collection for University of Texas, El Paso. AAI10151311.