Sparse Matrix Algebra for Quantum Modeling of Large Systems

Matrices appearing in Hartree–Fock or density functional theory coming from discretization with help of atom–centered local basis sets become sparse when the separation between atoms exceeds some system–dependent threshold value. Efficient implementation of sparse matrix algebra is therefore essential in large–scale quantum calculations. We describe a unique combination of algorithms and data representation that provides high performance and strict error control in blocked sparse matrix algebra. This has applications to matrix–matrix multiplication, the Trace–Correcting Purification algorithm and the entire self– consistent field calculation.