Solving the SCF problem in molecular orbital calculations through a sequence of quadratic programming: Extension to large systems

Abstract

An algorithm that avoids the diagonalization bottleneck of traditional electronic-structure calculations is proposed. This algorithm is based on matrix products and minimization of the electronic energy through a sequence of quadratic programming. Tests were made on small molecules to prove the validity and check the behavior of the algorithm. Extension to large systems was done using sparse matrix algebra. Benchmark examples were considered on polyglycine chains (up to 1403 atoms), polylysine chains (up to 3303 atoms), and on water clusters (up to 756 water molecules). This algorithm involves a small number of matrix products per iteration that become sparser and sparser close to the convergence, thus making it attractive for large systems studies.