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Improved Unconstrained Energy Functional Method for Eigensolvers in Electronic Structure Calculations

This paper reports on the performance of a preconditioned conjugate gradient based iterative eigensolver using an unconstrained energy functional minimization scheme. In contrast to standard implementations, this scheme avoids an explicit reorthogonalization of the trial eigenvectors and becomes an attractive alternative for the solution of very large problems. The unconstrained formulation is implemented in the first-principles materials and chemistry CP2K code, which performs electronic structure calculations based on a density functional theory approximation to the solution of the many-body Schrödinger equation. We study the convergence of the unconstrained formulation, as well as its parallel scaling, on a Cray XC40 at the National Energy Research Scientific Computing Center (NERSC). The systems we use in our studies are bulk liquid water, a supramolecular catalyst gold(III)-complex, a bilayer of MoS2-WSe2 and a divacancy point defect in silicon, with the number of atoms ranging from 2,247 to 12,288. We show that the unconstrained formulation with an appropriate preconditioner has good convergence properties and scales well to 230k cores, roughly 38% of the full machine.