A diagonalization‐free optimization algorithm for solving Kohn–Sham equations of closed‐shell molecules.

A local optimization algorithm for solving the Kohn–Sham equations is presented. It is based on a direct minimization of the energy functional under the equality constraints representing the Grassmann Manifold. The algorithm does not require an eigendecomposition, which may be advantageous in large‐scale computations. It is optimized to reduce the number of Kohn–Sham matrix evaluations to one per iteration to be competitive with standard self‐consistent field (SCF) approach accelerated by direct inversion of the iterative subspace (DIIS). Numerical experiments include a comparison of the algorithm with DIIS. A high reliability of the algorithm is observed in configurations where SCF iterations fail to converge or find a wrong solution corresponding to a stationary point different from the global minimum. The local optimization algorithm itself does not guarantee that the found minimum is global. However, a randomization of the initial approximation shows a convergence to the right minimum in the vast majority of cases. [ABSTRACT FROM AUTHOR]