The augmented Roothaan-Hall method for optimizing Hartree-Fock and Kohn-Sham density matrices.

We present a novel method for the optimization of Hartree-Fock and Kohn-Sham energies that does not suffer from the flaws of the conventionally used two-step Roothaan-Hall (RH) with direct inversion in iterative subspace (DIIS) acceleration scheme, improving the reliability of the optimization while reducing its cost. The key to its success is the replacement of the two separate steps of each RH/DIIS iteration by a single concerted step that fully exploits the Hessian information available from the previous iterations. It is a trust-region based method and therefore by design converges to an energy minimum. Numerical examples are given to illustrate that the algorithm is robust and cost efficient, converging smoothly to a minimum also in cases when the RH/DIIS algorithm fails to converge or when it converges to a saddle point rather than to a minimum. The algorithm is based on matrix multiplications and becomes linearly scaling for sufficiently large systems.