  We present a trust-region augmented Hessian implementation (TRAH-SCF) for
restricted and unrestricted Hartree-Fock and Kohn-Sham methods. With TRAH-SCF
convergence can always be achieved with tight convergence thresholds, which
requires just a modest number of iterations. Our convergence benchmark study
and our illustrative applications focus on open-shell molecules, also
antiferromagnetically coupled systems, for which it is notoriously complicated
to converge the Roothaan-Hall self-consistent field (SCF) equations. We compare
the number of TRAH iterations to reach convergence with those of Pulay's and
Kolmar's (K) variant of the direct inversion of the iterative subspace (DIIS)
method and also analyze the obtained SCF solutions. Often TRAH-SCF finds a
symmetry-broken solution with a lower energy than DIIS and KDIIS. For
unrestricted calculations, this is accompanied by a larger spin contamination,
i.e. larger deviation from the desired spin-restricted <S^2> expectation value.
However, there are also rare cases in which DIIS finds a solution with a lower
energy than KDIIS and TRAH. In rare cases, both TRAH-SCF and KDIIS may also
converge to an excited-state determinant solution. For those calculations with
negative-gap TRAH solutions, standard DIIS always diverges. If comparable, TRAH
usually needs more iterations to converge than DIIS and KDIIS because for every
new set of orbitals the level-shifted Newton-Raphson equations are solved
approximately and iteratively by means of an eigenvalue problem. Nevertheless,
the total runtime of TRAH-SCF is still competitive with the DIIS-based
approaches even if extended basis sets are employed, which is illustrated for a
large hemocyanin model complex.
