  In this work, we present a one-step second-order converger for state-specific
(SS) and state-averaged (SA) complete active space self-consistent field
(CASSCF) wave functions. Robust convergence is achieved through step
restrictions using a trust-region augmented Hessian (TRAH) algorithm. To avoid
numerical instabilities, an exponential parametrization of variational
configuration parameters is employed, which works with a nonredundant
orthogonal complement basis. This is a common approach for SS-CASSCF and is
extended to SA-CASSCF wave functions, in this work. Our implementation is
integral direct and based on intermediates that are formulated either in the
sparse atomic-orbital or small active molecular-orbital basis. Thus, it
benefits from a combination with efficient integral decomposition techniques,
such as the resolution-of-the-identity or the chain-of-spheres for exchange
approximations. This facilitates calculations on large molecules such as a
Ni(II) complex with 231 atoms and 5154 basis functions. The runtime performance
of TRAH-CASSCF is competitive with other state-of-the-art implementations of
approximate and full second-order algorithms. In comparison with a
sophisticated first-order converger, TRAH-CASSCF calculations usually take more
iterations to reach convergence and, thus, have longer runtimes. However,
TRAH-CASSCF calculations still converge reliably to a true minimum even if the
first-order algorithm fails.
