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Journal Article

A trust-region augmented Hessian implementation for state-specific and state-averaged CASSCF wave functions


Helmich-Paris,  Benjamin
Research Group Helmich-Paris, Max-Planck-Institut für Kohlenforschung, Max Planck Society;

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Helmich-Paris, B. (2022). A trust-region augmented Hessian implementation for state-specific and state-averaged CASSCF wave functions. The Journal of Chemical Physics, 156(20): 204104. doi:10.1063/5.0090447.

Cite as: https://hdl.handle.net/21.11116/0000-000A-A184-A
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 parameterization 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 in either 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 the 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.