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

Abstract

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.

References in corpus (8)

• Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and β-carotene
• Automated construction of molecular active spaces from atomic valence orbitals
• A general second order complete active space self-consistent-field solver for large-scale systems
• Second-Order Self-Consistent-Field Density-Matrix Renormalization Group
• A trust-region augmented Hessian implementation for restricted and unrestricted Hartree-Fock and Kohn-Sham methods
• Large-scale relativistic complete active space self-consistent field with robust convergence
• Relativistic Cholesky-decomposed density matrix MP2
• A black-box, general purpose quadratic self-consistent field code with and without Cholesky Decomposition of the two-electron integrals

Cited by in corpus (2)

• Excited states, symmetry breaking, and unphysical solutions in state-specific CASSCF theory
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive