Orthogonally constrained CASSCF framework: Newton–Raphson orbital optimization and nuclear gradients
Abstract
In a recent work [S. Yalouz and V. Robert, J. Chem. Theory Comput. 19, 1381 (2023)], we introduced the foundations of an orthogonally constrained complete active space self-consistent field (OC-CASSCF) framework that produces state-specific molecular orbitals for mutually orthogonal multiconfigurational electronic states. In the present study, we extend this approach by incorporating a Newton–Raphson orbital-optimization scheme, for which we derive the analytical expressions of the orbital gradient and Hessian. Furthermore, we outline a practical route toward the evaluation of analytical nuclear gradients, enabling geometry optimizations within the OC-CASSCF formalism. Benchmark calculations on the three lowest singlet states of LiH and H2O molecules demonstrate a systematic improvement as compared to conventional state-averaged CASSCF, even when using modestly sized active spaces.
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BibTeX
@article{delafosse2026orthogonally,
title = {{Orthogonally constrained CASSCF framework: Newton–Raphson orbital optimization and nuclear gradients}},
author = {Loris Delafosse and Vincent Robert and Saad Yalouz},
journal = {The Journal of Chemical Physics},
year = {2026},
month = jun,
doi = {10.1063/5.0324860},
url = {https://univoak.hal.science/hal-05754319v1},
note = {CC BY-NC 4.0},
}
RIS
TY - JOUR
TI - Orthogonally constrained CASSCF framework: Newton–Raphson orbital optimization and nuclear gradients
AU - Loris Delafosse
AU - Vincent Robert
AU - Saad Yalouz
PY - 2026
DA - 2026/06/28
JO - The Journal of Chemical Physics
DO - 10.1063/5.0324860
UR - https://univoak.hal.science/hal-05754319v1
AB - In a recent work [S. Yalouz and V. Robert, J. Chem. Theory Comput. 19, 1381 (2023)], we introduced the foundations of an orthogonally constrained complete active space self-consistent field (OC-CASSCF) framework that produces state-specific molecular orbitals for mutually orthogonal multiconfigurational electronic states. In the present study, we extend this approach by incorporating a Newton–Raphson orbital-optimization scheme, for which we derive the analytical expressions of the orbital gradient and Hessian. Furthermore, we outline a practical route toward the evaluation of analytical nuclear gradients, enabling geometry optimizations within the OC-CASSCF formalism. Benchmark calculations on the three lowest singlet states of LiH and H2O molecules demonstrate a systematic improvement as compared to conventional state-averaged CASSCF, even when using modestly sized active spaces.
SN - 0021-9606
SN - 1089-7690
ER -