Orthogonally Constrained CASSCF Framework: Newton-Raphson Orbital Optimization and Nuclear Gradients

In a recent work, 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 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 H$_2$O molecules demonstrate a systematic improvement as compared to conventional state-averaged CASSCF, even when using modestly sized active spaces.

Source: arXiv:2601.19699v1 - http://arxiv.org/abs/2601.19699v1 PDF: https://arxiv.org/pdf/2601.19699v1 Original Link: http://arxiv.org/abs/2601.19699v1