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

TL;DR

This paper extends the orthogonally constrained CASSCF framework by integrating a Newton-Raphson orbital optimization method and deriving analytical nuclear gradients, enabling improved geometry optimizations for multistate electronic systems.

Contribution

It introduces a Newton-Raphson scheme with analytical gradients for OC-CASSCF, enhancing state-specific orbital optimization and geometry calculations.

Findings

Systematic improvement over state-averaged CASSCF in benchmark tests

Effective for low-lying singlet states of LiH and H2O

Enables geometry optimization within the OC-CASSCF framework

Abstract

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.