Orthogonally constrained CASSCF framework: Newton-Raphson orbital optimization and nuclear gradients

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• The orthogonally constrained complete active space self-consistent field (OC-CASSCF) framework was previously established to generate state-specific molecular orbitals for orthogonal electronic states.
• Accurate description of electronic states is crucial for understanding molecular properties and reactivity.

Purpose of the Study:

• To extend the OC-CASSCF framework by integrating a Newton-Raphson orbital-optimization scheme.
• To develop analytical expressions for the orbital gradient and Hessian within the OC-CASSCF method.
• To enable geometry optimizations for multiconfigurational electronic states using the OC-CASSCF formalism.

Main Methods:

• Derivation of analytical expressions for the orbital gradient and Hessian for Newton-Raphson optimization.
• Development of a practical route for calculating analytical nuclear gradients.
• Application of the enhanced OC-CASSCF method to benchmark calculations.

Main Results:

• The study successfully incorporated a Newton-Raphson orbital-optimization scheme into the OC-CASSCF framework.
• Analytical expressions for the orbital gradient and Hessian were derived.
• A method for analytical nuclear gradients was outlined, facilitating geometry optimizations.
• Benchmark calculations on LiH and H2O demonstrated systematic improvements over conventional state-averaged CASSCF.

Conclusions:

• The enhanced OC-CASSCF method with Newton-Raphson optimization provides a robust approach for calculating electronic states and performing geometry optimizations.
• The developed formalism offers a systematic improvement compared to traditional methods, even with smaller active spaces.
• This work paves the way for more accurate and efficient computational studies of complex molecular systems.