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

Loris Delafosse1, Vincent Robert1, Saad Yalouz1

  • 1Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, 4 Rue Blaise Pascal, 67000 Strasbourg, France.

The Journal of Chemical Physics
|June 22, 2026
PubMed
Summary

This study enhances the orthogonally constrained complete active space self-consistent field (OC-CASSCF) method with Newton-Raphson optimization for improved electronic state calculations. The new approach enables accurate geometry optimizations and shows superior performance over conventional methods.

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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.