Second-order MCSCF optimization revisited. I. Improved algorithms for fast and robust second-order CASSCF...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Electronic Structure Theory

Background:

• The multiconfiguration self-consistent field (MCSCF) method is crucial for accurately describing electronic structures of molecules with strong electron correlation.
• The original Werner and Knowles implementation of the second-order MCSCF optimization method faced challenges with slow and unstable convergence, particularly in microiterations.
• Orbital optimization within MCSCF is often the bottleneck due to strongly coupled nonlinear equations.

Purpose of the Study:

• To present a significantly improved implementation of the second-order MCSCF optimization method.
• To develop more stable and efficient algorithms for the microiteration step, addressing challenges in orbital and configuration interaction (CI) coefficient optimization.
• To compare the performance of novel optimization strategies against the original implementation for various molecular systems.

Main Methods:

• Development of an iterative subspace method incorporating part of the orbital Hessian for improved orbital optimization.
• Implementation of a new solver treating orbital-CI coupling explicitly, leading to quadratic convergence in microiterations.
• Application of a quasi-Newton approach with Broyden-Fletcher-Goldfarb-Shanno updates for approximate treatment of orbital-CI coupling.

Main Results:

• All three presented methods demonstrate faster and more stable convergence compared to the original MCSCF implementation.
• The explicitly coupled solver achieves quadratic convergence, albeit with increased computational cost for density matrices.
• The quasi-Newton approach offers convergence comparable to the explicitly coupled method with reduced computational overhead.
• Performance was validated across 21 aromatic molecules and several transition metal and main group complexes.

Conclusions:

• The enhanced MCSCF optimization algorithms provide substantial improvements in efficiency and stability for electronic structure calculations.
• The choice between explicit coupling and quasi-Newton methods depends on the specific system and desired balance between accuracy and computational cost.
• These advancements facilitate more reliable and faster computations for complex chemical systems.