Second-Order Self-Consistent Field Algorithms: From Classical to Quantum Nuclei

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical chemistry

Background:

• Self-consistent field (SCF) methods are fundamental in quantum chemistry.
• Convergence issues in SCF calculations, especially for strongly correlated systems and nuclear-electronic problems, hinder accurate molecular modeling.
• Existing first-order optimization strategies often struggle with stability and efficiency.

Purpose of the Study:

• To develop a general framework for deriving Newton SCF orbital optimization algorithms.
• To extend the augmented Roothaan-Hall (ARH) algorithm to unrestricted electronic and nuclear-electronic calculations.
• To demonstrate ARH's effectiveness in improving convergence and computational efficiency.

Main Methods:

• Leveraging concepts from differential geometry to derive SCF orbital optimization algorithms.
• Extending the augmented Roothaan-Hall (ARH) algorithm.
• Applying ARH to unrestricted electronic calculations (e.g., iron-sulfur clusters) and nuclear-electronic calculations (e.g., protonated water clusters).

Main Results:

• The ARH algorithm provides a balance between stability and computational cost for difficult SCF problems.
• ARH successfully overcomes slow orbital convergence in strongly correlated electronic systems.
• ARH significantly accelerates convergence in nuclear-electronic calculations, even for small molecules.

Conclusions:

• The differential geometry-based framework offers a robust approach to SCF algorithm development.
• The extended ARH algorithm is a powerful tool for tackling challenging convergence problems in computational chemistry.
• ARH enhances the efficiency and applicability of SCF methods for complex molecular systems.