Analytic energy gradient of projected Hartree-Fock within projection after variation

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Accurate molecular structure optimization is crucial for understanding chemical properties.
• Traditional methods like variation-after-projection (VAP) can be computationally expensive and prone to convergence issues.
• Projected Hartree-Fock (PHF) offers a way to address nondynamic correlation and restore symmetry in electronic states.

Purpose of the Study:

• To develop a computationally efficient geometrical optimization technique for symmetry-adapted electronic states.
• To present projection-after-variation Projected Hartree-Fock (PAV-PHF) as a fast alternative to VAP.
• To enable black-box orbital selections and avoid convergence problems in structure optimization.

Main Methods:

• Development of a projection-after-variation (PAV) scheme for Projected Hartree-Fock (PHF).
• Utilizing Hartree-Fock (HF) orbitals instead of PHF orbitals to reduce computational cost.
• Testing the PAV-PHF method on systems with abundant nondynamic correlation: CH2, O3, and [Cu2O2]2+.

Main Results:

• PAV-PHF provides molecular geometries comparable to high-level methods like Complete Active Space Self-Consistent Field (CASSCF).
• The method achieves comparable accuracy to VAP-PHF but with significantly reduced computational expense.
• The approach successfully optimizes structures for systems dominated by nondynamic correlation.

Conclusions:

• The proposed PAV-PHF method is a fast and reliable alternative for optimizing molecular structures in symmetry-adapted electronic states.
• This technique is particularly beneficial for large molecular systems where nondynamic correlation is significant.
• PAV-PHF offers a practical solution for exploring stable structures across various electronic states with mean-field computational cost.