Analytic energy gradient for the projected Hartree-Fock method

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Projected Hartree-Fock (PHF) is a multi-reference method.
• Calculating energy gradients for PHF is computationally demanding.
• Existing methods require solving coupled-perturbed Hartree-Fock-like equations.

Purpose of the Study:

• To derive and implement an analytic energy gradient for the PHF method.
• To achieve mean-field computational scaling for PHF gradient calculations.
• To apply the new method to study benzyne biradicals.

Main Methods:

• Analytic energy gradient derivation for PHF.
• Implementation avoiding coupled-perturbed Hartree-Fock-like equations.
• Computational scaling analysis.

Main Results:

• The developed formalism achieves mean-field computational scaling and cost.
• The method successfully calculates analytic energy gradients for PHF.
• Benchmark calculations on ortho-, meta-, and para-benzyne biradicals were performed.

Conclusions:

• The new analytic gradient implementation for PHF is computationally efficient.
• This method enables the study of equilibrium geometries and vibrational frequencies of complex systems.
• The approach provides a cost-effective way to handle multi-reference character in electronic structure calculations.