Automatic Differentiation for the Direct Minimization Approach to the Hartree-Fock Method

Area of Science:

• Computational chemistry and physics
• Quantum chemistry
• Method development in computational science

Background:

• Automatic differentiation (AD) is crucial for optimization in computational science.
• The Hartree-Fock (HF) method is a fundamental quantum chemistry technique.
• Reverse-mode AD is typically more efficient but hindered by eigenvalue calculations in the Self-Consistent Field (SCF) method of HF.

Purpose of the Study:

• To propose a novel method for directly minimizing Hartree-Fock energy using reverse-mode AD.
• To overcome the limitation of eigenvalue calculations in conventional SCF methods.
• To enhance the efficiency and applicability of AD in quantum chemistry calculations.

Main Methods:

• Direct minimization of Hartree-Fock energy under molecular orbital orthonormality constraints.
• Implementation of reverse-mode automatic differentiation, specifically avoiding eigenvalue computations.
• Validation of the proposed method against conventional SCF approaches.

Main Results:

• The proposed method successfully minimizes Hartree-Fock energy without eigenvalue calculations.
• Demonstrated improved stability compared to the conventional SCF method.
• Achieved comparable accuracy to established SCF techniques.

Conclusions:

• The developed method offers a more stable and efficient alternative for Hartree-Fock energy optimization.
• Eliminating eigenvalue calculations expands the utility of reverse-mode AD in quantum chemistry.
• This advancement has implications for large-scale electronic structure calculations.