Exploiting the Hessian for a Better Convergence of the SCF-RDMFT Procedure

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• One-body reduced density matrix functional theory (1-RDMFT) is an alternative to density functional theory (DFT).
• 1-RDMFT can treat static correlation effects, which are crucial for many chemical systems.
• A major drawback of 1-RDMFT is the slow convergence of its self-consistent energy optimization.

Purpose of the Study:

• To accelerate the slow self-consistent energy optimization in 1-RDMFT.
• To reduce the computational cost associated with 1-RDMFT calculations.
• To improve the practical applicability of 1-RDMFT for electronic structure calculations.

Main Methods:

• Utilizing the Hessian of the energy, including the coupling term, to enhance optimization convergence.
• Investigating the effectiveness of the exact Hessian for reducing iteration counts.
• Developing a practical approximation for the Hessian using an inexpensive exact component combined with Broyden–Fletcher–Goldfarb–Shanno (BFGS) updates.

Main Results:

• The exact Hessian significantly reduces the number of iterations required for self-consistent convergence.
• The proposed approximation of the Hessian proves effective in practice.
• The new method substantially improves the efficiency of 1-RDMFT calculations.

Conclusions:

• The use of Hessian-based methods, particularly approximations, can overcome the slow convergence issue in 1-RDMFT.
• This work presents a computationally feasible approach to accelerate 1-RDMFT, making it more viable for complex systems.
• The developed method offers a promising avenue for more efficient electronic structure and materials science research.