Analytical Forces for the Optimized Effective Potential Calculations.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The optimized effective potential (OEP) equation presents ill-conditioning issues with finite basis sets, leading to unphysical oscillations in exchange-correlation (XC) potentials.
• Existing regularization methods for OEP solutions compromise energy's variational property and prevent analytical force derivation via the Hellmann-Feynman theorem.

Purpose of the Study:

• To develop a robust, nearly black-box OEP method that maintains the variational property of the system's energy with respect to the Kohn-Sham (KS) potential.
• To enable the derivation of analytical forces using the Hellmann-Feynman theorem within the OEP framework.
• To minimize the impact of regularization on calculated properties.

Main Methods:

• Incorporation of a penalty function that regularizes the XC potential into the energy functional.
• Regularization of the difference between the XC potential and an approximate XC potential to reduce the effect of regularization.
• Derivation of analytical forces from the modified energy functional based on the Hellmann-Feynman theorem.

Main Results:

• The developed method ensures the system's energy remains variational against the KS potential.
• Analytical forces can be accurately computed.
• Numerical tests demonstrate that forces and energy differences are insensitive to the regularization coefficient, allowing accurate property prediction without extrapolation.

Conclusions:

• The new OEP method provides a robust and accurate approach for electronic structure calculations.
• It is particularly beneficial for advanced, orbital-based functionals and applications requiring efficient force calculations, such as molecular dynamics and geometry optimization.