An efficient zero-order evolutionary method for solving the orbital-free density functional theory problem by direct...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Orbital-free density functional theory (OF-DFT) offers a computationally efficient alternative to traditional DFT.
• Optimization of energy functionals is crucial for accurate OF-DFT predictions.
• Existing methods often rely on derivative information, limiting applicability.

Purpose of the Study:

• To introduce a novel global optimization method for OF-DFT.
• To demonstrate the efficacy of the differential evolution (DE) method for energy functional minimization.
• To enable OF-DFT calculations for non-differentiable or non-closed form functionals.

Main Methods:

• Implementation of a differential evolution (DE) global optimization algorithm.
• Direct minimization of energy functionals for atomic ground state energies.
• Application to all-electron OF-DFT calculations.

Main Results:

• Accurate ground state energies for atoms H to Ar were obtained.
• Results align with established OF-DFT calculations using Newton-Raphson and trust region methods.
• The DE method successfully minimized energy functionals without derivatives.

Conclusions:

• The DE method provides a robust, derivative-free optimization technique for OF-DFT.
• This zero-order method expands the applicability of OF-DFT to a wider range of functionals.
• The approach facilitates accurate and efficient electronic structure calculations.