Unambiguous optimization of effective potentials in finite basis sets

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Effective potential optimization is crucial in density-functional theory (DFT) for evaluating functional derivatives and developing approximate functionals.
• Current methods face an ill-posed problem when using finite basis sets for Kohn-Sham orbitals, hindering satisfactory solutions.

Purpose of the Study:

• To introduce a novel approach for optimizing the effective local potential that accurately yields a given electron density.
• To overcome the ill-posed nature of finite-basis set methods in effective potential optimization.

Main Methods:

• A new scheme is presented to address the ill-posed optimization problem in finite-basis set DFT calculations.
• The method allows for independent variation of basis sets for orbitals and potentials.
• The approach is applicable to orbital basis sets of practical sizes.

Main Results:

• The proposed scheme successfully overcomes the ill-posed nature of effective potential optimization in finite basis sets.
• It provides an unambiguous potential that systematically converges towards the numerical reference.
• The method demonstrates applicability with reasonably sized orbital basis sets.

Conclusions:

• The new approach offers a robust solution for optimizing effective potentials in DFT using finite basis sets.
• This advancement facilitates the development of improved functionals and enhances the application of DFT-based embedding schemes.
• The ability to independently vary basis sets ensures greater flexibility and accuracy.