Effective electronic-only Kohn-Sham equations for the muonic molecules

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Materials Science

Background:

• Nuclear-electronic orbital density functional theory (NEO-DFT) enables calculations for systems with muons.
• Coupled electronic-muonic Kohn-Sham equations are computationally intensive.
• Muonic molecules, containing muons, present unique computational challenges.

Purpose of the Study:

• To derive and validate effective electronic-only Kohn-Sham (EKS) equations for muonic molecules.
• To establish the equivalence between EKS and NEO-DFT methods.
• To computationally investigate the stability of muoniated ferrocenyl radicals.

Main Methods:

• Derivation of effective electronic-only Kohn-Sham (EKS) equations.
• Optimization of effective non-coulombic external potentials.
• Application of EKS to muoniated organic radicals and ferrocenyl radicals.
• Design of an electronic basis set for the muon.

Main Results:

• The derived EKS equations are fully equivalent to coupled electronic-muonic Kohn-Sham equations.
• A mean effective potential and a muon basis set were developed for muonic species.
• The staggered conformer of muoniated ferrocenyl radical, with the muon on the cyclopentadienyl ring, was identified as the most stable.
• The findings reveal a duality between NEO-DFT and effective electronic-only DFT.

Conclusions:

• Effective electronic-only Kohn-Sham (EKS) equations provide a computationally efficient alternative to NEO-DFT for muonic systems.
• The EKS approach accurately predicts the preferred structure of muoniated ferrocenyl radicals.
• This work advances the computational study of muonic molecules and their properties.