Analytical and Parameter-Free Hückel Theory Made Possible for Symmetric H Clusters

Area of Science:

• Theoretical Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate chemical bond energetics prediction typically requires extensive parameterization in mathematical models.
• Existing methods often struggle to balance simplicity with high accuracy.

Purpose of the Study:

• To develop a simple, parameter-free mathematical framework for predicting chemical bond energetics.
• To accurately calculate relative energetics of hydrogen polygons (H_x, 2 ≤ x ≤ 15) in their ground states.

Main Methods:

• Developed a tight-binding-type mathematical framework.
• Recasted Hückel theory into a density functional theory (DFT) form.
• Utilized Anderson and Adams-Gilbert theories for localized orbitals.

Main Results:

• Achieved high accuracy in predicting relative energetics of H_x polygons.
• Demonstrated mean absolute errors of ~0.02 Å for edge lengths and ~0.15 eV/atom for energy minima.
• Showcased accuracy comparable to generalized gradient approximation (GGA) and superior to parameterized tight-binding and reactive potentials.

Conclusions:

• The novel framework provides accurate, parameter-free predictions for chemical bond energetics.
• This approach offers a significant advancement over existing semiempirical methods for H_x systems.
• The theoretical framework is generalizable to many-electron atomic systems.