Three-Center Tight-Binding Together with Multipolar Auxiliary Functions

Area of Science:

• Computational chemistry
• Materials science
• Quantum mechanics

Background:

• Semiempirical calculations often rely on approximations for effective potentials and minimal basis sets.
• Improving computational efficiency is crucial for studying larger and more complex systems.

Purpose of the Study:

• To develop a novel ab initio tight-binding method that enhances accuracy and speed in electronic structure calculations.
• To overcome limitations of existing semiempirical methods by refining approximations.

Main Methods:

• Utilizes three-center expansions for Hamiltonian matrix elements and repulsive energy terms.
• Employs an auxiliary basis expansion for atomic orbital products to handle self-consistency.
• Incorporates a two-center expansion for exchange-correlation kernels.
• Employs nonminimal basis sets (double-ζ plus polarization).

Main Results:

• The developed method achieves a significant increase in computational speed compared to numerical atomic orbital density functional theory.
• The method demonstrates good performance for calculations on small molecules, bulk compounds, and metal nanoclusters.
• A modest trade-off in accuracy is observed for the substantial gain in speed.

Conclusions:

• The new ab initio tight-binding method provides an efficient alternative for electronic structure calculations.
• This method balances accuracy and speed, making it suitable for a range of materials science applications.
• Further research can explore its application to larger and more complex chemical systems.