Efficient Parameterization of Density Functional Tight-Binding for 5f-Elements: A Th-O Case Study

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Chemistry

Background:

• Parametrizing density functional tight binding (DFTB) models for f-element species is challenging due to a large number of adjustable parameters.
• The computational cost for parameter optimization grows quadratically with the number of orbitals, making it expensive for f-elements compared to main group elements.
• Accurate DFTB Hamiltonians for f-elements are crucial for understanding their role in bonding interactions.

Purpose of the Study:

• To develop efficient approaches for mitigating the large parameter space challenge in DFTB parametrization for f-elements.
• To reduce the number of parameters and computational cost while maintaining accuracy for f-element DFTB models.
• To parametrize the DFTB Hamiltonian for the Th-O system and apply it to study ThO2 nanoparticles.

Main Methods:

• Developed novel group-by-orbital correction functions for two-center bond integrals to reduce parameters linearly with the number of elements.
• Accelerated parameter optimization using the mini-batch Broyden–Fletcher–Goldfarb–Shanno (BFGS) method for larger training sets.
• Employed a stochastic optimizer to overcome local minima in the objective function.

Main Results:

• Reduced the number of parameters by over 40% for f-elements while maintaining accuracy.
• Successfully parametrized the DFTB Hamiltonian for the Th-O system using a large training set (6322 structures).
• The optimized parameter set (LANL-ThO) showed good agreement with DFT-calculated properties for clusters and bulk ThO2.

Conclusions:

• The proposed efficient approaches significantly reduce computational costs and parameter numbers for DFTB parametrization of f-elements.
• This method demonstrates potential for challenging DFTB parametrization tasks involving elements with high angular momentum.
• The LANL-ThO parameter set provides a reliable tool for studying ThO2 nanoparticles and related systems.