Daubechies wavelets for linear scaling density functional theory.

Area of Science:

• Computational physics and chemistry
• Quantum mechanics and condensed matter physics

Background:

• Density functional theory (DFT) calculations are crucial for understanding material properties.
• Efficient representation of electronic wavefunctions is key to reducing computational cost in DFT.

Purpose of the Study:

• To develop a novel, computationally efficient basis set for representing Kohn-Sham orbitals in DFT.
• To achieve arbitrarily high and controllable precision in electronic structure calculations.

Main Methods:

• Utilizing Daubechies wavelets to construct optimized, localized, and adaptively contracted basis functions.
• Ensuring small amplitudes of basis functions on localization region surfaces via an optimization procedure.
• Combining the new basis set with sparse matrix algebra for linear scaling.

Main Results:

• Demonstrated accurate calculation of ground state energies and ionic forces.
• Achieved results comparable to direct Daubechies wavelets basis calculations.
• Enabled DFT calculations for systems exceeding 10,000 atoms with moderate resources.

Conclusions:

• The proposed method significantly reduces computational costs in DFT.
• The approach allows for linear scaling of computational complexity with system size.
• Facilitates large-scale simulations and optimizations in materials science and chemistry.