System-Specific Separable Basis Based on Tucker Decomposition: Application to Density Functional Calculations.

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Accurate representation of orbitals is crucial for efficient density functional calculations.
• Existing methods may face limitations in speed and accuracy for complex systems.

Purpose of the Study:

• To introduce a novel, system-specific separable basis for accelerating density functional calculations.
• To demonstrate the effectiveness of Tucker decomposition in constructing an efficient basis set.

Main Methods:

• Proposed a new basis set derived from Tucker decomposition of a finite-difference Hamiltonian matrix.
• Applied the method to seven 2D and 3D periodic systems.
• Analyzed computation time, atomization energy per atom, and band gap errors.

Main Results:

• Achieved computation time reductions of 2-71 times for density functional calculations.
• Maintained high accuracy with errors in atomization energy and band gap below 0.1 eV.
• Demonstrated systematic control over accuracy and speed by adjusting Tucker decomposition rank size.

Conclusions:

• The proposed separable basis offers a significant speed-up for density functional calculations.
• The method provides a tunable balance between computational efficiency and accuracy.
• This approach is promising for accelerating electronic structure calculations in materials science.