Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation with Applications to Hybrid...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• The interpolative separable density fitting (ISDF) decomposition is a key technique for compressing redundant information in orbital pairs, accelerating quantum chemistry computations.
• Accurate interpolation of orbital pairs relies on selecting optimal nonuniform grid points, a process traditionally dominated by the computationally expensive QR factorization with column pivoting (QRCP) procedure.

Purpose of the Study:

• To introduce a novel, computationally efficient method for selecting interpolation points for ISDF decomposition.
• To evaluate the accuracy and performance of the proposed method compared to the established ISDF-QRCP approach, particularly in hybrid functional electronic structure calculations.

Main Methods:

• Developed a new approach utilizing the centroidal Voronoi tessellation (CVT) method to identify interpolation points for ISDF.
• Implemented the CVT method using a K-Means algorithm, leveraging only electron density information.
• Compared the computational cost and accuracy of ISDF-CVT against ISDF-QRCP in large-scale hybrid functional calculations.

Main Results:

• The ISDF-CVT method achieves accuracy comparable to the ISDF-QRCP method.
• CVT significantly reduces the computational cost of selecting interpolation points; for a 1000-atom silicon system using HSE06, the cost dropped from 38.1s to 0.7s.
• ISDF-CVT demonstrates enhanced smoothness of the potential energy surface in ab initio molecular dynamics (AIMD) simulations with hybrid functionals.

Conclusions:

• The CVT-based approach provides a highly efficient and accurate alternative for selecting interpolation points in ISDF decomposition.
• This method offers substantial computational savings, making it particularly advantageous for large-scale electronic structure calculations employing hybrid functionals.
• The ISDF-CVT method shows promise for improving the reliability and efficiency of AIMD simulations.