The "Bubblepole" (BUPO) Method for Linear-Scaling Coulomb Matrix Construction with or without Density Fitting.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Algorithm Development

Background:

• Accurate computation of Coulomb-type matrices is crucial for quantum chemistry.
• Existing methods like Split-RI-J are efficient but can be outperformed by larger systems.
• Linear-scaling algorithms are needed to handle increasingly complex molecular systems.

Purpose of the Study:

• To develop a novel, computationally efficient algorithm for Coulomb-type matrix calculations.
• To achieve linear-scaling computational complexity with respect to system size.
• To provide high accuracy for large molecular systems using the resolution of the identity approximation.

Main Methods:

• Development of the Bubblepole (BUPO) algorithm, termed RI-BUPO-J.
• Utilizes resolution of the identity (RI) or density fitting (DF) approximation.
• Employs multipole approximations and hierarchical treatment within 'bubbles' (spheres) for grouping objects, avoiding hierarchical boxing.

Main Results:

• The RI-BUPO-J algorithm exhibits linear-scaling computational performance.
• It achieves submicro-Eh to nano-Eh accuracy in total Coulomb energy for systems up to 700 atoms.
• Outperforms Split-RI-J for systems with 300+ atoms, demonstrating scalability on large systems like solvated proteins.

Conclusions:

• The RI-BUPO-J algorithm is a highly efficient and accurate method for computing Coulomb-type matrices.
• Its linear-scaling nature and novel 'bubble' approach make it suitable for large-scale quantum chemical calculations.
• Represents a significant advancement in computational efficiency for electronic structure methods.