An efficient linear scaling procedure for constructing localized orbitals of large molecules based on the...

Area of Science:

• Computational chemistry
• Quantum chemistry
• Materials science

Background:

• Boys localized molecular orbitals (LMOs) are crucial for interpreting electronic structure.
• Calculating LMOs, especially for large systems, can be computationally intensive.
• Efficient algorithms are needed to overcome computational bottlenecks in quantum chemistry.

Purpose of the Study:

• To develop a linear-scaling algorithm for efficiently obtaining Boys localized molecular orbitals.
• To enable the calculation of Boys LMOs for larger and more complex molecular systems.
• To reduce the computational cost associated with Boys localization.

Main Methods:

• Developed a two-step algorithm: Cholesky decomposition of the density matrix followed by Boys localization.
• Utilized sparse matrix techniques and the inherent locality of Cholesky molecular orbitals.
• Implemented linear-scaling approaches for both computational steps.

Main Results:

• The algorithm achieves linear-scaling computational complexity for Boys localization.
• Successfully applied to diverse systems: alpha-helix peptides, water clusters, and protein molecules.
• Demonstrated asymptotically linear computational time as system size increases.

Conclusions:

• The developed algorithm provides an efficient and scalable method for Boys localization.
• Enables accurate electronic structure analysis of large molecular systems.
• Represents a significant advancement in computational quantum chemistry for LMO analysis.