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Bringing about matrix sparsity in linear-scaling electronic structure calculations.

Emanuel H Rubensson¹, Elias Rudberg

¹Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden. emanuel.rubensson@it.uu.se

Journal of Computational Chemistry

|February 2, 2011

Summary

This study introduces a novel, efficient scheme for removing small matrix elements in electronic structure calculations, ensuring controlled errors for linear scaling. The method significantly reduces computational overhead while maintaining accuracy in large molecular systems.

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Area of Science:

Computational chemistry
Materials science
Quantum mechanics

Background:

Linear-scaling electronic structure calculations are crucial for large systems.
Matrix sparsity is key to the efficiency of these calculations.
Controlling errors during matrix element removal is essential for accuracy.

Purpose of the Study:

To present an overview of matrix element removal strategies.
To introduce a novel, computationally efficient scheme for matrix sparsity.
To rigorously control errors in the occupied subspace.

Main Methods:

Overview of different matrix element removal strategies.
Proposal and analysis of a novel Euclidean norm-based truncation scheme.
Benchmark calculations on water clusters (up to 6523 molecules).
Investigation of matrix element decay with distance for various methods (Hartree-Fock, DFT).

Main Results:

The novel scheme offers significantly smaller computational overhead than existing methods.
Rigorous error control is achieved by bounding the Euclidean norm of the error matrix.
The scheme demonstrates desired asymptotic behavior for linear scaling.
Analysis of matrix element decay properties for different molecular systems and computational methods.

Conclusions:

The proposed method enhances the efficiency of linear-scaling electronic structure calculations.
Accurate and controlled error reduction is achievable with the new scheme.
Understanding matrix sparsity foundations aids in developing more efficient computational methods.