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Density matrix purification with rigorous error control.

Emanuel H Rubensson¹, Elias Rudberg, Paweł Sałek

¹Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, Stockholm, Sweden. emanuel@theochem.kth.se

The Journal of Chemical Physics

|February 27, 2008

Summary

This summary is machine-generated.

Density matrix purification is improved by removing small matrix elements, rigorously controlling errors in electronic structure calculations. This method ensures accuracy in eigenvalue and subspace approximations for better computational chemistry results.

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Area of Science:

Computational chemistry
Electronic structure theory
Quantum mechanics

Background:

Density matrix purification is crucial for linear scaling in electronic structure calculations.
Uncontrolled error accumulation has limited its practical application.
Accurate density matrix construction is essential for reliable computational results.

Purpose of the Study:

To propose a novel strategy for density matrix purification by removing small matrix elements.
To rigorously control forward error accumulation during the purification process.
To enhance the accuracy and reliability of electronic structure calculations.

Main Methods:

A strategy for removing small matrix elements in density matrix purification.
Separation of total forward error into eigenvalue and occupied invariant subspace errors.
Utilizing canonical angles to measure and control subspace differences.
Analysis of the conditioning of the density matrix construction problem.

Main Results:

The proposed method rigorously controls forward error in density matrix purification.
Canonical angles provide a reliable measure for occupied subspace approximation.
The strategy allows for accurate calculation of interior eigenvalues alongside purification.

Conclusions:

The developed method significantly improves the accuracy of density matrix purification.
This approach overcomes limitations of uncontrolled error accumulation.
It offers a more robust and reliable tool for electronic structure calculations.