Assessment of density matrix methods for linear scaling electronic structure calculations

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Accurate computation of the one-particle density matrix is crucial for electronic structure calculations.
• Linear scaling methods are essential for handling large systems in computational chemistry.
• Efficient algorithms are needed to minimize computational cost while maintaining accuracy.

Purpose of the Study:

• To compare the efficiency of purification and minimization methods for linear scaling computation of the one-particle density matrix.
• To evaluate the impact of different truncation approaches and eigenvalue distributions on method performance.
• To derive and validate an expression for the convergence of minimization methods.

Main Methods:

• Comparison of purification and minimization methods based on computational work required for a target accuracy.
• Numerical tests using orthogonal and non-orthogonal versions with element magnitude and cutoff radius truncation.
• Derivation of an iteration count expression for minimization methods, considering band gap and chemical potential.

Main Results:

• Purification methods demonstrate superior efficiency compared to minimization methods, even with optimal starting guesses.
• Minimization method performance is best when the chemical potential is near the center of the eigenspectrum.
• Convergence speed is influenced by the eigenvalue distribution of the Hamiltonian matrix.

Conclusions:

• Purification is a more efficient approach for linear scaling computation of the one-particle density matrix.
• The derived expression accurately predicts the number of iterations for minimization methods.
• Understanding eigenvalue distribution and chemical potential is key to optimizing minimization algorithms.