Computation of interior eigenvalues in electronic structure calculations facilitated by density matrix purification

Area of Science:

• Computational chemistry
• Quantum chemistry
• Electronic structure theory

Background:

• Accurate computation of molecular orbitals is crucial for understanding chemical properties.
• The Lanczos method is a common iterative technique for electronic structure calculations.
• Convergence in electronic structure calculations, particularly around the HOMO-LUMO gap, can be challenging.

Purpose of the Study:

• To introduce density matrix purification as a method to enhance electronic structure calculations.
• To accelerate the convergence of the Lanczos method for finding eigenpairs near the HOMO-LUMO gap.
• To demonstrate the effectiveness of purification in separating closely spaced eigenvalues.

Main Methods:

• Application of density matrix purification techniques.
• Utilizing the enhanced eigenvalue separation provided by purification.
• Employing the accelerated Lanczos method for eigenpair computation.

Main Results:

• Density matrix purification facilitates the computation of eigenpairs around the HOMO and LUMO.
• Purification significantly separates eigenvalues near the HOMO-LUMO gap.
• The proposed methods lead to finding new eigenpairs more frequently than every second Lanczos iteration.

Conclusions:

• Density matrix purification is an effective strategy for accelerating electronic structure calculations.
• The method improves the efficiency of the Lanczos algorithm for critical molecular orbital calculations.
• This approach offers a more rapid convergence for determining key electronic properties.