On-the-Fly Computation of Frontal Orbitals in Density Matrix Expansions

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Recursive polynomial expansion algorithms offer linear scaling computational cost for sparse systems.
• A drawback is the lack of readily available molecular orbitals compared to traditional diagonalization.
• Efficient computation of frontier orbitals (HOMO/LUMO) is crucial for understanding chemical and physical properties.

Purpose of the Study:

• To propose a novel method for computing frontier molecular orbitals (HOMO and LUMO) within recursive polynomial expansion algorithms.
• To develop an efficient eigenvalue solver as a byproduct of density matrix expansion.
• To enable accurate HOMO/LUMO computation with minimal additional computational cost.

Main Methods:

• Utilizes the polynomial of the density matrix expansion as an eigenvalue filter.
• Combines the eigenvalue filter with a shift-and-square (folded spectrum) method.
• Proposes a transparent selection of recursive expansion iteration and shift for eigenvector computation.

Main Results:

• A sharp eigenvalue filter is obtained as a byproduct of the density matrix expansion.
• The method provides a clear-cut and efficient eigenvalue solver for HOMO and LUMO computation.
• Accurate HOMO/LUMO orbitals are computed in a fraction of the total recursive expansion time, leveraging recent eigenvalue estimates.

Conclusions:

• The proposed method efficiently computes frontier molecular orbitals (HOMO/LUMO) with high accuracy.
• It integrates seamlessly into existing recursive polynomial expansion algorithms without significant overhead.
• Demonstrated applicability through self-consistent field calculations for large-scale systems.