Non-linear eigensolver-based alternative to traditional SCF methods.

Area of Science:

• Computational physics and chemistry
• Electronic structure theory
• Quantum mechanics

Background:

• Self-consistent field (SCF) methods are crucial for electronic structure calculations.
• Traditional SCF mixing schemes can suffer from slow convergence or failure to converge.
• Solving the non-linear eigenvalue problem H({ψ})ψ = Eψ is a central challenge.

Purpose of the Study:

• To introduce a novel, efficient, and robust algorithm for solving the non-linear eigenvalue problem in electronic structure calculations.
• To demonstrate the superiority of the new algorithm over traditional SCF mixing schemes.
• To reduce the computational cost of electronic structure simulations.

Main Methods:

• Generalization of the FEAST eigenvalue algorithm to handle non-linear Hamiltonians.
• Application to the density functional theory-Kohn/Sham (DFT-KS) model.
• Testing with numerical examples to assess performance.

Main Results:

• The proposed algorithm demonstrates a higher convergence rate compared to traditional methods.
• The new scheme achieves convergence to the correct solution irrespective of the initial guess.
• Significant reduction in eigenvalue solve time during simulations was observed.

Conclusions:

• The generalized FEAST algorithm offers a more efficient and reliable approach for electronic structure calculations.
• This method overcomes limitations of traditional SCF mixing schemes.
• The algorithm has the potential to accelerate large-scale quantum simulations.