Model Order Reduction Algorithm for Estimating the Absorption Spectrum.

Area of Science:

• Computational chemistry
• Theoretical physics
• Quantum mechanics

Background:

• Accurately describing absorption spectra computationally is challenging for large systems.
• Traditional methods struggle with dense spectral regions, leading to convergence issues.
• Solving spectrally shifted linear systems offers an alternative but is computationally expensive.

Purpose of the Study:

• To develop a computationally efficient method for ab initio X-ray absorption spectra prediction.
• To address the high computational cost associated with solving linear systems for spectral analysis.
• To present a novel adaptive solution using model order reduction techniques.

Main Methods:

• Employed model order reduction (MOR) techniques via interpolation.
• Utilized an adaptive approach to determine the order of reduced models based on user-defined tolerance.
• Applied the method to predict X-ray absorption spectra for water clusters near the oxygen K-edge.

Main Results:

• Demonstrated the efficiency and effectiveness of the proposed MOR algorithm.
• Successfully predicted X-ray absorption spectra for spectrally dense water clusters.
• Observed logarithmic increase in model order with problem dimension and quadratic scaling of computational cost.

Conclusions:

• The novel adaptive MOR technique significantly reduces computational overhead for X-ray absorption spectra prediction.
• The method provides an accurate and efficient alternative to traditional approaches for dense spectral domains.
• This work advances the capability of electronic structure theory in describing complex molecular spectra.