A new efficient method for the calculation of interior eigenpairs and its application to vibrational structure...

Area of Science:

• Quantum Chemistry
• Computational Spectroscopy
• Molecular Physics

Background:

• Vibrational configuration interaction (VCI) theory is crucial for computing molecular vibrational levels and spectra.
• Standard VCI methods face challenges with large configuration spaces and efficiently solving for interior eigenvalues.
• Existing methods like Davidson, Lanczos, and Jacobi-Davidson have limitations in speed and applicability for complex systems.

Purpose of the Study:

• To develop a more efficient and robust computational method for calculating vibrational states in molecules.
• To address the limitations of conventional eigenvalue solvers and iterative methods for large-scale VCI calculations.
• To accurately compute interior vibrational states with significant multireference character.

Main Methods:

• An iterative subspace method is proposed, targeting eigenvectors with significant contributions to a reference vector.
• The method utilizes an optimality condition for the residual norm to guide subspace extraction and expansion.
• The approach is designed to overcome the stagnation issues of Davidson and Lanczos methods for interior states.

Main Results:

• The proposed iterative subspace method demonstrates high efficiency in calculating interior vibrational states.
• The method effectively handles vibrational structure problems with strong multireference character.
• Benchmark calculations show competitive or superior performance compared to established algorithms like Jacobi-Davidson.

Conclusions:

• The novel iterative subspace method offers a significant advancement for VCI calculations, enabling efficient treatment of complex molecular systems.
• This method provides a more tractable approach for determining vibrational energy levels and spectra, particularly for challenging cases.
• The findings suggest broader applicability in computational spectroscopy and quantum chemistry for molecular structure investigations.