Computing vibrational energy levels by using mappings to fully exploit the structure of a pruned product basis

Area of Science:

• Quantum chemistry
• Computational physics
• Molecular spectroscopy

Background:

• Product basis sets are widely used for calculating molecular properties like spectra and reaction rates.
• However, these basis sets become computationally intractable for systems exceeding four atoms.

Purpose of the Study:

• To develop an efficient method for utilizing basis sets in large molecular systems.
• To overcome the computational limitations of traditional product basis sets for systems with more than four atoms.

Main Methods:

• A novel approach is demonstrated by removing functions associated with large diagonal Hamiltonian matrix elements from a product basis set.
• This method exploits the block diagonal nature of Hamiltonian matrix representations in specific basis-set orders.
• The Lanczos algorithm is efficiently implemented leveraging this block diagonality.

Main Results:

• The proposed method allows for the efficient use of reduced basis sets.
• Successful application to model Hamiltonians with up to 32 coordinates demonstrates the effectiveness of the approach.
• Significant reduction in computational cost is achieved for large molecular systems.

Conclusions:

• The developed technique offers a computationally feasible alternative for calculating properties of large molecular systems.
• This method enhances the applicability of basis set calculations in quantum chemistry and molecular dynamics.
• The findings pave the way for more accurate and efficient simulations of complex chemical processes.