Tensor decomposition in potential energy surface representations.

Area of Science:

• Quantum chemistry
• Computational physics
• Molecular spectroscopy

Background:

• Vibrational configuration interaction (VCI) theory is a powerful method for calculating molecular vibrational frequencies.
• High computational cost associated with VCI calculations, especially for multidimensional potential energy surfaces (PESs), limits its applicability.
• Developing efficient methods to approximate PESs is crucial for advancing VCI calculations.

Purpose of the Study:

• To introduce a tensor decomposition approach for simplifying multidimensional PESs.
• To reduce the computational operation count in VCI calculations.
• To assess the accuracy of VCI frequencies obtained using the tensor decomposition method.

Main Methods:

• Applied tensor decomposition to the analytical representation of multidimensional PESs.
• Decomposed coefficients within n-mode coupling terms of the PES expansion.
• Performed contractions of one-dimensional integrals with factor matrices derived from decomposition.

Main Results:

• Demonstrated the feasibility of decomposing PES coefficients.
• Achieved significant reduction in computational cost.
• Found negligible deviations in VCI frequencies for small molecules when using appropriately chosen factor matrix ranks.
• Provided recommendations for selecting suitable ranks and discussed relevant algorithms.

Conclusions:

• Tensor decomposition offers an effective strategy to reduce the computational burden of VCI calculations.
• The method maintains high accuracy in predicting molecular vibrational frequencies.
• This approach enhances the practicality of VCI theory for larger and more complex molecular systems.