Tensor decomposition techniques in the solution of vibrational coupled cluster response theory eigenvalue equations.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Molecular Spectroscopy

Background:

• Vibrational coupled cluster response theory is crucial for accurate prediction of molecular vibrational properties.
• Solving the associated eigenvalue equations can be computationally intensive, limiting routine application.
• Efficient algorithms are needed to make these calculations more accessible.

Purpose of the Study:

• To develop and present an efficient subspace projection method with Davidson update for solving vibrational coupled cluster response theory eigenvalue equations.
• To demonstrate the capability of using basis vectors represented as canonically decomposed tensors (CP decomposition).
• To enable direct calculation of vibrational wave functions in a tensor-decomposed format.

Main Methods:

• Employed a subspace projection method with Davidson update.
• Utilized stacked tensors decomposed into canonical (CP) form for basis vectors.
• Implemented orthogonalization of new vectors to old vectors followed by tensor decomposition to a threshold (TCP).

Main Results:

• The proposed algorithm achieves accuracy comparable to full vector approaches.
• It requires only a modest increase in the number of vectors for convergence.
• Optimal tensor decomposition thresholds (e.g., TCP = 10⁻²) allow accurate solutions and direct calculation of vibrational wave functions in tensor-decomposed format.

Conclusions:

• The developed method provides an accurate and efficient alternative for solving vibrational coupled cluster response theory eigenvalue equations.
• Tensor decomposition offers a viable strategy for representing and manipulating vibrational wave functions computationally.
• This approach enhances the feasibility of high-accuracy vibrational structure calculations.