Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank

Area of Science:

• Computational chemistry
• Quantum mechanics
• Molecular physics

Background:

• Computing vibrational energy levels for polyatomic molecules requires high-dimensional tensors, exceeding current computer memory limits.
• Direct product basis methods are memory-intensive, restricting calculations to smaller molecules (around five atoms).

Purpose of the Study:

• To develop a memory-efficient method for computing vibrational energy levels of polyatomic molecules.
• To address the limitations of direct product basis methods using tensor representations.

Main Methods:

• Utilizing the canonical polyadic (CP) tensor format to represent high-dimensional tensors.
• Computing energy levels by constructing a basis from solutions of linear equations, analogous to a CP-based block inverse iteration.
• Employing a fixed CP rank and solving linear equations without rank reduction or orthogonalization.

Main Results:

• Successfully computed vibrational energy levels for a 64-D model Hamiltonian and 12-D acetonitrile.
• The CP tensor format method avoids generating excessively large tensors, staying within computational memory constraints.
• The method eliminates the need for rank reduction and orthogonalization steps.

Conclusions:

• The CP tensor format provides an effective and memory-efficient approach for calculating vibrational energy levels of larger polyatomic molecules.
• This method significantly expands the scope of molecules accessible to high-accuracy vibrational energy level computations.
• The approach demonstrates the practical application of tensor decomposition techniques in computational quantum chemistry.