Tree tensor networks methods for efficient calculation of molecular vibrational spectra

Area of Science:

• Quantum chemistry
• Computational physics
• Spectroscopy

Background:

• Vibrational spectra are crucial for understanding molecular properties and dynamics.
• Accurate computation of vibrational spectra for large systems remains a challenge.
• Tensor network methods offer a promising approach for high-dimensional quantum problems.

Purpose of the Study:

• To develop and apply general tree tensor networks for computing vibrational spectra.
• To explore the impact of different tree architectures on accuracy and computational cost.
• To benchmark the performance of various tree tensor network structures against established methods.

Main Methods:

• Development and implementation of general tree tensor networks.
• Exploration of diverse tree architectures, including Matrix Product States (MPS) and multilayer multiconfiguration time-dependent Hartree (MCTDH) inspired structures.
• Utilization of locally optimal block preconditioned conjugate gradient and inverse iteration methods as eigensolvers.
• Numerical simulations performed using the PyTreeNet Python package.

Main Results:

• All tested tree tensor network topologies achieved high accuracy in vibrational spectra computations.
• Inverse iteration refinement reduced the error for 84 computed states of acetonitrile to below 1 cm⁻¹.
• The fork-4 tree architecture demonstrated an optimal balance between accuracy and computational cost.
• Matrix Product States (MPS) showed computational attractiveness, while more connected trees improved accuracy at a fixed bond dimension.

Conclusions:

• General tree tensor networks are effective tools for calculating vibrational spectra.
• The choice of tree architecture significantly impacts the accuracy-cost trade-off.
• PyTreeNet provides a flexible platform for advanced tensor network computations in quantum chemistry and physics.