Computing Vibrational Energy Levels Using a Canonical Polyadic Tensor Method with a Fixed Rank and a Contraction Tree

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Kallullathil, Sangeeth Das
Carrington, Tucker Jr.
In this paper, we use the previously introduced CP-Multiple Shift Block Inverse Iteration (MSBII) eigensolver [J. Chem. Phys. 155, 234105 (2021)] in conjunction with a contraction tree to compute vibrational spectra. The CP-MSBII eigensolver uses the Canonical Polyadic (CP) format. The memory cost scales linearly with the number of coordinates. A tensor in CP format represents a wavefunction constrained to be a sum of products (SOP). An SOP wavefunction can be made more and more accurate by increasing the number of terms, the rank. When the required rank is large, the runtime of a calculation in CP format is long, although the memory cost is small. To make the method more efficient we break the full problem into pieces using a contraction tree. The required rank for each of the sub-problems is small. To demonstrate the effectiveness of the ideas, we computed vibrational energy levels of acetonitrile (12-D) and ethylene oxide (15-D).