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Kentaro Hino1, Yuki Kurashige1,2,3

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A new algorithm efficiently compresses molecular potential energy surfaces into a grid-based matrix product operator (MPO). This method significantly reduces computational costs and enables accurate infrared spectrum predictions for molecular systems, leveraging GPU acceleration.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Accurate potential energy surfaces (PES) are crucial for understanding molecular systems.
  • Compressing complex PES data is essential for efficient quantum mechanical calculations.
  • Matrix product operators (MPO) offer a powerful framework for representing large quantum systems.

Purpose of the Study:

  • To develop an efficient algorithm for compressing many-body potential energy surfaces (PES) into a grid-based matrix product operator (MPO).
  • To reduce the computational cost associated with simulating molecular systems.
  • To enable accurate prediction of molecular properties, such as infrared spectra.

Main Methods:

  • Representing the PES using a full-dimensional or truncated many-body expansion obtained from ab initio calculations.
  • Compressing and merging expansion terms into a single MPO while minimizing bond dimension.
  • Utilizing a grid basis to reduce the tensor rank of MPO site operators, enabling efficient tensor contractions for real and imaginary time evolution of matrix product state (MPS) wave functions.

Main Results:

  • Achieved compression of the ab initio PES for H₂CO by over two orders of magnitude in site operator size without accuracy loss.
  • Demonstrated significant reduction in computational cost for tensor contractions using the grid-based MPO (Grid-MPO) Hamiltonian.
  • Successfully calculated the time correlation function of the Eigen cation to predict infrared spectra, showing good agreement with experimental and theoretical studies.
  • Examined the scaling of the multidimensional Henon-Heiles Hamiltonian, revealing considerable acceleration through GPU utilization due to small site operator sizes and VRAM storage.

Conclusions:

  • The proposed Grid-MPO algorithm provides an efficient method for compressing molecular PES.
  • The approach significantly reduces computational demands, making complex molecular simulations more feasible.
  • The method's applicability to various potentials and its GPU acceleration highlight its potential for broad use in computational chemistry and physics.