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Direct Canonical-Polyadic-Decomposition of the Potential Energy Surface from Discrete Data by Decoupled Gaussian

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A new Gaussian process regression (GPR) method, called CPD-GPR, directly constructs potential energy surfaces (PES) using discrete energies. This approach accurately models chemical reactions, like H + H2, offering a promising tool for computational chemistry.

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Area of Science:

  • Computational chemistry
  • Quantum mechanics
  • Chemical physics

Background:

  • Potential energy surfaces (PES) are crucial for understanding chemical reactions.
  • Constructing accurate PES, especially for multidimensional systems, is computationally challenging.
  • Existing methods for decomposing PES into simpler forms have limitations.

Purpose of the Study:

  • To introduce a novel Gaussian process regression (GPR) approach for directly constructing the canonical polyadic decomposition (CPD) of multidimensional potential energy surfaces (PES).
  • To evaluate the performance of the proposed CPD-GPR method in accurately representing chemical dynamics.
  • To compare the CPD-GPR method with existing algorithms for building decomposed PES.

Main Methods:

  • Developed a CPD-GPR method utilizing a kernel function that is a product of one-dimensional functions.
  • Applied the CPD-GPR method to construct the PES for the H + H2 reaction.
  • Calculated reactive probabilities as a function of kinetic energy using the CPD-GPR PES.
  • Compared dynamics results from CPD-GPR PES with those from an original PES.

Main Results:

  • The CPD-GPR method successfully constructed a decomposed PES from discrete training energies.
  • Dynamics simulations using the CPD-GPR PES showed good agreement with results from the original PES.
  • The study discussed previous algorithms for building decomposed forms of PES.

Conclusions:

  • The CPD-GPR method provides a viable approach for directly constructing decomposed potential energy surfaces.
  • The method shows promise as a general algorithm for building decomposed forms, though rank reduction requires further development.
  • CPD-GPR offers a potential new tool for developing decomposed potential functions in computational chemistry.