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Interpolating moving least-squares methods for fitting potential energy surfaces: Improving efficiency via local

Yin Guo1, Igor Tokmakov, Donald L Thompson

  • 1Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA.

The Journal of Chemical Physics
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A new local interpolating moving least-squares (IMLS) method efficiently constructs potential energy surfaces without requiring ab initio derivatives. This accurate method scales effectively with data points, offering a powerful tool for computational chemistry.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Constructing accurate potential energy surfaces (PES) is crucial for understanding chemical reactions and molecular properties.
  • Traditional methods for PES construction can be computationally expensive, often requiring ab initio derivatives.

Purpose of the Study:

  • To investigate the local interpolating moving least-squares (IMLS) method for efficient and accurate PES construction.
  • To assess the implementation details and accuracy of the local IMLS method.
  • To analyze the scaling behavior of the local IMLS method with respect to the number of data points.

Main Methods:

  • The study focuses on the local interpolating moving least-squares (IMLS) method.
  • The method avoids the need for ab initio derivatives, allowing the use of high-degree polynomials for accurate fitting.
  • Least-squares solutions are computed only once at data points, enhancing efficiency.

Main Results:

  • The local IMLS method achieves accuracy comparable to the standard IMLS approach.
  • The method exhibits power-law scaling with the number of data points (N).
  • The scaling exponent (q) depends on the polynomial degree (Q), dimensionality (d), and the energy range of the fitted data.

Conclusions:

  • The local IMLS method provides an efficient and accurate alternative for constructing potential energy surfaces.
  • This method is particularly advantageous when high accuracy is needed without the computational cost of derivative calculations.
  • The findings suggest broad applicability in computational studies requiring precise PES representations.