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An adaptive interpolation scheme for molecular potential energy surfaces.

Markus Kowalewski1, Elisabeth Larsson1, Alfa Heryudono2

  • 1Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden.

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Calculating potential energy surfaces for quantum dynamics is sped up by a new adaptive interpolation algorithm. This method uses fewer data points, making calculations faster and more reliable.

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Area of Science:

  • Computational chemistry
  • Quantum dynamics
  • Electronic structure theory

Background:

  • Calculating potential energy surfaces (PES) for quantum dynamics is computationally intensive, especially with high-level electronic structure methods.
  • Efficient PES representation is crucial for accurate quantum dynamics simulations.

Purpose of the Study:

  • To develop an adaptive interpolation algorithm for efficient and accurate PES calculation.
  • To reduce the number of required electronic structure calculations for PES construction.

Main Methods:

  • An adaptive interpolation algorithm combining polyharmonic splines and a partition of unity approach.
  • Local error estimation for adaptive node refinement.
  • Evaluation of the algorithm's performance and scaling in 2, 3, and 4 dimensions.

Main Results:

  • The adaptive algorithm significantly reduces the number of sample points needed for PES interpolation.
  • The method demonstrates improved speed and reliability compared to non-adaptive approaches.
  • The algorithm's scaling behavior was analyzed for multi-dimensional model functions.

Conclusions:

  • The proposed adaptive interpolation algorithm offers a more efficient and reliable way to construct potential energy surfaces for quantum dynamics.
  • This approach can accelerate computational chemistry workflows requiring accurate PES.
  • The method is effective in reducing computational cost while maintaining desired accuracy.