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Area Problem01:26

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Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
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Energy Diagrams - I01:14

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The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
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Updated: Jan 17, 2026

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
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Artificial Neural Networks Fitting of Potential Energy Curves and Surfaces: The 1/R Conundrum.

Siddhuram Rana1, Uday Sankar Manoj1, Upakarasamy Lourderaj1

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Summary

Artificial neural networks (ANNs) can more accurately fit ab initio computed electronic energy values than potential energy surfaces (PES). Adding the Coulombic internuclear repulsion energy to the fitted electronic energy yields an accurate PES.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Machine learning in chemistry

Background:

  • The Born-Oppenheimer approximation separates electronic and nuclear motion in molecular systems.
  • Potential energy surfaces (PES) are crucial for understanding molecular behavior and reactions.
  • Traditional methods for representing PES include analytic functions and interpolation.

Purpose of the Study:

  • To investigate the efficacy of artificial neural networks (ANNs) for fitting ab initio computed electronic energy values.
  • To compare the accuracy of ANNs in fitting electronic energy versus total potential energy.
  • To develop an accurate method for constructing potential energy surfaces.

Main Methods:

  • Ab initio computation of electronic energy values for a molecular system.
  • Fitting the computed electronic energy values using artificial neural network methodology.
  • Adding the exact Coulombic internuclear repulsion energy to the fitted electronic energy.

Main Results:

  • ANNs provide a more accurate fit for ab initio computed electronic energy values compared to potential energy values.
  • The fitted electronic energy, combined with the exact Coulombic internuclear repulsion, accurately reconstructs the potential energy surface.
  • This approach offers improved accuracy over traditional analytic functions and interpolation methods.

Conclusions:

  • Artificial neural networks are highly effective for accurately representing the electronic energy component of potential energy surfaces.
  • Combining ANN-fitted electronic energies with exact nuclear repulsion energies provides a superior method for PES construction.
  • This methodology enhances the accuracy of ab initio derived potential energy surfaces in computational chemistry.