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Related Concept Videos

Potential Energy00:52

Potential Energy

The energy stored by a structure and location of matter in space is called potential energy. For instance, raising a kettlebell changes its spatial location and increases its potential energy. Similarly, a stretched rubber band contains potential energy which, under certain conditions, can be converted into other forms of energy, such as kinetic energy.
Chemical bonds that form attractive forces between atoms also contain potential energy, called chemical energy. When a chemical reaction...
Potential Energy01:09

Potential Energy

A conservative force, such as a gravitational or elastic force, gives the body the capacity to do work. This capacity, measured as the potential energy, depends on the body's location or “position” relative to a fixed reference position or datum. The gravitational potential energy is considered zero at the reference point. Suppose a body is located at some vertical distance above a fixed horizontal reference or datum. In that case, the weight of the body has positive gravitational potential...
Potential-Energy Criterion for Equilibrium01:16

Potential-Energy Criterion for Equilibrium

Potential energy or potential function plays an essential role in determining the stability of a mechanical system. If a system is subjected to both gravitational and elastic forces, the potential function of the system can be expressed as the algebraic sum of gravitational and elastic potential energy. If the system is in equilibrium and is displaced by a small amount, then the work done on the system equals the negative of the change in the system's potential energy from the initial to the...
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

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Magnetic Vector Potential01:15

Magnetic Vector Potential

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Related Experiment Video

Updated: Jun 12, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Input vector optimization of feed-forward neural networks for fitting ab initio potential-energy databases.

M Malshe1, L M Raff, M Hagan

  • 1Mechanical and Aerospace Engineering, Oklahoma State University, 218 Engineering North Stillwater, Oklahoma 74078, USA.

The Journal of Chemical Physics
|June 3, 2010
PubMed
Summary

Optimizing neural network (NN) input vectors using interatomic distances, specifically R(ij)^(-n), significantly improves fitting accuracy for ab initio electronic structure calculations. This approach enhances accuracy more effectively than increasing database size or network complexity, with minimal computational cost.

Related Experiment Videos

Last Updated: Jun 12, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Area of Science:

  • Computational Chemistry
  • Materials Science
  • Machine Learning

Background:

  • Neural networks (NNs) are increasingly used to fit potential energy surfaces from ab initio electronic structure calculations.
  • The accuracy of NN fitting depends heavily on the choice of input vector elements.
  • Existing methods often use Z-matrix coordinates, which can lead to fitting inaccuracies due to discontinuities.

Purpose of the Study:

  • To investigate how the number and nature of elements in the input vector affect NN fitting accuracy.
  • To identify optimal input vector representations for fitting ab initio potential energy databases.
  • To compare the efficiency of input vector optimization versus increasing database size or NN complexity.

Main Methods:

  • Ab initio electronic structure calculations were performed for H(2)O(2), HONO, Si(5), and H(2)C[Double Bond]CHBr using DFT/B3LYP, MP2, and MP4 methods.
  • A total of 31 input vectors were tested, including interatomic distances, inverse powers, angles, and dihedral angles (both redundant and nonredundant).
  • The Levenberg-Marquardt algorithm was adapted to optimize parameters within the R(ij)^(-n) input vector form.

Main Results:

  • Z-matrix variables resulted in the lowest NN fitting accuracy, attributed to discontinuities in dihedral angles.
  • Using trigonometric functions of angles improved accuracy by eliminating discontinuities.
  • Input vectors of the form R(ij)^(-n) yielded the most accurate fitting, with optimal powers n in the range of 1.625-2.38.
  • Optimizing n for each bond type did not significantly improve accuracy for vinyl bromide.
  • R(ij)^(-n) input vectors reduced root-mean-square errors by factors of 1.31 to 2.83 compared to simple interatomic distances.

Conclusions:

  • Input vectors based on interatomic distances, particularly R(ij)^(-n), significantly enhance NN fitting accuracy for ab initio potential energy surfaces.
  • This method offers a computationally inexpensive way to improve accuracy compared to increasing dataset size or NN complexity.
  • The R(ij)^(-n) form effectively handles various chemical systems and bonding types, proving robust for diverse molecular structures.