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Thermodynamic Potentials

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...

Force and Potential Energy in One Dimension

Force and Potential Energy in One Dimension

Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...

The Energies of Atomic Orbitals

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.

Potential-Energy Criterion for Equilibrium

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...

Electronic Structure of Atoms

Electronic Structure of Atoms

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers: n, l, ml, and...

Calculations of Electric Potential I

Calculations of Electric Potential I

Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?
The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of λRdθ.

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Related Experiment Video

Updated: Jun 26, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

A self-starting method for obtaining analytic potential-energy surfaces from ab initio electronic structure

P M Agrawal¹, M Malshe, R Narulkar

¹Mechanical & Aerospace Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA.

The Journal of Physical Chemistry. A

|January 7, 2009

Summary

This study introduces a self-starting method combining direct dynamics (DD) with molecular dynamics (MD), novelty sampling (NS), and neural networks (NN) for accurate potential-energy surface calculations in complex chemical reactions.

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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

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Last Updated: Jun 26, 2026

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Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Area of Science:

Computational Chemistry
Chemical Dynamics
Theoretical Chemistry

Background:

Traditional methods for analytic potential-energy surfaces (PES) from ab initio calculations are not self-starting.
Initial sampling of configuration space for complex reactions (≥4 atoms, multi-center reactions, bond scission) is challenging due to vast computational space.

Purpose of the Study:

To develop a robust and self-starting method for generating accurate analytic potential-energy surfaces (PES) for molecular dynamics (MD) simulations.
To address the limitations of existing methods in handling complex chemical systems with multiple simultaneous reaction pathways.

Main Methods:

Integration of direct dynamics (DD) with molecular dynamics (MD), novelty sampling (NS), and neural network (NN) fitting.
Application to N-O bond scission and cis-trans isomerization reactions in HONO.

Main Results:

A novel, self-starting DD/MD/NS/NN method was successfully developed and applied.
The resulting neural network potential-energy surface for HONO reactions was validated against a semiempirical-initiated surface, showing agreement within fitting accuracy.

Conclusions:

The combined DD/MD/NS/NN approach offers a self-starting, robust, and accurate solution for first-principles MD studies.
This method is particularly effective for complex systems with four or more atoms undergoing simultaneous multi-center reactions.