Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

42.2K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
42.2K
The de Broglie Wavelength02:32

The de Broglie Wavelength

25.8K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
25.8K
Equations of Wave Motion01:02

Equations of Wave Motion

5.7K
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
5.7K
The Uncertainty Principle04:08

The Uncertainty Principle

23.3K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
23.3K
The Bohr Model02:18

The Bohr Model

52.9K
Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as...
52.9K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

36.5K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
36.5K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

QMCkl: A kernel library for quantum Monte Carlo applications.

The Journal of chemical physics·2026
Same author

Electron-Induced Fragmentation Dynamics of 1-Methylpyrene (C<sub>17</sub>H<sub>12</sub>) Dications and Trications: C<sub>2</sub>H<sub><i>x</i></sub><sup><i>q</i>+</sup> Release Pathways.

The journal of physical chemistry. A·2026
Same author

Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer.

The Journal of chemical physics·2025
Same author

Optimizing excited states in quantum Monte Carlo: A reassessment of double excitations.

The Journal of chemical physics·2025
Same author

Improved modularity and new features in ipie: Toward even larger AFQMC calculations on CPUs and GPUs at zero and finite temperatures.

The Journal of chemical physics·2024
Same author

Compactification of determinant expansions via transcorrelation.

The Journal of chemical physics·2024
Same journal

Photoinduced Charge-Transfer Suppresses Triplet Formation Efficiency in Thiocoumarins: Evidence from Ultrafast Spectroscopy and Theoretical Calculations.

The journal of physical chemistry. A·2026
Same journal

Porphyrin Aggregation Revisited: From the Four-Orbital Gouterman Model to an Eight-Orbital Framework in Porphin H-Dimers.

The journal of physical chemistry. A·2026
Same journal

Unraveling the Electronic Origin of Selectivity in Ambimodal Transition States with Valence Bond Theory.

The journal of physical chemistry. A·2026
Same journal

Mechanism and Kinetics of the Initial Oxidative Ring-Opening of Corannulene Radicals under Combustion Conditions.

The journal of physical chemistry. A·2026
Same journal

High-Resolution Absorption Spectroscopy of ND<sub>3</sub> between 59,000 and 93,000 cm<sup>-1</sup>.

The journal of physical chemistry. A·2026
Same journal

Twisted-Driven Photoionization of Aligned Chiral Molecules: Signatures of Circular and Helical Dichroism.

The journal of physical chemistry. A·2026
See all related articles

Related Experiment Video

Updated: Jun 24, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.4K

Modified Expression for the Hamiltonian Expectation Value Exploiting the Short-Range Behavior of the Wave Function.

Anthony Scemama1, Andreas Savin2

  • 1Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, 31062, Toulouse, France.

The Journal of Physical Chemistry. A
|June 7, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a modified formula for estimating electronic Hamiltonian eigenvalues using model wave functions. The new method improves energy estimations by differently scaling electron repulsion components, outperforming existing approaches.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K
Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

12.8K

Related Experiment Videos

Last Updated: Jun 24, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.4K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.5K
Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

12.8K

Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Electronic Structure Theory

Background:

  • The expectation value of the Hamiltonian with model wave functions is a standard method for estimating electronic Hamiltonian eigenvalues.
  • Existing models often struggle with accurately representing electron-electron repulsion, particularly for systems with long-range interactions.

Purpose of the Study:

  • To develop and validate a modified formula for calculating the expectation value of the Hamiltonian in the presence of long-range interactions.
  • To improve the accuracy of energy estimations for electronic systems compared to standard model wave function approaches.

Main Methods:

  • A modified formula was developed that uniquely scales the singlet and triplet components of the short-range electron repulsion.
  • Scaling factors were derived using only exact properties and depend on the model interaction parameter.
  • The method was tested on ground and low-lying excited states of two-to-six-electron Harmonium systems.

Main Results:

  • The modified formula demonstrated significant improvements in estimating the exact energy of Harmonium systems.
  • The new approach yielded better energy estimations than both the basic model energy and the standard expectation value of the Hamiltonian.
  • The improvements were observed across various electronic states and system sizes.

Conclusions:

  • The proposed modified formula offers a more accurate method for estimating electronic energies, especially for systems involving long-range interactions.
  • This approach provides a valuable refinement for quantum mechanical calculations relying on model wave functions.
  • The method's ability to improve energy estimations highlights its potential for broader applications in electronic structure calculations.