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

61.6K
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.
61.6K
Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

2.6K
When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
2.6K
Fermi Level Dynamics01:12

Fermi Level Dynamics

976
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
976
Quantum Numbers02:43

Quantum Numbers

54.2K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
54.2K
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

69.3K
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
69.3K
Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

50.3K
sp3d and sp3d 2 Hybridization
50.3K

You might also read

Related Articles

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

Sort by
Same author

Revisiting the Maximum Hardness Principle: A Quantitative Analysis on Reaction Datasets.

Journal of computational chemistry·2026
Same author

Automated Discovery of Algorithms for Molecular Electronic Structure Calculations Using Physics-Informed Program Synthesis.

Journal of the American Chemical Society·2026
Same author

Tethered Gaussian wavepackets for quantum dynamics simulations: Sticking together for better convergence.

The Journal of chemical physics·2025
Same author

Exploring New Algorithms for Molecular Vibrational Spectroscopy Using Physics-Informed Program Synthesis.

Journal of chemical theory and computation·2024
Same author

Anisotropic Dielectric Screened Range-Separated Hybrid Density Functional Theory Calculations of Charge Transfer States across an Anthracene-TCNQ Donor-Acceptor Interface.

Journal of chemical theory and computation·2024
Same author

Integrated computational and experimental design of fluorescent heteroatom-functionalised maleimide derivatives.

Chemical science·2024

Related Experiment Video

Updated: Mar 30, 2026

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

6.1K

Basis set generation for quantum dynamics simulations using simple trajectory-based methods.

Maximilian A C Saller1, Scott Habershon1

  • 1Department of Chemistry and Centre for Scientific Computing, University of Warwick , Coventry, CV4 7AL, United Kingdom.

Journal of Chemical Theory and Computation
|November 18, 2015
PubMed
Summary

This study introduces a novel trajectory-based method for quantum dynamics, offering a balanced approach to solving the time-dependent Schrödinger equation. The new method avoids issues of exponential scaling and numerical instability seen in traditional quantum dynamics techniques.

More Related Videos

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

8.8K
Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization
05:37

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

772

Related Experiment Videos

Last Updated: Mar 30, 2026

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

6.1K
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

8.8K
Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization
05:37

Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization

Published on: August 22, 2025

772

Area of Science:

  • Quantum mechanics
  • Computational chemistry
  • Theoretical physics

Background:

  • Solving the time-dependent Schrödinger equation is crucial for understanding quantum dynamics.
  • Traditional methods like global static or dynamic basis sets present significant challenges, including exponential scaling and numerical instability.
  • Existing approaches often lead to computational bottlenecks or conservation violations.

Purpose of the Study:

  • To propose a novel, more efficient, and stable method for solving the time-dependent Schrödinger equation.
  • To bridge the gap between global static and dynamic basis set approaches in quantum dynamics.
  • To address the limitations of existing computational methods in quantum dynamics.

Main Methods:

  • A new approach is presented that builds a basis set using trajectories.
  • Time-independent basis functions are strategically placed in relevant phase space regions for wave function propagation.
  • This method is demonstrated on challenging benchmark problems in quantum dynamics.

Main Results:

  • The trajectory-based basis set approach successfully solves complex quantum dynamics problems.
  • The method demonstrates potential to circumvent issues associated with traditional global static and dynamic basis sets.
  • Effective application shown for photoexcitation relaxation dynamics in pyrazine and the spin Boson model.

Conclusions:

  • The proposed trajectory-based method offers a promising alternative for quantum dynamics simulations.
  • This approach provides a "middle road" solution, balancing computational efficiency and numerical stability.
  • The successful demonstration on benchmark problems highlights the method's potential for broader applications in quantum dynamics.