Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

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.

Ampere-Maxwell's Law: Problem-Solving

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...

Graphing the Wave Function

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.

Maxwell-Boltzmann Distribution: Problem Solving

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

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.

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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

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

Chemical science·2024

Same author

Contact-Map-Driven Exploration of Heterogeneous Protein-Folding Paths.

Journal of chemical theory and computation·2024

Search research articles

Related Experiment Video

Updated: Sep 30, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Program Synthesis of Sparse Algorithms for Wave Function and Energy Prediction in Grid-Based Quantum Simulations.

Scott Habershon¹

¹Department of Chemistry, University of Warwick, Coventry, CV4 7AL, United Kingdom.

Journal of Chemical Theory and Computation

|March 16, 2022

Summary

Program synthesis (PS) creates self-writing code to solve the Schrödinger equation for molecular vibrations. This improved PS strategy accurately predicts wave functions and energy eigenvalues, offering computational advantages.

More Related Videos

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

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

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

Published on: August 22, 2025

Related Experiment Videos

Last Updated: Sep 30, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

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

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

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

Published on: August 22, 2025

Area of Science:

Computational Chemistry
Quantum Mechanics
Algorithm Development

Background:

Program synthesis (PS) has shown potential in generating algorithms for the vibrational Schrödinger equation.
Existing methods approximate wave functions for one-dimensional potential energy surfaces (PESs) using grid-based representations similar to discrete variable representation (DVR).

Purpose of the Study:

To enhance inductive PS strategies for predicting vibrational wave functions and energy eigenvalues.
To explore the application of PS to both one-dimensional and multidimensional model PESs.
To identify PS-generated algorithms with improved accuracy and computational efficiency.

Main Methods:

Utilizing an inductive program synthesis strategy to generate novel algorithms.
Employing grid-based representations for wave functions and PESs.
Testing algorithms on one-dimensional and multidimensional model PESs.

Main Results:

PS can generate algorithms that improve energy eigenvalue accuracy over standard DVR schemes.
PS identifies numerical methods employing sparse, tridiagonal matrices.
PS-generated algorithms reduce calculation times for grid-based eigenvector computation by over an order of magnitude for multidimensional problems.

Conclusions:

Enhanced PS strategies can effectively predict vibrational wave functions and energy eigenvalues.
PS offers computational advantages, including speed and sparse matrix utilization.
PS-generated algorithms show promise for quantum dynamics simulations and electronic structure evaluations.