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Atomic Orbitals

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

Quantum Numbers

Quantum Numbers

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.

Valence Bond Theory and Hybridized Orbitals

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
A σ bond (single bond in a Lewis structure) is a covalent bond in which the electron density is...

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.

Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

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...

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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Related Experiment Video

Updated: Nov 3, 2025

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Variational Quantum Chemistry Programs in JaqalPaq.

Oliver G Maupin¹, Andrew D Baczewski^2,3,4, Peter J Love^1,5

¹Department of Physics and Astronomy, Tufts University, Medford, MA 02155, USA.

Entropy (Basel, Switzerland)

|June 2, 2021

Summary

This summary is machine-generated.

We demonstrate quantum chemistry simulations using JaqalPaq on the QSCOUT platform. These simulations accurately compute molecular ground state energies, validating new quantum programming methods.

Keywords:

NISQ algorithms ion trap quantum computing quantum chemistry quantum computing quantum simulation quantum software

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Last Updated: Nov 3, 2025

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

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Published on: April 12, 2019

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Area of Science:

Quantum Computing
Computational Chemistry
Quantum Algorithms

Background:

Developing efficient quantum algorithms for molecular simulations is crucial for advancing computational chemistry.
The Quantum Scientific Computing Open User Testbed (QSCOUT) provides a platform for executing quantum algorithms.
Jaqal (Just Another Quantum Assembly Language) and its meta-programming language JaqalPaq facilitate the coding of quantum algorithms.

Purpose of the Study:

To present example quantum chemistry programs written in JaqalPaq.
To demonstrate the computation of ground state energies for H2, HeH+, and LiH molecules using the variational quantum eigensolver (VQE) algorithm.
To emulate the execution of these JaqalPaq algorithms on the QSCOUT platform and compare results with exact calculations.

Main Methods:

Utilized JaqalPaq, a Python meta-programming language, to write quantum chemistry algorithms in Jaqal.
Employed the variational quantum eigensolver (VQE) quantum algorithm for energy computations.
Leveraged PySCF for calculating second-quantized Hamiltonians and OpenFermion for fermion-to-qubit mappings.
Emulated algorithm execution on an error-free QSCOUT platform using JaqalPaq's emulator functionality.

Main Results:

Successfully computed ground state energies for H2, HeH+, and LiH molecules using JaqalPaq exemplars.
Emulated bond-dissociation curves for these molecules showed agreement with exact theoretical calculations.
Demonstrated the feasibility of using JaqalPaq for quantum chemistry simulations on the QSCOUT platform.

Conclusions:

JaqalPaq is a viable tool for programming quantum chemistry applications.
The VQE algorithm, implemented via JaqalPaq, can accurately determine molecular energies.
Emulation on the QSCOUT platform provides a reliable method for verifying quantum algorithm performance.