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Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

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.

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.

Band Theory

Band Theory

When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
The energy difference between these bands is known as the band gap.
Conductor, Semiconductor,...

Electron Orbital Model

Electron Orbital Model

Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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Related Experiment Video

Updated: Sep 8, 2025

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

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Published on: October 12, 2019

Quantum algorithm for electronic band structures with local tight-binding orbitals.

Kyle Sherbert¹, Anooja Jayaraj¹, Marco Buongiorno Nardelli²

¹Department of Physics, University of North Texas, Denton, TX, 76203, USA.

Scientific Reports

|June 14, 2022

Summary

This study introduces a simplified quantum computing method for calculating electronic band structures. The novel approach uses a single Hamiltonian and cost function, making quantum materials science more accessible.

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Area of Science:

Quantum computing
Materials science
Solid-state physics

Background:

Accurate calculation of electron correlation effects is a key challenge in quantum computing for materials science.
Current quantum algorithms for band structure often require optimizing many Hamiltonians and cost functions for each k-point and band.
Calculating higher energy bands typically involves complex modifications to cost functions.

Purpose of the Study:

To develop a more efficient and conceptually simpler quantum algorithm for calculating a periodic system's electronic band structure.
To advance the quantum computing
toolbox
for materials science applications.

Main Methods:

A direct space approach using a hybrid first/second-quantized qubit mapping.
Construction of a single Hamiltonian and cost function for the entire band structure calculation.
Utilizing additional parameters in the quantum circuit to select k-point and band index.

Main Results:

A technically and conceptually simpler method for quantum band structure calculations.
Elimination of the need for multiple Hamiltonians and complex cost function modifications.
The developed tools are applicable to solving for the entire electronic band structure.

Conclusions:

The proposed method offers a streamlined approach to quantum band structure calculations.
This work is expected to facilitate new strategies for studying highly-correlated materials.
The simplified approach enhances the accessibility of quantum computing for materials science.