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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.

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...

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

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.

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Updated: Sep 3, 2025

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

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Published on: May 27, 2020

Quantum Orbital Minimization Method for Excited States Calculation on a Quantum Computer.

Joel Bierman¹, Yingzhou Li², Jianfeng Lu^1,3,4

¹Department of Physics, Duke University, Durham, North Carolina 27708-0187, United States.

Journal of Chemical Theory and Computation

|July 25, 2022

Summary

This summary is machine-generated.

We introduce the quantum orbital minimization method (qOMM), a hybrid algorithm for finding quantum states. This variational method is less prone to local minima and converges faster for excited state calculations.

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Area of Science:

Quantum computing
Computational chemistry
Quantum algorithms

Background:

Finding ground and excited states of quantum systems is crucial for understanding molecular properties.
Existing methods can be limited by local minima and require deep ansatz circuits.

Purpose of the Study:

To propose a novel quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM).
To efficiently obtain ground and low-lying excited states of Hermitian operators, particularly in quantum chemistry.

Main Methods:

qOMM utilizes parametrized ansatz circuits to represent eigenstates.
It implements quantum circuits for the objective function within the orbital minimization method.
A classical optimizer adjusts ansatz parameters, leveraging an embedded orthogonality constraint.

Main Results:

Numerical simulations were performed for H2, LiH, and a four-atom hydrogen model using UCCSD ansatz circuits.
qOMM demonstrated reduced susceptibility to local minima compared to existing methods.
The algorithm achieved convergence with shallower ansatz circuits.

Conclusions:

qOMM offers an effective approach for calculating quantum states, especially excited states.
Its hybrid nature and embedded constraints enhance computational efficiency and accuracy.
This method shows promise for advancing quantum simulations in chemistry and physics.