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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 I

Molecular Orbital Theory I

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Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

Molecular Orbital Theory II

Molecular Orbital Theory II

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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.

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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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive.

Aaron Fitzpatrick^1,2, Anton Nykänen¹, N Walter Talarico¹

¹Algorithmiq Ltd, Kanavakatu 3C, Helsinki FI-00160, Finland.

The Journal of Physical Chemistry. A

|March 28, 2024

Summary

This summary is machine-generated.

We introduce a new quantum simulation method, ADAPT-VQE-SCF, for chemistry. This approach efficiently simulates molecules on near-term quantum computers using fewer qubits and resources.

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Published on: May 27, 2020

Area of Science:

Quantum Chemistry
Computational Chemistry
Quantum Computing

Background:

Near-term quantum computers require efficient algorithms for chemical simulations.
Variational Quantum Eigensolver (VQE) is a promising approach but often needs deep circuits.
Accurate quantum chemistry simulations are crucial for understanding molecular behavior.

Purpose of the Study:

To develop a hardware-efficient self-consistent field (SCF) approach for quantum simulations.
To enable accurate quantum chemistry on near-term quantum devices.
To reduce qubit requirements and circuit depth for VQE-based simulations.

Main Methods:

Implemented a self-consistent field (SCF) approach within the Adaptive Derivative-Assembled Problem-Tailored Ansatz VQE (ADAPT-VQE) framework.
Generated shallow-depth quantum circuits by minimizing an energy expression correct to second order.
Performed simultaneous orbital optimization within each ADAPT-VQE iteration.

Main Results:

Achieved convergence in orbital optimization without significant increase in two-qubit gates.
Demonstrated efficiency with calculations on ferrocene.
ADAPT-VQE-SCF requires fewer qubits compared to previous methods.

Conclusions:

ADAPT-VQE-SCF offers a hardware-efficient alternative for quantum chemistry simulations.
This method enables the use of large atomic orbital basis sets.
Paves the way for a paradigm shift in quantitative quantum chemistry on quantum computers.