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The Quantum-Mechanical Model of an Atom

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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.

Electronic Structure of Atoms

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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...

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The Aufbau Principle and Hund's Rule

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To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Quantum algorithms for electronic structures: basis sets and boundary conditions.

Jie Liu¹, Yi Fan¹, Zhenyu Li¹

¹Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China. zyli@ustc.edu.cn.

Chemical Society Reviews

|March 30, 2022

Summary

This summary is machine-generated.

Quantum computing promises to revolutionize chemical and materials science by enabling efficient electronic structure calculations. This review highlights the critical roles of basis sets and boundary conditions for accurate quantum algorithms.

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Area of Science:

Quantum computing
Chemical sciences
Materials science

Background:

Quantum computers offer significant advantages for computational chemistry and materials science.
Solving the electronic structure problem is crucial for theoretical design and characterization.
Existing quantum electronic-structure algorithms require careful consideration of computational resources.

Purpose of the Study:

To review recent progress in quantum electronic-structure algorithms.
To emphasize the importance of basis sets and boundary conditions in quantum algorithms.
To discuss challenges and considerations for applying quantum algorithms to realistic systems.

Main Methods:

Review of existing literature on quantum electronic-structure algorithms.
Analysis of the impact of basis sets on quantum circuit complexity.
Evaluation of boundary condition strategies for quantum simulations.

Main Results:

Basis set choice significantly affects quantum algorithm design and circuit complexity.
Inappropriate boundary conditions (e.g., periodic) can cause errors in material simulations.
Artificial boundary conditions can partition systems to conserve quantum resources.

Conclusions:

Basis sets and boundary conditions are critical for accurate electronic structure calculations on quantum computers.
Careful selection of basis sets and boundary conditions is necessary for efficient quantum algorithm design.
These factors are especially important for simulating complex, realistic chemical and material systems.