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The Quantum-Mechanical Model of an Atom02:45

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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.
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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...
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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.
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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.
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A general framework for active space embedding methods with applications in quantum computing.

Stefano Battaglia1, Max Rossmannek1,2, Vladimir V Rybkin1,3

  • 1Department of Chemistry, University of Zurich, Winterthurerstrasse 190, Zurich, 8057 Switzerland.

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We present a hybrid quantum-classical computing framework for materials science. This method accurately predicts optical properties of localized electronic states, showing promise for quantum chemistry applications.

Keywords:
Computational methodsElectronic structureTheoretical chemistry

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Area of Science:

  • Quantum computing
  • Computational chemistry
  • Materials science

Background:

  • Hybrid quantum-classical computing offers a powerful approach for simulating complex molecular and periodic systems.
  • Accurate modeling of localized electronic states in materials is crucial for understanding their properties.

Purpose of the Study:

  • To develop a general framework for hybrid quantum-classical computing applicable to molecular and periodic embedding.
  • To demonstrate the framework's capability in predicting optical properties of localized electronic states.

Main Methods:

  • Orbital space separation of fragment and environment degrees of freedom.
  • Implementation of periodic range-separated Density Functional Theory (DFT) coupled with a quantum circuit ansatz.
  • Utilizing variational quantum eigensolver and quantum equation-of-motion algorithms.

Main Results:

  • Accurate prediction of optical properties for the neutral oxygen vacancy in magnesium oxide (MgO).
  • Demonstrated competitive performance compared to state-of-the-art ab initio methods.
  • Excellent agreement with experimental photoluminescence emission peak, despite minor discrepancies in absorption band position.

Conclusions:

  • The developed hybrid quantum-classical framework is a viable approach for studying localized electronic states in materials.
  • The method shows significant potential for advancing quantum chemistry and materials science simulations.
  • Further refinement could improve accuracy for spectral features like absorption bands.