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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 vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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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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sp3d and sp3d 2 Hybridization
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Machine Learning Accelerates Precise Excited-State Potential Energy Surface Calculations on a Quantum Computer.

Qianjun Yao1, Qun Ji1, Xiaopeng Li2

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This study introduces a machine learning model to enhance quantum computing algorithms for predicting excited-state potential energy surfaces. This approach accurately models molecular systems, paving the way for future quantum chemistry applications.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Photophysics

Background:

  • Excited-state problems are vital in quantum chemistry with applications in photophysics and photochemistry.
  • Quantum computing offers a novel approach to solve the Schrödinger equation for potential energy surfaces (PESs).

Purpose of the Study:

  • To develop a machine learning-assisted algorithm for predicting excited-state PESs.
  • To utilize variational quantum deflation and subspace search variational quantum eigensolver algorithms for excited-state calculations.

Main Methods:

  • A deep neural network model was developed to predict quantum circuit parameters.
  • The model was integrated with variational quantum deflation and subspace search variational quantum eigensolver algorithms.
  • The algorithm was applied to study excited-state PESs of small molecules and the ArF system.

Main Results:

  • The machine learning-assisted quantum algorithm achieved highly accurate predictions for excited-state PESs.
  • The study successfully investigated the excited-state properties of the ArF system, crucial for gas lasers.

Conclusions:

  • The developed algorithm demonstrates the potential of quantum computing for solving complex excited-state problems.
  • Future advancements in quantum hardware could enable broad applications in quantum chemistry and related fields.