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The Quantum-Mechanical Model of an Atom02:45

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.
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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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Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
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Crystal Field Theory
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Periodic Electronic Structure Calculations with the Density Matrix Embedding Theory.

Hung Q Pham1, Matthew R Hermes1, Laura Gagliardi1

  • 1Department of Chemistry, Chemical Theory Center, and Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455 , United States.

Journal of Chemical Theory and Computation
|December 10, 2019
PubMed
Summary

We developed a periodic density matrix embedding theory (DMET) for electronic structure calculations in solids. This method accurately computes band structures and ground-state energies for periodic systems, offering a cost-effective approach for correlated materials.

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Area of Science:

  • Solid-state physics
  • Quantum chemistry
  • Computational materials science

Background:

  • Accurate electronic structure calculations are crucial for understanding solid-state materials.
  • Strongly correlated materials present significant challenges for traditional computational methods.
  • Existing methods for periodic systems often struggle with electron correlation.

Purpose of the Study:

  • To develop and validate a periodic version of Density Matrix Embedding Theory (DMET).
  • To enable accurate computation of electronic band structures and ground-state energies for periodic systems.
  • To provide a computationally efficient method for studying strongly correlated materials.

Main Methods:

  • Developed a periodic extension of Density Matrix Embedding Theory (DMET).
  • Incorporated various wave function methods (FCI, CC, MCSCF) to capture electron correlation.
  • Implemented a real-space to momentum-space transformation for quasiparticle band structure analysis.

Main Results:

  • Periodic DMET successfully computes ground-state energies and band structures for 1D solids.
  • The method accurately describes the quasiparticle band picture.
  • Results show good agreement with established many-body techniques.
  • Periodic DMET offers a reduced computational cost compared to other methods.

Conclusions:

  • Periodic DMET is a viable and efficient first-principles method for electronic structure calculations in periodic systems.
  • The developed method shows promise for the study of strongly correlated materials.
  • Periodic DMET provides accurate ground-state and excited-state properties at a lower computational expense.