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Band Theory02:35

Band Theory

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When two or more atoms come together to form a molecule, their atomic orbitals combine and molecular orbitals of distinct energies result. In a solid, there are a large number of atoms, and therefore a large number of atomic orbitals that may be combined into molecular orbitals. These groups of molecular orbitals are so closely placed together to form continuous regions of energies, known as the bands.
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Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
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The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
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Fermi Level Dynamics01:12

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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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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Crystal Field Theory - Octahedral Complexes02:58

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Crystal Field Theory
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Efficient Band Structure Calculation of Two-Dimensional Materials from Semilocal Density Functionals.

Abhilash Patra1, Subrata Jana1, Prasanjit Samal1

  • 1School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India.

The Journal of Physical Chemistry. C, Nanomaterials and Interfaces
|June 4, 2021
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Summary
This summary is machine-generated.

This study evaluates semilocal density functional theory methods for predicting the band gaps of two-dimensional (2D) materials. GLLB-SC and meta-generalized gradient approximations like TASK and MGGAC show promise for accurate 2D material band gap calculations.

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Area of Science:

  • Computational materials science
  • Condensed matter physics
  • Quantum chemistry

Background:

  • Two-dimensional (2D) materials are crucial for advanced semiconducting applications.
  • Accurate computational modeling of 2D materials requires efficient and precise methods.
  • Semilocal density functional theory (DFT) methods are vital for such calculations.

Purpose of the Study:

  • To assess the accuracy of recently developed semilocal exchange-correlation (XC) energy functionals and potentials for predicting 2D material band gaps.
  • To investigate the performance of specific XC potentials (LMBJ, GLLB-SC) and meta-generalized gradient approximations (TASK, MGGAC) in 2D systems.
  • To compare these DFT methods against established benchmarks like the GW method.

Main Methods:

  • Evaluation of LMBJ and GLLB-SC XC potentials.
  • Assessment of TASK and MGGAC meta-generalized gradient approximations.
  • Comparison of calculated band gaps with experimental and GW quasi-particle band gaps.

Main Results:

  • The LMBJ potential, adapted for 2D materials, underperforms compared to its bulk counterpart (MBJ).
  • GLLB-SC potentials yield larger band gaps, showing improved agreement with GW results in some cases due to derivative discontinuity.
  • TASK and MGGAC approximations demonstrate potential for accurate band gap predictions in 2D materials.

Conclusions:

  • The performance of XC functionals and potentials varies significantly between bulk and 2D materials.
  • GLLB-SC and certain meta-generalized gradient approximations show promise for accurate band gap prediction in 2D semiconductors.
  • Further investigation is needed to identify the optimal DFT methods for diverse 2D material systems.