This chapter discusses additional aspects of chemical bonding theory including the valence bond method, hybridization of atomic orbitals, multiple bonds, molecular orbital theory, delocalized electrons in molecules like benzene, and bonding in metals and semiconductors. The chapter focuses on photoelectron spectroscopy and includes example problems applying concepts like valence bond descriptions of molecular geometry, hybridization to explain molecular shapes, and molecular orbital diagrams of diatomic molecules.
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Part 1 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
Contents
The Atom
Materials Used in Electronics
Current in Semiconductors
N-Type and P-Type Semiconductors
The PN Junctions
Diode Operation, Voltage-Current (V-I) Characteristics
Bipolar Junction Transistor (BJT) Structure, Operation, and Characteristics and Parameters
Junction Field Effect Transistors (JFETs) Structure, Characteristics and Parameters and Biasing
Metal Oxide Semiconductor FET (MOSFET) Structure, Characteristics and Parameters and Biasing
The ATOM: Learning Objectives
Describe the structure of an atom
Discuss the Bohr model of an atom
Define electron, proton, neutron, and nucleus
Define atomic number
Discuss electron shells and orbits
Explain energy levels
Define valence electron
Discuss ionization
Define free electron and ion
Discuss the basic concept of the quantum model of the atom
Discuss insulators, conductors, and semiconductors and how they differ
Define the core of an atom
Describe the carbon atom
Name two types each of semiconductors, conductors, and insulators
Explain the band gap
Define valence band and conduction band
Compare a semiconductor atom to a conductor atom
Discuss silicon and germanium atoms
Explain covalent bonds
Define crystal
Describe how current is produced in a semiconductor
Discuss conduction electrons and holes
Explain an electron-hole pair
Discuss recombination
Explain electron and hole current
Describe the properties of n-type and p-type semiconductors
Define doping
Explain how n-type semiconductors are formed
Describe a majority carrier and minority carrier in n-type material
Explain how p-type semiconductors are formed
Describe a majority carrier and minority carrier in p-type material
Describe how a pn junction is formed
Discuss diffusion across a pn junction
Explain the formation of the depletion region
Define barrier potential and discuss its significance
State the values of barrier potential in silicon and germanium
Discuss energy diagrams
Define energy hill
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
(If visualization is slow, please try downloading the file.)
Part 1 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
Contents
The Atom
Materials Used in Electronics
Current in Semiconductors
N-Type and P-Type Semiconductors
The PN Junctions
Diode Operation, Voltage-Current (V-I) Characteristics
Bipolar Junction Transistor (BJT) Structure, Operation, and Characteristics and Parameters
Junction Field Effect Transistors (JFETs) Structure, Characteristics and Parameters and Biasing
Metal Oxide Semiconductor FET (MOSFET) Structure, Characteristics and Parameters and Biasing
The ATOM: Learning Objectives
Describe the structure of an atom
Discuss the Bohr model of an atom
Define electron, proton, neutron, and nucleus
Define atomic number
Discuss electron shells and orbits
Explain energy levels
Define valence electron
Discuss ionization
Define free electron and ion
Discuss the basic concept of the quantum model of the atom
Discuss insulators, conductors, and semiconductors and how they differ
Define the core of an atom
Describe the carbon atom
Name two types each of semiconductors, conductors, and insulators
Explain the band gap
Define valence band and conduction band
Compare a semiconductor atom to a conductor atom
Discuss silicon and germanium atoms
Explain covalent bonds
Define crystal
Describe how current is produced in a semiconductor
Discuss conduction electrons and holes
Explain an electron-hole pair
Discuss recombination
Explain electron and hole current
Describe the properties of n-type and p-type semiconductors
Define doping
Explain how n-type semiconductors are formed
Describe a majority carrier and minority carrier in n-type material
Explain how p-type semiconductors are formed
Describe a majority carrier and minority carrier in p-type material
Describe how a pn junction is formed
Discuss diffusion across a pn junction
Explain the formation of the depletion region
Define barrier potential and discuss its significance
State the values of barrier potential in silicon and germanium
Discuss energy diagrams
Define energy hill
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
2. Contents
12-1 What a Bonding Theory Should Do
12-2 Introduction to the Valence-Bond Method
12-3 Hybridization of Atomic Orbitals
12-4 Multiple Covalent Bonds
12-5 Molecular Orbital Theory
12-6 Delocalized Electrons: Bonding in the
Benzene Molecule
12-7 Bonding in Metals
Focus on Photoelectron Spectroscopy
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3. 12-1 What a Bonding Theory Should Do
• Bring atoms together from a distance.
– e- are attracted to both nuclei.
– e- are repelled by each other.
– Nuclei are repelled by each other.
• Plot the total potential energy verses distance.
– -ve energies correspond to net attractive forces.
– +ve energies correspond to net repulsive forces.
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5. 12-2 Introduction to the Valence-Bond
Method
• Atomic orbital overlap describes covalent
bonding.
• Area of overlap of orbitals is in phase.
• A localized model of bonding.
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7. Example 12-1
Using the Valence-Bond Method to Describe a Molecular
Structure.
Describe the phosphine molecule, PH3, by the valence-bond
method..
Identify valence electrons:
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8. Example 12-1
Sketch the orbitals:
Overlap the orbitals:
Describe the shape: Trigonal pyramidal
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9. 12-3 Hybridization of Atomic Orbitals
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19. sp3d and sp3d2 Hybridization
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20. Hybrid Orbitals and VSEPR
• Write a plausible Lewis structure.
• Use VSEPR to predict electron geometry.
• Select the appropriate hybridization.
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21. 12-4 Multiple Covalent Bonds
• Ethylene has a double bond in its Lewis structure.
• VSEPR says trigonal planar at carbon.
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23. Acetylene
• Acetylene, C2H2, has a triple bond.
• VSEPR says linear at carbon.
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24. 12-5 Molecular Orbital Theory
• Atomic orbitals are isolated on atoms.
• Molecular orbitals span two or more atoms.
• LCAO
– Linear combination of atomic orbitals.
Ψ1 = φ1 + φ2 Ψ2 = φ1 - φ2
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26. Molecular Orbitals of Hydrogen
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27. Basic Ideas Concerning MOs
• Number of MOs = Number of AOs.
• Bonding and antibonding MOs formed from AOs.
• e- fill the lowest energy MO first.
• Pauli exclusion principle is followed.
• Hund’s rule is followed
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28. Bond Order
• Stable species have more electrons in bonding
orbitals than antibonding.
No. e- in bonding MOs - No. e- in antibonding MOs
Bond Order =
2
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29. Diatomic Molecules of the First-Period
BO = (e-bond - e-antibond )/2
BOH += (1-0)/2 = ½
2
BOH += (2-0)/2 = 1
2
BOHe + = (2-1)/2 = ½
2
BOHe + = (2-2)/2 = 0
2
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30. Molecular Orbitals of the Second Period
• First period use only 1s orbitals.
• Second period have 2s and 2p orbitals available.
• p orbital overlap:
– End-on overlap is best – sigma bond (σ).
– Side-on overlap is good – pi bond (π).
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31. Molecular Orbitals of the Second Period
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41. 12-7 Bonding in Metals
• Electron sea model
– Nuclei in a sea of e-.
– Metallic lustre.
– Malleability.
Force applied
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42. Bonding in Metals
Band theory.
• Extension of MO theory.
N atoms give N orbitals that
are closely spaced in energy.
• N/2 are filled.
The valence band.
• N/2 are empty.
The conduction band.
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