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PHY.K02UF Molecular and Solid State Physics
Course outline
Introduction
Review of atomic physics
(pdf v.2018)
The solutions to the Schrödinger equation for the hydrogen atom
Atomic orbitals
1s
,
2s
,
2p
z
The Orbitron, another tool to visualize atomic orbitals
Slater's rules
Helium
Many-electron wavefunctions
Slater determinants
W
Singlet and triplet states
Exchange
W
The intractability of the Schrödinger equation
Many-electron atoms
Molecules
(pdf v.2018)
Molecular orbital theory
W
A quantum mechanical description of molecules
W
The Born-Oppenheimer approximation
W
Many-electron wavefunctions
Bond potentials
Rotational states
Vibrational states
Harmonic oscillator
Solving the molecular orbital Hamiltonian
Linear combination of atomic orbitals (LCAO)
W
Overlap matrix elements
Molecular hydrogen ion H
2
+
Molecular hydrogen H
2
Conjugated rings
,
Benzene
Conjugated chains
CO
,
NO
Valence bond theory
Heitler-London theory
Numerically calculated molecular orbitals
Carbon monoxide CO
,
Carbon dioxide CO
2
,
Water H
2
O
,
Hydrogen sulfide H
2
S
,
Nitrogen N
2
,
Ammonia NH
3
,
Methane CH
4
,
Ethene C
2
H
4
,
Ethane C
2
H
6
,
Butadiene C
4
H
6
,
Benzene C
6
H
6
,
Hexatriene C
6
H
8
Programs to calculate molecular orbitals
GAMESS
,
Gaussian
,
Quantum Espresso
,
FHI-aims
Rotational and vibrational energy levels of some diatomic molecules
Chemical bonds
Covalent bond
W
σ-bonds
W
π-bonds
W
sp, sp², sp³ orbitals
Double bond
W
Triple bond
W
Ionic bond
W
Polar bond
W
Metallic bond
W
Van der Waals bond
Hydrogen bond
W
Visualization tools
JSmol molecule viewer
MolView
(
MolView tutorial
),
Speck
,
Avogadro
,
ChemDoodle
,
NGLView (an IPython/Jupyter interactive widget)
Crystal structure
Crystals
The 7 crystal systems
Pearson symbols
Crystalographic directions
Miller indices
Symmetries
Crystal structures
Polymorphism
Crystal databases
For the exam
Periodicity, Fourier Series, and Reciprocal Space
Fourier series in one dimension
Review of exponential functions
Three-dimensional periodic functions
Reciprocal space
Periodicity conditions
Fourier series in 2-D
Fourier series in 3-D
For the exam
Crystal diffraction
Interference of scattered waves
Intensity of the scattered waves
Ewald sphere
Atomic form factors
Structure factors
Brillouin zones
Netplanes and lattice planes
Bragg diffraction
Powder diffraction
Electron diffraction
Low Energy Electron Diffraction
Neutron Diffraction
For the exam
Lattice Vibrations and Phonons
Normal Modes and Phonons
Using complex numbers to describe oscillations
The translation operator
1-d chain of atoms
1-d chain of atoms with two different masses
Phonons in 3D crystals
Phonon dispersion of an fcc crystal
Calculating the phonon dispersion of an fcc crystal
Plotting the phonon dispersion of an fcc crystal
Phonon density of states of an fcc crystal
Phonon dispersion of a bcc crystal
Plotting the phonon dispersion of a bcc crystal
Phonon density of states of a bcc crystal
Phonon dispersion of a simple cubic crystal
Plotting the phonon dispersion of a simple cubic crystal
Phonon density of states of a simple cubic crystal
Phonons of crystals with more atoms in the basis
Animations of some optical modes
Phonon data in databases
Measuring phonon dispersion
Phonon contribution to the thermodynamic properties of crystals
For the exam
Electrons
Electrons in a square well potential
The valence electrons of metals
The valence electrons become unbound
Free-electron model of metals
Sommerfeld expansion
For the exam
Energy bands
Differential equations with periodic coefficients
Hill's equation
Bloch theorem
Bloch waves in 1-D
Band structure in 1-D
Kronig-Penney Model
Empty lattice approximation
Fermi surface of a two-dimensional square lattice
Fermi surfaces of 3-D crystals
Metals, Semimetals, Semiconductors, and Insulators
The thermodynamic properties depend dramatically on the number of electrons in the primitive unit cell
Band structure calculations
Plane wave method
Tight binding
Electron contribution to the thermodynamic properties of a solid
Chemical potential μ(
T
)
Energy spectral density
u
(
E,T
)
Internal energy density
u
(
T
)
Specific heat
c
v
(
T
)
Helmholtz free energy density
f
(
T
)
Grand potential density φ(
T
)
Experimental verification of band structure calculations
For the exam
Semiconductors
Semiconductors
Boltzmann approximation
Transport properties
Drift and diffusion
The Hall effect
Drift and diffusion simulation
Electrical conductivity
The Einstein relation
Thermal conductivity
For the exam
