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Molecules
This course begins with a brief overview of molecular physics. I will review the solutions to the Schrödinger equation for the hydrom atom and then use the hydrogen wavefunctions to describe multi-electron atoms. Molecules are ussually described either in terms of valence bond theory where the solutions are constructed from hydrogen wavefunctions or molecular orbital theory where orbitals for a single electron are calculated and then these are used to construct a multi-electron wavefunction.
Outline
- The solutions to the Schrödinger equation for the hydrogen atom W
- Constructing many-electron atomic wave functions from the hydrogen wave functions
- Many body problem W
- The intractability of the Schrödinger equation
- The helium atom W
- Singlet and triplet states
- Identical particles W
- Pauli exclusion principle W
- Slater determinants W
- Exchange W
- Molecular orbital theory W
- Constructing the total molecular Hamiltonian
- The Born-Oppenheimer approximation W
- The single electron molecular orbital Hamiltonian
- Solving the molecular orbital Hamiltonian
- Linear combination of atomic orbitals (LCAO) W
- Hückel model W
- Constructing many-electron molecular wavefunctions from the molecular orbitals
- Valence bond theory W
- 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
Reading
Review the hydrogen atom: Demtröder - Das Wasserstoffatom
Read the section of this chapter on Helium: Demtröder - Atome mit mehreren Elektronen
Read the chapter on molecules: Demtröder - Moleküle
For the exam you should
- Be familar with the hydrogen wave functions
- Be able to construct the multi-electron wave functions of any atom as antisymmetrized products of hydrogen wave functions
- Be able to write down the total Hamiltonian for any molecule
- Be able to evaluate the energy of a trial wavefunction (a guess) in any Hamiltonian
- Be able to write down the electronic Hamiltonian of any molecule in the Born-Oppenheimer approximation
- By neglecting the electron-electron interactions in the electronic Hamiltonian, you should be able to solve it by the separation of variables and construct the molecular orbital Hamiltonian
- You should know how to solve the molecular orbital Hamiltonian using a Linear Combination of Atomic Orbitals (LCAO)
- Explain Hückel theory
- Be able to construct a multi-electron molecular wavefunction as an antisymmetrized product of molecular orbitals
- Be able to use valence bond theory to calculate a bond potential such as the Morse potential or the Lennard-Jones potential
- Be able to determine the vibrational states of a bond from the bond potential
- Be able to calculate the rotational states of molecules
- Be familar with the solutions to the Schrödinger equation for a particle in an infinite square well and a particle confined to a ring
- Be able to define: single bond, double bond, triple bond, polar bond, covalent bond, π-bond, σ-bond, metallic bond, ionic bond, valence bond theory, molecular orbital theory, sp orbital, sp² orbital, sp³ orbital, bonding orbital, antibonding orbital, singlet state, triplet state
Resources
Handbook of Basic Atomic Spectroscopic Data (NIST)
Molecular Spectral Databases (NIST)
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