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Molecules are treated similarly to atoms. First the energy eigenstates for one electron moving in a potential of fixed positive nuclei are found. These solutions are called the molecular orbitals. An approximation of the multi-electron wavefunction for any molecule can be constructed from an antisymmetrized product of molecular orbitals. Any property of a molecule can be calculated from the multi-electron wavefunction.

**Reading**

Read the notes on molecules that are linked in the outline.

- 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) and be able to say how these orbitals would be filled by teh electrons of the molecule.
- Explain what the Roothaan equations are.
- Be able to construct a multi-electron molecular wavefunction as an antisymmetrized product of molecular orbitals, be able to explain the exchange energy.
- Be able to use describe how the multi-electron wave function can be used to calculate a bond potential.
- Be able to determine the vibrational states of a diatomic molecule from the bond potential.
- Be able to calculate the rotational states of diatomic molecules from the bond potential.
- Be able to determine the number of translational states, rotational states, and vibrational states of a molecule.
- Be able to explain which photon energies a molecule can absorb.
- Be able to explain how bond lengths and bond angles can be calculated and how to determine if a chemical reaction is endothermic or exothermic
- Be able to sketch a bond potential (such as a Morse potential or a Lennard-Jones potential) given the bond length and dissociation energy
- Be able to define: single bond, double bond, triple bond, polar bond, covalent bond, π-bond, σ-bond, metallic bond, ionic bond, Van der Waals bond, valence bond theory, molecular orbital theory, sp orbital, sp² orbital, sp³ orbital, bonding orbital, antibonding orbital, singlet state, triplet state.

- H
_{2}bond potential, h2_bond_calc.nb, h2_bond_data.nb - H
_{2}bond potential Henögl / Pranter 2014 - Einführung in die Infrarotspektroskopie

**Resources**

Molecular Spectral Databases (NIST)

NIST Computational Chemistry Comparison and Benchmark DataBase (CCCBDB)