How does theory relate to molecular structure? As we discussed in the Background Material, the Born-Oppenheimer approximation leads us to use quantum mechanics to predict the energy E of a molecule for any positions (Ra)of its nuclei given the number of electrons N in the molecule (or ion ). This means, for example, that the energy of the arginine molecule in its lowest electronic state (i.e, with the electrons occupying the lowest energy orbitals)can be determined for any location of the nuclei if the Schrodinger equation governing the movements of the electrons can be solved Ifyou have not had a good class on how quantum mechanics is used within chemistry, I urge you to take the time needed to master the background Material. In those pages, I introduce the central concepts of quantum mechanics and I show how they apply to several very important cases including 1. electrons moving in 1, 2, and 3 dimensions and how these models relate to electronic structures of polyenes and to electronic bands in solids 2. the classical and quantum probability densities and how they differ, 3. time propagation of quantum wave functions, 4. the Huckel or tight-binding model of chemical bonding among atomic orbitals, 5. harmonic vibrations 6. molecular rotations 7. electron tunneling 8. atomic orbitals' angular and radial characteristics, 9. and point group symmetry and how it is used to label orbitals and vibrations.4 How does theory relate to molecular structure? As we discussed in the Background Material, the Born-Oppenheimer approximation leads us to use quantum mechanics to predict the energy E of a molecule for any positions ({Ra}) of its nuclei given the number of electrons Ne in the molecule (or ion). This means, for example, that the energy of the arginine molecule in its lowest electronic state (i.e., with the electrons occupying the lowest energy orbitals) can be determined for any location of the nuclei if the Schrödinger equation governing the movements of the electrons can be solved. If you have not had a good class on how quantum mechanics is used within chemistry, I urge you to take the time needed to master the Background Material. In those pages, I introduce the central concepts of quantum mechanics and I show how they apply to several very important cases including 1. electrons moving in 1, 2, and 3 dimensions and how these models relate to electronic structures of polyenes and to electronic bands in solids 2. the classical and quantum probability densities and how they differ, 3. time propagation of quantum wave functions, 4. the Hückel or tight-binding model of chemical bonding among atomic orbitals, 5. harmonic vibrations, 6. molecular rotations, 7. electron tunneling, 8. atomic orbitals’ angular and radial characteristics, 9. and point group symmetry and how it is used to label orbitals and vibrations