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Unformatted text preview: Lecture Series 1 Chem 1B Jim Heath There are a number of ways to determine molecular structure, ranging from x-ray diffraction measurements on crystal of molecules to nuclear magnetic resonance (NMR), mass spectrometry, and rotational, vibrational, and electronic spectroscopy. Some of these, such as NMR, XRD, and rotational spectroscopy, are methods that can yield bond lengths and bond angles, atomic masses, etc., while others, such as vibrational spectroscopy and mass spectrometry, are more indirect methods, and are used to fingerprint a molecule. Other techniques, such as electronic spectroscopy and photoelectron spectroscopy, can yield information regarding the electronic structure (energies and symmetries of molecular orbitals), but do not typically yield information regarding the atomic structure. NMR, rotational, vibrational, and electronic spectroscopies involve the interaction of light with matter, and are intrinsically quantum mechanical in nature. The above figure illustrates which components of the spectrum are associated with the various classes of molecular and atomic energies. Note that the various methods of molecular spectroscopy cover an energy range of ~10 14 cm-1 ! ( 1 cm-1 is roughly 0.1 meV) It should thus be no surprise that the range of molecular properties that are interrogated across this energy range are equally broad. In these first lectures we will cover, at a cursory level, rotational, vibrational, and electronic molecular spectroscopies. The goal is to introduce concepts that are used by chemists to determine molecular structure. We will later cover NMR (nuclear magnetic resonance) and mass spectrometry, which are two methods that are critical analytical and structural tools for chemistry and biochemistry, but the notes for those will be limited to the lecture notes from class. Since the molecular spectroscopies are inherently quantum mechanical in nature, we begin with a simple description of the particle-in-a-box. Particle-in-a-box We know that mass and light each have wave-like and particle-like characteristics, and that electrons in atoms are quantized they have discrete energies, or, equivalently, they have discrete values of the angular momenta. We have so far presented only the facts. Now we try to ask why. Our first question: Why does an electron become quantized? Quantum mechanics is not a particularly intuitive subject, and so analogies to real world phenomena are a little dangerous. Nevertheless, here is one that works a little bit. Imagine that we have a guitar string, tied down at either end, as if it were on a guitar. If we pluck the string, then we hear a note, and this note is the resonance frequency of the string. This is, of course, the basis for all stringed instruments. One selects an appropriate string, stretches it across some length, and then puts an appropriate tension on that string. These things we do to the string will tune it to a desired resonant frequency say an A note. Now it turns...
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