{"id":10196,"date":"2016-11-11T15:44:48","date_gmt":"2016-11-11T20:44:48","guid":{"rendered":"https:\/\/www.masterorganicchemistry.com\/?p=10196"},"modified":"2026-01-22T09:19:46","modified_gmt":"2026-01-22T15:19:46","slug":"bond-vibrations-ir-spectroscopy","status":"publish","type":"post","link":"https:\/\/www.masterorganicchemistry.com\/2016\/11\/11\/bond-vibrations-ir-spectroscopy\/","title":{"rendered":"Bond Vibrations, Infrared Spectroscopy, and the “Ball and Spring” Model"},"content":{"rendered":"

The “Ball And Spring” Mental Model\u00a0 For Infrared Spectroscopy<\/strong><\/p>\n

Table of Contents<\/strong><\/p>\n

    \n
  1. \u00a0Why do UV spectra have such broad peaks?<\/a><\/li>\n
  2. The “stadium” analogy. Introduction to vibrational energy levels.<\/a><\/li>\n
  3. Visualizing different vibrational energy levels<\/a><\/li>\n
  4. A useful analogy: the “ball and spring” model for bond vibrations<\/a><\/li>\n
  5. IR spectroscopy: a tool for observing bond vibrations<\/a><\/li>\n
  6. How IR spectroscopy differs from UV spectroscopy<\/a><\/li>\n
  7. A simple IR spectrum: H2O (water). How to tell the difference between the peaks and the baseline<\/a><\/li>\n
  8. Some terms defined: transmission, absorbance, wavenumber<\/a><\/li>\n
  9. Oh crap: a more complex IR spectrum. What do we do?<\/a> (Don’t panic!)<\/li>\n
  10. [Bonus track: using the “ball and spring model” to interpret IR spectra]<\/a><\/li>\n
  11. Notes<\/a><\/li>\n<\/ol>\n
    \n

    <\/a>1. Why Are Peaks In UV Spectra So Broad?<\/h2>\n

    In the past series of posts on UV spectroscopy,<\/a> we saw that \u00a0UV or visible light can promote electrons from a lower energy orbital to a higher energy orbital, with the energy gap, \u00a0delta E (\u0394E) roughly corresponding to the wavelength of light.<\/p>\n

    By “roughly” I mean that we saw that UV spectra are not sharp<\/strong>.<\/p>\n

    Look at 1,3-butadiene, for instance (below). \u00a0The \u03bbmax<\/sub> is 240 nm, but look how broad that region of the spectrum is:\u00a0photons with wavelengths\u00a0from about 235-245 nm (and beyond) will promote the same transition.<\/p>\n

    \"absorbance<\/p>\n

    So why\u00a0are energy levels \u00a0so “smeared out” in molecules?<\/p>\n

    After all, we learn in general chemistry that energy levels are quantized, like the difference in energy between steps on a staircase. Why is there so much leeway?<\/p>\n

    You know what’s sharp?\u00a0Atomic<\/strong> absorbance spectra. Look at sodium (below left). Look how crisply the lines at 589.0 nm and 589.6 nm are\u00a0distinguished.<\/p>\n

    \"absorbance<\/p>\n

    That’s more like it! We can visualize a difference of less than 1 nm of light in this\u00a0atomic<\/strong> absorbance spectrum.<\/p>\n

    So what’s the difference?<\/p>\n

    <\/a>2. Electronic and Vibrational Energy Levels: The Stadium Analogy<\/h2>\n

    The brief answer is that electronic energy levels in atoms<\/strong> are quite simple: they are pure transitions between orbitals. There’s a few small technicalities\u00a0(spin-orbit coupling<\/a>: not going to get into that<\/em>)<\/span> but the peaks are\u00a0sharp.\u00a0<\/em><\/p>\n

    The situation complicates once\u00a0covalent bonds<\/strong> enter the picture.<\/p>\n

    Chemical bonds behave a bit\u00a0like flexible springs that connect two balls: they can\u00a0vibrate<\/strong>, a general term we’ll use to cover such motions as stretching, bending, twisting, and others. At the molecular level, the energies of these motions are\u00a0quantized:\u00a0<\/strong>like steps on a staircase or ladder, each motion has a particular\u00a0energy level<\/strong>.<\/p>\n

    The steps between these “vibrational” energy levels are much smaller<\/strong> than the “steps” we saw between\u00a0electronic<\/strong> energy levels (i.e. orbitals) . In other words,\u00a0less energy<\/strong> is required for transitions between vibrational energy levels than is required for electronic transitions.<\/p>\n

    You can visualize it a bit like this. It’s not perfect, but it gets the point across.<\/p>\n

    \"electronic<\/p>\n

    Think of the “decks” as the energy levels of orbitals, and the “rows” as the vibrational energy levels.<\/p>\n

    The existence of these vibrational energy levels explains why delta E can take on a range of values, and hence why UV spectra for molecules can be broad.<\/p>\n

    Why? Because each of the following would be a valid electronic transition between orbitals:<\/p>\n

      \n
    • Ground level, row 1\u00a0\u2192 Lower deck, row 1 \u00a0(\u0394E1<\/sub>)<\/li>\n
    • Ground level, row 1\u00a0\u2192 Lower deck, row 2 \u00a0(\u0394E2<\/sub>)<\/li>\n
    • Ground level, row 1\u00a0\u2192 Lower deck, row 3 \u00a0(\u0394E3<\/sub>)<\/li>\n
    • Ground level, row 1\u00a0\u2192 Lower deck, row 4 \u00a0(\u0394E4<\/sub>)<\/li>\n<\/ul>\n

      and so on.<\/p>\n

      The\u00a0\u0394E values should correspond to a series<\/em> of absorbance peaks spaced out by the difference in energy between the vibrational energy levels (or the “spacing between rows” in our analogy).<\/p>\n

      In theory, \u00a0we should be able to observe the\u00a0spacing between these\u00a0peaks (so-called “fine structure”). In practice, we tend not to, for reasons that aren’t that important for our purposes. [ If you’re desperate to know why not, Note 1<\/a>.]<\/em><\/p>\n

      In rare cases we\u00a0can<\/em> see the fine structure\u00a0in UV spectra, however. For example, look at the UV spectrum of benzene, below. See those individual peaks?\u00a0Those represent transitions into individual vibrational energy levels.<\/p>\n

      \"uv<\/p>\n

      We sometimes represent transitions from ground to excited states using a Franck-Condon diagram<\/a>. You can think of it as a more rigorous version of our stadium analogy.<\/p>\n

      The bottom level (green line) attempts to show the spacing of vibrational energy levels in the ground state. Upon absorption of a photon of energy\u00a0\u0394E, an electron is promoted from the ground state to one of the vibrational levels in the excited state (red line). [Extra detail: The “minimum” of the green and red lines corresponds to the bond length in the ground and excited states respectively; they don’t overlap because the bond length in the excited state\u00a0is longer. The F-C diagram is a useful model because electronic transitions are fast, relative to movements of atoms.]\u00a0<\/em><\/span><\/p>\n

      This is more detail than you likely need. The “stadium analogy” is a perfectly fine intuitive model to use.<\/p>\n

      \"franck<\/p>\n

      <\/a>3. Visualizing Vibrational Energy Levels: The “Ball And Spring” Model<\/strong><\/h2>\n

      So how can we visualize exactly how these “vibrational energy levels” differ, and what they look like? \u00a0And how do they relate to energy?<\/p>\n

      The “ball and spring” model is a great mental model\u00a0to start with.<\/p>\n

        \n
      • Imagine two atoms (balls) attached by a spring (the bond).<\/li>\n
      • The spring allows for\u00a0vibration to occur. \u00a0We can visualize this vibration as standing waves.<\/strong><\/li>\n
      • In a resting state we can imagine a simple standing wave with no nodes (i.e. no locations where the amplitude is zero) along its length.<\/li>\n
      • If the energy is increased by a certain integer amount corresponding to \u0394E, \u00a0a transition occurs to a higher vibrational energy level where the wave now has a single node. This is the first “excited” vibrational state.<\/li>\n
      • As more energy is applied to the system, additional energy levels will appear with an increasing number of nodes, roughly in integer increments of\u00a0\u0394E<\/li>\n<\/ul>\n

        The main idea of increased vibrational energy levels is conveyed by this GIF \u00a0[Adapted from this video<\/a>]<\/p>\n