Main page VIBRATIONS: METHANE
 

You have probably wondered about the molecule in the top left corner of every page on our website. .What is it doing?  Is it exercising to stay in shape? Or is it trying to change its figure? When we talk about shapes of molecules we usually concentrate on static structures. We list bond lengths and bond angles as constants.  In reality what's constant is the change in the relative positions of atoms within molecules.  Atoms relentlessly oscillate around their "equilibrium" structure. The equilibrium positions of atoms are the source of our list of structural parameters, our blueprint for building models, but they do not explicitly account for molecular vibrations and internal rotations.

In other words, molecules are dynamic structures, constantly fidgeting as if ill at ease.   These motion are important in understanding shapes of molecules, their entropies, and how energy transferred in collisions is partitioned among various internal "modes".  Even reactions depend on these motions. For example, a bond stretch that goes "too far" may result in the complete breaking of the bond. 

 





 
 
 

The methane' "exercise" you see after loading this page is the symmetric stretching of all four C-H bonds in unison.  Indeed, this is the vibrational mode of our website icon.  For better visualization, the model shows the relative displacements of atoms with some exaggeration and we have added vectors to show the directions and relative magnitudes of atomic movements. It turns out that the "gym regime" of methane is quite diverse.  Some of the characteristic motions involve asymmetric stretching (a bit like shadow boxing), waging (simultaneous curls), twisting, or scissoring.  You should have no problem finding them all (and more) on the pull-down menu of all vibrational modes. The selected model will attempt a little re-orientation to better showcase its symmetry, but you can always reset it to the "standard" orientation, and as usual explore it in depth using mouse and the applet menu (right click).

   Methane has 5 atoms, each requiring 3 coordinates to describe its position. It would appear that we would have 15 "degrees of freedom" for this molecule and would need 15 different models to describe all atomic displacements fully. However, we are not interested here in the overall motion or rotations of the molecule as a whole.  We can, therefore. neglect three translational degrees of freedom (carbon moving in any direction and hydrogens following it in the identical fashion) and three rotations around any of the three axes (rotation of the whole molecule does not affect the relative positions of atoms).  Still, we are left with 9 degrees of freedom and have to deal with the chaos of all atoms moving in all directions (check "all" in the pull-down menu).. To do that we use 9 unique models to describe the relative motions of atoms within the molecule.  These models are selected in such a way as to not "interfere" with each other and are called normal modes. They are listed in the pull-down menu with their frequency numbers.

In general, a non-linear molecule will have 3N6 normal vibrational modes, and linear molecules will have 3N5 such modes, where N is the number of atoms in the molecule. Diatomics will have only one. Each of these vibrational modes is quantized (see below) and has its unique and discreet set of energy levels. Transitions between these levels correspond to absorption or emission of photons in the infrared part of the spectrum. Absorption of infrared light is the basis of IR spectroscopy commonly employed for identification and study of organic molecules.  Although not all normal modes are IR active, various functional groups have their characteristic frequencies by which they can be detected and recognized. These frequencies are most often reported as reciprocal of wavelengths, i.e. in wavenumbers (cm1). The numbers in the pull down menu are experimentally measured values and using the applet menu you can compare them with the calculated numbers for different models (the method of computation used is know to consistently overestimate the values by about 5%).. For methane the 1534 cm-1 and 2917 cm-1 modes are inactive in IR, but can be detected using Raman spectroscopy.  As the consequence of high molecular symmetry, some of the nodes are triply or doubly degenerate. The absorption and re-emission of IR radiation back to the surface of Earth by methane molecules in the atmosphere is one of the largest contributors to the greenhouse effect.

 
Highslide JS
Morse curve for hydrogen molecule (ro = 0.74 Å , BDE = 104 kcal/mol). The blue lines show the lowest 10 vibrational levels.

Let us stretch a bit our knowledge of vibrations as well, exploring a simple diatomic molecule. When two hydrogen atoms approach each other from infinite separation and their orbitals start to overlap, the energy of the system is lowered. The more overlap, the more sharing, the lower the energy, until the nucleus-nucleus repulsion starts to rapidly increase at small separation distances (r).  The energy minimum is reached at the "equilibrium" separation (ro = 0.74 Å for H2 molecule) as shown by the black curve (so called Morse curve) in the plot on the left.  However, the nuclei constantly oscillate around that equilibrium position (ro) between the "walls" of the Morse potential. The vibrations are quantized and described by a series of vibrational wavefunctions with their quantum numbers (n = 0, 1, 2,...). The level with n = 0 is the lowest possible energy that the molecule can have (so called "zero point energy, ZPE). At room temperature majorities of molecules are in the lowest energy vibrational state, but they do not stop vibrating even as the temperature approaches absolute zero. At higher temperatures higher vibrational states are occupied with larger atomic displacements from the equilibrium position, eventually reaching the "top" of the curve when the vibration leads to breaking of the bond (dotted line). The energy difference between the ZPE and separate atoms corresponds to the bond dissociation energy of H2 (104 kcal/mol). For larger molecules, each normal mode has a vibrational manifold similar to one shown on the left. 

 The vibrational energy levels at the bottom of the well resemble that of the harmonic oscillator. That is why the bonds are often treated as springs connecting the nuclei. This is, of course, just a visualization technique, but the mechanics of springs can be used as an approximation in understanding bond vibrations. In such quantum models the energy of the system is described by En = (h/2π) •ω• (n+½) where the frequency of the lowest vibration may be expressed as ω =(1/2π)(k/μ)1/2 where k is the force constant describing the bond (stiff or loose) and m is the reduced mass. In the harmonic oscillator the energy levels are equally spaced, but they converge in the case of the anharmonic oscillators describing the "real" bonds (as shown in the picture).

 
Molecular Gallery Last updated 08/22/10 Copyright 1997-2013
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