Monday, August 26, 2013

The Amazing Story of Molecular Vibration

Introduction by the Blog Author
This is going to sound boring at first, but hang on to it until it gets interesting. They don’t teach this in that introductory chemistry class that bored you. Guess what? A molecule isn’t a tinkertoy of atoms grouped together in a heap. The outer atoms of the molecule move – they twist and vibrate. This post has LINKS that show you examples of these motions. And at the end of the post I have a surprise for you – something you probably never were told by anyone about the natural world.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

From Wikipedia:

A molecular vibration occurs when atoms in a molecule are in periodic motion while the molecule as a whole has constant translational and rotational motion. The frequency of the periodic motion is known as a vibration frequency, and the typical frequencies of the molecular vibrations range from less than 1012 to approximately 1014 Hz.

In general, a molecule with N atoms has 3N – 6 normal modes of vibration, but a linear molecule has 3N – 5 such modes, as rotation about its molecular axis cannot be observed. A diatomic molecule has one normal mode of vibration. The normal modes of vibration of polyatomic molecules are independent of each other but each normal mode will involve simultaneous vibrations of different parts of the molecule such as different chemical bonds.

A molecular vibration is excited when the molecule absorbs a quantum of energy, E, corresponding to the vibration's frequency, ν
, according to the relation E = (where h is Planck’s constant). A fundamental vibration is excited when one such quantum of energy is absorbed by the molecule in its ground state. When two quanta are absorbed the first overtone is excited, and so on to higher overtones.
To a first approximation, the motion in a normal vibration can be described as a kind of simple harmonic motion. In this approximation, the vibrational energy is a quadratic function (parabola) with respect to the atomic displacements and the first overtone has twice the frequency of the fundamental. In reality, vibrations are anharmonic and the first overtone has a frequency that is slightly lower than twice that of the fundamental.

Excitation of the higher overtones involves progressively less and less additional energy and eventually leads to dissociation of the molecule, as the potential energy of the molecule is more like a Morse potential.

The vibrational states of a molecule can be probed in a variety of ways. The most direct way is through infrared spectroscopy, as vibrational transitions typically require an amount of energy that corresponds to the infrared region of the spectrum. Raman spectroscopy, which typically uses visible light, can also be used to measure vibration frequencies directly. The two techniques are complementary and comparison between the two can provide useful structural information such as in the case of the rule of mutual exclusion for centrosymmetric molecules.

Vibrational excitation can occur in conjunction with electronic excitation (vibronic transition), giving vibrational fine structure to electronic transitions, particularly with molecules in the gas state.
Simultaneous excitation of a vibration and rotations gives rise to vibration-rotation spectra.

Vibrational coordinates

The coordinate of a normal vibration is a combination of changes in the positions of atoms in the molecule. When the vibration is excited the coordinate changes sinusoidally with a frequency ν, the frequency of the vibration.

 

Internal coordinates

Internal coordinates are of the following types, illustrated with reference to the planar molecule ethylene,

H       H
  \      /
  C=C
 /      \
H    H
Ethylene
  Stretching: a change in the length of a bond, such as C-H or C-C
  • Bending: a change in the angle between two bonds, such as the HCH angle in a methylene group
  • Rocking: a change in angle between a group of atoms, such as a methylene group and the rest of the molecule.
  • Wagging: a change in angle between the plane of a group of atoms, such as a methylene group and a plane through the rest of the molecule,
  • Twisting: a change in the angle between the planes of two groups of atoms, such as a change in the angle between the two methylene groups.
  • Out-of-plane: a change in the angle between any one of the C-H bonds and the plane defined by the remaining atoms of the ethylene molecule. Another example is in BF3 when the boron atom moves in and out of the plane of the three fluorine atoms.

In a rocking, wagging or twisting coordinate the bond lengths within the groups involved do not change. The angles do. Rocking is distinguished from wagging by the fact that the atoms in the group stay in the same plane.

In ethene there are 12 internal coordinates: 4 C-H stretching, 1 C-C stretching, 2 H-C-H bending, 2 CH2 rocking, 2 CH2 wagging, 1 twisting. Note that the H-C-C angles cannot be used as internal coordinates as the angles at each carbon atom cannot all increase at the same time.
 

Vibrations of a Methylene group (-CH2-) in a molecule for illustration


The atoms in a CH2 group, commonly found in organic compounds, can vibrate in six different ways: symmetric and asymmetric stretching, scissoring, rocking, wagging and twisting as shown here:

Symmetrical stretching
  http://en.wikipedia.org/wiki/File:Symmetrical_stretching.gif

Asymmetrical stretching
  http://en.wikipedia.org/wiki/File:Asymmetrical_stretching.gif

Scissoring
  http://en.wikipedia.org/wiki/File:Scissoring.gif

Rocking
  http://en.wikipedia.org/wiki/File:Modo_rotacao.gif

Wagging
  http://en.wikipedia.org/wiki/File:Wagging.gif

Twisting
  http://en.wikipedia.org/wiki/File:Twisting.gif

The Wikipedia post for this text shows all six motions simultaneously:

http://en.wikipedia.org/wiki/Molecular_vibration
 
Afterword by the Blog Author
It is commonly – and falsely—believed that all motion ceases at the termperature of "absolute zero." This is not true. Molecules stop moving with resperct to other molecules at abolute zero; inter-molecular motion ceases. But the stretching and twisting and wagging of various groups of atoms continues, slowly but unstoppably, even at absolute zero. Bluntly, molecules are always moving, even if they are locked to each other at absolute zero.

Tomorrow there will be a post which demonstrates how these organic compounds can be detected with certainty in outer space. Tomorrow’s post also speculates about the formation of elements that took place earlier in the history of the universe – interstellar chemistry!

No comments:

Post a Comment