| MadSci Network: Chemistry |
There are two main methods for the precise determination of the angles. For large molecules, the main method is X-ray diffraction. This depends on being able to obtain the molecule as solid crystals, where the molecules are packed so that the structure repeats very regularly a large number of times. When a beam of X-rays strikes a crystal, most of the beam gose straight through, but parts of it are "diffracted" to produce a series of spots in various other directions. The positions and intensities of these diffraction spots can be measured, and with a complicated computer calculation*, they can be used to infer the positions of all of the atoms in the regular bit of the structure that repeats. (*It involves 3-dimensional Fourier transformation, and a process of guess and refinement). In the best quality studies, the positions are given to a precision of about 0.2 picometres for most types of atoms, or 1 picometre for a hydrogen atom. For comparison, chemical bonds are mostly between about 100 and 200 picometres long. Now if we know the positions of three atoms very precisely, calculating the angle between two bonds is a matter of simple trigonometry. Check out X-ray diffraction .
The other method that gives similar precision is microwave spectroscopy. This only works for small molecules, preferably with no more than 5 atoms, and for substances that can readily be obtained in the vapour state. Microwaves are light waves with a wavelength around 1 cm -- longer than infrared rays, but shorter than normal radio waves. They probe the rotational states of molecules. If a molecule absorbs microwave radiation it starts spinning faster. Measurement of the precise wavelengths of microwave absorbed by a molecule tells us its three principal moments of inertia. These in turn give us some information about the geometry of the molecule, including bond angles. They do not usually give us enough to determine the geometry fully. But the extra information needed can usually be obtained by also finding the moments of inertia for an isotopically substituted molecule (e.g. measuring frequencies for D2O as well as H2O) if the molecule has 3 or 4 atoms. It is a bit more difficult if it has 5 atoms, and is usually not attempted if the molecule has 6 or more atoms, unless there is high symmetry, or some other factor that simplifies the problem.
The other thing that I should mention in the answer to this question is that sometimes bond angles are precisely determined by symmetry, so that they do not need to be measured at all. Methane, for example, is CH4. We know that each of those four hydrogen atoms is exactly equivalent in every way. Now there are six HCH angles in methane. Only if these angles have the value of 109.45 degrees (the tetrahedral angle, given by cos theta = -1/3) can they all be the same. To give one of them any other value would mean that some HCH angles would be different to others, meaning either that there would be differences between hydrogen atoms, or differences in the relationships of some pairs of them. Similarly, because its chemical properties show that benzene must be a planar regular hexagon, each CCC angle must be precisely 120 degrees. And because there is no reason why a H atom would lean toward one of its next-but-neighbouring C atoms rather than the other, the CCH angles must also be precisely 120 degrees.
I think that just about covers the ground.
Regards, John.