The Chemical Cosmos by Steve Miller

Author:Steve Miller
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

The rotational states are once more quantized, like rungs on the ladder. Higher rungs represent more rotational energy. If a harmonic oscillator is a first approximation to the way in which a molecule vibrates, then the corresponding rotational approximation is that of the rigid rotor. Take the simple diatomic Hydrogen molecule, H2; in the rigid rotor picture, this looks like two balls on either end of a stick. The individual Hydrogen atoms are the balls, and the bond between them is the stick. The rungs of the ladder are evenly spaced, and on each vibrational bridge, the ladders also have the same distance between the rungs – easy!

Easy? If the diatomic Hydrogen molecule really were this simple, then it would be. But it is not. For starters, the idea that the molecule rotates rigidly becomes less and less tenable as more rotational energy is put into it. Instead, the average distance between the two atoms increases slightly. This has the effect of making the spacing between the rungs decrease the higher up the ladder you get. Secondly, the average distance between the atoms also increases as you go upwards from vibrational bridge to vibrational bridge, meaning that the distance between the rungs on the ladder on the first bridge is greater than the rungs for the ladder on bridge 2, which – in turn – has a larger rung spacing than for rotational ladder on bridge 3 – and so on up the bridges. Climbing up a rotational ladder does not put you from one bridge to another, however, and it is possible to climb right up from the Ground State to the plateau simply by going up its rotational ladder. (It takes our guide 46 rotational rungs to “get to the top” and break up.)

For our triatomic Hydrogen ion, H3+ matters are more ­complicated even than for its diatomic H2 cousin. The individual Hydrogen atoms in our chemical triangle are less tightly held together than for H2; after all, there are just two electrons to make a bond for three atoms while in H2 the two electrons only have two atoms to hold together. Then there is an additional rotational energy that the molecule picks up when it vibrationally bends out of shape, which can either add to the overall rotational energy or detract from it. It may only have three atoms, but our guide leads a complicated Quantum Mechanical life. That means that you do not have to go far up either the series of vibrational bridges or rotational ladders before trying to predict what energies correspond to what vibrations or rotations, and how the molecule is going to make jumps between them becomes a real handful.

When Joseph Hirschfelder first calculated the vibrations of triangular H3+ in 1938, based on his potential energy surface, he predicted that the wavelength region in which you would be able to measure the spectrum of the molecule would be around 9 μm. Had Takeshi Oka spent his time fishing in those waters, he would have come back with nothing but tall tales of the one that got away.

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