Diatomic IR Spectroscopy

This section supplements the discussion in Chapter 19 on the vibration-rotation energy levels and infrared spectra of heteronuclear diatomic molecules. It is also a supplement to Lab 2a, the Vibration-Rotation Spectrum of HCl and DCl.

You can change the fundamental vibration constant, the first anharmonic constant, the rigid-rotor rotational constant, and the vibration-rotation interaction constant to reflect the molecule of your choice (see Table 19.2 on page 708 of the text) or any fictitious molecule you can imagine. The default constants are close to those for HCl. You can also select the initial rotational quantum number J'' for a transition and the type of transition: J changes by plus one, (the R branch), or J changes by minus one, (the P branch). The transition energy will be calculated for your choice. (Keep J'' below 5.)

The top figure shows an energy level diagram for J = 0 through 5 in both the v = 0 and v = 1 vibrational states, labeled (v,J) at each level. Since the diagram is to scale and since rotational spacings are usually much smaller than vibrational spacings, the rotational levels are spread across the diagram. A black line connects the levels for the transition you choose.

The lower figure shows the schematic spectrum with the R(0) through R(7) and P(1) through P(7) transitions shown. The transition you select with your choice of J'' and P or R branch will have a blue square over it in the spectrum. The transition intensities are calculated for an experiment at a temperature of roughly 300 K.

Here are some things to try:

• If you set the anharmonic constant and the vib-rot interaction constant both to zero, you'll have the pure "rigid-rotor harmonic oscilator" model. You'll notice that the spacing from line to line in either branch is equal in this model. What causes an unequal spacing, anharmonicity or vibration-rotation interaction?
• If you reduce the rotational constant, you'll see the effect of temperature on the spectrum. As B_e is reduced, the line of greatest intensity in each branch will move to greater J'' values because the rotational level spacing in the v = 0 state is decreasing with B_e. At small enough B_e, the maximum will be at such a high J'' that you won't see it. The transitions will slowly increase in intensity as each branch marches out from the center of the spectrum, but they will not reach a maximum.

Back to hybrid orbitals. Ahead to symmetry effects in vibration-rotation spectra. Back to the Index.   Copyright 1999, 2000 John S. Winn. All rights reserved. Last updated September 8, 2000.