Elastic Rotor

So far, we assumed that rotation does not affect the shape of a molecule (rigid rotor). In fact, centrifugal forces that stretch the bonds to some extent will occur. We will confine the treatment of this problem in the example of the linear rotor.

An increased length of the bond corresponds to a higher moment of inertia (I = µr2). In turn, the rotational constant B (B ∝ I-1) falls, i.e. we would expect a rotational energy with a minor slope than in the case of Erot = Brigid J(J + 1).

This is a case where we have no general and exact solution to Schrödinger's equation, but we are able to deal with the problem and determine the eigenvalues for the rotational energy by using a series expansion. The newly introduced coefficient D is but a small correction, in other words, D is much smaller than B.
Erot  =  B · J(J + 1) - D · J2(J + 1)2 + ...

From the treatment of the elastic rotor, we would already expect that the weaker the bond, the more pronounced the deviations from the rigid rotor become. A weak bond corresponds to a low vibrational energy (Evib = hω(v + ½); ω = (k/µ)½; k: force constant of the bond). The value of D can be derived from spectral data.

We now want to focus on the selection rules for rotational spectra.


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