Rotational structure
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
487
2025-12-07
37
Rotational structure
Just as in vibrational spectroscopy, where a vibrational transition is accompanied by rotational excitation, so rotational transitions accompany the excitation of the vibrational excitation that accompanies electronic excitation. We therefore see P, Q, and R branches for each vibrational transition, and the electronic transition has a very rich structure. However, the principal difference is that electronic excitation can result in much larger changes in bond length than vibrational excitation causes alone, and the rotational branches have a more complex structure than in vibration–rotation spectra. We suppose that the rotational constants of the electronic ground and excited states are B and B′, respectively. The rotational energy levels of the initial and final states are
E(J) = hcBJ(J + 1) E(J′) = hcB′J′(J′+1)
and the rotational transitions occur at the following positions relative to the vibrational transition of wavenumber # that they accompany:
P branch (∆J =−1): vP(J) = v−(B′+B) J+(B′−B) J2
Q branch (∆J = 0): vQ(J) = v+(B′−B) J(J+1)
R branch (∆J =+1): vR(J) = v+(B′+B) (J+1) +(B′−B) (J+1)2
(These are the analogues of eqn 13.63.) First, suppose that the bond length in the electronically excited state is greater than that in the ground state; then B′ B′+B the lines start to appear at successively decreasing wavenumbers. That is, the R branch has a band head (Fig. 14.11a). When the bond is shorter in the excited state than in the ground state, B′>B and B′−B is positive. In this case, the lines of the P branch begin to converge and go through a head when J is such that (B′−B) J > B′+B (Fig. 14.11b).
Fig. 14.11 When the rotational con`stants of a diatomic molecule differ significantly in the initial and final states of an electronic transition, the P and R branches show a head. (a) The formation of a head in the R branch when B′B.
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