Concise Physical Chemistry

c18 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

292 EXPERIMENTAL DETERMINATION OF MOLECULAR STRUCTURE

expected transitions are conspicuously absent from experimental spectra owing to

selection rules which do not permit them. Despite these deviations from the simple

models described here, much invaluable bond distance information has been ob-

tained from microwave rotational spectra. For example, CO has a rotational spacing

of ̄ν= 3 .9cm−^1 (in the far-infrared region), which leads to a bond length of 113 pm.

By the way, your microwave oven activates a rocking frequency in H 2 O molecules,

thereby transmitting energy (heat) to your morning coffee.

18.5 MICROWAVE SPECTROSCOPY: BOND STRENGTH

AND BOND LENGTH

Given the input experimental data of the fundamental vibrational frequencyν 0 and the

line separation 2

(

h ̄^2

2 I

)

usually written 2B, in a vibration–rotation band of a diatomic

molecule, the bond strength in terms of the Hooke’s law force constantkfand the

bond length in picometers (pm) can be calculated.

18.6 ELECTRONIC SPECTRA

Electronic transitions require more energy than vibrational or rotational transitions.

They produce spectral peaks that frequently fall in the UV or visible part of the

electromagnetic spectrum. Theπ→π∗transition in ethene is an electronic transition

from the highest occupied molecular orbital (HOMO) to the lowest unoccupied

molecular orbital (LUMO). A simple model of electronic transition spectroscopy of

this kind is that of afree electrontrapped in a one-dimensional potential well, which

is the length of theπsystem in unsaturated molecules. An MM calculation (Chapter

19) of the distances between the terminal carbon atoms in ethene and 1,3-butadiene

gives the values 134 and 359 nm. The two electrons in ethene are in the lowest energy

level withE=h^2 / 8 mel^2 .Intheπ→π∗transition, one of them progresses to the

next higher energy state withE∗= 4 h^2 / 8 mel^2. The energy difference is

E=

3 h^2

8 mel^2

=

3 h^2

8 me( 134 )^2

= 5. 56 × 10 −^5

(

3 h^2

8 me

)

The 1,3-butadiene case has 4 electrons in twoπbonds (Fig. 18.4); hence the lowest

two levels are occupied and the transition is from then=2tothen=3orn^2 = 4

to then^2 =9level:

E=

(

9 h^2

8 mel^2

−

4 h^2

8 mel^2

)

=

5 h^2

8 mel^2

=

5 h^2

8 me( 359 )^2

= 3. 88 × 10 −^5

(

3 h^2

8 me

)

Even though the quantum number change in the second case is larger (5 vs. 3), the

transition for 1,3-butadiene is the smaller of the two energy differences because of