FTIR Rotational Spectroscopy Ron Woods1 and Giles Henderson Eastern Illinois University, Charleston, IL 61920 Although rotational spectroscopy is generally regarded as an important topic by the authors of modern physical chemistry texts, most undergraduate physical chemistry laboratories nrobablv do not have microwave and far-infrared specmmeters. 1.ahoratory contact with this topir has been rradition;ill\f limited to thc oh.iervation and analvsis of the rotational iine structure of the vibrational, bands of gas phase molecules (1-3). However, during the past decade, FTIR instruments have become commonplace in undergraduate schools. In most instances these instruments permit reasonable signallnoise measurements down to 200 cm-'. This extended range provides an opportunity to observe pure rotational transitions between high J levels of some light molecules of the form H,X. Here we wish to present representative examples of the spectra and the analyses for a linear molecule (HCl), a symmetric top molecule (NHd, and an asymmetric top (HzO). Any combination of these projects could be incorporated in a physical chemistry or molecular spectroscopy laboratory. General Considerations The measurements described here are in the IR and only the high-frequency portions of the rotational spectra are observed. Since these transitions involve molecules with relatively high angular velocitiek, centrifugal distortion effects will be very important. However, with a typical resolution of 0.5 cm-I, we can neglect nuclear spin hyperfine structure, which can cause splittings on the order of 0.002 cm-1. Linear Molecule (HCI) 'l'he IH rotational spectrum of HCI (Fix. 1) was measured in a 10-cmcell eoutoued . .. with Csl windowsat room temoerature and 200 rnm Hg. This spectrum was obtained with a Nicolet model 20DXB FTIR from the Fourier transform of the nmnaliz.ed sum ut' IUU interfcrugrams. The transition frequencit:~I t 1 arecharacteri~edby two parameters, Band D t4.51:
'
Current address: College of Medicine, University of Illinois. Urbana, IL6i8Ol.
OBSERVED
CALCULATED S E M I R I G I D ROTOR
R I G I D ROTOR
317
293
269
FREQUENCY
245
22 1
(CM- 1)
Figure 1. Pure ratstional spechum of HCI. Top: Experimental spemum with 200-mm Hg sample pressure at rwm temperature using a 10-cmceilwim Csl windows, 100 scans and 0.5 em-' resolution. Middle: Computer-simulated absorption profileof thecentrifugallydistartedrotor.Eonom: Rigid-rotw"stick spectrum" of natural abundance HSSCland H3'Ci. Note the isotopic splinings are only of the order 0.02 cm-'.
Volume 64 Number 11 November 1987
921
where J = 0, 1 , 2 . . . is the rotational quantum number,
B = h18rzpr;c
(2)
is the rotational cunstant and D = 4BJllo,2
(3)
is the centrifugal distortion constant, h is Planck's constant, + is the reduced mass, ra is the vibrationally averaged bond length, c is the speed of light, w, = (2ac)-'
(kl~)'"
(4)
is the harmonic oscillator vibrational frequency, and k is the Hooke's law force constant. It is evident from eq 1thatBand D can be estimated from any two of the observed transition freouencies hv simultaneouslv solvina two equations for two unknowns. These parameters may of course he determined more nreciselv" hv" carrvina . - out a least-s~uaresfit to all of the observed transition frequencies (6). Typical student results are reoorted in Table 1 aluna with literature values. Equations i-4 can be used to obtain values of the bond length, force constant, and vibrational frequency. Students may larrr compare these nwlerular propekies to those nhtained from the traditional vihmt~r~nal-rotatic,nal spectrum of HCI (1-3). The importance ofr.enrrifugnl distorttm at these high J levels ran he appreciated by coniparit~gsimulatrd ipectra mlrulated fur hoth the ririd rorur (1) = (11 and the semirigid rotor (D Z 0) as shown m Figure 1. Students are asked touse literature narameters 17) to calculate the transition frequencies and relative intensities for hoth the rigid rotor and the centrifugally distorted rotor where the relative intensities are assumed to be proportional to u3, the isotopic abundance of CP5 and Cl'" and the Boltzman populations (8). FORTRAN software is then provided to produce both the rigid rotor "stick spectrum" as well as an overall absorption profile of the centrifugally distorted rotor in which a sum of Gaussian components is computed over the digitized domain of the observed spectrum (Fig. 1).
R I G I D ROTOR
OBSERVED IR
-
Symmetric Top (NHd The suhsequent spectral expansions necessary to observe the effects of centrifugal distortion and inversion doubling on the rotational spectrum of NH3can be better appreciated by first examining the overall IR spectrum depicted in the lower trace of Figure 2. This spectrum was obtained a t 4 cm-' resolution and exhibits the 3 N - 6 vibrational modes of NH:I (two of which are degenerate (9))with their rotational fine structure. The low-frequency portionof this spectrum is greatly expanded in the upper trace and reveals a portion Table 1.
Molecular Parameters Obtalned from the Least-Squares Fit of the FTlR Rotational Spectrum of HCI
6 (cm-?
4 (~m-', re (A1 o. (cm-'1 Kldyns cm-'I
--J'
* J
Experimentala
Literature Valuesb
10.437(4) 0.00051(1) 1.2889(3) 2990130) 5.1(1)X lo5
10.4398 0.0005319 1.2867s 2990.946' 5.12436 X 10'
Obserred (cm-'1
Calculated
umbers in parenmsesrrprssentthe estimated precisiun inthe 1-1 repwedfigure. see ref. 7. iFr~mthe dtrect analysis rl the vibrational spectrum rafher m a n from a cenvifvgai
a
distortion analysis
922
Journal
of Chemical Education
2-29
ZS29
2029 WAVENUMBERS
1129
229
CCM-1)
.
Figure 2 IR SpecbLmalNH, Bonom 50-mm Hg, rwmtemp 10-cmCsl cell. 100 scans a14 0 cm-' resa ution Top Dlscrste ralat~on-lnvetsionoands are d Splayed n me expansion of me low-frequency portion 01 me speclrm and may be compared with me underlying rigid-rotor transition frequencies
of the pure rotational spectrum. Here we note that, in addition t o being significantly displaced from their rigid rotor freouencies. each feature is unusuallv broad compared with their HC1 cbunterparts in Figure 1.i n an attern& to better disclose the unresolved components of these bands, the measurement was repeated with 0.5 cm-' resolution and the J = 12 13 band is further exoanded and displayed in the top . . trace of Figure 3. It has been shown (10-12) that this fine structure is due to the combined effects of centrifugal distortion and inversion douhlina. Since we do not completely resolve the expected 2(J li = 26 components of this band, we are unable to determine the five centrifugal distortion parameters that characterize the rotation-inversion spectrum (11):
-
+
;(J,K) = 2B0(J+ 1) - (4DJ- 2F) ( J + U 3 + 6 F ( J + 115
- 2DJK(J+1 ) P + 4G(J + I ) ~+P2H(J + 1)K4
* 112 lE,,(J
+ 1 3 ) + E,,(J,K)I
(5)
where Bn is the rotational constant, D.r and DJK are the quartic centrifugal distortion cousta& issociated~withthe harmonic force field and F. G, and H are higher order constants associated with theanharmonic components of the molecular force field. Ei,, is the splitting of the energy levels due to inversion as given by Costain's formula ( 1 3 ) and J a n d K are the usual rotational quantum numbers of a symmetric top. However, it is instructive and satisfying to use literature values ( 1 1 ) of those parameters t o calculate the expected absorption profile and compare it with the observed spectrum. As in the case of HCl, students can use appropriate
The here become larger with both increasing J and K1. experimentally observed transitions and their assignments are compared with literature values (17) in Table 3. Quartic distortion constants can be calculated directly from the intramolecular harmonic force constants (18).
OBSERVED
CALCULATED PROF I LE
T@rs
= -1/2(%t%9
qy&-'
x[eAle(f i)r
