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Evidence for ν5, ν3+ν6 Fermi Resonance in Methyl IodideFrank D. Verderame and Eugene R. Nixon Citation: The Journal of Chemical Physics 45, 3476 (1966); doi: 10.1063/1.1728148 View online: http://dx.doi.org/10.1063/1.1728148 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/45/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Resonance Raman excitation profiles of methyl iodide in hexane J. Chem. Phys. 98, 21 (1993); 10.1063/1.464668 Cold jet infrared absorption spectroscopy: Fermi resonance in the ν5/2ν8 bands of PF5 J. Chem. Phys. 82, 3879 (1985); 10.1063/1.448977 Detailed analysis of ν5 of CH3I: Fermi and Coriolis resonances with ν 3 +ν 6 and ν2 J. Chem. Phys. 59, 1449 (1973); 10.1063/1.1680202 Fermi Resonance in the System 2ν 4 ,ν 4 +3ν 6 of Methyl Chloride J. Chem. Phys. 57, 2587 (1972); 10.1063/1.1678628 Vibrational Exciton Splitting, Fermi Resonance, and Crystal Structure of Methyl Iodide J. Chem. Phys. 44, 3547 (1966); 10.1063/1.1727263
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3476 LETTERS TO THE EDITOR J. CHEM. PHYS., VOL. 45, 1966
c= L oM ggH(Pg2), have been defined previously. An analysis of these transitions using Eq. (1) shows that the differences between the observed tlF=O transitions are dependent only on (MbbH-MccH) and R which is the proton-proton distance. The resultant analysis of the three transitions gives MbbH-MccH= -2.5±0.6 kc/sec and R=1.88XlO-s cm which agrees with the known structure.a,4 Combining MbbH-MccH= -2.5 kclsec with an earlier estimate of MbbH+ MccH = 5 kc/sec from an analysis of the H magnetic shieldingS
gives MbbH=1 kc/sec and MccH=4 kc/sec, which are analogous to the values in H2CO.7
The 31a-->312 transition in ketene-d1 is shown in Fig. 1 (b). This spectrum is interpreted on the basis of a In+ ]=Fl, IH +F1=F coupling scheme with the energy levels being given by Eq. (3) of Ref. 7. The spin-spin and spin-rotation parameters from the above analysis on ketene are used in the present analysis with the appropriate changes made for the different g value of the deuteron. The new parameters are the deuteron nuclear quadrupole coupling constants and the transition given here is dependent only on Xbb-Xcc as in ketene-d2.8 The resultant analysis of the transition is straightforward and the result is xbb-xcc=240±15 kc/sec.
A high-resolution trace of the 313-->312 transition in ketene-d2 is shown in Fig. 1 (a) where the improved resolution with the larger sized waveguide1,2 (L band) used here is evident when compared with our earlier works with a smaller waveguide (S band). This is direct evidence of the importance of wall collisions, as in the earlier work the tlF=O, F=2 and F=4 transitions were not resolved and they are completely resolved in Fig. 1 (c). The coupling scheme and analysis used here is identical to that used in D2C07 and the above values of the spin-spin and spin-rotation con· stants were again included in this analysis. Using Eq. (2) of Ref. 7 gives the value of Xbb-xcc=246±5 kc/sec.9 As the rotation of the principal inertial axes from ketene-d2 to ketene-d1 is only about 10 (compared to over 50 in the analogous H2CO system) we would expect the value of Xbb-Xcc in ketene-d2 to be nearly equal to the value in ketene-d1 as is found in this work. Assuming Xaa is near zero as discussed befores and that the field gradient tensor in the C-D bond axis system is cylindrically symmetric (as in H2CO) allows a determination of quadrupole coupling constant along the C-D bond axis in ketene. The result is Xbond = 240±20 kc/sec which is larger than the value of 170 kc/sec found in formaldehyde. The increase in Xbond
agrees well with the increase in the C-D force constants from H2CO to ketene and the linear relationship relating the force constant to the deuteron field gradient as given by Salem.8,10
* Present Address: Central Research, Monsanto Chemical Co., St. Louis, Mo.
t Alfred P. Sloan Fellow. 1 V. W. Weiss, Ph.D. thesis, University of Illinois, 1966.
2 M.-K. Lo, V. W. Weiss, and W. H. Flygare, J. Chern. Phys. 45, 2439 (1966).
3 R. B. Lawrence and M. W. P. Strandberg, Phys. Rev. 83, 363 (1951).
4 H. R. Johnson and M. W. P. Strandberg, J. Chern. Phys. 20, 687 (1952).
• H. Takurna, J. Phys. Soc. Japan 16, 309 (1961); P. Thoddeus, J. Loubser, L. Krisher, and H. Lecar, J. Chern. Phys. 31, 1677 (1959).
6 D. W. Posener, Australian J. Phys. 11, 1 (1958). 7 W. H. Flygare, J. Chern. Phys. 41, 206 (1964). 8 W. H. Flygare and V. W. Weiss, J. Am. Chern. Soc. 87,5317
(1965) . 9 Our earlier analysis of the lower-resolution spectrum in Ref. 8
gave 120 kclsec for Xbb-)(oc' However, in deriving the reduced energy expression an extra factor of 2 was included in the expression for two equivalent nuclei. The correct coupling constants for each nucleus are therefore twice the values given and the correct energy expressions are given in Ref. 7.
10 L. Salem, J. Chern. Phys. 38,1227 (1963).
Evidence for V6, Va + V6 Fermi Resonance in Methyl Iodide*
FRANK D. VERDERAME
Pitman-Dunn Research Laboratory, Frankford Arsenal Philadelphia, Pennsylvania
AND
EUGENE R. NIXON
Department of Chemistry and the Laboratory for Research on the Structure of Matter, University of Pennsylvania
Philadelphia, Pennsylvania
(Received 17 June 1966)
THE quartet of peaks in the V6 region of the infrared spectrum of polycrystalline films of CHaI, first re
ported by Dows,1 was originally interpreted by Hexter2 as due to a correlation field, or factor-group, splitting superimposed upon a much larger site-group splitting of this doubly degenerate CHa deformation mode. Kopelmana has now given a convincing argument that any site-group splitting is probably very small, and the four observed peaks result from two Fermi-resonant vibrations, V6 and va+v6, each of which is split into a pair by the factor-group effect. In the case of CDaI, in which this Fermi resonance is not of any significance, the V6 region exhibits only the two peaks given by the factor-group splitting of the fundamental.
We have made certain observations which lend strong support to the Kopelman interpretation. First, studies, more extensive than those previously reported, of the spectra of polycrystalline films of CHaI-CDaI mixtures are shown in Fig. 1. (Spectra were recorded on a Perkin-Elmer 521 spectrophotometer.) The spacings between the components of each pair of CHaI peaks decrease with increasing dilution until in the film with composition 15% CHaI-85% CDaI, the spacings (2.4 and 2.0 cm-1) are just about half as great as in pure CHaI (4.6 and 5.8 cm-1). A corresponding effect is observed with CDaI in which the spacing decreases from 10.0 cm-1 in pure CDsI to 5.1 cm-1 in the 15%
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J. CHEM. PHYS., VOL. 45, 1966 LETTERS TO THE EDITOR 3477
~ fCL 0: o (J) m «
I
- -- --------MOLE % CH,l
15
'~------~:~C:-;;-;C;-;-l
~50
~
~ , "' '" co
fS
33{-
15
'~----;I-;Ccd3O;-;5C-----C:ld-;C:25-;C-----:14,,;;112;----;-;;141~OO~-------'------:I~04o;;O;---~IO'co30-;:---~· ~_.J
FREQUENCY (CM-')
FIG. 1. Infrared spectra of the 1'6 regions of CHaI-CDsI mixtures as polycrystalline films of various thicknesses at SooK.
CDaI-85% CHaI film. These observations are consistent with the expectation that isotopic dilution would significantly affect the intermolecular factor-group splitting.
The alternative explanations for the larger spacing between the centers of the two pairs of peaks in CHgI are site symmetry splitting and intermolecular Fermi resonance. It can be seen that this spacing remains almost exactly constant at 23.7 cm-I,~independent of dilution. Substitution of CDaI molecules into the lattice should produce only a minor change in the static field at the molecular site and hence little effect upon site symmetry splitting. On the other hand, the work of Strizhevsky4 and others indicates that large effects upon Fermi resonance might result from the environmental change produced by isotopic dilution, particularly if the molecular interactions involved transition dipoles.
The results of the matrix isolation experiments with argon and nitrogen, however, provide proof that the larger splitting is due to Fermi resonance. Figure 2 shows that CHgI exhibits two peaks in the V5 region
whereas CDaI exhibits only one, clear evidence that the peaks in CHaI result from an intramolecular effect.
If, in the absence of any Fermi resonance, the combination band va+V6 has negligible intensity, then according to first-order perturbation, the ratio R of observed intensity of the lower frequency member of the Fermi dyad (ve) to that of the higher frequency one (VI) is given by6
(1)
in which 0 is the separation of the unperturbed vibrational energy levels, vco and vl, and the separation D of the perturbed levels is related to the Fermi interaction energy Wei:
(2)
In the pure CHaI crystal, ve=1399 cm-I , vI=1423 cm-I, D=24 cm-I, and R~1. It follows that veo~vl~ 1411 cm-I, and Wei = 12 cm-I .
In the case of the argon matrix, for example, Vc= 1399 cm-I, VI = 1432 cm-I, D =33 cm-I, and R~t. Thus veo=1405 cm-I, vl=1425 cm-I, and WcJ=13 cm-I .
---~---------------'MJL=-ECR"'ACiCTI"'O-T----~---MOLE RAm
z Q f-
FIG. 2. Infrared spectra of the P6 regions ~ of CHsI and CDs! examined in argon and ~ nitrogen matrices at about lOoK. <l
1440 1430 1420 1410
CH,IIA, CY N, CD,!! A, 1/200 Ar 1/657 Ar
1/200 N2
1/664 N,
1400
FREQUENCY (CM-')
1390
1/200
1050 1040
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3478 LETTERS TO THE EDITOR J. CHEM. PHYS., VOL. 45, 1966
The results of these approximate calculations show that the Fermi interaction energy is nearly the same in pure crystal and matrix but that a frequency shift of about +14 cm-1 occurs in the unperturbed V5 level upon going from pure crystal to the matrix case. This frequency shift compares favorably with the + 11 cm-1
change observed for 1'5 in CDaI between pure crystal and argon matrix.
* Supported by the Advanced Research Projects Agency under Contract SD-69.
1 D. A. Dows, J. Chern. Phys. 29, 484 (1958). 2 R. M. Hexter, J. Chern. Phys. 33, 1833 (1960). 3 R. Kopelman, J. Chern. Phys. 44, 3547 (1966). 4 v. L. Strizhevsky, Opt. Spectry. 8, 86 (1960). 6 G. Herzberg, Infrared and Raman Spectra of Polyatomic Mole
cules (D. Van Nostrand Co., Inc., New York, 1945), p. 215.
On the Liquid Self-Diffusion Coefficient Behavior in the Vicinity of Critical Point
A. P. WATKINSON AND J. LIELMEZS
Chemical Engineering Department, University oj British Columbia Vancouver 8, British Columbia, Canada
(Received 8 July 1966)
THERMODYNAMIC and transport properties of certain liquids are known to show quantum ef
fects-for example, reduced molar volume has been correlated with the square of the deBoer parameter A * = hj (mECT2) 1 (m, e, and CT measure the mass, potential well depth, and collision diameter, respectively) in the
quantum theory of corresponding states. However, attempts to fit reduced transport properties (for instance, diffusivity of several liquids to a corresponding-states equation D*=j(T*, P*), where D*=(DjCT)(me)!, T*=kTje, P*=(PCT)3je are the reduced diffusivity, temperature, and pressure, respectively) have met with only a partial success. In particular, Naghizadeh and Rice2 found that methane would not fit the same equation as the liquefied noble gases.
Reassessment of the available liquid self-diffusion data at the critical-point vicinity [Fig. lea), Table IJ presents, however, evidence of the possible uniqueness of a corresponding-state relation. It is striking that the cross sections of molecules largely determine the diffusivity-square of the deBoer parameter correlation. The correlating line is strongly curved, and, therefore, one could suspect that a linear extrapolation of constant activation energy of InD-vs-T-l curves converging to a common value as suggested by Douglass and McCall· underestimates the value of the self-diffusion coefficient at the critical point. This argument is further substantiated by recently shown4 strong positive temperature dependence of the activation energy. Therefore, points for n-hexane and n-nonane [Fig. 1 (a)] which were estimated using proposed Douglass and McCalP method are probably in error.
Similarly, plots [Figs. l(b) and l(c); Table P-12] of J.lcCT and kcCT(fJc is viscosity and kc is thermal conductivity of the critical point, respectively) versus square of the deBoer parameter corroborate the evidence as given by Fig. 1 (a).
TABLE 1. Summary of data.
Compound Ejk (OK)
Methane 144
Ethane 236
n-Propane 206
n-Butane 208
Neopentane 236
n-Hexane 423
n-Nonane 240
Argon 122
Carbon 100.2 monoxide
Carbon 150 dioxide
Nitrogen 91.5
Carbon tetra- 327 chloride
Benzene 308
a Extrapolated.
IT X 108 Reference (em)
3.796 1 (b)
4.384 l(b)
5.24 l(b)
5.869 l(b)
7.37 9
5.916 l(b)
8.448 1 (b)
3.40 l(b)
3.76 l(b)
4.07 l(b)
3.681 l(b)
5.881 5
6.9 1 (b)
106 De Reference 106 }ic Reference (cm2/sec) (gjcm.sec)
63 6
11.4 7
48.3 8
159 5
210 10
237 10
245 10
248 5
265 5
264
190
180.5
5
5
5
413 5
312 5
106ke
(caI/cm. sec·oK)
158
123.8
123.8
71
86.5
122
86.8
Reference
5
11
12
5
5
5
5
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