Ralph L. Arney
1968
Apparent Quadrupole Moments of Carbon Monoxide and Nitrogen and Their Librational Motion in the Liquid State Ralph L. Amey’ Edward Davies Chemical Laboratories, University College of Wales, Aberystwyth SY23 IN€, United Kingdom (Received July 3, 1973; Revised Manuscript Received April 26. 1974)
The far-infrared absorption spectra of compressed carbon monoxide a t 300 K have been measured from 10 to 100 cm-’ a t pressures up to 102 atm (1.03 X lo7 N m-2). An apparent quadrupole momeht for the compressed gas is calculated and compared with values of Qapparentfor pure CO and N2 computed from published far-infrared spectra of liquid CO and liquid Nz. I t is concluded that Q(C0) IQ(N2), which is in disagreement with previous estimates of Q ( C 0 ) .T h e molecular dynamics of liquid CO are analyzed in terms of the Larkin-modified models of Brot and Wyllie for hindered rotation. A very low barrier to molecular rotation (0.2-0.8 kJ/mol) and short dielectric relaxation (0.7-1.3 psec) and well residence times (0.7 psec) are predicted.
Introduction A number of’ papers have been concerned recently with the assessment of molecular quadrupole moments of simple molecules.’-’’Several methods, both direct and indirect, have been used. The results in many cases have been difficult to interpret due to their large experimental uncertainty and lack of agreement with other published values. The isoelectronic character of nitrogen and carbon monoxide make them worthy of comparison. Several values of the quadrupole moments of these two molecules have been reported.’ The values by Buckingham, et ~ l . are , ~generally given the most serious consideration since they have been obtained by the direct method of induced birefringence.5 , ~ reported the far-infrared spectrum of Gehbie, et ~ l . have compressed nitrogen From which Poll7 calculated a quadruesu (4.94 X 10-40 C m2) in pole moment of 1.48 X good agreement with Buckingham’s value of -(1.4 f 0.1) X IO-”’ esu (-4.7 X C m2). The far-infrared absorption technique, though an indirect one, recently has been applied by others to both polar2J and nondipolar8--IOmolecules with significant success. We present here t.he results of far-infrared studies a t room temperature on compressed carbon monoxide and the analysis of pubdished far-infrared spectra of liquid carbon monoxide and liquid nitrogen. A maximum value for the quadrupole moment of carbon monoxide is estimated, and the molecular motions in liquid CO and liquid nitrogen are discussed in terms of the Brot-Wyllie-Larkin models of hindered r0tati.m.
tional to the N p 2 terms (see Results), and the presence of this level of polar impurity increased the absorption by less than 0.5% over what it would have been if no impurity had been present. The pressure was measured on a Budenberg gauge with f1.5 X lo5 N m-2 uncertainty. Gas densities were obtained from literature values.12 All individual absorption spectra were obtained by ratioing the average of three transformed sample interferograms to the average of three transformed background interferograms. The background interferograms were obtained with the cell filled to approximately 5 X l o 4 N m-2 with carbon monoxide. Due to the high-pressure cell’s design it was not feasible to evacuate it further without movement of the quartz windows and a resultant change in path length. Results and Discussion
The transformed spectra are displayed in Figure 1. I t is assumed that the absorption intensity arises from the pure rotational contribution of the permanent dipole and from induced dipoles resulting from the dipolar and quadrupolar fields of the CO molecule. The former effect is proportional to the number density ( N ) of polar molecules and the square of their dipole moment ( p 2 ) , whereas the induced absorptions increase with N 2 . Following the treatment of Bake2 we write for the integrated intensity ( l i n t ) Iint
o ( V ) dF
=
= A,V -t A’,V2
band
Experimental Section
= A,V -1-
The far-infrared spectra were obtained by Fourier spectroscopy” using a Grubb-Parsons NPL Michelson interferometer with a Golay detector. The range of 20-100 cm-I was covered with a resolution of 4 cm-]. The variable-pathlength high-pressure sample cell which was used is described elsewhere.2 The gas, obtained from Matheson and Co., Ltd., was CP grade of nominal purity 99.5%. Total equivalent polar impurity concentration was less than 20 ppm. T o a good first approximation, the integrated absorptions were propor-
= AN
The Journal of Physical Chemistry Vol 78 N o 19 1974
+
A’
t RQ
(A,
+
A,Cd2)N2
where A P and A 4 are the temperature-dependent dipoleand quadrupole-induced integrated intensities respectively, a ( ; ) is the absorption coefficient, and the molecular quadrupole moment Q is defined4 by 8 = ],(A Clel(3z,2r i 2 ) , where the notation has its usual meaning. We have
Apparent Quadrupole Moments of GO and NZ I
1969
I
I
I
,
I
I
I
Figure 1. Far-infrared spectra of compressed gaseous carbon monoxide at 300 K: M, 16.0 f 0.1 atm N = 0.399 f 0.02 molecule ~ m - ~ A, ) ; 50.0 & 0.1 atm N = 1.24 f 0.02 molecules ~ m - ~ 0,102.0 ); f 0.1 atm (lo-'' N = 2.47 f 0.02 molecules ~ m - ~The ) . vertical lines give the frequencies and relative integrated intensities for some of the pure rotational ( J J i- 1) transitions. The dipole-induced transitions have the same frequencies and relative intensities as the pure rotational lines. The arrow indicates frequency of maximum relative integrated intensity for the quadrupole-induced ( J J 2) transitions -+
+
-+
evaluated A a t 300 K both from Gordon's sum rules1:{and J 1 transition from a summation of the individual J intensities. 14, These non-collision-broadened pure rotational line intensities are shown superimposed on the experimental spectra in Figure 1. Molecular parameters for CO used in these calculations were151i6pgas = 0.112 X esu (0.37 X lo-"(' C m) and moment of inertia 1.430 X 10-LiS) g cm2. T h e integrals in A @and AQ were evaluated using the rotational constantsi6 I3 = 1.9563 cm-' and I ) = 6.13 X lov6 cm, the mean molecular polarizabilityi7 CY = 1.95 X cm3, the Lennard-Jones parameteri8 tlk = 32.8 K (there is considerable variability in the values reported for this quantity; choice of extremum values for the calculation of Q however results in a SQ of only 0.1 X esu), and the tables of Buckingham and Pop1e.l:' A comparison of linLIN and A for pressures up to 102 a t m as well as an examination of Figure 1 indicates that within experimental error the absorption is due effectively to the permanent dipolar rotation spectrum and negligibly due to induced dipolar effects. The excess absorption a t about 92 ern--' is accepted as a foreign absorption of (inknown origin (possibly water vapor) and has been neglected in establishing the CO absorption envelopes. It has been suggested that the dip a t about 72 cm-I may be caused by incomplete cancelation of effects produced by polyethylene in the radiation path. Hence the contours are drawn and evaluated to include a maximum absorption near 70 cm-l so that QalIP i s most likely a maximum value. The current literature values1.4j7for 6)(Co) are q(CO):,, = -(2.4 f 0.3) X esu (R.0 X LO-"o C m2). Neumann and Moskowitz recently reported20 a self-consistent field MO calculation for CO which yielded a C ~ S S ( : ~ M ( ) = -2.1 X (7.0 x C m2). At 102 atm pressure, eq 1 indicates that a quadrupole moment of such magnitude would enhance the pure rotat.ional spectrum by 1&%, an increase which we do not observe. We estimate the uncertainty in our integrated ---+
+
TABLE I: Computed Coefficients of Eq I for the Integrated Absorption Intensities of Carbon Monoxide and Nitrogen
CO(g)
CO(1) N:(li
300 80 9 76 4
2 02 2 04
167 1 49
2 83 2 39 5 34
absorption as no more than f 7 % , a value which allows an undetected value of Q a p p _i 1.5 x 1o-"j esu (5.0 x 10-4~)C m2). Since the quadrupolar contribution to the intensity increases with N', we might expect an enhanced absorption in the liquid. Jones" has reported t.he far-infrared spectra of several liquefied gases including nitrogen and carbon monoxide. We have computed the ini,egrat,ed absorption intensities for both liquids as well as the appropriate conslants for eq 1 a t the reported liquid temperatures. T h e computed values are listed in Table I. For nitrogen the molecular parameters used were R = 1.961 ern-.', I1 = 5.8 x cm, I = 1.427 X 1 0-:'9 g cm2,u~~~~~~~ = 1.76 X 1 cm:{, clk = 47.6 K. For liquid nitrogen then, the data yield an apparc.nt quadrupole moment of Q(N,);,,,,, = (0.8 & 0.1) x esu (2.7 X C m2). 'This value is only about half that reported from compressed gas resultSi Such a reduction i n total ahsorption from that expected on the basis of pure dipolar and binary interactions may be credited to a partial cancelation by multibody interactions in the liquid; this is due to the increased symmetry of the inducing electric fields present a t high densities.": A similar effect has been observed in nitrous oxide.' From the spectrum of liquid CO, a similar calculation esu (1.3 X C yields Q(CO),,, = (0.4 f 0.3) X m2). This leads us to suggest that the upper limit for Q ( C 0 ) obtained from our compressed CO spectra may he a maxiThe J o i i r n a l o t Physical Chemistry V o : 76 ko 79 1974
1970
TABLE 11: Molecular Dipole and A p p a r e n t Q u a d r u p o l e M o m e n t s of C a r b o n Monoxide and N i t r o g e n
Ralph L. Arney
TABLE 111: Brot and Wyllie Parameters for Liquid Carbon Monoxide at 80.9 K _ _ l l _ l l _ _
W/2)-
V,*-d kJ mot-’
Model
Rrot“ Wyllie‘
0.81 0.20
kT, 10-12
r
sec
WO,
‘ri,
T ~ ,
10-12
10-12
sec
iiec
0.7 2.0
0.3
~ i ,
10-12 radians sec e-’
0.5
1.3
9.1 5.3
’
mum one. Indeed ie. appears that Q(CQ) 5 Q(N2) and the best estimate for Q(C0) may be as small as (0.8 f 0.4) X IOvz6 esu [(3 k 1) X G m2]. (See Table 11.) Although i t would be anticipated that the short cylindrical CO molecule wouitl have little hindrance on rotation in the liquid state, infrared spectra have provided some evidence o f the barrier involved.23The small dipolar and quadrupolar fields of the molecule would imply small disperson barriers of the order of 800 J/mol or less. Ewing has a barrier energy of approximately 500 J/mol for rotation a t 80 K. We have applied the librational models of Brot and of Wyllie-as adapted by Larkin25-to liquid CQ. T h e theoretical curves have been normalized to the a(max) of the experii-nental ciirve of the liquid and the results are shown in Figurc 2 and Table 111. Both models assume a central librating molecule with a coordination number which defines the angular aperture of the energy well containing the librator. Well definition and depth are then determined through parameters chosen to fit the observed spectrum. Ewing has suggested on the basis of infrared spectra that many of the molecules in liquid CO may experience an envirormenl- approaching that of hexagonal close packing, similar to that of the solid phase.24 Neither model reproduces satisfactorily the experimental data over the entire frequency range, Adjustment of the parameters of the WyIlie nnodel gives a somewhat improved fit with w&nax) = 53 >( 10l1 radiandsec ( 2 8 cm-l), although the calculated quadmpole absorption maximum occurs at 91 x 1011 radians/sec (48 cm-l). The Brot model incorporating the latter valiie of w&nax) (which represents the librational frequency not seen as a separate center in the absorption) does not give a good a fit as the Wyllie model: its halfwidth i s too large and its high-frequency tail falls well below observations. T h e experimentally observed absorption maximum varies with choice of half-angular aperture (t;) at constant t? and provides a better fit a t 0.75-correspondilrg to eight nearest neighbors-than a t a coordination number of 10 ( E -I 0.64) found suitable for the Wyllie rrsodei. A very low barrier to rotation is exhibited by both models: V = 0.2-Q.8 kJ/mol. This can be compared with the distinctly larger barriers found for quasispherical molecules of larger electric moments ( p = 2 D) such as 2,2-dichloroprnpane (CH3CClzCH3), 3-6 kJ/mol, and 2-chloro2-nitropropane ~ ~ ~ 3 ~ C ~ N 7-8 QkJ/mol, ~ C ~or3 for ) the slightly polar ( p = (I.’?$ D) but distinctly anisotropic propyne (CFI$%CM), 5-4 kJ/mol. The lower value for liquid CO is consistent with its smaller dipole ( p = 0.12 D) and its closer approximatlm l o spherical symmetry (length/diameter = 1.3). It is also ohserved that the time between weak thermal coliisions (T,) is about the same as the duration of a jump from one well to another ( T J and about half the time spent while residing i.1 a potential well ( T ~ ) .This is consistent with relaxation 31 mechanisms proposed by correlation function anal yshs o f simple Although the Debye The .loiirnal of Physical Chernislry. Voi. 78 No. 19. 1974
t: = 0.75 radians. TLD1.22, calculated from the Lorentz-Lorenz equation, the mean po!arizability,’7 and the liquid density a t 80.9 K, p = 0.793 g cm-3 (“Handbook of Chemistry and Physics,” 49th ed, Chemical Rubber Co., Cleveland, Ohio, 1968-1969). e E , = nD2 = 1.480. EO = 1.481, estimated from the Clausius-Mossotti equation; = 0.1.12 D, and the parameters of footnote b apply. Coordination number 10.
‘4
L
Lu
a
.I
$ i 1
!
50
100
I
F 50
200
I
i. Ern-’ )
Figure 2. Far-infrared spectra of liquid carbon monoxide at 80.9 K: 0 , smoothed experimental data from ref 21: A,data computed from Brot model; B, data computed from Wyllie model. The arrow indicates frequency of maximum relative integrated intensity for the quadrupole-induced(J-+ J 4- 2) transitions.
relaxation time (TD)for liquid CO has not been experimentally determined, the Brot model predicts T D w T,. sz 0.7 psec and the Wyllie model a value of similar magnitude: T D sz ({/2)FzT cz 1.3 psec. We found that efforts to improve the fit of these models did not lead to significantly different computed quantities. Whether such models lead to physically correct molecular parameters is still an open question.27 A further means of aFalyzing liquid data is in terms of the classical free rotational envelope, an expression for which has been derived recently by Brot2*
where
w
= 2nCc and I is the moment of inertia perpendicu-
Relaxation Times of Fourier Transform N m r lar to the axis containing the dipole mdment. This function has a maximum a t 2aumaxc= (3kT/Z)"* which can be compared with the experimental i&&Such a calculation for liquid CO yields v,,,(calcd) = 26 cm-I and b,,,(exptl) = 35 cm-' which suggests that molecules of CO in the liquid state are largely freely rotating. Thus these models are given qualitative support in that the resultant parameters are consistent with our expectations for the behavior of simple liquids: a very shallow potential well, a short dielectric relaxation time, and brief well residence times.
Acknowledgments. The author wishes to thank Professor Manse1 Davies for suggesting the problem, for many helpful discussions, and for a critical reading of this manuscript. He is indebted to M. Evans for invaluable assistance with preliminary measurements and to A. Baise and I. Larkin for the use of their programs. He is also pleased to acknowledge the hospitality and assistance of the University College of Wales Chemistry Department and staff during his sabbatical stay.
1971 A. D. Buckingham. Quart. Rev., Chem. Soc., 23, 183 (1959). H. A. Gebbie, N. W. B. Stone, and D. Wiiihms, Mol. Phys., 6, 215
(1963). J. D. Poll, Phys. Lett., 7, 32 (1963). D. R. Bosomworth and H. P. Gush, Can. J. Phys., 43, 751 (1965). A. Rosenberg and G. Birnbaum, J. Chem. Phys.. 52, 683 (1970). J. E. Harries, Roc. Phys. Soc.. London(At. Mo/. Phys.). 3,704 (1970). K. D. Mbller and W. G. Rothschild, "Far-Infrared Spectroscopy," WileyInterscience, New York, N. Y.. 1971. (a) E. P. Bartlett, H. C. Hetherington, H. M. Kvalnes, and T. H. Tremearne, J. Amer. Chem. Soc.,52, 1374 (1930);(b) Nat. Bur. Stand. (U. S.),Circ., No. 564, 219-236 (1955);"Matheson Gas Data Book," 5th ed, The Matheson Co., East Rutherford, N.J.. 1971,p 105. R. G. Gordon, J. Chern. Phys., 38, 1724 (1963). C. H. Townes and A. L. Schawlow. "Microwave Spectroscopy," McGraw-Hill, New York, N. Y., 1955. R. D. Nelson, D. R. Lide. and A. A. Maryott, Naf. Stand. Ref. Data Ser., Mat. Bur. Stand., No. 10 (1967). G. Herzberg. "Spectra of Diatomic Molecules" 2nd ed; Van Nostrand, New York, N. Y., 1950. H. A. Stuart, "Moiekulstruktur," Voi. 3, Springer-Verkig, West Berlin, 1967,p 35. J. 0. Herschfelder, G . F. Curtiss, and R. 8. Bird. "Molecular Theory of Gases and Liquids," Wiley, New York, N. Y., 1954. A. D. Buckingham. J. A. Pople, Trans. Faraday SOC..51. 1173 (1955). (20) D. 8. Neumann and J. W. Moskowitz. J. Chem. Phys., 50, 2216 (1969). (21)M. C. Jones, Nat. Bur. Stand. (U.S.),Tech. Note. No. 390 (1970). (22)G. Birnbaum, W. H6. and A. Rosenbwg, J. Chem. Phys.. 55, 1039
On sabbatical leave from Department of Chemistry, Occidental College, Los Angeles, Calif. 90041. (1)S. Kielich in "Dielectric and Related Molecular Processes," Vol. I, The Chemical Society. London, 1972. (2)(a) A. I. Raise. J. Chem. Soc.. Faraday Trans. 2, 68, 1904 (1972); Chem. Phys. Left.. 9,627 (1971);(b) A. Rosenberg and I. Ozier. ibid.,19
(1971). (23)G. E. Ewing. Accounts Chem. Res., 2, 163 (1969). (24)G. E. Ewing. J. Chem. Phys., 37,2250 (1962). (25)R. Haffmans and I. W. Larkin. J. Chem. Soc., Faraday Trans. 2,68, 1729 (1972). (26)R . Gordon. J. Chem. Phys.. 43, 1307 (1965). (27)A molecular dynamic method was used recently by J. Barojas, D, Levesque, and B. Quentrec, Phys. Rev. A, 7 , 1092 (1973),to simulate the
400 (1973). (3)M.Evans. J. Chem. SOC.,faraday Trans. 2. 69,763 (1973). (4)A. D. Buckingham, R.L. Disch. and D. A. Dunmur, J. Amer. Chem. SOC., 90,3104 (1968).
behavior of liquid nitrogen. The reorientational self-correlation functions were found to predict well residence times of the same order of magnitude as those reported herein. (28)A. Gerschel. I. Darmon. and C. Brot. Mol. Phys. 23.317 (1972).
References and Notes
Optimal Determination of Relaxation Times of Fourier Transform Nuclear Magnetic Resonance. Determination of Spin-Lattice Relaxation Times in Chemically Polarized Species' Kenner A. Christensen, David M. Grant,** Edward M. Schulman, and Cheves Walling' Department of Chemistry, University of Utah, Salt Lake Cify, Utah 84 1 12 (Received February 2 1, 1974) Publication costs assisted by the National Institutes of Health and the National Science Foundation
The optimal conditions for determining the spin-lattice relaxation times using Fourier transform techniques are discussed and the method which has been applied to polarized species produced by chemically induced dynamic nuclear polarization (CIDNP) has been developed. A number of T I measurements on the polarized products of benzoyl peroxide decomposition have been made from which carbon-13 CIIINP enhancement factors are determined.
I. Introduction In order to use chemically induced dynamic nuclear polarization as a probe to study the details of free-radical reactions, quantitative data on the enhancements of the polarized nuclei are often required. Since the observed enhancement is directly dependent on the spin-lattice relaxa~ method tion time, 7'1, of the polarized n u ~ l e u s , : a' ~reliable of measuring 7'1 values of such species in the most efficient
manner is essential to these studies. The use of Fourier transform methods provides a method for fast, accurate measurement of T I values of polarized nuclei i n a system undergoing chemical reaction providing optimal conditions are selected for the experiment. The T I value for polarized species arising from thermal decomposition may be measured by the yecovery of' polarization from saturation.5 In a photochemical reaction, T I The Journalof Physical Chernistrv Vol 7 6 No 79 1974
