Determination of quadrupole moments of light hydrocarbon molecules from rotationally inelastic state to state scattering cross sections

Chemical Physics 52 (1980) 39-46

@ North-Holland Publishing Company

DETERMINATION OF QUADRUPOLE MOLECULES FROM ROTATIONALLY SCATTERING CROSS SECTIONS Gerhard

MEYER

Max-Planck

and J. peter TOENNIES D-3400

Institut fir Str5mungsforschlmg.

MOMENTS INELASTIC

OF LIGHT HYDROCARBON STATE TO STATE

Giftingen. FRG

Received 25 February 1980

A new method fo: determining quadrupole moments from measurements of rotationally inelastic cross sections was recently introduced by Borkenhagen et al. This method is based on the observation that the magnitude of the cross section for the rotational transition (j, III)= (2,O)+ (3.0) of CsF in forward scattering is found, in agreement with the Born approximation, to depend linearly on the quadrupole moment of the target molecule. In the present paper we report on the determination of quadrupole moments for the following hydrocarbons: C2H2, CrH4, C3H1

(methylacelylene), C,H,, C3H8. &HI (butadiene). C4H8 (I-butene) and CJHg (isobutene), most of which have not been studied previously. The neiv results are compared with estimates based on a simple bond dipole moment model.

1. Introduction Molecular quadrupole moments are important for understanding molecular interactions in the gas, liquid and solid phase [l]. In addition they provide valuable insight into the electronic structure of molecules [I]. Despite considerable experimental effort, no completely reliable and universally applicable method of measuring quadrupole moments has been devised. As reviewed in 1966 [3] the available methods utilize either (i) the interaction of the molecule with a magnetic field (anisotropic susceptibility method), (ii) with a radiation field (induced optical birefringence method) or (iii) with another particle (second virial coefficient, spectral

line broadening etc.). The first method relying on microwave spectroscopy now provides very accurate data [4], but is limited to polar molecules. In the last method, which is universally applicable, kinetically averaged bulk quantities are analyzed in terms of intermolecular poten-

tials. More accurate information should thus be available from direct measurements of the underlying cross sections in scattering experiments.

In recent

years measured

cross sections

for the scattering of metastable atoms [5], ions [6] and polar molecules [7] have been suggested and tried in attempts along these lines. Probably the best results were obtained using polar molecules as probe molecules. In this method, on which the present work is based, the absolute inelastic cross section for the following process

is measured:

CsF( j, 172)+ M -+ CsF( j’, r7z‘) -i M,

(1)

where (j, m) and (j’, m’) denote the rotational quantum states (2,O) and (3,O) and M, the target molecule.whose quadrupole moment is to be determined. The conditions of the experiment are such that only small angle scattering is observed. The cross sections are measured at a collision energy of 80-150 meV. In agreement with predictions based on the Born approximation, the cross sections are directly proportional to the quadrupole moments. This was confirmed for Nz, CO, CO?, NaO and CiH2 using the

recommended quadrupole moments of Stogryn and Stogryn [8]. Once calibrated, the cross sections for other molecules are used to determine their quadrupole moments.

The paper briefly describes the apparatus, and the theory in the first two sections. The new results are presented and analyzed in the following section. The paper closes with a comparison with quadrupole moments estimated from bond dipole moments.

estimated error in the P

2. Apparatus The apparatus used to measure scattering cross sections of the type given by eq. (1) has recently been described in considerable detail [7] and is shown schematically in fig. 1. An electrostatic quadrupole field is used to focus, for example, only molecules in the (j, m) = (3,O) state out of a rotationally cold (T,,, = 10 K) seeded beam of velocity selected (v = 550 m/s; u/v = 2.9% nominal) CsF on to a target nozzle beam of molecules M. In the scattering region the CsF molecules are oriented by a weak electric field (300 V/cm) which is perpendicular to both the CsF velocity and the velocity of the target beam. Those CsF molecules which are scattered through small angles are accepted by a second quadrupole field which serves to focus only molecules in the final state (j, m) = (2.0) on to a hot wire surface ionization detector. With the aid of a dynamic expansion method the absolute flux of target gas in the target nozzle beam is measured. From the angular distribution of the target beam the absolute

skimmer and state sE~tap

0.4 X0.7 mm21.

3.

Data evaluation

The cross section meared tn the wmus is related to the di&erentral rnelas~~ xa~~a~wg cross section d’a/d’w by the express&~

where a is the most probable value of the r&ative velocity (~=[l~~~l’+6r+,+?]~” and vrbl B the apparatus transmission functmn. =brcR describes the overall collectjon effictency nf Fk apparatus as a function of the ~~t~cnng an& d in the center of mass system. 7161 ~5 obta~nrd Carlo anal>ws of trajcctom25 passing through the qu&rup&e t&&s and apertures 171. ~(6) has a maximum at 6 = 0 and Q typical half width M&, = 1.2 x IO-’ been fitted to an analytical ex d2c/d20 is known as a function d quadrupole moment eq. 42) can be in obtain a cross section for mmpar&m experiment. from a Monte

SIDE

VIEW

END

;l;WOF

SCATTERlNG REGION

Fig. 1. Schematic drawing of state selection apparatus used for measuring absolute cross sections for state-to+tate rotational trnnsitions of polarized CsF molecules scattering rhrough small angles. In the scattering region the electric lield direction of polarization is perpendicular to the relative velocity. Trajectories indicate that the incident beam of molecules in the rotational state (j, m)= (3,OJ is analyzed after scattering by a second quadrupole field which Focuses only molecules in the new state (2.0) on IO the detector.

4. Theory A number of approximattim are mtr in order to calculate d’c7/d’w“l .I’*’ ’ “’ The-se ;ese

o. Meyer, J.P. Toennies [ Ouadrupote moments of light hydrocarbon molecules necessary since at t h e p r e s e n t time n o completely satisfactory t h e o r y for calculating differential cross s e c t i o n s for m o l e c v ! e - m o l e c u l e collisions is available. T h e situation it, this respect is a n a l o g o u s t o t h e theoretical interp r e t a t i o n o f miCroWave l i n e b r o a d e n i n g e x p e r i m e n t s w h i c h are b a s e d o n t h e A n d e r s o n T s a 0 , C u r n e t t e t h e o r y [9]: The theoretical a p p r o a c h is similar; b u t since the Collision process is specified in a m u c l l m o r e d e t a i l e d way; fewe r a n d m o r e justifiable a p p r o x i m a t i o n s a r e possible, F o r o n e w e n o t e that in the p r e s e n t case we n e e d o n l y calculate t h e s c a t t e r ing cross section b e t w e e n two completely specified r o t a t i o n a l states, w h e r e a s in the t h e o r y of microwave line b r o a d e n i n g all the inelastic cross sections i n v o l v i n g t h e initial and final states in the m i c r o w a v e spectral transition m u s t b e accounted for. Since t h e theory for the differential cross s e c t i o n s used here is d e s c r i b e d in detail e l s e w h e r e [7], we only list and c o m m e n t briefly o n t h e i m p o r t a n t a p p r o x i m a t i o n s : (1) T h e p o t e n t i a l is d o m i n a t e d by the d i p o l e q u a d r u p o l e e l e c t r o s t a t i c interaction. T h e assumption is implicit in all e x p e r i m e n t a l m e t h o d s of type (iii) a b o v e . In the p r e s e n t ezperiments, t h e c o n d i t i o n s are especially favorable b e c a u s e of t h e large dipole m o m e n t of CsF (/t = 7.878 D ) a n d t h e fact that m o l e c u l e s with ./= 2 have a r o t a t i o n a l period (r--- 10 -~° s) which is long c o m p a r e d with the collision t i m e (t --- 2 R o / g = 10 -~z s, w h e r e Ro is the r a n g e of interaction). M o r e o v e r , only small angle collisions are p r o b e d a n d the effect of the repulsive p o t e n t i a l is e x p e c t e d to b e negligible. This has b e e n c o n f i r m e d b y calculations [10]. (2) Inelastic t r a n s i t i o n s of t h e target m o l e c u l e are not explicitly c o n s i d e r e d . T h e o r i e n t a t i o n a v e r a g e d i n t e r a c t i o n with t h e target m o l e c u l e q u a d r u p o l e is a c c o u n t e d for by a W i g n e r E c k a r t matrix e l e m e n t a s s u m i n g rotationaily elastic transitions. In fact we d o also expect s o m e rotational t r a n s i t i o n s to occur in the t a r g e t molecules b e c a u s e of t h e i r low rotational t e m p e r a t u r e s ( T = 10 K). H o w e v e r , since the target rotational c o n s t a n t s (e.g. for N: B = 0.2431 m e V ) are large c o m p a r e d with B = 0 . 0 2 2 9 m e V [11] f o r C s F a n d because of t h e

smaller t o r q u e p r o d u c e d by the q ~ a d r u p o l e m o m e n t c o m p a r e d with t h a t produced by tile dipole m o m e n t we expect the target transition probabilities to b e small c o m p a r e d with those of CsF. M o r e o v e r , since in d e t e r m i n i n g the q u a d r u p o I e m o m e n t s only t h e relative cross sections are c o m p a r e d , t h e only assumption which e n t e r s is t h a t all the target molecules h a v e on the a v e r a g e t h e s a m e inelastic behavior. (3) The inelastic t r a n s i t i o n probability Pt2"°~'t~'°~(b) of t h e C s F molecule for a given impact p a r a m e t e r b is calculated in first o;'dcr using the B o r n a p p r o x i m a t i o n . This a s s u m p t i o n is certainly true f o r m o s t of the small angle collisions a c c e p t e d b y the second rotational state analyzer b e c a u s e of the large impact p a r a m e t e r s a n d w e a k long r a n g e interaction. F o r some collisions with the largest scattering angles, which are collec'.ed with a smaller probability, this a s s u m p t i o n m a y no longer bc valid. Errors from s m a l l deviat;ons from the B o r n a p p r o x i m a t i o n are ,=or expected to b e serious since the m e t h o d relies only on the comparison of relative cross sections. (4) To calculate t h e small angle differential cross sections a d d i t i o n a l assumptions are needed. F o r o n e we a s s u m e t h a t the transition probability can b e r e l a t e d to an angular d e p e n d e n t transition p r o b a b i l i t y P ~ f ( 6 ) using ~he small angle classical deflection function. This is certainly a good a p p r o x i m a t i o n because of t h e relatively large m a s s e s (small de Broglie wave lengths) of the i n t e r a c t i n g particles and has b e e n tested by t.omparison with m o r e accurate ~,'attering calculations [12]. In addition we assume t h a t the inelastic cross section can be factor::d: (d2o'i~f/d2oJ)(~9)= Pi~f{tg)(d2o'ez/d'-to)(~9).

!3)

w h e r e d'-o-~t/d2to is t h e elastic differential cross section also calculated by a small angle classical approximation. I--ter¢~ t h e interaction leading to elastic deflection is also assurried to come from the d i p o l e - q u a d r u p o l e forces. With these a s s u m p t i o n s we find that the differential cross s e c t i o n is given by (d2o i-f/d2to)(O) = trlo-S,tgo i (6/tgo)- 1,

,,!!

G. Meyer, .I.&?Toennies / Quadrupole moments of lighthydrocarbon molecules

and where ,urcd is the reduced mass of the collision partners. & is an arbitrary reference angle typically equal to lo-'rad: Thus &‘80’ is the magnitude of the inelastic differential . cross section at the reference angle 40.’

5. Experimental results Table 1 piesents the measured results for the absoIute cross section u~~~‘-‘~.~)and a~3dpo’-“.“) described by eq. (2). The experiments on Nz, C02, N20, CzHb, C&L and C,H2 were used to calibrate the apparatus, since their quadrupote moments are considered to be reasonably well known. Each cross section was determined from scattering experiments at a total of at least 12 different target nozzle beam stagnation pressures_ The errors are the standard deviations of the resulting average value. We note that the cross sections for the (2,0)+(3, Oj and (3,0)+ (2,o) transitions are expected to be identical according to microscopic reversibility since the total energies are essentially equal. However, differences in the transmission function for the

Table 1 Measured cross sections for the rotationhl transitions (j. nr) = (2.0)+ (3.0) and (3.0) + (2.0) of CsF in collisions with other molecules. The errors are standard deviations from at least 12 measurements Target molecule

N2

co co2 NzO C2H6

CzH2 CA C& GH6 C3Ha CdH6 &Ha C,H,

(methylacetylene) (propme) (propane) (1.3-butadiene) (I-butene) (is-butene)

1s.35r 39.161 39.09i 44.76 k 5.96r 40.13’ 24.17r 47.8Ok 29.2Oi 13.652 22.89ir 27.815 35.89+

2.48 4.70 7.16 12.09 0.57 3.49 3.20 7.46 1.60 2.32 4.57 3.60 6.10

13.875 2.97 34.21 t 10.91 29.S2* 5.83 30.935 6.35 5.06+ 2.75 24.40* 6.06 13.19i 2.57 37.98& 6.93 24.56= 1.21 14.385 4.56 18.98~12.55 22.16r 2.26 27.935 4.25

two measurements lead to a greater cross section for the (2,0) + (3,0) transition. We do not expect exact agreement with the previous measurements [6] for configuration A, since the apparatus geometry is different in these experiments and corresponds roughly to configuration B. As discussed previously [7] the transmission function for the (2,0)+ (3,0) transition can be calculated with a greater accuracy than for the other transition. For this reason only these results were used to determine uo. The transmission functions were calculated using the ; same Monte Carlo method described previously [7] but for the new geometry. The results wkre converted to the laboratory system to determine a universal curve which was fitted to an analytic expression and transformed back to the cen’ter of mass system for each partner. Table 2 presents the fina data for a0 and compares the new results for the calibration targets Nr, COz, N20, &Hz, C,H_, and CzH6 with previously published values. Although those values should be in agreement the comparison shows that the new values are consistently smaller than the previous ones [7] by lo-20% except in the case of CO, where we feel the previously published value is too small (see fig. 10 of ref. [7]). Also listed are the values of the quadrupole moments used to correlate the data for the “calibration” targets. The quadrupole moments for the other molecules were determined by first plotting a0 for the calibration gases versus predQ as shown in fig.’ 2. As expected from eq. (5) these values were found te fall nicely on a straight line within experimental error. From this straight line we then use the measured values for a0 from table 2 to determine the quadrupole moments for C&, C3H6, C3Hg, GH6 and the two forms of C4Hs (1-butene and isobutene). The final results are presented in table 3, where they are compared with values obtained from a simple theory discussed in the next section. The errors take account of both the calculated uncertainty in the slope of the linear calibration curve shown in fig. 2 and the errors in a0 (see table 1). The only other experimental determinations

43

G. Meyer, J.P. Toennies / Quadrapole momenrsof light hydrocarbon molecules Table 2 Measured cross section magnitudes ua in A’ for the rotational transition (2,0)+(3,0) quadrupole moments used for calibration (and for CO) are indicated Target molecule

N2

CO?

N20 CzHz &HI Z? C,H* (methylacetylene,

propyne)

C3H6kxopenel C&Is CdH6 &Ha C,Ha

(propane) (1,3-butadiene) (1-butene) (iso-butene, 2-methylpropene)

Dipole moment [22] (debye)

present

previous [6]

0 0 0.17 0 0 0 0.13

5457 178”33 198-+-54 1os*11 7029 116k14 1852

73126 232*70 220*24

0.781 0.366 0.08 0 0.34 0.50

195*28 12657 615~10 123525 153’19 208&45

for all molecules studied. The known

Q (10ez6 esu cm’) predQ recommended [7] (arb. units)

uo (A2)

23+5 82*18

1.52 4.3 3.65 3.0 1.5 2.5 0.65

36 147 125 67 36

16

-

are those of Flygare [4] who finds for C3HA Q = 4.8*0.3, in agreement with our value and for CSHs, Q,, = 0.6, Q,, = 2.9 and Q,, = -3.5. Because of the molecular asymmetry these values are not easily compared with our rotationally averaged values.

The additional presence of a dipole moment (see table 2) is expected to lead to a systematic error which because of the additional longer range dipole-dipole interaction will lead to an additional contribution to the small angle cross section. If not accounted for the quadrupole moments will come out too large. Although the

Table 3 Comparison betwren measured quadrupole moments and estimates based on the model of bond-moments Molecule

Fig. 2. Inelastic differential cross section parameter for the (2,O) + (3,O) transition of CsF in scaltering from molecules with large quadrupole moments plotted against ~,.,Jj. The known quadrupole moments of the underlined mole-

cules were used for calibration.

‘XL CA CA C,Hs . &Ha (I-butenr) &Ha (iso-butene)

Q,uadrupole moments (1 O-‘6 esu cm’) present measurements

bond-moment method

4.15 1.3 2.5 + 0.6 1.2io.5 2.050.8 2.5 r0.8 3.3*1.3

3.1 2.4 0.72 2.6 3.0 2.1

exact size of this correction is difficult to calculate accurately we can quite simply make a rough estimate by referring to our earlier measurements on polar molecules [7,13]. These resufts indicate that dipole-dipole forces are important for symmetric top molecules where. if resonance is not present, the change in cross section with dipole moment is nearly linear and roughly given by 140 AZ/D [7] for proIate symmetric tops such as CHsBr. Methylacetylene (C3H4) is the only symmetric (prolate) top studied in this work, but the agreement with Flygate’s independently measured value suggests that its effect in C3H4 is less than expected. For nonsymmetric top molecules and linear molecules the effect of the dipole moment is definitely much smaller. This is best illustrated by comparing the cross sections measured with TIF for Hz0 and NH3 [13], which have nearly identical dipole moments. However, for the asymmetric rotor Hz0 the cross section is about 70 A’ while that for the symmetric top NH3 is about 600 A’. Since the cross sections for TIF and CsF are nearly identical [14] we can use this ratio to account for the effect of structure. Thus we expect for the asymmetric molecules studied here that the dipole-dipole contribution is of the order of 16 A2/D. For alI molecules (except C&) studied here this effect is thus estimated to be much less than statistical errors. 6. Semi-empirical calculation of quadrupole moments Since aliphatic hydrocarbons are made up of only two bond types, C-C bonds and polar C-H bonds, they are ideally suited to test semiempirical methods for estimating quadrupole moments. At the present time only the quadrupole moments for C&, CzH4 and C2Hb have been measured [8] and these will be used for test purposes in the present semi-empirical calculations, which are based on the ideas of “bond dipole moments” [3, 15,16]$. \ different but related method involving atomicdipole moments hns been used by Flygare [17].

In this mndcl the afftnity of thf C aud )2 cause a partial charge cm

are known the quad mumcnts can be eal

molecular center of mass and (t t While the geometric m of tk gated molecules are known [KS], at& dipole moments of C& and C:% I have been reported [15) To estimate the band die other molecules we proceed as all hydrocarbons have equal dipors BNXKZZX An additional amtribut%m to the dii%e momenta is induced by the clec?rie tfipk of all the other C-H bonds:

where E, is the field arising from the dipole moment of some other C-H kmd j and ucDI p5 the mean polarizabiiity of a C-H bond, which rS known to be 0.65 A” fur ail CH bonds independent of the state of hybridkcatiw, {W] According to this model the mrted differences between the bond drpnle momenh for the C-H bonds attached IO C-aaorr~ m

C2H, 1.19 C,H, 0.78

I .fm 1.061

I .23 0.97

t 18 iw

45

G. Meyer. J.P. Toeonies / Ouadrupofe moments of light hydrocarbon molecules

different states of hybridization [20] are due largely to inductive effects. This is supported by the resull~ r e p o r t e d in table 4 and discussed below. To estimate E w e assume that it is possible t o use the formula Ej = [3(pv • R ) R - ltIR2]/R ~,

(7)

where R is the distance b e t w e e n the dipole m o m e n t of b o n d / a n d b o n d i. This is at best a crude a p p r o x i m a t i o n , sinc~ eq. (7) implies that R is much g r e a t e r t h a n rj, the distance associated with the dipole m o m e n t / ~ . Moreover, since R is c o m p a r a b l e with ri our results for E d e p e n d sensitively o n the point, where the dipole m o m e n t is a s s u m e d to be located in t h e bond. The best results were obtained by placing the effective b o n d dipole m o m e n t on the H a t o m end of t h e b o n d . T h e error in the dipole m o m e n t s i n t r o d u c e d by these two assumptions is estimated to be o f the o r d e r of 2 0 - 3 0 % . This idea was u s e d to recalculate the zeroth o r d e r bond d i p o l e m o m e n t s for the two m o l e cules with k n o w n b o n d dipole moments. T h e results are s h o w n in table 4. Although the values for ~o differ b y about 25% this difference is s m a l l e r than that of the b o n d dipole m o m e n t s , providing evidence in favor of our assumption t h a t t h e z e r m h order C - H b o n d dipole m o m e n t is nearly a constant i n d e p e n d e n t of the state of hybridization of the C atom. From the a v e r a g e of the two values we get an effective positive c h a r g e o f (1.1 ± 0.1 ) × 10- ~o esu on the H a t o m s a n d a cancelling negative charge on the b o n d e d C atom. These charges were then used t o calculate zeroth o r d e r dipole m o m e n t s for all t h e C - H b o n d s in the larger hydrocarbons. T h e resulting electric field [eq. (7)] of the o t h e r b o n d s ~s calculated using z e r o t h o r d e r m o m e n t s . N e w dipole m o m e n t s are calculated from eq. (6) and new charges are obtained. The p r o c e d u r e is r e p e a t e d successively until t h e c h a n g e s in the effective charges are less t h a n 5 % . Table 5 shows the resulting effective charges on the H atoms of the h y d r o c a r b o n s with k n o w n quadrupole moments. For the m o r e complicated g e o m e t r y of the larger h y d r o c a r b o n s many more different

b o n d s are involved, all with somewhat different charges. From the effective charges q~ on the molecular atoms we can calculate the m - c o m p o n e n t of t h e / t h o r d e r multipole t e n s o r (I = 2 for quadrupole) of a m o l e c u l e using the multipolc expansion of the electrostatic potential caused by the molecular charge distribution [21]. T h e quadrupole t e n s o r has five spherical c o m p o n e n t s , which can b e calculated from the cartesian c o o r d i n a t e s of the atoms. They are obtained by averaging o v e r the charge distribution of the molecule:

0 2 . ~ 2 = ( 1 5 / 3 2 ~ ' ) '/2 X qi(X~ - Y~ + 2iXiYi), i

(8a) Oz.+l = (15/8~') t/2 ~- qi(±Xi 4- iYj)Zj,

(8b}

i

O2.o = (5/16~r) '/" Y- q,(2Z 2, - X~ - y2 i.

(8c)

i

The absolute m e a n q u a d r u p o l e m o m e n t is then: 1 4,-'r

2

Io.-I')

t/-"

,",

F o r the systems C z H : . C z H 4 a n d C 2 H 6 the results compare well with the values recomm e n d e d by Stogi-yn a n d Stogryn [8] shown in table 5. This indicates that this simple semi-

Table 5 C o m p a r i s o n betweer, t h e q u a d r u p o l e m o m e n t s calculated f r o m the m e a n effeL1ive c h a r g e s q . . by the present s e m i empirical m e t h o d a n d p r e v i o u s l y m e a s u r e d values "'- T h e q,::~ are the effective c h a r g e s on t h e H a t o m s used in calculat!n~ the quadrupole m o m e n t s Q ! 10-26 e s u cm-')

C_-H: CzH.s CzH~

m e a s u r e d ~'

c~l~ulateo

3.0 i.5 0.65

2.5 1.9 063

q.t~ ~E-t0 esu~

1.03-~ 0.g79 0.812

~' Values r e c o m m e n d e d a n d r e f e r e n c e d b~ Stogryn ,'and St offo'n [8].

46

G. Meyer. J.P. Toennies / Quadrupolemoments oflighthydrocarbon molecules

empirical method is capable of yielding reasonably reliable results. The calculated quadrupole moments for the larger hydrocarbons are compared with experimentally determined vaIues in table 3. In all cases the agreement is reasonably good and certainly within the combined errors. The largest.discrepancy is found for isobutene, which is not surprising sirice it has the most complicated structure of al! molecules studied.

7. Summary A new experimental molecular beam method has been applied to the experimental determination of the quadrupole moments of the nonpolar or only slightIy polar aliphatic hydrocarbon molecules with 3 and 4 carbon atoms. The method has been tested in two separate experiments on known gases and found to give reproducible quadrupole moments within about 20% and in good agreement with accepttd values. The method is recommended for use in determining quadrupole moments of other nonpolar molecules or those with relatively small dipole moments (e.g. CO, N20). A simple semiempirical technique is described and found to predict quadrupole moments in reasonable agreement with measurements.

References [1] T.

Kihara. Intermolecular forces (Wiley, New York, 1978). [21 A.D. Buckingham, J. Chem. Phys. 30 (1959j ‘1580. [3] V.P. Krishnaji, Rev. Mod.‘Phys. 38 (1966) 690. [4] W.H. Flygare and R.C. Benson, Mol. Phys. 20 (1971) 22s; W.H. Flygare, Chem. Rev. 74 (1974) 653. [5] J.I. Gersten, I. Chem. Phys. 51 (1969) 637; V. Dose and C. Semini. Helv. Phys. Acta 47 (1374) 623; V. Dose and J. Windrich, J. Phys. B, to be published;

[6] [7] [8] [9]

[lOI [I I] [12] [13] [14] [15] [16] [17] [18]

Acknowledgement We wish to express our appreciation to the theoreticians of our group, Dr. G. Barg and G. Drolshagen, for helpful explanations and to the technicians, G. Redlich and H. Wuttke, for their skillfu1 help with the measurements. We thank A. Richards (Wiirzburg) for calling our attention to ref. [4] and the referees for valuable suggestions.

[I91

[to]

[21] [22]

R.S. Kass and W.L. Williams, Phjx. Rev. A 7 (1973) 10. F.E. Budenholzer. E.A. Gislason, A.D. Jorgensen and J.G. Sachs, Chem. Phys. Letters 47 (1977) 429. U. Borkenhagen, H. Malthan and J.P. Toennies, .I. Chem. Phys. 11 (1979) 1722. D.E. Stogryn and A.P. Stogryn, Mol. Phys. 11 (1966) 371. P.W. Anderson, Phys. Rev. 76 (1949) 647; C.J. Tsao and B. Cumutte, J. Quant. Spectry. Radiat. Trans. 2 (1962) 41. G. Meyer, Max-Planck-Institut fiir StrBmungsforschung, Bericht 19 (1979). Ci. Herrberg, Spectra of diatomic molecules (Van Nostrand. Princeton. 1950). LJ. Borkenhagen, Max-Planck-Institut fiir Stromungsforxhung, Bericht 1 (1977). J.P. Toennies, Z. Physik 182 (1965) 257. U. Borkenhagen. M. Malthan and J.P. Toennies, Chem. Phys. Letters 41 (1976) 222. K.B. Wiberg and J-l. Wendoloski, Chem. Phys. Letters 45 (1977) 180; J. Am. Chem. Sot. 100 (1978) 723. B. Galabov and WJ. Orville-Thomas. J. Mol. Struct. 18 (1973) 169. W.H. Flygare, Chem. Rev. 74 (1979) 653. Landolt and Boernstein. Neue Serie, II/7 (Springer, Berlin, 1976). J.O. Hirschfelder, CF. Curtis and R.B. Bird, Molecular theory of gases and liquids (Wiley, New York, 19.54). NE. Hill, W.E. Vaughan, A.M. Price and M. Davies, Dielectric properties and molecular behaviour [Van Nostrand, Princeton, 1969) p. 247 ff. G. Eder, Elektrodynamik,BI HochschultaschenbBcher, Nr. 233 (Mannheim, 1967). R. Nelson, D.R. Lide Jr. and A.A. Maryott, Selected values of electric dipole moments for molecules in the gas phase, NSRDS-NBS 10 (National Bureau of Standards, 1967).