The Rotational Spectrum of thep-Fluorotoluene– Argon van der Waals Complex

Journal of Molecular Spectroscopy 195, 1–10 (1999) Article ID jmsp.1999.7802, available online at http://www.idealibrary.com on

The Rotational Spectrum of the p-Fluorotoluene– Argon van der Waals Complex J. Rottstegge,1 H. Hartwig,2 and H. Dreizler3 Institut fu¨r Physikalische Chemie der Christian-Albrechts-Universita¨t zu Kiel, Ludewig Meyn Str. 8, D-24098 Kiel, Germany Received April 21, 1998; in revised form December 2, 1998

The microwave rotational spectrum of the p-fluorotoluene–argon van der Waals complex was analyzed with a molecular beam Fourier transform microwave spectrometer. In the frequency splitting of molecular transitions caused by the internal rotation of the methyl group with respect to the aromatic ring is contained the structure and barrier information. Elucidation is reduced by the analysis of internal rotors direction with respect to the principal axis system of the complex the number of possible solutions in the structure. An r s and r 0 structure of the complex was calculated from these data. The argon is located 3.541(1) Å above the aromatic ring. By forming the complex, the barrier height of internal rotation is changed. An additional V 3 term in the potential function occurs in the complex because the molecular symmetry of the p-fluorotoluene, containing a V 6 but no V 3 term, is reduced by the argon. For assumed V 6 5 144.79(19) GHz or 57.777(76) J/mol, V 3 is found to equal 552.0(10) GHz or 220.31(40) J/mol. © 1999 Academic Press INTRODUCTION

V~ a ! 5

In the understanding of weak molecular interactions, van der Waals complexes play an important role. Inert gas complexes published in (1–3) as relative simple systems are a challenge for quantum chemical ab initio and model potential calculations. So we try to provide accurate experimental data of such systems. We prepared the van der Waals complex of p-fluorotoluene–argon (PFT–Ar) in a pulsed molecular beam by an expansion into vacuum. The rotational spectrum of the complex was recorded with a molecular beam Fourier transform microwave MB-FTMW spectrometer. The methyl group of the PFT–Ar rotates with respect to the frame composed of C6H4F and Ar. Its internal motion is hindered by a barrier. This hindered internal rotation results in a splitting of transitions and a more complex spectrum. On the other hand, the structure elucidation is improved by the internal rotation because the direction of the internal rotor axis in the complex fixed system contains information about the position of the argon atom in the complex.

V3 V6 ~1 2 cos 3 a ! 1 ~1 2 cos 6 a ! 1 · · · 2 2 with

V ~ a 5 0! 5 0,

[1]

where V n is the barrier height for n-fold symmetry. In Eq. [1], only 3n a terms exist, n 5 1, 2, . . . , because of the C3 symmetry of the methyl group. Normally it is found that V 3 @ V 6 @ V 9 @ . . . , so the Fourier expansion is terminated after the first term. The p-fluorotoluene (PFT) drawn in Fig. 1 has a C 2v symmetry of the aromatic frame. The C2 axis coincides with the internal rotation axis, so the period of the barrier of internal rotation of PFT is 2p/6 with V 6 as the lowest term in the potential function. This C 2v symmetry is destroyed in the PFT–Ar complex. An additional V 3 term in the barrier function resulted from this situation. The Hamiltonian of a molecule or complex containing one internal rotor with any direction of the internal rotation axis referred to the principal axis system (PAM system) is reported to be (4, 5):

THEORY

ˆ 5H ˆ PAM 1 H ˆ d. H

The internal rotation of the methyl group attached to the aromatic ring is hindered by a periodic barrier. A Fourier series of this potential as a function of the torsion angle a yields the following expression:

[2]

ˆ d for centrifugal distortion has been added. The Hamiltonian H In detail,

1

Present address: Max–Planck Institut fu¨r Polymerforschung, Postfach 3148, D-55021 Mainz, Germany. 2 Present address: PAC-AN, DSM Research, 6160 MD Geleen, The Netherlands. 3 To whom correspondence should be addressed. E-mail: [email protected]

ˆ PAM 5 APˆ 2a 1 BPˆ 2b 1 CPˆ 2c 1 H 1 Pˆ g9Pˆ g! 2 2

1 2

O

O

D gg9~Pˆ gPˆ g9

g,g95a,b,c gÞg9

Q gPˆ g pˆ 1 Fpˆ 2 1 V~ a !.

[3]

g5a,b,c

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ROTTSTEGGE, HARTWIG, AND DREIZLER

FIG. 1. p-Fluorotoluene and its principal inertia axis system.

The rotational constants modified by internal rotation are (cyclic in a, b, c): A5

S

D

l 2aI a \2 \2 11 5 1 F r 2a 2I a rI a 2I a

[4]

constants of the PAM Hamiltonian can be calculated by the inverse rotation from the constants of the RAM Hamiltonian. We used the combined axis method (CAM) for the analysis of the PFT–Ar spectrum. The program Xiam written by Hartwig and described in (8) is based on the principles which were first described by Woods in (9). The method was improved by Vacherand et al. (10). All matrix elements related to ˆ rot were calculated in the principal axis the pure rotation H ˆ IR system, and the matrix elements of the internal rotation H directly in the r system (a9 ( z9) axis parallel to r). This procedure is followed by an inverse rotation into the principal axis system. A final diagonalization yields the energy eigenvalues. The simplified matrix elements of the Hamiltonian ˆ CAM are H ˆ rotuC9rot& 1 ˆ CAMuC9& 5 ^C 0rotuH ^C0uH

OD

~ J! KK 0

*~ J! ~ v ! D KK 9~ v !

K9,K0

ˆ K,IRuC9K9,IR&, 3 ^C 0K0,IRuH

Further, \ 2l gl g9I a 5 F r gr g9 2rI gI g9

[5]

\ 2l g 5 Frg 2rI g

[6]

F5

\2 2rI a

[7]

rg 5

l gI a , Ig

D gg9 5

Qg 5

r512

O l II . 2 g

g

a

[9]

ˆ rotuC9rot& in the with matrix elements of pure rotation ^C 0rotuH ˆ PAM system, of internal rotation ^C 0K0,IR uH K,IR uC9K9,IR & in the ( J) RAM system, and D KK0 ( v ) as transformation matrix between RAM and PAM system. Details for the complicated treatment have been given in (8), where the procedure for a two top (internal rotor) molecule has been given. In the present case, a simplified version without the second top and the top–top interaction was used. ˆ d of [2] the A-reduction operator of For the Hamiltonian H Watson (11) for fourth-order centrifugal distortion was selected,

[8]

g

ˆ d 5 2D JPˆ 4 2 D JKPˆ 2Pˆ 2a 2 D KPˆ 4a 2 2 d JPˆ 2~Pˆ 2b 2 Pˆ 2c ! H

where l g is the direction cosine between internal and principal inertia axis g 5 a, b, c ( z, x, y in I r ), Pˆ g is the component of total angular momentum operator, pˆ is the total angular momentum operator of the internal rotor, I g is the moment of inertia derived from the structure of the complex, I a is the moment of inertia of the internal rotor about its internal rotation and C3 symmetry axis, and V( a ) is the potential function in equation [1] of internal rotation. According to Woods (6), it is possible to simplify the PAM Hamiltonian of internal rotation setup in an a, b, c ( z, x, y in I r ) principal inertia axis system for a molecule or complex containing one internal rotor by a special choice of the molecule fixed coordinate system, which is called RAM system (7) (rho axis method) with new coordinates a9, b9, c9 ( z9, x9, y9 in I r ). The new RAM a9 ( z9) axis is oriented parallel to the vector r 5 ( r a , r b , r c ) as demonstrated in Fig. 2. Therefore, two of the mixing terms Q i pˆ Pˆ i (i 5 a9, b9, c9) in [3] even at any orientation in space of the internal rotor disappear. The PAM and the RAM systems are connected by a rotation, leaving the energy eigenvalues of the problem invariant. The

2 d K@Pˆ 2a~Pˆ 2b 2 Pˆ 2c ! 1 ~Pˆ 2b 2 Pˆ 2c !Pˆ 2a#.

[10]

The internal rotation modifies the selection rules of the asymmetric rotor according to Dreizler (5). The invariance group of the Hamiltonian for the PFT–Ar is D3, if the argon atom is located in a ab plane of symmetry above the aromatic ring. This will be demonstrated below as result of the spectral analysis. With an ab plane of symmetry and components of the

FIG. 2. Schematic position of the r vector in the PAM system ( x, y, z) and the RAM system ( x9, y9, z9).

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ROTATIONAL SPECTRUM OF VAN DER WAALS COMPLEX

3

FIG. 3. Overview spectrum of 2% PFT in argon from 10.0 –10.4 GHz. It contains 1000 measurements with a frequency distance of 400 kHz. Each measurement of 1 K data points was repeated 512 times to improve the signal-to-noise ratio. The intensity maximum of the averaged measurement was plotted versus the spectrometer frequency.

molecular dipole moments m b ( m x ) and m a ( m z ), the K selection rules of the asymmetric rotor a-type spectra

ma Þ 0

DK 21 5 0, 62 . . . DK 11 5 61, 63 . . .

b-type spectra

mb Þ 0

DK 21 5 61, 63 . . . DK 11 5 61, 63 . . .

c-type spectra

mc Þ 0

[11]

spectrum. The selection rules of the asymmetric rigid rotor are broken for E-type levels (m 5 1, 2, 4, . . .). Here all rotational functions mix in a way (5, p. 109) that additional forbidden c-type transitions and forbidden transitions like DK 21 5 0, 62, . . . and DK 11 5 0, 62, . . . modify the spectrum. Nevertheless, the selection rules of the asymmetric rotor still provide the most intense lines of the spectrum.

[12]

DK 21 5 61, 63 . . . DK 11 5 0, 62 . . . , [13]

are modified. With respect to the direction of the molecular dipole moment m a , m b Þ 0, and m c 5 0, the estimated a- and b-type spectra are influenced depending on the different internal rotation levels m. For A-type levels (m 5 0, 3, . . .), the rotational functions mix (5, p. 108) in a way that additional weak b-type spectra occur in a-type spectra and weak a-type spectra occur in b-type spectra. This is only a small effect to the spectrum of the argon complex containing an a- and b-type

EXPERIMENTAL

A sample containing 2–3% PFT in argon or helium was prepared in a reservoir with a pressure of 200 kPa. The gas mixture was guided via a Teflon tube to a nozzle to inject a pulsed supersonic molecular beam into the tank of the MBFTMW spectrometer (12) evacuated to a vacuum of 1023 Pa to record the rotational spectra of the PFT–Ar complex. The velocity of the resulting supersonic gas jet with '1500 m/s for He and '560 m/s for Ar results in a spectrum with a Doppler doublet centered at the frequency of a static gas. Each Doppler line has a typical linewidth of 3 kHz HWHH. The accuracy of the frequencies is estimated to be on the order of 1 kHz. The

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ROTTSTEGGE, HARTWIG, AND DREIZLER

TABLE 1 Measured PFT–Ar Transition Frequencies nobs in the Internal Rotation States m 5 0 and 1

Note. They were all used in Fit 2 Table 2 to the Hamiltonian [9] of the CAM system. The difference Dn 5 nobs 2 ncalc between the observed and calculated frequencies are added.

transitions of the complex were as intense as the transitions of the 13C isotopomers of the PFT after sufficient optimization. The expansion through the nozzle into vacuum with inert gases as a carrier results in massive cooling (13). The rotational transitions in the internal rotation state m 5 0 ( A-type levels) and m 5 1 (E-type levels) are of similar intensity, although the

energy of m 5 1 states is above the m 5 0 levels. m 5 2 E-level transitions are of lower intensity, in agreement with Hepp, Winnewisser, and Yamada (14). The transitions of the PFT normal isotopomer and its 13C isotopomers were already investigated in (15, 16) with Stark-modulated spectrometers and in (17) with an MB-FTMW spectrometer. Therefore, we

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ROTATIONAL SPECTRUM OF VAN DER WAALS COMPLEX

5

TABLE 1—Continued

could eliminate all those well-known transitions in the spectrum. Overview spectra were recorded to find the spectral lines of the complex. The overview spectrum in the frequency range of 10 –10.4 GHz (Fig. 3) contains ca. 1000 measurements in logarithmic intensity scale with a frequency distance of 400 kHz. The intensity maximum of each measurement was plotted as function of the spectrometer frequency. Each measurement of 1 K data points was repeated 512 times to improve the signal-to-noise ratio. To verify the PFT–Ar frequencies, all found transitions of the PFT–Ar spectrum were recorded with 8 K data points and a point distance of 20 –100 ns in argon and in helium as carrier gas. Transitions of the PFT–Ar have to disappear with helium as carrier gas.

RESULTS OF THE SPECTRAL ANALYSIS

The rotational transitions in the m 5 0 and 1 state transitions of the PFT–Ar are reported in Table 1. To assure the assignment, all 79 found m 5 0 transitions of the PFT–Ar, even for high K values, were fitted to the model of the centrifugally distorted asymmetric rotor with Watson’s A reduction to a standard deviation of 3 kHz. The rotational constants are influenced by the internal rotation as shown in Eq. [4]. For the same purpose, all 67 recorded transitions in the m 5 1 state were checked to be consistent with an RAM Hamiltonian for internal rotation with a fixed hypothetical barrier V 3 5 100 GHz and V 6 5 144.79(19) GHz, taken

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ROTTSTEGGE, HARTWIG, AND DREIZLER

TABLE 2 Various Fit Results for the Rotational, Centrifugal Distortion (Watson A) Constants and Internal Rotation Parameters of the m 5 0, 1 Transitions with the CAM Procedure with Xiam to Hamiltonians [9] and [10]

Note. V 6 was fixed to 144.79 GHz, F to 160 GHz taken from (17). N is the number of transitions, s the standard deviation. The errors are given in units of the last digits.

from (17). Several forbidden transitions were included in the fit with a standard deviation of 67 kHz. The lost D6h symmetry of the Hamiltonian of the PFT in forming the PFT–Ar complex with D3 Hamiltonian symmetry results in the occurrence of a V 3 potential term. The internal rotation in the program Xiam is described by the parameters

FIG. 4.

uru, the angles b and g of the r vector referred to the principal axis (8), as shown in Fig. 2, and the potential terms V 3 and V 6 . Different fits of the 134 m 5 0 and 1 state transitions in Table 1 to the Hamiltonian [9] of the CAM system are presented in Table 2. The simultaneous determination of both potential terms was impossible because no transitions of the m 5 2 state

Dependence of V 3 and V 6 illustrating their correlation.

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FIG. 5. Expanded region of Fig. 4.

ROTATIONAL SPECTRUM OF VAN DER WAALS COMPLEX

7

A 5 1.20011018~25! GHz B 5 1.05686690~19! GHz

[14]

C 5 0.69897264~19! GHz. The low bond energy of the PFT–Ar complex is demonstrated by the larger centrifugal distortion constants of PFT–Ar in Fit, 1, Table 2 compared to those of PFT (17) in Table 4. The potential function term V 3 , which can be calculated from the splitting of the A (m 5 0) and E (m 5 1) state transitions, was found for assumed F 5 160 GHz and V 6 5 144.79(19) GHz to be FIG. 6. Structure 1 of the p-fluorotoluene–argon complex. The structure is symmetric to the paper plane. cm is the center of mass of PFT; CM is the corresponding one of the complex; P is the projection of argon on the plane; a, b, c are principal inertia axes of the complex; aPFT, bPFT, cPFT are those of the PFT. The angle between the internal rotor axis i and the a axis is 53.92°.

could be detected for the complex and no information about F (or I a ) can be derived from the spectra. So V 6 and F were fixed in all calculations to V 6 5 144.79(19) GHz as taken from (17) and F 5 160 GHz calculated with I a in the same publication. The value of F affects V 3 predominately, and uru, b, or g are of less influence to V 3 . In Fit 4 of Table 2, where all parameters were free, the angle g is found to be zero in the range of the error. According to Fig. 2, the internal rotor axis must be located orthogonal to the c axis of the complex in the ab plane, which becomes an ab mirror plane. Because of this mirror plane, the invariance group of the Hamiltonian changes to D3. In Fit 2 and 3, the transitions were evaluated with [9] by the assumption of this ab mirror plane resulting in two different angles of b, which are complements to 180 degrees of each other. Those two different b values, as angles between the r vector and the a( z) axis in the PAM system, are related to two different angular positions of the internal rotation axis with respect to the a axis of 54° and 126° (or 254°). They correspond to two different structure possibilities as will be seen below. At this stage of the analysis, we have no means to exclude one alternative by a knowledge of the structure from other sources. This is the case for normal molecules with one internal rotor. Fit 2, 3, and 4 result in similar standard deviations of 740 kHz. In the range of error, all values in these fits are equal, with the exclusion of b. The frequency deviations given in Table 1 are calculated with the parameters of Fit 2 in Table 2 as the difference of observed minus calculated frequency. The highest correlation in the correlation matrix of Fit 2 as an example is 0.981 for D J and d J . An additional fit of all m 5 0 state transitions given in column Fit 1 of Table 2 was performed with the program Xiam. All parameters of internal rotation were taken from the values of Fit 2, Table 2. Structural rotational constants free from contributions of the internal rotation for the structure elucidation were obtained:

V 3 5 552.0 6 1.0 GHz

[15]

as an average result of Fit 2 and 3. The strong dependence of V 3 especially, on the value of V 6 , is documented in Figs. 4 and 5. We obtained various pairs of V 3 and V 6 values for different assumed values of V 6 in Fit 2. The large value of V 3 relative to V 6 and the strong interdependence of both values correspond to the results of Huber et al. (18) for the argon complex of n-methylpyrrole. The analysis of spectra with partial deuteration of the methyl group in n-methylpyrrole and in the argon complex did not allow the determination of a unique equilibrium position of the methyl group. The true errors, especially of the parameters of internal rotation, are higher than the given ones because we did not make use of all transitions, especially for higher J and K and forbidden transitions in the m 5 1 state, which were influenced by centrifugal distortion caused by internal rotation and made worse by the fits. DETERMINATION OF THE STRUCTURE

From Fit 4 in Table 2 results g ' 0, so r is found to be in the ab ( xz) plane and l c ' 0. From the angle between the internal rotation axis and the c ( y) axis of 90° results that the

FIG. 7. Structure 2 of the complex with an angle of 126.08° between the a axis and the internal rotor axis i.

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ROTTSTEGGE, HARTWIG, AND DREIZLER

TABLE 3 Used PFT Structure for the r0 Structure Calculations of the PFT–Ar Complex

Note. The errors do not reflect methodological ones. 1) r s structure of the carbon frame with errors. 2) Average ab initio structure calculated by Gaussian ‘92. 3) Optimized r 0 structure parameters.

argon atom is located in the ab ( xz) principal inertia plane of the complex as shown in Figs. 6 and 7. Otherwise, the internal rotor axis would not be in the ab plane and the molecular symmetry of the complex would decrease. Both presented structures are symmetric to the paper plane with the possible exception of the methyl group. Van der Waals complexes are formed by relatively weak forces, so in good approximation, the structure of the PFT is

assumed to be unchanged by forming the complex. An r s structure of the PFT–Ar complex can be calculated according to Kraitchman (19) and Gordy and Cook (20) by substituting a mass zero in PFT by the mass of argon to get the PFT–Ar TABLE 5 The Cartesian Coordinates of the r0 Structure for the PFT–Ar Complex in the Principal Axis System of PFT

TABLE 4 r0 and rs Structure of PFT–Ar

Note. The r 0 structure of the argon in PFT–Ar was least-squared fitted in the axis system of the PFT. r cm-Ar is the distance between PFTs center of mass (cm) and the argon atom, /Ar-cm(PFT)-F is the angle between argon, PFT’s center of mass, and the fluorine. The a coordinate of the argon in the system of PFT is added.

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ROTATIONAL SPECTRUM OF VAN DER WAALS COMPLEX

complex. The r s structure can be calculated with the rotational constants of the PFT given in (17) Table 7 A PFT 5 5.509046~11! GHz B PFT 5 1.43032192~22! GHz

9

TABLE 6 The Cartesian Coordinates for the First Possible r0 Structure of the PFT–Ar Complex Drawn in Fig. 6 with an Angle w 5 53.92° between the a Axis and the Internal Rotation Axis

[16]

C PFT 5 1.14355373~21! GHz, and with those of the PFT–Ar under [14]. The possible r s coordinates of the argon atom relative to the PAM system of the PFT (see Fig. 1) in the I r representation with respect to the plane of symmetry are: a ~5z! 5 60.265 Å b ~5x! 5 0 ~assumed!

[17]

c ~5y! 5 63.541 Å. The number of possible argon positions in the plane of symmetry is reduced to four, two above and two below the aromatic ring. No error estimation according to van Eijck (21) and Costain (22) of this r s structure coordinates for the 40Ar versus 0 Ar (m Ar 5 0) substitution was performed, due to the absence of appropriate K factors in [18].

s ~ x! 5

K . uxu

[18]

Both vertical projections P of the argon atom to PFTs aromatic ring plane are inside the ring as presented in Figs. 6 and 7. The projections are located at a distance of 60.265 Å to PFT’s center of mass (cm). Relative to the center of the ring, the vertical projections P of the argon in the different structures have a distance of 0.373 Å in the direction of the fluorine or 0.157 Å toward the methyl group. A decision between both structures is impossible without data on isotope variants of the complex because both structures are compatible with the moments of inertia, which depend on the squares of the coordinates. Both structure possibilities in Fit 2 and 3 yield similar results in the standard deviation. The r 0 structure was elucidated and optimized by a weighted fit proportional to the relative inverse standard deviation of the rotational constants. It is an effective structure to the investigated state of vibration. A problem in the determination of the r 0 structure of the PFT–Ar is that no complete r 0 structure of PFT is given, so we took the PFT structure of (17) as r 0 structure. The structure of PFT is of type r s for the carbon frame, of type r 0 , and ab initio for hydrogen and the fluorine atoms as indicated in Table 3. Here we chose the average of the given ab initio values. The structure of PFT for the r 0 calculation of the PFT–Ar complex is given in Table 3. With this assumed structure, the r 0 coor-

Note. The coordinates refer to the principal axis system of the complex.

dinates of the argon atom in the principal inertia system of the PFT are: a ~5z! 5 60.282~28! Å b ~5x! 5 0 Å

[19]

c ~5y! 5 63.544~36! Å. They are similar to the assumed rs values in [17]. The results of the r0 structure calculations are given in Table 4. A complete list of Cartesian coordinates for all atoms of the complex in the principal axis system of PFT is given in Table 5, those corresponding to the system of both possible complex structures in Table 6 and 7. The optimization to both structures 1 and 2 yields similar standard deviations, so we cannot prefer one structure. Both r0 and rs structures are similar in the range of error. For both structures, the internal rotation parameter here designed by b# can be calculated a priori without doing the internal rotation fit from the angle w between the a axis and the internal rotation axis,

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tg~ b# ! 5

r a l bI a I a 5 5 tg~ w !. r b l aI b I b

[20]

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ROTTSTEGGE, HARTWIG, AND DREIZLER

TABLE 7 Cartesian Coordinates for the PFT–Ar r0 Structure 2 of Fig. 7 with an Angle w 5 126.08° between the a Axis and the Internal Rotation Axis

ment, A- and E-state transitions were initially fitted separately to two different sets of rotational constants, and finally together with an increased standard deviation. Starting from the structure of the p-fluorotoluene (PFT), we elucidated the structure of the argon complex. The multiplicity of possible structures was reduced by the analysis of internal rotation to two positions below and two above the aromatic ring of PFT. The calculated r s and r 0 structures are equal in the range of error with a distance of 3.541(1) Å between the argon and the aromatic ring. The barrier of internal rotation is changed by forming the complex. The presence of the argon reduces the symmetry so that the potential function is periodic in 2p/3 instead of 2p/6 for PFT. An additional potential function term V 3 5 552.0(10) GHz or 220.31(40) J/mol is introduced in addition to the V 6 term of PFT. The change in the internal rotation barrier was calculated by assumed V 6 5 144.79(19) GHz or 57.777(76) J/mol for the PFT. The new occurring V 3 term is three times larger than the original V 6 term of PFT. ACKNOWLEDGMENT We thank all members of our group for help and discussion. Also, we thank the Deutsche Forschungsgemeinschaft, the Fonds der Chemie, and the Land Schleswig Holstein for funds.

REFERENCES

With the structural rotational constants of [14], free from contributions of internal rotation [20], results in tg~ b# ! 5

B tg~ w !. A

[21]

The angle b# can be calculated from [14] and the angle w between the internal rotation axis and the a axis with w 5 53.92° determined for structure 1 and with w 5 126.08° for structure 2 to b# 1 5 50.39° and b# 2 5 129.61°. With respect to the angle b from Fit 2 and 3 with b1 5 50.95° and b2 5 129.06°, we are not able to prefer one structure. The difference of the angles b# i and bi (i 5 structure 1 and 2) is out of the given error range of Table 2. It reflects the limitation of the rigid frame–rigid top model applied to the weakly bound complex. SUMMARY

The rotational spectrum of the p-fluorotoluene–argon (PFT– Ar) complex was measured with an MB-FTMW spectrometer and assigned. The rotational constants, the fourth-order centrifugal distortion constants, and the parameters of internal rotation were derived from the spectrum. To assure the assign-

1. W. Stahl and J. U. Grabow, Z. Naturforsch. A 47, 681– 684 (1992). 2. E. Jochims, J. U. Grabow, and W. Stahl, J. Mol. Spectrosc. 158, 278 –286 (1993). 3. U. Dahmen, W. Stahl, and H. Dreizler, Ber. Bunsenges. Phys. Chem. 98, 970 –974 (1994). 4. C. C. Lin and J. D. Swalen, Rev. Mod. Phys. 31, 841– 891 (1959). 5. H. Dreizler, Fortschr. Chem. Forsch. 10, 59 –155 (1968). 6. R. C. Woods, Thesis, Harvard University, Cambridge, MA 1965. 7. J. T. Hougen, I. Kleiner, and M. Godefroid, J. Mol. Spectrosc. 163, 559 –586 (1994). 8. H. Hartwig and H. Dreizler, Z. Naturforsch. A 51, 923–932 (1996). 9. R. C. Woods, J. Mol. Spectrosc. 22, 49 –59 (1967). 10. J. M. Vacherand, B. P. van Eijck, J. Burie, and J. Demaison, J. Mol. Spectrosc. 118, 355–362 (1986). 11. J. K. G. Watson, in “Vibrational Spectra and Structure” (J. R. Durig, Ed.), Vol. 6, p. 39, Elsevier, Amsterdam, 1977. 12. J. U. Grabow, W. Stahl, and H. Dreizler, Rev. Sci. Instrum. 67, 4072– 4084 (1996). 13. W. Demtro¨der, “Laser Spectroscopy”, 2nd ed., p. 354, Springer–Verlag Berlin, 1991. 14. M. Hepp, G. Winnewisser, and K. G. Yamada, J. Mol. Spectrosc. 146, 181–186 (1991). 15. A. D. Rudolph and H. Seiler, Z. Naturforsch. A 20, 1682–1686 (1965). 16. P. N. Ghosh, J. Mol. Spectrosc. 138, 505–520 (1989). 17. J. Rottstegge, H. Hartwig, and H. Dreizler, J. Mol. Struct., in press, 1999. 18. S. Huber, J. Makarewicz, and A. Bauder, submitted for publication. 19. J. Kraitchman, Am. J. Phys. 21, 17–24 (1953). 20. W. Gordy and R. L. Cook, “Microwave Molecular Spectra”, 3rd ed., Chap. XIII.3, Wiley, New York, 1984. 21. B. P. van Eijck, J. Mol. Spectrosc. 91, 348 –362 (1982). 22. C. C. Costain, Trans. Am. Cryst. Assoc. 2, 157–164 (1966).

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