The Microwave Spectrum and Molecular Structure of the Hydrogen-Bonded Aniline–Methanol Complex

Journal of Molecular Spectroscopy 198, 263–277 (1999) Article ID jmsp.1999.7969, available online at http://www.idealibrary.com on

The Microwave Spectrum and Molecular Structure of the Hydrogen-Bonded Aniline–Methanol Complex Matthias Haeckel* and Wolfgang Stahl† *Institute for Physical Chemistry, Christian-Albrechts-University of Kiel, Kiel, Germany; and †Institute of Physical Chemistry, Rheinisch–Westfa¨lische Technische Hochschule (RWTH)-Aachen, Aachen, Germany Received March 4, 1999; in revised form August 11, 1999

The rotational spectrum of aniline–methanol was investigated in the frequency region 3–19 GHz using a pulsed molecular beam Fourier transform microwave spectrometer. Sixty-three measured a- and b-type transitions show a fine structure due to internal rotation of the methyl group. The resulting A and E lines are additionally split into hyperfine components arising from quadrupole coupling of the 14N nucleus. The torsional motion of the methyl group is hindered by an effective barrier V 3 of nearly 215 cm 21, which is almost one-half of the methanol barrier height. The structure of the complex was calculated assuming a common symmetry plane for the monomers. These form a linear N . . . H–O hydrogen bond. Its distance was found to be 3.03 Å, which is identical with that of aniline–water. © 1999 Academic Press I. INTRODUCTION

In the last few years, a number of hydrogen-bonded complexes have been studied because they may serve to understand processes in liquids, conformational structures of biomolecules, and other topics. They also may be used as simple model systems for studying intermolecular potentials and large amplitude motions because ab initio calculations of these complexes are still difficult. To get extensive information about hydrogen bonds, several complexes containing water or methanol were investigated. In some of these complexes, e.g., C 6H 5NH 2–H 2O (1) and NH 3– CH 3OH (2), water and methanol act as proton donors; in other ones, as proton acceptors, e.g., C 6H 5OH–H 2O (3) and C 6H 5OH–CH 3OH (4). They have both functions in dimers, e.g., (H 2O) 2 (5) and (CH 3OH) 2 (6). In the aniline–methanol complex, aniline acts as a Brønstedt base and methanol as an acid. The objectives of our work were to determine the structure of the complex as well as the 14 N-quadrupole coupling constants and the internal rotation parameters. The latter two effects yield information about the influence of the hydrogen bond on the electric charge distribution at the nitrogen nucleus and the hindering potential of the methyl internal motion. II. EXPERIMENTAL DETAILS

The rotational spectrum of the aniline–methanol complex was recorded in the frequency range from 3 to 19 GHz using a pulsed molecular beam Fourier transform microwave (MBFTMW) spectrometer with a confocal Fabry–Perot resonator (7, 8). For high sensitivity and resolution, the nozzle is mounted on the back side of one of the mirrors allowing the

molecular beam to propagate parallel to the cavity axis (9). Due to the Doppler effect, each molecular signal is split into a doublet. A gas mixture of 1% (by volume) methanol in helium as a carrier gas was enriched with aniline by allowing it to flow over a small aniline-containing stainless steel container. The container was kept at a temperature of approximately 40°C. A stagnation pressure of 50 kPa was used throughout. Molecular beam pulses of 0.3 ms duration were polarized by a short (2 ms) microwave pulse (0.18 mW) after 0.6 ms delay. The microwave frequency was chosen nearly resonant (Dn , 250 kHz) with a rotational transition of the complex. The free induction decay was digitized in 0.1 ms increments sampling 2– 8 K data points. To obtain a sufficient signal-to-noise ratio, typically 1 z 10 4–3 z 10 4 pulses were averaged. The spectral lines had a linewidth (FWHH) of about 5 kHz. Not all hyperfine components could be completely resolved, as shown in Fig. 1. Therefore, sometimes an analysis by least-squares fitting the free induction decay (10) is necessary to obtain the true frequencies. Since the Fourier transformation shifts the frequencies only within the measurement precision of a few kilohertz, this time-consuming work could be omitted. III. OBSERVED SPECTRUM AND ANALYSIS

The observed a- and b-type transitions (Table 1) are modified by the electric quadrupole coupling of the 14N nucleus (spin I 5 1) of aniline and the internal rotation of the methyl group of methanol. c-type transitions were not found, as predicted by transforming the dipole moment vectors of the monomers (11, 12) into the inertial axis system of the complex. The analysis of the spectrum was carried out with the program XIAM (13). It allows the simultaneous analysis of nuclear quadrupole coupling and internal rotation. The matrix

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and the principal axes of inertia are determined by the parameters b and g defined by Woods (15, 16). Since a symmetry plane was assumed, g was set to zero. Thus, only two parameters, V 3 and b, remained free. F and r were calculated from the rotational constants A, B, C and b, g, I a in each fitting cycle. The results of the least-squares fit are given in Table 2 (Fit I). The obtained standard deviation of 496.9 kHz is much too high if compared with the measurement accuracy of only a few kilohertz. A comparison of Fig. 2b (Fit I) and Fig. 2a (measurement) clearly illustrates this discrepancy. To reproduce the spectrum with higher precision, we subsequently implemented additional parameters which express the interaction between overall rotation and methyl torsion which arises from vibrational motions ˆ dT 5 D pi4 z pˆ 9 4 1 2D pi2J z pˆ 9 2 z Pˆ 2 H 1 D pi2K ~ pˆ 9 2 z Pˆ 2z 1 Pˆ 2z z pˆ 9 2 !

[1]

1 D pi22 z @ pˆ 9 z ~Pˆ 2 Pˆ ! 1 ~Pˆ 2 Pˆ ! z pˆ 9 #, 2

FIG. 1. Power spectrum of the 7 07– 6 06 transition of aniline–methanol with internal rotation splittings and quadrupole hyperfine structure. Internal rotation components are denoted by A and E, hyperfine components by F–F9, and the Doppler components with a separation of 147 kHz by brackets. Recording conditions: MW pulse width, 2 ms; pulse power, 0.18 mW; sampled data points, 8 K; experiment cycles, 30 000.

elements of nuclear quadrupole coupling are implemented as given in (14); those off-diagonal in J are neglected. The internal rotation is treated by the r-axis method (RAM) of Woods (15, 16) and by the modified theory of Vacherand et al. (17). We used XIAM to fit the rotational, centrifugal distortion (Watson’s A reduction (18, 19)) and 14N-nuclear quadrupole coupling constants, the hindering barrier V 3 of the methyl group and the angles between the internal rotation axis and the principal axes of inertia. In the first part of the analysis, we will report on the fine structure caused by the torsional motion of the methyl group of methanol. The assignment of the symmetry species turned out to be difficult, especially for adjacent K doublets (K 2 5 3, 4). This problem was solved by Fortrat-like diagrams where the J quantum number was drawn over the frequency difference between the transitions of the A and E state (D n A–E 5 n A – n E ). n A and n E are the hypothetical center frequencies of the quadrupole hyperfine splittings. This was done separately for each K 2 branch. Figure 2a shows the graphs of five different K 2 branches. The moment of inertia of the methyl group for rotation about the internal rotation axis was fixed at a value of I a 5 3.21222 a.m.u. Å 2 (12). The angles between the internal rotation axis

2 x

2 y

2 x

2 y

2

with pˆ 9 5 pˆ a 2 u r u Pˆ z9 . This Hamiltonian term was originally developed by Kirtman (20) and applied by Herbst et al. (21) to analyze the spectrum of methanol. There should be almost no correlation between the parameters D pi4 , D pi2J , D pi2K , and D pi22 since they are also included in Nakagawa’s (22) reduced Hamiltonian, where correlation is known to be small. However, they should be considered as “effective” parameters, which can be fitted independently. The fits, including these additional parameters, are shown in Table 3. D pi2J reduces the standard deviation by about 430 kHz (Fit II), D pi2K and D pi22 only by about 140 kHz (Fit III and IV). D pi4 produces a negative potential (Fit V), which indicates strong correlation with V 3 . In Fit VI and VII, two additional parameters are fitted simultaneously. All results of Fit II and VII are given in Table 2. A second attempt to reduce the standard deviation of Fit I was tried in Fit VIII (Table 2). The Hamiltonian employed here consists of an additional set of three rotational constants A, B, C, which is added for the E state (s 5 1) and is ignored for the A state (s 5 0). The internal rotation is still treated with the RAM from Woods. The complete Hamiltonian is

ˆ95 H

1 1 Pˆ 9 t I9 21 Pˆ 9 1 Pˆ 9 t I9 21 ~ s !Pˆ 9 2 2 1 1 ~ pˆ 2 u r uPˆ z9 ! 2 1 V~ a !, 2rI a a

with

1 2

[2]

Pˆ 9 t I9 21 ( s )Pˆ 9 as an additional term for the rotational

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ANILINE–METHANOL: MW SPECTRUM AND MOLECULAR STRUCTURE

TABLE 1 Observed and Calculated Frequencies of the Aniline–Methanol Complex

Note. The measured frequencies (obs.) and the differences between measurement and calculation (Fit I, II, VII, and VIII) are given in MHz. Copyright © 1999 by Academic Press

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TABLE 1—Continued

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TABLE 1—Continued

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TABLE 1—Continued

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TABLE 1—Continued

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TABLE 1—Continued

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TABLE 1—Continued

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aniline, an off-diagonal element, x ac , is possible, but it is not documented in literature; therefore,

x aniline 5

S

2.3844 0 0 0 1.8424 0 0 0 24.2268

D

~in MHz!.

@3#

The transformation from the inertial axis system of aniline into the one of the complex is described by the following matrix:

S

D

0.747 0 0.665 D aniline3complex 5 20.665 0 0.747 . 0 1 0

[4]

The quadrupole coupling tensor of aniline–methanol is calculated as follows: 21 x complex 5 D aniline3complex z x aniline z D aniline3complex

S

D

20.535 23.283 0 0 5 23.283 21.307 . 0 0 1.842

FIG. 2. Measured (a) and calculated (Fit I) (b) internal rotation splittings D n A–E 5 n A – n E .

constants of the E state. uru is the length of Woods’ rho vector and r 5 1 2 S l g2 (I a /I g ). The resulting rotational constants can be represented as “effective” values for each torsional state. This way, the standard deviation decreased to only 11 kHz without further additional interaction terms. Although this is still about a factor of two bigger than the experimental accuracy, we did not try to improve further. In addition to the twofold splitting due to methyl torsion, each A and E line shows a hyperfine structure caused by the 14 N-nuclear quadrupole coupling which will be considered in the second part of the analysis. The total width of the triplets (,500 kHz) is smaller than the hyperfine splitting of the aniline monomer. The coupling constants can be estimated by transforming the quadrupole coupling tensor of aniline into the inertial axis system of the complex. The structure of the monomers and the electronic surrounding of the quadrupole nucleus are assumed to remain unchanged while the complex is formed. Furthermore, only the O 1 state of aniline was considered because the inversional O 2 state which lies 40.8 cm 21 (23) above the inversional ground state, O 1 , could not be detected in the molecular beam. The calculation of the quadrupole coupling tensor of aniline–methanol uses the coupling constants determined by Kleibo¨mer and Sutter (23). Because of the symmetry plane in

[5]

Due to the fact that aniline probably has an off-diagonal element x ac , we restrict ourselves to the comparison of the x bb of aniline with the x cc of the complex. If compared with the fitted quadrupole coupling constant x cc (Table 2), it is obvious that the electronic surrounding of the 14 N nucleus changes if the complex is formed. The reason for this effect is that the free electron pair of the nitrogen takes part in the hydrogen bond and electron density is abstracted from it. It was not possible to determine off-diagonal elements of the 14 N-nuclear quadrupole coupling tensor because the secondorder effects of the off-diagonal elements were too small compared with the experimental uncertainties. The differences between the observed and the calculated frequencies, Dn 5 n obs. 2 n calc., of the Fits I, II, VII, and VIII are listed in Table 1. IV. MOLECULAR STRUCTURE

Hydrogen bonds between amines and proton donors are rather strong and are readily formed under molecular beam conditions, e.g., aniline–water (1), piperidine–water (24), morpholine–water (25). Hence, it is assumed that aniline and methanol form a hydrogen-bonded complex where aniline is a Brønstedt base and acts as a proton acceptor while methanol serves as a proton donor. Due to the lack of isotopomers, we were only able to calculate a r 0 structure. It turned out to be possible to determine two parameters, one angle and one bond length, associated with the hydrogen bond. Necessarily, a few assumptions were required. The monomer geometries are assumed to be constant while forming the heterodimer, despite the fact that

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TABLE 2 Results of the Spectral Analysis

a

Values in MHz. Values in kHz. c Values in GHz. d Dimensionless. e Angles in degree. f Mean standard deviation in kHz. g Indices A and E describe the symmetry species. b

small changes of the H atom of methanol associated with the hydrogen bond may occur. Second, this bond is taken linear and the symmetry plane in the monomers was assumed to lead to a symmetry plane in aniline–methanol, too. The remaining two unknown parameters are the distance between O and N,

d N–O, and the angle between the phenyl ring plane of aniline and the hydrogen bond, / CNO. As monomer bond parameters, the complete r S structures from Lister et al. (11) for aniline and Gerry et al. (12) for methanol were used. Eight structures were found to be in agreement with the

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TABLE 3 Influence of Additional Rotation–Vibration–Interaction Parameters

Note. All values are given in MHz. a In GHz. b Mean standard deviation in kHz.

determined moments of inertia. These are illustrated in Fig. 3; the respective values are listed in Table 4. To determine the structure, the experimental rotational constants of Fit I were used. The structures c, d, g, h of Fig. 3 were eliminated because the hydrogen bond length is typically about 2.5–3.5 Å. Some examples are aniline–water with 3.03 Å (1), piperidine–water with 3.023 Å (24), morpholine–water with 2.911 Å (25), and ammonia–methanol with 3.289 Å (2). Besides, from the r S structure of aniline–water (1), which was also confirmed by ab initio calculations, it can be deduced that interactions between the hydrogen of the hydroxyl group and the p electrons of the phenyl ring, as Suzuki et al. (26) and Gutowski et al. (27) found for benzene–water, cannot be favored for aromatic amines. Another criterium to exclude some possibilities is the position of the free electron pair of the nitrogen which is used to build up the hydrogen bond. The VSEPR (valence shell electron pair repulsion) model of Gillespie and Nyholm (28) demands the free electron pair of nitrogen to be on the opposite side of the phenyl ring plane relative to the protons of the amino group. This fact eliminates the structures b, d, f, h. Only two possibilities remain, a syn-periplanar (structure a) and an anti-periplanar (structure e) conformation. We were able to decide between these two when looking at the angles between the internal rotation axis and the principal axes of inertia (Table 2) that were obtained from the spectral analysis. Therefore, the final structure of the aniline–methanol complex is structure a (Fig. 4). Now we want to discuss the assumption of the symmetry plane in the heterodimer. First, we fitted g in the spectral

FIG. 3. Possible structures of aniline–methanol (the definition of the bond parameters is given in structure a; the paper represents the mirror plane, i.e., the ab plane of the inertial axis system).

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ANILINE–METHANOL: MW SPECTRUM AND MOLECULAR STRUCTURE

TABLE 4 Structural Data of the Eight Possible Geometries

V. DISCUSSION

/(i,g) angle between internal rotation axis i and principal axis of inertia g (calculated from cartesian coordinates of the principal axis system of inertia). a

analysis which was fixed to zero so far. These fits are marked with an “a” and are given in Table 5. The deviations from g 5 0 are small and the derived values differ from each other beyond the accuracy range. Therefore, an assumption is necessary. A second argument that supports the symmetry plane is obtained from the planar moments. That one perpendicular to the mirror plane in the complex is P c and it can be calculated from those of the monomers which are perpendicular to their symmetry plane,

The derived structural parameters of the hydrogen bond can be compared to those of aniline–water (1), which was studied earlier in our group. The hydrogen bond in both complexes has nearly the same length (3.03 Å) within the standard errors. In the aniline–water complex, it was not possible to decide definitely whether the second H atom of the water which is not involved in the hydrogen bond points to the phenyl ring of aniline or into the opposite direction. This question can probably be answered by taking the results of this work into account. The aniline–water complex may be considered as an aniline–methanol complex, where the methyl group is substituted by the free water proton. Since the methyl group is directed to the ring, it should be the same for the proton. This may result from polarization of the methyl group, carrying a positive partial charge, through the dislocated p-electron cloud of the phenyl ring with its 2I effect. Probably this weak interaction stabilizes the structure of the complex and modifies the barrier to internal rotation. The second proton of water should exhibit the same orientation as the methyl group. The analogous angle in aniline–water (101.3°) is about 6.5° bigger than in our complex (94.9°), which indicates that the polarization in aniline–water is less intensive. Further, we will compare the 14N-nuclear quadrupole constants in the two aniline complexes. Therefore, both coupling tensors must be transformed into a common inertial axis system. We chose that of aniline–methanol. The transformation matrix is

S

0.969 0 0.247 20.247 0 0.969 D aniline–water3aniline–methanol 5 0 1 0

P c ~complex! 5 P b ~aniline! 1 P c ~methanol!

D

[6]

5 89.788 1 1.589 5 91.377 a.m.u. Å 2.

and the nuclear quadrupole coupling tensor of aniline–water is (1)

The planar moments obtained from the spectral analysis (Fit I), marked with (exp.), are given in Table 6 together with those from the monomers. P c (exp.) and P c (calc.) only differ within their standard errors. Additionally, some planar moments were calculated with the methyl group of methanol tilted out of the symmetry plane through rotation about the hydrogen bond. Table 7 shows the calculated P c and the difference between P c (exp.) and P c (calc.). This difference grows if the symmetry plane is given up. We inferred from these two arguments that the assumption of a symmetry plane is justified. The r 0 structure was calculated using the program RU111 (29). The derived uncertainties of the bond parameters mainly result from the errors of the monomers (11, 12) which were obtained by error propagation. Table 8 gives the results of the structure determination, the calculated rotational constants, and the deviation from the spectral constants A, B, C.

FIG. 4. Three-dimensional structure of the hydrogen-bonded complex aniline–methanol within the principal inertial axis system as it was determined by the structural analysis. The size of the spheres represents the relative proportions of the van der Waals radii of the different atoms.

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TABLE 5 Proof of the Symmetry Plane from Internal Rotation Parameters

a

Dimensionless. Angles in degree. c Mean standard deviation in kHz. d Index indicates the symmetry species A and E. b

S

D

20.2590 0 23.35 0 1.6427 0 x aniline–water 5 , 23.35 0 21.3851

[7]

where the off-diagonal element x ac is derived from an analysis of C 6H 5NH 2–H 216O and C 6H 5NH 2–H 218O. The coupling tensor of aniline–water in the inertial axis system of aniline–methanol,

x 9aniline-water 5 D aniline–water-aniline–methanol 3 x aniline–water z D 21 aniline–water-aniline–methanol

S

D

[8]

which are of the same magnitude as those of aniline–methanol within the experimental accuracy (see Table 2). The charge distribution perpendicular to the symmetry plane, represented by the quadrupole coupling constant x bb of aniline, is affected by the formation of the heterodimers, i.e., the hydrogen bond. This can be concluded from the coupling constants x cc of aniline–methanol and x bb of aniline–water, which have evident lower values. Finally, the derived value of the potential barrier for internal rotation, V 3 , is to be discussed. The value of nearly 215 cm 21 is about a factor of two smaller than that of methanol (373

21.932 23.211 0 0.288 0 5 23.211 , 0 0 1.643 has the diagonal quadrupole coupling constants x aa , x bb , x cc ,

TABLE 7 Difference between Calculated and Experimental Planar Moment When Turning the Methyl Group out of the Symmetry Plane

TABLE 6 Planar Moments of the Monomers and the Complex Taken from Spectral Analysis

Note. Planar moments are given in a.m.u. Å 2 .

Note. Planar moments are given in a.m.u. Å 2.

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ANILINE–METHANOL: MW SPECTRUM AND MOLECULAR STRUCTURE

TABLE 8 Results of the Structural Analysis

Note. Rotational constants are given in MHz.

cm 21) as reported for other complexes containing methanol on the acceptor site, e.g., (CH 3OH) 2 (6) and CH 3OH–CO (30). Fraser et al. (31) suggest that librational motions of the hydroxyl group of methanol substantially effect the A–E splittings and provide an additional term in describing the torsional motion of the methyl group which reduces the hindering barrier V 3 . Nevertheless, the potential barrier seems to be a very sensitive probe for the potential situation in the complex, especially in the environment of the hydrogen bond. ACKNOWLEDGMENT The authors thank the Kiel microwave group for help and discussion.

REFERENCES 1. U. Spoerel and W. Stahl, J. Mol. Spectrosc. 190, 278 –289 (1998). 2. G. T. Fraser, R. D. Suenram, F. J. Lovas, and W. J. Stevens, Chem. Phys. 125, 31– 43 (1988).

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3. M. Gerhards, M. Schmitt, K. Kleinermanns, and W. Stahl, J. Chem. Phys. 104, 967–971 (1996). 4. U. Gudladt, “Diplomarbeit,” Universita¨t Kiel, 1996. 5. J. A. Odutola and T. R. Dyke, J. Chem. Phys. 72(9), 5062–5070 (1980). 6. F. J. Lovas, S. P. Belov, M. Y. Tretyakov, W. Stahl, and R. D. Suenram, J. Mol. Spectrosc. 170, 478 – 492 (1995). 7. J.-U. Grabow, Thesis, Universita¨t Kiel, 1992. 8. U. Andresen, H. Dreizler, J.-U. Grabow, and W. Stahl, Rev. Sci. Instrum. 61(12), 3694 –3699 (1990). 9. J.-U. Grabow and W. Stahl, Z. Naturforsch. A 45, 1043–1044 (1990). 10. I. Merke and H. Dreizler, Z. Naturforsch. A 43, 196 –202 (1988). 11. D. G. Lister, J. K. Tyler, J. H. Hog, and N. W. Larsen, J. Mol. Struct. 23, 253–264 (1974). 12. M. C. L. Gerry, R. M. Lees, and G. Winnewisser, J. Mol. Spectrosc. 61, 231–242 (1976). 13. H. Hartwig, Thesis, Universita¨t Kiel, 1996. 14. H. P. Benz, A. Bauder, and H. H. Guenthard, J. Mol. Spectrosc. 21, 156 –164 (1966). 15. R. C. Woods, J. Mol. Spectrosc. 21, 4 –24 (1966). 16. R. C. Woods, J. Mol. Spectrosc. 22, 49 –59 (1967). 17. J. M. Vacherand, B. P. van Eijck, J. Burie, and J. Demaison, J. Mol. Spectrosc. 118, 355–362 (1986). 18. J. K. G. Watson, J. Chem. Phys. 46, 1935–1949 (1967). 19. J. K. G. Watson, J. Chem. Phys. 48, 4517– 4524 (1968). 20. B. Kirtman, J. Chem. Phys. 37, 2516 –2539 (1962). 21. E. Herbst, J. K. Messer, F. C. de Lucia, and P. Helminger, J. Mol. Spectrosc. 108, 42–57 (1984). 22. K. Nakagawa, S. Tsunekawa, and T. Kogima, J. Mol. Spectrosc. 126, 329 –340 (1987). 23. B. Kleibo¨mer and D. H. Sutter, Z. Naturforsch. A 43, 561–571 (1988). 24. U. Spoerel and W. Stahl, Chem. Phys. 239, 97–108 (1998). 25. O. Indris, W. Stahl, and U. Kretschmer, J. Mol. Spectrosc. 190, 372–378 (1998). 26. S. Suzuki, P. G. Green, R. E. Bumgarner, S. Dasgupta, W. A. Goddard, and G. A. Blake, Science 257, 942–945 (1992). 27. H. S. Gutowski, T. Emilsson, and E. Arunan, J. Chem. Phys. 99(7), 4883– 4893 (1993). 28. R. J. Gillespie, J. Chem. Educ. 40, 295–301 (1963). 29. H.-D. Rudolph, “RU111,” University of Ulm, 1991. 30. F. J. Lovas, S. B. Belov, M. Y. Tretyakov, J. Ortigoso, and R. D. Suenram, J. Mol. Spectrosc. 167, 191–204 (1994). 31. G. T. Fraser, F. J. Lovas, and R. D. Suenram, J. Mol. Spectrosc. 167, 231–235 (1994).

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