Detection and characterisation of a weakly bound dimer of allene and hydrogen fluoride by rotational spectroscopy

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15 January 1988

DETECTION AND CHARACTERISATION OF A WEAKLY BOUND DIMER OF ALLENE AND HYDROGEN FLUORIDE BY ROTATIONAL SPECTROSCOPY A.C. LEGON Department of Chemistry. UniversityofExeter, Stocker Road, Exeter EX4 4QD, UK

and

L.C. WILLOUGHBY Christopher Ingold Laboratories, Dejartment of Chemistry. UniversityCollege London, 20 Gordon Street, London WClH OAJ, UK Received 4 November 1987

Rotational spectra have been detected in each of two low-energy vibrational states (A and B) for both allene...HF and allene.,.DF by pulsed-nozzle, FT microwave spectroscopy, Analysis of nuclear hype&e structure in the lo, eOOOtransition of each state leads to the coupling constants D,HFfor allene...HF and 1: and D,“d for allene...DF. Rotational constants A=9385(2), &3722.479(26) and C=2697.449(24) MHz determined for state A of allene...HF are interpreted in terms of an Lshaped hydrogen-bonded geometry for the dimer.

1. Introduction We report an investigation of the rotational spectrum of a hydrogen-bonded dimer of allene and hydrogen fluoride. The aim of the investigation is to establish the angular geometry of this dimer which, as discussed below, is a prototype involving the possibility of a hydrogen bond to one of two equivalent n-bonds. As a result of analyzing the rotational spectra of a number of carefully chosen hydrogen-bonded dimers, a set of simple rules for predicting the angular geometries of B...HX has been enunciated [ 1,2]. The rules are implicitly electrostatic in origin, recognising that non-bonding (n) and x-bonding electron pairs on the acceptor molecule B offer regions of high electron density. The rules postulate that the electrophilic H in HX seeks such regions and that in the equilibrium geometry HX lies along the symmetry axis of an n- or n-bonding pair. A detailed review of the observed angular geometries of B...HX in the light of the predictions from the rules has been given elsewhere [ 2 1. A quantitative electrostatic model for an214

gular geometries due to Buckingham and Fowler [ 31 leads to excellent agreement with experiment. The rules are straightforward in application when B carries only one n- or x-bonding pair, HCN...HF [ 41 and ethylene...HCl [ 51, respectively, representing prototype dimers in these two classes. When the acceptor atom in B offers two n-pairs, two subclasses are possible: those in which the two n-pairs are equivalent or inequivalent, respectively. Interesting possibilities of tunnelling through low potential energy barriers between equilibrium geometries then present themselves. In the first subclass, the prototype dimer H*O...HF exhibits two equivalent equilibrium conformations having a pyramidal arrangement at oxygen but separated by a low potential energy barrier at the planar form [ 61. The prototype dimer SOz...HF in the second subclass also has an experimental angular geometry consistent with the rules [ 7,8]. A class of dimers so far uninvestigated is that in which B carries no n-pairs but two equivalent double bonds. The prototype molecule B here is allene, in which the x-bonding orbitals are usually envisaged

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3. Results 3.1. Analysis of rotational spectra

Fig. 1.Schematic diagram of the r-electron density in allene and the geometry predicted for allene...HF.

as lying at 90” to each other (fig. 1). The rules then predict for allene...HF an Lshaped equilibrium geometry of the type shown in fig. 1. Of course, four equivalent geometries of this type are possible and in general there will be non-zero potential energy barriers between them. We expect that the form of the rotational spectrum of allene...HF will reflect the size of the potential energy barriers. If they are all high, the spectrum will be of the usual effective-semirigid-rotor type. If not, deviations from this behaviour are possible. We discuss below the rotational spectrum of allene...HF observed using the technique of pulsed-nozzle, Fourier-transform microwave spectroscopy. The angular geometry of the dimer is deduced following preliminary analysis of the spectrum.

2. Experimental Rotational spectra of the dimer formed between allene and hydrogen fluoride were observed with a pulsed-nozzle, Fourier-transform microwave spectrometer [ 9, lo] of the type originally described by Balle and Flygare [ 111. The gas mixture pulsed into the evacuated Fabry-Perot cavity through a 0.7 mm diameter nozzle consisted of about 1% each of allene (Argo) and hydrogen fluoride (B.D.H. Chemicals Ltd.) or deuterium fluoride (Ozark-Mahoning) in argon at a total pressure of z 1 atm, and room temperature. One or two dilutions of the gas mixture with approximately equal volumes of argon were possible without serious loss of signal strength. When observing the DF species, prolonged prior dosing of the stainless-steel gas reservoir with D20 proved advantageous in preventing loss of intensity through H/D exchange on the walls.

Initial predictions of the rotational spectrum of allene...HF were made using an Lshaped, hydrogenbonded model geometry of the type shown in fig. 1, with the HF axis bisecting a C=C bond and with F at a distance of 3.14 8, from the C-C midpoint, as in ethylene...HF [ 121. A rotational spectrum of the nearly prolate, asymmetric-rotor type was thereby expected with only the loltOOO transition at m6.4 GHz and the three J= 2~ 1 transitions centred at R 12.7 GHz falling within the frequency range of the spectrometer. Preliminary searches for the J= 2t 1 transitions made in the ranges 11.59-11.80 GHz, 12.55-12.71 GHz and 13.60-13.80 GHz led to the identification of a pair of transitions in each region. Each pair showed evidence of partially resolved H, F nuclear spin-nuclar spin hyperfine structure which was very similar within each pair but which varied from one pair to the next, that of the central pair being the simplest. This evidence points to an assignment of the pairs as pairs of 2,*+ l,,, 202c l,,, and 2,,4- ll0 transitions, in order of increasing frequency. Model calculations confirmed that, as observed, the K_ l = 1 transitions should have a more complicated hyperfime structure but its resolution and assignment was precluded through convolution with the inherent doubling effect of the spectrometer [ 111. The two sets of transitions are presumably associated with different vibrational states, which we shall label as A and B. In view of the low effective temperatures normally associated with supersonically expanded gas pulses, the states A and B are almost certainly the ground state and a very low energy vibrationally excited state. A search in the frequency range 6.25 to 6.45 GHz revealed two transitions that could be assigned unambiguously as lol~OOo from their completely resolved, characteristic patterns of H, F nuclear spinnuclear spin hyperflne structure, as shown in fig. 2. The similarity of the two patterns in fig. 2 provides further evidence that the rotational spectrum in two vibrational states of allene...HF has been identified. The frequencies (accuracy x 1 kHz) and assignments of the hyperfine components in the l,,+O,, transitions of allene...HF are shown in table 1. For 215

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frequencies are given in table 2 while the H, F nuclear spin-nuclear spin coupling constants Dj$ so determined are given in table 3. The residuals are slightly in excess of the experimental error in a pattern similar to that observed for, e.g. HIO...HF [ 141, This suggests that the fit might similarly be improved by including a description of spin-rotation coupling involving the H and F nuclei but such an approach was not considered worthwhile here. In an attempt to identify further rotational transitions of allene...HF, we extended the frequency range of the spectrometer at the upper end to 2 1 GHz. As a result, we observed two 3 13c 2 12transitions but only one each of the 303c302 and 3r2c2r1 transitions. Again, the K1 = 1 transitions had a more complicated, partially resolved hyperflne structure which aided their assignment. Low microwave power and spectrometer sensitivity, both of which decrease rapidly as the frequency increases beyond 18 GHz, were probably responsible for our failure to observe the two higher-frequency transitions of state B. These factors, coupled with the small population of the K_ 1= 2 levels at the low temperature of the gas pulse, also precluded observation of the 3,,+2,, and 32,t220 transitions. The frequencies v. of the unperturbed J= 3+-2 and J= 2t 1 transitions, estimated with an accuracy of z 10 kHz by locating the centre of gravity of the hyperline pattern, are in-

J III\‘ IllY_li I

:

I

---zr-!

1

64199

6360-4

63603

FrequensylMHt

Fig. 2. Frequency-domain recordings of the ls, tOOa transitions in the states A and B of allene...HF. The hypertine splitting arises from H, F spin-spin coupling. The stick diagrams indicate the calculated frequencies and intensities of the hypertine components. The frequency spacing between adjacent points is 3.90625 kHz.

each state A and B, the frequencies were fitted in a standard iterative least-squares procedure in which the matrix of the familiar [ 13,141 Hamiltonian operator describing the spin-spin interaction was set up in the coupled basis IF+ I,, = I, I+ J=F and diagonalized. The residuals of the lit are’included in table 1, the values v. of the unperturbed line-centre

Table 1 Observed and calculated frequencies of hypertine components in the lo, CO,,,,transitions of states A and B of allene...HF and allene...DF Isotopic species

Hyperfine transition

vob, - ~c.lc

Vobr (MHz)

&Hz)

I’Fcl”F”

allene...HF

1 It1 1 0 It00 12-11 10-l 1

allene...DF

312 112~312 1/Z+ l/2 312 112

I

112312-312 3/2t 112312 112 312512~312 312

1

312312~ 312 112312 l/2 112ll2+ 112 112 l/2 l/2+312 312

1

216

state A

state B

state A

state B

6419.7642 6419.8076 6419.8200 6419.8911

6360.3002 6360.3348 6360.3503 6360.4111

- 1.8 -0.5 3.5 - 1.2

-0.8 -3.2 4.9 -0.9

6380.1844

6361.3957

-0.2

-0.1

6380.2680

6361.4733

-3.5

-3.8

6380.2860

6361.4928

4.0

3.8

6380.3332

6361S363

1.4

1.7

6380.3582

6361.5636

- 1.6

-1.7

Table 2 Values ofline-centre

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fre.quen&sv0for rotational transitions in states A and B of allene...HF and allene...DF

Isotopic species

State B YO(MHz)

State A

Transition J;;_,K,+JL,K,

vo (MHz)

vobs - VC,lC (MHz) -0.027 -0.002 0.021 0.002 0.002 -0.006 -0.001

allene...HF

lo,+Om 212+-l,, 2& 10, 2ll+llo 3~212 30,+20, 312t211

6419.808( 2) a1 11814.47 12712.24 13863.86 17646.04 18672.41 20708.95

allene...DF

lo,+-000 2,*+1,, 202* lo, 2,,+1,0 3,+2,z 303t202 3,,+2,,

6380.289(2) 11716.78 12600.83 13705.30

6350.338(2) 11708.17 12580.52 13814.10 17508.43

6361.495(2) 11661.59 12548.95 13694.47 17427.33 b’ 18521.74

18607.40 20508.93 b,

a) For the lo, +-Owtransitions the quoted error in v. is that generated in the least-squares fit of the hyperfine frequencies given in table 1. The estimated error in the remaining v. values is about 10 kHz (see the text for discussion). b, The assignment of these frequencies to the indicated state is tentative since only one frequency has been identified in these regions for allene...DF.

eluded in table 2 with the more accurate values for the lolcOOo transitions. The analysis for allene...DF followed a similar path. Two loI coo0 transitions were detected, each exhibiting a similar, completely resolved hyperfine pattern of the type that is characteristic of the presence of both D-nuclear quadrupole and D, F spin-spin coupling as shown in fig. 3. Frequencies and assignments of the hyperfine components are given in table 1. The values of the components x& and 0:: of the D-nuclear quadrupole and D, F spin-spin cou-

pling tensors obtained for the states A and B by fitting the hyperfine frequencies using the method described in ref. [ 141 are given in table 3 while the residuals of the fit are given in table 1 and the unperturbed centre frequencies v. are included in table 2. As for the HF species, 212~ 1,1, 202~10, and 2,, t 1,. tranmsitions were observed in both of the states A and B of allene...DF and were assigned on the basis of the similarity of the hyperfine structure within each pair and its added complexity for the K_ , = 1 transitions. The J= 3t2 transitions of al-

Table 3 Spectroscopic constants determined for states A and B of allene...HF and allene...DF Spectroscopic constant

D:jD’F’ (kHz) x,“, (Hz) A (MHz) B (MHz) C(MHz) A, (kHz) ‘~JK 65

(HZ) W-Iz)

Allene...HF

Allene...DF

state A

state B

state A

state B

- 168(6)

- 148(8)

-38(6) 206(7)

-42(8) 195(7)

9385(2) 3722.479(26) 2697.449( 24) 23(l) - 14(17) lO.S(7)

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of transitions has been detected for allene...H(D)F to allow progress with determining the nature of the potential surface at this stage. 3.2. Molecular geometry Although the foregoing analysis suggests that allene...HF may be a non-rigid rotor, it is possible to draw some general geometrical conclusions about the dimer from the spectroscopic constants recorded in table 3. First, we note that the quantity P,=-i(&-I,-I,)=qm,cf 6360.4

6360,3

6360.2

6361.6

63615

Frequency/MHz

Fig. 3. Frequency-domain recordings of the I,,, +000 transitions in the states A and B of allene...DF. The hypertine splitting arises from D-nuclear quadrupole and D, F spin-spin coupling. The stick diagrams indicate the calculated frequencies and intensities of the hypertine components. The frequency spacing Between adjacent points is 3.90625 kHz.

lene...DF were also difficult to observe and are incomplete. The v. values (accuracy = 10 kI-Iz) estimated from the partially resolved hyperfine structure in each of the J= 2~ 1 and 3 c 2 transitions are shown in table 2. The seven v. values for state A of allene...HF have been fitted using the Watson S-reduction [ 151 in the I’ representation to determine the rotational constants A, B, C and the centrifugal distortion constants AJ, AJKand 6,. The residuals of the fit for this state, which are given in table 2, are satisfactory but slightly larger than expected, thus raising the possibility that allene...HF is not an effective semirigid rotor. The spectroscopic constants (table 3) are of commensurate accuracy, although the standard deviations should be treated cautiously because six constants are fitted to seven frequencies. We were unable to fit the transition frequencies for state B without residuals of tens of MHz. The same is true for both states A and B of allene...DF, even after extensive permutation of the transition frequencies. In view of the possibility of several equivalent minima in the potential surface separated by low barriers, the deviation of the observed transition frequencies from the usual effective-semirigid-rotor behaviour is understandable. Unfortunately, an insufficient number 218

(1)

6361.4

for free allene has the value 1.755 amu A2 when determined from the ground-state rotational constants [ 161. In the approximation that equilibrium principal moments of inertia can be replaced by groundstate values, eq. (1) indicates that P, depends only on the out-of-plane coordinates ( ci) of two hydrogen atoms. For allene...HF the value P,= 1.13 amu A’ is only slightly smaller and therefore suggests that the HF molecule and the C=C=C axis are coplanar. Of course, any angle of rotation of allene about the C=C=C axis is consistent with this result and a small deviation of the hydrogen atom from the plane cannot be precluded. The small difference in P, between allene...HF and allene can be attributed to vibration-rotation interaction given that the corresponding values for ethylene...HCl and ethylene are 2.85 and 3.505 amu A’ [ 51, respectively, and that two pairs of hydrogen atoms are responsible for the nonplanar moment in these cases. Secondly, we note that A = 9385 (2) MHz for state A of allene...HF is significantly different from Bo=Co=8883.5(2) MHz [16] of the free allene molecule. If allene...HF were T-shaped, with the HF molecule lying along a line through the central C atom and perpendicular to the C=C=C axis, A for the complex and B. of the free molecule would be identical, apart from vibration-rotation effects. This, taken with the argument involving P,, suggests that allene...HF has an Lshaped geometry of the type discussed in section 1 and shown in fig. 1. If we take the HF axis to be perpendicular to the C=C=C axis and assume that the r. geometries of allene [ 161 and hydrogen fluoride [ 17,181 given in table 4 survive dimer formation, a least-squares fit of the observed

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Table 4 Spectroscopic and molecular properties of hydrogen fluoride and allene Spectroscopic/ molecular property

Allene

HF

DF

616365,5 b) -286.75(5)

325584.98 ” -44.34(9) d, 354.238( 78) d,

AI (GW go (MHz) D:cD)F (kHz) x0” &Hz) r, geometry

d,

0.925592 A e,

0.923240 A e’

144.1(3) a) 8883.5(2) a) _ r(C=C)=l.3084(3) Aa) r(C-H)=1.0872(13) 8, LHCH=118.17(17)’

a) Ref. [ 161. b, Ref. [ 171. c1Ref. [ 181. d’Ref. [ 191. cl Calculated from the appropriate B, value.

rotational constants leads to the geometry ‘for allene...HF shown in fig. 4 with F lying 3.098(7) A from the C-C-C axis and with the HF axis displaced by 0.126( 9) ,-&from the midpoint of the C-C bond towards the central carbon atom. The calculated rotational constants in the final cycle of the tit are Az9383.8 MHz, 8=3715.0 MHz and C~2711.5

MHz. The calculated rotational constants are independent of the angle of rotation of the allene subunit about the C-C% axis. Moreover, geometries having small changes in orientation of the allene and hydrogen fluoride subunits in the plane cannot be precluded. Finally, the geometry shown in fig. 4 is consistent

Fig. 4. The geometry determined from the rotational constants of state A of allene...HF shown in projection in the ab principal inertial plane. The two hydrogen atoms attached to C, lie 0.933 A above and below the plane, respectively.

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with the observed coupling constants 0:: and xF= and with the observed frequencies of the loltOoo transitions of allene...DF. Thus, B + C is predicted as 6365.1 MHz for the DF species, a value in good agreement with the frequencies of the 10ltODOtransitions given in table 2. This agreement tends to indicate that the weak interaction between the molecules is indeed of the hydrogen-bonding type. The geometry shown in fig. 4 implies an angle of 6’= 19.5 Qbetween the HF axis and the principal inertial axis a. Taking this as an equilibrium arrangement and assuming that the components of the H(D) F hypertine coupling tensors along the H ( D ) F direction are unchanged from the free molecule values [ 191 #I (see table 4) the observed values of D,“d and x: would be given by, for example, D,H,F=fD~F(3~~~2B-l)(3~~~2~-l),

(2)

where the angular brackets indicate the quantummechanical average over the vibrational state and @ is the instantaneous angle between the H(D)F direction and its direction in the equilibrium arrangement. Using 19=19.5”, we find the operationally defined angles & = cos- ’( cos’d) “2= 26( 1) ’ and 30( 2) ’ for the states A and B of allene...HF and correspondingly & = 27( 1) ’ and 33( 3) ’ for allene...DF. While these values are internally consistent, they are systematically larger than 19.8( 12) ’ and 21.5(11)” for HF and DF with acetylene [ 131 and 19.8(17)” and 22.0(11)* for HF and DF with ethylene [ 121. Evidently, the H( D)F subunit in allene...H( D)F is undergoing larger oscillations in both states A and B that it is in acetylene...H(D)F or ethylene...H(D)F. This result, taken with the conclusion that the HF axis does not pass through the midpoint of a C=C bond in the “effective” geometry but is displaced towards the central carbon atom, is not inconsistent with tunnelling of HF between equivalent minima. We might envisage a model for the motion which involves a rotation of the allene molecule about its C=C=C axis coupled with a synchronous translation of the HF molecule, the net result being interconversion between the four a’Note that D!jF and 0:’ quoted in table 4 and in refs. [ 12- 141 are - 2 times the values of ref. [ 191.

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equivalent geometries one of which is shown in fig. I. The position of the HF axis in the “effective” geometry would be displaced from the midpoint of a C-C bond in the direction of the central carbon atom and the excursions of the HF molecule would be rel- I atively large, as observed. Acknowledgement Research grants from the SERC are gratefully acknowledged. We thank Professor D.J. Millen for the loan of a K-band backward-wave oscillator. References [ 1] A.C. Legon and D.J. Millen, Faraday Discussions Chem. Sot. 73 (1982) 71.

[ 21AC. Legon and D.J. Millen, Accounts Chem. Res. 20 (1987) 39. [3] A.D. Buckingham and P.W. Fowler, Can. J. Chem. 63 (1985) 2018. [ 41AC. Legon, D.J. Millen and SC. Rogers, Proc. Roy. Sot. A370 (1980) 213. [ 51P.D. Aldrich, A.C. Legon and W.H. Flygare, J. Chem. Phys. 75 (1981) 2126. [ 61 Z. Kisiel, A.C. Legon and D.J. Millen, Proc. Roy. Sot. A38 1 (1982) 419. [ 71 A.J. F&y-Travis and AC. Legon, Chem. Phys. Letters 123 (1986) 4. [ 81 A.J. Fillery-Travis andA.C. Legon, J. Chem. Phys. 85 (1986) 3180. [ 91 AC. Legon and L.C. Willoughby, Chem. Phys. 74 (1983) 127. [lo] AC. Legon, Ann. Rev. Phys. Chem. 34 (1983) 275. [ 111 T.J. Balleand W.H. Flygare, Rev. Sci. Instr. 52 (1981) 33. [ 121 J.A. Sheaand W.H. Flygare, J. Chem. Phys. 76 (1982) 4857. [ 131 W.G. Read and W.H. Flygare, J. Chem. Phys. 76 (1982) 2283. [ 141 AC. Legon and L.C. Willoughby, Chem. Phys. Letters 92 (1982) 333. [IS] J.K.G. Watson, J. Chem. Phys. 46 (1967) 1935; 48 (1968) 4517. [16]A.G.MakiandR.A.Toth,J.Mol.Spectry. 17(1965) 136. [ 171 G. Guelachvili, Opt. Commun. 19 (1976) 150. [ 181 F.J. Lovas and E. Tiemann, J. Phys. Chem. Ref. Data 3 (1974) 697. [ 191 J.S. Muenter and W. Klemperer, J. Chem. Phys. 52 (1970) 6033; 56 (1972) 5409 (E).