##
1The rotational spectrum of thiophene⋯HBr and a comparison of the geometries of the complexes B⋯HX, where B is benzene, furan or thiophene and X is F, Cl or Br
Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj1

1

The rotational spectrum of thiophene⋯HBr and a comparison of the geometries of the complexes B⋯HX, where B is benzene, furan or thiophene and X is F, Cl or Br

Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj1

2

The ground-state rotational spectra of three isotopomers C

_{4}H_{4}S⋯H^{79}Br, C_{4}H_{4}S⋯H^{81}Br and C_{4}H_{4}S⋯D^{79}Br of a weakly bound complex formed by thiophene and hydrogen bromide have been observed in the gas phase by means of a pulsed-jet, Fourier-transform instrument.
Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj1

3

Each spectrum was analysed and fitted to give rotational constants

*A*_{0},*B*_{0}and*C*_{0}, centrifugal distortion constants*Δ*_{J},*Δ*_{JK},*Δ*_{K},*δ*_{J}and*δ*_{JK}and the components*χ*_{aa},*χ*_{bb}–*χ*_{cc}and*χ*_{ab}of the bromine nuclear quadrupole coupling tensor.
Type: Goal |
Advantage: None |
Novelty: None |
ConceptID: Goa1

4

A detailed analysis of the spectroscopic constants established that the geometry of the complex is of the face-on type.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con1

5

The Br atom of HBr is located close to the perpendicular drawn through the centre of mass of the thiophene ring and the H atom of HBr lies between the Br atom and the ring.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con2

6

The angle

*α*_{az}made by the HBr internuclear axis*z*with the*a*-axis has the two possible values ±9.83°.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res1

7

The preferred structure is that generated when the positive value of the angle is chosen and has the HBr sub-unit pointing in the direction of the S atom of thiophene.

Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res2

8

The determined geometrical parameters are

*r*(S⋯H) = 2.728(3) Å,*φ*= 116.0(2)° and*θ*= 7.08(4)°, where*φ*is the angle made by the S⋯H internuclear line with the local*C*_{2}axis of thiophene and*θ*is the angular deviation of the S⋯H–Br nuclei from collinearity.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con3

## Introduction

9

Molecules B that exhibit both non-bonding (n) and π- bonding electron pairs are dealt with by the third part of some rules put forward in 1982 to account for the observed angular geometries of hydrogen-bonded complexes B⋯HX, where B is a simple Lewis base and HX is a hydrogen halide.

^{1}
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac1

10

Part 3 of the rules states that, in such a complex, the n-pair is definitive of the angular geometry.

Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac1

11

Furan⋯HCl evidently obeys this rule because it was shown

^{2}to have a planar geometry of*C*_{2v}symmetry, with the HCl lying along the*C*_{2}axis of the furan subunit so as to form a hydrogen bond to O. The experimental geometry of this complex is shown, drawn to scale, in Fig. 1, which also includes diagrams of related molecules.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod1

12

The furan⋯HCl complex was detected and characterised by means of its rotational spectrum, as observed by pulsed-nozzle, Fourier-transform microwave spectroscopy.

Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met1

13

In this technique the complexes are produced by supersonic expansion and therefore only the lowest energy conformer in its zero-point state is usually detected.

Type: Method |
Advantage: Yes |
Novelty: Old |
ConceptID: Met1

14

Thus, the zero-point state of the most stable form of furan⋯HCl has an angular geometry predicted by the rules.

Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac2

15

Subsequently, it was shown,

^{3}by using the same experimental method, that the related complex furan⋯HF has an angular geometry of the same type as that of furan⋯HCl.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac3

16

A recent investigation

^{4}of the rotational spectrum of the complex furan⋯HBr led to an unexpected result, namely that it was not isomorphous with the HCl and HF complexes of furan.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac4

17

Instead, the observed angular geometry of furan⋯HBr resembles that of benzene⋯HBr,

^{5}in the sense that the Br atom lies above the centre of the face of the aromatic ring and the H atom of HBr appears to form a hydrogen bond to the π electrons system in each case.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac5

18

This is clear from the structures shown in Fig. 1, which compares the experimental results for furan⋯HCl, furan⋯HBr and benzene⋯HBr.

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod1

19

The series of complexes pyridine⋯HX, where X is F, Cl or Br, all have the

*C*_{2v}geometry,^{6–8}as expected from the rules, that is the HX molecule lies along the*C*_{2}axis of pyridine and forms a hydrogen bond to N. The hydrogen bond is reasonably strong in each case and indeed there is evidence of a significant contribution of the ionic form C_{5}H_{5}NH^{+}⋯Br^{–}to the valence-bond description of the complex with HBr.^{8}
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac6

20

A reason why the pyridine⋯HX series is homogeneous in its angular geometry while the furan⋯HX series is not becomes apparent when the molecular electric dipole

**and quadrupole moments***µ***of the heterocyclic aromatic molecules pyridine and furan are compared.***Θ*^{9}
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac7

21

In pyridine, both

**and the component***µ**Θ*_{zz}of**, where***Θ**z*is the*C*_{2}axis, are large and negative, corresponding to a prominent nonbonding electron pair on N. In furan,**is smaller and***µ**Θ*_{zz}is close to zero, suggesting that the n-pair in furan is more involved in the ring.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac8

22

It has been proposed that the change from the

*C*_{2v}to the face-on geometry when HX is HBr arises from a reduced contribution of electrostatic factors coupled with an increased dispersion effect.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac9

Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac9

24

Both changes are in a direction that favours a face-on geometry, as observed in benzene⋯HBr.

Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac10

25

For thiophene,

**is even smaller and the component***µ**Θ*_{zz}is positive.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac11

26

This suggests that the non-bonding electron pair formally associated with the heteroatom is progressively withdrawn into the ring as we pass from pyridine, through furan, to thiophene and therefore that thiophene should behave more like benzene.

Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp1

Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp1

28

We report here an investigation of thiophene⋯HBr by means of its ground-state rotational spectrum observed by the pulsed-jet, Fourier transform (FT) method.

Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met2

29

The aim of the investigation is to identify and characterise this complex and, in particular, to establish whether its angular geometry is isomorphous with those of thiophene⋯HF and thiophene⋯HCl, as predicted by the arguments rehearsed earlier.

Type: Goal |
Advantage: None |
Novelty: None |
ConceptID: Goa2

## Experimental

30

The rotational spectrum of thiophene⋯HBr was observed with a pulsed-jet, Fourier transform microwave spectrometer based on the original design of Balle and Flygare.

^{15}
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met2

31

Recent modifications

^{16}have been outlined elsewhere.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met2

32

A fast-mixing nozzle

^{17}was used in conjunction with the spectrometer to preclude any possible reaction between thiophene and hydrogen bromide that might have occurred when these two substances were mixed in a conventional, stainless steel stagnation vessel in the common way.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met2

33

Thiophene vapour above a liquid sample held at room temperature was flowed continuously through the central glass (0.3 mm internal diameter) capillary of the mixing nozzle into the evacuated chamber containing the Fabry-Pérot cavity.

Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp1

34

The flow rate was adjusted to yield a nominal pressure of

*ca.*10^{–4}mbar in the chamber.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp1

35

A mixture consisting of HBr and argon in the partial pressure ratio 2∶100 and held at a stagnation pressure of 3 bar was pulsed into the outer stainless steel tube of the mixing nozzle at a rate of 5 Hz by means of a Series 9 solenoid valve (Parker Hannifin).

Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp2

36

The outer tube of the mixing nozzle is concentric and approximately coterminous with the glass capillary, an arrangement that enabled thiophene⋯HBr complexes to be formed at the interface of the thiophene and HBr/Ar gas flows.

Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met3

37

Such complexes were rotationally polarized with 1 µs pulses of microwave radiation of appropriate frequency and the subsequent free-induction decay at rotational transition frequencies was processed as described elsewhere.

^{16}
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp3

38

Individual Br nuclear quadrupole hyperfine components in observed transitions of the isotopomers based on HBr had a full-width at half height of

*ca.*20 kHz, which led to 2 kHz as the estimated accuracy of frequency measurement.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs1

39

Thiophene and HBr gas were obtained from Aldrich and used as received.

Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp4

40

DBr was prepared by the exchange of HBr gas with D

_{2}O adsorbed on the walls of the stainless steel stagnation vessel.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp5

41

To saturate the walls of the vessel with D

_{2}O, the vessel was heated to*ca.*70–80 °C and then the vapour from above a warmed sample of the liquid D_{2}O was brought into contact with the vessel walls while they cooled.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp6

42

The vessel was then reheated and the HBr gas added.

Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp7

43

After a period to allow exchange of D for H, the required partial pressure of argon was added.

Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp7

44

In this way a sample of DBr with

*ca.*70 atom% D was produced.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs2

## Results

### Spectral assignment and analysis

45

The search for the rotational spectrum of thiophene⋯HBr was guided by predictions of transition frequencies made using a face-on model of the complex based on thiophene⋯HCl.

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod2

46

This model was constructed by taking the observed angular geometry

^{14}of thiophene⋯HCl, but with the distance*r*(S⋯Cl) increased by the difference between the van der Waals radii of Br and Cl to give a rough estimate of the distance*r*(S⋯Br).
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod2

47

After a short search, a spectrum that required both HBr and thiophene was detected.

Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res3

48

Identification of the observed spectrum with the complex thiophene⋯HBr was reinforced through the observation of nuclear quadrupole hyperfine patterns characteristic of the presence of a Br nucleus in the molecular source of the spectrum.

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod3

49

The first transitions assigned in the rotational spectrum of thiophene⋯HBr were of the R branch type allowed by the

*a*component of the electric dipole moment.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod3

50

Each transition consisted of several hyperfine components arising from Br nuclear quadrupole coupling.

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod3

51

An initial set of spectroscopic constants obtained by fitting these

*a*-type transitions was then used to predict*b*-type transitions, which were subsequently observed and readily assigned on the basis of their frequencies and their Br nuclear quadrupole hyperfine structure.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod4

52

Observed frequencies and assignments of hyperfine components in

*a*- and*b*-type rotational transitions of each of the three isotopomers C_{4}H_{4}S⋯H^{79}Br, C_{4}H_{4}S⋯H^{81}Br and C_{4}H_{4}S⋯D^{79}Br are recorded in Table 1.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs3

53

For each isotopomer, observed frequencies were fitted by a non-linear, least-squares analysis with the aid of the program SPFIT, developed and made available by Pickett.

^{18}
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod5

54

The Hamiltonian

*H*constructed for this purpose was of the form*H*=*H*_{R}+*H*_{Q}+*H*_{SR}where*H*_{R}is the rotational energy operator for a semi-rigid asymmetric rotor and*H*_{Q}= –^{1}/_{6}*Q*_{Br}:▽*E*_{Br}is the operator describing the energy of interaction of the Br nuclear electric quadrupole moment*Q*_{Br}with the electric field gradient ▽*E*_{Br}at Br.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod6

55

The weaker, magnetic mechanism for coupling

**and***I***, namely Br spin–rotation coupling, contributed in a minor but just detectable way to observed frequencies and hence the appropriate operator***J**H*_{SR}=**·***I***·***M***, where***J***is the familiar spin–rotation coupling tensor, was added to the Hamiltonian, as shown in eqn. (1).***M*
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod7

56

The matrix of

*H*in the coupled basis**+***I***=***J***was diagonalised in blocks of the quantum number***F**F*.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod8

57

The forms of the elements of

*H*_{R},*H*_{Q}and*H*_{SR}in this basis are well known.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod7

58

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod7

59

The spectroscopic constants obtained in the final cycle of the fit are given in Table 2 for each isotopomer investigated.

Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs4

60

It should be noted from Table 2 that only three independent components of the Br nuclear quadrupole hyperfine coupling tensor

*χ*_{αβ}=*eQ*∂^{2}*V*/∂*α*∂*β*(namely,*χ*_{aa},*χ*_{bb}–*χ*_{cc}, and*χ*_{ab}) were required to fit the spectra with a rms error similar in magnitude to the estimated error of frequency measurement.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res4

61

Values of the other two off-diagonal elements

*χ*_{ac}and*χ*_{bc}were not determinable; attempts to fit them gave values near to zero and smaller in magnitude than their associated standard errors.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res4

62

An equilibrium geometry of

*C*_{2v}symmetry in which the HBr molecule forms a hydrogen bond to the sulfur atom and lies along the*C*_{2}axis of the thiophene sub-unit is immediately precluded by the fact that*χ*_{ab}is non-zero and by the observation of*b*-type transitions.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res5

63

In that case, all three off-diagonal elements

*χ*_{ab},*χ*_{ac}and*χ*_{bc}of the Br hyperfine coupling tensor in the principal inertial axis system would be zero, as would the component*µ*_{b}of the electric dipole moment.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res5

64

The contribution from Br spin–rotation coupling to the observed frequencies allowed only the diagonal components

*M*_{bb}of the tensor**to be determined.***M*
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res5

65

Only quartic centrifugal distortion constants were necessary to give satisfactory rms deviations

*σ*of the fits.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs5

66

It should be noted that four of the five quartic distortion constants had the expected positive sign but that

*Δ*_{K}is negative.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs6

67

This is a real effect, true for all three isotopomers investigated.

Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs6

68

Residuals Δ

*ν*=*ν*_{obs}–*ν*_{calc}from the final cycles of the least-squares fits are included in Table 1 while the rms deviations*σ*of the fits are given in Table 2.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs7

69

The values of

*σ*for all three isotopomers are close to the estimated error of frequency measurement (2 kHz).
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs7

### Symmetry of thiophene⋯HBr

70

The magnitude of the rotational constant

*A*_{0}in each of the three isotopomers of thiophene⋯HBr investigated is such that a geometry of*C*_{2v}symmetry for the complex can be ruled out immediately.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6

71

If the HBr sub-unit were to lie along the

*C*_{2}axis of thiophene,*A*_{0}of the complex should be almost identical in value to that of the free thiophene molecule.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp2

72

A comparison of the values of the

*A*_{0}for each of the isotopomers of the complex (Table 2) with that of thiophene^{20}(Table 3) shows that the change in*A*_{0}is large and clearly HBr cannot lie along the*C*_{2}axis of thiophene.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs8

73

Thus, the highest symmetry that thiophene⋯HBr can have is that associated with the point group

*C*_{s}.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con4

74

Such a conclusion is consistent with the observation of

*b*-type transitions and a non-zero value of the component*χ*_{ab}of the Br nuclear quadrupole coupling tensor.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con4

75

We also note from Table 2 that the change in the rotational constant

*A*_{0}when either^{81}Br or D is substituted in the HBr sub-unit of the isotopomer thiophene⋯H^{79}Br is less than 2 MHz in each case.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs9

76

This observation means that the HBr sub-unit must lie almost along the principal inertia axis

*a*of the complex.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res7

77

Moreover, the

*A*_{0}values of these isotopomers are not very different from the rotational constant*C*_{0}of free thiophene^{20}(see Tables 2 and 3).
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs9

78

Therefore, in the complex, the Br atom sits on or close to the local

*c*axis of the free thiophene molecule.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res8

79

Support for the assignment of a geometry of C

_{s}symmetry, in which the HBr subunit lies in the molecular symmetry plane, comes from the values of the planar moment*P*_{c}of the three isotopomers of thiophene⋯HBr investigated.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs10

80

*P*

_{c}is defined in eqn. (2) and depends only on the principal-axis co-ordinates

*c*

_{i}of the atoms

*i*.

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod9

81

2

*P*_{c}= –(*I*_{a}+*I*_{b}–*I*_{c}) = 2∑*m*_{i}*c*2*i*Values of*P*_{c}for each of the isotopomers of the complex are included in Table 2.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod9

82

We note that this quantity is essentially invariant among thiophene⋯H

^{79}Br, thiophene⋯H^{81}Br and thiophene⋯D^{79}Br.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs11

83

Moreover,

*P*_{c}is similar in magnitude to the corresponding planar moment*P*_{b}of thiophene itself (see Table 3).
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs12

84

The invariance of

*P*_{c}to isotopic substitution in the HBr subunit provides strong evidence that HBr lies in the*ab*principal inertial plane and that this plane is the molecular symmetry plane.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9

85

The near-identity of

*P*_{c}of the complex and*P*_{b}of thiophene indicates that the geometry of thiophene is not significantly perturbed by complex formation.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9

86

The observation of smaller changes in the rotational constants

*B*_{0}and*C*_{0}between the H^{79}Br and D^{79}Br isotopomers than between the H^{79}Br and H^{81}Br isotopomers (see Table 2) suggests (but does not prove-see below) that the H atom of HBr lies closer to the thiophene subunit than does Br.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res10

87

However, it is advisable to be cautious in using D substitution to locate the H atom of HBr within the complex.

Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac12

88

This atom will necessarily contribute little to the equilibrium principal moments of inertia, and hence to the equilibrium rotational constants.

Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac12

89

On the other hand, the large changes in zero-point motion that accompany D for H substitution at the hydrogen-bond H position in weakly bound complexes tend to increase the rotational constants.

Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res11

90

Accordingly, the changes in the rotational constants of thiophene⋯H

^{79}Br when D is substituted for the H in the HBr sub-unit carry little information about the exact location of this atom within the complex.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac13

91

Some progress with the location of the H atom is possible

*via*the value of the off-diagonal element*χ*_{ab}of the Br nuclear quadrupole coupling tensor, as discussed in Section 3.3
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res12

### Quantitative geometry of thiophene⋯HBr

92

The qualitative model of the complex proposed in the preceding section has the Br atom lying on or close to the

*c*axis of the thiophene sub-unit and the H atom of HBr lying between the face of the thiophene ring and the Br atom.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp3

93

The geometry is therefore of the face-on type shown in Fig. 2.

Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod10

Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp4

95

In that approximation, the quantitative geometry of the complex may be described by means of the values of three quantities

*φ*,*θ*and*r*(S⋯H), as defined in Fig. 2.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod10

96

The angle

*φ*, the angular deviation*θ*of the S⋯H–Br nuclei from collinearity and the distance*r*(S⋯H) were then determined in a non-linear least-squares fit to the nine principal moments of inertia of the isotopomers C_{4}H_{4}S⋯H^{79}Br, C_{4}H_{4}S⋯H^{81}Br and C_{4}H_{4}S⋯D^{79}Br as follows.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod11

97

In view of the difficulty in locating the H atom of HBr through its contributions to the rotational constants, as discussed in Section 3.2, an alternative method of establishing the position of this atom was necessary.

Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs13

98

It was demonstrated some time ago

^{22,23}that a good approximation to the value of the angle*α*_{az}between the*a*axis and the HX internuclear axis*z*in a complex of*C*_{s}symmetry, such as thiophene⋯HBr, is given in terms of the components of the Br nuclear quadrupole coupling tensor*χ*_{αβ}by the expression*α*_{az}= ½ tan^{–1}{–2*χ*_{ab}/(*χ*_{aa}–*χ*_{bb})}If the distance*r*(H–Br) is unchanged from the free molecule, it follows that the angle*α*_{az}provides the location of H, once the position of Br is fixed by the principal moments of inertia.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod12

99

The necessary values of

*α*_{az}calculated from eqn. (3) for each of the three isotopomers of thiophene⋯HBr investigated are given in Table 4.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs14

100

The angle

*α*_{az}was used in the least-squares fit in the following way.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met4

101

The angle

*φ*and the distance*r*(S⋯H) were fitted to the nine principal moments of inertia, with the angle*θ*fixed at an initial estimate.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met4

102

The angle

*α*_{az}appropriate to the isotopomer C_{4}H_{4}S⋯H^{79}Br was then calculated from the angles*φ*and*θ*and the distance*r*(S⋯H) determined in the fit.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met4

103

Its difference from the value of

*α*_{az}obtained*via*eqn. (3) was then used to produce a refined estimate of*θ*.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met4

104

Iterations of this procedure were carried out until agreement was achieved between the observed and calculated values of

*α*_{az}.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met4

105

The converged values of

*φ*,*θ*and*r*(S⋯H) are given in Table 4.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs15

106

The error δ

*θ*in*θ*was estimated from the errors in*φ*,*r*(S⋯H) and*α*_{az}by the method described in .^{ref. 22}
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met5

107

This geometry is also shown, drawn to scale, in Fig. 2.

Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs16

108

Only the magnitude of the angle

*α*_{az}is available from eqn. (3).
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac14

109

Necessarily, the geometry in which the HBr sub-unit is rotated anti-clockwise, in the

*ab*plane, by an angle 2*α*_{az}about its centre of mass (the angle between the*a*and*z*axes is then –*α*_{az}) fits the observables with the same precision as does the chosen geometry.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5

110

Similarly, the angle that the C

_{2}axis of the thiophene sub-unit makes with the*b*axis of the complex could also be of the same magnitude but opposite in sign.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5

111

The arrangement chosen here, and shown in Fig. 2, is isostructural with those of thiophene⋯HF

^{13}and thiophene⋯HCl,^{14}for each of which isotopic substitution of^{34}S for^{32}S in the thiophene subunit allowed a distinction between the two possible orientations of the thiophene local C_{2}axis with respect to the*b*axis of the complex.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac15

112

Attempts to observe the rotational transitions of

^{34}S-thiophene⋯H^{79}Br in natural abundance failed and hence the experimental distinction available in the cases of thiophene⋯HF and thiophene⋯HCl is not available for thiophene⋯HBr.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs17

113

The Br nuclear quadrupole coupling tensor

*χ*_{αβ}in the principal inertia axis system (*α,β*=*a*,*b*or*c*) provides some information about the motion of the HBr sub-unit in the zero-point state of the complex.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac16

114

The rotational spectrum of each isotopomer of thiophene⋯HBr could be fitted with a standard deviation comparable to the estimated accuracy of frequency measurement by using only one non-zero off-diagonal element, namely

*χ*_{ab}.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod13

115

As indicated in Section 3.1,

*χ*_{bc}and*χ*_{ac}are both either zero or close to zero.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res4

116

If we assume these two components to be identically equal to zero, as required by a geometry of C

_{s}symmetry, the complete*χ*_{αβ}tensor has been determined.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp5

117

Diagonalisation then yields its principal components

*χ*_{zz},*χ*_{xx}and*χ*_{yy}, where*z*is the HBr internuclear axis direction and*x*lies in the symmetry plane of the complex.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod14

118

The values of these principal components for each of the three isotopomers of thiophene⋯HBr investigated are shown in Table 4.

Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs18

119

We note that in each case

*χ*_{xx}≠*χ*_{yy}.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs18

120

From the geometry shown in Fig. 2, it is evident that, even in the equilibrium conformation, the components of the electric field gradient tensor at Br along the

*x*and*y*directions are different and hence the equilibrium values of the elements*χ*e*xx*and*χ*e*yy*will be unequal.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res13

121

The observed quantities are zero-point values and it is clear that the zero-point motion of the HBr sub-unit will for the same reason be anisotropic, so that the H atom of HBr will in general describe an ellipse rather than a circle in the

*xy*plane.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp6

122

An inequality of

*χ*_{xx}and*χ*_{yy}is therefore to be expected.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp6

123

In fact,

*χ*_{xx}and*χ*_{yy}differ by only a few percent.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res14

124

If the motion of the HBr sub-unit in the

*xy*plane is assumed to be circular in reasonable approximation and if the electric field gradient tensor at Br in free HBr is assumed to be unaffected by the presence of the thiophene sub-unit (*i.e.*any electronic redistribution in HBr is ignored and the electric field gradient (EFG) at Br arising from the presence of the thiophene electric charge distribution is negligible), a rough estimate of the extent of the zero-point angular excursion of the HBr sub-unit from its equilibrium position can be made.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp7

125

In this approximation, the familiar expression

*χ*_{zz}= ½*χ*_{0}〈3 cos^{2}*β*– 1〉,relates*χ*_{zz}to*χ*_{0}, the Br nuclear quadrupole coupling constant of the free HBr molecule^{10,24}(see Table 3).
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod15

126

Eqn. (4) then leads to the result

*β*_{av}= cos^{–1}〈cos^{2}*β*〉^{1/2}= 22.8° for thiophene⋯H^{79}Br, where*β*is the angle between the instantaneous HBr axis and its equilibrium direction*z*and the angular brackets indicate an average over the zero-point angular excursions of the HBr sub-unit.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod16

127

Values of

*β*for all isotopomers investigated are recorded in Table 4.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs19

128

In view of the possible ambiguity in the sign of the angle

*α*_{az}and the consequent ambiguity concerning the exact position of the H atom of HBr in the complex (see Section 3.2), a more extended discussion of the angular motion of the HBr sub-unit in the complex seems inappropriate.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac17

## Discussion

129

The ground-state rotational spectra of three isotopomers of a complex thiophene⋯HBr, as observed with a pulsed-jet, Fourier transform microwave spectrometer, were interpreted in terms of a geometry in which the HBr subunit lies approximately perpendicular to the plane of the thiophene ring.

Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met2

130

The complex has been shown to possess

*C*_{s}symmetry, with the principal inertial plane*ab*coincident with the molecular symmetry plane and containing the HBr subunit, in the equilibrium arrangement.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con4

131

The H atom of HBr probably lies between the Br atom and the thiophene ring (see Fig. 3), although some doubt remains about the exact orientation of the HBr sub-unit in the equilibrium geometry.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con2

132

It is clear from comparison of the experimental geometries of furan⋯HCl, furan⋯HBr and benzene⋯HBr (Fig. 1) and thiophene⋯HBr (Fig. 2) that the last of these has a geometry different from that of furan⋯HCl but very similar to those of furan⋯HBr and benzene⋯HBr.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con6

133

Furan⋯HCl obeys part 3 of the rules for predicting angular geometries of hydrogen-bonded complexes, as discussed in the Introduction, in the sense that the HCl sub-unit lies along the axis of the non-bonding electron pair carried by the O atom and does not interact with the aromatic-π electron system.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con6

134

This is clearly not so for either furan⋯HBr or thiophene⋯HBr, since the determined geometries indicates that HBr interacts with the π electron system of the heteroaromatic molecule in each case.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con7

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con8

136

Evidently, thiophene behaves more like benzene in forming complexes with HF, HCl and HBr than does furan.

Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con9