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

The ground-state rotational spectra of three isotopomers C4H4S⋯H79Br, C4H4S⋯H81Br and C4H4S⋯D79Br 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.

Each spectrum was analysed and fitted to give rotational constants A0, B0 and C0, centrifugal distortion constants ΔJ, ΔJK, ΔK, δJ and δJK and the components χaa, χbb – χcc and χab of the bromine nuclear quadrupole coupling tensor.

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

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.

The angle αaz made by the HBr internuclear axis z with the a-axis has the two possible values ±9.83°.

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.

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 C2 axis of thiophene and θ is the angular deviation of the S⋯H–Br nuclei from collinearity.


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

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

Furan⋯HCl evidently obeys this rule because it was shown2 to have a planar geometry of C2v symmetry, with the HCl lying along the C2 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.

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

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.

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

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.

A recent investigation4 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.

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.

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

The series of complexes pyridine⋯HX, where X is F, Cl or Br, all have the C2v geometry,6–8 as expected from the rules, that is the HX molecule lies along the C2 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 C5H5NH+⋯Br to the valence-bond description of the complex with HBr.8

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 µ and quadrupole moments Θ of the heterocyclic aromatic molecules pyridine and furan are compared.9

In pyridine, both µ and the component Θzz of Θ, where z is the C2 axis, are large and negative, corresponding to a prominent nonbonding electron pair on N. In furan, µ is smaller and Θzz is close to zero, suggesting that the n-pair in furan is more involved in the ring.

It has been proposed that the change from the C2v to the face-on geometry when HX is HBr arises from a reduced contribution of electrostatic factors coupled with an increased dispersion effect.

The former occurs because the electric dipole moment of HBr10 is smaller than that of HF11 or HCl12 while the latter is expected to increase in the order HF < HCl < HBr.

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

For thiophene, µ is even smaller and the component Θzz is positive.

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.

The fact that the complexes of thiophene⋯HF13 and thiophene⋯HCl14 involve the π type, face-on arrangement is consistent with these conclusions deduced from the charge distributions of the heteroaromatic molecules and indicates that thiophene⋯HBr should also have the face-on geometry.

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.

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.


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

Recent modifications16 have been outlined elsewhere.

A fast-mixing nozzle17 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.

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.

The flow rate was adjusted to yield a nominal pressure of ca. 10–4 mbar in the chamber.

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).

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.

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

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.

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

DBr was prepared by the exchange of HBr gas with D2O adsorbed on the walls of the stainless steel stagnation vessel.

To saturate the walls of the vessel with D2O, the vessel was heated to ca. 70–80 °C and then the vapour from above a warmed sample of the liquid D2O was brought into contact with the vessel walls while they cooled.

The vessel was then reheated and the HBr gas added.

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

In this way a sample of DBr with ca. 70 atom% D was produced.


Spectral assignment and analysis

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.

This model was constructed by taking the observed angular geometry14 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).

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

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.

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.

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

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.

Observed frequencies and assignments of hyperfine components in a- and b-type rotational transitions of each of the three isotopomers C4H4S⋯H79Br, C4H4S⋯H81Br and C4H4S⋯D79Br are recorded in Table 1.

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

The Hamiltonian H constructed for this purpose was of the form H = HR + HQ + HSR where HR is the rotational energy operator for a semi-rigid asymmetric rotor and HQ = –1/6QBr:▽EBr is the operator describing the energy of interaction of the Br nuclear electric quadrupole moment QBr with the electric field gradient ▽EBr at Br.

The weaker, magnetic mechanism for coupling I and J, namely Br spin–rotation coupling, contributed in a minor but just detectable way to observed frequencies and hence the appropriate operator HSR = I·M·J, where M is the familiar spin–rotation coupling tensor, was added to the Hamiltonian, as shown in eqn. (1).

The matrix of H in the coupled basis I + J = F was diagonalised in blocks of the quantum number F.

The forms of the elements of HR, HQ and HSR in this basis are well known.

For HR, the Watson A reduction19 was employed.

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

It should be noted from Table 2 that only three independent components of the Br nuclear quadrupole hyperfine coupling tensor χαβ = eQ2V/∂αβ (namely, χaa, χbbχcc, and χab) were required to fit the spectra with a rms error similar in magnitude to the estimated error of frequency measurement.

Values of the other two off-diagonal elements χac and χbc were not determinable; attempts to fit them gave values near to zero and smaller in magnitude than their associated standard errors.

An equilibrium geometry of C2v symmetry in which the HBr molecule forms a hydrogen bond to the sulfur atom and lies along the C2 axis of the thiophene sub-unit is immediately precluded by the fact that χab is non-zero and by the observation of b-type transitions.

In that case, all three off-diagonal elements χab, χac and χbc of the Br hyperfine coupling tensor in the principal inertial axis system would be zero, as would the component µb of the electric dipole moment.

The contribution from Br spin–rotation coupling to the observed frequencies allowed only the diagonal components Mbb of the tensor M to be determined.

Only quartic centrifugal distortion constants were necessary to give satisfactory rms deviations σ of the fits.

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

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

Residuals Δν = νobs – νcalc 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.

The values of σ for all three isotopomers are close to the estimated error of frequency measurement (2 kHz).

Symmetry of thiophene⋯HBr

The magnitude of the rotational constant A0 in each of the three isotopomers of thiophene⋯HBr investigated is such that a geometry of C2v symmetry for the complex can be ruled out immediately.

If the HBr sub-unit were to lie along the C2 axis of thiophene, A0 of the complex should be almost identical in value to that of the free thiophene molecule.

A comparison of the values of the A0 for each of the isotopomers of the complex (Table 2) with that of thiophene20 (Table 3) shows that the change in A0 is large and clearly HBr cannot lie along the C2 axis of thiophene.

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

Such a conclusion is consistent with the observation of b-type transitions and a non-zero value of the component χab of the Br nuclear quadrupole coupling tensor.

We also note from Table 2 that the change in the rotational constant A0 when either 81Br or D is substituted in the HBr sub-unit of the isotopomer thiophene⋯H79Br is less than 2 MHz in each case.

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

Moreover, the A0 values of these isotopomers are not very different from the rotational constant C0 of free thiophene20 (see Tables 2 and 3).

Therefore, in the complex, the Br atom sits on or close to the local c axis of the free thiophene molecule.

Support for the assignment of a geometry of Cs symmetry, in which the HBr subunit lies in the molecular symmetry plane, comes from the values of the planar moment Pc of the three isotopomers of thiophene⋯HBr investigated.

Pc is defined in eqn. (2) and depends only on the principal-axis co-ordinates ci of the atoms i.

2Pc = –(Ia + Ib – Ic) = 2∑mic2iValues of Pc for each of the isotopomers of the complex are included in Table 2.

We note that this quantity is essentially invariant among thiophene⋯H79Br, thiophene⋯H81Br and thiophene⋯D79Br.

Moreover, Pc is similar in magnitude to the corresponding planar moment Pb of thiophene itself (see Table 3).

The invariance of Pc 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.

The near-identity of Pc of the complex and Pb of thiophene indicates that the geometry of thiophene is not significantly perturbed by complex formation.

The observation of smaller changes in the rotational constants B0 and C0 between the H79Br and D79Br isotopomers than between the H79Br and H81Br 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.

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

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

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.

Accordingly, the changes in the rotational constants of thiophene⋯H79Br 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.

Some progress with the location of the H atom is possible via the value of the off-diagonal element χab of the Br nuclear quadrupole coupling tensor, as discussed in Section 3.3

Quantitative geometry of thiophene⋯HBr

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.

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

To determine the geometry of thiophene⋯HBr, we shall assume that thiophene20 and hydrogen bromide21 are negligibly changed in geometry (the free-molecule geometries are given in Table 3 for convenience) when they are subsumed into the complex.

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.

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 C4H4S⋯H79Br, C4H4S⋯H81Br and C4H4S⋯D79Br as follows.

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.

It was demonstrated some time ago22,23 that a good approximation to the value of the angle αaz between the a axis and the HX internuclear axis z in a complex of Cs symmetry, such as thiophene⋯HBr, is given in terms of the components of the Br nuclear quadrupole coupling tensor χαβ by the expression αaz = ½ tan–1{–2χab/(χaa – χbb)}If the distance r(H–Br) is unchanged from the free molecule, it follows that the angle αaz provides the location of H, once the position of Br is fixed by the principal moments of inertia.

The necessary values of αaz calculated from eqn. (3) for each of the three isotopomers of thiophene⋯HBr investigated are given in Table 4.

The angle αaz was used in the least-squares fit in the following way.

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.

The angle αaz appropriate to the isotopomer C4H4S⋯H79Br was then calculated from the angles φ and θ and the distance r(S⋯H) determined in the fit.

Its difference from the value of αaz obtained via eqn. (3) was then used to produce a refined estimate of θ.

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

The converged values of φ, θ and r(S⋯H) are given in Table 4.

The error δθ in θ was estimated from the errors in φ, r(S⋯H) and αaz by the method described in .ref. 22

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

Only the magnitude of the angle αaz is available from eqn. (3).

Necessarily, the geometry in which the HBr sub-unit is rotated anti-clockwise, in the ab plane, by an angle 2αaz about its centre of mass (the angle between the a and z axes is then –αaz) fits the observables with the same precision as does the chosen geometry.

Similarly, the angle that the C2 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.

The arrangement chosen here, and shown in Fig. 2, is isostructural with those of thiophene⋯HF13 and thiophene⋯HCl,14 for each of which isotopic substitution of 34S for 32S in the thiophene subunit allowed a distinction between the two possible orientations of the thiophene local C2 axis with respect to the b axis of the complex.

Attempts to observe the rotational transitions of 34S-thiophene⋯H79Br 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.

The Br nuclear quadrupole coupling tensor χαβ 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.

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 χab.

As indicated in Section 3.1, χbc and χac are both either zero or close to zero.

If we assume these two components to be identically equal to zero, as required by a geometry of Cs symmetry, the complete χαβ tensor has been determined.

Diagonalisation then yields its principal components χzz, χxx and χyy, where z is the HBr internuclear axis direction and x lies in the symmetry plane of the complex.

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

We note that in each case χxx ≠ χyy.

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 χexx and χeyy will be unequal.

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.

An inequality of χxx and χyy is therefore to be expected.

In fact, χxx and χyy differ by only a few percent.

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.

In this approximation, the familiar expression χzz = ½χ0〈3 cos2β – 1〉,relates χzz to χ0, the Br nuclear quadrupole coupling constant of the free HBr molecule10,24 (see Table 3).

Eqn. (4) then leads to the result βav = cos–1〈cos2β1/2 = 22.8° for thiophene⋯H79Br, 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.

Values of β for all isotopomers investigated are recorded in Table 4.

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


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.

The complex has been shown to possess Cs symmetry, with the principal inertial plane ab coincident with the molecular symmetry plane and containing the HBr subunit, in the equilibrium arrangement.

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.

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.

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.

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.

When the choice of the sign of the angle αaz for thiophene⋯HBr is made to be consistent with those of thiophene⋯HCl14 and thiophene⋯HF,13 the geometries of all three thiophene⋯HX are isomorphous and are similar in type (i.e. face-on) to those of the corresponding benzene⋯HX.

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