Faraday Discuss. Chern. Soc., 1982, 73, 71-87 Determination of Properties of Hydrogen-bonded Dimers by Rotational Spectroscopy and a Classfication of Dimer Geometries BY A. C. LEGON AND D. J. MILLEN Christopher Ingold Laboratories, Department of Chemistry, University College London, 20 Gordon Street, London WC1 H OAJ Received 21st December, 1981 Rotational spectroscopy is a rich source of information about the molecular geometry, the potential-energy function and the electric-charge distribution of simple hydrogen-bonded dimers in the gas phase. Techniques for the observation of such spectra are now available and have led to a considerable amount of information for a wide range of dimers. We outline two techniques that have been used and then review the various molecular properties that can be derived from the observed spectroscopic constants.We indicate how vibrational ground-state rotational and centrifugal distortion constants can lead to information about the molecular geometry and potential-energy function and how observations of the Stark effect and nuclear quadrupole hyperfine structure allow conclusions about charge redistribution on dimer formation. We also show how important inform- ation can be obtained by the study of rotational spectra of dimers in vibrationally excited states. Two specific examples, HCN * HF and N2 * * HF, are examined in detail before a general discussion of results for a number of dimer species is presented in which geometries, force constants and dissociation energies are compared systematically.We show that, although the observed geometries correspond to broad potential energy minima, it is nevertheless possible to propose a simple rule which accounts for the preferred equilibrium conformation. Rotational spectroscopy is a rich source of information about the molecular properties of simple hydrogen-bonded dimers B - - HA. Moreover, since the spectra are obtained at low pressure, the molecular properties so determined refer to the isolated dimer unencumbered by lattice or solvent interactions. The molecular properties that can be obtained in this way include (i) the principal parameters charac- terizing the one-dimensional radial potent ial-energy function of the dimer, namely the geometry (re), the force constant (.fD) and the dissociation energy (De), (ii) details of the hydrogen-bond bending potential-energy function and (iii) information about the electric-charge distribution in the dimer, namely the electric dipole moment (‘p) and the electric field of gradients (a2 V/az2) at certain nuclei. In this paper we discuss briefly two experimental methods for detecting rotational spectra of species B - - HA, with special emphasis on the advantages and limitations, and consider the use of each technique by detailed reference to (HCN,HF) and (N,,HF).We then discuss the results for four types of simple dimer: (a) species B * * HX in which the acceptor atom carries only one non-bonding electron pair, (h) species B * HX in which the acceptor atom carries two non-bonding pairs, (c) species B . - * HX in which the acceptor atom has three non-bonding pairs and (d) species B - * - HX in which the acceptor molecule B has a 7c bond but no non-bonding pairs.Finally, we propose a simple rule which accounts for the observed geometries.72 ROTATIONAL SPECTROSCOPY OF HYDROGEN-BONDED DIMERS EXPERIMENTAL In this paper we discuss results derived from rotational spectra that have been obtained mainly by two techniques. The first of these involves conventional Stark modulation micro- wave spectroscopy of dimers in binary gas mixtures at equilibrium at temperatures 7200 K and pressures of ca. 50 mTorr. *' The second technique involves Fourier-transform micro- wave spectroscopy of a pulse of gas mixture (B and HA diluted in, say, argon) expanded supersonically from a nozzle into an evacuated Fabry-Perot cavity. The microwave pulse induces a macroscopic polarization in the gas when it is in collisionless expansion, It is required that the half-life, T2, for the decay of the macroscopic polarization is much greater than that (z,) for decay of the microwave pulse within the Fabry-Perot cavity.Accordingly, when the polarized dimers in the cold gas ( T FZ 5 K) begin to emit at some rotational tran- sition frequency and the detector is opened, the microwave pulse has dissipated and only the molecular emission survives to be detected. Details of the theory and operation of this technique have been de~cribed.~.~ Although equilibrium rotational spectroscopy is restricted mainly to moderately strongly hydrogen-bonded dimers and has moderate resolution, it has the significant advantage that rotational spectra are obtained in vibrationally excited states of the low-lying hydrogen-bond modes as well as in the vibrational ground state.The pulsed-nozzle, Fourier-transform method has a very high sensitivity to molecular dimers and a high resolution because of the low effective temperature of the gas pulse and because the molecular emission occurs while the gas is in collisionless expansion. Very weakly bound molecular dimers can be investigated with this instrument. A con- comitant disadvantage of the low effective temperature is, however, that spectra in the vibrational ground state only are observed. The equilibrium method, through the Stark effect, readily furnishes electric dipole moments of dimers, while the high resolution of the pulsed nozzle, Fourier-transform method allows the investigation of nuclear quadrupole and nuclear-spin-nuclear-spin coupling effects.Results obtained by other groups using molecular-beam electric resonance spectroscopy will also be discussed. The two techniques outlined above are complementary. RESULTS AND DISCUSSION (i) EQUILIBRIUM ROTATIONAL SPECTROSCOPY; HCN 9 HF The many molecular properties that can be determined from the rotational spectrum of a hydrogen-bonded dimer are well illustrated by the example of the linear complex HCN - - - HF.' Fig. 1 shows the J = 5t4 transition of this species in the ground state and various excited vibrational states, observed using the technique of equili- brium rotational spectroscopy. The strongest transition (at 35 908.35 MHz) is as- signed to the vibrational ground state and the remainder to vibrational satellites associated with the low-lying vibrational modes.On formation of a linear hydrogen- bonded dimer, the loss of three degrees of translational freedom and two degrees of rotational freedom results in three new vibrational modes, of which two are doubly degenerate and all are expected to have a considerably smaller energy spacing than any of the monomer modes. The approximate form of these new modes for HCN * - H F is shown in fig. 2. The doubly degenerate bending modes are denoted by va and vB, in order of increasing energy, and the stretching mode by v D . Tn fig. 1 the progressions in the low-frequency bending mode vs are identified using the convenient notation (va, uB'ti), where I is the vibrational angular momentum quan- tum number.An explicit label for the mode vB is not included in this notation because states with uB > 0 are not sufficiently populated at the experimental temperature. * 1 Torr = (101 325/760) Pa.A . C . LEGON AND D. J . MILLEN (0,001 73 I l l l r l l l l l l l r l l l r l I l l l l l l l l l L 3 8.0 37- 5 37.0 36.5 36.0 35.5 frequency/GHz FIG. 1 .-J = 5+4 transition of HCN - * HF in the vibrational ground state (0,OO) and in vibrationally excited states (u,,upl !). .... % vB ....- FIG. 2.-Diagrammatic representation of the low-frequency normal modes of HCN * * HF.74 ROTATIONAL SPECTROSCOPY OF HYDROGEN-BONDED DIMERS There is much information to be derived from the spectrum in fig.1. First, the ground-state transition frequency, taken with those of other J + 1 t J transitions, leads to accurate rotational constants for this and other isotopic species of the dimer. Under the well-established assumption of unchanged monomer geometries on dimer formation, the set of ro(N * * F) distances shown in table 1 results. The agreement TABLE VA VALUES OF ro(N - - - F) FOR HCN - - - HF isotopic species ro(N - - - F)/A between the values obtained from different isotopic species is remarkably good. We note that deuterium substitution leaves ro(N - - F) sensibly unchanged. A similar result has been obtained for CH3CN * HF.4a Secondly, the intensities of vibrational satellites relative to that of the ground state give the vibrational separation up = l+O as 91 20 cm-I and u, = It0 as 197 & 15 cm-’ in the two lowest-energy modes of the molecule.By combining these values with those of the analogous high-frequency modes vB and v,, obtained from infrared spectroscopy, 4b stretching and bending quadratic force constants have been obtained. From a model involving motion essentially along the dissociation coordin- ate of the dimer, the force constantf, is found to have a value of 26.3 N m-l. For the angle bending force constants we use the result obtained from a similar investigation 4b of CH3CN * HF, from which it was established, with the aid of the centrifugal distortion constant DJK, thatfo, (see fig. 3 for a definition of internal coordinates in HCN * * HF) is effectively zero. A similar assumption in the present case leads to the set of values f v = 3.7 x and fe = 6.3 x J for H”C14N.. .H19F. FIG. 3.-Internal coordinates used to describe bending of the HCN * * - HF molecule. Thirdly, while relative intensities lead to force constants, absolute intensities of rotational transitions in the equilibrium gas mixture of HCN and H F lead to the dissociation energy of the dimer.’ For a rotational transition originating from a state characterised by the rotational and vibrational quantum numbers J and u, the absolute (or integrated) intensity is given by I = (8n3n,,J/3ckT)Ipij]2v~ (1) where nu, J is the number density of molecules in the state u,J. Thus, if ,u is known (see below), can be determined directly. If the partition function of each of the molecules M participating in the dimer formation H C N + H F = H C N * * * H F (2) no,o(HCN - HF)/no,o(HCN)no,o(HF) = (h2/2npkT)3/2exp(D,/RT) (3) is known, values of E*,~(M) are then readily obtained and lead through the relationshipA .C . LEGON AND D. J . MILLEN 75 to the zero-point dissociation energy Do. The results of such determinations are Do = 18.9 Fourthly, the Stark effect, which can be distinguished in fig. 1 by its phase difference of n, provides a direct route to the determination of the electric dipole moment p of the dimer and its enhancement Ap over the sum of the monomer moments of this linear species. The mean value obtained from a number of measurements gives p = 5.612 & 0.01 D * and Ap = 0.80 D.6 Finally, it is in principle possible in a given rotational transition to resolve the nuclear quadrupole hyperfine structure arising from the I4N nucleus.The change in the 14N nuclear quadrupole coupling constant on dimer formation leads to additional information about the electric-charge redistribution that accompanies dimer form- ation. While results are not yet available for HCN - - - HF, these changes have been determined for other dimers, for example N2 - - HF,7 and will be discussed below. 1.1 kJ mo1-I and D, = 26.1 & 1.6 kJ mol-'. (ii) PULSED-NOZZLE, FOURIER-TRANSFORM SPECTROSCOPY: Nz * HF The dimer formed between molecular nitrogen and hydrogen fluoride is more weakly bound (see below) than that in which hydrogen cyanide is the acceptor molecule. Consequently, in order to observe its rotational spectrum, recourse to the pulsed-nozzle, Fourier-transform technique is appropriate.The spectrum is characteristic of a linear molecule but, because this technique detects only transitions in the vibrational ground state, the arguments used to establish the linear equilibrium geometry for HCN * HF are not available here. There is, however, considerable J -L____L___y -1.4 -1.2 -1.0 -+- frequency /MHz FIG. 4.-J = It0 transition in the vibrational ground state of 14N "N HF showing 14N nuclear quadrupole and H, I9F nuclear-spin-nuclear-spin hyperfine structure. Reconstructed from observed spectroscopic constants with frequencies offset from vo = 6355.4038 MHz. but less direct evidence for a similar geometry for N2 * * HF. Each rotational transition carries a complicated hyperfine structure arising from nuclear quadrupole coupling of the two I4N nuclei and the nuclear-spin-nuclear-spin coupling of H and 19F.This structure simplifies appreciably for the species l4NI5N - - HF, as shown for the J = It0 transition in fig. 4, in which is reproduced a computer simulation based * 1 D M 3.3356 x C m.76 ROTATIONAL SPECTROSCOPY OF HYDROGEN-BONDED DIMERS on the experimentally determined spectroscopic constants. Each separate component in fig. 4 has been resolved, thus illustrating the very high resolution of the pulsed- nozzle technique. Analysis of the hyperfine structure gives the nuclear quadrupole coupling constants x,,(l) and x,,(2) as displayed in table 2. The labelling of the N TABLE 2.-sPECTROSCOPIC CONSTANTS OF Nz * * HF 14N14N * * * HF 3195.3534 17.2 - 4.91 (14) - 4.75(14) 107(6) 15N14N * * * HF 3 11 6.4771 16.0 - -4.697(2) 1 lO(3) l4NISN - - - HF 3177.7361 17.1 - 4.978(3) - 115(5) lSN1'N * * HF 3101.1081 16.0 - - 105(1) ' S, is the H, 19F nuclear-spin-nuclear-spin coupling constant; see ref.(7) for details. atoms is such that N(2) is that involved in the weak binding. The difference AX,, = x,,(l) - x,,(2) = -0.286 MHz is significant and can be shown to be a lower limit to the equilibrium value of this quantity. Taking Ax,, as the equilibrium value allows us to discuss the electrical changes that occur in the N2 molecule on dimer formation. Two electrical effects make contributions to Ax,,: first, the presence of the HF molecule gives rise to different electric field gradients, and therefore nuclear quadrupole coupling constants, at N(l) and N(2) and, secondly, the electron polarization of the nitrogen molecule by the HF molecule has a similar result.As the electric multipole moment expansion of HF and the dimer geometry are known, the first of these contributions can be calculated (including the effects of Sternheimer shielding at the N nuclei) and hence the difference in the I4N nuclear quadrupole coupling constants caused by polarization of N2 by HF, Ax:, = -0.33 MHz, can be estimated. An interpretation of Ax:, is possible in terms of a simple valence-bond model. The valence-bond structures assumed to contribute to the N2 * HF dimer ground state are shown in table 3. Using the Townes-Dailey model for nuclear quadrupole TABLE 3 .-14N-NUCLEAR QUADRUPOLE COUPLING CONSTANTS, X/MHZ, FOR VALENCE- BOND STRUCTURES OF N2 * * ' HF valence-bond structure X U ) a X(2) Ax ~~~ ~ ~~~~~~~ (I) N=N * * H-F -5 -5 0 (11) k=N * * * H-F -12.5 0 - 12.5 (111) N=6 - - * H-F 0 - 12.5 f12.5 x values calculated for N, N+ and N - using the Townes-Dailey model [see C.H. Townes and A. L. Schawlow, Microwme Spectroscopy (McGraw-Hill, New York, 1955), p. 2391. coupling constants allows the values x (1) and x (2) shown for each structure in table 3 to be estimated. The final assumption is that dimer formation stabilizes structure I1 relative to structure 111. Since transfer of 1 electron from N(l) to N(2) in I to give I1 results in Ax = -12.5 MHz, the observed value corresponds to the analogous transfer of ca. 0.03e as HF takes up its equilibrium position.A.C . LEGON A N D D . J . MILLEN 77 (iii) A DISCUSSION OF DIMER PROPERTIES BASED ON A SIMPLE ELECTRON-PAIR MODEL FOR THE ACCEPTOR MOLECULE Now that a number of simple hydrogen-bonded dimer geometries is available from rotational spectroscopy, it is possible to present a discussion of dimer properties with the aid of a classification based on an electron-pair (n and n type) model for the acceptor molecule B. Each of the four classes (a) one non-bonding pair, (b) two non- bonding pairs, (c) three non-bonding pairs and (d) n-bonding pairs will be discussed in turn. (a) ONE NON-BONDING ELECTRON PAIR ON ACCEPTOR ATOM The dimers HCN - H F and N2. - HF, both of which are linear species and have been discussed above, are isoelectronic.We can understand the preferred geometry if the H atom in HF seeks the non-bonding pair on an N atom in each case, with the HF molecule lying along the supposed axis of the conventionally viewed non- bonding pair. In HCN there is only one non-bonding pair while in NZ, of course, there are two equivalent pairs. A third molecule forming a dimer in the isoelectronic series is carbon monoxide, which has two inequivalent axial non-bonding pairs. If, as is observed in the above examples, the HF molecule prefers to bind to a non-bonding rather than a n-bonding pair, the question arises as to which non-bonding pair is the better acceptor. Mixtures of CO and HF have been examined using the pulsed-nozzle Fourier- transform spectrometer and exhibit rotational spectra characteristic of a linear mole- ~ u l e .~ . ~ The J = 1-0 transition attributed to a species (C0,HF) is shown in fig. 5. frequency/MHz FIG. 5.-J = It0 transition in the vibrational ground state of l6OI2C * * * H19F showing H, 19F nuclear spin-nuclear-spin hyperfine structure. Each component is split further into a doublet as a result of the phenomenon of Doppler doubling. Frequencies are offset from 6127 MHz. There are four hyperfine components arising from the effects of H, 19F nuclear-spin- nuclear-spin splitting and each of these is further split into a doublet by a spectro- meter artefact. Spectroscopic constants have been obtained for five isotopic species, which allows five values for the distance r,(C F) to be calculated under the usual assumption that monomer geometries survive dimer formation.Only if the atoms78 ROTATIONAL SPECTROSCOPY OF HYDROGEN-BONDED DIMERS are assumed to be in the order 0-C * - HF does the internally consistent set of values displayed in table 4 result. This demonstrates unambiguously that the hydro- gen atom is bound to the carbon atom. TABLE 4.--r,(C - - - F) DISTANCES FOR OC * . - HF isotopic species ro(C * * * F)/A a Linear model, CO and HF bond lengths assumed unchanged on dimer formation. In the isoelectronic series B - HF, where B = HCN, N2 or CO, it is important to obtain and compare the strengths of the intermolecular binding as measured by D, andf,. While these are directly available for B = HCN from equilibrium rotational spectroscopy [see section (i)], they must be obtained less directly for B = N2 and CO.The method used relies on the pseudodiatomic approximation for B - - HF and the assumption that the hydrogen-bond stretching potential function is of the Lennard- Jones type.2 Thus the centrifugal distortion constant DJ is related to fa and D, as follows: and Dj = 4BZ/o: (4) D, = for2/72. (5) TABLE 5.-cOMPARISON OFf& Go and D, DETERMINED BY TWO METHODS FOR HCN - - * HF 27 200 24.8 26 1 9 7 i 15 26.1 f 1.6 diatomic approximation a experimental values L. W. Buxton, E. J. Campbell, M. R. Keenan, A. C . Legon and W. H. Flygare, unpublished bA. C. Legon, D. J. Millen and S. C. Rogers, Proc. R. SOC. London, Ser. A , 1980, 370, results. 213. Table 5 compares values so calculated for HCN - * HF with the more directly deter- mined values.The agreement in table 5 is sufficiently good to allow use of this method to make the comparison within the isoelectronic series shown in table 6. We TABLE 6.-COMPARISON OF BINDING STRENGTHS IN THE ISOELECTRONIC SERIES B a * * HF (B = HCN, CO, N,)A . C. LEGON AND D . J . MILLEN 79 note that, in this series, we generate the next member by moving a proton from the extreme left-hand nucleus in the dimer to the adjacent nucleus. Evidently, in proceed- ing from HCN to N2, the nitrogen atom thus becomes a worse acceptor. In the next step, we therefore assume that the oxygen atom becomes a worse acceptor than the carbon atom. Consequently, the most stable dimer of HF and CO has the atomic order OC Moreover, the carbon atom in CO has become a better acceptor than the nitrogen atom in NZ.It is also of interest to compare the strengths of binding calculated on the basis of the pseudodiatomic model within the series (HCN, HX), where X = F, C1 and Br, and within the corresponding series (OC, HX), for which the results are recorded in table 7.8-13 The order F > C1 > Br in each case is as expected. HF. TABLE 7.-cOMPARISONS OF THE BINDING STRENGTHS IN THE SERIES HCN ’ ’ HX AND OC - . HX WHERE X = F, C1, Br HC4N * - * HF 27 200 24.8 HCi4N * - H3’Cl 11.2 111 14.3 HC15N - - * H79Br 8.5 85 12.0 OC * Hi9F 10.8 125 11.8 oc . - - ~ 3 5 ~ 1 4.5 69 6.8 OC - * H79Br 3.3 52 5.6 In summary, it is found for a number of hydrogen-bonded dimers in the series B * - - HX (where B = HCN, N2, CO and X = F, C1, Br) that the geometries are all linear even though binding energy varies by as much as a factor of five.Thus, in all cases the H-X direction coincides with that of a non-bonding pair. This conclusion has also been shown to apply to RCN - * - HF, where R = CH3,4 (CHJ3C l4 and NC,I5 and to HCN - HCN.16*17 (b) TWO NON-BONDING ELECTRON PAIRS ON ACCEPTOR ATOM In order to test more severely the conclusion of the preceding paragraph it is necessary to investigate the geometries and properties of dimers in which the acceptor atom in B has more than one non-bonding pair of electrons. A convenient starting point is provided by molecules B in which an oxygen atom is the acceptor. The simplest possible hydrogen-bonded dimer in which an oxygen atom is the acceptor is (H20, HF). The rotational spectrum of this species has been investigated in an equilibrium gas mixture of water and hydrogen fluoride by using a Stark- modulation microwave s p e c t r ~ m e t e r .~ ~ * ~ ~ The pattern of rotational transitions is characteristic of that of a very nearly prolate rotor with a 3 : 1 nuclear spin statistical weighting of intensities appropriate to a molecule in which a pair of equivalent protons is exchanged by the operation C;. Moreover, the magnitude of the observed rotational constants accords with a dimer model in which H20 is the proton acceptor and HF is the proton donor. These facts exclude all geometries for (H,O,HF) except the C,, planar model and the C, non-planar form with a barrier to inversion of the configur- ation at the oxygen atom sufficiently low that the vibrational wavefunctions can be classified according to the C2, symmetry point group.It is crucial now to distinguish experimentally between the C, and Cfv equilibrium conformations. The equilibrium conformation of H20 * - HF has been established unambiguously80 ROTATIONAL SPECTROSCOPY OF HYDROGEN-BONDED DIMERS by a careful analysis 2o of the rotational spectra in excited vibrational states that are associated with the low-energy hydrogen-bond modes, the form of each of which is shown schematically in fig. 6. Vibrational satellites in the rotational spectrum have **.*4$ .... Q 1 % FIG. 6.-Diagrammatic representation of the low-frequency normal modes of H20 * * HF. been identified for a number of states, including (1 ,O,O), (2,0,0), (0,l ,O) and (0,2,0) where the notation (us(,), up(i), u,) is used.Three types of information gained from the satellite spectra have been employed, First, the variation of the rotational con- stants with Fig. 7 shows how (B + C), varies with and ug(i, will be considered.A . C. LEGON A N D D . J . MILLEN 81 each of ~ g ( ~ ) and vg(i). We merely note for the moment the striking difference in behaviour. Secondly, the vibrational spacings v = It0 and 2+l shown in table 8 TABLE 8 .-VIBRATIONAL SEPARATIONS FOR THE LOW-FREQUENCY HYDROGEN-BOND MODES AND VS(i) OF HzO * - HF vibrational separation/cm- mode v = It0 v = 2 4 VB(0) 64f 10 267 d= 35 VB(i) 157f 10 330 f 30 have been obtained from relative intensity measurements of the appropriate vibrational satellites for states associated with each of the modes vpt0) and V/j(i).We note that, while vB(i) exhibits effectively harmonic behaviour, the order of the spacing in vg(o) is 1 +O < 24- 1. A similar contrast has already been noted in the variation of (B + C), with v , where the mode Vpti) shows familiar behaviour but that of vg(o) is irregular. These results for v ~ ( ~ ) are characteristic of vibrational states governed by a double- minimum potential-energy function that has a low barrier, examples of which are known from the study of puckering modes in small ring molecules. The qualitative conclusion must be therefore that the equilibrium conformation of H20 . HF is that with C, symmetry. By using the usual one-dimensional approximation, we can determine the equili- brium value of the out-of-plane angle p (as defined in fig.8) simultaneously with a FIG. 8.-Out-of-plane angle p in HzO HF. determinatipn of the quantitative form of the potential function Y(p). We take the optimum potential-energy function Y(q) to be that which best reproduces the observed vibrational spacings in V B ( ~ ) and the observed variation of ( B + C), with V B ( ~ ) . The result is numerically : V(V)/cm-l = 328p4 - 406p2 (6) and graphically as shown in fig. 9, in which vibrational energy levels are also included. We have also used the observed variation of the electric dipole moment p with vg(o) as an additional constraint. A curvilinear model for the motion of the hydrogen atoms was assumed in order to obtain V(p) from Y(z), where z is a dimensionless reduced coordinate, in terms of which such calculations are conveniently made. It can be seen from fig.9 that the equilibrium value of 9 is 46" and that the barrier height is 126 cm-'. The value of p is not far removed from the value of approxim- ately half the regular tetrahedral angle expected if the four electron pairs (two bonding, two non-bonding) were tetrahedrally disposed about the central oxygen atom and if, at equilibrium, the HF molecule were to lie along the supposed axis of a non-bonding pair, as conventionally envisaged. We note that if the HF molecule is considered bound to a given non-bonding pair, the other such pair would exert a cooperative82 ROTATIONAL SPECTROSCOPY OF HYDROGEN-BONDED DIMERS effect on its binding in a manner that reduces both the barrier at the planar conforma- tion and the equilibrium value of p.The fact that a low barrier is observed and a consequent large vibrational amplitude occurs for H20 - * - HF even in the zero-point state draws attention to the need for caution in evaluating geometrical parameters from ground-state rotational constants in molecules of this type. Now that the non-bonding pair approach is found to be in accord with the I I I I I I I -80 - 4 0 0 4 0 8 0 V1° in fig. 8. FIG. 9.-Variation of the potential energy V(V) with p in H20 HF. The angle rp is defined equilibrium geometry of the dimer H,O - * HF, it is important to examine the con- figuration at oxygen in hydrogen-bonded dimers in which the angle between the non- bonding pair axes is expected to differ significantly from that in water.Itjs commonly assumed that for the molecules oxiran and oxetan the decreased angle COC is accom- panied by an increased angle between the non-bonded pair axes. The three molecules B = H20, (CH&O and (CH2)20 thus form a series in which the angle / \ pro- gressively decreases (104'3 1 ', 91 "44' and 61 "38') while presumably the angle between the non-bonded pairs increases correspondingly. Rotational spectra have accordingly been observed for dimers formed by hydrogen fluoride with each of oxiran 21 and oxetan.22 Ground-state rotational constants have been evaluated and used with the assumption of unchanged monomer geometries on dimer formation to determine the quantities r,(O - . F) and p in each case. Fig. 10 compares these two quantities for B - - HF where B = H20, (CH2)30 and (CH2),0.0 The striking result is that q increases in a manner that parallels the decrease in the/ \ angle noted above, a result which is consistent with the simple non-bonded pair approach. A further result which fits the general pattern is that for H20 * * HOH, where a value of p =58 & 6" (not far removed from half-tetrahedral) has been reported.23 Two other gas-phase dimers involving hydrogen bonding to oxygen should be men- 0A . C . LEGON A N D D . J . MILLEN 83 FIG. 10.-Comparison tioned. For N,O * of uo(O * F) and v, values in B HF, where B = H20, (CH2)30 and (CHAO. H F the angle between the N,O and HF axes has been reported 24 to be 47" (which is approximately the value expected from the simple model) while for C 0 2 - - - H F a linear geometry has been reported.2s (C) THREE NON-BONDING ELECTRON PAIRS ON ACCEPTOR ATOM Only two examples have been reported in which the acceptor atom in B has three non-bonded pairs of electrons.Both of these examples involve hydrogen bonding to the F atom in HF; one is (HF),, in which HF is also the proton donor and the other is HF - Both species have been investigated by Klemperer et al. using the molecular-beam electric-resonance technique. A detailed study of the HF dimer and its deuterated species 26 establishes a non-linear model for the geometry in which the F F distance is 2.7 & 0.05 8, and the HF unit acting as the acceptor is bent ca. 70" from the F - * * F axis. A similar non-linear geometry 27 holds for H F - * - HCl.These observations can be interpreted in terms of the non-bonding pair model if it is assumed that the three non-bonding pairs and the bonding pair in HF are disposed tetrahedrally about the fluorine nucleus. Then if the axis of the HF donor molecule coincides with the axis of one non-bonding pair an angle corresponding to that reported (ca. 70") would result. HCl, in which HCl is the proton donor. (d) "C-BONDING ELECTRON PAIRS WITH NON-BONDING PAIRS In the isoelectronic series B - - HF (where B = HCN, N,, CO) discussed above, the acceptor molecule has n-bonding electron pairs as well as non-bonding pairs. In view of the linear geometry established in each case, the proton of H F evidently prefers to seek the axis of the non-bonding pair rather than the region of high n- electron density. It is, therefore, of interest to enquire into the geometry of the dimer in which the isoelectronic acceptor molecule B is acetylene, since this has no non-84 ROTATIONAL SPECTROSCOPY OF HYDROGEN-BONDED DIMERS bonding valence electrons.Recently the rotational spectrum of (HC=CH, HC1) in its vibrational ground state has been detected by the technique of pulsed-nozzle, Fourier-transform microwave spectroscopy.28 The rotational constants have been interpreted unambiguously in terms of the T-shaped geometry for the dimer shown diagrammatically in fig. 1 l(a). The HC1 molecule lies along the C2 axis of acetylene, its hydrogen atom pointing at the centre of the C=C bond. The distance from the mid-point of C r C to C1 is obtained under the usual assumption of unchanged monomer geometry.This is the first example of a hydrogen bond to a n-bond detec- ted in the gas phase. A similar investigation of (ethylene, HCl) 29 leads to the geometry shown in fig. ll(b). Again the HCl molecule lies along the C2 axis that is in free ethylene per- C FIG. 11 .-Dimer geometries for B * HCl, where B is (a) acetylene, (b) ethylene and (c) cyclopropane. pendicular to the molecular plane. This result shows conclusively that the proton in HC1 seeks the region of maximum electron density offered by the n-bond, which is along the axis in question. Cyclopropane is well-known to behave in some ways like an unsaturated hydro- carbon. It is of interest that it forms a dimer with HCl of the geometry shown in fig. 11(~).3'-~~ The HCl axis coincides with a median of the cyclopropane equililateral triangle and the H atom points at the centre of a C-C bond.This result accords with the Coulson-Moffitt model of cyclopropane, which predicts a region of highA . C . LEGON AND D. J . MILLEN 85 electron density on the median but displaced away from the ring, and which for the purposes of hydrogen bonding allows cyclopropane to be viewed, at the edge of interest, as a distorted ethylene molecule. Finally, by use of the pseudodiatomic model [eqn (4) and ( 5 ) above] it is possible to compare the quantities (fo and D,) that define the strength of intermolecular bind- ing in a number of molecules B - - - HCl. These quantities are recorded for the TABLE COMPARISON OF BINDING STRENGTHS IN THE SERIES B - - HCl Ar 1.2 32 1.5 oc 4.5 69 6.8 H2C=CH2 6.6 84 7.5 HC=CH 6.9 88 7.7 (CH2)3 8.7 87 11.5 HCN 11.2 1 1 1 14.3 a Ref.(33). series B = Ar,33 OC, HC=CH, H2C=CH2, cyclopropane and HCN in table 9. The increase in these quantities from B = Ar to B = HCN is understandable in terms of the expected electron-donor ability of B. C 0 N C L U S I 0 N S An important conclusion about the preferred equilibrium geometries can be drawn from the results obtained for the variety of simple hydrogen-bonded dimers discussed in the preceding section. Care must be taken in drawing general conclusions about geometry because, as already noted for H20 - - * HF, distortion from equilibrium by bending the hydrogen bond costs little in energy. In case it might be thought that, because of the double-minimum potential-energy function, the ease of hydrogen-bond bending in H20 * HF is unique, we now present an analysis which shows that bend- ing of this type is relatively easy even when it is governed by a single-minimum potential-energy function.This is followed by a simple rule in terms of which the preferred equilibrium geometries can be understood, even though the energetic stability of the observed conformer is so small. It is possible to examine the energetics of angular distortion of the hydrogen bond in CH,CN * HF for each of the angles shown in fig. 3. Values of the energy AE required to produce angular distortions of A0 and A9 in the range 0-30" are given in table 10. The calculations are based on the harmonic force constants [given in ref.(4)]. Although it has not been established that the force field is harmonic over that range, the nearly uniform spacings observed in the satellite progression for several quanta of the bending mode v p suggest that for this mode at least the harmonic assumption may well be a good approximation. Table 10 also gives distortion ener- gies as a percentage of the dissociation energy based on the value of D, for HCN - - - HF, since that for CH,CN - * HF is not available. The value of D, for the latter is probably somewhat larger and so percentages in table 10 are likely to be a little over- estimated. It is seen that distortion from linearity at N is relatively easy to bring about ; even a distortion of A8 = 30" reduces the hydrogen-bond energy by only 15%.By contrast distortion away from linearity at H leads to a more rapid reduction in binding energy. Thus for Arp = 30" the result is a reduction in binding energy of86 ROTATIONAL SPECTROSCOPY OF HYDROGEN-BONDED DIMERS TABLE ~~.-HYDROGEN-BOND DISTORTION ENERGIES FOR CH,CN * - HF distortion A9 AP angle/" AElkJ mol-' AEID, AEIkJ mol-' AEID, 10 0.4 2% 1.5 6% 20 1.7 7% 5.9 22 % 30 3.8 15% 13.8 53% 53%. These findings can readily be interpreted in terms of repulsion energy between N and F that rises rapidly as H moves away from the N * * - F line. This is in contrast to the situation in which the hydrogen bond remains linear (A0 > 0, Av) = 0), when resistance to bending is small. Although large changes in the angle 0 (see fig. 3) can be made at the cost of very little energy, a simple rule can be proposed which summarises the equilibrium geo- metries for the species B - * - HX discussed in this paper and which can be assumed to apply to gas-phase, hydrogen-bonded dimers generally : THE RULE The gas-phase geometry of a dimer B - HX can be obtained in terms of the non- (i) the axis of the HX molecule coincides with the supposed axis of a non-bonding bonding and n-bonding electron pairs on B as follows: pair as conventionally envisaged, or, if B has no non-bonding electron pairs but has n-bonding pairs, (ii) the axis of the HX molecule intersects the internuclear axis of the atoms form- ing the n-bond and is perpendicular to the plane of symmetry of the n-orbital.Rule (i) is definitive when B has both non-bonding and n-bonding pairs.The investigations reported here that use the pulsed-nozzle, Fourier-transform microwave spectrometer were carried out in collaboration with the late W. H. Flygare while one of us (A. C . L.) was on sabbatical leave at the University of Illinois in 1980. We thank L. C . Willoughby for obtaining the spectrum reproduced in fig. 1 . A research grant from the S.R.C. is gratefully acknowledged. A. C. Legon, D. J. Millen and S. C . Rogers, Proc. R. SOC. London, Ser. A, 1980, 370, 213. T. J. Balle, E. J. Campbell, M. R. Keenan, and W. H. Flygare, J. Chem. Phys., 1980, 72, 922. T. J. Balle and W.H. Flygare, Rev. Sci. Instrum., 1981, 52, 33. (a) J. W. Bevan, A. C. Legon, D. J. Millen and S. C. Rogers, Proc. R. Soc. London, Sev A, 1980, 370,238. A. C. Legon, D.J. Millen, P. J. Mjoberg and S. C. Rogers, Chem. Phys. Lett., 1978,55, 157. A. C. Legon, D. J. Millen and S. C. Rogers, J. Mol. Spectrosc., 1978, 70, 209. P. D. Soper, A. C . Legon, W. G. Read and W. H. Flygare, J. Chern. Phys., 1982, 76, 292. * A. C. Legon, P. D. Soper, M. R. Keenan, T. K. Minton, T. J. Balle and W. H. Flygare, J. Chew Phys., 1980, 73, 583. A. C. Legon, P. D. 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C . Rogers, Proc. R. SOC. London, Ser. A , 2o Z . Kisiel, A. C. Legon and D. J. Millen, Proc. R. SOC. London, Ser. A , in press. 21 A. S. Georgiou, A. C . Legon and D. J. Millen, Proc. R. Soc. London, Ser. A, 1981,373, 511. 22 A. S. Georgiou, A. C. Legon and D. J. Millen, J. Mol. Struct., 1980, 69, 69. 23 T. R' Dyke, K. M. Mack and J. S. Muenter, J . Chem. Phys., 1977, 66, 498. 24 C. H. Joyner, T. A. Dixon, F. A. Baiocchi and W. Klemperer, J . Chem. Phys., 1981, 74, 6550. 25 F. A. Baiocchi, T. A. Dixon, C. H. Joyner and W. Klemperer, J. Chem. Phys., 1981, 74, 6544. 26 T. R. Dyke, B. J. Howard and W. Klemperer, J. Chern. Phys., 1972,56,2442. '' K. C. Janda, J. M. Steed, S. E. Novick and W. Klemperer, J. Chern. Phys., 1977, 67, 5162. A. C. Legon, P. D. Aldrich and W. H. Flygare, J. Chem. Phys., 1981,75, 625. 29 P. D. Aldrich, A. C . Legon and W. H. Flygare, J. Chem. Phys., 1981, 75, 2126. 30 A. C. Legon, P. D. Aldrich and W. H. Flygare, J . Am. Chem. SOC., 1980, 102, 7584. 31 A. C. Legon, P. D. Aldrich and W. H. Flygare, J. Am. Chem. SOC., in press. 32 L. W. Buxton, P. D. Aldrich, J. A. Shea, A. C. Legon and W. H. Flygare, J. Chem. Phys., 1981, 75, 2681. 33 Calculated from results given by S. E. Novick, P. Davies, S. J. Harris and W. Klemperer, J. Chem. Phys., 1973, 59, 2273 and S. E. Novick, K. C. Janda, S. L. Holmgren, M. Waldman and W. Klemperer, J. Chem. Phys., 1976, 65, 11 14. 1980,372, 441.