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Br nuclear quadrupole and H,Br nuclear-spin-nuclear-spin coupling in the rotational spectrum of H2O…HBr
Volume 150, number 1,2
CHEMICAL PHYSICS LETTERS
9 September 1988
Br NUCLEAR QUADRUPOLE AND H,Br NUCLEAR-SPIN-NUCLEAR-SPIN COUPLING IN THE ROTATIONAL SPECTRUM OF H*O...HBr A.C. LEGON and A.P. SUCKLEY Department of Chemistry, University ofExeter, Stocker Road, Exeter EX4 4QD, UK
Received 9 June 1988
Partially resolved hyperfine structure arising from H,Br nuclear-spin-nuclear-spin coupling has been identified in each Brnuclear quadrupole component of the l,,, +O,,,, transition of H,O...HBr. Lineshape simulation leads to a value of D,,= - 23 (2) kHz for the spin-spin coupling constant for both H,0...H79Br and H20...H8’Br. An apparent inconsistency between this value and the respective Br-nuclear quadrupole coupling constants x0.=424.326( 9) and 354.490( 2) MHz is resolved by allowing for the influence of the HZ0 electric charge distribution on the value ofkn.
1. Introduction We report the detection in the gas phase of a weakly bound dimer formed between water and hydrogen bromide. Each of the isotopic species Hz0...H79Br and H20...Hs1Br has been identified through the highly characteristic nuclear hyperfine structure of its 101t Oooground-state rotational transition which arises from Br-nuclear quadrupole and H,Br nuclearspin-nuclear-spin coupling. The splitting due to the latter lies at the limit of resolution of the pulsed-nozzle, Fourier-transform microwave spectrometer used to observe the rotational transitions and we have found it necessary to resort to lineshape simulation to determine the H,Br spin-spin coupling constants. An important conclusion of the investigation is that the hypefine structure of the loleOoo transitions can be reproduced completely without the need to invoke the presence of spin-spin coupling arising from the two protons in the HZ0 subunit. The absence of such coupling is expected if the dimer has either a sufficiently low potential energy barrier or no barrier to the planar arrangement H20...HBr of Czv symmetry. By taking advantage of a recent determination of the component & of the electric-fieldelectric-field gradient response tensor of HBr [ 11, we have been able to demonstrate that an apparent inconsistency in the oscillation angle when determined indepenBa”=cos-‘(cos2~)“2
dently in the conventional manner from each of the coupling constants xanand Da,can be resolved if the electrical influence of the HZ0 subunit on the HBr molecule is allowed for using a simple electrostatic model of H*O...HBr.
2. Experimental The 100+Ooo transitions of H20...H79Br and Hz0...H8’Br have been observed at frequencies near 5.6 GHz with a pulsed-nozzle, Fourier-transform microwave spectrometer. The microwave radiation was coupled into and out of the Fabry-Perot cavity by means of coaxial waveguide components and looped antennae of suitable dimensions located at the centres of the mirrors. The searching rate and the sensitivity of our original spectrometer [ 2 ] have been improved recently [ 31 by the introduction of an Elonex 280-Turbo (IBM AT compatible) computer, which controls the HP8671 B synthesized source of microwave radiation and also collects and processes the time-domain signals from the cavity. The data collection rate is thereby sufficiently improved that a Series 9 valve (General Valve Corporation) operating at a repetition rate of up to x 100 Hz with gas pulse lengths of = 200 ps can be used. At the rate of z 20 Hz employed here, there was no loss of signal per gas pulse compared with the prototype spectrom-
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
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eter operating at 0.5 Hz with x 3 ms gas pulses, This represents a useful improvement in the signal-tonoise ratio for a given averaging time and the consumption of comparable amounts of gas. Gas mixtures composed of water at its room-temperature vapour pressure, hydrogen bromide (partial pressure 2 50 Torr) and argon (partial pressure x 760 Torr) were pulsed into the evacuated FabryPerot cavity via a 0.7 mm circular orifice in the Series 9 valve. Hypertine components whose frequencies fell with the admittance band of the cavity were polarized by 1.1 us microwave pulses from the HP8671 B frequency synthesizer and the delayed coherent emission was digitized at a rate of 0.5 us/point for 5 12 points. After sufficient averaging, the timedomain recording was subject to Fourier transformation to yield a power spectrum of 256 data points at 3.90625 kHz intervals. Examples of such power spectra are shown in figs. 1 and 2. Following a suggestion by Dr. Z. Kisiel, the points in figs. 1 and 2 have been connected by a cubic spline function instead of joining them by straight lines. This greatly improves the spectral display and allows a more confident identification of features that are only partially resolved.
3. Results
55LioL
9 September 1988
%iizzzz2;56 FrequcncylMHz
Fig. 1. Composite diagram of the three Br-nuclear quadrupole components in the Ii,, +Onotransition of Hz0...H79Brat 5541.08, 5625.56 and 5731.88 MHz (see table 3). The upper trace shows the observed transitions in which adjacent points (large dots) are spaced by 3.90625 kHz and are joined by means of a cubic spline function (small dots). The substructure of each component arises from H,Br nuclear-spin-nuclear-spin coupling and a slight instrumental doubling effect. Each stick diagram shows the calculated frequencies and intensities of the spin-spin components after allowance for the doubling of 7 kHz. The solid curve is then the lineshape function obtained by representing each stick by a Gaussian function having a full-width at half-height of 6.7 kHz and an amplitude proportional to the height of the stick. The observed spin-spin coupling constant II,,= -23(2) kHz was obtained by adjusting its value to give the best reproduction of the observed lineshape.
3. I. Determination of hyperfine coupling constants The ground-state rotational spectrum of H20...HBr has considerable complexity as a result of the simultaneous occurrence of Br-nuclear quadrupole coupling, H,Br nuclear-spin-nuclear-spin coupling, a very small asymmetry splitting and a small isotopic shift between H,0...H79Br and HzO...H*‘Br. Thus, for Hz0...H79Br, the unperturbed line centres of the 21*+ Ill, 202 c 1 o, and 2,, c 11otransitions are spread over a frequency range of only x 42 MHz centred at x 11.29 GHz while the Br-nuclear quadrupole splitting of each of these transitions covers a frequency of ~200 MHz. For H20...H8’Br, a similar pattern results but displaced lower in frequency by z 50 MHz. Moreover, each individual Br-nuclear quadrupole component exhibits additional substructure. A similar complexity is observed in the J=3+2 transitions. The detailed information about 154
H*O...HBr that is contained in the J=2+ 1 and 3~2 transitions is more readily accesible if a preliminary analysis of the lo1t O,,,,transitions of H20...H79Br and Hz0...H8’Br is made. This preliminary analysis is reported here. The 10,tOoo transitions of H20...H79Br and H,O...H*‘Br each consist of a gross Br-nuclear quadrupole triplet of large splitting centred at x 5625 and x 5603 MHz, respectively, as illustrated by the composite spectral recordings in figs. 1 and 2. A striking feature in each case is that each of the three Br-nuclear quadrupole components carries an additional, incompletely resolved substructure which is highly reproducible. We note further from figs. 1 and 2 that this substructure is essentially identical for the two isotopomers. The only possible sources of the substructure are the various nuclear-spin-nuclear-spin couplings that can occur between the I> l/2 nuclei
CHEMICAL PHYSICS LETTERS
Volume 150, number 1,2
9 September 1988
the spin-spin coupling tensor D having elements given by Dij=(~uo/4n:)ga,gH~~(R26ij-3RiRj)lR5
>
(4)
where the Ri are Cartesian components of the vector joining the H and Br nuclei and the other symbols have their usual meaning. The final term in eq. ( 1) allows for the magnetic coupling of the Br-nuclear spin angular momentum Z,, to the rotational angular momentum I and is given by H,,=--I,,*M*J,
YequencylMHz
Fig. 2. Composite diagram of the three Br-nuclear quadrupole components in the lo, ~000 transition of H20...H8’Br at 5532.17, 5602.80 and 5691.59 MHz (see table 3). For a detaileddescription of this figure, see the caption for fig. 1, which applies equally here.
in H,O...HBr. Since spin-spin coupling constants vary as ( r -3), where r is the distance between the pair of nuclei in question, any cross couplings between the subunits would lead to negligible effects in the observed spectrum. In fact, we shall establish below that the observed substructure in the lo,+-Ooo transitons can be completely assigned by invoking only H-Br spin-spin coupling and consequently that intercoupling of the Hz0 protons is absent. The analysis of hyperflne structure in the lo1CO,, transitions was carried out in several stages to give the Br-nuclear quadrupole and H,Br spin-spin coupling constants x=(1and D,,. In general, the matrix of the Hamiltonian H=H,+ZZo+N,,+&,
(1)
was constructed in the coupled basis Z,+Z,,=Z, Z+J=P and diagonalized in blocks of F. In eq. ( 1 ), HR is the familiar rotation Hamiltonian while HQ accounts for the interaction of the Br-nuclear electric quadrupole moment 0 and the electric field gradient VE at the Br nucleus according to HQ=-~$l:VE.
(2)
The term H,, describes the H,Br spin-spin interaction and has the form H,, =Z,,*D*Z,
,
(3)
(5)
where M is the Br spin-rotation tensor. The matrix elements of Ho, H,, and HSR in the above coupled basis are given elsewhere [ 4,5 1. In fact, for each of the three types of coupling, only a single constant can be determined from the lo, tOOOtransition, namely the components xaa, D,, and i( Mbb t Mcc) of the nuclear quadrupole, spin-spin and spin-rotation tensors, respectively. Initially, the frequencies of the three Br-nuclear quadrupole components of the loltOOo transition were estimated by ignoring the substructure and the Hamiltonian in eq. ( 1) was truncated after the second term to obtain a first estimate of xap and the unperturbed frequency vo. Then using the initial estimate of x=0the quantity ( cos2B) was calculated, where 1 is the instantaneous angle between the a axis of the dimer and the HBr symmetry axis. The method of calculation of ( cos2/3) from xaa and the Br-nuclear quadrupole coupling constant x0 of free HBr is discussed below and allows for the contribution made to x~~by the electrical and geometrical changes induced in HBr by the presence of H20. This contribution is significant and reduces b,,=cos- ’ x (cos2/9) ‘I2 from 21.58” to 12.7”. The spin-rotation constant f ( Mbb+ M,,) can then be estimated from the expression [ 4 ] ;(MbbtMcc)=M,,l?o(
1+cos2/3>/2bo,
(6)
where MO and b. are the spin-rotation constant [ 61 and the rotational constant [ 7 ] of free HBr (see table 1) . The quantity B. = f (B. + Co) can be replaced by 1v. = f (B. + Co) - 20, with sufficient accuracy for the present purposes. The next stage in the analysis was to choose a value of Da, which together with the initial estimates of xaa 155
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CHEMICAL PHYSICS LETTERS
9 September 1988
Table 1 Spectroscopic and molecular properties of HBr and Hz0 Quantity
H79Br
H*‘Br
B,, (MHz) =) xo (MHz) b, Da (kHz) b, MO (kHz) b’ rn(HX) (A) L HXH (deg)
250358.510 532.3059(2) -20.59( 14) -290.796(28) 1.42426‘)
250280.582 444.6807(2) -22.28(10) -313.370(21) 1.42426‘)
Hz0
0.9577(6) d, 104.66(8) d,
‘) Ref. [7]. b, Ref. [ 61. Note that our definitions of Do and MOare -2 and - 1, respectively, times those in ref. [ 61. ‘I r,-,(HBr) has been calculated from the Be value using B0=h/8rr2&. d, Mean r. geometry calculated from I, and Zbof 13 isotopomers of H,O, as quoted in ref. [ 10 ]
plitude for each component and then to adjust Da, and the full-width at half-height until the observed pattern was reproduced. The resulting simulated line shapes are included in figs. 1 and 2 for HZ0...H79Br and H20...H81Br, respectively, while the values of D, so determined are in table 2. In the final stage of the analysis, x~~was redetermined after correcting the frequencies of the Br-nucleur quadrupole component for the small shifts caused by spin-spin and spin-rotation effects. The unperturbed Br-nuclear quadrupole frequencies are recorded in table 3 for H20...H7’Br and Hz0...H8’Br. The final values of xaa and v. are in table 2.
and 4 ( Mbb + M,, ) allowed the partially resolved substructure of the quadrupole components (see figs. 1 and 2) to be produced. The procedure was to assume a Gaussian lineshape function of appropriate amTable 2 Spectroscopic quantities determined from the loi tO,,e transitions of H20...H79Br and H20...H*‘Br Spectroscopic quantity
H,O *..H79Br
HZ0 ,** H8’Br
“0 (MHz) x,, (MHz) D, (kHz) a) f (Mhh+K) (kHz) b1
5646.4980( 16) 424.326(9) -23(2) 3.20
5620.3270(3) 354.490(2) -23(2) 3.43
3.2. Dimer geometry
a) Values estimated by adjusting Dnato best reproduce the partially resolved H,Br spin-spin structure in the three Br-nuclear quadrupole hype&me components of the lo,+Ooo transition (see text for discussion and figs. 1 and 2). b, Estimated using eq. (6) with the corrected value of ( COS’ZZ) and values of M,, and Ziofrom table 1.
The above interpretation of the nuclear hyperfine structure in the lolcOoo transitions of H20...H79Br and Hz0...H8’Br carries implications for the zeropoint geometry of the dimer. The fact that the struc-
Table 3 Observed and calculated values of the corrected ‘) Br-nuclear quadrupole components in the 1,,+O, HZ0 . .H”‘Br Transition F’tF”
H,0...H79Br vobs
l/2-3/2 5/2+3/2 3/2t3/2
(MHz)
5541.0820 5625.5617 5731.8842
transitions of H20...H79Br and
Hz0 ..H*‘Br vca~c
(MHz)
5541.0808 5625.5639 5731.8832
vobs
(MHz)
5532.1704 5602.7998 5691.5898
5532.1702 5602.8002 5691.5896
” The observed frequency of each Br-nuclear quadrupole component has been corrected for the shift due to Br spin-rotation coupling and the partially resolved H,Br spin-spin coupling effects (see text for discussion).
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CHEMICAL PHYSICSLETTERS
Volume150,number1,2
ture is satisfactorily described without invoking H,H spin-spin coupling within the Hz0 subunit means that the lo, and Ooo rotational energy levels of H,O...HBr occur only in combination with the spin state I, + I, = 0, where Ii and Iz are the nuclear spin vectors of the Hz0 protons. On the other hand, we shall describe elsewhere [ 81 how the nuclear hyperfine structure in transitions of H20...Br involving KI=l (e.g.,212+lll, etc.) cannot be accounted for unless the spin state of the Hz0 protons is 1I1 +I, I = 1. According to the Pauli principle, these experimental observations only consistent with a ground-state geometry of H*O...Br in which the Hz0 protons are exchanged by the symmetry operation C,. Since, as expected by analogy with H*O...HF and H,O...HCl, the nuclei can be shown to be in the order H,O...HBr by a detailed consideration [ 8 ] of observed rotational constants, the above arguments require either that the dimer has a planar equilibrium geometry with Czv symmetry or a pyramidal configuration about 0 at equilibrium (C,) but with a sufficiently low potential energy barrier to the Czv planar form that the zero-point vibrational wavefunction has Czv symmetry. If the equilibrium geometry has C, symmetry, the barrier to the planar form must be very small indeed, for this quantity is only 1.5 kJ mall ’ in the more strongly bound analogue H*O...HF [9]. When the geometries of Hz0 [ lo] and HBr [ 71 (see table 1) are assumed unchanged by formation of H20...HBr and the distance between the two subunits in the Cz,.planar geometry is adjusted to reproduce v. = B+ C-4D,, the value r(O...Br) ~3.4108 A results.
plying that /.I*”determined in this way is close to zero. The origin of this apparent contradiction lies in the assumption that HBr in H20...HBr is electrically and geometrically unaffected by the presence of H,O. A more complete analysis of the relationship of xaa to x0 reveals [ 1 ] that xaa= t (3 co+
1) [x0+ (~xolWW
+ t (3 c&P-cos
~)x,+~o
of the HBr
subunit
If the HBr bond length and the electrical environment of the Br nucleus were unchanged on formation of H20...Br, the coupling constant C,, would be related to the free molecule value Co by c,,=~co(3cos2~-l))
(7)
where C=x or D and fi is as defined in section 3.1. When C=x, the values from tables 1 and 2 lead in eq. (7) to /?~,=cos-‘(cos2/3)‘~2=21.580 for both the H20...H79Br and H20...H*‘Br isotopomers. On the other hand, D,, is unchanged from Do for each isotopomer within experimental error, thereby im-
(8)
The terms xp= - (eQ/h)S$F= and xQ= - (eQ/h) x %F,, account in first order for the contributions to xnnthat arise from the response of the HBr subunit to the electric field F, and the electric field gradient Fzz due to Hz0 in the equilibrium (assumed as C,,) conformation of H*O...HBr. Similarly, (axo/&)Sr allows for the change in x0 that accompanies a lengthening 6r of the HBr bond when HBr achieves its equilibrium position in H20... HBr. The approximations inherent in formulating eq. (8) and the necessary values of axo/ar and the components g’, and 4: of the response tensors are given elsewhere [ 11. The values F,=-2.70~10~ V m-* and F,Z=2.16X10’9Vm-2attheBrnucleusintheequilibrium form of H,O...Br can be calculated by using the distributed multipole analysis (DMA) of Hz0 due to Buckingham and Fowler [ 111 and the electrostatic formalism of Buckingham [ 121. The distance r( origin...Br) = 3.4760 8, from the origin of the DMA of Hz0 to the Br nucleus required for the calculation is available from r(O...Br) ~3.4108 8, and the known geometry of H20 (table 1), Given F, and F,,, the known [ 1 ] values of &, Ce, and Q lead to - - 54.0 and 34.2 MHz for Hz0...H79Br. XPFor H20...Hg1Br the corresponding values are smaller bythefactorQ(f$l)/Q(79)=0.83539 [6].Ifitcan be assumed that 6r( H,O...HX)/&( HCN...HX) is identical for X = Cl [ 13 ] and X = Br [ 11, the values 6r=0.025 A and (aXo/ar)Gr= 14.7 MHz can be estimated for HBr in H20...HBr. The experimental value ik0.017 A for H20...HF [ 141 suggests that these estimates are probably upper limits. Given numerical values of the various other quantities, eq. (8) can be solved to give &= cos-‘(cos~~)“~= 12.70” for H20...H79Br with the approximation that the term ( 3 cos3p-cos /3) can be written as (3 cos2/3- 1) (cos /I>. The value for H20...HB’Br is insignificantly different. We note that xQ=
3.3. The dynamics
.
-
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CHEMICAL PHYSICS LETTERS
/IaVso determined is considerably smaller than the value 2 1.58 ’ obtained by using xUain eq. ( 7 ) . Moreover, the corrected value of j3,” is now more consistent with the experimental values of D,,. The spinspin constant will be unaffected by electrical effects due to the presence of Hz0 and the estimated upper limit 6r= 0.025 A to the lengthening of the HBr bond on formation of HBr would change D,, by only 5%. Consequently, use of the corrected Payin eq. (7) with the appropriate Do values from table 1 should lead to calculated D,, values in agreement with experiment. The results -19(l) and -21(l) kHz for H20...H79Br and H,0...H8’Br are in satisfactory agreement with Da,= - 23( 2) and - 23 (2) kHz, respectively.
Acknowledgement
We thank the SERC for equipment grants and for a studentship (APS).
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References [ 11A.C. Legonand D.J. Millen, Chem. Phys. Letters 144 ( 1988) 136. [2] A.C. Legon, Ann. Rev. Phys. Chem. 34 (1983) 275. [ 3 ] CA. Rego, R.C. Batten and A.C. Legon, J. Chem. Phys., to be published. [4] W.G. Read and W.H. Flygare, J. Chem. Phys. 76 (1982) 2238. [ 51 M.R. Keenan, D.B. Wozniak and W.H. Flygare, J. Chem. Phys. 75 (1981) 631. [ 61 O.B. Dabbousi, W.L. Meerts, F.H. de Leeuw and A. Dymanus, Chem. Phys. 2 (1973) 473. [ 71 EC. DeLucia, P. Helminger and W. Gordy, Phys. Rev. A 3 (1971) 1849. [ 81 A.C. Legon and A.P. Suckley, to be published. [ 91 Z. Kisiel, A.C. Legon and D.J. Millen, Proc. Roy. Sot. A 381 (1982) 419. [lo] P. Helminger, F.C. DeLucia, W. Gordy, P.A. Staats and H.W. Morgan, Phys. Rev. A 10 (1072) 1974. [ 111 A.D. Buckingham and P.W. Fowler, Can. J. Chem. 63 (1985) 2018. [ 121 A.D. Buckingham, in: Intermolecular interactions: from diatomics to biopolymers, ed. B. Pullman (Wiley, New York, 1978) p. 1. [ 131A.C. Legon and D.J. Millen, Proc. Roy. Sot. A 417 (1988) 21. [ 141AC. Legon and D.J. Millen, proc. Roy. Sot. A 404 (1986) 89.
CHEMICAL PHYSICS LETTERS
9 September 1988
Br NUCLEAR QUADRUPOLE AND H,Br NUCLEAR-SPIN-NUCLEAR-SPIN COUPLING IN THE ROTATIONAL SPECTRUM OF H*O...HBr A.C. LEGON and A.P. SUCKLEY Department of Chemistry, University ofExeter, Stocker Road, Exeter EX4 4QD, UK
Received 9 June 1988
Partially resolved hyperfine structure arising from H,Br nuclear-spin-nuclear-spin coupling has been identified in each Brnuclear quadrupole component of the l,,, +O,,,, transition of H,O...HBr. Lineshape simulation leads to a value of D,,= - 23 (2) kHz for the spin-spin coupling constant for both H,0...H79Br and H20...H8’Br. An apparent inconsistency between this value and the respective Br-nuclear quadrupole coupling constants x0.=424.326( 9) and 354.490( 2) MHz is resolved by allowing for the influence of the HZ0 electric charge distribution on the value ofkn.
1. Introduction We report the detection in the gas phase of a weakly bound dimer formed between water and hydrogen bromide. Each of the isotopic species Hz0...H79Br and H20...Hs1Br has been identified through the highly characteristic nuclear hyperfine structure of its 101t Oooground-state rotational transition which arises from Br-nuclear quadrupole and H,Br nuclearspin-nuclear-spin coupling. The splitting due to the latter lies at the limit of resolution of the pulsed-nozzle, Fourier-transform microwave spectrometer used to observe the rotational transitions and we have found it necessary to resort to lineshape simulation to determine the H,Br spin-spin coupling constants. An important conclusion of the investigation is that the hypefine structure of the loleOoo transitions can be reproduced completely without the need to invoke the presence of spin-spin coupling arising from the two protons in the HZ0 subunit. The absence of such coupling is expected if the dimer has either a sufficiently low potential energy barrier or no barrier to the planar arrangement H20...HBr of Czv symmetry. By taking advantage of a recent determination of the component & of the electric-fieldelectric-field gradient response tensor of HBr [ 11, we have been able to demonstrate that an apparent inconsistency in the oscillation angle when determined indepenBa”=cos-‘(cos2~)“2
dently in the conventional manner from each of the coupling constants xanand Da,can be resolved if the electrical influence of the HZ0 subunit on the HBr molecule is allowed for using a simple electrostatic model of H*O...HBr.
2. Experimental The 100+Ooo transitions of H20...H79Br and Hz0...H8’Br have been observed at frequencies near 5.6 GHz with a pulsed-nozzle, Fourier-transform microwave spectrometer. The microwave radiation was coupled into and out of the Fabry-Perot cavity by means of coaxial waveguide components and looped antennae of suitable dimensions located at the centres of the mirrors. The searching rate and the sensitivity of our original spectrometer [ 2 ] have been improved recently [ 31 by the introduction of an Elonex 280-Turbo (IBM AT compatible) computer, which controls the HP8671 B synthesized source of microwave radiation and also collects and processes the time-domain signals from the cavity. The data collection rate is thereby sufficiently improved that a Series 9 valve (General Valve Corporation) operating at a repetition rate of up to x 100 Hz with gas pulse lengths of = 200 ps can be used. At the rate of z 20 Hz employed here, there was no loss of signal per gas pulse compared with the prototype spectrom-
0 009-2614/88/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division )
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eter operating at 0.5 Hz with x 3 ms gas pulses, This represents a useful improvement in the signal-tonoise ratio for a given averaging time and the consumption of comparable amounts of gas. Gas mixtures composed of water at its room-temperature vapour pressure, hydrogen bromide (partial pressure 2 50 Torr) and argon (partial pressure x 760 Torr) were pulsed into the evacuated FabryPerot cavity via a 0.7 mm circular orifice in the Series 9 valve. Hypertine components whose frequencies fell with the admittance band of the cavity were polarized by 1.1 us microwave pulses from the HP8671 B frequency synthesizer and the delayed coherent emission was digitized at a rate of 0.5 us/point for 5 12 points. After sufficient averaging, the timedomain recording was subject to Fourier transformation to yield a power spectrum of 256 data points at 3.90625 kHz intervals. Examples of such power spectra are shown in figs. 1 and 2. Following a suggestion by Dr. Z. Kisiel, the points in figs. 1 and 2 have been connected by a cubic spline function instead of joining them by straight lines. This greatly improves the spectral display and allows a more confident identification of features that are only partially resolved.
3. Results
55LioL
9 September 1988
%iizzzz2;56 FrequcncylMHz
Fig. 1. Composite diagram of the three Br-nuclear quadrupole components in the Ii,, +Onotransition of Hz0...H79Brat 5541.08, 5625.56 and 5731.88 MHz (see table 3). The upper trace shows the observed transitions in which adjacent points (large dots) are spaced by 3.90625 kHz and are joined by means of a cubic spline function (small dots). The substructure of each component arises from H,Br nuclear-spin-nuclear-spin coupling and a slight instrumental doubling effect. Each stick diagram shows the calculated frequencies and intensities of the spin-spin components after allowance for the doubling of 7 kHz. The solid curve is then the lineshape function obtained by representing each stick by a Gaussian function having a full-width at half-height of 6.7 kHz and an amplitude proportional to the height of the stick. The observed spin-spin coupling constant II,,= -23(2) kHz was obtained by adjusting its value to give the best reproduction of the observed lineshape.
3. I. Determination of hyperfine coupling constants The ground-state rotational spectrum of H20...HBr has considerable complexity as a result of the simultaneous occurrence of Br-nuclear quadrupole coupling, H,Br nuclear-spin-nuclear-spin coupling, a very small asymmetry splitting and a small isotopic shift between H,0...H79Br and HzO...H*‘Br. Thus, for Hz0...H79Br, the unperturbed line centres of the 21*+ Ill, 202 c 1 o, and 2,, c 11otransitions are spread over a frequency range of only x 42 MHz centred at x 11.29 GHz while the Br-nuclear quadrupole splitting of each of these transitions covers a frequency of ~200 MHz. For H20...H8’Br, a similar pattern results but displaced lower in frequency by z 50 MHz. Moreover, each individual Br-nuclear quadrupole component exhibits additional substructure. A similar complexity is observed in the J=3+2 transitions. The detailed information about 154
H*O...HBr that is contained in the J=2+ 1 and 3~2 transitions is more readily accesible if a preliminary analysis of the lo1t O,,,,transitions of H20...H79Br and Hz0...H8’Br is made. This preliminary analysis is reported here. The 10,tOoo transitions of H20...H79Br and H,O...H*‘Br each consist of a gross Br-nuclear quadrupole triplet of large splitting centred at x 5625 and x 5603 MHz, respectively, as illustrated by the composite spectral recordings in figs. 1 and 2. A striking feature in each case is that each of the three Br-nuclear quadrupole components carries an additional, incompletely resolved substructure which is highly reproducible. We note further from figs. 1 and 2 that this substructure is essentially identical for the two isotopomers. The only possible sources of the substructure are the various nuclear-spin-nuclear-spin couplings that can occur between the I> l/2 nuclei
CHEMICAL PHYSICS LETTERS
Volume 150, number 1,2
9 September 1988
the spin-spin coupling tensor D having elements given by Dij=(~uo/4n:)ga,gH~~(R26ij-3RiRj)lR5
>
(4)
where the Ri are Cartesian components of the vector joining the H and Br nuclei and the other symbols have their usual meaning. The final term in eq. ( 1) allows for the magnetic coupling of the Br-nuclear spin angular momentum Z,, to the rotational angular momentum I and is given by H,,=--I,,*M*J,
YequencylMHz
Fig. 2. Composite diagram of the three Br-nuclear quadrupole components in the lo, ~000 transition of H20...H8’Br at 5532.17, 5602.80 and 5691.59 MHz (see table 3). For a detaileddescription of this figure, see the caption for fig. 1, which applies equally here.
in H,O...HBr. Since spin-spin coupling constants vary as ( r -3), where r is the distance between the pair of nuclei in question, any cross couplings between the subunits would lead to negligible effects in the observed spectrum. In fact, we shall establish below that the observed substructure in the lo,+-Ooo transitons can be completely assigned by invoking only H-Br spin-spin coupling and consequently that intercoupling of the Hz0 protons is absent. The analysis of hyperflne structure in the lo1CO,, transitions was carried out in several stages to give the Br-nuclear quadrupole and H,Br spin-spin coupling constants x=(1and D,,. In general, the matrix of the Hamiltonian H=H,+ZZo+N,,+&,
(1)
was constructed in the coupled basis Z,+Z,,=Z, Z+J=P and diagonalized in blocks of F. In eq. ( 1 ), HR is the familiar rotation Hamiltonian while HQ accounts for the interaction of the Br-nuclear electric quadrupole moment 0 and the electric field gradient VE at the Br nucleus according to HQ=-~$l:VE.
(2)
The term H,, describes the H,Br spin-spin interaction and has the form H,, =Z,,*D*Z,
,
(3)
(5)
where M is the Br spin-rotation tensor. The matrix elements of Ho, H,, and HSR in the above coupled basis are given elsewhere [ 4,5 1. In fact, for each of the three types of coupling, only a single constant can be determined from the lo, tOOOtransition, namely the components xaa, D,, and i( Mbb t Mcc) of the nuclear quadrupole, spin-spin and spin-rotation tensors, respectively. Initially, the frequencies of the three Br-nuclear quadrupole components of the loltOOo transition were estimated by ignoring the substructure and the Hamiltonian in eq. ( 1) was truncated after the second term to obtain a first estimate of xap and the unperturbed frequency vo. Then using the initial estimate of x=0the quantity ( cos2B) was calculated, where 1 is the instantaneous angle between the a axis of the dimer and the HBr symmetry axis. The method of calculation of ( cos2/3) from xaa and the Br-nuclear quadrupole coupling constant x0 of free HBr is discussed below and allows for the contribution made to x~~by the electrical and geometrical changes induced in HBr by the presence of H20. This contribution is significant and reduces b,,=cos- ’ x (cos2/9) ‘I2 from 21.58” to 12.7”. The spin-rotation constant f ( Mbb+ M,,) can then be estimated from the expression [ 4 ] ;(MbbtMcc)=M,,l?o(
1+cos2/3>/2bo,
(6)
where MO and b. are the spin-rotation constant [ 61 and the rotational constant [ 7 ] of free HBr (see table 1) . The quantity B. = f (B. + Co) can be replaced by 1v. = f (B. + Co) - 20, with sufficient accuracy for the present purposes. The next stage in the analysis was to choose a value of Da, which together with the initial estimates of xaa 155
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9 September 1988
Table 1 Spectroscopic and molecular properties of HBr and Hz0 Quantity
H79Br
H*‘Br
B,, (MHz) =) xo (MHz) b, Da (kHz) b, MO (kHz) b’ rn(HX) (A) L HXH (deg)
250358.510 532.3059(2) -20.59( 14) -290.796(28) 1.42426‘)
250280.582 444.6807(2) -22.28(10) -313.370(21) 1.42426‘)
Hz0
0.9577(6) d, 104.66(8) d,
‘) Ref. [7]. b, Ref. [ 61. Note that our definitions of Do and MOare -2 and - 1, respectively, times those in ref. [ 61. ‘I r,-,(HBr) has been calculated from the Be value using B0=h/8rr2&. d, Mean r. geometry calculated from I, and Zbof 13 isotopomers of H,O, as quoted in ref. [ 10 ]
plitude for each component and then to adjust Da, and the full-width at half-height until the observed pattern was reproduced. The resulting simulated line shapes are included in figs. 1 and 2 for HZ0...H79Br and H20...H81Br, respectively, while the values of D, so determined are in table 2. In the final stage of the analysis, x~~was redetermined after correcting the frequencies of the Br-nucleur quadrupole component for the small shifts caused by spin-spin and spin-rotation effects. The unperturbed Br-nuclear quadrupole frequencies are recorded in table 3 for H20...H7’Br and Hz0...H8’Br. The final values of xaa and v. are in table 2.
and 4 ( Mbb + M,, ) allowed the partially resolved substructure of the quadrupole components (see figs. 1 and 2) to be produced. The procedure was to assume a Gaussian lineshape function of appropriate amTable 2 Spectroscopic quantities determined from the loi tO,,e transitions of H20...H79Br and H20...H*‘Br Spectroscopic quantity
H,O *..H79Br
HZ0 ,** H8’Br
“0 (MHz) x,, (MHz) D, (kHz) a) f (Mhh+K) (kHz) b1
5646.4980( 16) 424.326(9) -23(2) 3.20
5620.3270(3) 354.490(2) -23(2) 3.43
3.2. Dimer geometry
a) Values estimated by adjusting Dnato best reproduce the partially resolved H,Br spin-spin structure in the three Br-nuclear quadrupole hype&me components of the lo,+Ooo transition (see text for discussion and figs. 1 and 2). b, Estimated using eq. (6) with the corrected value of ( COS’ZZ) and values of M,, and Ziofrom table 1.
The above interpretation of the nuclear hyperfine structure in the lolcOoo transitions of H20...H79Br and Hz0...H8’Br carries implications for the zeropoint geometry of the dimer. The fact that the struc-
Table 3 Observed and calculated values of the corrected ‘) Br-nuclear quadrupole components in the 1,,+O, HZ0 . .H”‘Br Transition F’tF”
H,0...H79Br vobs
l/2-3/2 5/2+3/2 3/2t3/2
(MHz)
5541.0820 5625.5617 5731.8842
transitions of H20...H79Br and
Hz0 ..H*‘Br vca~c
(MHz)
5541.0808 5625.5639 5731.8832
vobs
(MHz)
5532.1704 5602.7998 5691.5898
5532.1702 5602.8002 5691.5896
” The observed frequency of each Br-nuclear quadrupole component has been corrected for the shift due to Br spin-rotation coupling and the partially resolved H,Br spin-spin coupling effects (see text for discussion).
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Volume150,number1,2
ture is satisfactorily described without invoking H,H spin-spin coupling within the Hz0 subunit means that the lo, and Ooo rotational energy levels of H,O...HBr occur only in combination with the spin state I, + I, = 0, where Ii and Iz are the nuclear spin vectors of the Hz0 protons. On the other hand, we shall describe elsewhere [ 81 how the nuclear hyperfine structure in transitions of H20...Br involving KI=l (e.g.,212+lll, etc.) cannot be accounted for unless the spin state of the Hz0 protons is 1I1 +I, I = 1. According to the Pauli principle, these experimental observations only consistent with a ground-state geometry of H*O...Br in which the Hz0 protons are exchanged by the symmetry operation C,. Since, as expected by analogy with H*O...HF and H,O...HCl, the nuclei can be shown to be in the order H,O...HBr by a detailed consideration [ 8 ] of observed rotational constants, the above arguments require either that the dimer has a planar equilibrium geometry with Czv symmetry or a pyramidal configuration about 0 at equilibrium (C,) but with a sufficiently low potential energy barrier to the Czv planar form that the zero-point vibrational wavefunction has Czv symmetry. If the equilibrium geometry has C, symmetry, the barrier to the planar form must be very small indeed, for this quantity is only 1.5 kJ mall ’ in the more strongly bound analogue H*O...HF [9]. When the geometries of Hz0 [ lo] and HBr [ 71 (see table 1) are assumed unchanged by formation of H20...HBr and the distance between the two subunits in the Cz,.planar geometry is adjusted to reproduce v. = B+ C-4D,, the value r(O...Br) ~3.4108 A results.
plying that /.I*”determined in this way is close to zero. The origin of this apparent contradiction lies in the assumption that HBr in H20...HBr is electrically and geometrically unaffected by the presence of H,O. A more complete analysis of the relationship of xaa to x0 reveals [ 1 ] that xaa= t (3 co+
1) [x0+ (~xolWW
+ t (3 c&P-cos
~)x,+~o
of the HBr
subunit
If the HBr bond length and the electrical environment of the Br nucleus were unchanged on formation of H20...Br, the coupling constant C,, would be related to the free molecule value Co by c,,=~co(3cos2~-l))
(7)
where C=x or D and fi is as defined in section 3.1. When C=x, the values from tables 1 and 2 lead in eq. (7) to /?~,=cos-‘(cos2/3)‘~2=21.580 for both the H20...H79Br and H20...H*‘Br isotopomers. On the other hand, D,, is unchanged from Do for each isotopomer within experimental error, thereby im-
(8)
The terms xp= - (eQ/h)S$F= and xQ= - (eQ/h) x %F,, account in first order for the contributions to xnnthat arise from the response of the HBr subunit to the electric field F, and the electric field gradient Fzz due to Hz0 in the equilibrium (assumed as C,,) conformation of H*O...HBr. Similarly, (axo/&)Sr allows for the change in x0 that accompanies a lengthening 6r of the HBr bond when HBr achieves its equilibrium position in H20... HBr. The approximations inherent in formulating eq. (8) and the necessary values of axo/ar and the components g’, and 4: of the response tensors are given elsewhere [ 11. The values F,=-2.70~10~ V m-* and F,Z=2.16X10’9Vm-2attheBrnucleusintheequilibrium form of H,O...Br can be calculated by using the distributed multipole analysis (DMA) of Hz0 due to Buckingham and Fowler [ 111 and the electrostatic formalism of Buckingham [ 121. The distance r( origin...Br) = 3.4760 8, from the origin of the DMA of Hz0 to the Br nucleus required for the calculation is available from r(O...Br) ~3.4108 8, and the known geometry of H20 (table 1), Given F, and F,,, the known [ 1 ] values of &, Ce, and Q lead to - - 54.0 and 34.2 MHz for Hz0...H79Br. XPFor H20...Hg1Br the corresponding values are smaller bythefactorQ(f$l)/Q(79)=0.83539 [6].Ifitcan be assumed that 6r( H,O...HX)/&( HCN...HX) is identical for X = Cl [ 13 ] and X = Br [ 11, the values 6r=0.025 A and (aXo/ar)Gr= 14.7 MHz can be estimated for HBr in H20...HBr. The experimental value ik0.017 A for H20...HF [ 141 suggests that these estimates are probably upper limits. Given numerical values of the various other quantities, eq. (8) can be solved to give &= cos-‘(cos~~)“~= 12.70” for H20...H79Br with the approximation that the term ( 3 cos3p-cos /3) can be written as (3 cos2/3- 1) (cos /I>. The value for H20...HB’Br is insignificantly different. We note that xQ=
3.3. The dynamics
.
-
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CHEMICAL PHYSICS LETTERS
/IaVso determined is considerably smaller than the value 2 1.58 ’ obtained by using xUain eq. ( 7 ) . Moreover, the corrected value of j3,” is now more consistent with the experimental values of D,,. The spinspin constant will be unaffected by electrical effects due to the presence of Hz0 and the estimated upper limit 6r= 0.025 A to the lengthening of the HBr bond on formation of HBr would change D,, by only 5%. Consequently, use of the corrected Payin eq. (7) with the appropriate Do values from table 1 should lead to calculated D,, values in agreement with experiment. The results -19(l) and -21(l) kHz for H20...H79Br and H,0...H8’Br are in satisfactory agreement with Da,= - 23( 2) and - 23 (2) kHz, respectively.
Acknowledgement
We thank the SERC for equipment grants and for a studentship (APS).
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References [ 11A.C. Legonand D.J. Millen, Chem. Phys. Letters 144 ( 1988) 136. [2] A.C. Legon, Ann. Rev. Phys. Chem. 34 (1983) 275. [ 3 ] CA. Rego, R.C. Batten and A.C. Legon, J. Chem. Phys., to be published. [4] W.G. Read and W.H. Flygare, J. Chem. Phys. 76 (1982) 2238. [ 51 M.R. Keenan, D.B. Wozniak and W.H. Flygare, J. Chem. Phys. 75 (1981) 631. [ 61 O.B. Dabbousi, W.L. Meerts, F.H. de Leeuw and A. Dymanus, Chem. Phys. 2 (1973) 473. [ 71 EC. DeLucia, P. Helminger and W. Gordy, Phys. Rev. A 3 (1971) 1849. [ 81 A.C. Legon and A.P. Suckley, to be published. [ 91 Z. Kisiel, A.C. Legon and D.J. Millen, Proc. Roy. Sot. A 381 (1982) 419. [lo] P. Helminger, F.C. DeLucia, W. Gordy, P.A. Staats and H.W. Morgan, Phys. Rev. A 10 (1072) 1974. [ 111 A.D. Buckingham and P.W. Fowler, Can. J. Chem. 63 (1985) 2018. [ 121 A.D. Buckingham, in: Intermolecular interactions: from diatomics to biopolymers, ed. B. Pullman (Wiley, New York, 1978) p. 1. [ 131A.C. Legon and D.J. Millen, Proc. Roy. Sot. A 417 (1988) 21. [ 141AC. Legon and D.J. Millen, proc. Roy. Sot. A 404 (1986) 89.