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79Br-Nuclear quadrupole coupling in the rotational spectrum of HC15N⋯D79Br: determination of the H(D)Br oscillation amplitudes and force constant
Volume 140, number 3
CHEMICAL PHYSICS LETTERS
2 October 1987
79Br-NUCLEAR QUADRUPOLE COUPLING IN THE ROTATIONAL SPECTRUM OF HC’5N...D79Br: DETERMINATION OF THE H(D) Br OSCILLATION AMPLITUDES AND FORCE CONSTANT A.C. LEGON Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD. UK
Received 1June 1987; in final form 18July 1987
The ground-state rotational spectrum of the linear, hydrogen-bonded isotopomer HC’5N...D79Brhas been investigated by pulsednozzle Fourier-transform microwave spectroscopy to give the spectroscopic constants &= 1374.4429( 3) MHz, D,= 1.790( 9) kHz, x( 79Br)=438.645( 9) MHz and M( 79Br)=2.4( 3) kHz. The HBr subunit oscillation amplitudes /3: = 15.069( 8) o and 8: = 12.726( 7) O,determined by combined use ofX( 79Br) for HC’5N...H19Brand HC’5N...D79Br,lead to the HBr oscillation force constant kBP=6.93(2) x 10-” J rad-‘. The variation of kBBwith k, is considered for the series B...HX, where B=CO, PH3, HCN and X = Cl or Br.
1. Introduction We have been examining the rotational spectra of several series of hydrogen-bonded dimers B...HX with the aim of establishing how the various molecular properties that can be determined from the spectra (e.g. angular and radial geometries, hydrogen-bond stretching and bending force constants) vary as B and then HX are varied. These investigations have allowed us to make some generalizations about the hydrogen bond. For example, we have presented rules for predicting angular geometries [ 1,2], a method for predicting the hydrogen-bond stretching force constant k, from properties assigned to the individual molecules B and HX [ 31, a relationship between k, and the lengthening 6r of the HX bond when dimers B...HF are formed [4,5], and a relationship between k, and the HX oscillation force constant k,,
161. The last two relationships are based on models for interpreting nuclear hyperfine coupling constants associated with the HX subunit. In these models, we envisage that the nuclear quadrupole coupling constant x0 of the free HX molecule is changed by an amount Ax0 on formation of the dimer so that the equilibrium coupling constant xe of the dimer is given by 161
xe=xo+Axo .
(1)
The term Ax0 contains contributions that result from the lengthening 6r of the HX bond on dimer formation [ 4,5] and from the electrical effects at the X nucleus due to the presence of B [ 71. Obviously, Ax0 is an important quantity containing information about the geometrical and electrical changes in HX when it forms a hydrogen bond. Unfortunately, xe is not directly available from rotational spectroscopy but only its value x averaged over the vibrational state in question (usually the zero-point state) according to
=t(~o+A~o)(3cos~~-l),
(2)
where B is the angle between the HX symmetry axis and the instantaneous u-axis of the dimer. Nevertheless, we have shown elsewhere [6] that Ax0 can be determined if x is available for both B...HX and B...DX. Briefly, this approach assumes that, for axially symmetric dimers B...HX, the oscillatory motion of the H( D)X subunit in the zero-point state can be described as a two-dimensional, isotropic harmonic oscillator. Then the ratio (&)l( /3b) of the H(D)X mean-square amplitudes is given by [ 81
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ml
>/m >=(~Dx&+x)“* 7
(3)
where 1, ( DjX is the moment of inertia of H(D) X. If we can replace (88 ) “* by Bav= cos- ’ (cos*/3) “* to a sufficient approximation, eq. (3) becomes
B,“yZBa”v = (ZDxZZ”x)1’4*
2 October 1987
PHYSICS LETTERS
(4)
Finally, under the reasonable assumption that Ax0 is sensibly invariant between the HX and DX species, we can use eqs. (2) and (4) to determine Ax,,, 8:” and /IF”. In practice, trial values of Ax0 are chosen until the ratio pFVvlZ?aDv (as determined from use of appropriate x values in eq. (2)) is as required by eq. (4). The advantage of the above procedure is that not only is Ax,, determined but also more reliable values of Bay than those commonly derived by neglecting Ax0 are available. The above method has been applied [6 ] to an extended series of dimers B...H( D)Cl. The Ax0 values so determined have been interpreted subsequently in terms of the electric charge redistribution in HX that accompanies formation of B...HX [ 71. Moreover, the values of Pav thereby available lead directly to the quadratic oscillation force constant k,, through the expression [ 81
dimer are determined and then interpreted in the above manner to give AxO,/3!!, j?.“v,k,, and &.
2. Experimental The pulsed-nozzle, F-T microwave spectrometer used in the work reported here has been described elsewhere [ 131. Transition full widths at half height in HC’5N...D79Br were about 10 kHz and measured frequencies have an accuracy of about 1 kHz. A frequency-domain recording of the F= 1l/2+9/2 and g/2+7/2, 79Br-nuclear quadrupole components of the J= 4c 3 transition is shown in fig. 1 in which the familiar Doppler doubling effect is also evident. Some hyperfine components showed an additional very small ( x 10 kHz) splitting that undoubtedly arose from the presence of the D(Z= 1) quadrupolar
112
BI” = 0% > =fiQk,,Z,x)
(5)
and thence to the wavenumber &, of the high-frequency, hydrogen-bond bending mode via 2+(21cc)-‘(k&3/zHx)
I/2
.
(6)
Eq. (5) follows from a simple model [ 81 for describing the zero-point oscillation amplitudes (Yand /3 of the B and HX subunits, respectively, under the assumption that the interaction constant Zc,,= 0. A similar attack on the series B...HBr is also clearly desirable. Unfortunately, of the axially symmetric species that have been investigated by rotational spectroscopy (B=CO [9], PHs [lo], HCN [ll], and NH, [ 12]), the analysis to give AxO,j3rV,j?:, kas and I&,can be carried out only for B=CO and PH3 since the B...DBr species have not been observed for B =HCN and NH3. We therefore report here the observation of the ground-state rotational spectrum of HC1SN...D79Br by pulsed-nozzle, Fourier-transform microwave spectroscopy. The spectroscopic constants B,,, DJ, x( 79Br) and M( 79Br) ?f this linear 316
F = 1112 c
I
10992.0
I
912
+
F
+
q
l_L I
91.90
,
I
91.80
I
912
-
712
I
91.70
Frequency/MHz
Fig. 1. Frequency-domain recording of the F= 1l/2+9/2 and F= 912~ 712,79Br-nuclear quadrupole hypertine components in the J=4+-3 transition of HC15N...D79Br.The spacing between adjacent points is 3.90625 kHz and the observed frequencies are at 10991.8523 MHz and 10991.7971 MHz, respectively. Thestick diagram indicates the calculated frequencies and relative intensities of the two components.
CHEMICAL PHYSICS LETTERS
Volume 140, number 3
nucleus. Such additional splitting was ignored and only the frequency of its centre of gravity was recorded. HC”N was prepared by the action of H,P04 (previously dried through addition of P,O,) on NaC15N (99% “N, Amersham International PLC) . DBr was prepared by dropping a concentrated solution of DBr in DzO onto P205 and collecting the gas evolved. The stainless-steel gas reservoir was heated to temperatures in excess of 100’ C and dosed repeatedly with DzO while hot in order to minimise D/H exchange on its walls. Nevertheless, the spectrum of HC”N...HBr was always observable with substantial intensity and that of HC15N...DBr was, correspondingly, weaker than expected when mixtures of x 2% each of HC15N and DBr in argon were made in the reservoir.
3. Results The observed frequencies of Br-nuclear quadrupole hypertine components in the J=3+2 and 4-3 ground-state rotational transitions of the linear molecule HC’5N...D79Br are recorded in table 1. These frequencies were fitted to give the rotational constant B,,, the centrifugal distortion constant DJ, the 79Br-nuclear quadrupole coupling constant x( 79Br) and the 79Br-spin-rotation constant M(79Br) in an Table 1 Observed and calculated rotational transition HCISN ...D79Br U&S (MHz)
Transition J’F
+J”F”
7f2t2 912~2 512~2 312~2 512~2 912 +3 1112~3 712-3 5/2+3
512 712 312 l/2 512 712 912 512 312
8241.2789 8241.3867 8267.7764 8268.7105 8191.2056 10991.7971 10991.8523 11004.2177
11004.4697
frequencies of
v.Jbs- V,.lC &Hz) a’ A
B
1.5 5.0 1.4 -4.4 -3.3 1.8 4.3 -1.7 -4.4
-1.3 -0.2 2.2 -1.1 0.4 0.3 0.4 -0.2 -0.5
p) The values in column A refer to the fit of observed frequencies when spin-rotation coupling of the 79Br nucleus is ignored while those in column B are appropriate to the full analysis.
2 October 1987
iterative least-squares analysis in which the matrix of the Hamiltonian H=BoJ2-D,,J4-;Q:VE+MI.J
(7)
was diagonalized. The H matrix was constructed in the F=I+ J basis in which the elements of the various operators in eq. (7) are well known. Because of the relatively large value of x compared with that of B,, all non-zero elements of the nuclear quadrupole interaction operator were included in H. In the initial analysis, the spin-rotation term in eq. (7) was neglected. The resulting differences of observed and calculated frequencies shown in column A of table 1 are somewhat larger than expected. Subsequent inclusion of the spin-rotation term led to a signilicantly improved tit (column B of table 1) and to spectroscopic constants B,, D, and x( 79Br) (columns A and B of table 2) correspondingly increased in precision. The previously determined spectroscopic constants of HC’5N...H79Br [ 111 are included in table 2 for convenience. We note that M is identical within experimental error for the two species, and take this as evidence in support of including the spin-rotation term. We also note from table 2 that the value of B. for HC’5N...D79Br exceeds that of HC’5N...H79Br. A similar order was observed for OC...HBr [9] and arises because the substituted H atom lies close to the dimer centre of mass. The change AZ$ in the equilibrium moment of inertia on substitution of D for H is then very small and positive. On the other hand, the change AZ: in the zero-point effective moment of inertia can be written as M; +6, where S accounts for the effect of the change in the zeropoint motion. The term 6 is generally small and negative but, when substitution of D for H occurs very near to the mass centre in dimers B...HX, can be larger in magnitude than Mf. Hence, Zg will then decrease and B. will increase on substitution. The Br-nuclear quadrupole coupling constants for the species HC’5N...H79Br and HC’5N...D79Br allow Axe=-57.55(5)MHztobedeterminedwiththeaid of eqs. (2) and (4). The concomitantly generated values of /I,“” and /I.“” are given in table 3 together with the k,, and Ffl obtained from eqs. (5) and (6). The necessary spectroscopic constants x0, ZHBrand ZDBrof the free H79Br and D79Br molecules [ 14- 161 are recorded in table 4. 317
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2 October 1987
Table 2 Spectroscopic constants of HC’5N...D79Br and HC’SN...H79Br Spectroscopic constant
HC15N...D79Br a’
HCSN ...H’9Br L”
A
B
1374.4424 1.78( 3) 438.66( 3)
1374.4429( 3) I .790(9) 438.645( 9) 2.4( 3)
So (MHz) 0, (kHz) x( ‘9Br) (MHz) M(79Br) (kHz)
*’ The values in column A result from the tit of observed frequencies when spin-rotation those in column Bare appropriate to the full analysis. “’ Values taken from ref. [ 111.
1372.5055(3) 1.865(6) 426.623( 6) 2.5(4) coupling of the 79Brnucleus is ignored while
Table 3 Values of the oscillation amplitudes /?.“yand fi:, the hydrogen bromide oscillation force constants kssand the hydrogen-bond bending wave numbers Fa for HC’5N...H(D)79Br
Species
BL (des)
HC”N ...H79Br HC”N ...D79Br
15.069(S) ”
8g (de&
k,&10-20 Jrad-*)
FB(cm-‘)
12.726(7)
6.93(2) 6.93(2)
241 172
a’ The errors quoted here are those transmitted from the x( 79Br). They take no account of the approximations involved in the analysis (see text).
Some comment on the approximations implied by the use of eqs. (2)-( 5) to determine Ax,-,,/3,“v,jig and k,, is appropriate here. First, we have assumed in writing eq. (2) that Ax0 is independent of 8. Because Ax,, contains contributions from both the HBr bond lengthening 6r and the electric-field gradient at the Br nucleus arising from the nearby HCN molecule, the extent of the validity of this assump tion is difftcult to gauge. Secondly, we note that eq. (3) applies strictly only for an isotropic, two-dimensional harmonic oscillator and similarly for eq. (4) but with the additional requirement that (b2) I’*=jIav. We must enquire whether eqs. (3) and (4) are sufficiently accurate when applied to oscillations of the magnitude considered here. In fact, it
has been shown elsewhere [8] that when (/32) “2 is as large as 20”) the difference /3,,,- (8’ ) l/2 is unlikely to exceed 0.5”. Moreover, even for Ar...H79Br [ 201, where presumably Ax0w 0 and where /Ja”yhas the large value 42.1”) eq. (4) is remarkably accurate. Thus, use of /?.“vin eq. (4) predicts B,“vas 35.6” while the observed value is 34.4”. Evidently, these equations will represent an even better approximation for dimers like HCN...HBr (pa””z 15’ ). Finally, eqs. (3) and ( 5) hold rigorously only if coupling with other modes is neglected. The effect of such neglect on values of k,, determined with the aid of eq. (5) has been considered in ref. [ 81.
Table 4 Spectroscopic constants of H79Br, D79Brand HC”N Spectroscopic constant
H79Br
D79Br
HC”N
Bo (MHz)
250 358.510 a’ 2.0186092 532.30590 d’
127 357.639 e’ 3.9681642 530.6315 =’
43027.69 b’ 11.74537
i (amu A*) C’ x(‘% p’ Ref. [ 141. b’ Ref. [IS].
318
” Ed=505376
MHzamu AZ. d’ Ref. [IS].
” Ref. [ 161
CHEMICAL PHYSICS LETTERS
Volume 140, number 3
Table 5 Comparison of k,, and k,, for B...H79Br, where B=CO, PHs and HC”N B
krss(10-20 J rad-‘f
k,,(Nm-‘)
co
1.65(l) =) 4.0(l) 8’ 6.93(2) ‘)
2.99 b’ 5.05 b’ 7.26( 2) ( Hr9Br) d, 7.58(4) (D79Br) ct
PI+ HC”N
srRef. 161. “T~enfromref. f3]. ‘)Thiswork. d, Calculated from data in ref. [ f 1 ] using eq. (8).
4. Discussion
2 October 1987
mHx), The values of k, calculated for HC1JN...H79Br and HC’5N...D79Br using eq. (8) with the spectroscopic constants [ 14-16,181 of tables 2 and 4 are included in table 5 together with those [2,3] of OC...H79Br and H3P...H79Br calculated in the same way. We show in fig. 2 a plot of k,, against k, for the dimers B...H79Br, where B=OC, PH3 and HCYN. We also give in the same diagram the results for the co~es~nding B...HJSCi series #‘. For both series k,, increases linearly with k,, the two lines being nearly parallel. #IThe results for OC...H%l and HC1SN...H35Clare taken from ref. [ 61. Those for HsP...H3’Cl are calculated from ref. [ 19 1.
Values of the HBr oscillation force constant kflfi have now been determined [ 61 for the three axially symmetric dimers OC...H79Br, H3P...H79Br and HC15N...H79Br and are collected in table 5. This quantity is the restoring force per unit infinitesimal displacement of the subunits as they oscillate with respect to their respective mass centres from their equilibrium positions and thus provides one measure of the strength of the hydrogen bond. Another measure is the hydrogen-bond stretching force coustant k, which is available, for linear or symmetric top dimers, from the centrifugal distortion constant B_,via the expression [ 171 k,=(161c2B~~~~)(1-3,13,-B,IB,,),
(8)
where & and BHXare the rotational constants of the free molecules B and HX and fi=mBmHxl( m,+ 10-l 9876102’~~~ IJ rad’ 5I-
3” 21, -I
I . * , , t23456789K)
I
,
,
,
,
k&Nm-t Fig. 2. Variation of &a#with k, within each of the two series of hydrogen-bonded dimers B...HCl and B...HBr, where B =CO, PHs and HCN. The points o refer to the series B...HBr and the points a to the series B...HCl.
References [ 1] A.C. Legon and D.J. Millen, J. Chem. Sot. Faraday Discussions73 (1982) 71. [ 21 A.C. Legon and D.J. Millen, Accounts Chem. Res. 20 (1987) 39. [3]A.C.lRgonandD.J.Millen, J.Am.Chem.Soc. 109(1987) 356. [4] A.C. Legon and L.C. Willoughby, Chem. Phys. Letters 95 (1983) 449. [ 5 ] A.C. Legon and D.J. Millen, Proc. Roy. Sot. A404 (1986) 89. 16] P. Cope, A.C. Legon and D.J. Millen, J. Chem. Sot. Faraday Trans. II, to be published. [7] A.C. Legon and D.J. Millen, Proc. Roy Sot. A, to be published. [ 81 P. Cope, A.C. Legon and D.J. Millen, J. Chem. Sot. Faraday Trans. II 82 (1986) 1189. [9] M.R. Keenan,T.K. Minton,A.C. Legon,T.J. Balleand W.H. Flygare, Proc. Natl. Acad. Sci. US 77 (1980) 5583. [ lo] L.C. Willoughby and AC. Legon, J. Phys. Chem. 87 (1983) 2085. [ II] E.J. Campbell, A.C. Legon and W.H. Flygare, J. Chem. Phys. 78 (1983) 3494. [ 121 N.W. Howard and A.C. Legon, J. Chem, Phys., to be published. [ 13f A.C. Legon, Ann. Rev. Phys. Chem. 34 (1983) 275. [ 141 F.C. DeLucia, P. Helminger and W. Gordy, Phys. Rev. A3 (1971) 1849. [ IS] O.B. Dabbousi, W.L. Meet%, F.H. de Leeuw and A. Dymanus, Chem. Phys. 2 (1973) 473. [ 161 F.A. van Dijk and A. Dymanus, Chem. Phys. 6 (1974) 474. [ 171 D.J. Mitten, Can. J. Chem. 63 (1985) 1477. [ 181 A.G. Maki, J. Phys. Chem. Ref. Data 3 (1974) 221. [ 191 A.C. Legon and L.C. Willoughby, unpublished observations. [20] MR. Keenan, E.J. Campbell, T.J. Balle, L.W. Buxton, T.K. Minton, P.D. Soper and W.H. Flygare, J. Chem. Phys. 72 (1980) 3070.
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CHEMICAL PHYSICS LETTERS
2 October 1987
79Br-NUCLEAR QUADRUPOLE COUPLING IN THE ROTATIONAL SPECTRUM OF HC’5N...D79Br: DETERMINATION OF THE H(D) Br OSCILLATION AMPLITUDES AND FORCE CONSTANT A.C. LEGON Department of Chemistry, University of Exeter, Stocker Road, Exeter EX4 4QD. UK
Received 1June 1987; in final form 18July 1987
The ground-state rotational spectrum of the linear, hydrogen-bonded isotopomer HC’5N...D79Brhas been investigated by pulsednozzle Fourier-transform microwave spectroscopy to give the spectroscopic constants &= 1374.4429( 3) MHz, D,= 1.790( 9) kHz, x( 79Br)=438.645( 9) MHz and M( 79Br)=2.4( 3) kHz. The HBr subunit oscillation amplitudes /3: = 15.069( 8) o and 8: = 12.726( 7) O,determined by combined use ofX( 79Br) for HC’5N...H19Brand HC’5N...D79Br,lead to the HBr oscillation force constant kBP=6.93(2) x 10-” J rad-‘. The variation of kBBwith k, is considered for the series B...HX, where B=CO, PH3, HCN and X = Cl or Br.
1. Introduction We have been examining the rotational spectra of several series of hydrogen-bonded dimers B...HX with the aim of establishing how the various molecular properties that can be determined from the spectra (e.g. angular and radial geometries, hydrogen-bond stretching and bending force constants) vary as B and then HX are varied. These investigations have allowed us to make some generalizations about the hydrogen bond. For example, we have presented rules for predicting angular geometries [ 1,2], a method for predicting the hydrogen-bond stretching force constant k, from properties assigned to the individual molecules B and HX [ 31, a relationship between k, and the lengthening 6r of the HX bond when dimers B...HF are formed [4,5], and a relationship between k, and the HX oscillation force constant k,,
161. The last two relationships are based on models for interpreting nuclear hyperfine coupling constants associated with the HX subunit. In these models, we envisage that the nuclear quadrupole coupling constant x0 of the free HX molecule is changed by an amount Ax0 on formation of the dimer so that the equilibrium coupling constant xe of the dimer is given by 161
xe=xo+Axo .
(1)
The term Ax0 contains contributions that result from the lengthening 6r of the HX bond on dimer formation [ 4,5] and from the electrical effects at the X nucleus due to the presence of B [ 71. Obviously, Ax0 is an important quantity containing information about the geometrical and electrical changes in HX when it forms a hydrogen bond. Unfortunately, xe is not directly available from rotational spectroscopy but only its value x averaged over the vibrational state in question (usually the zero-point state) according to
=t(~o+A~o)(3cos~~-l),
(2)
where B is the angle between the HX symmetry axis and the instantaneous u-axis of the dimer. Nevertheless, we have shown elsewhere [6] that Ax0 can be determined if x is available for both B...HX and B...DX. Briefly, this approach assumes that, for axially symmetric dimers B...HX, the oscillatory motion of the H( D)X subunit in the zero-point state can be described as a two-dimensional, isotropic harmonic oscillator. Then the ratio (&)l( /3b) of the H(D)X mean-square amplitudes is given by [ 81
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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ml
>/m >=(~Dx&+x)“* 7
(3)
where 1, ( DjX is the moment of inertia of H(D) X. If we can replace (88 ) “* by Bav= cos- ’ (cos*/3) “* to a sufficient approximation, eq. (3) becomes
B,“yZBa”v = (ZDxZZ”x)1’4*
2 October 1987
PHYSICS LETTERS
(4)
Finally, under the reasonable assumption that Ax0 is sensibly invariant between the HX and DX species, we can use eqs. (2) and (4) to determine Ax,,, 8:” and /IF”. In practice, trial values of Ax0 are chosen until the ratio pFVvlZ?aDv (as determined from use of appropriate x values in eq. (2)) is as required by eq. (4). The advantage of the above procedure is that not only is Ax,, determined but also more reliable values of Bay than those commonly derived by neglecting Ax0 are available. The above method has been applied [6 ] to an extended series of dimers B...H( D)Cl. The Ax0 values so determined have been interpreted subsequently in terms of the electric charge redistribution in HX that accompanies formation of B...HX [ 71. Moreover, the values of Pav thereby available lead directly to the quadratic oscillation force constant k,, through the expression [ 81
dimer are determined and then interpreted in the above manner to give AxO,/3!!, j?.“v,k,, and &.
2. Experimental The pulsed-nozzle, F-T microwave spectrometer used in the work reported here has been described elsewhere [ 131. Transition full widths at half height in HC’5N...D79Br were about 10 kHz and measured frequencies have an accuracy of about 1 kHz. A frequency-domain recording of the F= 1l/2+9/2 and g/2+7/2, 79Br-nuclear quadrupole components of the J= 4c 3 transition is shown in fig. 1 in which the familiar Doppler doubling effect is also evident. Some hyperfine components showed an additional very small ( x 10 kHz) splitting that undoubtedly arose from the presence of the D(Z= 1) quadrupolar
112
BI” = 0% > =fiQk,,Z,x)
(5)
and thence to the wavenumber &, of the high-frequency, hydrogen-bond bending mode via 2+(21cc)-‘(k&3/zHx)
I/2
.
(6)
Eq. (5) follows from a simple model [ 81 for describing the zero-point oscillation amplitudes (Yand /3 of the B and HX subunits, respectively, under the assumption that the interaction constant Zc,,= 0. A similar attack on the series B...HBr is also clearly desirable. Unfortunately, of the axially symmetric species that have been investigated by rotational spectroscopy (B=CO [9], PHs [lo], HCN [ll], and NH, [ 12]), the analysis to give AxO,j3rV,j?:, kas and I&,can be carried out only for B=CO and PH3 since the B...DBr species have not been observed for B =HCN and NH3. We therefore report here the observation of the ground-state rotational spectrum of HC1SN...D79Br by pulsed-nozzle, Fourier-transform microwave spectroscopy. The spectroscopic constants B,,, DJ, x( 79Br) and M( 79Br) ?f this linear 316
F = 1112 c
I
10992.0
I
912
+
F
+
q
l_L I
91.90
,
I
91.80
I
912
-
712
I
91.70
Frequency/MHz
Fig. 1. Frequency-domain recording of the F= 1l/2+9/2 and F= 912~ 712,79Br-nuclear quadrupole hypertine components in the J=4+-3 transition of HC15N...D79Br.The spacing between adjacent points is 3.90625 kHz and the observed frequencies are at 10991.8523 MHz and 10991.7971 MHz, respectively. Thestick diagram indicates the calculated frequencies and relative intensities of the two components.
CHEMICAL PHYSICS LETTERS
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nucleus. Such additional splitting was ignored and only the frequency of its centre of gravity was recorded. HC”N was prepared by the action of H,P04 (previously dried through addition of P,O,) on NaC15N (99% “N, Amersham International PLC) . DBr was prepared by dropping a concentrated solution of DBr in DzO onto P205 and collecting the gas evolved. The stainless-steel gas reservoir was heated to temperatures in excess of 100’ C and dosed repeatedly with DzO while hot in order to minimise D/H exchange on its walls. Nevertheless, the spectrum of HC”N...HBr was always observable with substantial intensity and that of HC15N...DBr was, correspondingly, weaker than expected when mixtures of x 2% each of HC15N and DBr in argon were made in the reservoir.
3. Results The observed frequencies of Br-nuclear quadrupole hypertine components in the J=3+2 and 4-3 ground-state rotational transitions of the linear molecule HC’5N...D79Br are recorded in table 1. These frequencies were fitted to give the rotational constant B,,, the centrifugal distortion constant DJ, the 79Br-nuclear quadrupole coupling constant x( 79Br) and the 79Br-spin-rotation constant M(79Br) in an Table 1 Observed and calculated rotational transition HCISN ...D79Br U&S (MHz)
Transition J’F
+J”F”
7f2t2 912~2 512~2 312~2 512~2 912 +3 1112~3 712-3 5/2+3
512 712 312 l/2 512 712 912 512 312
8241.2789 8241.3867 8267.7764 8268.7105 8191.2056 10991.7971 10991.8523 11004.2177
11004.4697
frequencies of
v.Jbs- V,.lC &Hz) a’ A
B
1.5 5.0 1.4 -4.4 -3.3 1.8 4.3 -1.7 -4.4
-1.3 -0.2 2.2 -1.1 0.4 0.3 0.4 -0.2 -0.5
p) The values in column A refer to the fit of observed frequencies when spin-rotation coupling of the 79Br nucleus is ignored while those in column B are appropriate to the full analysis.
2 October 1987
iterative least-squares analysis in which the matrix of the Hamiltonian H=BoJ2-D,,J4-;Q:VE+MI.J
(7)
was diagonalized. The H matrix was constructed in the F=I+ J basis in which the elements of the various operators in eq. (7) are well known. Because of the relatively large value of x compared with that of B,, all non-zero elements of the nuclear quadrupole interaction operator were included in H. In the initial analysis, the spin-rotation term in eq. (7) was neglected. The resulting differences of observed and calculated frequencies shown in column A of table 1 are somewhat larger than expected. Subsequent inclusion of the spin-rotation term led to a signilicantly improved tit (column B of table 1) and to spectroscopic constants B,, D, and x( 79Br) (columns A and B of table 2) correspondingly increased in precision. The previously determined spectroscopic constants of HC’5N...H79Br [ 111 are included in table 2 for convenience. We note that M is identical within experimental error for the two species, and take this as evidence in support of including the spin-rotation term. We also note from table 2 that the value of B. for HC’5N...D79Br exceeds that of HC’5N...H79Br. A similar order was observed for OC...HBr [9] and arises because the substituted H atom lies close to the dimer centre of mass. The change AZ$ in the equilibrium moment of inertia on substitution of D for H is then very small and positive. On the other hand, the change AZ: in the zero-point effective moment of inertia can be written as M; +6, where S accounts for the effect of the change in the zeropoint motion. The term 6 is generally small and negative but, when substitution of D for H occurs very near to the mass centre in dimers B...HX, can be larger in magnitude than Mf. Hence, Zg will then decrease and B. will increase on substitution. The Br-nuclear quadrupole coupling constants for the species HC’5N...H79Br and HC’5N...D79Br allow Axe=-57.55(5)MHztobedeterminedwiththeaid of eqs. (2) and (4). The concomitantly generated values of /I,“” and /I.“” are given in table 3 together with the k,, and Ffl obtained from eqs. (5) and (6). The necessary spectroscopic constants x0, ZHBrand ZDBrof the free H79Br and D79Br molecules [ 14- 161 are recorded in table 4. 317
CHEMICAL PHYSICS LETTERS
Volume 140, number 3
2 October 1987
Table 2 Spectroscopic constants of HC’5N...D79Br and HC’SN...H79Br Spectroscopic constant
HC15N...D79Br a’
HCSN ...H’9Br L”
A
B
1374.4424 1.78( 3) 438.66( 3)
1374.4429( 3) I .790(9) 438.645( 9) 2.4( 3)
So (MHz) 0, (kHz) x( ‘9Br) (MHz) M(79Br) (kHz)
*’ The values in column A result from the tit of observed frequencies when spin-rotation those in column Bare appropriate to the full analysis. “’ Values taken from ref. [ 111.
1372.5055(3) 1.865(6) 426.623( 6) 2.5(4) coupling of the 79Brnucleus is ignored while
Table 3 Values of the oscillation amplitudes /?.“yand fi:, the hydrogen bromide oscillation force constants kssand the hydrogen-bond bending wave numbers Fa for HC’5N...H(D)79Br
Species
BL (des)
HC”N ...H79Br HC”N ...D79Br
15.069(S) ”
8g (de&
k,&10-20 Jrad-*)
FB(cm-‘)
12.726(7)
6.93(2) 6.93(2)
241 172
a’ The errors quoted here are those transmitted from the x( 79Br). They take no account of the approximations involved in the analysis (see text).
Some comment on the approximations implied by the use of eqs. (2)-( 5) to determine Ax,-,,/3,“v,jig and k,, is appropriate here. First, we have assumed in writing eq. (2) that Ax0 is independent of 8. Because Ax,, contains contributions from both the HBr bond lengthening 6r and the electric-field gradient at the Br nucleus arising from the nearby HCN molecule, the extent of the validity of this assump tion is difftcult to gauge. Secondly, we note that eq. (3) applies strictly only for an isotropic, two-dimensional harmonic oscillator and similarly for eq. (4) but with the additional requirement that (b2) I’*=jIav. We must enquire whether eqs. (3) and (4) are sufficiently accurate when applied to oscillations of the magnitude considered here. In fact, it
has been shown elsewhere [8] that when (/32) “2 is as large as 20”) the difference /3,,,- (8’ ) l/2 is unlikely to exceed 0.5”. Moreover, even for Ar...H79Br [ 201, where presumably Ax0w 0 and where /Ja”yhas the large value 42.1”) eq. (4) is remarkably accurate. Thus, use of /?.“vin eq. (4) predicts B,“vas 35.6” while the observed value is 34.4”. Evidently, these equations will represent an even better approximation for dimers like HCN...HBr (pa””z 15’ ). Finally, eqs. (3) and ( 5) hold rigorously only if coupling with other modes is neglected. The effect of such neglect on values of k,, determined with the aid of eq. (5) has been considered in ref. [ 81.
Table 4 Spectroscopic constants of H79Br, D79Brand HC”N Spectroscopic constant
H79Br
D79Br
HC”N
Bo (MHz)
250 358.510 a’ 2.0186092 532.30590 d’
127 357.639 e’ 3.9681642 530.6315 =’
43027.69 b’ 11.74537
i (amu A*) C’ x(‘% p’ Ref. [ 141. b’ Ref. [IS].
318
” Ed=505376
MHzamu AZ. d’ Ref. [IS].
” Ref. [ 161
CHEMICAL PHYSICS LETTERS
Volume 140, number 3
Table 5 Comparison of k,, and k,, for B...H79Br, where B=CO, PHs and HC”N B
krss(10-20 J rad-‘f
k,,(Nm-‘)
co
1.65(l) =) 4.0(l) 8’ 6.93(2) ‘)
2.99 b’ 5.05 b’ 7.26( 2) ( Hr9Br) d, 7.58(4) (D79Br) ct
PI+ HC”N
srRef. 161. “T~enfromref. f3]. ‘)Thiswork. d, Calculated from data in ref. [ f 1 ] using eq. (8).
4. Discussion
2 October 1987
mHx), The values of k, calculated for HC1JN...H79Br and HC’5N...D79Br using eq. (8) with the spectroscopic constants [ 14-16,181 of tables 2 and 4 are included in table 5 together with those [2,3] of OC...H79Br and H3P...H79Br calculated in the same way. We show in fig. 2 a plot of k,, against k, for the dimers B...H79Br, where B=OC, PH3 and HCYN. We also give in the same diagram the results for the co~es~nding B...HJSCi series #‘. For both series k,, increases linearly with k,, the two lines being nearly parallel. #IThe results for OC...H%l and HC1SN...H35Clare taken from ref. [ 61. Those for HsP...H3’Cl are calculated from ref. [ 19 1.
Values of the HBr oscillation force constant kflfi have now been determined [ 61 for the three axially symmetric dimers OC...H79Br, H3P...H79Br and HC15N...H79Br and are collected in table 5. This quantity is the restoring force per unit infinitesimal displacement of the subunits as they oscillate with respect to their respective mass centres from their equilibrium positions and thus provides one measure of the strength of the hydrogen bond. Another measure is the hydrogen-bond stretching force coustant k, which is available, for linear or symmetric top dimers, from the centrifugal distortion constant B_,via the expression [ 171 k,=(161c2B~~~~)(1-3,13,-B,IB,,),
(8)
where & and BHXare the rotational constants of the free molecules B and HX and fi=mBmHxl( m,+ 10-l 9876102’~~~ IJ rad’ 5I-
3” 21, -I
I . * , , t23456789K)
I
,
,
,
,
k&Nm-t Fig. 2. Variation of &a#with k, within each of the two series of hydrogen-bonded dimers B...HCl and B...HBr, where B =CO, PHs and HCN. The points o refer to the series B...HBr and the points a to the series B...HCl.
References [ 1] A.C. Legon and D.J. Millen, J. Chem. Sot. Faraday Discussions73 (1982) 71. [ 21 A.C. Legon and D.J. Millen, Accounts Chem. Res. 20 (1987) 39. [3]A.C.lRgonandD.J.Millen, J.Am.Chem.Soc. 109(1987) 356. [4] A.C. Legon and L.C. Willoughby, Chem. Phys. Letters 95 (1983) 449. [ 5 ] A.C. Legon and D.J. Millen, Proc. Roy. Sot. A404 (1986) 89. 16] P. Cope, A.C. Legon and D.J. Millen, J. Chem. Sot. Faraday Trans. II, to be published. [7] A.C. Legon and D.J. Millen, Proc. Roy Sot. A, to be published. [ 81 P. Cope, A.C. Legon and D.J. Millen, J. Chem. Sot. Faraday Trans. II 82 (1986) 1189. [9] M.R. Keenan,T.K. Minton,A.C. Legon,T.J. Balleand W.H. Flygare, Proc. Natl. Acad. Sci. US 77 (1980) 5583. [ lo] L.C. Willoughby and AC. Legon, J. Phys. Chem. 87 (1983) 2085. [ II] E.J. Campbell, A.C. Legon and W.H. Flygare, J. Chem. Phys. 78 (1983) 3494. [ 121 N.W. Howard and A.C. Legon, J. Chem, Phys., to be published. [ 13f A.C. Legon, Ann. Rev. Phys. Chem. 34 (1983) 275. [ 141 F.C. DeLucia, P. Helminger and W. Gordy, Phys. Rev. A3 (1971) 1849. [ IS] O.B. Dabbousi, W.L. Meet%, F.H. de Leeuw and A. Dymanus, Chem. Phys. 2 (1973) 473. [ 161 F.A. van Dijk and A. Dymanus, Chem. Phys. 6 (1974) 474. [ 171 D.J. Mitten, Can. J. Chem. 63 (1985) 1477. [ 181 A.G. Maki, J. Phys. Chem. Ref. Data 3 (1974) 221. [ 191 A.C. Legon and L.C. Willoughby, unpublished observations. [20] MR. Keenan, E.J. Campbell, T.J. Balle, L.W. Buxton, T.K. Minton, P.D. Soper and W.H. Flygare, J. Chem. Phys. 72 (1980) 3070.
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