Q(37Cl)

Volume 2 15,number 6

CHEMICAL PHYSICS LETTERS

17 December 1993

Equilibrium nuclear quadrupole coupling constants from the rotational spectrum of BrCl: a source of the electric quadrupole moment ratios Q( 79Br)/Q( 81Br) and Q( 35C1)/Q( 37Cl) AC. Legon and J.C. Thorn Departmentof Chemutry, Umvewty ofExeter, StockerRoad, Exeter EX4 4QD, UK Received 8 October 1993

The nuclear hyperfine structure m the J= 1+O transItions of the four lsotopomers 79Br3sC1,79Br37Cl,81Bti3’C1 and “‘B?‘Cl has been observed m the mbrational states u=O and u= 1 by pulsed-nozzle, Founer-transform microwave spectroscopy Accurate values of the nuclear quadrupole coupling constants XL(X), where X=Br or Cl, and the spin-rotation coupling constants Mib(X) are determined from the spectra Eqmhbnum values x,&(X) and Mib(Br) are denved from the vibrationally averaged quantities and the former lead to precise lsotopx ratios, Q( “Br)/Q( *‘Br) = 1 197048(3) and Q( W)/Q( “Cl) = 1 26889(3), for the nuclear electnc quadrupole moments

1. Introduction The rotatlonal transltlons of the mterhalogen dlatomic molecule bromine monochlonde are rich in a nuclear hyperfine structure that arises from the electric and magnetic couplmg of the Br and Cl nuclear spm vectors to the rotational angular momentum vector Conveniently, the J= 1+O transitions of all four stable lsotopomers 79B?sC1,79Br37C1, *lBr3%1 and *‘Br3’C1fall m the range 8 5-9 5 GHz and can therefore be observed with the combined high sensitivity and high resolution available to a pulsednozzle, Founer-transform microwave spectrometer A determination of the halogen nuclear quadrupole couplmg constants m the vibrational ground state v=O IS then possible with high accuracy These constants do not appear to have been measured prevlously by using a molecular beam/Jet technique and the values m the literature are early determmatlons

111 Although the pulsed-nozzle, FT spectrometer employs a supersonic Jet, thereby conferring a very low rotational temperature on the expanded gas, the vibrational temperature could be slgmficantly higher This IS because the vibrational wavenumber of BrCl 554

IS w, = 444 cm- ‘, which IS large enough that transfer of molecules from the v= 1 to the u=O state dunng the supersonic expansion might be meffklent At room temperature the v= 1 state is appreciably populated and if the vibrational temperature were unaffected by the expansion the rotational spectrum m the v= 1 state would be observable in the gas pulse We report the observation of the J= 1e0 tranntlons m both the v=O and v= 1 states of all four ISotopomers of bromine monochlonde Very accurate values of the halogen nuclear quadrupole couplmg constants x:,( X) are determined m each case, so enabling the equlhbnum quantities x& ( 79Br), &(*‘Br), &(‘%l) and &J3’C1) to be denved The ratios &(79Br)/&(81Br) and &( 35Cl)/ &( 37C1) then lead, wlthm the Born-Oppenheimer approxlmatlon, to ratios of the appropnate nuclear electnc quadrupole moments The ratio for Cl IS shown to be slgmficantly more accurate than those hltherto available. Spin-rotation coupling constants determined concomitantly allow a comparison of the axial magnetic field strength at the Br and Cl nuclei induced by the molecular rotation

0009-2614/93/$ 06 00 0 1993 Elsevier Science Pubhshers B V All nghts reserved

Volume 2 15, number 6

I7 December 1993

CHEMICAL PHYSICS LETTERS

2. Experimental The J= 160 transltlon of bromine monochlorlde was observed by using a pulsed-nozzle, Founertransform microwave spectrometer [ 2,3 ] with a Series 9 (General Valve Corporation) solenoid valve m the conventional configuration A gas mixture composed of approximately 2% each of chlorine (Argo International ) and bromine (Aldrich) m argon at a total pressure of 1 7 atm was pulsed into the Fabry-PCrot cavity of the spectrometer m the usual way The eqmhbnum constant for Cl2+ Br,*2BrClls about 5 [ 41 arm 1s therefore sufficiently large to ensure that a substantial fraction of the gas mixture before expansion consists of bromme monochlonde. Observed hyperfine components m the J= 1+O transitions had a full width at half maximum of between 8 and 16 kHz (see fig 1) depending on the precise expansion condltlons and the delay between the opening of the solenoid valve and the formation of the microwave pulse Each hyperfine component was measured six times and hence frequencies were estimated to have a precision of about 1 kHz An accuracy of 1 kHz was ensured by calibrating the spectrometer with the J= lt0 transltlon of 1aO’ZC32S, which has a frequency of 12162.9790( 1) MHz, as calculated from very precise rotational and centnfugal distortion constants obtained from a wide range of transitions [ 5 1, and for which the frequency spread over 10 measurements was only 0 5 kHz

3. Results The observed frequencies of hyperfine components m the J= 1+O transitions of the lsotopomers 79Br35C1,79Br37C1,81Br35C1and “Br3’Cl m then ground vibrational states (v= 0) are recorded m table 1 The correspondmg set of frequencies for the v= 1 states 1s given m table 2 All but one of the possible components were observed for the v=O states (the missing component 1s predicted to be weaker than the strongest component by several orders of magnitude) For the v= 1 states only three components were too weak to detect, even for the least abundant lsotopomer The observed hyperfine frequencies for each vi-

I I

8853 30

8

I

53 40

53 50

Frequency / MHz Rg I Two hypertine components in the J= 1CO transItions of bromine monochlonde The hne at 8853 3288 MHz arises from the v= 1 state of 79Br35C1 whale that at 8853 4458 MHz belongs to the v= 0 state of s’Br”‘C1 (see tables 2 and 1, respectively, for identification of I and F values) AdJacent points are spaced by 3 90625 kHz and are ~olned by straight hnes The stick hagram represents mtensities calculated by takmg mto account hne strength factors and isotopic abundance A Boltzmann factor ap propnate to a vibrational temperature of 300 K has been meluded and identical rotational temperatures are assumed The observed v= 1 transition IS enhanced m mtensity because the Fabry-Ptrot canty was tuned to its exact frequency

brational state of each lsotopomer were fitted by an iterative least-squares procedure m which the matnx of the Harmltoman operator was set up m the coupled basis IBr+& =I, I+ J=P and diagonahzed m blocks of F The form of the Hamlltoman operator employed was 555

1

1

1 1 3 3 0 0 0 1

1 1

1

1

2 1 3 2

1

3 2 0

2 1 3 2 0 1 2 1 3 2

I

2

1

1

2 3 0

1

2 3 2 3

I

2 3 2 3

1

1

2 0

2 0

1

2 3 0

I

I

3 3 2 2 2 4 1 1 1 0 3 3 1 1 1 2 2 2

3

3

8899 6490 8899 6490 8899 9787 8900 6549 8900 9823 8901 3088 9063 7071 9064 0370 9074 9591 9074 9591 9075 2855 9080 8375 9088 7517 9089 0789 9089 4050 9274 7074 9291 6820 92920114 9292 3213 9292 6497 9292 9758 9307 9488 9307 9488 9308 2772

2 2 2

3 3 3 2 2 2 2 2 2 2 2 3

F”

vok (MHz)

I”

F’c

I’

frequencies

79Br35C1

and calculated

TransItIon

Table 1 Observed

-05 -05 14 06 02 -11 -12 09 07 07 -07 02 08 02 -15 -05 -08 09 05 11 -06 -04 -04 02

Av &Hz)

‘)

of nuclear hyper!ine

8559 8559 8559 8560 8560 8560 8725 8725 8733 8733 8734 8738 8745 8745 8745 8938 8951 8951 8951 8952 8952 8964 8964 8964

5108 5108 7808 0764 3437 6099 4469 7171 9893 9893 2559 8436 2554 5235 7899 1523 4203 6900 7393 0067 2733 2466 2466 5149

-07 -07 09 16 05 -16 -12 07 03 03 -14 04 11 08 -11 02 -07 07 14 05 -13 -03 -03 -03

AD (kHz)

a)

of the J= 1+O transItIon

v,I,. (MHz )

79B?7C1

components

8865 8865 8866 8867 8867 8867 9001 9001 9013 9013 9013 9018 9026 9026 9027 9176 9193 9193 9194 9194 9195 9209 9209 9210

7494 7494 0267 0592 3340 6094 5422 8208 1644 1644 4389 7858 5177 7926 0657 4367 5472 8244 4563 7319 0067 8158 8158 0918

voba (MHz)

8’Br35C1

-06 -06 08 11 00 -06 -16 II 09 09 -05 03 13 03 -25 -0 1 -11 02 10 07 -04 -0 1 -01 00

Au (kHz)

‘)

m the v=O state of bromine

8525 8525 8525 8526 8526 8526 8663 8663 8672 8672 8672 8676 8683 8683 8683 8839 8853 8853 8853 8853 8854 8866 8866 8866

7202 7202 9479 4868 7113 9365 3107 5385 0845 0845 3090 7765 0874 3129 5370 8608 2174 4458 7071 9332 1569 0469 0469 2728

-06 -06 11 12 -02 -10 -12 06 08 08 -07 02 08 03 -15 -0 1 -13 11 08 09 -13 00 -0 1 -0 1

Au (kHz)

lsotopomers

uoba (MHz)

S’Br37Cl

monochlonde

‘)

2 2 2 1 1 1 3 3 2 2 2 4 1 1 1 0 3 3 I 1 1 2 2 2

3 3 3 2 2 2 2 2 2 2 2 3 1 1 1 1 3 3 0 0 0 1 1 1

” Au= v,-

FcI”

I’

TransitIon

Observed

Table 2

,,,

v~=

3 1 2 0 1 2 3 2 3 1 2 3 0 1 2 1 3 2 0 1 2 1 3 2

3 1 2 0 1 2 3 2 3 1 2 3 0 1 2 1 3 2 0 1 2 1 3 2

F”

,,

and calculated

,,,

-02 00 03 09 06 -04 -04 -03 -07

9228 9245 9245 9245 9246 9246 9261 9261 9261

,m

2390 2377 5681 8174 2072 5363 5272 5272 8569

-06 -06 03 15 07 -14 02 09 -11 -11 -15 00 23 04

Av (kHz)

‘)

,,

of nuclear hypertine

8852 9918 8852 9978 8853 3288 8854 0050 8854 3343 8854 6623 9017 1318 9017 4626 9028 3993 9028 3993 9028 7290 9034 2854 90422118 9042 5400

yob (MHz)

79Br3sCl

frequencies

8894 2807 8907 5682 8907 8403 8907 8867 8908 1550 8908 4249 89204118 89204118 8920 6838

,,

,,,,,,

16 -04 -07 -08 -08 10

11

-02 -08

-02 02 -11 03 07 07 -05 01 00 -03

2910 5616 4684 7400 0244 0244 2934 8849 3024 5723

8516 8516 8681 8681 8690 8690 8690 8694 8701 8701

Av (kHz) -08 -08 15

(MHz)

of the J= It0

8515 4565 8515 4565 8515 7290

vh

79Br”7Cl

components

‘)

transItIon

,,,

9130 9147 9147 9148 9148 9149 9163 9163 9164

8819 8819 8819 8820 8821 8821 8955 8955 8967 8967 8967 8912 8980 8980

../

4808 6147 8943 5254 8020 0786 9055 9055 1840

6438 6438 9222 9550 2310 5107 4961 7767 1379 1379 4141 7666 5065 7844

v,~ (MHz)

*‘BPCl

10 -10 08 16 03 -09 -08 -08 -02

-06 -06 00 10 -09 10 -20 02 04 04 -13 10 07 07

,,

Av (kHz)

,,

‘)

m the v= 1 state of bromme

,,

,,,

I#

8796 8809 8810 8810 8810 8810 8822 8822 8822

8483 8483 8619 8620 8628 8628 8628 8633 8639 8639

,,,>,,

4923 8670 0984 3575 5859 8119 7173 1113 9428

1950 4215 8564 0840 6411 6411 8684 3375 6586 8839

8482 2004 8482 2004 8482 4283

-06 -24 15 -02 07 -08 13 13 -08

13 02 13 13 -02 -02 -05 -15 10 -12

-06 -06 -02

Au (kHz)

lsotopomers

vob. (MHz)

*‘BI=“CI

monochlonde

a)

Volume 2 15, number 6

+HSR(CI)

+Hss

CHEMICAL PHYSICS LETTERS

(1)

In eq ( 1), HR 1s the conventional rotational energy operator for a dlatomlc molecule, HR=BvJ2-D,J4,

(2)

while Ho(x) and HsR(x) are the energy operators descnbmg the interaction of the halogen nuclear electric quadrupole moment Q(X) and magnetic dipole moment px =gxpNIx with the electric field gradient V’(X) and the magnetic field strength H,, respectively The forms of these operators are [ 6,7] HQW)

= -

@(X>*V”(X)

(3)

and HsR(x) = -I,*M”(X)*J

(4)

In eq (4) M”(X) 1s the spin-rotation couplmg tensor of the nucleus X m the vibrational state u. The final term m eq ( 1) describes the BrCl nuclear spmnuclear spin interaction and 1s gven [ 71 by HSS=I,,*S”*I,,

,

(5)

where S” 1sthe spm-spm coupling tensor for the state u The matnx elements of the vaflous terms m eq ( 1) m the above-defined coupled basis have been set out by Flygare and co-workers [ 6,7 1. When dealing with a J= 1t0 transition, the only determinable components of the hyperfine coupling tensors are xan(X) = -eQC,W), Mib:,(X), ad S& for the nuclear electnc quadrupole, spm-rotatlon and spin-spin interactions, respectively The rotational constant B, and the centnfugal distortion constant D, are not separately determinable when fitting a single transition, but D, for each state o of each lsotopomer 1s avsulable Hflth l~gh accuracy from the Dunham constants Y,,which have been obtained by fitting the mllhmetre-wave spectrum of BrCl [ 8 ] Thus the value of D, was fixed at its known value m the least-squares fit of the J= 1t0 hyperfine structure The effect of centnfugal dlstortlon on the nuclear quadrupole couplmg constant was excluded from eq ( 1) The ratio of the coefficient fi of the Jdependent term to the value of the rotationless coupling constant [ 91 1s expected to be of the order of D&o 5 x lo-’ and would then make a neghgble 558

17 December 1993

17 December 1993

CHEMICAL PHYSICS LETTERS

Volume 215, number 6

tnbutron to the observed frequencres of J= 1+O transrtions The various spectroscoprc constants denved from the fits are recorded m table 3, while the residuals Au= v&s- Vdc from the final least-squares cycle are included m tables 1 and 2 It should be noted that the standard devratron of the fit for each state of each lsotopomer 1s close to 1 kHz (see table 3), the estlmated accuracy of frequency measurement. As well as fixmg D, m each case, the value of the spin-spin couplmg constant S:, was constramed to its accurate calculated value which 1s available from the expression [7] S~=-(2/h)(Clo/4n)g,,g,,~~(r-3)..,

(6)

m which the g, are the known [lo] nuclear g-factors, pN 1sthe nuclear magneton and p. is the permeability of a vacuum The average values ( re3) tr,V can be calculated from the Dunham constants [ 8 ] according to the expressron set out for a dlatomrc molecule by Herschbach and Laune [ 111

(7)

-(4&lw)(v+t)l

The symbols B,, r,, co, and aI have then familiar meanings and values of these quantities are available m ref [ 8 ] The calculated values of S& are included m table 3 In fact, the contnbutron from the term m SL to the observed frequencres 1s barely outside the expenmental error for all but a few hyperfine components Nevertheless, m trials where S:, was released in the fit, the value obtained agreed in all cases wrthm expenmental error (which was about one half of the magnitude) with that calculated usmg eq (6)

4. Discussion Table 3 shows that the halogen nuclear quadrupole coupling constants xL( X) for v=O and v= 1 have been accurately deterrnmed for each nucleus X in all four rsotopomers 79Br35C1,79Br37C1,*lBr3’C1 and 81Br37C1The values of B,, and B, agree within experimental error wrth those rmphed by the Dunham constants given m ref [ 81 The M~L,(X) are also satlsfactonly determined, grven their small magnitude The set of xi. (X ) for a gtven halogen (X = Br or Cl) provrdes the opportumty to establish an accurate value of the ratio Q(X)/Q(X’) of the nuclear electric quadrupole moments of the pan of nuchdes X and X’ If the ,& (X ) can be expanded as a power senes m v+ f about the equrhbnum value x&(X ) m a manner analogous to that used for rotational constants, I e x~~:o(x)=x~.(X)+(v+1)6+(v+f)2~+

,

(8)

It IS possible to denve equrhbnum halogen nuclear quadrupole couplmg constants x,&(X) Given that the corresponding expansion of B, IS rapidly convergent (the ratio of terms m the second and first power of v+ f 1s approximately 10m4 [ 81) and that for a particular halogen nuchde the fractronal change m x& on vrbratronal excrtatlon IS < 10 -3, the contnbutron of terms m (v+ 1)” to eq. (8) 1s hkely to be smaller than the expenmental error m x&(X) values The results for the various nuchdes are given m table 4 A srmrlar approach 1spossible for the spmrotation coupling constants Mgb( Br ) We note from eqs (9)-( 11) of ref [7] that M&,(Br) scales as gBrBp The values of A&( Br) /g,,B, are given m ta-

Table 4 Equlhbnum values of the halogen nuclear quadrupole coupling constants in bromme monochlonde Coupling constant

79Br3SC1

xZ(Br) (MHz)

875 078(2) -102377(2)

xFi,(Cl) (MHz)

79Br”7C1

875 077(l) -80 683(2)

8LBr35C1

731031(l) -102 378(2)

Mean values

Ratlo

x&J 79Br)=875 078( 1) MHz ,&(*‘Br)=731 030(l) MHz ,y~(3’C1)=-102378(1)MHz ,~Z(~‘Cl)=-80683(1)MHz

1197048(3)

*‘Br.“Cl

731 028(l) -80 683(2)

126889(3)

559

Volume 2 15, number 6

CHEMICAL PHYSICS LETTERS

17 December 1993

Table 5 Expenmental values of the ratio M&,(Br)/ga,B, State

79Br35C1

‘9B?‘Cl

slBr%l

8’Br37C1

Lb0

-2 48(2)x10-‘j -2 56(3)~10-~ -244(2)x10-6

-2 47(2)x lO-6 -2 57(2)x 1O-6 -2 42(2)~10-~

-2 47(3)x10-6 -2 51(2)x10-6 -2 45(2)x 1O-6

-2 46(2)x lO-6 -2 54(3)X 10-s -242(2)x10-6

v=l v=-l/2

meanMXb(Br)/garB,=

ble 5 for each state of each lsotopomer Wlthm expenmental error this quantity IS indeed mvanant between lsotopomers for a gven state The equlhbnum quantity M&,(Br)/g,,B, obtamed from the analogue of eq. (8) 1s also shown m table 5. The errors associated with the M&(Cl) make the corresponding analysis unsatisfactory. Wlthm the Born-Oppenheimer approxlmatlon, the ratios and &( 35C1)/ x:,(79Br)l&(81Br) ~“,~(~‘cl) are equal to the correspondmg ratios, Q( 79Br)/Q( “Br) and Q( ‘%l)/Q( “Cl), ofthe nuclear electnc quadrupole moments. Usmg the mean halogen coupling constants from table 4, the result for bromine IS Q(79Br)/Q(81Br)=1.197048(3), which should be compared wth the accepted value [ lo] of 1 19707( 3) A very accurate measurement of Xz11(79Br)and Xi,(81Br) m HBr and DBr by the molecular beam electnc resonance techmque [ 12 ] leads, after vlbratlonal correction usmg a somewhat different method from that applied here, to Q( 79Br)/ Q( 81Br) = 1 197050( 1), which 1s m excellent agreement with the present value. Both are m dlsagreement with the ratlo 1 1970568( 15) from atomic spectroscopy [ 131, however The ratio Q( ‘%Zl)/ Q( 37C1)= 1 26889(3) obtamed here seems to be slgmficantly more precrse than the accepted hterature value 1 26878( 15) [lo] while the molecular beam measurements for H35C1/H37C1and D”Cl/ D3’C1corresponding to those in ref [ 121 do not appear to have been made Finally, the ratlo of the spm-rotation couplmg constants M$, ( 79Br) /M&,( 35C1) gives a measure of the ratlo of the values of the average magnetic field strength (H) V,V at the two nuclei The expression for the magnitude of the average axial magnetic field strength at nucleus X m a rotational state J of a dlatomic molecule is [ 10 ]


[J(J+ 1)11’2

(9)

-2 43(2)x

10e6

Using the known values of gx, and the Mgb( X) from table 4, we find that (Z-Z)V,uIS z 2 1 x 10m4T at 79Br and %4 x 1OV4T at 35C1in the .I= 1 state of 79Br35C1

Acknowledgement We thank the Ruth Kmg Trust of the University of Exeter for a studentship for JCT. One of us ( ACL) thanks A D.C. Legon for askmg a question that inltlated this mvestlgatlon

References [ 1] D F Smith, M Tldwell and D VP Wdhams, Phys Rev 79 (1950) 1007L [2]TJ BalleandWH

Fly8are,Rev

Scl Instrum 52(1981)

[ 31 i3C Legon, m Atomic and molecular beams methods, Vol 2, ed G Stoles (Oxford Univ Press, New York, 1992) ch [4] i Moeller, Inorganic chemistry (Wiley, New York, 1952) p 449 [ 51 A Dubrulle, J Demalson J Bune and D Boucher, Z. Naturforsch a 35 (1980) 471 [ 61 M R Keenan, D B Wozmak and W H Flygare, J Chem. Phys 75 (1981) 631 [7] W G Read and W H Fly8are, J Chem Phys 76 (1982) 2238 [ 81 R E Wfflls and W W Clark, J Chem Phys 72 (1980) 4946 [ 91 J Bune, D Boucher, J Demruson and A Dubrulle, Mol Phys 32 (1976) 289 [lo] W Gordy and R L Cook, m Techmques of organic chemstry, Vol 18, Mlcrowave molecular spectra, ed A Welssberger (Wiley, New York, 1984) [ 111 D R Herschbach and VW Laune, J Chem Phys 37 (1962) 1668 [12]DW JohnsonandNF Ramsey,J Chem Phys 67(1977) 941 [13]HH BrownandJG Kmg,Phys Rev 142(1946)53