The pure rotational spectrum of ScBr

Wei Lin, Corey J. Evans and Michael C. L. Gerry*

Department of Chemistry, T he University of British Columbia, 2036 Main Mall, V ancouver,British Columbia, Canada V 6T 1Z1. E-mail : mgerry=chem.ubc.ca

Received 27th September 1999, Accepted 5th November 1999

The pure rotational spectra of Sc79Br and Sc81Br have been measured in two vibrational states (v\ 0 and 1)in the 5È24 GHz spectral region, using a cavity pulsed jet Fourier transform microwave spectrometer. Thesamples were prepared by ablating Sc metal in the presence of contained in the Ar backing gas of the jet.Br2The equilibrium internuclear distance has been determined along with estimates for the harmonic vibrationrefrequency and the dissociation energy, Nuclear quadrupole coupling constants and spinÈrotationue De .constants have been determined for both Sc and Br. The ionic character of the ScBr bond is estimated to beD95%. Magnetic shieldings for both nuclei have been estimated.

1 IntroductionScandium is the Ðrst of the transition metals, so its atomshave only one d-electron in the ground electronic state. Inter-est in its compounds thus arises because they can be con-sidered as prototypes for understanding the role thatd-orbitals play in chemical bonding.

The spectra and structures of scandium monochloride(ScCl) and scandium monoÑuoride (ScF) have been the subjectof many theoretical and experimental studies.1 The latter havegenerally been carried out using electronic spectroscopic tech-niques. Recently the pure rotational spectra of ScCl and ScFhave been measured in this laboratory using a Fourier trans-form microwave (FTMW) spectrometer.2 The results showedthat the hyperÐne structures in the spectra, particularly of themetal, are difficult to interpret using just simple bonding argu-ments. Investigation of the other scandium monohalides mayhelp in improving our understanding of transition metalbonding. Of the scandium monohalides, scandium mono-bromide (ScBr) is the least studied spectroscopically. No high-resolution studies on ScBr have been previously reported.Fischell et al.3 measured radiation lifetimes and gave estimatesof rotational constants for three electronic states. Langho† etal.4 have reported theoretical values of the spectroscopic con-stants in the X 1&` and a 1* electronic states.

In this paper we report the Ðrst measurement of the purerotational spectrum of ScBr. Rotational transitions have beenmeasured for Sc79Br and Sc81Br, in the ground and Ðrstexcited vibrational states. Rotational and centrifugal distor-tion constants have been determined and have been used toevaluate the equilibrium bond distance, and to estimate there ,harmonic vibration frequency and dissociation energy. Thedetermined hyperÐne parameters have been used to investi-gate further the nature of the bonding in the molecule.

2 Experimental procedureThe pure rotational spectrum of ScBr was measured using aBalleÈFlygare type Fourier transform spectrometer,5 that hasbeen described in detail elsewhere.6 The spectrometer consistsof a cavity formed by two spherical aluminium mirrors 28 cmin diameter and with 38.4 cm radius of curvature, heldapproximately 30 cm apart. One mirror is Ðxed, while theother is used to tune the cavity to the microwave excitationfrequency. A scandium rod (Goodfellow, 92% scandium, 8%tantalum) was held near the center of the Ðxed mirror by a

stainless steel nozzle cap 5 mm from the oriÐce of a GeneralValve series-9 pulsed nozzle.7 The scandium metal wasablated by the radiation from the second harmonic of aNd : YAG laser (532 nm), in the presence of a gasBr2/Armixture, which was then supersonically expanded into thecavity via a 5 mm diameter nozzle. This arrangement resultedin each line being split into two Doppler components since thepropagation of the microwave radiation was parallel to that ofthe supersonic beam. The use of such a parallel conÐgurationresults in improved sensitivity and resolution.6 The measure-ment accuracy is estimated to be better than ^1 kHz. Forwell resolved lines the frequency was obtained by averagingthe frequencies of the Doppler components in the frequencydomain spectrum. For closely spaced or overlapped lines, thefrequencies were obtained by Ðtting directly to the timedomain signals8 to eliminate e†ects of line shape distortion inthe power spectrum.

As was found for ScF and ScCl (ref. 2) the best signals wereobtained with very small concentrations of precursor. ForBr2ScBr, the optimal gas mixture consisted of 0.003% in ArBr2(achieved by successive dilutions) at a stagnation pressure of5È6 atm. Typically 4000È10 000 averaging cycles wererequired for each measurement to obtain adequate signal-to-noise.

3 ResultsThe three lowest frequency rotational transitions (J \ 1È0,2È1 and 3È2) of the ground vibrational state of ScBr wereavailable for study in the frequency range of the spectrometer(5È24 GHz). Since no accurate experimentally determinedrotational constant was available the theoretical value fromreref. 4 was used to estimate of Sc79Br. To decrease theB0search range the value of ScBr was reÐned by using there revalues from ScF and ScCl,2 and comparing them against theirtheoretical values from ref. 4. Lines from the J \ 2È1 tran-sition of Sc79Br were found within 200 MHz of the predictedfrequency. As with ScF and ScCl2 the lines were very weak,even after careful optimization of the experimental conditions.There are several possible reasons for this : (a) problems withablating Sc metal, (b) being more stable than the mono-ScX3meric species, ScX, and/or (c) an uneven surface on the Sc rod.

ConÐrmation that we were observing ScBr was obtained bythe prediction and measurement of lines from Sc81Br. In total,lines were measured and assigned to the J \ 1È0, 2È1 and 3È2transitions of the ground vibrational state for both Sc79Br and

Phys. Chem. Chem. Phys., 2000, 2, 43È46 43

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Table 1 Molecular constants for ScBr in MHza

Parameters Sc79Br(v\ 0) Sc79Br(v\ 1) Sc81Br(v\ 0) Sc81Br(v\ 1)

Bv

3106.490 59(11) 3093.591 39(17) 3078.685 84(12) 3065.959 99(18)D

v] 103 1.169(8) 1.143(11) 1.148(11) 1.167(12)

eQq(Sc) 65.2558(32) 65.1139(81) 65.2597(38) 65.1129(70)eQq(Br) 39.0857(24) 41.0992(51) 32.6438(19) 34.3215(66)C

I(Sc)] 102 2.0478(62) 2.133(12) 2.0244(61) 2.105(23)

CI(Br)] 102 1.706(16) 1.691(24) 1.824(17) 1.795(24)

a Numbers in parentheses are one standard deviation in units of least signiÐcant Ðgure.

Sc81Br. For the Ðrst excited vibrational state, lines were mea-sured and assigned to the J \ 2È1 and 3È2 transitions forboth isotopomers. Since the nuclear quadrupole coupling con-stants of 45Sc(I\ 7/2, 100%) and 79Br(I\ 3/2, 50.53%) and81Br(I\ 3/2, 49.46%) are comparable in magnitude, a““parallel ÏÏ coupling scheme was employed in the assignments :

F \ I ] J. Measured frequencies and their assign-I \ I1] I2 ;ments are available as supplementary data.¤ The lines wereÐtted to within experimental uncertainty using PickettÏsweighted-least squares program SPFIT.9 The Hamiltonianwas

H \ Hrot] Helec quad] Hspinhrotn (1)

where

Hrot\ B0 J2 [ D0 J4 (2)

Helec quad\ [16(VSc(2)QSc(2)] VBr(2) QBr(2)) (3)

Hspinhrotn\ CI(Sc) ISc Æ J ] C

I(Br)IBr Æ J (4)

The results of the Ðts are listed in Table 1. The ground statee†ective bond distances are 2.383 316 7(9) and(r0)2.383 304 2(9) for Sc79Br and Sc81Br, respectively. No e†ectA�of nuclear spinÈspin coupling was found.

4 Analysis

(a) HyperÐne constants

The ratios of the hyperÐne parameters found for Sc79Br andSc81Br can be related to the ratios of certain nuclear andmolecular properties. In particular, the spinÈrotation constant

is proportional to the product where is the nuclearCI

gIB, g

Ig-factor. Thus the ratios of and for two isotopomersCI

gIB

should be the same. These are given for both Sc and Br inTable 2 ; the agreement is well within the uncertainties.

The ratio of the nuclear quadrupole coupling constantsshould be that of the quadrupole moments of 79Br and 81Br.However, within experimental error, this is not the case for theconstants for v\ 0 and v\ 1 state, as shown in Table 2. Toexamine the vibrational dependence of the nuclear quadrupol-ecoupling constants, an expansion in terms of vibrational con

Table 2 Comparison of hyperÐne constants for ScBra

CI(79Br)

CI(81Br)

CI(Sc in Sc79Br)

CI(Sc in Sc81Br)

eQq(81Br)

eQq(81Br)

v\ 0 0.935(12) 1.0116(43) 1.197 34(10)v\ 1 0.953(19) 1.020(13) 1.197 47(27)Equilibrium 1.197 26(18)Lit. valueb 0.939 995(2)c 1.0090d 1.197 050(1)e

a Numbers in parentheses are one standard deviation in units of leastsigniÐcant Ðgure. b Literature values are the ratios of for andg

IB C

I,

of the nuclear quadrupole moments for eQq. c Ref. 14. d Inverse ratioof reduced masses of Sc79Br and Sc81Br. e Ref. 10.

¤ Available as electronic supplementary information. See http : //www.rsc.org/suppdata/cp/a9/a907769c.

tributions was made :

eQqv\ eQqe ] a

eQq(v] 1/2) (5)

where is the equilibrium nuclear quadrupole couplingeQqeconstant and is the vibrationÈrotation correction term.aeQqUsing the nuclear quadrupole coupling constants obtained in

the ground and Ðrst excited vibrational states, the followingtwo expressions have been derived :

eQqv(79Br) \ 38.0789(36)] 2.0135(56)(v] 1/2)

eQqv(81Br) \ 31.8049(38)] 1.6777(68)(v] 1/2)

The ratio of the values of Sc79Br and Sc81Br noweQqeagrees with the ratio of the quadrupole moments withinexperimental error : evidently vibrational e†ects cause signiÐ-cant distortion of the Ðeld gradients of Br.11,12

(i) Nuclear quadrupole coupling constants. The ionic char-acter of the ScBr bond can be calculated from the brominenuclear quadrupole coupling constant, eQq(Br). If contribu-tions from the d-orbitals of the Br atom are neglected in thebonding orbitals, the ionic character can be related to thecoupling constants by :

ic \ 1 ] eQq0(Br)/eQq410(Br) (6)

where is the quadrupole coupling constant foreQq410(Br)a singly occupied orbital of atomic bromine4p

zMHz13]. The result is[eQq410(79Br) \ [ 769.76 ic \ 94.9%,indicating an almost entirely ionic ScBr bond. Table 3 com-pares the ionic character calculated by this method with thoseof several alkali and alkaline earth metal monobromides, andof ScCl and YBr. For the Sc and Y derivatives, the resultsfollow the expected periodic trends in electronegativity, withScBr less ionic than ScCl and YBr. It is interesting to notethat the ionicity of ScBr is comparable to that of NaCl (ic \94.8%),17 which is widely considered to be fully ionic.

Table 4 shows that the value of eQq(Sc) in ScBr is very closeto, though somewhat smaller than, the corresponding valuesin ScO (ref. 18), ScF and ScCl.2 On the surface this wouldseem to imply that the electronic structures near the Scnucleus are essentially the same for all four molecules. Thoughthis is probably true for the halides, other factors must also beconsidered. ScO has one fewer valence electron than thehalides ; the similarity between its eQq value and those of thehalides must have a signiÐcant contribution from the fact thatthe HOMO (from which the extra electron has been removed)has a large amount of Sc 4s character, which does not contrib-ute to eQq.19 Given the ionic character of ScBr, and the factthat Br is less electronegative than F or Cl it might beexpected that amongst the halides the valence electron densityon Sc would be highest for ScBr. Ab initio calculations for ScFand ScCl in ref. 2 are consistent with this view. Unfortunatelya simple application of the modiÐed TownesÈDailey theory,also discussed in ref. 2, would lead to a higher eQq(Sc) valuefor ScBr than for the other two halides. However, the ab initioresults also predict directly reasonable values for the eQq(Sc)values of ScO, ScF and ScCl, including correct trends.Attempts to account for variations in eQq(Sc) values betweenthe molecules (including ScBr) using a simple picture appearnot to be fruitful.

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Table 3 Comparison of for Sc79Br and some related speciesicSc79Br Y79Bra Mg79Brb Na79Brc Ca79Brd Sc35Cl

eQq0(79Br)/MHz 39.087 12.935 110.313 58.6080 20.015 [3.786ic (%) 94.9 98.3 85.7 92.5 97.4 96.6

a Ref. 14. b Ref. 15. c Ref. 16. d Ref. 12. e eQq(35Cl) and ionic character from ref. 2. f Ionic character, deÐned by eqn. (6).

(ii) Nuclear spin–rotation constants. For a diatomic mol-ecule, the spinÈrotation coupling constant, can beC

I,

expressed as the sum of nuclear and electronic terms.20,21

CI\ C

Inucl] C

Ielec (7)

The nuclear part depends only on the nuclear positions, andfor a diatomic molecule is given by21

CInucl\

[2ekN gIBZ

l+cr12

(8)

where e is the charge on the proton, c is the speed of light, kNand are the nuclear magneton and the g-factor of thegInucleus, respectively, B is the rotational constant, is ther12internuclear separation and is the atomic number of theZ

lsecond nucleus. From eqn. (9) and (10) both parts of wereCIcalculated and are listed in Table 5. From Table 5 we Ðnd the

dominant contribution of is given byCI

CIelec.

The average magnetic shielding determines the chemi-(pav)cal shift which is obtainable from NMR measurements. Theparameter is composed of two parts,22 a diamagnetic partpavand a paramagnetic part(pd) (pp) :

pav \ pd] pp (9)

For a diatomic molecule, is directly proportional topp CIelec.

pp \e+C

Ielec

6mckN gIB

(10)

For both nuclei of ScBr the values of have been calculatedppusing eqn. (10). These results are listed in Table 5. A simpleestimate of was given by Flygare et al. :23,24pd

pd\ pd(a)[e+

6mckN gIB

CInucl (11)

where is the diamagnetic shielding for the atom and canpd(a)be found in ref. 25. The values of for Sc and Br arepd(a)1521.35 and 3121.19 ppm, respectively. Combining eqn. (9)È

Table 4 Sc nuclear quadrupole coupling constants of ScBr andrelated moleculesa

Molecule eQq(Sc)/MHz

ScO 72.240(5)bScF 74.086(5)cScCl 68.207(3)cScBr 65.256(3)

a Numbers in parentheses are one standard deviation in units of leastsigniÐcant Ðgure. b Ref. 18. c Ref. 2.

(11) we can calculate the average magnetic shieldings, includ-ing the paramagnetic and diamagnetic parts. These results arelisted in Table 6.

(b) Equilibrium structure of ScBr

The equilibrium rotational constants, of Sc79Br andBe ,Sc81Br were evaluated using

Bv\ Be [ ae(v] 1/2) ] ce(v] 1/2)2 (12)

where is the rotational constant for the v vibrational state,Bvand and are the vibrationÈrotation constants. The equi-ae celibrium structure was investigated using four di†erent

methods. For Method 1, was taken as zero and only andce Bewere evaluated. Since has not been determined experi-ae cementally, it was estimated by assuming the ratio of andae cefor ScBr is the same as found for ScCl.2 With Ðxed atce0.0043 MHz, and were re-evaluated ; this was Method 2.ae BeThe results, including values, from Methods 1 and 2 arerelisted in Table 7. The standard deviations in are derivedrefrom the uncertainties in the atomic masses, rotational con-stants and fundamental constants.

Because of the high ionic character of ScBr the(ic \ 94.9%)distance was also calculated using ionic masses. The varia-retion should give at least a rough idea of where breakdown of

the BornÈOppenheimer approximation might be expected.Bond lengths obtained using ionic masses corresponding toMethods 1 and 2 are given under Methods 3 and 4, respec-tively, in Table 7.

The equilibrium bond lengths of Sc79Br and Sc81Br showisotopic variation within their uncertainties D10~6 indicat-A� ,ing no observable BornÈOppenheimer breakdown. They alsoagree well with the theoretical result of 2.43 (ref. 4) andre A�are greatly improved over the value of Fischell et al.3 whoestimated the ScBr bond length as 2.6 by using empiricalA�rules.

The harmonic vibration frequency, and the vibrationalue ,anharmonicity constant, of ScBr were estimated usingue xe ,the relations developed by Kratzer26 and Pekeris,27 respec-tively

ue \S4Be3

DJe

(13)

ue xe \ BeAae ue

6Be2] 1B2

(14)

where is the equilibrium centrifugal distortion constant,DJewhich is approximated as the ground state value. The disso-

Table 5 Nuclear and electronic contributions to the experimental spinÈrotation constants and corresponding paramagnetic shieldings in ScBra

Sc Br

CI/kHz C

Inucl/kHz C

Ielec/kHz pp/ppm C

I/kHz C

Inucl/kHz C

Ielec/kHz pp/ppm

Sc79Br 20.478(62) [0.95 21.43(6) [3107(9) 17.06(16) [0.59 17.65(17) [2476(23)Sc81Br 20.244(61) [0.94 21.18(6) [3098(9) 18.24(17) [0.63 18.87(18) [2396(22)

a Numbers in parentheses are one standard deviation in units of least signiÐcant Ðgure.

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Table 6 The magnetic shieldings of the nuclei in ScBra

Sc Br

pp/ppm pd/ppm pav/ppm pp/ppm pd/ppm pav/ppm

Sc79Br [3107(9) 1659 [1448(9) [2476(23) 3204 728(23)Sc81Br [3098(9) 1659 [1439(9) [2478(22) 3204 726(22)

a Numbers in parentheses are one standard deviation in units of least signiÐcant Ðgures.

Table 7 Equilibrium parameters of ScBra

References

Parameters M1b M2b M3b M4b Theo.c Expt.c

Sc79Brae/MHz 12.8992(2) 12.9078(2) 12.8992(2) 12.9078(2)Be/MHz 3112.940 19(15) 3112.943 42(15) 3112.940 19(15) 3112.943 42(15) 2623re/A� 2.380 846 5(10) 2.380 845 3(10) 2.380 843 5(10) 2.380 851 5(10) 2.432 2.60

Sc81Brae/MHz 12.7259(2) 12.7345(2) 12.7259(2) 12.7345(2)Be/MHz 3085.048 77(15) 3085.052 00(16) 3085.048 77(15) 3085.052 00(16) 2623re/A� 2.380 845 1(10) 2.380 843 9(10) 2.380 842 3(10) 2.380 850 4(10) 2.432 2.60

ue/cm~1 338.8(11) 327 275(5)uexe/cm~1 1.099(11)De/eV 3.4 3.74

a Numbers in parentheses are one standard deviation in units of least signiÐcant Ðgure. b M1, M2, M3, and M4 stand for Methods 1, 2, 3 and 4as discussed in the text, M2 and M4 use an estimated Estimated uncertainties in are derived from rotational constants, fundamentalce . reconstants, and reduced masses. c Ref. 4, no isotope e†ect speciÐed, average values are used. d Ref. 3.

ciation energy can be approximated by the relationDe

De Due2

4ue xe(15)

These expressions have been found to provide reasonable esti-mates of the vibration frequency and dissociation energy forScCl.2 The results for ScBr are listed in Table 7. The calcu-lated values of and are in good agreement with theue Detheoretical values from ref. 4. The discrepancy between thevalue of from this work and that from Fischell et al.3 arisesuebecause Fischell et al.3 overestimated the ScÈBr bond lengthin their analysis of the ScBr laser induced Ñuorescence spec-trum. Their standard deviation of ^5 cm~1 for is ambi-uetious considering the number of approximations made in theiranalysis.

5 ConclusionsThe microwave spectrum of ScBr has been measured for theÐrst time to produce rotational and centrifugal distortion con-stants, along with nuclear quadrupole and spinÈrotationcoupling constants. The equilibrium bond distance and vibra-tion frequency of ScBr have been determined. From thenuclear quadrupole coupling constants, the ScBr bond hasbeen shown to be highly ionic, though slightly less so than thebonds in YBr and ScCl. The electronic structures at Sc in thescandium halides have been found to be similar.

AcknowledgementsThis work has been supported by the Natural Sciences andEngineering Research Council of Canada, and by the Pet-roleum Research Fund administered by the American Chemi-cal Society.

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Paper a907769c

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