The rotational spectrum of iodine dioxide, OIO

Transcription

1 Havrford Collg Havrford Scholarship Faculty Publications Chmistry 2003 Th rotational spctrum of iodin dioxid, OIO Charls E. Millr Havrford Collg Edward A. Cohn Follow this and additional works at: Rpository Citation Millr, Charls E., and Edward A. Cohn. "Th rotational spctrum of iodin dioxid, OIO." Th Journal of chmical physics 118 (2003): This Journal Articl is brought to you for fr and opn accss by th Chmistry at Havrford Scholarship. It has bn accptd for inclusion in Faculty Publications by an authorizd administrator of Havrford Scholarship. For mor information, plas contact

2 Th rotational spctrum of iodin dioxid, OIO Charls E. Millr and Edward A. Cohn Citation: J. Chm. Phys. 118, 6309 (2003); doi: / Viw onlin: Viw Tabl of Contnts: Publishd by th Amrican Institut of Physics. Additional information on J. Chm. Phys. Journal Hompag: Journal Information: Top downloads: Information for Authors:

3 JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 10 8 MARCH 2003 Th rotational spctrum of iodin dioxid, OIO Charls E. Millr a) Dpartmnt of Chmistry, Havrford Collg, Havrford, Pnnsylvania Edward A. Cohn b) Jt Propulsion Laboratory, California Institut of Tchnology, Pasadna, California Rcivd 30 Sptmbr 2002; accptd 3 Dcmbr 2002 Th rotational spctrum of th OIO radical has bn obsrvd for th first tim. Spctra of both th ground and first two xcitd bnding vibrational stats hav bn analyzd. Rotational, cntrifugal distortion, fin, and hyprfin constants hav bn drivd. Ths constants hav bn usd to dtrmin th molcular structur, harmonic forc fild, and lctron distribution. Th OIO molcular paramtrs ar compard with thos of OClO and OBrO Amrican Institut of Physics. DOI: / INTRODUCTION Iodin oxids hav bn known for mor than 100 yars, yt thir chmical and physical proprtis rmain poorly charactrizd. For mor than 70 yars only IO, th prototypical iodin oxid, had bn idntifid in th gas phas. 1 Studir and Huston 2 first rportd th dtction of gas phas IO 2 which thy obsrvd in th thrmal dcomposition of I 2 O 5. Gills, Polak and Linbrgr 3 obtaind ngativ ion photolctron spctra of IO 2 that thy assignd to OIO( 2 B 1 ) OIO ( 1 A 1 ) transitions basd on th vibrational frquncy argumnts. Howvr, it was not until th work of Himmlmann t al. 4 on th IO slf-raction that th xistnc of gas phas OIO was widly acknowldgd. Himmlmann t al. 4 obsrvd a strong, structurd vibronic spctrum spanning th nm rang and dducd that th carrir was OIO basd on similaritis btwn th nw spctrum and th lctronic spctra of OClO 5 and OBrO. 6 Subsqunt studis hav shown that OIO is th principal product of th IO BrO raction, 7 that OIO is rmarkably stabl with rspct to photodissociation in th visibl, 8 and that OIO may srv as th starting point for th formation of iodin arosols in th marin boundary layr. 9,10 Littl additional spctroscopic or structural information xists for OIO. Athrton t al. 11 obsrvd lctron paramagntic rsonanc EPR spctra of OIO in KIO 2 F 2 crystals, dtrmining th g factor as wll as th hyprfin and 127 I quadrupol coupling constants. Bybrg 12,13 obsrvd OIO in KClO 4 crystals for normal and 16 OI 17 O and drivd lctronic charg and spin distributions that wr vry similar to thos found for OClO and OBrO. 14 Mair and Bothur 15 obsrvd infrard IR and lctronic spctra of OIO isolatd in Ar and O 2 matrics. Most rcntly, Misra and Marshall 16 calculatd an OIO structur at th MP2 FC/6-311 G 3df lvl of thory. This papr rports th rotational spctrum and structural dtrmination of OIO. Th rotational spctrum of OClO has Th xprimntal procdurs wr initially idntical to thos rcntly dscribd by Millr and Cohn 22 for th gnration of IO. OIO was discovrd during th masurmnt of highly xcitd vibrational stats of IO using an xtrnal microwav discharg through O 2 and passing th products ovr solid I 2 hld in a cm dp boat within th sampl cll. Th first fatur obsrvd which suggstd th prsnc of scondary products is shown in Fig. 1. It is th strong N Ka K c,j,f 26 2,25,26.5, ,24,25.5,28 transition at th lft of th scan. Two smallr faturs latr idntifid as th v 2 1, 8 8,1, 8.5,11 7 7,0, 7.5,10, and 8 8,1,8.5,10 7 7,0,7.5,9 transitions li within th IO v 11 hyprfin pattrn. Possibly bcaus of changing conditions du to dposits of iodin and its oxids on th cll walls, production of OIO using an xtrnal oxygn discharg dtrioratd svrly. OIO production was considrably nhancd by passing a DC discharg through O 2 flowing ovr a containr of I 2 as dscribd in Rf. 22. I 2 was placd in a long nckd glass bulb at th bottom of a1mby7.3cmi.d. doubl pass aba Elctronic mail: cmillr@havrford.du; millr/millr.html b Elctronic mail: dward.a.cohn@jpl.nasa.gov; bn wll studid and w hav rcntly rportd an analysis of th OBrO spctrum. 21 Th OIO spctrum was discovrd whil sarching for rotational transitions of highly xcitd vibrational lvls of th IO X 2 1 3/2 stat. 22 Subsquntly, six-lin hyprfin splitting pattrns wr obsrvd which had strong Zman ffct. Ths wr clar indications of an iodin containing radical. It was assumd that th radical was OIO and xtnsiv sarchs wr conductd for mor transitions. Evntually w assignd a sufficint numbr of transitions to provid an xtnsiv analysis of th ground and 2 1 stats. Aftr th xprimnts wr compltd, a smallr numbr of prviously unassignd transitions wr assignd for th 2 2 stat and som paramtrs wr dtrmind for that stat as wll. Th following sctions dscrib th xprimntal procdurs for gnrating OIO, th assignmnt and analysis of th spctrum, and th intrprtation of th spctral paramtrs in trms of molcular proprtis. Ths rsults ar compard to thos of th rlatd molculs OClO and OBrO. EXPERIMENT /2003/118(10)/1/9/$ Amrican Institut of Physics

4 2 J. Chm. Phys., Vol. 118, No. 10, 8 March 2003 C. E. Millr and E. A. Cohn th difficulty in maintaining constant xprimntal conditions, xtnsiv signal avraging was not don and many masurmnts wr takn dirctly from survy scans. Som faturs which wr masurd in th discharg showd dviations from calculatd positions of khz which could b attributd to thir vry strong Stark ffct. Such transitions wr not fittd. Howvr, smallr Stark shifts may hav gon unnoticd. As a rsult, th uncrtaintis assignd to vn th bst faturs wr 70 khz and no 2 2 faturs wr assignd uncrtaintis of bttr than 100 khz. A fw wak faturs, som of which ar from paramagntic spcis, rmain unassignd. Howvr, larg dviations from thrmal population wr not obsrvd as thy wr for IO in th sam xprimnt, and highly xcitd OIO stats wr not sufficintly populatd to b assignabl. FIG. 1. Th first fatur lft thought to indicat th prsnc of scondary products in th synthsis of IO. Th calculatd IO v 11 positions ar shown by th stick spctrum. OIO faturs ar indicatd by circls. Th baslin has bn rmovd. S txt for dtails. sorption cll. O 2 was passd through th cll at 25 l/s at prssurs of 10 Pa. A DC discharg of 35 ma at 1.3 kv was passd through th mixtur. Th cathod was a thin strip of 7.6 cm wid stainlss stl shim stock which conformd to th insid diamtr of th sampl cll at on nd whil a groundd mtal bllows valv in th sidarm to th pump srvd as th anod at th othr nd. A schmatic viw of th inlt rgion of th cll is shown in Fig. 2. A suitably strong fatur for tuning th chmistry was chosn as th flow rat was throttld back whil kping th total prssur narly constant until a maximum signal was attaind. Th xact flow rat was thn not known, but it was stimatd at 4 6 l/s. Th cll was maintaind nar room tmpratur by circulating mthanol through an outr jackt. Th conditions wr difficult to maintain and rproduc du to copious solid dposits on th walls, lctrods and windows. Nvrthlss, th strongst faturs wr obsrvabl in survy scans with S/N of 40 for dwll tims of 200 ms/point and 100 khz stps. All spctra wr rcordd using ton burst frquncy modulation 23 which producs a scond drivativ lin shap. In ordr to confirm that th initially obsrvd faturs wr du to radical spcis, a constant magntic fild was applid with a Zman coil wound around th sampl cll. Latr assignmnts rlid primarily on comparisons of obsrvd positions and hyprfin pattrns with prdictions. Bcaus of FIG. 2. A schmatic top viw of th cathod rgion of th discharg cll. Th gass ar pumpd out at th opposit nd of th cll through a sidarm and mtal bllows valv which srvs as th groundd anod. Th drawing is approximatly to scal with th bulb nck bing 22.9 cm long. Th cooling jackt and Zman coil surrounding th cll ar not shown. RESULTS Th spctrum and assignmnt OIO is a prolat asymmtric rotor ( ) with C 2v symmtry about th b axis and a 2 B 1 lctronic ground stat. Th oxygn spin statistics allow only rotational lvls with K a K c odd in th ground and othr totally symmtric vibrational stats. Th rotational, lctron spin, and nuclar spin angular momnta ar coupld in th following way: N S J, J I F. Thrfor, ach rotational lvl has fin structur doubling du to th lctron spin and furthr splitting into sxtts by th spin 5/2 iodin nuclus. In th frquncy rgions sarchd, only th F J N transitions wr xpctd to b obsrvabl giving ris to doublts of sxtts. Spctra wr prdictd using fin and hyprfin constants from th ESR work of Bybrg. 12,13 Th rotational constants wr initially calculatd using structural paramtrs stimatd from thos of rlatd molculs. Ths calculations indicatd that th C rotational constant was about 5.2 GHz. N 1 N transitions with a constant valu of N K c hav charactristic spacings of 2C for high N and K c N. Ths transitions wr also prdictd to hav fin structur doubling of lss that 200 MHz and hyprfin splittings of th ordr of svral MHz to svral tns of MHz which wr not strong functions of N. Thus, it was xpctd that a survy of 11 GHz would rval at last on rcurring pattrn. Fortuitously, th transitions with K c N J 1/2 hav all six strong hyprfin componnts within 2 MHz. Ths ar only partially rsolvd from ach othr and giv th apparanc of a strong asymmtric doublt with th strongr componnt at high frquncy. Bcaus of th blndd lins, ths ar by far th strongst faturs in th spctrum. Th first of ths discovrd wr th 40 1, , F 39 0,39, 38.5, F 1 transitions nar GHz. Th rcurring pattrn was quickly confirmd by skipping to th frquncy rgion of nxt lowr N and conducting a short sarch. Furthr confirmation was thn obtaind from th positions of prviously unassignd faturs containd in survy scans at othr frquncis takn during th rcntly rportd IO study. 22 A small rgion of th OIO spctrum nar GHz is shown in Fig. 3 undr

5 J. Chm. Phys., Vol. 118, No. 10, 8 March 2003 Rotational spctrum of iodin dioxid 3 TABLE II. OIO fin structur paramtrs/mhz. Paramtr a X 000 X 010 X 000 X 020 X 000 2X 010 aa bb cc D S N S D KN D NK S D S K d S d S S H S K H KKN a Th numbrs in parnthss ar 1 uncrtaintis in units of th last digit. FIG. 3. A portion of th OIO spctrum nar MHz top and a simulation using calculatd lin positions bottom. Th rlativ strngths ar not rproducd du to powr fluctuations of th millimtr wav sourc and th prsnc of an lctric discharg in th sampl. Th spctrum was rcordd using scond harmonic dtction. Th baslin has bn rmovd from th obsrvd spctrum by taking th scond diffrnc using 0.5 MHz btwn points. narly optimum conditions. Evntually it was possibl to includ in th fit a total of 621 ground-stat faturs containing 703 transitions, 198 v 2 1 faturs containing 219 transitions and 72 v 2 2 faturs containing 83 transitions. Svral additional faturs wr wll dscribd by prdictions basd on th analysis, but containd blnds of diffrnt vibrational stats and wr not includd in th fit. Analysis Th OIO Hamiltonian can b writtn as H H rot H fs H hfs, TABLE I. OIO rotational paramtrs/mhz. whr H rot is a Watson S rduction of th rotational Hamiltonian in th I r rprsntation 24 which contains up to octic cntrifugal distortion trms; H fs is a fin structur Hamiltonian dscribing th lctron spin rotation with up to sxtic distortion trms; and H hfs is a hyprfin structur Hamiltonian which includs spin spin coupling with quartic distortion trms, and nuclar quadrupol and nuclar spin rotation coupling. Th cntrifugal distortion trms for H fs ar basd on th work of Brown and Sars. 25 All trms in th Hamiltonian ar dfind in Rf. 21. Although th Hamiltonian is similar to th on usd for OBrO, 21 th smallr numbr of lss prcisly masurd spctral faturs do not allow th dtrmination of quit as many paramtrs as wr rportd for OBrO. Nvrthlss, th paramtrs for th OIO ground and v 2 1 stats that ar to b usd to driv th structur and othr molcular proprtis ar wll dtrmind. Th paramtrs rquird to fit th spctrum for H rot, H fs, and H hfs, ar listd in Tabls I III, rspctivly. An output fil containing corrlation cofficints as wll as a complt list of fittd lins, stimatd xprimntal uncrtaintis, and calculatd positions is availabl from th Elctronic Physics Auxiliary Publication Srvic EPAPS of th Amrican Institut of Physics. 26 Also availabl ar input fils which can b usd with th program SPFIT 27 to gnrat th calculation rportd hr. Paramtr a X 000 X 010 X 000 X 020 X 000 2X 010 A B C D J D JN D N d d H N H NK H KN H K h h h L KKN L K l a Th numbrs in parnthss ar 1 uncrtaintis in units of th last digit. TABLE III. OIO hyprfin paramtrs/mhz. Paramtr a X 000 X 010 X 000 a F T aa T bb T cc T aa T aa T K 10 3b aa bb cc K 10 3b C aa C bb C cc a Th numbrs in parnthss ar 1 uncrtaintis in units of th last digit. b T K T K bb T K cc, K K bb K cc.

6 4 J. Chm. Phys., Vol. 118, No. 10, 8 March 2003 C. E. Millr and E. A. Cohn TABLE IV. Halogn dioxid structurs. O 35 ClO O 79 BrO OIO Paramtr a r 0 r r r 0 r r r 0 r r r/pm /dg a Th r 0 s ar calculatd from th planar momnts. Th r s ar xprimntal for OClO Rf. 20, calculatd from th r z and th Kuchitsu Rf. 28 rlationship for OBrO Rf. 21, and stimatd for OIO. Th r s ar th dcrass in bond lngths from th X 1 2 3/2 stats of th corrsponding monoxids. DISCUSSION Structural paramtrs Th OIO ground-stat ffctiv structur, r 0 can b calculatd from any two of th thr momnts of inrtia or th a and b planar momnts. Th lattr is givn in Tabl IV. Th uncrtaintis of th rotational constants ar vry small, howvr, th accuracy of th r 0 structural paramtrs is limitd by vibrational ffcts which lad to diffrnt valus dpnding on th choic of momnts. Thus, th uncrtainty of ach of th r 0 paramtrs is approximatly two units in th last figur quotd. Tabl IV also compars th r 0 structur with thos of OClO and OBrO. For th lattr two molculs, th quilibrium structurs giv bond lngths of 0.5 pm shortr and bond angls 0.1 smallr than th r 0 structurs whn th planar momnts ar us for th calculation. 21 Similar diffrncs may b xpctd for OIO. Sinc considrably lss data xist for th dtrmination of th harmonic forc fild than wr availabl for OBrO, th mor rigorous dtrmination of r z and r structurs that was don for OBrO has not bn don for OIO. Th trnd toward smallr bond angl is apparnt in going from Cl to I as is shown in Tabl IV. Also shown for comparison ar th dcrass of th quilibrium bond lngths from thos of th X 2 1 3/2 stats of th corrsponding monoxids. It can b sn that th shortning of th bond is only slightly smallr for OIO and than for OBrO and that both ar significantly lss than is found for OClO. This is to b xpctd if th bonding is lss ffctiv btwn atoms of disparat siz. Ab initio calculations of th structural paramtrs for OIO and IO by Misra and Marshall 16 giv pm and for th quilibrium bond lngth and angl in OIO and pm for th bond lngth in IO. Th calculatd diffrnc in bond lngth btwn IO and OIO is vry clos to that obsrvd, but both th bond lngth and OIO angl ar largr than th xprimntally dtrmind valus by 1.1 pm and 1.5, rspctivly. Th cntrifugal distortion constants ar consistnt with thos of OClO and OBrO. Ths can b usd along with th masurd vibrational frquncis 15 for 1 and 3 and th inrtial dfcts for th ground and xcitd bnding stat to roughly dtrmin th harmonic forc fild. In th fit with th program NCA, 29 th vibrational frquncis ar wightd tn tims gratr rlativ to thir magnitud than ar th cntrifugal distortion constants and inrtial dfcts. Bcaus th bnding mod frquncy, 2, is not wll dtrmind, with valus of and 250 cm 1 having bn rportd, 3,4 it is not includd in th dtrmination of th harmonic forc fild. Th forc constants and th obsrvd and calculatd molcular constants ar shown in Tabl V. For comparison, th rsults of a calculation don for OBrO utilizing only data and wighting corrsponding to thos usd for OIO ar also shown. Th valu calculatd for th bnding frquncy of OBrO as wll as th valus for th diagonal forc constants ar not significantly diffrnt from thos drivd from th mor xtnsiv data usd in Rf. 21. Th calculatd valus of f rr and f r for OBrO chang from 5.0 and 6.1 Nm 1 in Rf. 21 to 0.4 and 6.8 Nm 1 for th mor limitd data st usd hr. Thus vn with th smallr data st it is apparnt that changs in th constants f r and f on rplacing Br with I ar much lss than thos whn Cl is rplacd by Br. This is consistnt with th obsrvation that th O X bond lngth changs ar rlativly lss for both th Br and I on going from th monoxid to th dioxid and that doubl bond formation is lss ffctiv in both havir dioxids. Th harmonic forc fild calculation prdicts th 2 frquncy to b 263 cm 1, which is only 13 cm 1 highr than th stimat of Himmlmann t al. 4 Th corrsponding calculation of for OBrO givs a rsult that is 4 cm 1 lowr than th obsrvd frquncy. This is not ncssarily prdictiv of th diffrnc btwn th OIO calculatd and actual 2. Howvr, th prsnt rsult crtainly favors th stimat of 250 cm 1 from th study of th ultraviolt UV spctrum 4 ovr th much lowr valu obtaind from photolctron dtachmnt. Morovr, Hullah and Brown 30 rcntly TABLE V. Comparison of harmonic forc fild calculations for OIO and OBrO using similar data sts and wighting. Paramtr OIO O 79 BrO Obs. Calc. Obs. Calc. 1 /cm a /cm 1b c /cm a D J /khz D JK /khz D K /khz d 1 /khz d 2 /khz /amuå /amuå f r /Nm f /Nm f rr /Nm f r /Nm a From Rf. 15. b Not includd in th fit for ithr molcul. c From Rf. 4.

7 J. Chm. Phys., Vol. 118, No. 10, 8 March 2003 Rotational spctrum of iodin dioxid 5 TABLE VI. Normalizd lctron spin rotation coupling constants, lctronic g valus, and ratios of ii OXO. OIO O 79 BrO O 35 ClO I Br Br Cl for i ii /2 a g ii a ii /2 g ii ii /2 g ii ii ii a b c a Gas phas; ii ii /B i. Matrix ESR; g ii g ii g. studid th TO 2 lctronic spctrum and found cm 1. Th valu of 2 in OBrO is 45 cm 1 lss than in SO 2, and this may b takn as an uppr limit for th diffrnc btwn th 2 valus of OIO and TO 2. Thus, th faturs attributd to 2 hot bands in th OIO UV spctrum rportd by Himmlmann t al. 4 ar probably corrctly assignd. Elctron spin rotation coupling constants Tabl II shows th lctron spin rotation constants, thir cntrifugal distortion constants, and thir dpndnc on th 2 xcitation. In Tabl VI th normalizd spin rotation constants, ii ii /B i, ar compard with thos of OBrO and OClO as wll as th g valus, g ii g ii g dtrmind by ESR spctroscopy of matrix isolatd molculs. Th rlationship proposd by Curl 31 btwn th normalizd lctron spin rotation constants and th lctronic g valus obtaind from ESR xprimnts ii /2 g ii g, whr g is th fr lctron, g factor prdicts th trnds obsrvd for th g valus in matrix isolatd sampls. 12,32 Possibl structural prturbations in th matrix prvnt dtaild intrprtation of th diffrncs btwn obsrvd and calculatd valus for th havir halogn dioxids. Th normalizd spin rotation constants incras from OClO to OIO, but th incras from OBrO to OIO is nithr as larg nor as uniform as would b stimatd from th incras from OClO to OBrO. In th lattr cas, both aa and bb incras by an amount which is vry clos to th spin dnsity wightd avrag of th atomic spin orbit coupling constants and by a slightly largr factor than for th ratio of spin orbit coupling constants in th monoxids. For OIO th corrsponding stimatd chang would b mor than an additional factor of 2 incras compard to OBrO as is sn in th spin orbit coupling of IO. 3 Howvr, aa incrass by an additional factor of only 1.64 and bb by a factor of only Sinc th xcitation nrgis ar smallr for OIO than for th lightr dioxids, this is an indication that th matrix lmnts conncting th ground stat with th prturbing stats ar smallr than would b stimatd by considring only p orbital spin orbit couplings. Th incras in magnitud of cc is vry larg and may indicat incrasd partici- pation of d orbitals in th xcitd stats that contribut to th lctron spin rotation constants or contributions from stats rquiring xcitation of mor than on lctron. Curl 33 has discussd this topic for th cas of OClO. A complt st of quartic and som sxtic spin rotation distortion trms ar rquird to fit th ground rotational stat spctrum. Th trnds obsrvd for OBrO and OClO ar continud for OIO in th sns that trnds to mor positiv or mor ngativ valus ar maintaind for th quartic constants. Th valus ar actually quit diffrnt among th thr molculs and ar compard in Tabl VII. Lss data ar availabl for th xcitd bnding stats than for th lightr dioxids and only two indpndnt quartic distortion trms could b dtrmind for th 2 stat. Th changs in spin rotation constant with bnding mod xcitation follow th trnd shown in OClO and OBrO. This is shown in Tabl VIII whr th changs with xcitation of ii, B i, and ii dividd by thir ground stat valus ar givn. Th valus of aa dcras by a rlativly gratr amount for th havir halogns whras th chang in bb starts as positiv for OClO, bcoms ngativ for OBrO and mor strongly ngativ for OIO. Although cc is mor than a factor of 10 largr for OBrO than it is for OClO and incrass by almost anothr factor of 4 for OIO th rlativ TABLE VII. Comparison of th OXO lctron spin rotation constants and quartic distortion trms/mhz. Paramtr OIO O 79 BrO O 35 ClO aa bb cc D S N D NK D KN D S K d S d S

8 6 J. Chm. Phys., Vol. 118, No. 10, 8 March 2003 C. E. Millr and E. A. Cohn TABLE VIII. Changs of th normalizd lctron spin rotation constants, rotational constants, and lctron spin rotation constants for OXO with xcitation of 2. Th tabulatd quantitis ar 100(X 010 X 000 )/X 000. OIO O 79 BrO O 35 ClO i ii B i ii ii B i ii ii B i ii a b c changs with xcitation actually dcras slightly for th havir molculs. Spin spin coupling constants Th spin spin coupling constants for both th ground and 2 stats hav bn dtrmind as hav som cntrifugal distortion constants common to both stats. Th availabl 2 2 data hav bn adquatly fit by assuming linar changs with xcitation of th bnding mod for all of th hyprfin constants shown in Tabl III. Th anisotropic or dipolar coupling tnsor, T, and scalar or Frmi contact trm, a F, ar wll dtrmind and consistnt with th trnds obsrvd for OClO and OBrO. Th signs and magnituds of th cntrifugal and vibrational trms ar also consistnt with thos of OBrO and OClO, but ar lss prcisly dtrmind than th OBrO constants. Of intrst is th ngativ a F valu of 90.07(6) MHz which can b compard to th 95.8(3.8) MHz Frmi contact trm of IO. 22 Bybrg 12,13 obtaind a similar rsult in his study of th OIO ESR spctrum and pointd out that a ngativ valu of about this magnitud is prdictd from th calculatd rlativistic atomic valu for an iodin 5p lctron 34 and th spin dnsity on th iodin. For a spin dnsity of 0.5 on th I atom, on prdicts a F 115 MHz. Th contact trm for a singl 5s lctron in atomic iodin is 46.6 GHz. 35 Thrfor, as was also found for OClO and OBrO, thr must b almost no halogn s charactr in th orbital containing th unpaird lctron. Th dipolar coupling tnsor is vry narly axially symmtric about an axis paralll to th c principal axis of th molcul. Th componnts of th tnsor ar givn by T xx g g N N 3 cos 2 x 1 /r 3 S, whr x is on of th principal axs of th molcul and cos x is th dirction cosin of th vctor from th nuclar spin to th lctron spin. It is usually assumd that th spin dnsity at th halogn in th OXO molculs is primarily du to a p lctron in an orbital prpndicular to th molcular plan with th atomic angular distribution givn by 3 cos 2 x 1 0.8, 0.4, 0.4 for x c,a,b, rspctivly. For th prsnt cas, T aa is slightly lss ngativ than T bb so that cos 2 a cos 2 b. For OClO, OBrO, and OIO th asymmtry paramtr T T aa T bb /T cc, has valus of , , , rspctivly. A similar trnd toward incrasing asymmtry is sn in th sris NH 2,PH 2, and AsH although in th cas of th group V dihydrids th unpaird lctron is in a p bonding orbital with th spin dnsity almost ntirly on th cntral atom. In th halogn dioxids th unpaird lctron is in an antibonding orbital with about half th spin dnsity on th cntral atom. This slight axial asymmtry of th dipolar coupling tnsor may b thought of as a contribution from a small amount of in-plan lctron spin dnsity du to mixing of th X 2 B 1 stat with xcitd lctronic stats of A 1 and B 2 symmtry, primarily by off-diagonal lmnts of th spin orbit coupling. Ptrson 40 has rcntly prformd ab initio calculations for OClO and OBrO. Using th sam lvl of thory dscribd in Rf. 40, h has calculatd small 1% in-plan spin dnsitis for both OClO and OBrO orintd oppositly to that in th p c orbital with most of th in-plan spin dnsity along th symmtry axis. 41 Whil such small calculatd valus ar to b tratd cautiously, thy ar th magnitud and sign indicatd by th obsrvd asymmtry of th dipolar coupling tnsor. As mntiond in th discussion of th spin rotation constants, th ii s of OIO do not closly follow th trnd xpctd for similar halogn spin dnsitis for th thr dioxids. Howvr, th ii s ar dscribd primarily by th intraction of th ground stat with various xcitd lctronic stats whras th spin spin intractions as wll as th quadrupol coupling constants discussd blow ar primarily dscribd by th ground-stat wav function. For th halogn monoxids, th spin dnsity can b drivd dirctly from th Frosch Foly 42 constants d c/3 S XO g g N N r 3 S atom, whr th S subscript rfrs to th appropriat xpctation valu for th radial distribution of th lctron spin. For th dioxids th angular dpndnc cannot b rmovd. If on ignors th small amount of in-plan spin dnsity, th approximat spin dnsity for a p orbital may b drivd from a similar xprssion with 5T cc /4 rplacing d c/3 on th lft-hand-sid of th abov quation. Thus, on obtains S OXO / S XO 5T cc /4 / d c/3. This ratio quals 1.42, 1.38, and 1.33 for th Cl, 20,43 Br, 21,44 and I 22 compounds, rspctivly. This shows that th shift in spin dnsity to th mor lctropositiv lmnt is lss pronouncd in th dioxids than in th monoxids. A singl lctron in th valnc p c orbital would rsult in T cc valus of , , and MHz for I, 79 Br, and 35 Cl, rspctivly. Th T cc s ar dtrmind by using th rlativistic valus calculatd by Pyykkö and Wisnfld 35 to obtain th r 3 S s for th atoms. Th hyprfin intgrals from Tabl A2 of Rf. 35 ar rlatd to th r, r, and r trms from Rf. 34: V(1) 2r, V(1, 2) r /2 and V( 2) r. Th atomic iodin radial xpctation

9 J. Chm. Phys., Vol. 118, No. 10, 8 March 2003 Rotational spctrum of iodin dioxid 7 valus ar thn dtrmind from th rlationships r 3 L (4r 4r r )/9 and r 3 S ( 8r 40r 5r )/27. Whr th L and S subscripts rfr to orbital and spin distributions. Th numrical rsults rquir a factor of a to convrt thm into SI units. Ths valus of T cc lad to halogn spin dnsitis of 0.508, 0.498, and for OIO, OBrO, and OClO rspctivly. Th xprimntal magntic constants for 35 Cl atom rportd by Uslu t al. 45 would giv a T cc of MHz and rsult in a Cl spin dnsity of for OClO. Not that th ffct of th positiv charg on th halogn has not bn considrd whn using th atomic valu of r 3 S for ithr th monoxids or th dioxids. In fact, th halogns ar positivly chargd in both compounds and it may b mor appropriat to apply a corrction factor to account for th nuclus bing lss shildd from th valnc lctrons. For all th halogn nucli a factor of n is usd for quadrupol coupling, 46 whr n is th charg on th atom. If w assum that this is primarily du to a chang in r 3 T for all th lctrons, thn a similar factor may b applicabl to r 3 S. In that cas th spin dnsity on th halogns would b lss than that givn abov, or about 0.4 for all thr dioxids. Th dtails of th calculation which taks charg into considration ar discussd in th sction on quadrupol coupling. Rcnt studis of th halogn monoxids hav shown that th angular distribution of th lctron about th halogn atom in thos molculs changs from slightly longatd to slightly comprssd with rspct to th atomic p orbital as th atomic numbr incrass. 22 For th dioxids it is apparnt from th slight asymmtry of th coupling tnsor about th c axis that thr is at last som diffrnc in th angular distribution of th spin dnsity about th halogn from that of a pur p c -orbital and that th diffrnc incrass with atomic numbr. Th uncrtainty rgarding th angular distribution of th spin dnsity as wll as th uncrtainty of th thortical radial functions limit th accuracy of th spin dnsity drivd from th spin spin coupling tnsor. Should th angular distribution of th lctron chang in a mannr similar to that obsrvd for th monoxids, thn th spin dnsity of I would b gratr, and that of Cl lss than that givn by th calculation dscribd in th prcding paragraph. Howvr, Bybrg s ESR study 13 of 17 O nrichd OIO and OClO showd littl chang in spin dnsity at th oxygn. That rsult was consistnt with his arlir studis of th 16 O compounds 12 which showd similar spin dnsitis at th halogns in ach of th dioxids. This suggsts that th angular distribution of th lctron spin about th halogn is quit wll dscribd by that of an atomic p-lctron and is about th sam for all thr OXO dioxids. Th fact that th ffct of th doubl bond on bond lngth and strngth is much lss in OBrO and OIO than it is in OClO may not b an important considration, sinc th lctron distribution closst to th coupling nuclus is most significant in th dtrmination of th dipolar coupling tnsor. Nuclar quadrupol coupling constants Th quadrupol coupling constants ar consistnt with thos of OBrO and OClO. Ths may b intrprtd in trms of th in-plan p lctron population if th out of plan population is fixd to that drivd from th spin spin coupling tnsor. Bcaus th and * orbitals ar orthogonal, th total p lctron dnsity at th I atom is givn by 2 c s whr c s is th spin dnsity dtrmind from T cc. On thn obtains th total in-plan p lctron dnsity at th I atom from t a t b 2 2 s c cc /Qq ff 510. t Th x ar th total lctron dnsitis in th p a and p b orbitals. Th individual dnsitis may b dtrmind from t a t b 2 aa bb / 3Qq ff 510. Th ffctiv atomic quadrupol coupling constants ar corrctd for th positiv charg on th halogn which rquirs information on th participation of s and d orbitals in th bonds. Ptrson 41 has found littl contribution from d orbitals in both OClO and OBrO and th sam will b assumd tru for OIO. If on dscribs th in-plan orbitals in trms of th usual sp n hybridization, thn 1 1 2a s 2 1/2 s 2 1/2 a s pb, 2 a s s 1/2 a s 2 1/2 pb 2 1/2 pa, 3 a s s 1/2 a 2 s 1/2 pb 2 1/2 pa, whr a 2 s cos /(cos 1) and OXO. 47 Sinc th lctron dnsity in ach of th two orbitals in th oxygn dirctions must qual a, on has l b a 1 2a s 2 /2a s 2, s 1 2a s 2 l 2a s 2 a, n 7 a b c s, whr l is th population of th lon pair orbital dscribd by 1 and s is th total s orbital population. Ths quations may b solvd for l, s, and n with a s fixd by th bond angl or for a s and th rmaining paramtrs with l fixd. Sinc a, b, and c dpnd on n du to th multiplicativ factor of n applid to th atomic quadrupol and magntic coupling constants, th quations must b solvd itrativly. If on uss s fixd to th valus obtaind from th r 0 ff structurs, Qq n10 corrctd for rlativistic ffcts as discussd by Pyykkö and Sth, 48 and s c dtrmind from T cc, thn on obtains th p orbital lctron populations givn in Tabl IX. For I, 79 Br, and 35 Cl, th rspctiv rlativistic ff corrction factors and rsultant valus of Qq n10 for th nutral atoms ar , , and giving , , and MHz. For OClO th calculation was don with both atomic T cc valus mntiond in th prcding sction. This calculation givs similar in-plan p lctron dnsitis for all of th halogns and dos not show th xpctd trnd to lowr lctron dnsity on th mor lctropositiv lmnt. If th amount of s charactr in th halogn bonding orbitals wr dtrmind solly by th OXO angl, thn it would b ncssary to rmov about 0.5 lctron from th lon pair orbital for all of th halogns in ordr to rproduc th obsrvd quadrupol couplings. With

10 8 J. Chm. Phys., Vol. 118, No. 10, 8 March 2003 C. E. Millr and E. A. Cohn TABLE IX. Orbital populations and rlatd paramtrs drivd from th hyprfin constants. Fixd hybridization a Full lon pair b OIO OBrO OClO OClO c OIO OBrO OClO OClO c a b c s c s l a s n a Th s charactr givn by a 2 s is dtrmind by th r 0 bond angl shown hr in dgrs. b Th lon pair orbital population, l, is fixd at 2. Th s charactr and rsultant angl ar calculatd. c Calculatd using T cc for a singl lctron drivd from th atomic constants dtrmind by Uslu t al. Rf. 45. th lon pair orbital on th halogn fully occupid, Tabl IX shows that th rquird valus of a s 2 and th corrsponding bond angls ar considrably lss than thos dtrmind from th positions of th nucli. Th calculatd angls dcras as do th xprimntal angls, but all ar much smallr. Th orbital populations givn in Tabl IX show that th main diffrnc in th two calculations is that th lattr kps th lon pair in an orbital that is largly s charactr. Th smingly anomalous rsult that th I atom is lss positiv than Br or Cl is common to both calculations and may indicat a mor important rol for d orbitals in I or that th simpl modl usd hr is not capabl of showing subtl trnds. It is clar, howvr, that thr is littl chang in th valnc lctron distribution closst to th cntral atom in spit of significant changs in bond angl. Although th xprimntally dtrmind and thortically calculatd valus of T cc for Cl atom produc somwhat diffrnt drivd lctron distributions, ths diffrncs do not affct th abov conclusions. It is intrsting that th ab initio calculations of Ptrson 40,41 at th B3LYP/aug-cc-pVDZ lvl of thory giv about 13% s charactr for th halogn bonding orbitals on OClO and OBrO with littl d charactr. This may b compard with th 14.3% or 15.1% OClO and 12.6% OBrO s charactr shown in Tabl IX. Thus, both thory and th quadrupol coupling constants indicat considrably lss s charactr than th bond angl would indicat. Ptrson s calculations also show that for OClO and OBrO th lctron distributions at th halogns ar almost th sam. Exprimnt supports this and xtnds th similarity to OIO. In addition to th Ptrson calculations thr hav rcntly bn ab initio calculations for OClO which hav yildd hyprfin constants 49 in good agrmnt with xprimnt. Th hyprfin constants rportd in this study should b usful in tsting th quality of such calculations for OIO. Nuclar spin rotation constants Th nuclar spin rotation coupling constants hav bn wll dtrmind for OIO and ar compard with thos of OBrO and OClO in Tabl X along with th normalizd constants givn by n ii C ii / B i g n r 3 l, whr g n is th nuclar g factor. Th trnd toward largr valus of n ii is as xpctd for molculs with lowr lying xcitd lctronic stats. Unlik, n is narly isotropic for all thr halogn dioxids. It is intrsting that th halogn monoxids all hav normalizd nuclar spin rotation coupling constants vry clos to thos of th OXO dioxids. Ths ar 5.5, 4.3, and m 3 for IO, BrO, and ClO, rspctivly. CONCLUSION This invstigation of th rotational spctrum of OIO has compltd th sris of studis of th known OXO halogn dioxids. An xtnsiv st of molcular paramtrs has bn dtrmind which can provid accurat prdictions of th rotational spctra of th ground and first xcitd bnding stat and will b hlpful in th analysis of any rotationally rsolvd OIO spctra. It has bn possibl to lucidat trnds in structur and harmonic forc fild for th Cl, Br, I sris. Th forc fild calculation has providd confirmation for th dtrmination of th bnding frquncy from th optical spctrum and has shown that thr is rlativly lss diffrnc in bond strngth btwn th IO and BrO bonds than btwn th BrO and ClO bonds. Th valus of aa and bb ar somwhat smallr than xpctd basd on th stimatd spin orbit coupling for th molcul and th corrsponding valus for OClO and OBrO. Th hyprfin paramtrs ar in good agrmnt with ESR rsults 12,13 indicating only minor matrix ffcts in th arlir study. Both th magntic and TABLE X. Nuclar spin rotation coupling constants, for OIO, OBrO, and OClO. OIO OBrO OClO n a n a n a i C ii /khz ii C ii /khz ii C ii /khz ii a b c a n ii C ii /(B i g n r 3 l ) /m 3.

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