ir lfil

st. Joh n 's

THE ELECTRONICBAND SYSTEMS OF1ZClI;O+

BY

Cha n d ra n Ha r i d a s s

Athesissubmi tted tothe Sc h oo l of Gradua te St u diesin partial fu lfil lmen t of the

re qu i re ments for thede g r e e of Ma s t er of Science

Depar tme ntof Physics Memori a l Un i versi t yofNe~'foundl a nd

May 19 90

New f ound l and

11+.

o--~.~

ICI/\O"U

Theauthorhas grantedM Irrevocablenon- exclusivelicence allowingthe NationalUbrary of Canadatoreproduce,loan,dIsbibute or sen copiesofhis/herthesisby anymeansand in anyformOfformat.makingthisthesisavailable to interestedpersons.

Theauthor retainsowner~01the copyright in hislherthesis.Neither lhe thesis nor substantial extractsfromitmaybeprinted or olhefwi sereproducedwithouthislherper- miSS;On.

L'auleura accceoeunelicencejrrevocabteat non exclusivepermeuantalaBib6otM~ue naliooaledu Canada derepeodulre,preter.

dislribuer ouvendra descopiesde sathOse dequelquemantere atsousquelquelorme evecesoilpourmeltreoesexen c talresde cenethese aIadisposition des persomes lntere ssee s.

L'auteurconserveIapropricl ed.Jdroitd'tlUlcur quiprotege sa these.NiIatheseIIi descxlrnlts substantielsdeceae-cne doivent6lrc mprinesoueutrerncottcproduilssansson autorisalion.

Cana da

ACKNOWLEDG MENTS

I wis h toexpress my grateful th a n ks tomysuperv Lscr, Prof e ssorS.P.Reddy, forhis enc ouragementand quIdancein the various st a g e s of myresearchpr oj e ctandot he r acade mi c purs u i t s.

Mysi nc e r e apprec iation to Dr. C. V. V. Pra sad wh os e constructive and valuable cri t i c ism ha s helped in the imp r ov e me nt of th is thesis.

I extendmy thanks tothe followingte chn i calper s onn e l fo j.· theirhelpincomp l e t i n g the researchproject : Me ssrs.'r.

G. white, M. Ryan, and W. Holly fo r the mech an ica lwork ; D.

Seymour,M.Hatswell, and T. Pe rks for their sk il lf ul q Las.s blowi ng;R. Guestfo r some draft ingwork;and R. Bra dl ey for somephotographicwork. It is my pleasureto thank Mrs. Joy Simmons for. her patient andskillfuL typingof the manus cr ip t.

I would like to tha nk Mr. Robin Kelly fo r his hel p in performingsome comp u t a t i onalwork.

I thank the Memorial Uni v e r si t y of Ne wf oundl a nd for pr ovidi n g financial support in the form of a Gr ad uate Fellowshipand Graduate Teach i n g Assi stantships and burs a ry fromDr. Reddy'sNSERCgrant.

1am immenselyindebted to Dr.N. Kris hnamurthy,Ma d ur a i Kamaraj University, Madura! , India, who inspired me to undertakeresearch in molecular spe c troscopy .

- i i-

The electronic band spectrum of the molecular ionUC¹⁶0·

is of considerable importanceto a!.>trophysicsas this species isone ofthe major cons t ituen t of the solar chromosphere, stellar atmospheres,and cometta il s . It has also application in thestudy of radiativeheating of hypersonic space craft at escape velocityand in the atmospharic fringe of the planet Venus.

The molecular ion co' was excited in a hollow-cathode discharge tube of special design (S. P. Reddy and c. V. V.

Prasad,J.Phys.E.Sci.Instrum.il, 306 (1989). The cornet- ta i l (AZnl - XZ1;+)bandsystemof thismolecular ion occurring inthe cathode glow of the discharg e tUb e was photographed in the spectral re g i on 3345- 8500 A on a 2mBauschand Lomb dual-grating spectrograph in the fi r s t order of a 600 grooves/mmgrating unde rmedium re s o lut i o n. Spectrawerealso recorded underhighre s olu tio n on thesame spectrograp hin the second and third ordersof a 1200grooves/mm grating as well as on a 3.4 m Jarrell-AshEbert grating spectrograph in the second, third,and fourthordersof a120 0 grooves/mm grati ng. Of the seventeenbands withv· - 0 to 8 and v" _

°

^{to 4}

recorded in this system, detailed rotational an alysis of twelve (0-0,4-0, 3-0,2-0 ,1-0,2-1,1-1,0-1 ,2-3,0-2,0-3, and 0-4) bands have been carried out. Rotationa l constants were obtained fo r the AZn! and XZI;+states using the effective Hamiltonianproposedby Brown andhis co-workers (J.M. Brown

nu.,

J.Mol. Spcctrosc. li, 294 (1979)). - i i i -

- iv-

Experimental data en the rotational structure of the fi r st negative (B~'£'- XZl:')sysb~m(Rao, Astrophys. J.lil. 50 (1950) andMi s r a gt.e.l••J. MrJI.Spectrosc.li.2. 54 (1987) ).

the Baldet-Johnson(Sz;E'- AZndsystem (JakubekI I.iLl.,Can.

J. Phys. §2. 94 (1987»), and the microwavespect rum of the v

""0 level (Sastry§..t.21. ,Astrophys.J. 1.2.Q.. L9 1 (1981) and ofth e v<= 0, I, and2leve l s (Bog e yg,t!!.l. ,J. Chern.pnys.1:1.

4704 (1983») of co' have been r-aana Lysodusingthe erroc tIvc Hamiltonian. A e LnqLe set of molecular co ns t ants werethen obta i ne d for the X, A, and B states of CO'by th e method ofa global fit of the molecular constants obta i n e d from the analysisof the comet-tail,Baldet-Johnsonand first negative systems andthe microwave data. Thevi bra t i o na l constantsfor these three stateswe r e obtained from the ba nd origindata.

Page ACKNOWLEDGMENTS

AOSTRACT

CHAPTER 1: INTRODUCTION

1.1 Significance of molecular spectra

~~t~~~~~~~~~iCphysLcs and 1.2 Electronic spectra of CO and CO' 1.3 Presentinv e s ti g a t i o n CIIAPTER2: EXPERI MENTALTECHNIQU ES

i i iii

16 2.1 The ho ll o w- c at h od e dischargetube 16 2.2 Mecha n i sm of hollow-cathode

discharge 23

2.3 Spectrographs 24

(i)The 2 mBauschand Lomb dual

grating spectrograph 24

(i i )The 3.4mJarrell-AshEbert

grating spectrograph 26

2.4 Exp e ri ment a l procedure 27

2.5 Measure mentof spectra CIIAPTE R3: COMET-TAIL (A~nl- XZE·)SYS TEMOF

nCIIIO·

"

31 3.1 Vibr atio nal and ro t atio na l

str uctureof an electronicband

sys t e m 31

(i) Electronicand vibrational

terms 31

(ii) Rotatio nalterms of singlet

elect ro nicstates 34

(ii i) coupling betweenrotation and

electroni c motion 34

- vi -

3. 2 Method of eota t tonet analysLs (i) Effe c t i v eHamiL't.orri.en (ii) Method of merging 3. 3 Th e rotat ion a l struct u r eofa band

ofa-n, - 21;'trans ition

J7

-11

3.4 Rota t io nal analysisof the conet>

tai l system of CO' iIiI

CflAPrER 4: GLOBALFIT OF TilE EXP ERIMENTAL DATAOF

CO' 87.

REFERENCES:

4.1 The firs t negative {B~};' - Xl~: ' ) sy s t em

4.2 Th e aajdet.e.r o h nccn (Bl~:' - ,.,211 .) syste m

4.3 'inemic ro wavedata 4.4 Global fit

es

no

INTRODUCTION

1.1 Si g ni f ica n ce of molecular sp ect r a in atmosphericphys ics and astrophysics

T:le spec troscopic st udies of the molecules progre s s e d wi t hthe developme nt of thequantumth eo ryinthelate 1920 ·s. The el e c t r o ni c spec t ra of the moleculespr ov i d e information abo u t th e vib ra t ionan d ro t atio n of the i r nu c l e i and the i r electro nic str uct u re. Fro m the elect r on ic at ru ct. ure, an insightintothe impo r t a nt propertie s suchasche mi c al val ence canbeach i e v e d. From adetai led anal ys isof the ele c t r o nic epe ctr-umof a mo l e cu l e, i ts ele ct r oni c , vibr a t i o na l, and rotat i on al level s ca n be derived ve ry precise ly. From th is , one can ob ta in Lnformat Ion ab ou t its mome nt of inert ia , internuclear separatio n, an d nat ure of the coup l ing bet we en theelectronicandrotationalmotion s of differe nt ele ct r onic state s. Intensi t ie sof the bands of the elect roni c spectra can be calCUl a ted fr om the vibra t i onal and rotat i o na l constantsofthe electron icstate s and othermolecu la r da ta. From the vibrational fre quencies and the corr esp ond i ng anh armoni cities , forcesbetweenthe at o ms ofa mol ecu l e and its dissoci ation energy ca n be estimated. Thermodyn a mi c pro p e r ti essuchasspeci fi cheat , entropy,and freeenergy ca n be esti mated from th e kn owledg e of the vi b rat io na l and ro tat i onal part i tion fun c t i on s. Thus the stUdy of the el ect r o nicsp ectr aofa molecu le ena b lesone tounderstandi ts

- 1-

- 2 -

variousphysical and chemicul properties.

Mo l e c u l a r spectraalso playa very importantro l e in the atmospheric and astrophysical phenomena . Examples of tho so are the molecular abso rption spectr um of th e eart hIs atmosphere, the emi s sio n band spect.re of the aurora, the radiat ionfrom the night skyand the twilightproduced inthe upper layers of the atmosphnre, solar spectrum, cometary spectra, and spectrumof lightnlng etc. From the intensity di str ibuti on of the emission spectra of these celestial objects, their te mpera t ures canbe inferred. The presence of polyatomic molecules in the planetary atmosph eres cun be esta b l i s h e d fr omthe ir abso rptio nspectra. As an exampleof the app lica tion of molecular spectra to astroph ysics the cometaryspect raare brief lydiscussedhere. Various parts of a typic a l comet are shownin Fig.!. It consists of a coma tha t appears as a round and di ffusenebulous glow, a nuc l e us in the middl e of the coma, and two tails. The gas atoms released fr o m thenuc l eu s by the radia tion from the sun ha ve a ve locity of - I km/s. The nuc .ieus has an approximate diameter of I to10km, The coma and the nucleustoge the r constitute thehead of thecome t. Oneofthe twota i l s , known as iontail , isnearl yst raigh t andconsistsofmole c Ul a r ions suc has CO',N2',and H20' etc. The other ta i l is knownas dust tailas it consistsof most lydust particles. The frozensolid nucleus of the comet can be see n fro m the ea r th by the sunl ight it refl e c t s . Thecomagi ve s molecular emissionfrom the radicalsC2, eN, OH, NH,andNH2etc .•ove r l a ppe d by a weak

- 4 -

continuumwith Fraunhoferli ne s. When th e comet is far away from the sun th e parent molecu les of tl1e most abundant radicals are presumedto be "lO, Ctf., and NHJ• It wa s found that for the band systems observedin comets the lower state is the groundstate ofthe particular molecu le. This suggests thatth e seband s areex c i t e d by sunl ight th r o ugh aresonanc e fluorescence mechanism . This fluorescence mechanism is confirmedby a study of the intensit y distrib uti o n in tho rotati onal structure of the cometary bands. The partial molecula r dens i ty in the comets is estimated fromthe total intens ityofthe bands (see for example,Wurm 1943, Herzberg 1950, and Abell 1975).

1.2Elec t ronicspectra of co andCO'

The ne utra l ca rbon monoxide co and its 10n co' are impo rta nt for ^i'. numbe r of reasons including fo r their ast rophysica l significanc e. Carbon monox ide is present in solarch r omos ph ere, stellar atmospheres, andtails of comets.

Al s o ,the comet-tail (AzIII - X^l:<:+) band systemof CO' was first observe d in the tail at: the Comet Morehouse - 1906c by P1uvi neland Ba1det (1909 and 1911) andwas later observed in the laboratory by Fowler (1909 and 191 0 ).

The type ofthe molecular binding and the na tu r e of the elec t ron i c statesof amol ecul e arede t e r mi ne d byelectronsin the ou ter most sh ells of the constituent atoms of the molecule. The electronic co nf i g ura t i o n s of the groundstates

ofthe ca rbo nandcxyge n at oms are

C: K2522p2; 0: K 25 22P~ [1.1]

The elect roni cconfi gura tio nof thegroundstate (X1;E') of the COmoleculeiswrit t en as (Mulli ke n 193 2 )

[1.2]

andthoseofth e low lyingex cited sta tesofCOarewritte nby promot i n g oneof thexoelectrons tothev." orb!taland one of the w.,. ele ctrons to the VIt orbital.

config uratio nsare

(WIr)" (xo) (V'If) : e-n,andAln, and

The resultin g

[1.3 ]

I1I;-, and 01ll.. [1.4]

The11:+ stateinEq. (1.4 ]hasnot yetbeenob s erved. Highe r excit e d state s of coare obta inedby ra i singone of the xo ele ctr on s ofEq. [1.2 ) tothewa orb i t al and one of theWlf electron s to theUo or b i t a l sas given below:

and

- - -- (WIl")3(xu)l (UO') :JIl l andIn.

[1.5J

(1.6) However, noneuf th e s e fo ur st a t e s ha s beenobser vedso far. Fu rth er hi g herexcitedstate s of COar e obta i n e dby promoti ng oneof the xc electro nstothe Rydberg orbitals 3so , 3po, and 3pl'r etc., whi ch ar e id entified as

(Wl'r)~ (xv) (3so) :b3l;+and B1I;+. [1.7 ] - (3Pq) jJ ~+and C1I;+. (1.8]

- (3 pl'r) dill andE1n. (1.9 ]

- 6-

The s e Ryd bergstate sconve rge to the groundstate(X2~;' ) of the CO· mo lecule (Le f e b v r e-Bri an g.t

ar.

1964). The electroni c sp ectrumofCOha e be en ex te nsivelystudied bo th in emission andabsorpti o n inthe spe ctr alre g i on 600 - 86 00 h. A total of 30electro nictrans it ionsareobs e r v ed fr om the 24 known electronic.sta t esof CO. Ofthese,thepr o mine nt bandsystems are(1) the Ang strom(alE' -A1n ) system(4100-6600 II), (ii) th e He r z b erg (CIE' - x' m system (3680 - 571 0 A), (iii) the th i r d posit i v e (b3I;' - a'l1rlsystem (2600- 3800 A), and (iv) th efourth posi t i ve(A1n- Xl:!:;') syste m (11 4 0- 2800A) .

The elec tr oni cconfig urat i ons of th eground(X~):')andtho first threeexcitedstates {I',?n H 821:', andC2ll.,l of co'ar c

and

KK(20)2(yoj2(Wllj4(Xo) :X2~', _ (YO)2 (W1f)J()CO) 2 :A2ITI , - (yo) (W1f)4(xo ) 2 : 62 ~', - (YO )2(W...)J(xo) (V1f) :CZIJ. ,.

( 1010 )

( lol l]

[1.1 2 ] [1.13]

The electronic statesX2I; ' andA2IT

Idissoc i at e int o c'('P) anu O(3P )atomswhe r e asthe6²>:'statedissociate s intoC'(2P) and O( ID) at oms. Th e molecular states whi ch are of prese nt interest are X2!;',A2UI , and62I: 'andtheirRKR potential energy curve s alongwi ththat of the ground st ate (Xl~ ') of neu t r a l COaregiv e n in Fig . 2 (modified fro mxrcpe n t e196 6 ) .

For the co' molecu l e , theX, A,and 6 st ates are clearly ident if iedandthe ba nd sys te m ari s i n g from these statesare (i) the comet-tail (A2n

l - X2~+) syst emP08U - 8500 A), (ti )

the6a l d et-J ohnson (Bl~'- A2ntl syste m(3315 - 4236 A), and

200 oo0r - r --.--,---.,--r-r

---,,.-r-=;:::;;= =:;=j

160000

160 000

40 000

'e

_o ¹⁴⁰⁰⁰⁰

>-

~

^{120 000}

W Z W oJ

« i= z

WI-

~

20000

o

0.6

INTER NUCLEAR DISTANCE

(AI

RIo:RpoteutiaII!n<!rg ycurvesforthe grou n dstateofCO and the X,.\ .rmdBar at esofCO+.

- 8-

(iii) the first negative (B2E~- X2I; ' )system (1800 - 3102 ,I.).

The transit ionC26_r- A1n1 in co' was identified by Marchand 2.t li.(1969),but its vibrational numbering is uncertain andthe rotational st ructu re is not completelyresolved.

After the laboratory work of Fowler (1909 and HIlO) several researchers also observed the bands of the comet-tail (A-X) system (see Krupenie1966 and HuberandHerzberg 1979). Baldet (1~25a,b) observed most of th e known bands of this

system and Bi r ge (1925) identified the transition as (A?l1 ,- X2I: ' ) . CosterU Ai. (1932), schmid and ce ro (1933), and Bulthuis(1935) performed the rotational analysis for several bands (v' "" 2 to11 and v"- 0 to 2). nee(1950a) did the

rotationa l analysis of the 0-2, 0-3, and 0-4 bands of this system and identifiedthe upper state as an inverted n state and revised the vibrational assignments of this state by lo we r i n g th e previous assignments by 3 units. These new assignments were la t er confirmed by Asundi gtl i. (1970) and Ohumwad IIli. (1979) from the isotope shifts of the bands of th e A-X system and the B-A system of lJC^160' and 17.C^I"0 '. re s pe c t i vely , from the corre s pond i ng bands of 12CI60'. Gagnaire and Goure (1976) reanalysed the 2-0 band of this system of CO', Coxon andFoster (1982) carried out the deperturbation analysis of the v = 0, 5, and 10 levels of A7. 111using the experimenta l da ta of Costerg,t~. (1932), Bul t huis (1935), andRao (1950a), These authors found that the ground state rotational constantsobtained by GagnaireandGoure (19 7 6 ) are

-

, -

inco r rec t . Katayamaan d Welsh (1981) and Browng.ttl. (1984) rei nvest i gated the rotational structure of the 0-0 band.

Vujis i c and peS i c (1988) rein v es t ig a t edth e 4-0, 3-D, and 0-2

bands ofthis systemof ucll()+. The previousvork doneon the rotati onal ana lysi s of the comet-tail systell since 1932is SU'"la r ized inTable1.1.

The fi rst ne g ative (B~~+ - X~:E') system of co- which consis tsof single-headedband sdegraded tolonger wa ve lengths was inve stig a t ed by sever a l res e a r che r s. Blac kburn (1925) gave thefi rs t vibra t iona lassignments for th e bands of the system. Bi s ka mp (19 3 3) ext e nded thi s syste m to shorter wavele ngths and identified 22 additiona l ban ds under low dispe rsion inan intense hi gh fr e que ncy disch arg e in helium containing a tra c e of co. Coster n Al.. (1932) and Sc hmid (1932) perforJlled therotationalanalysis ot a few ba n ds of this system prio r to Bis kamp without providing reliable rotational co ns t a nts. schlllid observedth e split tingonly in the sp ectra l lineswith high rot ati o na l quant umnumber (J _ 30-34 ). Schai d and Gere' s wo r k (19 3] ) on the rotational analys isof"the0-0 ban dof this system establ i shed th at the ground state isthe common lower stateof thecomet-tailand firs t negative sys tems. The spin split t i n gin the zEstates of CO" was firs t stUdi e d by Wood s (19 4 3 ) . Rao (1950b ) analy z e d fifteen bands of this syste m rota t i ona l l y an d reportedthe rotational and vibra tional co ns tants fo r the X and 8 statesalongwit h the I.,,,,'- .,."1di f fe rencesfor somo

- 10-

TARLE 1.1 Rotarionulaunl yeisoft.lwc"md-Lai l(A~ ^-X~~:+l"""L"1Il of12C160 + prIo rLothe pfl' s L'n Lwo rk

Autho r I\;md( s)

Coat. .t..tU. 119m ~:~'~. o,1·0 ~:~n:~~l:~'~~~';~'~:,r~"~';~'::':_;" 'lR:,:S')~(I) ,Io·crc....dtho,,'U~'t'..,·"t.h"J",dl~

Scl,.ldi.e..o(l9B) )·0,4 · 0 , 4 '1 S,1toer.urk s . .obove.

~.1,'.2,1·2

BulthuIs(193) 9· 0 .10· 0 ,ll-l s... r...orks. ..hove. :~: ~ '13, 1,13·2

Rao(19) 0) (1. 2, 0 '],0·4 A'n ... . Id ..ntHI.d . . ,,'

." 'a. -nu byCoot erI t l l.(193' 1,So'1,.ld AndCoro(l'Hl) ,AndBullh..l. (l9U).... ro .... .,ru. ,d by,..nl t••

eot nAlre &Co"r.

(1976)

K.t .y....&1I.hh (1981)

Co. on6Foster (198 1)

Th.bond " lI. notr" l ly ruolv"don<!th.l r

".lIbra tl on ...ed to b. . .non' o". . . .".p.eted byCo.on. nd FOIt"r(\ 981).

Thlobond"0.noltedbylosor,',xlu" ..d n" or" "" "" o llethod;ob..r".dutrol l nuln the'01/1''E'...b.b .nd:.0n.,lu~dth.t the

••tnlin. ...ondu. t. ponurbAtlon.or", .._ObyX:,,_l O.

~.O,10· 1,10.2 Nono..np.r1..,nul d.U. O"punurb. t l on 0· 2 A.... ty. 1o....dono £01' 110.d. u orthe~.o

(Co.U t I.tal.19 )2: 1·0>. 10·1, \0·2 Uutthuh.19) ),1).1, 1l. 2) .nd O· 2(Roo, 19~0 )bondA. (on.\u d. dth.tA,"_0,~And lO..er.per t urbed.

Br olm.u U.(19!4) 0·0 Ob. ...ed thllb.nd (A1IO..."Kot.y"...ond 110 1011,1981)Inl. .e~·I ~dy". dn""rao.,.n•• . Efte . t1voH.lllltonl .nte.hnlq u e ....".edfor th"lIJ'per hvl\.Th... .. ulll or•• on.lud..dt!>11

~hedlto ofS.lIlIl d AndGer,;(19) ])or.

q"eot( on.bl0.

VUJd e&-Petl e (1988)

2- 0,).0,4·0 Theilere the~·o,6· 0,.nd1· 0b.nlb r"port.d by Coat.r t l U.(I9]2 ),Kol"e uh , .onst.nh

"en de urlllnd,bu torfo"tl v.U••llt onl.n t""hnlqu"... . notuled

bands. Rao'sl~,,'-~./· Ivalues are one half of those reported by woods. For the previous work done on this system, the reader is referred to Krupenie (1966) and Huber and Herzberg (19 7 9 ) . Misra.§.t Al. (1987) reexamined the 0-0,0-1,and 0-2 bands of the B-X system and reported the spin splitting constants for various vibrational levels by combining the earlier experimental data of Rao (1950b). Misra.@..t. sl.

included in theiranalysis the microwave data reported by Sastry~ai. (1981) for X2.I;', v= 0 and Bogey~.sUo(1982)

The Baldet-Johnson(el I;'-Alntl system consists of double dou b l e-h e a d ed bands degraded to shorter wavelengths. Baldet (19 2 4 ) and Johnson(1 9 25) were the first to investigate this system. Later Bulthuis(19 3 4 ) gave the rotational analysisof the 0-0and0-1 bands. Rao and Sarma (1953) summarized the work on all three observed transitions for CO'stressing the revision ofvi b r a tio n a l numbering for the A state. Conkie II aj . (1976) reinvestigated the rota tionalstructureof the 1-0 band ofIZC1 60 '. Jakubek~sUo (1987) photographed0-0, 0-1, and 1-0 bands under high resolution and obtained precise values for the molecular constants of theB2E+,V= 0 and 1 and A2U

I Iv= 0 and 1 states.

The CO'ion has a strongelectric dipole moment and hence is expectedto have a strongmicrowave spectrum. Dixonand Woods (19 7 5) were the first to observe co' terrestrial lyby microwave spectroscopy. In the laboratory, its millimeter

- 12 -

(Sastr yl l.5!.l. 1981and piLt ch

n

li.198 2) and suon.tir Ieot er (Vande nHeuve l~21.1(82 )wa v espe c t r u m was measured in tho ground vibrational state. Bogey g.!;.£1. (1962) r-epcr-todthe obs e rv at i on of the rotationa l transition in the vibrational sta tesv=0andL subsequently Boge y§..tli. (1963) ext e n d ed themea s urements tohi g h er vibrat ional lev el s of l~·CI60 'and to otherisotopomers [v:!4forIZC'6 0 · , v- 0and 1fo r I~C I "O'and 13CI60·, an dv= 0fo r UCI~O· ).

Conside rab le work onthe rotati onalstructureof the A-X, B-i\ , an d B-Xsystemsof th eotherisotopomersofCO'has also been carried out. Re ce ntl y in our laboratorythe rota ti onal analyses of the comet- tail band system (Pr a s a d ...nd Reddy , 19 6 9 ) , Baldet -Joh nso nsystem (Reddy andPrasad,1989d)andthe firs tne g ati vesystem (PrasadandRe dd y , 1(90) of 1.1C'"O' were perfo rmed. For the ref e re nc e s on the work done on the el ectronicband sy s t em of otheriso topome r s ofco",the reader is referred to these th r e epapers. It may be ment ionedthat Br owng.t.ai. (1983) refitted the experimental data of the rotational struct ur e of th e (2-0) and (0-0) bands of the comet - tailsystemof IJC160· , repo r t e d by Vujisic tlli (1960 ) and concludedthatth e latter 'sworkwas erroneo us.

1.J Pr ese nt invest i ga tio n

The present workis concernedabout thespectroscopyof the molecular ion12CI60·. Prior toth e present work sovcra1 research ersinvestigatedthe i\-X,B-X, and B-i\systemsofCO',

As fa r as the comet-tail system is concer ned,eventhough 15 bands have been analyzedro t a tio n a lly overalong pe riod , the struc tureof several strong bands have not been analy z ed.

Analysis of the experimental da t a using the effecti ve Hamil to nianof Brown~l i. (197 9) fo r 2n stateis expectedto give accurate molecular constantsand none of theprevious wo rk e r s had the opportuni tyto use this method, except Brown t lli. (1984) who ana lyzed th e 0-0 ba nd of the A- X system, exc tted by laser-induced fluorescence. As mentioned in the previ ous sect ion all the recentstudies on the come t-t a il systemwere done on a few selectedbands only(s e e Table 1.1) and hence it is conside red es s e nt i a l to reinvestigate th i s important band system of CO· more exhaustively. In the pres ent work the molecular ion 12C160' was excited in the cathode glow of a holl ow discharge tube of special design (Reddy and Prasad19 89b ) . Seventeenbands withv ' =0 to 8 andv'' = 0 to 4 of the cornet-tai l (A2n_l- X²E· ) sys temof this molecular ion occurringin the spectral reg i o n 3410 - 8480 A werephotographedunder med i um resolution . Ofthe s e , twe l ve band s(6-0, 4-0,3-0,2-0, 1-0, 2-1, 1-1, 0-1,2-3, 0~2, 0-3 , an d 0-4) ....ere photographedunder higher resolution and th eir detail ed rotational analy si s has been carried out. The structureof six (6-0 , 1-0, 2-1, I- I , 0- 1, and 2-3 ) of these twel ve bands were analyzed for th e first time since Rao (1950a ) decreasedthev' assignmen tsby 3un i t sand correctly ide nti f i e d the A state asanin v e rt e d2nstate. Rotational constantswereobtained for the A2111and X2_{I; .} statesusingthe

-14 -

effectiveHamiltoni ansfor the

en

^{(Br ownU £1. 19 79) and "x'}

states. Th e same me t hod was use d for the analys is of the experimental da ta of Jaku b e kII gl. (1()S7) for the narctot- Johnson (52};" - A2nll system. A simil a r me th od wi t h <111 effe ctive Hami ltonianof zI;' stat e was used fo r the ana l y s i s of the experimental data ofMi sra t ll i. (19B7 ) and R<1O (195 0b ) fo r th e fi r stnega t i ve (SlE' - Xl}~ ') system and the microwavedata ofSast ryI IAJ.. (1961) and Bogeytlg l.(1983) for the v '" 0, 1, and 2 lev e l s of the X~};' sta te. The rota t i onal constan t s of various vi brat i on a l le ve l s and th"!

band or iginsof several ba nds thu s obtainedfromthe ba nd- b y- ban dfitsand from themicro wave da t awe r e allmergedtog e t h er in ste p by step approach us i ng a correieted least-squ a res met hod. A uni qu e setof molecular cc n st. e nts for the X~ }: ', A2.nll and52_1:' stat es, and the ba n d originsof all thebands usedinthe ana l y sis,of 1ZC1~O'were obtained from thi s global lea s t-squares fit. Thus, th is type of globa l fit combini ng al l th e available expe rimental data was attempted for the fi rst time fo r the CO" ion . The pr e s ent ...ork pro vi des st a tis t i ca llyandspec t rosc opicallymor emeaningfu lmolecular co nstants for thre e electronic states of CO' which is important astr oph y sic a ll y. InChap ter 2,adescrip t ionof the hoLjow cathode discharg e tube and the datilll s of the ex p eri menta l techniq u es are pre s onted. Themethodof anal ysis and the results obta i ne d from therotationa l anal ys isof the inte nsebands of theA-Xsystem are gi ve n in ChapterJ. The proce dure us e d for a global fit of all the avail able

experimental data and the final results are discussed in Ch a p t e r 4.

CHAPl'ER 2

EXPERIMENTALTECHNIQUES

Thesp ec trumofthe mole c ular ionco'WdSexc ited in the cathodeco lum nof a hollow-ca thodedischa r getube. Seve nt ee n band s of thecomet-ta il (A2n

1- X2_:r;+) syst em of th i smo l ecula r ion were photograph ed unde r med iu mre sol u ti o n. Of these, twelvebands we r e pho togra ph e d under high rewotutIon, The hollow-cathodedischargetube,twooptical spectrogra p hsused in the experimenta lwork, an d th e expe ri mental procedureare descr i be d in thi s chap te r. A brie f descri pt io n of the me chan i s m of the hollow-ca thodedischarg e s andthemeasureme n t of thespec t r a are also inclu ded here.

2.1 Thehollow cathodedis c h a r ge tube

The hollow- c a tho de discharge tube and the gas handl ing systemare sch ematicallyshown inFi g . 3.The di s c h a rg etub e co n s ists of a hollowca t h od e (C) made fr om a copper cy li nd er 75 mmlo ng , 17 mmin outer diame ter and 1.5 mm in wall thi ckne s s. It wa s silver so lde r ed (8) toa Ko v a r tube of a Kov a r Pyr e xsea l (K) , 19 mm in inne rdiameter. rne Pyrex end of this se al wa s joined to the Pyre xglas sbod y (P), 140 mm lon g and 46 mm in outer diameter . Aside arm (A) 17 mmin outerdiame ter was at.tia cb eu to the mai nbody. A tungste n anode(T ) wasfusedinto the bra nch of thi s sid e ar m. Two Sl- UVquartz wi ndow sWIand W21 1.5 mm thick , su p plied by Esco ProductsInc., wereatta chedtothe ground end surf aces ofthe

- 16 -

en

N

0.

- 18 -

anode and cathode branches of the discharge tube, with Torr Seal, a low vapor pressure resin suppliedby Varian Associates Inc. A ball and socket arrangoment, which is not shown in Fig. 3, is provided to facilitate the connection or disconnection of the discharge tube to or from the pumping system.

In the present designthe provision of separatecolumns for th e anode and cathode facilitates photographing the two glows independently. The present design of the hallow-cathode discharge tube is somewhat similar to the oneuse d byHer-abe rq rtaj. (1981) for the excitation of the spectra of triatomic moleculesHJ and OJin th e cathode column which is immersed in liquid nitrogen. Inert gases likehelium or neon can he used as a carrier gas to produce spectra of molecular ians or to suppress the spectra of neutral molecules. But for the productionof theCOoemissionno carrier gas was found to be necessary.

Reddy and Prasad (198gb) have demonstrated that in the modifiedhollow-cathodedischargetube the cathode glow is a rich source of positive molecu larions and the anode column consists exclusively of neutral molecules. Figure 4 illustrates the remarkable difference in the two spectra photographed from the anode and the cathode columns, respectively. The emission from anode column shown in Fig. 4 (a) comprises of the JA (cJI:+- aJn_r

>,

the fourth positive (A1n- XI;E+ ),and the third positive (bJI:+- aJnr)systems of tho neutralCOmolecule with no trace ofth e CO'spectrum, while

(A) (8)

2327.39A

'

0

~

^0-'

5-14 - 6-161

I rs tt i , 6 t ^.Jj'6 r t t ^{llf T jS ;'S}

(el

2988.47

A

I

° i'

^(d)

spectrumof the cathode glow, shownin Fig. 4(b) consists of thefi r s t negative(6^21:+~X²1:+)systemof the molecularionCO+

andthe two strong bandhe a d s of the A2r.u^+- X2IT

A, j system of CO2^+. From Fig. 4, it is amply clear that two entirely different spect ra can be obtainedfrom th e same di s c h a r g e tube. The spectral broadenings such as Dopplerbroadeni ng, pressurebroadening ,andSta rkbroadeni ngare minimizedin the hollow cathode discharges compared to the excitations in straight dvc,arcsand conventiona lelectrodele s sdi s c h a rge s . An applieddsc, voltageof 1.1kV from a power supply unit rated at 2 kV and 0.25 Awas used to maintain the discharge in the hollow-cat hodedischargetub e. A detailed circuitdiagram of thisun i t is shown in Fig. 5. Theunit consistsof a powerstat (P)Whichcontrolsthe primar yvoltage of the step-up tra nsfo rme r T. Theou tpu t ofthetr an s f o r me r was connected to a bri d g e rectifier throug h a resisto r R1

rated as 10 0 0, 100 W. The bridgerect if ierconsis tsof four hi g h voltage diodes 01toD~. The output from the rectifier wa s conne ctedto the bleeder resistors R3to R₆ (DALEHI OO) each of Which is rated at 20 kll, 100 W. Thevari a b l e resistor R2 acts as a bleeder re s i s t o r when it is set at 20 kn. The main functionof thebleeder resistoris to quicklydischarge the capacito rwhen th euni t isswi t ch e d off. Thepu r p os e of the resistorR] is to calibratethe voltmeter whichmeasuee s the voltage across the resistorR6accord i n g to the voltage on the capacLt.or-, There qui r e d voltageacross theelectrodesof the di s c ha r g e tubewas obtainedby adjusting the powers t at.

- 22 -

>

8

₀

20 b

u

Th edLao ha rqe wasopera tedinthe stationa,,"ycond i tionotthe gas. An app lied d.c, voltage of 1100 V gave acu r r en t of 60 to 65 rnA undernor mal operatingcondit ions of the di s ch a r g e tu be. In the best operati ng conditio ns the pressure inside the discharge tu be wa s foun d tobe approxi ma tel Y0.8Torr as readon a thermocouplegauge.

2"2Me c h ani sm of hollow-cathodedischarge

The emissionofra dia tio n in the hollow-cathodedischa rge tube is due to the collisionsbetween the accelerated free electrons, released from the cathode because of theap pl i ed d.c. vo l tage between the electrodes, and the at oms or molecu lesof the experime nta lgas. Inthiscollis ionprocess, the translational ki ne t i c energy of the free el e c t ron s is tr a n sfe r r e d to the atoms or molecules, exciting them to different hi g h er atomicstatesor rotatio nal,vibrational,and el e c t roni c molecularstates. Since thesehi g he r sta tesofthe atoms and eot ecut.ea are unstable, they retu rn toth e lower energy states through th e emission of electromagnetic radiationof energy hvr, hbe i ng the Planck 'sconstantandtI' be ing the fr e que ncy in S"I. The energyhtl' is equ alto the energydifferen ce between the upper and lower sta tes . Th e emi s s i o n of radiation is maintained conti nuous l yas lon g as the dischargetub e is subjectedto the electricfield .

In the collision process some of the fr e e electrons released fromthe cathode acquiresu fficient ki net icen e rgy

- 24-

and ion ize the molecules. Th e s e positive molecular ion s concentrate around the cathode and the excited neut r al mo l ecu l es sp r e a d out into the anode branch of the discharge tube. This proposit ionis ver y clea r fromFig. 4 where the cathodeglowshows the spectrum of theCO'ion and the anode glowsh ows that of the neutral CO mo l e c ul e.

2•3 Spectrograp hs

The emi ssi on spectrum of CO' from the cathodeglow was photographed on a 2 m Bausch and Lomb (B&L) dual gra t in g spectrograph and a 3.4 m Jarrell-Ash (J -A) Ebert gra t in g spectrog raph. Thesetwo spectrographsar e briefly described in thissection .

(i) Th e 2m Ba u s c h and lpmbdua l gr a ti ng spectrograph

A schematicrepresentation of the optical layout of th is spectrographisshownin Fig. 6. A variableslitS allows the light froma sourcetoenter thespectrog r a ph. The lig h t is then reflectedby a planemirro r M onto the upperpor t i on of a sphericalmirror (SM),which hasa focal length of2m and a numerical aperture of f/15.5 . Th e ad v a ntag e of thi s spec trographis th a t i t has two gratingsmounted ba ck toba ck on a ro t a t abl e turret T. The re q u i r e d grating (Gl or Gl l, either th e onewith600 grooves/mmblazedat2.5I,m or theone with 1200 grooves/mm blazedat 1.0 J'm,e achnavLnq a rUled area of 10.2 em K12.8 em,can be selected by rotating th e turret.

.~

- 26 -

The collimated light from the spherical mirror is dispersed by the selected grating. The dispersed light from thegrating is then incident on the lower section of the spherical mirror, which focusesit onto the photographic plate (P). The plate holder accommodates one plate of size 10.16cm x 25.40cm or two plates each of size 5.08 em x 25.40em. The Hartman diaphragm located in front of the slit on the spectrograph enablesth e spectra to be photographed in juxtaposition . The measured reciprocal dispersions of the spectra photographed on the B&L spectrograph are 8.:1A/mm at 5000 A in the first order of the 600 grooves/mm grating and 1.05A/mm at 7200 A in the second order of the120 0 qr-ocvesyrnta grating.

(ii) The 34m Jarrell-AshEbert grati n gspectrograp h

The optical layout of this spectrograph is almost the same as that of the B&L spectrograph, except that the slit anel the plate holderare on the same side of the spectrograph. In this instrument light fromth e source is incident directly on the upper section of the concave mirror afterpassing through two quartzcylindricalle ns e s (one collimating lens 10.0 em in focal length and 3.0 emindiameter and the other a condensing le n s 45.0em in focal le ng t h and 3.0 em in diameter). The concave mirror, which has a radius of curvature of6.655 m, a diameter of 40.6 em and a numerical aperture of f/35, collimatesthe light ontoth e grating. The dispersed light from the grating is focused onto the photographic platebyth~

lower section of the concavemirror. Best focus for a fixed

slit positionis obtainedby til t i ng the pla teholder about the vertical axis. This t i l t is found to ha v e a l in e ar

dependenceonthe gra ting angle. AB&Lplan e grat i ng having

12 00 grooves/mmblazed at 1.4 Jim and an MIT echellegrating having 300 grooves/mm blazedat 5. 7~mareavaila b le forthi s spectrograph. Both thesegratingshave a ruled widthof 186 mm an da groove le ng th of 63rom. Inthe presen tworkthe1200 grooves/mmgr a t ing was used inth e second, thir d, and fourth orders. The measured re c ipro c a l dispe rsionsof th e spectra are 0. 34A/mm at 3450 Ain the fo ur t h orderan d 0.98A/mm at 5100 Ain the second ord er.

2.4 Experi me ntal procedur e

Thecarbon mo no xidegaswho s e puri t yisgive n as 99.99%

supplied by Mathes on Ga s products. The gas-h a n d ling system made of Pyrex glass which was attach ed toth e hol l o....- ca t h o de dischargetu b e is shown inFig.3. The discharge tube and the secondary reservoi r R2 wer e thoro ug hly evacuated.

First, a small qu a nt i ty ofCO from the pr imary res e rvoi r R₁ wa s admittedinto R2byope n ing th e stop cock51" The stop cock 53wasclose dandth e gas wasadmi t te d intoth e discharge tube through stop cock 52" A d.c, voltage of 1100 V was appliedbetwe e nth eele c tr od e s of thedisc harge tube and th e discha rge was ini tia ted using a Te s la coiL Und er normal operating conditions, the pr e s s u r e insidethe dis c h a rge cube was monitored to be approximately0.8Torr as re a d ona

- 2& -

thermocouple gauge. The emission spectraofCO' in the region 3000 - 8000A.was photographedunder medium dispersion em the B&L spectrograph and under hi";lh resolution on this spectrograph as well as on the J-A spectrograph. The slit widt hwas maintained at 20 ,..m for the formerand 30 I,mfor the latter. An re-ne ho llow- c a t h o de lampwa s used as a source for the standard spectrum. The details of the twelve bands photographed under highresolution are given in Table 2.1- Kodak SWR, Spectrum Analysisno. I, 103 a-O, 103-F, andI-N plates were used to photograph the spectrum in different spectral regions. Overlappingorders of the spectra were elimi natedby using corning and Hoya glassfilters. Exposure ti me s variedfrom 1 min to 12 h depending on the intensityof the ban d , sensitivity of the photographic plates, and the tr a n s mi t t a nc e of the filters. The photographic plates were devel oped in Kodak developer 0-19 at room temperature for about 4 minutes and were then fixedinKodak fixer.

2.5Measurement of spect r a

A l inear comparator, model M 12 05C , su p p li e d by the Gaertner optical Company, Chicago, was used to measure the pho tographic plates. Al t.hough the least count of th e in str ument is 0.001 mm, the readings can be estimated to an accuracy of 0.0005 mm, Th e relation between th e air wavelengths Pd.) of the spectral lines andth e i r comp a r ato r readin gs (d) is givenby the formUla

'fAIl1.E 2.1 Cornet -taUb.lnds of CO+; r ecc rdf ngdet a il s

Spectrograph Grati ng Order

(,- 0 120 0 1j mm Four t h

(186mm )(63 mm)

J·A Third

)· 0 J·A Third

~-O J· A Third

1·0 J·A Third

~·1 J· A Thi r d

1·1 J·A Sec ond

0·' J·A Se c on d

0·1 B&L 1200 1/ nm Se c on d

(128millx102 nun)

2-) B&L Seco nd

0-3 B&L Second

B&L 6001jll\lll Third

(128/lllllx 102mm)

- 30 -

12. 11 where dois the comparator reading of the first standard line.

The comparator readings (dl were obtained forthe bandheads , rotational li n e s , andstandard Fe-Neline s. The coeffic ients 210, all a2, .. . etc.,wereobtained using the method of least- squares by fitting the air wavelengthsA.I,of the sta ndardFc- Ne li ne s and their co r res po nd i ng comparatorreadings to Eq.

[2.1j. In most of the cases a second degree polynomialfit wa s found to bead e quate . The wavelengthsof thestnnd a r d Fe- Ne line s were taken from Crosswhi te (19 5 8 and 1975). In general th e standard deviat ionsof the fit were found to be around0.03 A and 0.003A forth e medium and highresoluti o n spectra,respectively . The air wavelengthsof the band heads andthe rotationallines wexe calculated from Eq , [2.1]after determi ningthe coefficients. They were thenconv ertedinto vacuum wavenumbers ,,(em-i) by using Edlen'sformula(1953) for therefractiveindexn of air,

n= 1+64 32.8x10-8

+

l4/:4~~~O _ }

⁺⁴¹

x2~~:~,r ~ .~1

where"=n

xl~8

^,(A.1t in units of Angstroms). atr

Anite rativemethod was employedto calculatetheva c u um wavenumbers andthe itera t ionwas continued untilthe ebso Iut;e value ofth e differencebetween the successivevaluesof thf) wavenumbers was le s s tha n or equal to IO-IOcm-l . A VAX 11/785 computer was used to performth enu me ri c a l calculations.

Vi bra tiona l and ro tatio na l st ructu re of anele ct ronic

~

(i) Electronicand vib ra tiona lterms

Wi t h in the Bo r n- Opp enhe i me r approximation, th e total energy E (usuallyexpressed in ergs) of a diatomicmolecule (\Jit.h the exc l usio nof the translational an d nu clear spin energies) can be represented as th e sum of its electronic ene rqyE., vibrational ene r g y Eyt and rota tional ene rgy E•.

Th us

[3.1]

The term val ueT (in em-I) ofanen e rg y level is givenby

T.::T.+G(v ) +Fv(J), [3. 2 ]

where v and J are the vibrat i on a l and rotationa l quantum numbe r s , respective ly, and TO' G(v ), and Fv(J) ar e the electro nic, vibra tio nal androtationa l terms re s p e ct i v ely .

The electronic terms of different multipl et components are ge ne r all y exp res s ed in th e first app ro x ima ti on (i. e . , consideringthe case of ze ro rotation) as

where TDis the ele c tronic term, A and :E. ar e the quantiz e d projections alo ng the inte rnucle ar ax i s , of the electron orbital anqu jar- momentum L, and the electron spin angUlar momentum s, re spe ct i vel y , andA is the sp in-orbit coupling

- 31 -

- 32 -

constant for the given electronic multiplet state. The electronic states are designated as E, n, II, e , corresponding to fo. = 0, 1, 2, 3, ..., respectively. The quantity A is positive or negative depending on whecnnrthe state is regUlar or inverted. The electronic states~:(A'"0) are designated as E+ or E-, depending on whether the electronic wave function ~. remains unchanged or changes sign upon reflection at a plane passing through the internuclear axis.

The mUltiplicityof an electronicstate is given by 25 +1, which is the number of E.components along the internuclear axis. For example S(E. '" 0) is zero for all singlet electronic states.

The vibrational terms G(v) of an electronic state or a molecule are expressed as

where

w .

isthe vibrational frequency and w.x., w~y.,etc.

the anharmonic terms of the vibrational motion. 'rne wavenumber (in en") of a spectral line arising from a transition between the vibrational levels neglecting tho contributionfrom the rotational levels is given by

vv.v· '"v.+ w'.(V'+1/2) -w'.x'.(V'+l/2)z+w'.y'.(V' +1/2) l+ •.

- w".{V"+1/ 2 ) + ",".x".(v"+1/2)2- w"S".(V"+l/2)J+•.[J . 5 ]

The constants v., "'., w.x., ",.y., " ' , etc., can be obt ained either from a detailed rotational analysis of the band

structure or directly from the measured wavenumbers of the band heads. Equation[3.5] can be written in a simplified matrix form as

Y- .{J+6 [3.6]

where Y is a column vector containing either the values of the band origins (determined from the rotational analysis) or the vacuum wavenumbers of measured band heads as the input parameters and {J is a column vector containing molecular constants to be estimated as output parameters. The coefficient matrix X contains the coefficients of II••w.."'.x••

"'.V.. '." etc.. and 6 is a column vector containing the

unknown errors of measurements. The method of least-squares is used to obtain the molecular constantsIJvh Lch is given by [3.7]

(where - on fJindicates that(Jis an estimate obtained from the least-squares fit). The estimated variance of the least- squares fit is given by

,;z= (Y _XIJ)T (Y - XIJ)/f (3.8]

where f is the number of degrees of freedom. The dispersion matrixVis given by

[3.9]

and the variance-covariance matrix associated with

p

is given by

[3.10J The uncertainties in the estimated values of the molecular constants are the square roots of the diagonal elements of ;.

- 34-

( i i) Rotationaltermsof singletelectron icsta-S.§

The rotationalterms of a given vibrational level 01:a single t elect ronicsta teare represented by

Fy(J) = By[J(J+l) - fl2] - Dy{J(J+1) - ,\212+ " ', [J.ll } where

a. -

^(h/81f2cp) (l/r/) is the rotational constant, IIand r, being the reduced mass and the internuclear distance respectively of the molecule and D. = 4B//1ol2 is the centrifugaldistortion constant. The constantsByand n, ca n be expressedin terms of the vibrational quantum number v and the equilibriummolecu larconsta ntsas

By=B.- "'. (v+1/2 ) +'Y. (v+1/2)1.+ •••, [J.12) and

where

Dy=D.+IJ. (v +1/ 2 )+ .•., [J.13]

[J.14] Here"'.« B.,1.« "'.and IJ.« D. . In the present work,the constants1. and P.could notbe estimated because of their very small magnitudes.

(iii) Cou p ]in g betweenrota t io n and electronic mot i o n

Spin-orbitcoupling: The interactionof the spin anqu Lar- momentum of theelectrons withtheir orbital anqu l ar-momentum (usually kno wnas spin-orbit co up ling ) causes splitting in the electronicstates. There is no spin-orbitcoupling for1.>;,:1>: , etc., states. But states suchas en, In, •• • , 1.'"

J ".

..., are spl i t into25+1components, Which are disti nguished

by the quantum number b. which ta ke s values S, S-l, ..., -S and re pr e s e nt s the component of the spin an gul a r momentum along the internuclearaxis. "rheresultantof the electronic or b i t a l and spin angular momenta in the direction of the internuclear axis, representedby the quantum number n is givenby

n..A+b_o• [3.1 5 ]

The value ofois indicated as a subscript followingthe term symbo l. Thus the components arising from the spin-orbit couplingof a2n state are20J/2and2 II I/2. If the rotational angular momentum R of the molecule is imposed on the spin splitting, we come across several coupling cases, which are

cl a s ~tif i e d into five cases by Hundand are known as Hund's coupli..,g cases. Ofthe s e five,Hund's case (a ) and case (b) are importantfor the present work.

In Hund ' s ca s e (a), Rand 0combine to form the total angular momentumJ. For a givenvalue of the quantum number 0,J has the values

J= 0, 0 +1,n+2, ..• [J.16]

Both J and c ha ve either integer or half inte ger values depending onwhetherthe mUltiplic ityofthe state is odd or even, respectively.

A-t y p e doubling: The couplingbetwaen tha rotation of themol e c u leandthe orbitalmotion of its electrons is very sma ll. However, th i sgive s a splittingof the dege neracythat arises for electronic stateswithA .. o. This splittingis called A-typedoubling. The split levels are eitherpositive

- 36 -

(+) or negative (-)corresponding to the positiveand negative eigen functions that correspond to the orbital motion of the electrons around the internuclear axis. This positive and negative character of the rotational levels is known as parity.

Hund's case (b) arises when the spin vector 5 is very weakly coupled to the internuclear axis as a consequence of its coupling with the axis of rotation of the molecule. Such a situation applies to1:states almosta Lwaysr it. also applies to n. s, ...states for small atomic numbers. In Hund's case (b ) n is not defined. The component of L along the internUclearaxis. i.e., h,combines with R to form the new vectorN. which is thetot a l enqu La r momentum apart from the spin. The possible values of the quantum number Nar e

N=1\, h+1,h+2 • •• • {J .171

If h- 0, N takes all integer values from zero onward. The vectorNcombineswith S to formJ. For a given N,Jhas the vafues

J=N+S,N+S- 1• •• . IN- SI. {J.lS ) Thus each rotational level N has (25+1) components which represent the mUltiplicityof the states. Kopp and Hougen (1967) introducedthe following convention forlab e ll i ng the rotational levelswith half integerJ values:

'Levels withparity[+(_l) J-I/Zj are e levels and those with parity[_C_1) J-1lz) are f levels.'

Later Brown ~!!l. (1975) extended this labelling convention to the rotational levels with integral J values which Ic

sta t e d as follows :

'Levelswithpar i t y(+ (_ l)J]areele v els,and those wit h par i t y[-(-II^J) are fleve ls.'

l.2Method ofrota ti on., . ana lysis

(i) Ef f ect i ve Hamilt o nia n

The eff ective Ha milt oni a nfo r a di atomi cmolecule inthe abs enc e of externalmagneticor el ectr ic field is givenby

[3.1 9 ] whereH~includes thete rmswh i ch are independent of rotation and represents thev ibronic te rmene r g y T. forthe allowed vi br a tiona l sta t esot' thedi ffere nt elect ronic st a t e s . The term H...representsthe Hamil toni a n desc ribi ngthe rotati onof the nucle i, and isg1 venby

H...• B(rl W

- (h/a.2~rl (J-L- S )z,

{l.20]

(3.20 a ]

whe r e OCr) is the radi al part of the rotational energy ope r a to r, I' is the reduced ma s s, r is the internucle ar dist a nce, andR isth e rotat ional angularmome ntum operator.

Thete r l'lHedinEq. (3.19] re presentsthe Hami l tonia nfor the centrifuga l distortio nandis givenby

{l.2l]

whe r e D and H are thequartic and sexti cdistortion constants.

The thi r d ten Hh inEq.(l .19] des cribes the finestructure

- 38 -

of spectral levels and is composed of four parts. It is writtenas

He.'"H.o+M.. +H..+"ld' [3 .22]

where H.o represents the spin-orbi t interac tion and can be writtenas

"00 '"

A(r) L• S+---- [3 . 22a]

'" A(r) (L,.s.+1/ 2 L,5.+1/ 21..5.) (J.22b )

where A(r) is the spin-orb it coup l i n gco nst ant. Eq u atio ns

[3.22 a & b] also contain additional terms involv ing tho

centrifugalcorrections to theco n s ta nt A, Le.• terms with A[)v. A_IIv, ALv• et c. The term H••in Eq. [3. 2 2 )represents the spin-spininterac tionterm and isze r o foralldoublet sta t es as shownbelow. Thete rm H..can be repre sentedas

[3.22c]

The matrix element for 5. is1:.andfordou b l et sta tesi ttak e s

va lue s +1/2&-1/2,and that of 52is writ ten as5(5+1)and

is equalto 3/ 4. With thehe l p of thema t ri x elements j;.and 5(5+1) it can be easily verified that the express i on [31:.2-5(5+1 ) ] is alwaysequaltoze r o for the doubl etstates. The term H••in Eq. [3.22] is the spin-rotationHamiltoni anand is giv en by

H••'" "'fer ) R•5

.. "'f( r ) (J-L-S) .5,

[3.22dJ [3. 22a]

where ^"J(r l is thespin -rotat ioncon stant. Thela s t term H1d

in Eq. (3.2 2]repre s entsthe A-d o ubl i nq inrotationa lle v e ls and co nt ai n s thete n swi t h theA-d oubl i ng para.et ers0,P.q, and theircentri:tuqal corrections. Th isHa mil ton i a n canbe expre ssedas

(J. 22 f ]

The A-doubl i ngparallleteroCr)inth i sex p r ess i on has non-ze ro value onl yfo r thestates wit hmUltiplicitythree and higher.

Only the pa r ame t e rs p( r) an dq(r) and in some ca s e s their centrifugal correctionsare significant for the 2nstate s.

Thela s t term Hh h in Eq. [3.1.9Jrepres entstheHami lton i a n for the hyperfine structure, which is rare ly re sol v e d in the optica l spectraandis notconsideredhere.

Brown.w;Al.. (1979) discussedthe effect i veHa.l1ton ia n (Eq. 3. 19 ] for the :In state in deta i l and calculated the corr e s pond i ng matrb: efenen t;s, tate r Amio t i..t.U. (1981) lis t e d the matrixel eme nts ofthe compl eteHamiltonianforthe 2nand'1:'state s. The mat r i x el eme nts of theseHamiltonio!lns whi charerel evan t to thepresent work are91 ven inTabl e 3.1.

Theme a s ur e d line posit ions are comparediter a tive l ywith the calcu lated line positions which are th e approp ri!lote dlrfer e ncesbetweenthe term val ues of the upper and lower el ec troni c stat e s. Th e s e te r m values ar e obtainedas the eiqen value s of the Hami l to nian mat r i x. In the computer

- 40 -

TABLE 3.1Ma t r ix ele mentsofthe f1l1mllton i nl1tOI'stlll:f'!f1

-s-

anden

Molecu l a r

B.

D.

P.

LabelLfng "

1,1 2,2 3,3 1,1 2,2 3, 3 2,3 1,1 2,2 3,3 2,]

1,1 2,2 3,3 2,2 3,3 3, ] 3,3 2,3

x(xH) x^2.} x²+1 _(x z_1l^l/ 2

xZ(xTl)Z _xz ( x l_ll _x2(x2+ 3 )

2x 2 ( x 2_l ) 11?

O.5(xTl) 0,'

·0 . 5

0.5(x2.1) .0 . 5 ( x:Z!'1 ) fO.5x

±O. 5x ( xZ_l ) IO

-Labe ls1, 2,and 3re f e rto stnteses-.zn~n.11m!2Ull Z, res pe c t i v e l y .

bx-J+0.5.

eInthe notation±andl'the upperHndlowers Iy,nsn,r"r t.o theeandf levels, re s pectively(se cBrowntl.!!.l .. 1'J7~).

program, the matrix fanned with the matrix elements listed in Table 3.1 is diagonalized to obtain the eigen values, i.e., the term values of the upper and lower states involved in the transition. The molecular constants appear as adjustable parametersin the effective Hamiltonian . An improved set of molecular constants is generated from a least-squares fit of the calculated line positions to the observed ones. This non- linear least-squares pr o c e du r e is repeated until satisfactorysetof molecularconstants is obtained.

(Ii) Method of merging

In the analysis of the molecular spectra, multiple estimates of a given molecularparameter are often obtained.

These multiple es t i ma t e s can be reduced to a single 'best possible ' estimatei:l several ways. Amongthese,the method of 'me r gi n g ' is oftenus e d in molecularspectroscopy. In this method,multiple estimates of the mcrecu rer constants obtained from the individual bands by the method ofle a s t - squ a r e s are comb i nedtogether,taking intoaccount theiruncertaintie sand the correlationsexistingamong them. In thepresent work the molecular constantswere obtainedby analyzingth e rotational structure of th e individual bands using the effective Hamiltonianproposed by Brown,g..t,ill. (1979). Thesemolecular con s t a nt s , th e i r standard deviations, and the ir var-Iance - covariance ma t r i c e s are used as input parameters for the correlated least-squa resmergingfit. The relation between these input parameters and the best "po s s ib l e es t i ma t e s"

- 42-

obt ai ned as output parameters in the merging procedure is given by theset ofequationsin matrixnotationas (si mil ar to Eq.3.6)

(3. 23J Here Y,P. and&are the columnve c t o r sre p r e s e n ti ngtheinput parameters , the out p ut para meters , and the unkn own erro r s respectively;the coeffici entmatrix X re latesthe va lues of Y to the values of fJ. The le a s t-squa r e s solut ion of Eq, [3.2 3 ) gives mol e cularconstants fJas output pa rametersin such a way that the squares of the deviati ons are mini mi zed sub j e ct to the inter-relations among s, The equation forp (the symb ol· indi c atesthat itisan esti mat e fr omthele ast- sq u a res fit) in matrix notation is given by

[3.24 ] wh e r e~ isa no nd i ago n a l generaliz ed we i g ht matrix, whichis comp ose d of thevariance-covariancematricesobtainedfromthe band byband fits. The estimated variance

;z

isgi v en by

;z.. (Y _ XP)t~'l( y_XfJ)/f, [3.25]

where f is the number of degrees of freedom. The merged dispersionmatrixis written as

(3.26]

Th e estimatedva r i a nc e- cova r i a nce matrix9 whichisass ociated withiJis gi ve n by

[3.2 7) Th e uncertainties in the mergedmolec ular constantsWhi chare obtained as output pa r ame t e rs are the square roo t s of the diagonalelements of the matrix9. For fnr-t.hez- deta ils of the

method ofmerg i ng the reader is re f erredto Albrittonn .11.

(1977) , Coxon(1978) , and Prasadand Reddy (1988 ) .

J.3 The rota ti o na l structure oC a band pf a Jn~

~

A2R1st a t econsistsof a seri e sofrotat i onallevels for eac h of the subs tatesInll^2.(J .. 0.5 , 1. 5, •..) and In;'/2- (J ..

1.5, 2.5 , •..) with the le vel s of In_m having lower ene rgy thanthe correspond ingleve ls of ~nlli' The Instate is called an invertedstatebecause the spin-orbitcoupling constantA is negat ive. It belongs to Hund's cas e(a)be c aus e A is large inmag n i t ude. Normally a 2I;statebelongstoHund' scase(b) . Th e spli t ti ng of ill 1:1: state is due tothe lIagn etic mo ment pa-o d uceclby the lIIo tionof the nuc l ei and precessio n ofthe el e ctro nic orb i t al angUlar moment umabo ut the in te r n u c l ear axis. Asthe t....osta t e s en ,and 1:1:'belongtoHund's cases(a) an d (b), res pe c t i vely , a en,- 11;' trans i tion is known as a mi x e d casetran s ition.

The rotation al st ru c t u r e ofa band arising from a In, - 21;' tran sit ion consists of twe l ve branc hes. The select i o n rules tobe sa t i s fie d in thi s trans itionare

AJ .. 0 AJ - t l

e- f a - a, f - f +- -,+ + +, -+ -.

The twelve d!fferemtbranc hes are designated in eccoxdence wit h the select i on rule sgivenabove asRIl••,RUf fo Qzu.. Qn .f'

- 44-

ene rgylevel diagrallshowingal l thetwelvebr a nc h e s isgi ven inFi g .7,inwhic h thepa rity of the levels isindica t e din theel fnota tiongivenby xepp andHouge n(196 7 )an dBrownn Al.. (1 975). I fthe ban dsof this systemde g r a d e to longe r wavele ngths , as in the case of comet -tail sy s t e m, then the R u .. ,QzH.lRu rt , Ru ••,andQl1fJRu Hbranchesform four diff erent he ads in the rotat i onal st ructureof the band. Eac hband of thi s system ha stwoband origins , one for eachof th e

znll~ - z1:. and~n3 1~ - ~I:+ sub-eband s , In the prese nt wo r k ,

ins t e a d of two origins , only the (T..~ - T..!;) val ue is determine d. The ban dorigi ns of the two sub-syst ems can be calcu l a ted fro. (T\'Il-T..r)± (1/2 )(Ay- 28..).

3.4 Rotational analys i s of the comet - tailsyst e m ofco'

Thespectru mof thecathode910wof th e hollow-cathodo di s chargetub e(d e s c ri b e d inCh a pt er 2), photographedinthe re gion3345 - 8500A under me di u mdispersi onisshow ninFig.

S. Inthis figu re,in addi tio n tothe17bands of thecomet- tail sys t e m of CO·,seve ra l bands belo ngi ng to th e Baldet- John s o n (8z_I:+- AZl1d system of CO' , the Angstrom (81_{1.' -} AlII) and theHer Zbe rg (C11;+- x'm sys t ems of theneutral molecule COare also iden t i f ied. The vacuumwev enumbec s of the band he ads of the comet- ta i l sy s t em of CO·, thei r rela t i ve int ensiti e s andvih"cat ionalqu a ntumnumbersarc given in Table 3.2. The fourhellds iden tif iedfor eac hband are formed by

J' 45

'.5

2n'/2

(F

₂) - - -·--f

- -- --f--- --- . -

^+e

:- - - --- -+f

_. __ .: : --- -e

'+ _

I-- -j-- - --,,--

J'

5'

4.'

' 5

2.5 1.5

~'

J"

4 45 +e F.

'5 --ffll-'tilit1'---tttiIi'--'-jtl---t\It--Iitll/l-~L.-__t'_-+fFZ

:'

Fil\Ur.,7. fIsc hcmatieenergy l cveIdiagr-amshowing thefir st few rot.et Ioua l transi ti on s of,111thetwelvebr-anchc s ofit ha nd ora 211i- 2):+tra nsiti o n .