Experiment 6, page 1 Version of March 17, 2015

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1 Exprimnt 6, pag 1 Vrsion of March 17, 015 Exprimnt 6 VIBRATION-ROTATION SPECTROSCOPY OF DIATOMIC MOLECULES IMPORTANT: Th cll should b stord in th dssicator whn not in us to prvnt moistur in th atmosphr (Ys, this is Dlawar!!!) from injuring th cll windows. Thory Figur 6.1. Th ffctiv lctronmdiatd intrnuclar potntial as a function of intrnuclar sparation. For a diatomic molcul, th stat of th nucli may b considrd to b th rsult of an ffctiv lctron-mdiatd potntial nrgy that dpnds on nuclar sparation, E(R). [Figur 6.1.] R is th intrnuclar sparation and R th quilibrium sparation. D is th quilibrium lctronic nrgy rlativ to th vacuum, or th wll dpth. In quantum mchanics, on solvs Schrodingr s quation for th nuclar motion to giv th ignstats and thir nrgis as a function of th quantum numbrs: E = D + Evib + Erot (6.1) Th nrgy consists of an lctronic contribution, D, a vibrational contribution, E vib, and a rotational contribution, E rot, ach with its own quantum numbrs. In th harmonic approximation, th vibrational nrgy dpnds on a quantum numbr, n, which can b any non-ngativ intgr: 1 Evib, n = n + hcω, (6.) in which c is th spd of light in fr spac, and ω is th fundamntal vibrational frquncy dtrmind by th forc constant, K, and th rducd mass, µ. 1 1 Various units ar usd to xprss nrgy. If h has units of nrgy tim, ω has units of lngth -1. In this rgion of th spctrum, nrgis ar oftn quotd in cm -1, th official IUPAC/IUPAP nam for which is th kaysr. (It is namd for Hinrich Gustav Johanns Kaysr, a Grman physicist who mad studis of th spctroscopy of chmical lmnts in th lat 19 th and arly 0 th cnturis.) Th nrgis in this rgion ar thrfor givn by E ( cm 1) = E / vib hc. In this xprimnt, w writ all nrgis in units of cm -1. Convrsion to othr units is possibl by multiplication by th appropriat factor.

2 Exprimnt 6, pag Vrsion of March 17, 015 ω = 1 K πc µ. (6.3) Th nrgy in quation (6.) is corrct only if th molcul is subjct to a harmonic K potntial [i.., V = ( x x q ) ]. On may rlas this assumption through inclusion of anharmonic trms to giv a mor complt dscription of th vibrational nrgy. Th rsulting xprssion for th vibrational nrgy is a sum of contributions: En = n + ω n + xω + n + yω +... (6.4) Th additional trms contain nrgy paramtrs x ω, y ω,... to account for th anharmonicity of th potntial function. Usually only th first corrction trm is of significanc, th sum bing truncatd at th harmonic and first anharmonic trms. Typical data for svral diatomic molculs ar givn in Tabl 6.1. Tabl 6.1. Ground-stat Spctroscopic Constants of Slctd Diatomic Molculs a Molcul ω /cm -1 x ω /cm -1 B /cm -1 α /cm -1 1 H C 16 O H 79 Br H 19 F H 19 F a Noggl, J. H. Physical Chmistry, 3 rd Edition; Harpr-Collins: Nw York, Vibrational Spctroscopy. Whn a sampl is in contact with a radiation fild, it may tak up or mit nrgy by having molculs chang stat. Th nrgy xchang only occurs at rsonanc, i.. if th nrgy spacing in th molcul is qual to th quantum of nrgy of th fild, ω. E final Einitial = ω (6.5) For th momnt, considr only changs in vibrational nrgy of a diatomic molcul such as HCl or CO. For most molculs, hcω >>> k b T nar room tmpratur. 3 Thrfor, most molculs in a sampl ar in th lowst-nrgy (or ground) vibrational stat (n = 0). Undr ths conditions, on only considrs transitions from this stat to xplain absorption spctra, i.. E initial = E vib,0. Whthr a transition occurs dpnds not only on nrgy matching at rsonanc, but also on quantum mchanical slction ruls. Thr ar two important slction ruls. For infrard spctroscopy, th molcul must hav a dipol momnt and transitions ar allowd btwn all stats: 4 n = ± 1, ±, ±, (6.6) Sinc th ground stat is so havily populatd undr typical conditions, th dominant fatur of vibrational spctroscopy is th transition from n = 0 to n = 1, calld th fundamntal. To within th first anharmonic corrction, th nrgy of th photon ncssary to xcit this transition is: Latr w add th possibility of rotational-nrgy transitions. 3 k b is Boltzmann s constant, J K For a pur harmonic oscillator, only th n = ± 1 transition is allowd.

3 Exprimnt 6, pag 3 Vrsion of March 17, 015 Evib = ω xω. (6.7) For transitions in which th nrgy changs by mor than 1 quantum, on may driv formulas for th xpctd wavnumbr of th transition, as wll. For xampl, th n = 0 n = transition is known as th first ovrton and occurs at an nrgy: Eovrton = ω 6xω (6.8) to th sam lvl of approximation. Singl-quantum ( n = ± 1) transitions from stats with n > 0 ar allowd, but th smallr populations of ths stats at thrmal quilibrium at room tmpratur mak such transitions lss intns and mor difficult to obsrv at room tmpratur. For xampl, th transition from th stat with n = 1 to th stat with n = occurs at Ehot = ω 4xω (6.9) This is clos to th fundamntal. Such transitions ar calld hot bands bcaus thir intnsitis incras (rlativ to th fundamntal) as on incrass th tmpratur. Rotational Transitions. To analyz infrard spctra proprly, on must includ th ffcts of rotational-nrgy changs, as wll as vibrational-nrgy changs. Ths may b tratd, to a first approximation, as nrgtically indpndnt of th vibrational stat. In th rigid-rotor approximation, th rotational nrgy of a diatomic molcul dpnds on th rotational quantum numbr, J. 1 E rot, Jm = m R J ( J + 1), (6.10) whr th nrgy, in this quation, is in rgs or jouls. <.> indicats an avrag ovr th vibrational wav function. As a first approximation, on trats th molcul as if it xists only at th quilibrium bond distanc, R, and 1 1 = R R. Th quilibrium momnt of inrtia I (= µr ) and th quilibrium rotational constant, B, ar dfind in trms of this quantity. B = 4πIc (6.11) and Erot, Jm = B J ( J + 1), (6.1) whr th nrgy and B ar xprssd in cm Th quilibrium rotational constant dpnds on th momnt of inrtia, which in turn dpnds on th rducd mass and th quilibrium bond lngth. Th rducd mass dpnds on th mass of ach isotop. In Tabl 6. ar th xact masss of svral atoms (xprssd on a molar basis). Tabl 6.. Exact Masss of Svral Atoms Atom Mass (g/mol) Atom Mass (g/mol) 1 H O H (D) O C 1 (xactly) 35 Cl C Cl In ths quations, th units of B and E rot ar cm -1, providd that is in rg s, c is in cm s -1, and I is in g cm.

4 Exprimnt 6, pag 4 Vrsion of March 17, 015 For a ral diatomic molcul, th avrag ovr th vibrational stat dos not xactly giv th rotational constant B. Instad, it is found that th rotational constant dpnds on vibrational stat. Th rotational constant including th corrction for vibrational avraging is givn th symbol B n, whr th xplicit dpndnc on th vibrational stat is indicatd by th subscript. In this way, th rotational nrgy of a diatomic molcul in a stat with quantum numbrs, n, J and m is givn by: EnJm = Bn J ( J +1) (6.13) Prturbation thory givs th vibration-dpndnt rotation constant, in a first approximation, as: 1 Bn = B α n +. (6.14) α is th vibration-rotation constant. It dscribs how th vibrational stat affcts th rotational nrgy. In analyzing spctra, it is tratd as a paramtr to b dtrmind, just lik B. In addition to this corrction, thr is anothr purly rotational prturbation that changs th rotational nrgy of a stat - th cntrifugal distortion. This ffct is takn into account by an additional trm in th nrgy dtrmind by th cntrifugal distortion cofficint, D c. Vibration-Rotation Enrgy. With all ths dfinitions, th total vibration-plus-rotation nrgy of a diatomic molcul in a stat with quantum numbrs n, J and m J is (again in units of cm -1 ) 1 1 En, J, m = D + n + ω n + xω + BnJ ( J + 1) DcJ ( J + 1). (6.15) J Bcaus th nrgy sparations of th rotational stats (ach having a diffrnt valu of J) may not b much gratr than k b T, a sampl may contain apprciabl numbrs of molculs in xcitd rotational stats, vn at room tmpratur. Whn rotational nrgis ar considrd, transitions from stats with various valus of J ar sn in a spctrum. Vibration-Rotation Spctroscopy. Infrard spctroscopy concrns changs of vibrational and rotational stat, without chang of lctronic stat. Hnc, th infrard spctrum is a vibrationrotation spctrum. Th usual slction ruls ar: n = ± 1 (Transitions of highr ordr ar known as ovrton bands and occur at highr frquncis; w shall not considr thm furthr hr, xcpt in th Discussion Qustions.) J = ± 1 (for th htronuclar diatomic molculs xamind hr) Th molcul must hav a prmannt lctric dipol momnt. Considring only transitions that involv th ground vibrational stat, th nrgy chang is: α E = ω xω + B [ J '( J ' + 1) J ( J + 1) ] [ 3J '( J ' + 1) J ( J + 1) ] (6.16) c[ J ' ( J ' + 1) J ( J + 1) ] with th quantum numbr of th initial rotational stat bing J and that of th final rotational stat bing J. Whn J = J + 1, thr is a nt absorption of rotational nrgy; whn J = J 1, thr is a nt mission of rotational nrgy (although ovrall thr is absorption of nrgy). Transitions of th formr kind form th R branch and thos of th lattr form th P branch of

5 Exprimnt 6, pag 5 Vrsion of March 17, 015 th spctrum. 6 Using quation (6.16), th approximat nrgis of transition dpnd on th quantum numbr J for th initial stat. Nglcting th cntrifugal distortion trms, this givs: E = ω (1 x ) + ( B a )( J + 1) a ( J + 1) R branch E = ω (1 x ) ( B + a ) J a J P branch Th infrard spctrum consists of a sris of transitions du to th diffrnt rotational stats involvs. (6.17) Intnsitis in th Infrard Spctrum. On apparnt quality of such a spctrum is th variation in intnsity of ths transition lins. Th intnsity distribution givs th rlativ probabilitis of occupation of th initial rotational stats (thos with quantum numbr J). From ths intnsitis, on can dfin a rotational tmpratur, T r, for th distribution, assuming it to b Boltzmann in form. Th intnsity of a lin that ariss from th stat with quantum numbr J (compard to that for th lin that coms from a stat with J = 0) is givn by th following quation that accounts for th Boltzmann factor and th dgnracy of th rotational lvl on m. I J N J g J = = xp[ ( EJ E0) / ktr ] = (J + 1) xp[ BnhcJ ( J + 1) / ktr ] (6.18) I 0 N 0 go whr g J is th dgnracy of th rotational lvl with quantum numbr, J, and k is Boltzmann s constant. A comparison of intnsitis allows on to stimat T r ; or, knowing T r, on may stimat B n. In som xprimnts in which systms ar prturbd by lasr xcitation, on can chang th distribution of molculs in th rotational stats (at last for a sufficintly long tim to mak a masurmnt) such that th rotational tmpratur is diffrnt from th laboratory tmpratur. Undr th conditions of this xprimnt, th rotational dgrs of frdom ar in quilibrium with th translational dgrs of frdom and th rotational tmpratur is th sam as th laboratory tmpratur. Quantum Calculations. Th quantum thory discussd abov assums that th intrnuclar potntial nrgy function is known or can b approximatd. In actuality, this function is an intgral ovr th instantanous lctronic wav function of th molcul. Empirical paramtrs that dscrib th function lik th forc constants ar givn in a complt thory by intgrals ovr th lctronic stat of th molcul. To calculat ths, on must hav knowldg of th lctronic stat of th systm. With prsnt-day computrs, on may do numrical stimations of th lctronic wav functions rathr asily and with quit good prcision. 7 Onc known, th wav functions can b numrically intgratd to giv stimats of paramtrs such as th forc constant, K, or th fundamntal frquncy, ω. Many complx oprations involvd in such calculations hav bn collctd into cannd programs such as GAUSSIAN09 8 or SPARTAN, so that th chmist may us th computr without daling with problms of computr programming or numrical analysis. 6 In spctra of diatomic molculs, th transition for which J = 0 is not allowd. This transition is calld th Q branch of th spctrum. For mor complx molculs, this transition may b allowd, and a Q branch may b part of th spctrum, showing as an intns transition btwn th R and P branchs. 7 Only a fw yars ago, such calculations wr only don by a rathr small numbr of xprts on rathr larg computrs. Today thy may b don with th aid of a prsonal computr at on s dsk. 8 John Popl was awardd th 1998 Nobl Priz in Chmistry principally for th dvlopmnt of GAUSSIAN.

6 Exprimnt 6, pag 6 Vrsion of March 17, 015 Howvr, thr is a grat dal of chmical knowldg on must still bring to bar on th procss to obtain rliabl rsults. Th principal problm on must cop with in carrying out ab initio quantum calculations is that any procdur uss som approximation to th molcular lctronic wav function(s). Th quality of th approximation dtrmins how good calculatd proprtis ar. A commonly usd mthod is linar combination of atomic orbitals (LCAO), in which on xprsss th molcular lctronic wav function (or molcular orbital [MO]) in trms of atomic orbitals of th constitunt atoms. Sinc th forms of atomic orbitals ar not wll known xcpt for hydrogn, vn th choic of functional forms of atomic orbitals is an approximation whos quality affcts th rsults. Th st of functions usd is calld th basis. A commonly usd basis is th Slatrtyp orbitals (STO), but othr bass ar somtims usd, for xampl Gaussian-typ orbitals (GTO). Ths basis sts hav nams that dnot crtain faturs of th st of orbitals, such as 3-1G or 6-31G or G(d,p). In principl, an infinitly larg basis st allows on to solv th lctronic stat xactly. Howvr, that would tak a grat amount of tim, so that calculations ar always don with a truncatd basis; again, th quality of th rsults dpnds on how wll th truncatd st approximats th ral wav function. Onc chosn, th basis is usd to dtrmin th bst lctronic wav function by som critrion, such as minimization of nrgy. A common mthod is th Hartr-Fock slfconsistnt-fild (HF-SCF) mthod, which mphasizs th avrag ffcts of intrlctronic intractions, rathr than instantanous intractions. This itrativ mthod finds paramtrs of th xpansion of th molcular orbital that minimiz th variational nrgy intgral. Anothr common tchniqu is known as dnsity functional thory (DFT). This mthod combins a rasonably low computational cost (i.., th calculations ar quick) with an accuracy that is sufficint to obtain rliabl chmical rsults. Th ssnc of this tchniqu lis in th ability to rduc th 3N spatial coordinats that dscrib th intracting lctrons of a systm into a thrdimnsional function dscribing th lctron dnsity. Convnintly, computr programs lik GAUSSIAN do all of th tdious work, onc on dtrmins th dsird basis for th situation appropriatly, rturning usabl information on th stat in th form of paramtrs. Procdur CAUTION: HCl and DCl ar corrosiv gass. ALWAYS handl th matrials xtrmly carfully. Obtaining th Infrard Spctra. Th instrumnt for masuring th spctra is a Nicolt Magna IR 550 FTIR spctromtr. If you hav not alrady larnd how to us this instrumnt, your laboratory instructor can hlp you with th oprating paramtrs for th instrumnt. If you hav takn instrumntal analysis, this instrumnt should b familiar to you. It has a liquid-nitrogncoold cadmium tllurid dtctor. Bfor bginning any spctroscopy, obtain liquid nitrogn and fill th rsrvoir until liquid nitrogn ovrflows th fill hol. An important part of gtting rliabl data is positioning th sampl. Th cll holdr must b positiond accuratly to allow th full IR intnsity to b dtctd. Mak sur th bam passs through th cntr of th cll. Tak grat car in insrting th sampl into th sampl compartmnt. Do not forc th sampl to go in, as that may brak th sampl. Wait at last two minuts to allow th systm to b purgd of air aftr closing th compartmnt lid.

7 Exprimnt 6, pag 7 Vrsion of March 17, 015 Whn obtaining th spctrum of th mixtur of HCl and DCl, rcord all prtinnt data so you hav thm whn doing th analysis. 1. You should bgin by obtaining a background spctrum of th instrumnt without a sampl prsnt. Follow th procdur for collcting a background spctrum which is ultimatly subtractd from th spctrum of ach sampl.. For th sampls of gass, w hav a woodn cradl into which th cll fits. Install th cradl carfully. If it dos not fit proprly, do not forc it. Hav th laboratory instructor hlp you with this stp if you ncountr any problms. 3. Bfor taking th spctrum of a gas sampl, tak a background spctrum of th mpty compartmnt, using th sam paramtrs as you intnd to us in th xprimntal masurmnt. This is don with th command Collct Sampl, whr it prompts you to tak a background spctrum, which it automatically subtracts from your nxt spctrum. (If you hav problms, ask th laboratory instructor for hlp.) 4. Carfully insrt th gas cll into th cradl. Again, if it dos not fit asily into th spac, s th laboratory instructor bfor procding. 5. A window appars prompting you to tak th xprimntal spctrum. Install th sampl, and wait for th purg for a fw minuts. Click on th button to tak th spctrum. HCl is an impurity in a sampl of DCl that can b idntifid bcaus of its lowr signals in th spctrum. 6. Look at th spctrum to b crtain you s both th bands of th HCl and DCl. Thr may b othr bands from a bit of watr vapor in th compartmnt, and thr ar som bands from th poxy that holds th windows on som clls. Th important point is that th spctrum contains bands from HCl and DCl that you can asily discrn. 7. Whn you hav rcordd th spctrum, ach studnt should sav th data on hr/his flash driv so that th data may b latr analyzd. Us th Sav As command, bing sur th fil typ is CSV. A fil of this typ can b importd into a program lik EXCEL on your computr for crating a graph and prcisly rading th pak positions. 8. Obtain a spctrum of th CO sampl in th sam mannr. 9. Sign th logbook. Calculational Chmistry. Th calculations ar don on MACs in th laboratory. Thr ar two oprations: (1) stting up th calculation with GaussViw, and () running a Gaussian calculation with Gaussian09. Subsquntly, on can viw th rsults with GaussViw. Start th MAC, using th password providd. 1. Click on th GaussViw icon. This action should display th main mnu of GaussViw, as shown on th nxt pag.. To build th HCl molcul. Click on th atom icon of th main display; this action gts you to th priodic tabl. Thn click on th Cl on this display. Clos th Slct Elmnt display. You should s an HCl molcul in th Currnt Fragmnt display. 3. Click on th Nw fil window and this should put a copy of th HCl molcul into your nw fil. 4. Click on th bond lngth icon on th main mnu. This action causs th Currnt Fragmnt display to bcom blu. Go to th HCl window. 5. Click first on ithr th H or Cl atom and thn on th othr. A window should opn with a slidr to st th lngth of th bond. St it at som distanc (in Angstrøm units) such as 1.35.

8 Exprimnt 6, pag 8 Vrsion of March 17, 015 Atom Icon Bond Lngth Inquir Currnt Fragmnt Nw fil Window 6. Go to th Calculat mnu and slct Gaussian. This action brings up th Calculat mnu in a window with various tabs. Mak sur that th Calculation Typ is Enrgy undr th Job Typ tab. In th Mthod tab, slct ground-stat DFT with unrstrictd spin. Slct th functional B3LYP and us th basis st G(3df,3dp). 7. Submit th job. Th program asks you to sav an input fil. Us a nam lik HCl135. Mak crtain it is savd as a Gaussian job fil (.gjf) in th pchmusr foldr. Th calculation should start at this point. 8. Whn th calculation is finishd (in a fw sconds), th computr opns a window tlling you th job is finishd. You may click Ys to clos th Gaussian window. From GaussViw a box pops up asking if you want to opn th fil, click Ys to opn th fil. You must indicat that th output fil nds with th xtnsion.log to gt output. You can rad th fil from GaussViw using th Rsults mnu. You may click on Summary, which causs a box with prtinnt rsults to b shown. You may viw th ntir fil as wll, if you wish. 9. If you ar looking at th full fil, th output bgins with a lot of prliminary stuff. Sarch th fil to find th lin that bgins with SCF Don. Th quantity calld E(UB3LYP) is th calculatd nrgy of th molcul, in atomic units, a. u., or hartrs. This rportd nrgy is th total nrgy, that is, th nrgy rquird to

9 Exprimnt 6, pag 9 Vrsion of March 17, 015 sparat all of th lctrons and nucli to infinity. Rcord this numbr along with th intrnuclar sparation in your notbook. 10. Rpat this calculation for a sris of diffrnt bond lngths. Each bond lngth that you dfin yilds a diffrnt quantity for E(UB3LYP). It is asist to call back th first fil you mad, click on th two atoms aftr clicking on th bond lngth icon and stting th nw lngth. Sav th fil with a uniqu nam that hlps to idntify which fil corrsponds to which bond lngth upon starting th Gaussian calculation. Us a st of bond lngths that run from about 1. Å to 1.5 Å. B sur to gt sufficint points that you can dfin th potntial nrgy function wll nough to dtrmin th point at which it is a minimum. (It hlps to plot ths as you ar calculating, to s what is going on.) 11. Onc you hav found th lowst nrgy, crat a fil having th bond lngth giving th lowst nrgy abov. St up a nw calculation, choosing Opt+Frq undr th Job Typ tab. Undr th Mthod tab, choos to run a ground-stat DFT calculation using rstrictd spin. Slct th functional B3LYP and th basis st G(3df,3dp). This action dos an optimization and a frquncy calculation. Whn this calculation is finishd, b sur to rcord th optimizd bond lngth (click on th Inquir button, thn on th two atoms) and th dipol momnt from th Summary. This calculation rports th vibrational frquncy, ω, of HCl in wavnumbrs and th rotational constant, B. B sur to rcord ths numbrs from th rsults, as thy must b rportd. Th vibrational frquncy can b found in th Rsults mnu undr Vibrations. To find th rotational constant you hav to viw th whol log fil. Undr th Rsults mnu, click Viw Fil. This opns th log fil and you must scroll down towards th nd and look for Thrmochmistry. Locat th zro-point nrgy and rcord it in your notbook as wll. 1. To calculat th hmolytic dissociation nrgy of HCl, calculat th ground-stat nrgis of isolatd chlorin and hydrogn atoms. Ths ar two sparat calculations. Th sum of ths two nrgis rprsnts th nrgy whn th atoms ar at an infinit distanc from ach othr. Whn you plot th potntial wll as a function of th distanc sparating th hydrogn and chlorin atoms, this valu should b tratd as a rfrnc (i.., this valu should b plottd as zro and all points calculatd at a finit distanc hav som ngativ valu rlativ to this valu). To prform ths calculations, plac a singl atom on your window and calculat th nrgy using dnsity functional thory using unrstrictd spin. Slct th functional B3LYP and th basis st G(3df,3dp). Rcord th nrgis of ths atoms in your notbook whn th calculations finish.

10 Exprimnt 6, pag 10 Vrsion of March 17, 015 Calculations Data Analysis of th Spctroscopic Rsults 1. Analysis of HCl Spctra a. Mak sparat tabls for 1 H 35 Cl and 1 H 37 Cl of th positions of th lins (in cm -1 ) and th corrsponding valus of J. 9 [On must sarch through th EXCEL fil for th paks in ach spctrum. It is asist to rcord ths as spradshts in EXCEL. You hav to dcid which paks to associat with ach molcul and which valu of J.] b. For ach typ of molcul, on on graph, plot th lin positions of transitions in th R branch vrsus J + 1 and th lin positions of transitions in th P branch vrsus J. [Us a dummy indx, m, for J + 1 or J to mak ths plots.] c. By multipl-rgrssion analysis of th plots for both spcis, dtrmin ω -x ω, B, and α for ach matrial. (You should do th analysis for both th R and P branchs and assum D c is zro.) 10. Mak a tabl of lin positions for ach DCl spcis and analyz ths data by th sam mthod as in stp Analyz th data for CO by th sam mthod as in stp Summariz all drivd rsults on all gass in a singl tabl. Thortical Chmistry 5. From th rsults of th Gaussian09 calculations, mak a tabl of bond lngth and nrgy. Rfrnc your nrgy scal such that th sum of th nrgis of th isolatd hydrogn and chlorin atoms is zro in whatvr unit you us. Convnint units for this purpos ar kj/mol. 6. Mak a plot of th calculatd nrgy vrsus bond lngth. 7. Compar th optimal bond lngth dtrmind in th optimization calculation with th valu, R, from your analysis of th plot mad in stp 6, and with th litratur valu. 8. Rport th dipol momnt at th optimal bond lngth prdictd by this calculation. Compar ths xprimntal and thortical paramtrs with litratur valus. [B sur to quot your litratur sourc.] 9. Compar th calculatd (with GAUSSIAN09) valus of ω for HCl to your xprimntal valus of ω x ω and with th litratur valu. Assuming your xprimntal valu is corrct and that th litratur valu of ω is corrct, find x ω. Discussion Qustions 1. Driv quations (6.7) and (6.8).. Why can on distinguish th spctroscopic transitions of 1 H 35 Cl and 1 H 37 Cl (or H 35 Cl and H 37 Cl)? Suppos that th rsolution was 5 cm -1. Could on distinguish ths diffrnt spcis undr thos xprimntal conditions? 9 J is th rotational quantum numbr of th initial rotational stat in ach cas. B carful. 10 B sur to includ stimats of uncrtainty in your valus for ths paramtrs.

11 Exprimnt 6, pag 11 Vrsion of March 17, Calculat th momnts of inrtia of ach of th four possibl spcis in th HCl/DCl sampl from th rotational constants, B, you dtrmind. From ach momnt of inrtia, calculat R for ach of th four isotopomrs. Within xprimntal rror, ar ths bond distancs diffrnt from ach othr? Explain your answr. 4. Th xpctd position of th Q branch of HCl is diffrnt from that of DCl. What ar your xprimntal valus? Assuming that th anharmonic trm is zro, calculat th ratio of th rducd masss of H 35 Cl and D 35 Cl from you data for th xpctd positions of th Q branch. How dos this agr with litratur data for this quantity? 5. Explain why th IR cll is constructd th way it is. In particular, why is it not mad compltly out of glass?