Stark quantum beat spectroscopy: The vibrational dependence of the dipole moment in the A1Σ+ state of BaO

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sensitive measure of the electronic charge distribu~ tion _in a molecular state It provides valuable infom+ion on the type of binding in a specific electronic state, determines the transition strength in rotational spectra and mfhtences the cross sections in molecular scattering processeS_ From a theoretical -point ‘of view it Gstitutes an extremely useful test q&&y for ab initio MC SCFcalculations [l]_ This is all the moretrue if dipole moments are measured.over an extended range of different vibrational levels of au electronic state_ With such data -the approximate wavefunctions can be gauged at different _intemucleiX distances which is not possible with scalar energy level info&

-. mation. An impressive amount. of- experimental fesults on molecular dipole moments has been obtained from high-resolution microwave and radio-’ frequency spectroscopy. [2]- These methods are limited to stable. ground -or ~metastable; excited gates, however: Experimentally determiued dipole moments of short-lived excitedstates are still_rare_ _~ ‘~

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If _-th&rou&-*tate dip&e moment is &e&y. known the excited-state moment can be e&acted~ from Stark shifts and splittings in. op tical spectra_ Without using high-resolution laser spe&rOscOpic methods the resolution is limited by. the Doppler effect ana .mther l&e electric~fie1d.s~~~. required [3]. In. some cases excited-state dipole momems have been measured by Doppler-free level crossing and double resonance techniques [4]. The viirational dependence of excited-state dipole~moments could be~studied by different methods in d3A of CO [S],~A311, of ICl[6) and A%+ of LiH [7,8] and A% * of NaH [9] so afar_ In time-resolved spectroscopy the:effe& of orientation alignment Coup’hng leads to decay signals -followiug coherent excitation. of sublevels split&d by ‘an electric field Subsequent. observation of polarized .fluorcscence exhibits mod&+-.. Ed tic$s in thd exponential .decay_ The. modulation frequency-of these so-called quantum beats is di-. :rectly related to .the Stark splitting inthe’ejrdted -state.. Q&turu beat spectroscopy~ (QBS) using pulsed lasers aS ~&citation-+rce has proven to be .a useful high-resolutions techniqGe in various e& perjments to determine energy--level splittings ‘in excited states of. at&& and molecules, i_e he_ .. hyper-fine’ and Z&man splittin& [lo]_ .-7Xe utility of the quantum -beat. method for. investigatioti of ..field-free. spl.idn~~~i;l~ poly&omic molecul~es was recently reviewed by Chaiken’and :&Dona@[ll]. .- F previous wo&[7,9,12] .we have-. shown that the

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anaIysis of Stark quantum beats represents a method well suited to determine electric field induced energy splittings in short-lived excited states_ The use of tunable dye lasers enables one to excite as many vibrational levels as are Franck-Condon accessible from thermaily populated ground state levels_ Since the quantum beat frequency is insensitive to saturation effects f13& the method is superior to the related Stark-Hanle rffect method in the cnse of laser excitation_ We report on measurements of electric dipole momats of four vibrational Ievek of the A’%’ state of rssBar60_ A primary goal of the present work is the extension and improvement of previous measurements done with the Stark-Hanle effect method [la]_ Lifetime and Zeeman effect studies in perturbed leve!s of the A’S’ state have also been performed and wiIl be published elsewhere [15]_ A theoretical treatment of ehxtric field quantum beat and HanIe effect signals does not yet exist in the Literature_ With a view towards further developing laserexited quantum beat method in molecular spectroscopy we present such a treatment in a forthcoming paper [la].

In a typical laser-induced quantum beat experiment a short pulse of resonant light of polarization e exci~ts an ensemble of molecules from the initital state ( Ii}} to the excited states { le))_ Timeresolved observation of the fluorescent light with pokuization u gcmcxa~ed when the exited states decay to the final states { If>) exhibits moduiations on tbe exponential decay_ These so-called quantum beats are caused by quantum-mechanical interference of the different transition amplitudes invoIved_ In the most general way the time-dependent intensity of the fhrorescen L light can be expressed as

x


with D being the electric dipole operator &( - T) the density operator of the initial state prior LO the exciting pulse which lasts from - T to 0, T, = rg ’ the radiative decay constant and o,,. the excitedstate splitting_ Several conditio~ns have to be met in order LO detect quantum beat signak (1) The length of the exciting pulse AT should be short in comparison with the characteristic times of the molecuIe; AT -Z r- and AT -X o=Q!_ (2) The spectral width of the exciting light AoL should be “broadline” so that all sublevels of interest are excited simuhaneously: Ao, > o,,._ (3) The pohuization of the-exciting light pulse and of the detected fhrorescen ce should be chosen so that an alignment and/or orientation of the excited states is produced and detected. A detailed treatment of the sums of transition matrix elements in connection with the time-dependent factors is necessary to visualize the last requirement_ This provides conditions for the occurrence, phases and amplitudes (modulation depths) of quantum beat signals. The most concise treatment makes use of the density operator formalism_ The introduction of state multipoles by using a spherical irreduciiIe tensor basis of this density matrizx takes maximum advantage of the rotational symmetry of the experiment_ Such treatments have aheady been given for fine 15) and hyperfiie structure [17] as well as Zeeman quantum beats [lS]_ The theory of quancum beats arising from second-order Stark effect splittings which shows some peculiarities is given in the forthcoming paper [16]_ Assuming that the initial state is not pokuized and the relaxation constants are determined by the excited-state radiative lifetime, the result can be summarized in the expression

J’-2

xexp

(-z-f),

with o being the Stark-effect splitting factor which for a ‘2

o = ( E2&/hcBu.h) x [3/2J’(J’+

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(3)

Contributions due to polarizability terms [I93 are neggected in this formula The coefficients if, B,,, CM., &. are independent of time but functions of the angular moments involved and the geometrical arrangement of the experiment. By a proper choice of detection geometry and detection sensitivity to polarization any two of the sets of coefficients &r-p <,f -* DAI. can be selected so that they vanishThe first sum represents quantum beats arising from AM’= 1 splittings which may occur with different phases (cos, sin) whereas AM’ = 2 beats represented by the second sum appear with a fixed phase onlySince we observe second-order Stark splittings, the individual quantum beat signal depends on the absolute value of the magnetic quantum number M’. In the case of higher angular momentum (J’ > 2) the signal becomes a superposition of contributions -with different frequencies and amplitudes Therefore it is convenient to use excitation to J'= 1 or S=2 levelswhere easily evaluabie -tignals with only one single beat frequency are obtained_ Exciting a R(0) [J’ = 1 +J = O]transition and observing the combined R(0) and P(2) [J'= 1 +J” = 2] fluorescence leads to the foilowing simple expression for the fluorescence intensity I(r)

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Here the exciting beam and the observed fluorescence are linearly pohirized at 45” to the electric field E and propagate perpendicular to E and under the angle of 135” to each other. From the beat frequency 0 the electric dipo!e moment p can be derived using expression (3)_ Reggng unit

conversions one gets p,(debye)

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BaO molecules are produced by chemi&l rea&’ tion of Ba atoms in an atomic beam entering a reaction chamber filled with SO, gas at a pressure of lo-4 mbar_ The apparatus was des&ibed~m detail in a previous paper [14]_ SO2 was chosen as an oxidant because of its large reactive cross see-tion with barium and the fact that hardly any che@uminescence appears in the reaction Ba -!- SO, --, BaO + SO_ The BaO molecules are produced principally in lower rotational and vibrational levels of the ground state_ Smith and Zare 1201reported a product state distribution over the vibrational levels of V, I U, : I+ = 1 : 03 I O-005 and average rotational temperatures of 400 and 200 K for E,, and t‘t respectively_ This is especially advantageous since the experiments are performed by exciting R(0) lines in different ( IJ’, 0”) bands of the A’ZC-X ‘2’. system of BaO_ The reaction re8ion is. situated between two circular aluminum Stark plates of 50 mm diameter and 10 mm distance which provide the necessary homogeneous electric field. The exciting light source is a home-built dye laser oscihator amplifier system pumped by a 1 MW nitrogen laser (l+mbda Physik Ml00 A)_ Solutions of rhodamine 6G in ethanol and rhodamine 110 in ethylene glycol are used as laser dyes_ The laser produces pulses of 2 11slenght with a bandwidth of l-5 GHz The excitation requirements for. QBS mentioned above are thereby fuIfilIed_ On the .other hand, the laser bandwidth is small enough to resoive-the R(O)- line from the nearby lying R(8) transition separated by a distance of t_ypically 2 %HZ Fig 1 shows part of the BaO A + X(1,0)- excitation spectrum using a Mod. 699-21 (Coherent) cw dye laser in.single mode operation_ In ‘thisease the spectral resolution of the Iaser-induced fluorescence spectra is limited by the Doppier broadening The identification of the lines is of = O-8 GHt straightforward using the assignments and molecular coustauts @en -by Lagerqvist et al_ [21]_ The weakR(0) line.which the experiment is performed on is marked by an asterisk-

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The fluorescence light folIowing the laser pulse is directed through a 025 m monochromator (Perkin-Elmer) on to a RCA C31034 A photomuhiplier tube_ In this way the decay to a different vibrational level of the ground state is observed and no stray lig,ht of the exciting laser reaches the photocathode- The photomultiplier tube is cooled down to - 30°C resulting in a low dark count rate (20 cps)_ Linear polarizers are used in excitation (fixed) and observation (tumable)_ Table 1 gives the wavelengths of the bandheads of the transitions which have been se&ted for excitation and obsemation tooether with the Franck-Condon factors and the relative vibrational population of the ground state product mokculeslime-correlated single-photon counting is used to get a time-resolved decay signal followiq the exciting l&er p&e: A time-to-amplitude converter is started by the htser p&e and stopped by the first ffuorescence photon detected by the photomultiplier_ Pulse-height anaIysis and storage in a muhichannel analyzer (MCA) generates the moduIated decay curves~ In order to avoid pile-up effects caused by the accumulation of more than one detected ffuo rescence photon after a Iaser pulse, the fhxorcscence rate is kept lower than one tenth of a ff uo rescence photon per laser p&e_ Due to the low repetition Hz)

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ratio- The decay curves were transferred from the lMCA to a HP 1000 computer to treat l dre data_ Beat frequencies and decay rates were obtained by means of a least-squares fit program

4_ Results Fig 2 shows decay sigmds obtained with different directions of the polarization in the detection channel. The polarization determines the phase of the fluorescence modulation. The upper signal was observed with “crossed” polarizations of the exciting and observed light with respect to the direction of the electric field_ The second signal was obtained with “parallel” pohuizers and shows a TabIe 1 h-=sigued

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in -the sign of the cosine-like modulated. part of the signal- The.third cm-v&is the different+ between the two decay curves which exhibits oscjllations with a d&blexI amplitude damp&i by thecoherence time constant of the excited states_ The part which is due to the exponential decay of t& population has been subtra+zd here. Table 2 lists the quantum beat frequencies obtained from Ieast-squar& fits of the recorded quantum beat.curv&s to expression (4) at different field strengths. From the beat frequencies we calculated the electric. dipoIe moments of the A’Z+(c’ = 0, l-2, 3) states using formula (5)_ Fig_ 3 compares quantum beat signals of the three different states obtained with identical eIectric field strexigth. Note the significant longer beat period from the u’ = 1 level_ Table 3 gives the results in comparison with some earlier measurements. The error limits are determined by the following contributions to the total uncertainty: (1) The time caIiirations had a maximum uncertainty of 15% since the positions of time calibration pulses were determined with an accuracy of one channel and their distance was 66 channels_ (2) The error in determining the beat frequen.change

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ties by means of the least-squares fit routine was below.l.O%_ (3) The uncertainty in measuring the electric field strength - voltage and distance of Starkplates - was 125% (4) The error caused by the inaccuracy of the rotational constants is sma.Uer than 4X lo-‘% WIThus the overall error in our dipoIe moment measurements is found to be 25% As the main contributions arise from the time caliiration and the determination of the electric field strength, an accuracy of better than 1% should be possiiIe in principle by reducing &se uncertainties_ It is important to note that the relative error of the differ-~ ent dipore moments is given by (2) and (4): and. therefore less than OJ%_ If one compares the results with the e&lie= Stark-HanIeeffect m easuremen~ [14] agreement is only obtained for the d = 1 level The disagreement is most probable due to saturatiori effects caused by singlsmode cw laser excitation u&d in

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curves is known to be extremely sensitive to varif24s]-_~l-he -_ cy. sat&ati& broad&g& * valud f& D’ = 1: bf ‘the-ea.&Y’measure- jctk$.g’was obtained by- eful ‘e+apc&ti& .i&. z&o_ light’ . .ionic ground to a covalent &x-kitedsiaie.%ey &I&.! ffti The influende‘bf sat&&on on q&urn beat showed, that small admixtures,of ic& _(&,@&j:sign& lx+ dso.been coG$ered and shown- to &z ~._ character in the excited (ground) s&e could kes&:. small p3)_ -Even if ‘ohe ‘takes&to acc+nt -6 possi-_ I in significant parallel oscillator ~engthk Follo~$g: ble effect on the’ quantum w< sign& &re is a ingthoseargumentsthis& implksionic-c&a~_decisive differencez‘in Hank-~ expe&ents the lent mixing in the A*Z+ state of Baa; Okthe : width of the Ioreptzian from which thk_splittingis other hand, we have io cokkider the ei&dyextrxted is. broadened by saturation. In the case. complicated nature of this electronic state, Which __. of &antum beats only the.ampKtude of the~modmay mask the expected behaviour-

-is affected [13] which is Grele~knt foi the Stark splitting _information. The quantum-beat method is therefore c&My superior to Hanle-type experiments when lasers are Used as exciting light so-_ Thus we believe the results pkented here are f&of systematic ekors caked by s&r&on and should overrule the earIierfrnd@8s_ ulation

5. Discussion It.was alr&dy hot& [26] that the X’Zi ground state of BaO wit& a dipole mo%nt of .7_995 D (o”=o) is predomina&y ionic (Ba?O-) whereas our experimental results for the A%’ state indicate a much more covalent binding_ The -percentag? ionic character” jt/eR, f&r th&- ground state is 85%. and is only 30% for the-A??? State (e is the electron charge and R, the equilibrium intemuckar distance)_.Thk has been explained in terms of an oxygen-to-metal charge transfer[14,22]. HoweGer, the Ioni rakatiye lifetimk~of the A’ZT state (= 3OO.ns)Fms to be inconsistent with such degree of charge ~transfer-The t&&ion moments of charge transfer transitionsare usually &mparal Me to eR, (= 10 D here) [27]. Even f& a partial charge c&u&y transfer,. = 055 e, a large osciliatoi segth and consequenil~ a‘shoG -?fetim< being an order of magnitude sma.Uer than observed, ~: w&Id be expected_ ’ Anothe~.~c+ous feature’ is the ‘domintice of paralIelz($4 = 0) ..&er 1‘&&+ii$q_. (Ad_= 1) : transitions cotikciin~ i& bJZ+:-stat& w$hCti.thki: elec~onic -states [27& Z&C and-‘Herrkhbach [28] observed thi opposite’-p&nom&on :ti-is&c.-..

Unfortunately, no ab i&o- cakkations e&t for. the BaO ~electronicstates. Ii ti. interesting to note-that ab initio calculations of the related A’Zi state of CaO [32] predict -a stiong ionitiity &mparable to the ground state. Apart from the-value u’ = i which shows ~~irre&ar beh&iou.&e BaO. resuhs & well as the CaO ~calcuiateddi&le .moments follow ~increasing functions of the vibra-m tional &kntum number. At kger internu&ar distances the di~ole~moments are expected to decrease cause. by the fact that the A’Z’ state dissociates to th$ atomic states Ba(3D) and 0(3P)_ This is in agreement with the smaller value for v’ = 7 .obtained by Wormsbecher et Zt- [22] with the microwave optical doubie-resoknce method_ The de&easing slope indicates indeed a maximum ~. ; -_ value aroucd u’~= 3, me relatively ‘small keasured dipole eotient. _ for the v’ =‘l level seems to indicate ;iperturbation The .A’Z+ state of BaO % knckn to be p&&be& by the neighbouring a3Xi &‘lI add -~. b311&. k&k [21,30] land a caref@ a&y&s of Stark-effect data should- kgard &ossibld cont.rib& tions of the perturbing states_- Fortunately, a veiy detaikd deperturbaiion analysis of- the low-lying -. electronic states of the BaO provides us with mixing co+fi&ents for.all studied levels 129,311. The :ksults show only negggible admixTure+(OS%) from-~., the b311 state to. the levels consideti here: m .& electric -fiel&_ polar&abilities :aused. by nearby roiribronidlevels.may. als0 contribute-to the-splittings [19]~:~The~in$zctiOn‘qf term e&t&es sh&& -, t$at the ‘shortest distances to &ies of :-&ffeie& pariw, w&l-&J 4.0, -&l:'vary. from 565--&n_’ -ai: u'= 0 to 13 cm-! at U’ = 3: This a&d the fact’thtit :

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no Q lines co&d be iriduced by the ekctric field indicate that ekctric field mixing from diffmt ekctronic states is ako negIigik_ Thus thk stsiking imegukity of the value for a’ = 1 remains unexplained AII possibIe contriiutions of a second-order Stark-effect. calculation, direct terms and crossed terms, have-been considered carefully, It should be noted that a!so other observables su& e the re@procaI Iifetimes show a simiIar w behaviour as a function of the viiratiand quantxn number. This is demonstrated in fig- 4* where vzduesfor these observabks are depicted in depezndenceon cf_

We thank Professor Robert W_ Field and Dr_ Richard A Gottscho for helpful dismssiotx ce work was supported by. the Deutsche- Forschungsgemeinschaft, Sonderforscbungsbereich 161_

(31 D_H_ Phdps and F-W_ tiby. Can Ji Phys 43 (l965) 1444; R Thomson and F-W_ Dalby. Can J__Phys 46 (1968) _ 2815; 47 (l%9) 1155: T_AR_ fnvin snd F-W_ Dalby. Can J. phys. +. (l965) 1766; ti Scat-land F-W_ DaIby. Caa J_ Pays 49 (l97l) 28.55 14) SJ. Sikiq TH Bagamm~andW_KIcm+er.J_chGn wys 52 (1970) 4385; LcLW&OCkaedRN_zarr.;:chmPh~58(l973) 4319; T~_~andD~Leuy.J_chanphys.~9~‘973)us7; TsBcr&mamandRXtarr.J_Champhyr61(l974) [5] z&ndw. Kkmp&.i_uumPh~m(l979~& [6) FE Crummings and W_ Kkmpqa,~-chanphyr60 0974) 203x m N-Briqcr,AHesgkRamndASoc?&_Ch~Phyr Lct.ers 76 (1980) 465. [q PL Dagdigim I Ghan Ph>x 73 (1980) 2049_ 191 MBriegcr.AHcscAFtennatdAScd&C%inPh~ jctcas 78 (l981) 153_ [lo] Sf-h-ockin~Higb~udon!ascr~y,cd_K ==da(springcr. Berlis 1976). pi] J. Cbaikm and J.D. McDonaId, Advan Laser Specuy_ 1 (1982) 17-L

[14] G_ Dohn~-A- Hca. A Ram -&xd I-LS Sdmaia. phys. 42 (l979) 183_, [~~]ARcxus.KB~~s.I-LSS&~~~~AH&SCO~ ‘i publishaL

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[16]HSSchwa4A+and~Hae.tl1anPhys,subUtilledfQfpLIbkmm Il7l R &pa-t and J- van Gacn-J_ Phys B18 (1977) 3627. PSI P-J- Bru~at aud RN- zarr. I Ghan Phys 78 (I9833 100. [I91 M. Bxiqcr, Chum P&s_ 89 0984) 275

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