Ω-type doubling reversal in the B 3 Π 1 state of 200 HgAr as a probe of the long-rangepotential of the A 3 Π 0 + stateAkiyoshi Hishikawa, Hirokazu Sato, and Kaoru Yamanouchi Citation: The Journal of Chemical Physics 108, 9202 (1998); doi: 10.1063/1.476415 View online: http://dx.doi.org/10.1063/1.476415 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/108/22?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Spin-forbidden c Σ 1 + 3 ← X Σ + 1 band system of YF J. Chem. Phys. 126, 144309 (2007); 10.1063/1.2714525 Spectroscopic characterization of the first singlet (Ã 1 B 1 ) excited state of 7 Li 16 O 7 Li J. Chem. Phys. 119, 10169 (2003); 10.1063/1.1614773 The structures of fluorene– ( H 2 O ) 1,2 determined by rotational coherence spectroscopy J. Chem. Phys. 119, 1970 (2003); 10.1063/1.1584031 Spectroscopic characterization of excited Ca (4s4dδ 3 D J ) RG ( 3 Δ 1,2 ) states ( RG=Ar , Kr, Xe): No “heavy-atom” mixing of RG (ndδ) character into the wave functions J. Chem. Phys. 111, 981 (1999); 10.1063/1.479380 Mass-resolved two-photon and photoelectron spectra of Xe 2 in the Xe (4f) region above the first molecularionization limit J. Chem. Phys. 109, 3944 (1998); 10.1063/1.476994

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

130.133.66.132 On: Thu, 04 Dec 2014 14:29:16

V-type doubling reversal in the B 3P1 state of 200HgAr as a probeof the long-range potential of the A 3P01 state

Akiyoshi HishikawaDepartment of Chemistry, School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku,Tokyo 113-0033, Japan and Department of Pure and Applied Sciences, College of Arts and Sciences,The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan

Hirokazu Satoa)

Department of Pure and Applied Sciences, College of Arts and Sciences, The University of Tokyo,Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan

Kaoru Yamanouchib)

Department of Chemistry, School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku,Tokyo 113-0033, Japan and Department of Pure and Applied Sciences, College of Arts and Sciences,The University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan

~Received 19 February 1998; accepted 30 March 1998!

The mass-resolved excitation spectrum of theB 3P1–X 1S1 transition of HgAr was measured bythe two-color resonantly enhanced two-photon ionization method using a high-resolution reflectrontime-of-flight mass spectrometer. The rotational structures were recorded with high spectralresolution (;0.05 cm21) for the (vB,0) bands (vB50 – 9) of a single isotopomer200HgAr. Fromthe rotational analysis, the presence of anV-type doubling was identified for the first time, whichis caused by the rotational perturbation from the nearby highly excited vibrational levels of theA 3P01 state. The spacing between theV-type doublets was found to exhibit a characteristicreversal as a function ofvB . From the deperturbation of theV-type doubling, the vibrational levelenergies of theA state in the vibrationally highly excited region were derived, from which itslong-range interaction potential was determined. ©1998 American Institute of Physics.@S0021-9606~98!02822-0#

Determination of a long-range potential between atomshas been an important subject in molecular spectroscopy.1

Among various spectroscopic methods, direct measurementsof a high-resolution spectrum of diatomic molecules near thedissociation threshold could afford the most precise informa-tion of the attractive long-range force. However, the applica-bility of this method is limited because the highly excitedregion near the dissociation threshold is in general hardlyaccessible due to the Franck–Condon restriction. Such alimitation could be overcome by adopting a multistepFranck–Condon pumping scheme as demonstrated byStwalley and co-workers2 for alkali–metal diatomic mol-ecules. Alternatively, a long-range attractive potential couldbe studied by utilizing perturbation with a nearbybrightelectronic state, a transition to which has a sufficiently largeFranck–Condon factor. The presence of perturbing vibra-tional levels bound by a long-range interatomic potential be-comes evident in the spectra as a small energy shift of abright transition peak from its unperturbed energy, or weakextra features around thebright transition peak. Since themagnitude of such perturbation is sensitively dependent bothon the energy gap betweenbright and dark levels and ontheir vibrational wave function overlap, precise determina-tion of the long-range interatomic potential as well as thelevel energies of the high-lying vibrational states can be

achieved. In the present letter, we demonstrate such‘‘perturbation-facilitated’’3 determination of an interatomicpotential through the analysis of the weak rotational pertur-bation evidenced in theB 3P1–X 1S1 transition of HgAr,resulting in the determination of the long-range potential ofthe A 3P01 state.

The potential energy curves of theA(V501) andB(V51) states near the dissociation threshold, Hg(63P1)1Ar, are shown in Fig. 1 with their bound vibrational levels.Since the equilibrium internuclear distance of theB state,r e54.65 Å, is substantially larger than that of theX state,r e54.0 Å, the entire region of theB–X band has a brightFranck–Condon character. Thus, in the laser-induced fluo-rescence~LIF! spectra, the clearB–X (vB,0)(vB50 – 9) vi-brational progression is observed, which is followed in thehigher energy region by a continuum spectrum, where thedissociation process, HgAr (B 3P1)→Hg(6 3P1)1Ar, oc-curs.

On the other hand, due to the limited Franck–Condonfactors for theA–X band, only the (vA,0) transitions for thelower vibrational levels withvA50 – 6 were observed in theLIF spectra. If we assume a Morse potential for theA state4

with ve541.20 cm21, vexe51.207 cm21, 16 vibrationallevels in total are expected to be bound in theA state. There-fore, only through the measurements of the excitation spec-trum of theA–X band, information regarding the higher ly-ing vibrational levels abovevA56 could not be obtained, sothat the long-range part of theA state potential and its dis-

a!Present address: Ebara Research Co. Ltd., Center for Advanced Technol-ogy, 4-2-1 Honfujisawa, Fujisawa-shi, Kanagawa 251-0875, Japan.

b!Author to whom correspondence should be addressed.

JOURNAL OF CHEMICAL PHYSICS VOLUME 108, NUMBER 22 8 JUNE 1998

92020021-9606/98/108(22)/9202/4/$15.00 © 1998 American Institute of Physics

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

130.133.66.132 On: Thu, 04 Dec 2014 14:29:16

sociation threshold remain uncertain in spite of the recentextensive spectral measurements.4–13

Since the first measurements of the rotational structureof the A–X and B–X transitions of HgAr performed byYamanouchiet al.,7 rotational structures of the vibronic tran-sitions have been used only to determine the rotational con-stants and the rotational band origin wave numbers. So far,no evidence related to the weak interaction between theAandB states has been reported mainly due to the overlappingof vibrational bands of the six abundant isotopomers,mHgAr(m5198, 199, 200, 201, 202, 204! with small isotope shiftscomparable with the rotational transition spacings. In thepresent study, high-resolution excitation spectra of theB–Xtransition were recorded free from the isotopic congestion bydetecting a mass-selected200HgAr1 dimer ion producedthrough the two-color resonantly enhanced two-photon ion-ization ~RE2PI! via theB state, and the level energies of thehigh-lying vibrational levels of theA state were determinedthrough evidence of the weak rotational perturbations iden-tified in theB–X transitions.

The experimental setup is similar to the one describedpreviously.14 Briefly, the HgAr dimers formed in a super-sonic jet were excited to theB state by a frequency doubledoutput (l1'253 nm! of a dye laser, pumped by a XeClexcimer laser, and were further excited to the ionization con-tinuum by another laser (l25220 nm) pumped by the sameexcimer laser. An intracavity etalon was inserted for the firstlaser to achieve a high spectral resolution (;0.05 cm21)when sweeping its wavelength to record the two-colorRE2PI spectrum. The wave number of the excitation laserwas calibrated by recording the LIF spectra of I2 ~Ref. 15!simultaneously. The produced ions were detected by a highresolution (M /DM;800) reflectron time-of-flight~TOF!

mass spectrometer. Due to the high resolving power, singleisotopomers were completely resolved in the TOF spectrum,enabling us to record the mass-resolved rotational structureof theB–X(vB,0)(vB50 – 9) transitions of200HgAr withoutisotope congestion.

Figure 2 shows the mass-resolved rotational structure ofthe ~4,0! band of theB–X transition of200HgAr. The high-Jpart of the observed spectrum is compared with a simulatedrotational contour obtained by assuming that thee and fparity rotational sublevels in theB ~V51! electronic state aredegenerate. In the simulation, the rotational constant for thevB54 level of theB state was determined by a trial-and-error fit to the low-J part of the observed spectrum, fromwhich the assignment ofJ rotational quantum numbers wasestablished. As can be seen clearly in Fig. 2, the observedrotational peaks assignable to theP and R branches areshifted lower in energy by;0.1 cm21 from the peak posi-tions predicted by the simulation though the peak positionsfor the Q-branch transitions agree well with the predictedpositions. Because of the selection rule for the electric dipoletransition, theP and R branches in theB–X transition ter-minate ate parity sublevels of theB state while theQ branchterminates at thef parity sublevels.16 Therefore, the ob-

FIG. 1. The potential curves of theA 3P01 and B 3P1 states of200HgArnear the dissociation threshold. The two vertical broken lines represent theclassical inner and outer turning points of the vibrational ground level (vX

50) of the electronic ground state. The interatomic distance region betweenthese two lines can be regarded as the Franck–Condon region for theA–X(vA,0) andB–X (vB,0) transitions. The solid and dotted lines represent,respectively, the bright and dark vibrational levels to which the electronictransition occurs from thevx50 state. ThevA50 – 6 levels in theA stateand all the levels in theB state are the bright levels. The level energies ofthe highly excited dark vibrational levels in theA state are determined in thepresent study from theV-type doubling reversal in theB state.

FIG. 2. The overall~a! and expanded~b! views of the rotational structure ofthe B–X ~4,0! band of 200HgAr recorded by the mass-resolved two-colorRE2PI method~i!, in comparison with the simulation with noV-type dou-bling (qvB

50) ~ii !, and with theV-type doubling (qvB522.031024) ~iii !.

The energy shift between theP andR branches are clearly illustrated in theexpanded high-J region of the spectra. The relative wave number measuredfrom the rotational band origin at 39 512.46 cm21 is plotted in the abscissa.

9203J. Chem. Phys., Vol. 108, No. 22, 8 June 1998 Communications

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

130.133.66.132 On: Thu, 04 Dec 2014 14:29:16

served shifts in theP andR rotational lines indicate that onlythe e parity components shift lower in energy from the un-perturbed level energies.

A pair of split levels withe and f parities, which areoriginally degenerate, is called theV-type doublet, resultingfrom the coupling between the electronic angular momentumand the molecular rotation. ThisV-type doubling is causedby a perturbation from near-lying rotational levels in anotherbound electronic state, which interacts differently withe andf parity sublevels. The selection rule for the perturbation isexpressed as16 e↔e and f↔ f . Therefore, from the aboveobservation that only thee-parity sublevels are shifted in theB state, theV501 electronic symmetry is assigned to theperturbing electronic state which consists only ofe-parityrotational levels.

The two spin–orbit sublevels of the Hg 63P state, 63P2

and 63P0 , are located, respectively, at 4630.7 above and1767.2 cm21 below the 63P1 state17 to which the A(V501) and B(V51) states are correlated. From the 63P2

state, three molecular states of HgAr withV502, 1, 2 elec-tronic symmetries are formed, while only a 02 state isformed from the 63P0 state.18 The only electronic statewhich is located near theB state and hasV501 symmetryis theA state. Therefore, the electronic state perturbing theBstate is uniquely identified as theA state.

The nonzero off-diagonal matrix element of the Hamil-tonian between theA state and theB state originates fromtheL-uncoupling (HJL), and theS-uncoupling (HJS), termsin the rotational Hamiltonian.16 When these interactions aretreated by second-order perturbation theory, the energy shiftDE of thee levels of theB1 state caused by the perturbationcan be expressed as:

DE5(vA

u^B1,vB,JuHJL1HJSuA01,vA ,J&u2

EvB2EvA

~1!

5qvBJ~J11!, ~2!

where

qvB5(

vA

BvAvB

2hel2

EvB2EvA

, ~3!

with a rotational coupling parameter,hel ,

hel52^B1uL11S1uA01&, ~4!

and a vibrational overlap function,BvAvB,

BvAvB5^vAu2

1

2mr 2 uvB&. ~5!

A trial-and-error simulation of the rotational structures of theB–X transitions was performed by taking account of therotational perturbation above. In the simulation, the rota-tional constantBv and theV-type doubling constantqvB

ofthe B state as well as the band originn0 , and the rotationaltemperatureTr were adopted as adjustable parameters. Therotational constant of thev950 level of the groundX statewas fixed to the values for200HgAr obtained from the micro-wave spectroscopy.19 The obtained best-fit simulated spec-trum for theB–X ~4,0! band is compared with the observed

one in Fig. 2. The other observed rotational contours of theB–X (vB,0)(vB50 – 3,5– 9) were also fitted successfullyby the present simulation, andn0 , Bv , andqvB

were derived.TheBv andn0 parameters for the ten (vB50 – 9) vibrationallevels were fitted by the Dunham expansion formula toyield Y10512.486(1) cm21, Y20520.591(2) cm21, Y01

50.0234(5) cm21, Y11521.1(4)31023 cm21, Y21

52.9(8)31025 cm21, and Y31525(4)31026 cm21,where the number in parentheses represents an estimatedlimit of error.

In Fig. 3, the dependence of theV-type doubling param-eter qvB

on the vibrational quantum number,vB , in the B

state is illustrated. For the low vibrational levels (vB<2),the qvB

parameter is positive and increases asvB increasesfrom 0 to 2, where the jump fromvB51 to 2 is significant.However, atvB53, it abruptly changes its sign to becomenegative. This drasticvB dependence nearvB52 and 3 in-dicates the presence of a resonant perturbation from darkvibrational levels of theA state. For higher vibrational levels(vB>4), qv exhibits a rather smooth variation around2231024, with a shallow local dip atvB58. Hereafter, werefer to this characteristic behavior ofqv accompanying thesign change as anV-type doubling reversal or aqv reversal.

As expressed in Eq.~3!, the magnitude of this perturba-tion is governed by the three factors, i.e., the rotational cou-pling constanthel , the squared modulus of the vibrationaloverlap function,BvAvB

2 , and the energy gap,EvA2EvB

, be-

tween the interacting vibrational states in theA andB states.Thus, it can be understood from Eq.~3! that the energy gap,EvA

2EvB, governs the sign change of theqv parameter. The

positive qvBvalue for vB<2 and the negativeqvB

for vB

>3 indicate, respectively, that dominant perturber levels intheA state are located below and above the vibrational levelsin theB state. From the characteristic vibrational dependenceof qv, we determined the long-range potential parameters,C6 andC8 , in theA state in the following manner.

FIG. 3. The determinedV-type doubling parameter,qvBexhibiting a clear

reversal as a function ofvB . TheqvBparameters calculated using the opti-

mized long-range potential of theA state are also drawn by a solid line. Thedotted lines represent the calculatedqvB

values when onlyC8 is varied bysmall amounts (61.03106) from its optimized value. It can be seen that theqvB

value is sensitively dependent on theC8 coefficient.

9204 J. Chem. Phys., Vol. 108, No. 22, 8 June 1998 Communications

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

130.133.66.132 On: Thu, 04 Dec 2014 14:29:16

First, the potential curve of theB state was constructedby connecting three potential energy functions for the short~I!, intermediate~II !, and long~III ! internuclear distance re-gions, respectively. The RKR potential curve of theB statewas determined using the term values and the rotational con-stants of the vibrational levels in theB state obtained in thepresent study forvB50 – 9 and those obtained in the mea-surements of the204HgAr isotopomer forvB510– 11.20 Thederived RKR potential covers a wide range of internucleardistance between 4 and 15 Å. The short-range potential func-tion ~I! was expressed by the Morse functional form with theve and vexe constants determined in the present study,which agrees well with the RKR potential forr<r 1

56.5 Å. According to the criterion proposed by Stwalleyet al.,21 the expansion expression for the long-range potential~III !, i.e.,De2SCn /r n, is expected to be applicable to theBstate forr>r 257 Å, where the overlap between the elec-tron clouds of Hg (6p) and Ar is sufficiently small. TheLeRoy–Bernstein plot22 for the B state in this internucleardistance range showed that its long-range potential can beexpressed asDe2C6 /r 62C8 /r 8. By fitting this function tothe RKR potential forr>r 2 , the long-range potential coef-ficients were determined asC657.273105 cm21/Å6, andC856.393107 cm21/Å8, when the dissociation energy,De

561.25 cm21, for the B state20 of 200HgAr was adopted.These short-~I! and long-range~III ! potential functions wereconnected smoothly in the intermediate region~II ! (r 1<r<r 2) by a polynomial functiona2r 21a3r 31a4r 41a5r 5

1a6r 61a7r 7 to calculate the vibrational wave functions forvB5029.

Then, the potential function of theA state of200HgArwas constructed in a similar manner as theB state. The po-tential was divided into three regions, i.e., short (r<r 1

54.5 Å) ~I!, intermediate (r 1<r<r 255.5 Å) ~II !, andlong (r>r 2) ~III ! ranges. The short-range potential was ap-proximated by the Morse function given by Lawrenceet al.4

For the long-range part, theDe2C6 /r 62C8 /r 8 functionalform with De5368.60 cm21 ~Ref. 20! was also adopted asfor the B state.

For given coefficientsC6 in the 5.8– 10.93105 cm21/Å 6

range andC8 in the 20.3– 1.63107 cm21/Å8 range, the vi-brational energies and wave functions in theA state werecalculated and the least-squares fit to the experimentalqvb

values shown in Fig. 3 was performed by evaluatingqvBin

Eq. ~3! with a variable parameterhel .A contour map of the chi-square value,x2, of the fit

plotted against the two potential coefficients,C6 and C8 ,showed that the global minimum ofx2 is located aroundC658.83105 cm21/Å6 and C854.83106 cm21/Å8. Forthe optimizedC6 andC8 values, the rotational coupling pa-rameter was determined to behel52.00(2), indicating thatthe electronic structure of theA andB states can be approxi-mated well by a 6s6p-type single configuration.18 The de-pendence of the calculatedqvB

value on theC8 coefficient isillustrated in Fig. 3 with theC6 coefficient fixed at 8.723105 cm21/Å6 which could give approximately the globalminimum of x2. When the contour ofx256, which corre-sponds to the reduced chi-square ofxn

250.9'1, is taken as a

limit of the uncertainty of the two potential parameters,they are presented with uncertainties asC658.8(8)3105 cm21/Å6 and C855(3)3106 cm21/Å8. The previ-ous values,C658.453105 cm21/Å6, derived on the basis ofthe far-wing absorption measurements,23 and C856.023106 cm21/A8, determined10 by a simple fit to the long-range part of the Morse potential, are in good agreement withour determined values.

As presented here, the long-range potential function ofthe A (V501) state of 200HgAr was determined by theperturbation-facilitated analysis utilizing theV-type dou-bling reversal phenomenon in theB (V51) state, which wasfound to be sensitively dependent on the potential curve ofthe A state. A part of the determined potential energy curveof the A state is plotted in Fig. 1 with the high-lying vibra-tional levels, which clearly illustrates the relative positions ofthe vibrational levels in theA andB state potentials. For thevB<2 vibrational levels in theB state, the dominant per-turber in theA state is located lower in energy, while thevibrational levelsvB>3 are perturbed by theA state vibra-tional levels located high in energy.

The present study has been supported partly by ResearchFund for Selected Area from College of Arts and Sciences,the University of Tokyo, by a Grant-in-Aid from the Minis-try of Education, Science, Sports and Culture of Japan~Nos.07240106, 8640636, 08740446! and by CREST~Core Re-search for Evolutionary Science and Technology! fund fromJapan Science Technology Corporation.

1See, for example, E. Tiemann, H. Kno¨ckel, and H. Richling, Z. Phys. D37, 323 ~1996!.

2A. M. Lyyra, P. D. Kleiber, and W. C. Stwalley, inMolecular Dynamicsand Spectroscopy by Stimulated Emission Pumping,edited by H. L. Daiand R. W. Field~World Scientific, Singapore, 1995!.

3L. Li and R. W. Field, J. Phys. Chem.87, 3020~1983!.4S. J. Lawrence, D. N. Stacey, I. M. Bell, and K. Burnett, J. Chem. Phys.104, 7860~1996!.

5K. Fuke, T. Saito, and K. Kaya, J. Chem. Phys.79, 2487~1983!.6K. Fuke, T. Saito, and K. Kaya, J. Chem. Phys.81, 2591~1984!.7K. Yamanouchi, S. Isogai, M. Okunishi, and S. Tsuchiya, J. Chem. Phys.88, 205 ~1988!.

8L. Krim et al., Chem. Phys. Lett.200, 267 ~1992!.9L. Krim, B. Soep, and J. P. Visticot, J. Chem. Phys.103, 9589~1995!.

10C. J. K. Quayle, I. M. Belle, E. Takacs, X. Chen, K. Butnett, and D. M.Segal, J. Chem. Phys.99, 9608~1993!.

11J. Koperski, J. B. Atkinson, and L. Krause, Chem. Phys.186, 401~1994!.12J. Koperski, J. Chem. Phys.105, 4920~1996!.13T. Tasaka, K. Onda, A. Hishikawa, and K. Yamanouchi, Bull. Chem. Soc.

Jpn.70, 1039~1997!.14S. Liu, A. Hishikawa, and K. Yamanouchi, J. Chem. Phys.108, 5330

~1998!.15S. Gersteinkorn and P. Luc,Atlas du Spectre d’Absorption de la Molecule

d’Iode ~Editions du Centre National de la Pecherche Scientifique, Paris,1978!.

16H. Lefebvre-Brion and R. W. Field,Perturbations in the Spectra of Di-atomic Molecules~Academic, Orlando, 1986!.

17C. E. Moore,Atomic Energy Levels~U.S. GPO, Washington, DC, 1971!,Vol. III.

18K. Onda and K. Yamanouchi, J. Chem. Phys.104, 9376~1996!.19Y. Ohshima, M. Iida, and Y. Endo, J. Chem. Phys.92, 3990~1990!.20A. Hishikawa, H. Sato, and K. Yamanouchi~unpublished!.21B. Ji, C.-C. Tsai, and W. C. Stwalley, Chem. Phys. Lett.236, 242~1995!.22R. J. LeRoy and R. B. Bernstein, J. Chem. Phys.52, 3869~1970!.23Z. Ben Lakhdar, D. Perrin, and R. Lennuier, J. Phys.~France! 39, 137

~1978!.

9205J. Chem. Phys., Vol. 108, No. 22, 8 June 1998 Communications

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

130.133.66.132 On: Thu, 04 Dec 2014 14:29:16