Lithium Hydrides and Lith ium Dimers: Sub-Doppler Spectroscopy and Dynamics

Transcription

1 Jour nal of the Chi nese Chem i cal So ci ety, 2002, 49, Invited Pa per Lithium Hydrides and Lith ium Dimers: Sub-Doppler Spectroscopy and Dynamics N. Bouloufa, P. Cacciani, G.-H. Jeung and R. Vetter* Laboratoire Aimé Cot ton, C.N.R.S.II, Bât.505, Orsay cedex, France Deep in sights into mo lec u lar struc tures and dy nam ics were ob tained for lith ium dimers and lith ium hy - drides by sub-doppler spec tros copy com bin ing mo lec u lar beams and cw tun able la ser beams. For 7 Li 7 Li spe - cies, ac cu rate spec tro scopic stud ies of the B 1 u-x 1 g + sys tem were car ried out, with the mea sure ment of hun dreds of wave num bers and with the de ter mi na tion of dis so ci a tion rates due to tun nel ing through the po - ten tial bar rier of the B 1 u state. They led to the full de scrip tion of the B state po ten tial, in clud ing its barrier. For 6 Li 7 Li spe cies, weak but non-negligible dis so ci a tion rates in the B 1 u state were ob served, mea sured and in ter preted as sum ing that an elec tronic cou pling be tween the B 1 u and 1 1 g states takes place through an ungerade-gerade sym me try break ing. For LiH spe cies, the A 1 + -X 1 + sys tem was re vis ited for both isotopomers. For this mol e cule, dy nam i cal ef fects are pre dicted in highly-excited Rydberg states, that could be stud ied by use of sim i lar sub-doppler tech niques. I. IN TRO DUC TION Mo lec u lar spec tros copy has known spec tac u lar ad - vances in the last de cades, ow ing to the in tro duc tion of end - less grow ing means of cal cu la tions and to the par al lel de vel - op ment of new and pow er ful ex per i men tal tools and tech - niques among which Fou rier Trans form Spec tros copy and La ser Spec tros copy are cer tainly the most pop u lar ones. There is no doubt that Fou rier Trans form Spec tros copy is the most pow er ful tech nique to achieve the anal y sis of ab - sorp tion and/or emis sion mo lec u lar spec tra since it pro vides ac cu rate and ex haus tive mea sure ments of line wave num bers, from IR to near UV. 1-3 Let s just men tion some bench-mark stud ies: the anal y sis of plan e tary at mo spheres 4 the car ry - ing-out of io dine At lases 5 and the ex haus tive stud ies of al kali dimers. 6,7 How ever, in these stud ies, the spec tral res o lu tion is gen er ally lim ited by the Dopp ler-broadened na ture of the light sources. In con trast, La ser Spec tros copy is gen er ally as so ci ated with high res o lu tion since it is pos si ble to get rid of the Dopp - ler broad en ing. It does not en ter the scope of this ar ti cle to men tion all the Dopp ler-free ex per i ments that have been per - formed in the past. 8 Let s just men tion the mea sure ments of hyperfine struc tures in so dium and io dine mol e cules 9,10 the study of highly-excited vi bra tional states in so dium 11 and the for ma tion of cold mol e cules through photo-association pro cesses. 12 Al ter na tively, real-time femto-second ex per i - ments have led to deep in sights into intra-molecular dy nam - ics. 13,14 How ever, the highly-sophisticated na ture of these ex - per i ments lim its their range of ap pli ca tion to sim ple mo lec u - lar sys tems. In the pres ent ar ti cle, we wish to re view a se ries of sub-doppler la ser ex per i ments that we re cently car ried out and to show how their complementarity led to orig i nal re sults about the spec tros copy and dy nam ics of lith ium hy drides and lith ium dimers. They were per formed by cross ing a mo lec u - lar beam of LiH/Li 2 with a cw tun able la ser beam and by col - lect ing the la ser-induced flu o res cence ver sus fre quency. This tech nique leads to the re cord ing of nar row ab sorp tion pro - files al low ing both for the ac cu rate mea sure ment of wave num bers and for the study of dy nam i cal ef fects linked to dis - so ci a tion and per tur ba tion pro cesses. Our orig i nal aim was to char ac ter ize the A 1 + -X 1 + sys tem of LiH mol e cules by sub-doppler spec tros copy. For this, we im ple mented an ef fu sive beam of LiH and we re - corded its ab sorp tion spec trum in the blue and near UV. 15 How ever, we were immediatly faced to the pres ence of lith - ium dimers in the mo lec u lar beam and we were com pelled to as sign Li 2 tran si tions as well as LiH ones. Then, a ma jor dif fi - culty arised from the Dopp ler-limited knowl edge of lith ium ab sorp tion spec tra, which forced us to re visit the B 1 u-x 1 + sys tem of Li Dur ing the course of this study, we ob served the broad en ing as so ci ated with tun nel ing through the po ten - tial bar rier of the B 1 u state, for the tran si tions that end to lev els ly ing above the (2p+2s) dis so ci a tion limit of this state. 17 Later, in the par tic u lar case of the 6 Li- 7 Li isotopomer, we mea sured weak but non-negligible dis so ci a tion rates due to a cou pling be tween the B 1 u and 1 1 g states, through an

2 468 J. Chin. Chem. Soc., Vol. 49, No. 4, 2002 Bouloufa et al. ungerade-gerade sym me try break ing. 18,19 The pres ent ar ti cle is or ga nized as fol lows: the ex per i - ment is de scribed in Chap ter II, with em pha sis on the three types of mesurements that we car ried out: -the ac cu rate fre quency cal i bra tion of LiH and Li 2 ab - sorp tion lines -the mea sure ment of Li 2 dis so ci a tion rates via pro file anal y sis -the mea sure ment of Li 2 weak dis so ci a tion rates through the dis crim i na tion be tween atomic flu o res cence and mo lec u lar flu o res cence. The spec tral anal y ses of the A-X and B-X sys tems of LiH and Li 2 that we achieved are de scribed in Chap ter III and Chap ter IV re spec tively; in par tic u lar it is shown that the three pre vi ous types of mea sure ments are nec es sary and com - ple men tary to de scribe the B state of Li 2. The mea sure ment of weak dis so ci a tion rates in 6 Li 7 Li and the in ter pre ta tion in terms of an ungerade-gerade sym me try break ing are de - scribed in Chap ter V. Finally, it is shown in Chap ter VI that sev eral dy nam i cal ef fects pre dicted in highly ex cited states of the LiH mol e cule by ab in itio cal cu la tions could be re vealed by use of these sub-doppler ex per i ments. cated in the in ter ac tion cham ber, 15 cm down stream of the noz zle (ac tu ally, the quartz microbalance mea sures the to tal flux of par ti cles, Li, LiH and Li 2). It was con stant for hours with out re fill ing. 2. La ser Beam For the study of lith ium dimers, the la ser beam was pro - vided by a cw sin gle-mode tun able dye la ser op er at ing in the blue, around 445 nm. It de liv ered a typ i cal power of 10 mw over a spec tral band width of 5 MHz (30 MHz are equiv a lent to 10-3 cm -1 ) and a solid an gle of 1 in the in ter ac tion cham - ber. The la ser fre quency con tin u ously scanned over ranges of 1 cm -1 was cal i brated with re spect to the ab sorp tion spec trum of tel lu rium mol e cules 20 and to ref er ence fringes pro vided by a spher i cal Fabry-Perot etalon (750 MHz-free spec tral range). For the study of lith ium hy drides, the cw tun able la ser beam in the near UV was ob tained by dou bling the fre quency II. EX PER I MEN TAL A sche matic view of the ex per i men tal set-up is shown on Fig. 1. Briefly, the sub-doppler na ture of the ex per i ment is achieved by cross ing at right an gle an ef fu sive beam of LiH/Li 2 by a cw tun able la ser beam and by col lect ing the non-dispersed la ser-induced flu o res cence (L.I.F.) ver sus la - ser fre quency. 1. Mo lec u lar Beam The ef fu sive beam of lith ium dimers was sim ply gen er - ated by radiatively heat ing a ver ti cal stain less steel cru ci ble filled with lith ium metal scraps. At 1000 K, a vapour pres sure of the or der of 0.1 Torr was achieved in side the cru ci ble and the beam ef fused through a 0.3 mm-diameter noz zle. The beam of lith ium hy drides was more dif fi cult to im ple ment since the LiH mol e cule is readily dis so ci ated by heat ing. Sev - eral tri als were nec es sary to ob tain a dense and sta ble mo lec - u lar beam. A so lu tion was found by send ing a per ma nent flux of hy dro gen mol e cules to the back of a long hor i zon tal stain - less steel cru ci ble radiatively heated around 900 K. 15 The solid an gle of the mo lec u lar beam was re stricted to 1 by use of cir cu lar di a phragms that also lim ited the black - body ra di a tion emmitted by the cru ci ble at high tem per a ture. The beam flux was mon i tored by a quarz microbalance lo - Fig. 1. Block-diagram of the set-up for Li 2 ex per i - ments. The stain less steel cru ci ble is radiatively heated at1000 K by a thin tan ta lum re sis tor sur - rounded by me tal lic shields. Q.B. is a quartz microbalance used to mea sure the beam flux. The la ser beam is pro vided by a com mer cial cw tun able dye la ser whose fre quency is cal i brated by si mul ta neously re cord ing the ab sorp tion spec trum of the tel lu rium mol e cule and ref er - ence fringes pro vided by a spher i cal Fabry- Perot etalon. A fourth la ser beam is used to mon i tor the light ab sorp tion by the tel lu rium cell. A mi cro-computer is used to treat the four sig nals. For LiH ex per i ments, a flux of mo lec u - lar hy dro gen is sent to the back of a 10-cm long hor i zon tal cru ci ble and the la ser beam is pro - vided by a cw tun able Ti:Sa la ser whose fre - quency is dou bled in an ex ter nal cav ity.

3 Spec tros copy and Dy nam ics of LiH and Li 2 J. Chin. Chem. Soc., Vol. 49, No. 4, of a cw sin gle-mode tun able Ti:Sa la ser op er at ing in the red. The fre quency dou bling, achieved with an ex ter nal cav ity, de liv ered a typ i cal power of 40 mw at 375 nm, over a spec tral band width of 3 MHz and a solid an gle of 1 in the in ter ac tion cham ber. The la ser fre quency con tin u ously scanned over ranges of 2 cm -1 in the UV (1 cm -1 in the red) was cal i brated with re spect to ab sorp tion lines of io dine mol e cules (in the red) 21 and to ref er ence fringes pro vided by a spher i cal Fabry- Perot etalon (750 MHz-free spec tral range, in the red). 3. De tec tion Scheme The non-dispersed la ser-induced flu o res cence was col - lected by a large-angle par a bolic mir ror whose fo cus co in - cided with the in ter ac tion vol ume and was for warded to a photomultiplier tube (P.M.T. Hamamatsu R943) through a se - ries of op ti cal fil ters. Their role was to limit the par a sitic sig - nal due to la ser stray light and to se lect the spec tral win dow for col lec tion of the flu o res cence light. In or der to elim i nate the sig nal due to the blackbody ra di a tion emmitted by the cru - ci ble, the la ser beam was chopped at 750 Hz be fore en ter ing the in ter ac tion cham ber and the L.I.F. sig nal was de tected by use of a lock-in am pli fier. The three sig nals --LiH/Li 2 ab sorp - tion spec trum, I 2 /Te 2 ref er ence spec trum and Fabry-Perot fringes-- were si mul ta neously re corded on a PC for data stor - age and anal y sis (a fourth di rect la ser beam was used to mon i - tor the ab sorp tion spec trum of Te 2, see Fig. 1). The speed of the fre quency scan ning was ad justed to the sam pling fre - quency, 10 Hz, and to the time con stant of the am pli fier, 0.3 s, to avoid a shape al ter ation of the re corded pro files and to yield high sig nal-to-noise ra tios (see Fig. 2, with the ab sorp - tion spec trum of Li 2). Var i ous iso to pic con cen tra tions were used when nec es sary to op ti mize the sig nal of in ter est. 4. Fre quency Cal i bra tion The raw data were treated by com par ing the fre quency scales pro vided by the Fabry-Perot fringes and by the ab sorp - tion lines of I 2/Te 2. This led to elim i nate the fre quency jumps and to linearize the fre quency scale. The in ten sity vari a tions of the la ser beams were also cor rected by a fur ther treat ment us ing the in ten sity of the ref er ence fringes and/or the in ten - sity of the fourth di rect la ser beam (only for Li 2 ). Un der these con di tions, the ac cu racy of the wave num - ber cal i bra tion was of the or der of cm -1 for LiH (in the UV) and of cm -1 for Li 2. The ac cu racy is better for Li 2 Fig. 2. Sub-Doppler B-X ab sorp tion spec trum of Li 2 around cm -1 (a) with the ab sorp tion spec trum of tel lu rium (b) and ref er ence fringes 750 MHz apart (c). The labell 77 at the end of the line iden ti fi ca tion cor re sponds to the 7 Li 7 Li spe - cies and the 67 to the 6 Li 7 Li one. Note the linewidth, typ i cally be tween 90 and 120 MHz F.W.H.M.

4 470 J. Chin. Chem. Soc., Vol. 49, No. 4, 2002 Bouloufa et al. be cause tel lu rium lines are sym met ri cal whereas io dine ones are not (see 22 ). 5. Pro file Anal y sis Ab sorp tion lines were an a lyzed as Voigt pro files, the con vo lu tion of nar row Gaussians due to a re sid ual Dopp ler ef fect by Lorentzians due to the fi nite life time of the up per level. Through out the ex per i ments over Li 2, the Gaussians widths were always rang ing be tween 50 and 70 MHz F.W.H.M., in agree ment with the an gu lar di ver gence of mo lec u lar and la ser beams. For all Li 2 lines be tween bound states, the Lorentzian widths were typ i cally rang ing be tween 30 MHz and 60 MHz, much larger than the nat u ral width, L 0 = 1/2 = 18 MHz, ex pected from the life time of the up per state. 23 This is due to the co her ent sat u ra tion re gime that holds when prob - ing mo lec u lar sys tems, even with the mod er ate pow ers pro - vided by cw la sers. 24,25 A spe cial treat ment was thus nec es - sary to take this ef fect into ac count and to re cover the true ho - mo ge neous width. 17 Tun neling is likely to oc cur for Li 2 tran si tions that end to lev els of the B 1 u state lo cated well above the (2p+2s) dis - so ci a tion limit (level 1 on Fig. 3), with dis so ci a tion of the mol e cule and light emis sion over the 2p 2s line of lith ium at oms at 671 nm. The life times of these lev els are re duced and the Lorentzians are broad ened ac cord ingly. Their widths L can be di rectly ex tracted by a Voigt anal y sis of the re corded pro files since the Dopp ler width is small and con stant. The dis so ci a tion rates k are then de ter mined from the straight for - ward ex pres sion: L = L 0 + k. The L val ues that can be ex - tracted in this man ner nec es sar ily range be tween 30 MHz and 5.5 GHz. The lower limit arises because extraction of Lorentzian com po nents be comes im pos si ble when their widths are much smaller than the Gaussi an ones, a prob lem that be comes more com pli cated in the case of sat u ra tion. 17 The up per limit arises be cause for broad lines the top in ten sity be comes com pa ra ble with the ex per i men tal noise. The cor re spond ing k val ues range be tween /s and 35, /s. 6. In ten sity Discrimination For the Li 2 tran si tions that ex hibit very small dis so ci a - tion rates, an al ter na tive tech nique was tried with suc cess by dis crim i nat ing the mo lec u lar flu o res cence from the atomic one. It was readily achieved by mea sur ing the top in ten si ties of the lines, with two col ored fil ters suc ces sively: -a first (yel low) fil ter, with col lec tion of the atomic flu - o res cence at 671 nm, plus a frac tion of the mo lec u lar one ( is de ter mined from the trans mis sion curve of the fil ter with re spect to Franck-Condon and Hönl-London fac tors). -a sec ond (red) fil ter, with col lec tion of the atomic flu o - res cence at 671 nm only. If the two col ored fil ters have the same trans mis sion fac tor at 671 nm and if the quan tum yield of the P.M.T. is flat over the spec tral do main un der con sid er ation --both con di - tions that ap ply to the pres ent case-- the in ten sity ra tio for a given line is = I(yel low)/i(red) = ( A + k)/k in which A is the spon ta ne ous tran si tion prob a bil ity for this line. 23 It yields k = A/( - 1). Large val ues, up to 100, can be mea sured in this man - ner. Since typ i cally ranges around 0.8, the mea sure ments lead to the de ter mi na tion of k val ues much smaller than A, only lim ited by the sig nal-to-noise ra tio of the ex per i ment. In deed, k val ues have been mea sured be tween 10 6 /s and /s. Note, how ever, that k is poorly de ter mined for val ues close to 1. In es sence, this tech nique is free from Dopp ler broad en ing and sat u ra tion ef fects but it rests on the ac cu racy over A and val ues. III. SPEC TRO SCOPY OF LiH Fig. 3. Li 2 po ten tials dis so ci at ing to (2p+2s). Level 1 dis so ci ates by tun nel ing through the bar rier and level 2 dis so ci ates by ungerade-gerade cou - pling (for 6 Li 7 Li only). Lith ium hy drides in volve two va lence elec trons and two core elec trons only. For this rea son and for their in ter est in sev eral fields of fun da men tal and ap plied phys ics and chem is try, as tro phys ics in par tic u lar, 26 they were in ten sively stud ied in the past, both ex per i men tally and the o ret i cally. 27 LiH is char ac ter ized by a strongly ionic ground state, with an ef fec tive charge trans fer of 0.76 from Li to H and a large di pole mo ment of 2.29 a.u. at R(Li-H) = 3 a.u. 28 This is due to a pro nounced ionic-neutral avoided cross ing that per - turbs the ex cited states at long and in ter me di ate dis tances.

5 Spec tros copy and Dy nam ics of LiH and Li 2 J. Chin. Chem. Soc., Vol. 49, No. 4, Actually, the sim plis tic view of this pro to type mol e cule is no lon ger valid when one con sid ers its ex cited states be cause mul ti ple avoided cross ings oc cur be tween va lence and Rydberg states. More over, as LiH has a small re duced mass, iso to pic ef fects and non-adiabatic ef fects are quite large. Con se quently, fit ting po ten tial en ergy curves by semiclassical Dun ham or RKR forms be comes of ten dif fi cult. Most quan tum chem i cal cal cu la tions in volve ef fec tive-core po ten tials and, in a few cases, core-valence cor re la tions through the ef fec tive op er a tor method, but no core-core cor - re la tion was in tro duced un til re cently. 28 De spite in ten sive spec tro scopic stud ies, only the X 1 +, A 1 + and B 1 states were char ac ter ized in the past, mostly by use of con ven tional spec trom e ters and Dopp - ler-broadened light sources. To our knowl edge, only one ex - per i ment in volv ing a la ser beam-molecular beam con fig u ra - tion was re ported, with the re cord ing of A 1 + -X 1 + ab sorp - tion lines in the near UV. 29 The ob ser va tions of C 1 + and D 1 states were pub lished only re cently. 34,35 Our ex per i ments con cern the sub-doppler ab sorp tion spec trum of the A 1 + -X 1 + sys tem be tween 357 and 385 nm, with the mea sure ment of 384 lines to an ac cu racy of cm -1 (see Fig. 4). 15 The as sig na tion of 7 LiH lines (v = ; v = 10) was first achieved by it er a tion be tween mea - sured wave num bers and cal cu lated ones. 30 Through out these fit tings, the X 1 + state was taken as a ref er ence since it is well de scribed by 17 ac cu rate Dun ham co ef fi cients is sued from mea sure ments of in fra red ro ta tion-vibration and ro ta - tion-rotation tran si tions. 32,33 They led to the de ter mi na tion of 39 Dun ham co ef fi cients that fully de scribe the A state, with an r.m.s. er ror of cm -1. The as sig na tion of 6 LiH lines (v = 0 ; v = 9) was con ducted in the same man ner, us ing scaled Dun ham co ef fi cients and 3 sup ple men tary mass- dependent cor rec tion co ef fi cients. A fi nal r.m.s. er ror of cm -1 was ob tained for this isotopomer. Such a large num ber of Dun ham co ef fi cients is nec es sary to de scribe the A state since this state is highly an har mon ic. IV. SPEC TRO SCOPY AND DY NAMICS OF Li 2 Lith ium dimers that also in volve a lim ited num ber of elec trons, were the sub ject of many ex per i men tal and the o ret - i cal stud ies. Among the low est ex cited states that dis so ci ate to wards the (2p+2s) limit, the B 1 u state ex hib its a po ten tial bar rier due to dipolar in ter ac tions at long dis tances and to an Fig. 4. Sub-Doppler A-X ab sorp tion spec trum of LiH around cm -1 (a) with the ab sorp tion spec trum of io dine (b, in the red) and ref er ence fringes, 750 MHz apart (c, in the red).

6 472 J. Chin. Chem. Soc., Vol. 49, No. 4, 2002 Bouloufa et al. elec tron ex change in ter ac tion. This bar rier leads to dis so ci a - tion of the mol e cule by tun nel ing. The first anal y ses of the B 1 u-x 1 g + sys tem were car ried out by use of con ven tional spec trom e ters and Dopp ler-broadened light sources, 36 with the sub se quent de ter mi na tions of usual mo lec u lar con stants for both states, cov er ing v = 0 13 in the B state but not its bar rier. The bar rier was stud ied later, through an X 1 g + A 1 g + F 1 g + two-step la ser ex ci ta tion and a Fou rier Trans - form anal y sis of the F B flu o res cence. 37 For 7 Li 2 it led to a bar rier height of ( ) cm -1 at the internuclear dis tance R = 5.9 Å. Dis so ci a tion rates cor re spond ing to bound-free tran si tions were also mea sured and in ter preted in the frame of a quasi-classical model. 1. De scrip tion of the B State As is ex plained above, our sub-doppler ex per i ment is well suited to re visit the B state. How ever, al though most re - corded lines are very nar row and their fre quency cal i bra tion very ac cu rate --typ i cally cm their as sig na tion by it - er a tion be tween mea sured and cal cu lated wave num bers is not ob vi ous. This is be cause the pre vi ously-published mo lec - u lar con stants are not pre cise enough and be cause the ab sorp - tion spec trum is rather con gested, with more than 10 lines/ cm -1 in av er age when one takes into ac count the three iso - topomers of Li 2 (see Fig. 2). Gen erally speak ing, as sig na tion of an ab sorp tion line is made more easy and more safe ei ther when it is broad ened by tun nel ing through the bar rier or when it ex hib its a non neg li gi ble flu o res cence in ten sity at 671 nm: in both cases it au to mat i cally ends to a dis so ci ated level of the B state. All in all, 1200 lines be tween cm -1 and cm -1 were mea sured in this man ner and as signed to 6 Li 2, 7 Li 2 and 6 Li 7 Li spe cies. For the most abun dant isotopomer, 7 Li 2, 329 lines were mea sured which ter mi nate on e-par ity lev els of the B state (P and R branches) and 163 that ter mi nate on f-par ity lev els (Q branch). 16 They cover v = 0 7 in the ground state and v = 3 16 in the B state. Among these lines, the ones end ing in the range cm -1 from the top of the bar rier (v = 13 16) were broad ened by tun nel ing. 17 First, the ground state X was pre cisely de scribed by mix ing our sub-doppler ac cu rate data over the B-X sys tem (in clud ing bound-bound tran si tions only) with less ac cu rate data over the A-X sys tem, with a smaller weight. 36 Later, the B state was de scribed by treat ing all avail able data over the B-X sys tem (in clud ing the lines broad ened by tun nel ing) with a con ve nient weight. The rel e - vant mo lec u lar con stants ob tained by it er a tion re pro duce the sub-doppler data with an r.m.s. er ror of 10-3 cm -1. For 7 Li 2, the com plete po ten tial curve of the B state was built by com bin ing a short-range po ten tial ob tained from the spec tro scopic data, with a long-range po ten tial gen er ated by as ymp totic cal cu la tions of Coulombic and ex change en er - gies, the in ter me di ate part be ing pro duced by a sim ple in ter - po la tion. The short-range po ten tial, R < 7.5 Å, was ob tained by di rectly fit ting the mea sured mo lec u lar en er gies (666 rovibrational lev els) with an RKR po ten tial as a start ing sam - ple. A cu bic spline was then used to gen er ate the po ten tial from 1.8 to 7.5 Å. Once again, the lev els dis so ci ated by tun - nel ing could be used be tween 6 and 7.5 Å so that, at the end, both en ergy lev els and linewidths were re pro duced sat is fac - to rily: for en ergy lev els, an r.m.s. er ror of cm -1 was ob - tained for 658 lev els of f-par ity (v 16). This po ten tial ex - tend ing up to 7.5 Å cor re sponds to an en ergy about 375 cm -1 above the dis so ci a tion limit of the B state. The out er most part of the curve, R > 9 Å, was gen er ated from as ymp totic cal cu la - tions tak ing into ac count the Coulombic at trac tion terms, the ex change terms due to the in ter ac tion be tween Li(2s) and Li(2p) and the spin-orbit cou pling of the Li 2 P atomic state. Coulombic and ex change pa ram e ters were de duced from other elec tronic states cor re lat ing to the same (2p+2s) dis so - ci a tion limit. The rest of the po ten tial, 7.5 Å < R < 9 Å, was gen er ated from a sim ple in ter po la tion be tween the two pre vi - ous parts. At the end, the whole po ten tial is nu mer i cally de - scribed by 83 points, from 1.8 Å to 70 Å. 16 Finally, from this nu mer i cal po ten tial, it is pos si ble to re pro duce all mo lec u lar en er gies up to v = 16, with an r.m.s. er ror of cm -1 (i.e. the over all ex per i men tal ac cu racy) and to cal cu late dis so ci a tion rates to within 5% when they are mea sured un der sub-doppler con di tions and to within 10% un der Fou rier Trans form con di tions. As for the rotationless bar rier, its height was es ti mated to ( ) cm -1 in agree ment with the pre vi ous de ter mi na tion but its shape ap - peared no tice ably dif fer ent, the pre vi ous curve un der es ti mat - ing the width of bound-free lines close to the top of the bar - rier. 2. Dis so ci a tion by Tun neling As ex posed be fore, dis so ci a tion by tun nel ing is likely to oc cur for the B-X tran si tions that ter mi nate to v 13. We mea sured the cor re spond ing dis so ci a tion rates for v = for dif fer ent ro ta tional quan tum num bers, ei ther through di rect ho mo ge neous line broad en ing for /s < k < 34, /s or through dis crim i na tion of flu o res cence in ten si ties for /s < k < /s lines were mea sured by use of the first tech nique and 15 lines by use of the sec ond one, the mea - sure ments ex tend ing over 4 or ders of mag ni tude with some over laps. They ex tend over 5 or ders of mag ni tude when in tro - duc ing the large dis so ci a tion rates mea sured by Fou rier Trans form anal y sis at Lyon. 37

7 Spec tros copy and Dy nam ics of LiH and Li 2 J. Chin. Chem. Soc., Vol. 49, No. 4, These re sults were in ter preted in the frame of a quasiclassical model in which k is sim ply ex pressed as P /2, P be ing the prob a bil ity to cross the bar rier and /2 the fre - quency with which the par ti cle hits the bar rier. P and are re - lated to the char ac ter is tics of the B state po ten tial, e.g. en ergy lev els, turn ing points, etc, all quan ti ties that can be de ter - mined from our pre vi ous spec tro scopic stud ies. The com par i - son be tween ex per i ment and the ory is very sat is fac tory since the dif fer ence (obs. - calc.) is less than 25% over 5 or ders of mag ni tude for v = 16 (see Fig. 5). 17 These ex per i men tal k val ues were used to fit the po ten tial curve of the B state rel a - tive to 7 Li 2. In turn, us ing the pre vi ous de ter mi na tion of the po ten tial curve of the B state --its bar rier in par tic u lar (see IV,1)-- would cer tainly in crease the agree ment be tween mea - sured and cal cu lated dis so ci a tion rates. 3. Sym me try Breaking in 6 Li 7 Li Dur ing the course of the pre vi ous dis so ci a tion rate mea sure ments over the B-X sys tem, in par tic u lar when mea - sur ing the flu o res cence in ten si ties, we no ticed that two lines as signed to 6 Li 7 Li ex hib ited small but non-negligible dis so ci - a tion rates al though, ter mi nat ing close to the dis so ci a tion limit (level 2 on Fig. 3) they should not un dergo dis so ci a tion by tun nel ing (see the ab sorp tion spec trum, Fig. 6). 18 The in - ter pre ta tion was found in an ungerade-gerade sym me try break ing in this spe cies, due to the fact that the cen ter of masses does not co in cide with the cen ter of elec tric charges. The cou pling that takes place be tween the mo tion of elec trons and the mo tion of nu clei re sults in a non-adiabatic term in the Hamiltonian. Con se quently, the B 1 u lev els close to the dis - so ci a tion limit dis so ci ate via the con tin uum of the g state, its part ner in sym me try : in other words, dur ing the course of its vi bra tional mo tion, the mol e cule has a small prob a bil ity to jump from one po ten tial to the other one around their cross - ing point. This drags small but not neg li gi ble dis so ci a tion rates for these bound-quasi-bound tran si tions that end close to the dis so ci a tion limit. In a first step, 18 dis so ci a tion rates were cal cu lated in the frame of the per tur ba tion the ory, by solv ing the cou pled Schrödinger equa tions through the use of Fig. 5. Dis so ci a tion by tun nel ing. Mea sured and cal cu - lated rates for the B 1 u (v = 16) level of 7 Li 2 are plot ted (in semi-log co or di nates) ver sus the en ergy gap to the top of the bar rier (roughly pro por tional to J (J +1)). The mea sure ments per formed at Orsay (black di a monds) cor re - spond to Ref. 17 with 10% er ror bars and the ones per formed at Lyon (open di a monds) to Ref. 37. The con tin u ous line cor re sponds to the cal cu la tions. Fig. 6. Sub-Doppler ab sorp tion spec trum of 6 Li 7 Li re - corded with two dif fer ent col ored fil ters: a (yel- low) GG 475 fil ter which trans mits the atomic flu o res cence at 671 nm and a pro por tion of the mo lec u lar one (a) and a (red) RG 645 fil ter which just trans mits the atomic flu o res cence (b). The 8-2 Q(47) 6 Li 7 Li line leads to dis so ci a - tion by ungerade-gerade sym me try break ing. Note the dif fer ent in ten sity scales. The mea - sure ment of top in ten si ties leads to = 12.2, hence the cor re spond ing dis so ci a tion rate k = /s.

8 474 J. Chin. Chem. Soc., Vol. 49, No. 4, 2002 Bouloufa et al. the Mapped Fou rier Grid Rep re sen ta tion Method. 38 A con - stant cou pling strength h ver sus internuclear dis tances was as sumed and eval u ated at R from the iso tope shift of the atomic res o nance line of lith ium at 671 nm (h = cm -1 ). A rough agree ment was found for the two lines that were mea sured. Later, we mea sured 70 dis so ci a tion rates as so ci ated with bound-quasi-bound tran si tions ex tend ing from v = 6 to v = 14, by dis crim i nat ing their flu o res cence in ten si ties. 19 Mea sured rates range from /s (a lower limit) to /s, with reg u lar vari a tions in side a given vi bra tional band (see Fig. 7). They are sys tem at i cally lower than the cal cu - lated rates by 40%-50% and for three lines of e-par ity, they are largely higher than ex pected and largely out side ex per i - men tal er ror bars. We have looked for a better agree ment by ad just ing the cou pling strength to a unique ex per i men tal value (Fig. 7). The best fit has been found for h = cm -1 (in stead of cm -1 ). A pos si ble ex pla na tion for the dis crep ancy over the three above-mentionned lines which still re mains might be found in the cou pling with a third elec tronic state. This state should ex hibit a po ten tial bar rier, share the same dis so - ci a tion limit and have well-localized co in ci dences with the B state. A good can di date is the 2 1 g state that pres ents these three char ac ter is tics. 39,40 Un for tu nately, its lev els above the dis so ci a tion limit are not known and can be es ti mated by ex - trap o la tion from the bound ones only. It would be de sir able to re al ize new ex per i ments to lo cal ize these co in ci dences and to per form new cal cu la tions in clud ing this third state be fore con clud ing about this ef fect. Fig. 7. dis so ci a tion by ungerade-gerade sym me try break ing. Mea sured and cal cu lated dis so ci a tion rates for four vi bra tional lev els of the B 1 u state of 6 Li 7 Li are plot ted ver sus the en ergy above the dis so ci a tion limit. Dis tinc tion is made be - tween lev els of e-par ity (black di a monds) and lev els of f-par ity (open squares). The con tin u ous line (drawn for clar - ity) cor re sponds to dis so ci a tion rates cal cu lated with a cou pling strength h = cm -1 (Note the ab nor mal dis so ci - a tion rates mea sured for v = 7, J = 52; v = 8, J = 48; v = 9, J = 50 (e-par ity) that lie largely out side er ror bars and the bunch of cal cu lated rates. Note also the rapid in crease of the rates when dis so ci a tion by tun nel ing be comes ef fi cient (v = 11, J = 49). Er ror bars are typ i cally 10%, ex cept for very low k val ues for which a con stant er ror of /s was adopted.

9 Spec tros copy and Dy nam ics of LiH and Li 2 J. Chin. Chem. Soc., Vol. 49, No. 4, It is worth while to men tion here that such a mass ef fect due to the break ing of ungerade-gerade sym me try was ob - served in the HD isotopomer only 41,42 the ef fect be ing less and less ob serv able as the mass of the mol e cule in creases. V. DY NAMICS OF LiH As said be fore, the large non-adiabatic cou plings in the C 1 + and D 1 ex cited states give rise to strong avoided cross ings and radiationless tran si tions. 34,35 In deed, as it was ob served by spec tro scopic ex per i ments, the C state ex hib its a dou ble well due to a va lence-rydberg avoided cross ing at short dis tances and an ionic-neutral avoided one at larger dis - tances (see Fig. 8) and both C and D states are highly pre dis - so ciated. The ex pla na tion of such ef fects re quires an ac cu rate quantum chemistry calculation method. The Born-Oppenheimer ap prox i ma tion that is as sumed ef fec tive in ab in itio or in ef - fec tive-core po ten tial cal cu la tions should be com ple mented here with non Born-Oppenheimer ef fects, i.e. ef fects in clud - ing the nu clear mo tion. A re cent work has shown the de fi - ciency of the B-O ap prox i ma tion to ex plain the fre quency shifts and the line broadenings ob served in the C state of LiH. 43 De veloping a new method to in clude these ef fects into elec tronic state cal cu la tions through a sim ple and el e gant way still re mains a chal lenge to the quan tum chem ists. An other prob lem is to interprete the line in ten si ties since the na ture of elec tronic states changes dras ti cally as a func tion of the internuclear dis tance, as is shown on Fig. 9 for the tran si tion di pole mo ments be tween the A, C and D states. This is con nected with the change of the wave func tion from Rydberg to va lence, va lence to ionic and ionic to va lence again. As a con se quence, D-A and D-C tran si tions should show ir reg u lar in ten sity pat terns ver sus rovibrational quan - tum num bers, a phe nom e non that can not not be ex plained by sim ple Franck-Condon ta bles. A close col lab o ra tion be tween experimentalists and the o re ti cians would be in valu able in that re gard. For still higher mo lec u lar Rydberg states, ionic-neutral avoided curve cross ings oc cur more and more sharply, with a pro gres sively weaker diabatic cou pling strength. This means that ionic-neutral cou plings do not bring about im por tant predissociation pro cesses (of course, va lence-rydberg and Rydberg-Rydberg avoided cross ings still re main). How ever, as shown re cently, the po ten tial en ergy curves of Rydberg states un du late, even in the ab sence of any avoided cross - ing. 44 This is due to the ef fect of atomic or bital un du la tion that orig i nates from the pres ence of nodal planes in atomic Rydberg states. In LiH Rydberg states, bondings at short internuclear dis tances are es sen tially pro vided by the LiH + bond ing, the spec tro scopic con stants con verg ing to those of LiH +. This is be cause high Rydberg states have gi gan tic elec - tron dis tri bu tions that do not per turb the LiH + core strongly, ex plain ing why the multi-channel quan tum de fect the ory (M.Q.D.T.) can be ap plied suc cess fully. At in ter me di ate and long internuclear dis tances, the ef fect of atomic or bital un du - la tion should be in tro duced into po ten tial cal cu la tions. This is il lus trated for the elec tronic state of LiH that dis so - ci ates into (5s+1s) (Fig. 10). This state is es sen tially 4f in na - ture all along internuclear dis tances, ex cept at very long ones where it merges with the Li + +H - ionic state that dis so ci ates Fig. 8. Po ten tial curves for the five low est elec tronic states of LiH. Fig. 9. Tran si tion di pole mo ments for the D-A and D-C tran si tions of LiH.

10 476 J. Chin. Chem. Soc., Vol. 49, No. 4, 2002 Bouloufa et al. Fig. 10. Po ten tial curve for the state of LiH. be tween 4f and 5s atomic as ymp totes. NaH and KH mol e - cules also show spec tac u lar po ten tial curves orig i nat ing from all these ef fects: ionic-neutral cou pling, va lence-rydberg cou pling, Rydberg-Rydberg cou pling and un du la tion ef - fects. 44 Ap pli ca tion of op ti cal-optical dou ble res o nance tech - niques (OODR) may re veal the dy nam ics of these highly ex - cited states. 8 For LiH, up to now, the only at tempts were achieved with pulsed la sers whose broad bandwidths pre - vented the shape anal y sis of re corded ab sorp tion pro files, thus the de ter mi na tion of ho mo ge neous broadenings due to predissociation. 35 On the con trary, the com bined use of cw tun able la ser beams and mo lec u lar beams could re sult in the dras tic re duc tion of the Dopp ler ef fect, thus in the pre cise de - ter mi na tion of ho mo ge neous broad en ing. The first step was re al ized with the sub-doppler study of the A-X sys tem of LiH that we car ried out for both 6 LiH and 7 LiH spe cies. 15 It opens the way to the study of predissociation pro cesses in the C and D states of lith ium hy drides as it was done for lith ium dimers. curve of the B state, in clud ing its po ten tial bar rier, and to ob - tain ac cu rate mo lec u lar pa ram e ters for the three isotopomers. An ungerade-gerade sym me try break ing has been put into ev i dence in the 6 Li 7 Li spe cies. There is no doubt that this en - sem ble of high res o lu tion re sults could not have been car ried out by use of con ven tional tech niques of spec tros copy and Dopp ler-broadened light sources. In ad di tion, the so phis ti - cated OODR ex per i ments that are planned for lith ium hy - drides will bring new in for ma tion about cou pling pro cesses be tween neigh bor ing elec tronic states and new in sight about the break ing of the Born-Oppenheimer ap prox i ma tion. One could ar gue that lith ium dimers and lith ium hy - drides just rep re sent good can di dates for sub-doppler stud - ies, two iso lated cases in side the crowd of diatomics. This is not the case since many high res o lu tion stud ies were per - formed in the past over di atomic mol e cules, al though more lim ited than the ones pre sented in this ar ti cle: Cs 2, 45 CrO, 46 NbN, 47 CaO, 48 and BaI, 49 all achieved with the same tech - nique, i.e. a mo lec u lar beam crossed by a cw tun able la ser beam. The case of TiO --a mol e cule of as tro phys i cal in ter - est 50,51 -- is an other good ex am ple since its ab sorp tion spec - trum is so con gested (100 lines/cm -1 in av er age) that only sub-doppler ex per i ments can lead to the as sign ment of high ro ta tional quan tum num bers or to the de ter mi na tion of iso - tope shifts Crossed-beam re ac tion dy nam ics ex per i - ments in which prod uct mol e cules are cre ated in their na scent states can also lead to high res o lu tion spec tro scopic mea sure - ments: let s just men tion here the stud ies over IF and ScO mol e cules. 55,56 Re ceived Feb ru ary 19, Key Words Lith ium hy drides; Lith ium dimers; Spec tros copy; Dy nam ics; Tun neling; u-g Sym me try break ing; Rydberg states. VI. CON CLUDING REMARKS Ow ing to the na ture of our sub-doppler ex per i ment and to the ap pli ca tion of com ple men tary tech niques, it has been pos si ble to mea sure the wave num bers of hun dreds of ab sorp - tion lines of lith ium dimers, to as sign them to the B-X sys tem and to study the dis so ci a tion phe nom e non due to tun nel ing through the po ten tial bar rier of the B state. From these mea - sure ments, it has been pos si ble to de scribe the full po ten tial REF ER ENCES 1. Jacquinot, P. J. de Phy sique et le Ra dium (Paris) 1958, 19, Amiot, C.; Vergès J. J. de Phy sique (Paris) 1987, 12, Sloan, J. J. In Atomic and Mo lec u lar Beam Methods; Vol. 2.; Scoles, G., ed.; Ox ford Uni ver sity Press, Connes, P.; Connes, J.; Ben e dict, W. S.; Kaplan, L. D. Astrophys. J. 1967, 147, 1231; Connes, P.; Connes, J. Astrophys. J. 1974, L-29.

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