Con cen tra tion De pend ence of the Fifth-Order Two-Dimensional Raman Sig nal

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1 Jour nal of the Chi nese Chem i cal So ci ety, 2000, 47, Con cen tra tion De pend ence of the Fifth-Order Two-Dimensional Raman Sig nal Keisuke Tominaga a * and Keitaro Yoshihara b a In sti tute for Mo lec u lar Sci ence, Myodaiji, Okazaki, Ja pan and De part ment of Chem is try, Fac ulty of Sci ence, Kobe Uni ver sity, Nada, Kobe , Ja pan b In sti tute for Mo lec u lar Sci ence, Myodaiji, Okazaki, Ja pan and JAIST, Hokuriku, Tatsunokuchi, , Ja pan The con cen tra tion de pend ence of the fifth or der two-dimensional Raman sig nal in ten sity is re ex am ined. The in stan ta neous re sponse of the fifth or der sig nal co mes from the fifth or der sus cep ti bil ity. The de layed re - sponse of the fifth or der sig nal is con sis tent with a gen u ine fifth or der Raman rather than a cas cad ing pro cess of the third or der nonlinearity. IN TRO DUC TION Since Tanimura and Mukamel pro posed fifth or der two- dimensional (2D) spec tros copy, 1 there has been rap idly grow ing in ter est in this spec tros copy This is an op ti cal an - a logue of the well-known 2D NMR tech nique, which dis en - tan gles com pli cated spec tra of many in ter act ing spins by spread ing them along the two fre quency axes. 17,18 In their orig i nal pa per they showed that this tech nique is ca pa ble of dis tin guish ing ho mo ge neous and inhomogeneous con tri bu - tions to low fre quency vi bra tional modes. Fol low ing the first pro posal, the fifth-order time do main Raman spec tros copy re - ceived con sid er able at ten tion both the o ret i cally 3-6 and ex per i - men tally The 2D fifth or der Raman ex per i ment is shown sche - mat i cally in Fig. 1(a). A se ries of five nonresonant short pulses are in ci dent on a sam ple. These pulses are used to cre - ate vi bra tional co her ences in all Raman ac tive modes within the band-width of the ex ci ta tion pulses. Two ini tial ex ci ta tion pulses ex cite vi bra tional co her ence, and af ter a time de lay t 1, a sec ond Raman in ter ac tion al lows the ini tial co her ence to be trans ferred to new co her ences. The new co her ence evolves over a sec ond pe riod t 2 un til the fifth pulse probes it. The sig nal re sults from the fifth or der sus cep ti bil ity (5), which ap - pears at a di rec tion sat is fy ing the phase-matching con di tion, k s = k p - (k 2 - k 2 ) + (k 1 - k 1 ). The ex per i men tal ef forts have mainly in volved prob ing the intermolecular modes of liq uid CS 2, a stan dard sys tem in nonresonant Raman spec tros - copy. 7-14,16 One of the dif fi cul ties in mea sur ing the true (5) re - sponse is avoid ing con tam i na tion from cas cad ing third-order ( (3) ) pro cesses. 13,16,19-25 There are two types of third or der cas cades that can lead to an over all fifth or der sig nal, and they are re ferred to as se quen tial 13,23 and par al lel. 16,25 The lad der di a gram for the par al lel cas cade is shown in Fig. 1(b). It be - gins with the prep a ra tion of vi bra tional co her ences on sep a - rate chromo phores as re sults of in ter ac tions with the first and sec ond pulses of la ser fields. The prob ing in ter ac tion on one of the chromo phores then re sults in a field that is in volved in a prob ing in ter ac tion on the other chromo phore. Since these Fig. 1. (a) A pulse con fig u ra tion of the fifth or der twodimensional Raman ex per i ment. (b) The lad der di a gram of the par al lel cas cad ing third or der sig - nal.

2 632 J. Chin. Chem. Soc., Vol. 47, No. 4A, 2000 Tominaga and Yoshihara pro cesses gen er ate sig nals in the same phase-matched di rec - tion and with the same over all de pend ence on the la ser in ten - (5) sity as the true re sponse, care ful con sid er ation is re quired to iden tify the dom i nant non lin ear pro cess. In our ex per i ment we ex am ined the con cen tra tion de pend ence of the sig nal in or - der to con firm that the sig nal re sulted from (5) and not from the cas cad ing pro cess of (3). In this work we re ex am ine our data of the con cen tra tion de pend ence. De tails of the ex per i - men tal setup and method are al ready de scribed else where RE SULTS AND DIS CUS SION A typ i cal fifth or der two-dimensional Raman sig nal from CS 2 is shown in Fig. 2(a). The sig nal is shown as a func - tion of the sec ond op ti cal de lay, t 2, with a fixed t 1 at 0.5 ps. At t 2 = - t 1 there is an in stan ta neous re sponse re sult ing from third or der sus cep ti bil ity. In this non lin ear pro cess the fifth pulse, k p, acts as a pump pulse ; there fore, only the elec tronic re sponse of (3) con trib utes to the sig nal. At t 2 > 0 an in stan - ta neous elec tronic re sponse ap pears again, which is fol lowed by the de layed nu clear re sponse. The sig nal in ten si ties of these sig nals are pro por tional to the fifth power of the la ser in - ten sity, and we con cluded that the sig nal re sults from (5), and not from the cas cad ing pro cess of the third or der nonlinearity, in the fol low ing way. The de pend ence of the scat ter ing chromo phore den sity was of ten used to iden tify the dom i nant non lin ear pro cess. 20,22 A rel a tive in ten sity of the homo dyne-detected sig nal due to the higher or der sus cep ti bil ity, I (5), with re spect to the homo - dyne-detected cas cad ing sig nal in ten sity, I cas, de pends on the num ber of mol e cules per unit vol ume N and the length of the in ter ac tion be tween the light and mat ter l in the fol low ing way, I cas /I (5) = (l 4 N 4 )/(l 2 N 2 ). (1) This is true only when the polarizability is ad di tive with re - spect to the num ber of mol e cules, and, for ex am ple, Berg and co work ers showed that their sev enth or der Raman echo sig nal from the intramolecular mode de pends on a square of the con - cen tra tion, which clearly shows that the sig nal re sults from the sev enth or der non lin ear sus cep ti bil ity. 26 Since it is very dif fi cult to mea sure ab so lute mag ni tudes of the non lin ear sig nal and in ves ti gate its con cen tra tion de - pend ence, we use the third or der sig nal, I (3) in Fig. 2(a), as an in ter nal ref er ence to study the con cen tra tion de pend ence. We first com pare the sig nal in ten sity of the third or der sig nal I (3) with the in stan ta neous re sponse of the fifth or der sig nal I (5;e), which is prob a bly due to an elec tronic re sponse. We nor mal - Fig. 2. The two-dimensional Raman sig nals from so lu - tions of CS 2 as a func tion of the sec ond time de - lay t 2. The con cen tra tions of the so lu tion and the first time de lay t 1 are shown in each fig ure.

3 Fifth-Order Two-Dimensional Raman J. Chin. Chem. Soc., Vol. 47, No. 4A, ize both the sig nal in ten si ties, I (3) and I (5;e), with re spect to the la ser power, since I (3) and I (5; e) are pro por tional to the third and fifth power of the la ser in ten sity I L, re spec tively, r = (I (5;e) /I L 5 )/(I (3) /I L 3 ). (2) We mea sured fifth or der sig nals from so lu tions of CS 2 with n-hex ane (Fig. 2(b) and (e)) n-dec ane (d), and deuterated meth a nol (b). 9 Alkanes and al co hols do not give any de tect - able third or der nor fifth or der sig nals by them selves in this phase-matching con fig u ra tion. Fig. 3(a) shows a de pend ence of the r value on the rel a tive con cen tra tion N/N 0, where N 0 is the con cen tra tion of the pure CS 2. In Fig. 4 we show im pul sive stim u lated Raman scat ter - ing (ISS) sig nals from so lu tions of CS 2 with n-hex ane. Fig. 4(d) il lus trates the rel a tive in ten sity of the elec tronic re sponse of the ISS sig nal as a func tion of the con cen tra tion of CS 2. Since CS 2 is a polarizable liq uid, there may be an in ter ac - tion-induced ef fect even in the third or der elec tronic re sponse. How ever, Fig. 4(d) shows that the in ten sity of the elec tronic re sponse is ap prox i mately pro por tional to a square of the con - cen tra tion, sug gest ing that a ma jor con tri bu tion to the third or - der elec tronic re sponse co mes from sin gle-molecule polar - izabilities. The cri te rion of eq. (1) can be used to ex am ine whether the fifth or der in stan ta neous re sponse co mes from the cas cad - ing pro cess of the elec tronic (3) or not, since sin gle-molecule polarizabilities dom i nantly con trib ute to the third or der elec - tronic re sponse. The rel a tive value of N al ters from one to 0.18 in Fig. 2. There fore, if the cas cad ing sig nal is dom i nant, the value of r al ters from one to How ever, the value of r stays al most con stant for all the so lu tions, which sug gests that the fifth or der in stan ta neous re sponse has the same con cen tra - tion de pend ence as the third or der elec tronic re sponse. As can be seen from Fig. 3(a) the con cen tra tion de pend ence sup ports the con clu sion that the fifth or der in stan ta neous re sponse re - Fig. 3. (a) The value of r, de fined in eq. (2) and Fig. 2(a), is shown as a func tion of the rel a tive con - cen tra tion N/N 0. (b) The ra tio of I (5;n) /I (5;e) is shown as a func tion of the rel a tive con cen tra tion N/N 0. I (5;n) and I (5;e)) are de fined in the text and Fig. 2(a). The straight line is for an eye guid - ance. Fig. 4. Im pul sive stim u lated Raman scat ter ing sig nals from so lu tions of CS 2 with n-hex ane. The rel a - tive con cen tra tion is fol low ing; (a) pure CS 2, (b) N/N 0 = 0.645, and (c) (d) A rel a tive in ten - sity of the elec tronic re sponse in the ISS sig nal as a func tion of the rel a tive con cen tra tion.

4 634 J. Chin. Chem. Soc., Vol. 47, No. 4A, 2000 Tominaga and Yoshihara (5). sults from Next we ex am ine the de layed nu clear re sponse of the fifth or der sig nal. Gen erally, the nu clear re sponse in the low fre quency re gion is dom i nated by the intermolecular con tri bu - tions. There fore, the sig nal de pends on the con cen tra tion in a com pli cated man ner if many-body ef fects in flu ence the non - lin ear op ti cal re sponse, and the sim ple N 2 -N 4 de pend ence in eq. (1) does not hold in that case. How ever, pre vi ous stud ies showed that a ma jor con tri bu tion to the nu clear re sponse of the third or der op ti cal Kerr ef fect (OKE) sig nals and ISS sig - nals from CS 2 co mes from sin gle-molecule polarizabilities. Nel son and co work ers con cluded that the de layed nu clear re - sponse ob served in their ISS data re sults from sin glemolecule polarizabilities since the short-time dy nam ics change lit tle in their tem po ral form as CS 2 is di luted from 100 per cent to as lit tle as 1 per cent vol ume frac tion. 27 This in di - cates that dy nam ics ob served in pure CS 2 are sim i lar to librational dy nam ics of CS 2 in so lu tion. Fig. 4 tells us that the in ten sity of the third or der nu clear re sponse de pends on the con cen tra tion in a sim i lar way to that of the elec tronic re - sponse, which is also in di cat ing that the third or der nu clear polarizability is mo lec u larly ad di tive in this con cen tra tion range. A sim i lar phe nom e non was ob served by Kenney- Wallace and co work ers who mea sured OKE sig nals from so - lu tions of CS 2 with var i ous al kanes. 28 They sim u lated tem po - ral files of the sig nals by a sum of four com po nents: an elec - tronic re sponse, librational re sponse, in ter me di ate con tri bu - tion, and orientational ani so tropy. They found that the rel a - tive in ten sity of the elec tronic re sponse with re spect to that of the librational re sponse does not change sig nif i cantly in the con cen tra tion range of 0.2 N/N 0 1. Fourkas and co work ers car ried an in stan ta neous nor mal mode anal y sis on CS 2 and sug gested that sin gle-molecule ef - fects do in deed dom i nate the third or der spec trum. 29 Fur ther sup port for this con clu sion co mes from mo lec u lar dy nam ics sim u la tions by Gei ger and Ladanyi on the Ray leigh wing in - ten sity in CS 30 2 and the nu clear re sponse of the OKE sig nal from CS Al though im por tance of the in ter ac tion-induced polarizabilities in these com po nents was sug gested, they showed that the great est con tri bu tion co mes from sin glemolecule polarizabilities. We next plot the rel a tive in ten sity of the fifth or der nu - clear re sponse I (5;n) with re spect to that of the fifth or der elec - tronic re sponse I (5;e) as a func tion of the rel a tive con cen tra - tion. Con sidering the dis cus sion above, the ra tio of I (5;n) /I (5;e) is pro por tional to a square of N/N 0 in a qual i ta tive level if the nu clear re sponse co mes from the cas cad ing pro cess of (3). There fore, the ex per i men tal re sult also sug gests that the fifth or der nu clear re sponse is not dom i nated by the cas cad ing con - tri bu tion. Fur ther more, this in di cates that a ma jor con tri bu - tion of the fifth or der nu clear re sponse co mes from sin - gle-molecule polarizabilities. Cur rently, the o ret i cal ef forts have been de voted to in ter pret (5) in the low fre quency re gion in a mo lec u lar level by mo lec u lar dy nam ics sim u la tion. 5,6 This will clar ify whether sin gle-molecule polarizabilities dom i nate or many-body ef fects con trib ute to (5) in the low fre quency re gion. In sum mary, it is nat u ral to con clude that both the in stan - ta neous re sponse and de layed nu clear re sponse of the fifth or - der sig nal from CS 2 ob served in our ex per i ment dom i nantly re sult from the true (5) com po nent, rather than the third or der cas cad ing pro cesses. AC KNOWL EDG MENTS We thank Prof. John Fourkas for care ful read ing of the manu script and valu able com ments on it. We are also grate ful to Prof. Shaul Mukamel, Prof. John Wright, and Prof. Shinji Saito for fruit ful dis cus sion. This work is par tially sup ported by a Grant-in-Aid ( ) and that on Pri or ity Area of Chemical Re ac tion Dy nam ics in Con densed Pha ses ( ) from the Min is try of Ed u ca tion, Sci ence, Sports, and Cul ture and a JSPS re search grant for the Fu ture Pro gram. Re ceived Jan u ary 25, Key Words Op ti cal two-dimensional spec tros copy; Non lin ear op ti cal spec tros copy; Ultrashort pulsed la ser. REF ER ENCES 1. Tanimura, Y.; Mukamel, S. J. Chem. 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