Mallick, Prabal Kumar

Mitra, Arindam

IACS Institutional Repository

Indian J. Phys. 6 8 B (1). 47-55 (1994)U P  B- an international journalA model calculation of Raman scattering for resonance excitation to the region of a triplet stateArindam Mitra and Prabal Kumar MallidcDepartment o f  Physics. Burdwan University, Golapbag. Burdwan-713 104, West Bengal, India Received 9 July 1993, accepted 9 November 1993A b stra ct : The contributions from the triplet states to vibrational Raman scattering have been discussed and a calculation, based on the parameters o f  quinoxulinc, is presented for understanding the effect o f  a low lying triplet state on the preresonance Raman excitation profiles o f  several totally sym nietnc vibrations The calculations predict that the triplet state contnbuiion  will depend on the linew idihs o f  the tnplcl state vibrapons. In this connection the contnbutions from som e low lying allowed electronic Stales and their interference effects have also been taken into consideration.I^cy w o r d s  ; Vibronic coupling, spin orbit interaction, Raman excitation profilesP A C S  N o. : 3.  ^ 20.Fb1. IntroductionVibronic coupling is a very clTcclive mechanism I'oi mixing two electronic slates and thereby making an otherwise forbidden electronic transition allowed by borrowing intensities 111 Irom nearby suitable allowed electronic iransiiions. Albrecht used this mechanism and pioneered ihcorelical work |21 on vibrational Raman spectroscopy. He showed »hai there arc three terms (namely A , B and C ) which contribute to Raman scattering. Of these, the A-tcrm is a zero order term which is responsible for enhancing totally symmetric vihralionsdbr tuning the excitation lo the resonance region of an allowed electronic transition The validity of the other two terms has been verified in several cases [3-11 \. In Albrecht formulation forbidden clccironic states generally do not contrihuic lo Raman inlensiiies except in some special cases where the conirihuiion from the C-lcrm becomes impoitant due lo presence of suitable low lying states. But in the last two decades several experimental evidences have been found which indicate (hat in some cases forbidden electronic .states do contribute significantly. Sic\r\ etui 112]1994 I ACS48 Arindam Mitra and Probed Kumar Mallickfound antiresonance of some totally symmetric modes of transition metal complex ion for resonance excitation to the absorption maximum of a Laporte forbidden transition. Zgiersky[13] interpreted this phenomenon in terms of second order perturbation theory. Korenowsky etal [14] reformulated this theory and applied it do the V\ mode of benzene molecule. They predicted a resonance or antiresonance effect for this mode for excitation in resonance with the symmetry forbidden electronic transition ^  which got support from the experiment of Asher and Johnson [15]. Henneker etal, using numerical approach and nonadiabatic term [16,17] obtained theoretical excitation profiles. They also considered a system [17] where vibronically coupled allowed and forbidden electronic slates exist. Okamoto and co-workers [18] included the contribution of forbidden electronic state for explaining the experimentally observed Raman excitation profiles of tetradesmethyl- carotine aggregate even when the excitation is tuned to the allowed electronic transition. Ito et al[\9] and Hirakawa and Tsuboi [20] discussed the contributions of forbidden transitions from preresonance Raman experiment. Okamoto [21,22] showed that forbidden electronic states may contribute to Ramcn intensities through second order terms. Several works on enhancement of combination and overtone bands in the Raman spectra have been done for excitation to the region of fofbidden electronic transition. Aramaki and co-workers [23] reported a detailed analysis of the fundamental, overtone and combination Raman intensities of the 0 - 2^ modes of copp>er tetraphenyl porphyrin. Ohta and Ito [24] and Ziegler and Hudson [25,26] studied the overtones and combinations of Vg and Vp of benzene.In 1971, Rimai etal [27] found peaks in the Raman excitation profiles of vitamin-A (irans-rctinal, tran.s-retinol) and Napthalene at positions where no peaks were obtained in the respective electronic absorption spectra. They showed very convincingly that these peaks correspond to the 7, transition in the respective molecules. Same kind of observations was al.so observed in rctinylidenc Schiff base [28]. In the present paper,*we have introduced the contributions Irom the triplet states to Raman intensities within the frame work of damped Kramcrs-Heiscnbcrg-Dirac (KHD) formula using spin-orbit mixing of state vectors in the Crude Bom Oppenheimer (CBO) adiabatic basis set and made a model calculation for Raman excitation profiles (REP) in order to understand the phenomena of resonance scattering in the vibrational manifold of a triplet stale.2. TheoryTo describe vibrational Raman effect, a crude adiabatic Born-Oppenheimer (C B O) basis set is intrcxJuccd as a zero order state.Tlie total .state vector|5..v) = |5).|.v),where the capital letter denotes the electronic part and the small letter corresponds to a vibrational level of the respective electronic state. Remember that the electronic state vectorA model calculation o f  Raman scattering fo r  etc 4915) is a CBO state Le. this wave function corresponds to equilibrium configuration. With this basis set the scattering tensor for a Raman transition from an initial vibrational level 1«) to a final level |v) of the ground electronic state |C) becomes [29].M . a.o, = C/M I I/ I VfiGu -(2)Here, = {G\Mp\l) is the p-th component of the transition dipole matrix, r,, is thelinewidth of the state |//) and for simplicity the linewidths of the initial (|G«)) and the final (|Cv)) levels have not been included. For. resonance and near resonance excitation (ICm) —»I f/)), the first term in the square bracket is most effective. The contribution from the second term becomes significant for non-rcsonant excitation.Let us now consider the case for which the excitation is in resonance or near­resonance with a triplet stale |7). For most molecular systems, the ground electronic state is a singlet state. Singlet-triplet transition is forbidden in the Zerocth order but becomes allowed in the higher order due to mixing of singlet and triplet states through spin-orbit interaction (301. Thus, the transition moment (A/)ot becomes{S\Hso\T)( M ) o t  =  { G \ M \ T )  =  X  r  F (3>where |5) is an allowed singlet state and the spin orbit interaction Hamiltonian is given by [30]H,n =2e - I S (4)2m c — —  r,,where I, and S, are respectively the orbital and spin angular momentum operators ot the i-\h electron at a distance r/^ , from the -^th nucleus with atomic number In eq. (3) we have neglected the mixing of the ground electronic state |G) with others.Thus, the contribution of 4-ierm [31] to the polarizability tensor for resonance or near resonance excitation becomesI11h ^  VT^.,.-Vn-iTr, ''Ttc.u -  •'0 -  ‘ ‘n § ^ . S- (^7 ■  ^.v)(^7 -  )(5)50 Arindam Mitra and Prabal Kumar MallickHere, all the small letters are the vibrational levels of the corresponding electronic states denoted by capital letters. Eq. (5) indicates that the scattering tensor becomes appreciable if and only if the resonating triplet state |7 ) has at least one nearby allowed singlet state with sufficiently large spin-orbit interaction between them. But under such condition the preresonance contribution from the nearby allowed singlet slate becomes important. For resonant excitation in the region of such a triplet stale, the resonance and preresonance contributions may be compared from eqs. (2) and (5). For preresonance contribution only the A-term from the resonant part (first term in the square bracket of eq. (2)) is considered. Thus, we geta ResPre Res{»so) Er --i2S^sCii 0^ -/r/Tr(6 )For aromatic heterocyclic (oxygen and nitrogen) and carbonyl molecules (30,32) {Hso) = 10 cm ', -  Er = 1000 cm"', thenC^IResJ’re Res I Or(7)7>Thus, wc ‘icc that triplet linewidth plays an important role in determining the magnitude of the resonance contribution. This is expected to be very significant in supercooled supersonic jet molecules. Thus, there is a possibility of finding the triplet stales, which arc inaccessible by other methods (like electronic absorption or emission speclro.scopy), by examining the REP of such molecules.3. A model calculation and discussionExcitation frequency dependence of the intensities of different normal vibrations of qumoxahne molecule in Raman scattering was previously studied by Amin/.adch gtul |33). In order to lest the above ideas, we have used this molecule as a model system and calculated REPs o! some totally symmetric vibrations and critically examined the nature ol the profiles near the lowest singlet triplet transition.The low lying electronic states of the molecule are shown in Table I. The lowest triplet state at 2I4S0 enr’ i*- a triplet of ;r;r*-iype character |34|. Of the singlet stales only the lowest one IS an tin -state ol symmetry Hence this is the only singlet slate which can mix significantly with the above triplet stale through spin-orbit interaction (35). The /-values of different GY= Sa) —> S, transitions, their directions of polari.salion and ab.solute magnitudes of the transition dipole moments in some arbitrary unit are afso shown in Table I.Since we are considering only totally symmetric vibiations, only the diagonal elements and a,-) ol the polarizability tensor (Sec Table I) will contribute to their Raman intensities. The triplet, \T) and the lowest singlet, |5 .) stales will contribute to cl. and theA model calculation o f  Raman scattering fo r  etc 51other singlet states to the -component. The two components are (considering both resonance and off-resonance excitation simultaneously)Table 1. Particulars about some low energy electronic states of quinoxalincandElectronic states * (symmetnes)Energies . cm~*/-values of different G —» Sf transitions with their directions of polari­zation indteated within tlic bracketsAbsolute values of the corresponding transition dipole iTK)iiicnts in some arbitrary unit ^G = -S,(U,) 07-{’a ) 2148027070 0 0174''(Calc Z) 0 4CXX)i2 ( 'A ) 32268 0 130 (X) 1.000041158 0 ■«05 (X) 1 3245■v^ Ca ) 51 (XX) 0 606 (X) 1 7174" [34. 39, 41JThis value is calculated Irom the data given in the rcicrence (34J ^ These values are calculated from the t<nmula ^GS, -  const 'V7.V(sk y z iFAT,)-FAS.)1( - /)c;i ■*' '^ 0(v|,s,)(.V||h)-  '^ 0 - ‘h f)_______ 1_______(8a)X  sl» ) (8b)Here one thing is worthy to mention. Since we have calculutetj REP over a wide range of <-'xciiation frequencies, we wanted to express the intensity by a single formula for both52 Arindam Mitra and Prabal Kumar Mallickresonance or near resonance and off-resonance excitation. This is the reason for using both the resonance and the off-resonance parts of the scattering tensor in eqs. 8(a) and 8(b). Using independent mode approximation [36], the multidimensional overlap integral may be reduced to the product of one dimensional integrals. Neglecting the distortion of the excited state potentials, the one dimensional overlap integrals may be obtained from the recurrence relations of Manneback [37]. For small displacement of the excited state potential minima with respect to that of the ground slate, it can be shown [38] that (for excitation of the fundamental vibration of the a-th nonnal mode)(v|/> < /|m) = for •/„ = 0 = - a ', for /. = 1(9)where is the vibrational quantum number associated with the a-th normal mode in the excited electronic state | /) and is the displacement of the potential minimum of the excited stale I /) with respect to that the ground state along the cz-th normal mode of vibration. Thus, eqs. 8(a) and 8(b) become2uCOG\ (" = L ,i E(T)~E(S,)[ ( ''TOGO -  ''o - > h ) {  VJOGO +  n, -  V'o -  '^ r )  '' {^7-oco +  V o - i ' ^ r )  { v t o g o  ~ ' ' a  +(^06-0 -  V'o -  ‘h, ) ( ‘’sooo + n, -  0^ -  'Ti- )( -  'Ts,)(V.VH,,, -  V'„ + v„ -  (rv,)(lOa){% m  -  ‘'o - ‘h , ) ( +  n, -  »'« - ‘h . )( ''s,0G0 + 0^ -  ‘h , )( ‘'s.oGo -  K, + -  '■ h , )(I Ob)A model calculation o f  Raman scattering fo r  etc 53Here, we have assumed = r-p and = r^, = Thus, we havecalculated Raman intensities in some arbitrary unit Le.C c .  = C ( v o - v j ' ‘ [ |(a ^ )“o c ifaGOG I ( 11)In eq. (11), not only the diagonal contributions from individual states but also the interference effects of the contributions from appropriate states have beeh taken into consideration. Expressions similar to Clark and Dines [36J for the interlerence terras, appearing from both the resonant and off-resonant part of the scattering tensor, for intensities have been used. Since we have special interest in the region of resonance excitation to the G —► T transition, the linewidih of triplet state (tp) will play some in^rtant role whereas the effect of the linewidths of the singlet states are practically negligible. Thus we have calculated REPs of some totally symmetric vibrations of quinoxaline of fnequencies 532, 758, 1204, 1367, 1415 and 1570 cm"' for some selective values of the parameters : <Hso> = 15 cm“‘ and Tp ^  10, 1 and 0.1 cm"*. The calculations are shown in Figure I. For each normal vibration, the intensities arc normalized relative to that asstxriated with the excitation frequency ( Vq =s 20490 cm"*). The results arc compared with the corresponding observed profiles f33). The fitting isF iK urc I. C alcuiaicd Raman excn a iion  profiles ol som e totaily sym m eiric vibrations ot c|utno\alinc a .^32 ciu * b 758 cm  c 1204 cm  d 1^67 cm  *, c 1415 cm  * and I 1570 cm  ‘I Raman cxcifaiion pmfdcs ;\rc calculated lor r ; = 10 and 1 cm  ' ( I ) and 0  I cm  ' < 2 ) | .more or less fair. In order to sec the effect of triple! state linewidth on the Ram^n scattering, we have calculated REPs for three values of Tp mentioned above. They arc lound to be identical except at exact resonance {i,e. at Vq »= and Vri)Oo 4- v j  where resonanceenhancement is predominant for the lowest value ot Tp = 0. I cm * This means thatb8B (8)54 Arindam Mitra and P ratal Kumar Mallickmolecules, possessing such order of triplet state linewidth, resonance enhancement in the region of the triplet state may be observed. This possibility was previously pointed out by Mallick [40]. This is expected in supercooled molecules in the supersonic jet.In this model calculation, we have assumed that the shift of all the excited state potential minima with respect to that of the ground state are equal. This may be one of the reasons of having results not in absolute agreement with observation. Exclusion of the distortion of excited state potential may also yield some error in calculating REPs. Besides these, we have found that contributions from the |5 ,) and \T) states interfere significantly only in the resonance or near-resonance excitation to the triplet state |T). This interference is both constructive and destructive depending respectively on the excitations lying beyond and below the resonance. The contributions from the other three singlet states belongihg to the symmetry species interfere constructively significantly (specially [53) and [54) with 152)).R e fe r e n c e sf l]  G Herzberg and E T eller 1933 Z  PhysiL Chem. B21 4 1 0  [2J A C Albrecht 1961 /  Chem. 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A Model Calculation of Raman Scattering for Resonance Excitation to the Region of a Triplet State

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A Model Calculation of Raman Scattering for Resonance Excitation to the Region of a Triplet State

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