The exciton model in molecular spectroscopy

THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY M .. KASHA, H. R. RAwLs and M. AsHRAF EL-BAYOUMI Institute of Molecu/ar Biophysics and Department of Chemistry, Florida State University, Tallahassee, Florida INTRODUCTION The molecular exciton model has received its mostextensive development and application in the field ofmolecular crystals1 •2 • More recently, numerous applications to non-crystalline molecular composite systems have been made, including van der Waals and hydrogen-bonded dimers, trimers, and higher order aggregates. Another type of composite system has also been investigated, namely the composite molecule consisting of covalently bonded molecular units, with intrinsic individual unsaturated electronic systems so isolated by single bonds that but little or insignificant electronic overlap between units may occur. It is now weil established that in molecular aggregates and in composite molecules, exciton effects may be observed if sufficiently strong electronic transitions exist in the component sub-units. The result of exciton splitting of excited states in the composite molecule may be the appearance of strong spectral shifts or splittings (which may be of the order of 2000 cm-1) of the absorption bands for the component molecules. At the same time, as a consequence ofthe exciton splitting ofthe excited state manifold, an enhancement of triplet state excitation may result. The purpose of this paper is to present a summary of the various type cases for molecular dimers, trimers and double and triple molecules in the description of the molecular exciton strong-coupling model. Then it will be shown by new experimental examples that, even in those cases where no significant exciton effect is observable in the singlet-singlet absorption spectrum for the composite molecule (intermediate and weak coupling cases), the enhancement of lowest triplet state excitation may still be conspicuous and significant. The ideas which are summarized in this paper have a curious history. Long ago, Kautsky and MerkeP demonstrated experimentally that aggregation of dyes facilitated their action as photophysical sensitizers in photochemical reactions, at the sametime diminishing their fluorescence efficiency. Kautsky attributed these easily demonstrated effects to enhancement of metastable state excitation in the aggregate dye. There is no doubt today that the metastable state he described is the lowest triplet state of the molecules studied. However, he did not distinguish between intrinsic and enhanced metastable (triplet) state excitation, so his interpretations were largely overlooked. Förster in 19464 used the quasi-classical vector model to 371 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY explain the excited state splitting in dye molecule dimers, tentatively suggesting that the metastable lowest singlet state resulting for parallel (transition dipole) dimers was the origin of metastable state emission (phosphorescence) in organic molecules. However, after learning of the Lewis and Kasha triplet state studies 5, Förster in 1949 6 withdrew entirely his suggestion on the nature of the metastable state and replaced it by the intrinsic molecular (triplet) interpretation instead of the intermolecular (exciton) interpretation. Curiously, both aspects were later recognized as being involved in the enhanced emission properties of dimers. Thus, Levinson, Simpson and Curtis 7 showed that in a pyridocyanine dimer, fluorescence was quenched, and greatly enhanced triplet-singlet emission was observed, conforming to the excitation paths predicted by a simple exciton splitting for the singlet excited states. McRae and Kasha8 •9 arrived at the same conclusion as an explanation of some luminescence observations made by Szent-Györgyi on dyes frozen in water-ice10, and showed that, in general, molecular aggregation could Iead to triplet state excitation enhancement by the exciton model. Hoijtink11 has applied the molecular exciton model to the excimer (excited-state stabilized dimer) problem. THEORETICAL FRAMEWORK The physical basis of the molecular exciton model12, the classification of exciton types13, and the detailed origin of the theoretical treatment9 , have been covered in previous papers from this laboratory, in addition to those works cited earlier1 •2 • 7 •11 • In this section we shall present the simplest skeletal outline of the molecular exciton theory for the case of molecular dimers as a complementary paper to those listed above, omitting (electron exchange) anti-symmetrization 2 • The strong coupling case of Simpson and Peterson will be assumed14• The molecular exciton model is a state interaction theory. If the intermolecular (interchromophore) electron overlap is small, so that the molecular (chromophore) units preserve their individuality in the composite molecule or aggregate, the molecular exciton model will satisfy the requirements of a perturbation theory. We may then seek solutions (wave-functions and energies) for the aggregate in terms of the wave-functions and energies for the (in our case, electronic) states of the components. The wave-function formalism is rather parallel to molecular orbital theory, but the physical basis and the interpretations are entirely different. The ground state wave-function of the dimer has the unique description: 'YG = 1/Jui/Jv (1) where iflu represents the ground state wave-function of molecule u and 1/Jv the corresponding one for molecule v (all wave-functions assumed real). The Hamiltonian operator for the dimer is H = Hu + Hv + Vuv (2) where Hu and Hv are the Hamiltonian operators for the isolated molecules, u and v, and Vuv is the intermolecular perturbation potential. The latter is a 372 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-ßAYOUMI coulombic potential, approximated by the point-dipole point-dipole terms of the point-multipole expansionD. The energy of the ground state of the dimer is derivable from the Schrödinger equation as: (3) which factors into (4) The last term represents the van' der Waals interaction energy (an energy lowering) between the ground states ofmolecules u and v, and Eu and Ev are the ground state energies of the isolated molecules. The excited state dimer wave-functions (exciton wave-functions) may be written (5) where ,P~ and ,P~ represent excited state wave-functions for a particular under study (u and v assumed identical) excited state (with energy E!, E~) of molecules u and v; and r and s are coefficients to be determined. The Schrödinger equation for the excited state in question is: (6) Multiplying both sides of this equation by tfo~v, and integrating over Ieads coordinates for molecules u and v, and repeating this process for tfou~, to two simultaneous equations, containing terms symmetrical in (identical molecule coordinates) u and v: Huu( =Hvv) =II Huv(=Hvu) = tfottfovHt/Jttfov dTu dTv fI t/Jtf/JvHtfout/Jt dTu dTv (7) The determinant of the coefficients r and s in these equations is set equal to zero for non-trivial solutions: =Ü Hvu (8) Hvv- EE The roots EE are, in view of the equivalence of terms in (7): E:E = Huu Ei= Huu Evaluating E:E and + Huv with 'Y E = v'~Z) - Huv with 'Yi = v'(~) (tfottfov + tPutfot) (tfotf/Jv - 1/Juf~) (9) E'E by the results in equation (7), we have, owing to the 373 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY intrinsic orthonorma1ity conditions for the wave functions for each molecu1e: E~ + Ev +I I tfottfov(Vuv)tfottfov dru drv + = E~ Ei = E~ +II tfottfov(Vuv)tfoutfot dru drv + Ev +I I tfottfov(Vuv)tfottfov dru drv - -II tfottfov(Vuv)tfoutfot dru drv (10) The last term in the equations (10) is the exciton splitting term: rff =IItfottfov(Vuv)tfoutfot dru drv (11) which in the point-dipo1e point-dipo1e approximation becomes9 rff = Mu.Mv _ 3(Mu.r) (Mv.r) r5 r3 (11a) and represents an interaction energy due to exchange of excitation energy between mo1ecu1e u and mo1ecu1e v. The third term in equations (10) is ana1ogous to the corresponding term in equation (4), and represents the van der Waa1s interaction (energy lowering) between an excited mo1ecu1e u and the ground state mo1ecu1e v. Mu is the transition moment in mo1ecule u, and r is the position vector of the v dipo1e referred to the u dipo1e as origin. If we take the difference ofthe van der W aals terms of eq ua tions (l 0) and (4) as t:.D, we may give the transition energy for the composite mo1ecule as the differences between equations (10) and equation (4): 6.Ecomposite = 6.Eunit + t:.D ± rff (12) This is the characteristic form of the transition energy between states of an aggregate by mo1ecular exciton theory. As will be evident from equation (12) and from the exciton state energy level diagrams which follow in this paper, the exciton model describes a resonance splitting of the excited state composite molecule energy Ievels which were non-degenerate in the individual molecule or light-absorbing unit. The ground state is merely displaced by van der Waals interaction compared with the initial molecule ground states. The molecular exciton wave-functions have the same form as molecular orbital wave-functions, but the dagger represents excitation in the individul molecule, so the nodes are not related to charge distribution as they would be in molecular orbital theory. The nodes in molecular exciton wave-functions correspond to a change in the phase relation of transition dipole. Since mutual phase relations between molecules may be arbitrari1y chosen, the interpretation of the nodes in the wave-functions (9) depends on the phase relation convention9 • In the following section, a graphical presentation is made of equations ( 10) for type cases of various composite systems. In the diagram, t:.D is shown relative to a fixed ground state, and the exciton sp1itting rff is shown as a function of a geometrica1 parameter for the composite mo1ecu1e. 374 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI EXCITON ENERGY DIAGRAMS FOR COMPOSITE MOLECULES In this section we shall review some typical simple cases involving smaU groupings of molecules or light absorbing units. The results will apply equally well to molecular aggregates such as loosely bonded dimers and trimers, or covalently bonded double molecules15 and triple molecules; to satisfy the application of the exciton model, electron overlap between the light absorbing units must be small. The cases we are dealing with could be described by a detailed quantum mechanical treatment9 • However, the molecular exciton modellends itself to the applicant of the quasi-classical vector model, since we may approximate the excited state resonance interaction by considering the interaction of transition moment dipoles electrostatically. Weshall use this description in this section, which is an elaboration of a previous paper16 • Parallel transition dipoles in a composite double molecule lead to the exciton energy level diagram shown in Figure I. The ovals correspond to the molecular profile, and the double arrow indicates the polarization axis for the molecular electronic transition considered (the long molecular axes need not be parallel to the transition polarization axis). To the right ofthe exciton states E' and E" are indicated the vector diagrams which permit (separately) the evaluation qualitatively of (i) the energy of the exciton splitting rf, and (ii) the transition moments M measuring the transition probability between the ground state and the exciton states E' and E" of the composite molecule. Parallel transition dipoles CDCD 2f f tit tl G-~ Monomer Ievels Dimer Ievels c Dipole phase relation Blue- shift case Figure 1. Exciton band energy diagram for a molecular dimer, or a double molecule, with parallel transition dipoles The out-of-phase dipole arrangement corresponds electrostatically to a lowering of energy ( rf negative), so E' lies lower than the van der Waals displaced states of the component molecules; and the in-phase dipole interaction gives repulsion, so rf is positive, and E" is displaced upwards from the displaced origin. The transition moment is given by the vector sum 375 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY of the individual transition dipole moments in the component molecule. Thus, transitions from the ground state to exciton state E' are forbidden, while transitions from the ground state to exciton state E" are allowed (oscillator strength 2j/dimer, or no change in oscillator strength predicted per monomer concentration, in the present approximation; actually hypoand hyperchromic effects are found and predicted in a higher order approximation17·18). As mentioned earlier, Förster used this type of discussion for ee In-line transition dipoles E G~- -- ---2;-· Monomer levels Dimer levels Dipole phase relation Red-shift case Figure 2. Exciton band energy diagram for a molecular dimer, or a double molecule, with in-line transition dipoles dye-dimer excited states in a tentative explanation of metastable state formation in molecules. There are two physical consequences ofthe exciton splitting which may be observed spectroscopically. The first is immediately obvious from the diagram (Figure 1), namely, that the singlet-singlet electronic transition in the dimer will be blue-shifted with respect tothat in the monomer; the blue shifts are calculated tobe quite large for strongly absorbing monomer units, such as dye molecules 7•9 • The second consequence of the exciton band formation is not quite as apparent: that enhancement oflowest triplet state excitation will occur in the dimer, accompanied by a quenching of the fluorescence. Weshallreturn to this problern at the end ofthis section since it involves the triplet electronic states of the molecules which have been omitted from the diagram in Figure 1. Figure 1 corresponds to one ofthe most frequently occurring van der Waals dimers, the London-force dimer between planar conjugated molecules. Dimers of this type have been widely studied and invariably exhibit a blue shift in the range 1000-2500 cm-1, accompanied by a characteristic fluorescence quenching. It is interesting that as one studies theoretically the further aggregation of the dye into the long thread-like polymers, the exciton model predicts that the band splitting will be about 2·4 times the splitting observed for the dimer9. Extensive experimental studies19 in 376 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI the field of spectra of dyes absorbed on polymers, as weil as spectra of dyes absorbed on cellular surfaces (in cytological staining), conform to this description ofthe dye molecule adsorbed as dimer or as polymer. Thus, the phenomena of metachromatia of adsorbed dye are understandable in terms of the exciton model. ln-line transition dipoles in a composite double molecule Iead to the exciton energy Ievel diagram shown in Figure 2. As before, the polarization axis for the electronic transition under study in the unit molecule is shown aligned with the long axis of the molecule represented in oval profile; however, a more frequent case of in-line transition dipoles would occur for the long geometrical axes of the molecule parallel, but with transition dipoles polarized along the short axis of a unit molecule (in-line in the dimer). Oblique transition dipoles G-~ Monomer Ievels Dimer Ievels Dipole phase relation Band-splitting case Figure 3. Exciton band energy diagram for a molecular dimer, or a double molecule, with oblique transition dipoles Again we may use the quasi-classical vector model to analyse the energy of the exciton states produced in the dimer, as weil as the transition moment for transitions from the ground state to the resultant exciton states. From the diagram it is readily seen that the in-phase arrangement oftransition dipoles Ieads to an electrostatic attraction, producing the excited state E' of Figure 2, whereas the out-of-phase arrangement of transition dipoles causes repulsion, producing the state E". On the other hand, the transition moments are finite for electric dipole transitions from the ground state to E', and 0 to the state E" from the ground state. Thus, it will be apparent that the in-line transition dipole case will Iead to the observation of a strong spectral red shift for the transition in the dimer 377 M.S.-9 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY or double-molecule compared with that for a monomer. A number of experimental examples of this type of dimer are known. 18,D Oblique transition dipoles in a composite double molecule Iead to the exciton energy diagram shown in Figure 3. In this case, the in-phase arrangement of transition dipoles for the monomer is attractive and Ieads to a lowering of energy, and the out-of-phase arrangement of transition dipoles is repulsive and causes a raising of the excited state energy for the composite molecule. The transition moments for electric dipole transitions from the ground state to the exciton states of the dimer are in this case both non-vanishing. Characteristic of the exciton model, we find that the oscillator strengths f' and J" for transitions to the two exciton states are polarized mutually perpendicularly. The exciton splitting energy, corresponding to the separation ß. tff = E" - E', is given by: ß. ß = 2IMI2 - 3- (cos cx Yuv + 3 cos 2 0) (13) where M is the transition moment for the' singlet-singlet transition in the monomer, ruv is the:teiltre to centre distance between molecules u and v, cx is the angle between-polariiation axes for the component absorbing units and 8 is the angle made by the polarization axes of the unitrnplecule with the line of molecular centres. The transition moments to the exciton ·states E' and E" are given by: M' = V (2M cos 0) Mn = V(2M sin 0) (14) where the symbols are as defined for equation (13). A characteristic feature of exciton theory is illustrated by cquation (13). It is seen that the exciton splitting energy is directly related to the square of the transition moment for the component molecules. Thus, the greater the intensity of light al?s9!'Ption in the unit molecule, the greater is the exciton band splitting. Tb"e)quare of the transition moment M is a measure of the oscillator strengthffm: the transition. ·· Another characteristic feature of exciton theory is the dependence of the exciton splitting on the inverse cube of the intermolecular distance ruv· Finally, the geometrical parameters enter in the manner characteristic ofthe structure of the composite molecule. Equations (13) and (14) apply equally well to Figures 1, 2, and 3 with a selection of suitable parameters. It may be mentioned that to apply Figure 3 tö an experimental case, one would generally speaking, have to consider a hydrogen-bonded dimer which could fix the transition moment axes in an oblique orientation. To date no experimental examples ofsuch a hydrogenbonded dimer have been studied, although there are numerous possibilities. Coplanar inclined transition dipoles in a composite molecule Iead to the exciton energy diagram shown in Figure 4. This case covers continuously the variation of angle 0 between polarization axes and the line of molecule centres. Thus, 0 degrees corresponds to Figure 2 and 90 degrees corresponds to Figure 1, covering our previous cases. 378 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI Co-planar inclined transition dipoles ~ e ' ' E" , .... ..., I lI I -----tE' I I I I I I I I I I I I G~-ao5srl Monomer Ievels Dimer Ievels Figure 4. Exciton band energy diagram für a molecular dimer, or a double-molecule, with coplanar transition dipoles inclined to interconnected axis by angle 8 The exciton band splitting in this case is given by the formula 8 •9 : ß.C= 2 1MJ 2 (1-3cos 2 8) (15) r~v with the symbols as previously defined. It is evident that for the value of 8 = arc cos lfy3 = (54·7°), the exciton splitting is zero, i.e., the dipoledipole interaction is zcro for this orientation of transition moments in the component molecules, irrespective of intermolecular distance ruv· Non - planar transition dipotes 21 -----rE". I II _______ , E' tlt 't I I !I I I I G~-90o 0 Monomer Ievels {)( Dimer Ievels Blue- shift case Dipole phase relation Figure 5. Exciton band energy diagram for a molecular dimer, or a double molecule, with non-coplanar transition dipoles with angle a bctween molecular planes 379 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY The transition moments for this case are given 9 by M' = 0 and M" = 2 M, where M is the electric dipole transition moment for the transition under study in the component molecule, M' and M" correspond to the out-of-phase and in-phase arrangement of transition dipoles corresponding to the labelling of exciton states E' and E" of Figure 4. Equation (15) and the discussion of transition moments in this paragraph, apply equally well to Figures 1 and 2, parameters. with a selection of~uitable Figure 4 illustrates a common type of exciton band energy diagram wherein an exciton state forbidden for excitation by electric dipole radiation interchanges position on 'the energy Ievel diagram with an allowed exciton state, as a function of geometry of the aggregate. Non-planar transition dipoles in the composite double molecules Iead to the exciton energy diagram showp in Figure 5. This case may be considered as another geometrical variation of the parallel transition dipole case of Figure I. The exciton splitting energy in this case is given by: 2IMI2 (cos cx = -·-- - 3 cos2 8) ( 16) V~ where cx is the · angle between the two molecular planes defined by the diagram in Figure 5 and () is the angle between the polarization axes and the line of molecular centres. The transition moments for electric dipole transitions from the ground state to the two exciton states E' and En vary continüously with angle cx. The vector diagrams show the phase relationship between transition dipoles for the two extreme values of angle cx. In particular, the case of the out-of-phase dipole array Ieads to a progressively more allowed exciton state as the angle cx approaches 90 degrees lltff Cyclic trimer transition dipole arrays ~ I: I I I I . I I I ~ Dipolephase relations for in-plane arrays (Angle 8 indicates rotation convention for out:of-plane correlation) Figu~ ? ~ ·~? ~ . I ': I ,...,.., ,. ""'.,. ... . : J .. t ~ ""' .,. ~.", ... • I . . I 0 Dipolephase relations fbr out-of-plane arrays 6. Transition dipole vector diagrams for exciton model of cyclic trimer or cyclic triple molecule 380 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI {for electric dipole transitions from the ground state). lf the diagram were continued to 180 degrees in cx, it would of course be symmetrical and would feature a lowest exciton state which always has some forbidden character. This is a feature we shall meet again for composite triple molecules. Cyclic trimer transition dipole arrays in a composite triple molecule are diagrammed by the vector model in Figure 6. Each apex of the triangle corresponds to a component molecule or light-absorbing unit, with transition dipoles designated by an arrow. The lowest exciton wave-function (for inplane arrays, upper half of Figure 6) is taken as nodeless, with transition dipoles in phase. For a figure with a threefold axis of symmetry, the next exciton wave-functions are doubly degenerate. Thus, Figure 6 shows a similar pair of one-noded vector diagrams corresponding to single-noded exciton wave-functions. The node corresponds to a change of phase relation in the transition dipole as one goes around the triangle. For convenience, the node has been chosen through the apex in both cases. It is clear that for the in-plane array the nodeless wave-function corresponds to the lowest energy exciton state, while the single-noded degenerate wave-functions correspond to repulsive exciton states. On the other hand, the nodeless wave-function correspondi to an exciton state which is forbidden with respect to electric dipole transitions from the ground state, while the doubly degenerate arrays correspond to allowed exciton states for electric dipole transitions. Cyclic trimer transition dipoles ~-;.' E' I I I I I I I I I ----··' .. I I ·~E' I ~=LG Monomer 9 oo 90 o Ievls~ Trimer Ievels Figure 7. Schematic exciton band energy diagram for a cyclic trimer or a cyclic triple molecule (if. Figure 6 for phase relations and angle of rotation) . Out-of-plane arrays can be considered analogously, corresponding to the lower half of Figure 6. Angle 6 measures the angle between the component transition dipoles and the normal to the plane of the trimer array at the triangle apex. By variation of the angle 6, one may correlate the vector diagrams for the in-plane dipole arrays with those out-of-plane dipole arrays. This correlation Ieads to the exciton energy Ievel diagram depicted in Figure 7. In the monomer the excited states under study are triply degenerate by definition. In the_ 90 degree trimer array the upper exciton state is doubly 381 THE EXCITON. MODEL IN MOLECULAR SPECTROSCOPY degenerate and allowed (for electric dipole transitions from the ground state) and the lower exciton state is non-degenerate and forbidden (correspondingly). In the 0 degree trimer array, the upper exciton state is noridegenerate and allowed (for electric dipole transitions from the ground state), while the lower exciton states are doubly degenerate and forbidden (correspondingly). Thus we see in Figure 7 that the triple degeneracy of the three monomer units is only partially split in the exciton diagram of the trimer and, moreover, the lower exciton state always has some forbidden character and at the extreme Iimits of () = 0 and 90 degrees, the lower exciton states are completely forbidden for excitation by electric dipole radiation. This forbidden character of the lower exciton state will have a profound effect on the excitation pathways in trimeric composite molecules. Excitation pathwaysfor exciton diagrams in composite molecules are typified by the diagram shown in Figure 8 for the parallel transition dipole dimer case 7- 9 • In the monomer, absorption is taken as strongly allowed for electric dipole radiation. Fluorescence will then be commonly observed under favourable conditions. On the other hand, phosphorescence in such cases will be of limited intrinsic quantum efficiency. Such excitation properties are commonly found in many dye molecules and other polyatomic molecules with 7T - 1r* electron transitions. s' 'f"o; II I I I I T : _j_., ___ _ I ' 'I I I II --..1-,.-----·--+-----'- II ' I I I I II I I I A D;I,ll I I (O)f: 2f :A I I F:P I I I P I I I ! I : l : I I I I s'l" T-r I I i s'f"o;I I M Dimer Monomer Figure 8. Paths of excitation between singlet and triplet states without and with exciton splitting (parallel transition dipole dimer case) In the composite molecule, considering the most favourable case for our discussion, in which the lower exciton state is forbidden, we have the probable pathways as shown on the right side of Figure 8. Here absorption to the lower exciton state is forbidden, whereas absorption to the upper exciton state is still strongly allowed. Since the exciton splitting depends on the oscillator strength of the transition, only the singlet states of the composite molecules are split in a gross fashion. The triplet states of the monomer will remain nearly degenerate in thecomposite molecule and are shown as unsplit in the diagram. 382 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI Mter excitation to the allowed upper exciton singlet state of Figure 8, the rapid intemal conversion between singlet states may be expected to completely prevent the fluorescence from the allowed exciton state (back to the ground state), so that the forbidden exciton state will not be excited with high efficiency. Radiative transitions from the lower exciton state to the ground state are formally forbidden (distortions in the aggregate geometry may Iead to a small probability of transition, corresponding to lifetimes in the millisecond range). Consequently, the radiationless intersystem crossing process, which has rate constants on the order of 10 7 sec-1, may be expected tobe the important next step, leading to highly efficient triplet excitation in this dimer. Finally, phosphorescence or triplet state emission in the composite molecule may be expected to proceed with relatively high efficiency. The pathways of excitationdescribed above were proposed by Levinson, Simpson and Curtis 7 in their sturlies of pyridocyanine dimers and by McRae and Kasha 8 •9 in their sturlies of luminescence in molecular aggregates. The descriptions given correspond to the common observation that London-force parallel dimers of dye molecules exhibit a complete quenching offluorescence of the monomer, and a corresponding great increase in the phosphorescence quantum efficiency. We may thus expect enhanced lowest triplet state excitation in composite molecules which exhibit exciton splitting of lowest singlet excited states, especially when the lowest exciton state assumes a forbidden character with respect to radiative transitions. TRIPLET EXCITATION ENHANCEMENT IN COMPOSITE MOLECULES In this section we shall present an experimental study of triplet state excitation enhancement as a consequence of exciton splitting phenomena. The cases considered here will be covalently bonded composite molecules such as the aryl methanes and aryl amines. It will be shown that even in cases where the exciton splitting is quite small, so that the weak or intermediate coupling exciton model14 •16 applies, triplet state excitation enhancement is nevertheless demonstrable. In such cases the exciton splitting will hardly be observable in low resolution solution spectra, but owing to the greater sensitivity of luminescence methods, a gross effect on the phosphorescence fluorescence quantum yield ratio may be observed. Although some previous sturlies have been made on the exciton effect in some of these molecules in high resolution 20°K absorption spectra of crystals 20 • 21 , no luminescence sturlies related to the exciton splitting phenomenon have been previously reported for these molecüles. Our discussion will be qualitative and will relate to the exciton energy Ievel diagrams of the previous section. Diphenylmethap.e and triphenylmethane offer a clear-cut example of the triplet state enhancement through exciton splitting. Diphenylmethane is pictured in Figure 9 in a two-fold axis geometry. Diphenylmethane may be considered 20 as a covalent dimer of toluene, for which the lowest absorption band has molar absorption coefficient of approximately ~: = 200. The lowest singlet excited state of toluene is of Lb type and is pölarized along the short axis ofthe molecule by a factor of2 over long axis polarization 21 (long axis is the CHn-phenyl axis). McClure assumed 20 that the C-CH 2-C angle in 383 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY Figure 9. Diphenylmethanc as a double molecule, showing vertical two-fold axis and symmetric phase relation of transition dipoles for two-fold rotation diphenylmethane is about 112 degrees, close to the tetrahedral angle. He then calculated the exciton splitting as a function of the angle of rotation rf. of the phenyl groups about the C-C bond, measured from the perpendicular position. McClure also calculated the transition moment to each of the two exciton states, and concluded that the higher state always has the higher transition moment. McClure's formula (corrected) for the exciton splitting in diphenylmethane is: 2IMI2 (2·308 sin2 rf. 3- l:!.tff = - 1) (17) 1 uv i i i H I c Figure 10. Triphenylmethane as a triple molecule, showing vertical three-fold axis and symmetric phase relation of transition dipoles for three-fold rotation 384 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI where the cfo is taken to be 0 for the phenyl rings perpendicular to the C-CH 2-C plane, and the rotation of the two rings is taken in-phase; the C-CH 2-C apexangle was assumed tobe 112°. The spectral results in the crystal indicated that cfo is approximately 30° in diphenylmethane. An angle Totuene 14 Figure 11. Total luminescence spectrum of toluene in EPA rigid glass solution at 77°K. Singlet-singlet emission (fluorescence) on right. Triplet-singlet emission (phosphorescence) on left. Corrected emissivity curves, ordinate: arbitrary intensity units; abscissa: wavenumbers X IO-• ofOo would correspond in principle to an exciton band energy diagram ofthe type shown in Figure 1, with excitation paths described in Figure 8. McClure's exciton band energy diagram for diphenylmethane is of a type analogaus to our Figure 5, except that his two exciton states cross at cfo = 41°. Thus, in diphenylmethane, the lower exciton component has some forbidden character, and an enhancement of lowest triplet excitation would be expected. Triphenylmethane is pictured in Figure 10 in a three-fold axis geometry. We may anticipate that qualitatively the exciton band energy diagram for Oiphenylmethane 15 39 Figure 12. Total luminescence spectrum of diphenylmethane in EPA rigid glass solution at 77°K. Singlet-singlet emission (fluorescence) on right. Triplet-singlet emission (phosphorescence) on left. Corrected emissivity curves, ordinate: arbitrary intensity units; abscissa: wavenumbers x J0-3 385 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY this molecule may conform to the diagrams of Figures 6 and 7, although the apex angle correction would alter the quantitative results to a degree. Thus, in this case also, an enhancement of triplet state excitation would be anticipated from the diagrams, in reference to the excitation paths of Figure 8, for a lowest singlet-exciton Ievel of forbidden character.- Triphenylmethane 15 39 Figure 13. Total luminescence spectrum of triphenylmethane in EPA rigid glass solution at 77°K. Singlet-singlet emission (fluorescence) Oll right. Triplet-singlet emission (phosphorence) on Iift. Corrected emissivity curves, ordinate: arbitrary intensity units; abscissa: wavenumbers X J0-3 The experimental results for toluene, diphenylmethane, and triphenylmethane are shown in Figures 11, 12, and 13, and are numerically summarized in Table I. It is seen that the phosphorescence-ftuorescence ratio increases conspicuously in this series, while at the same time the phosphorescence mean lifetime remains relatively constant. . Table 1. Intersystem crossing enhancement in composite molecules (hydrocarbons) Moleeule Intersystem crossing ratio, iPpfiPF Mean lifteime, -rp (sec) 0·94 1-46 4·12 8·8 9·4 7·9 Toluene Diphenylmethane Triphenylmethane It is interesting that a decrease in ftuorescence to the advantage of pho~­ phorescence would not be predictable from the kinetic analysis 22 of excitation paths if exciton interaction were neglected. Thus, the lowest singlet-singlet absorption band in toluene (log € = 2·3), in diphenylmethane 23 (log € = 2·7), and in triphenylmethane 24 (log € = 2·9) becomes progressively stronger; this would suggest that the ftuorescence lifetime should decrease, and that ftuorescence should compete progressively more favourably in this series. The fact that the opposite is the case requires a novel explanation, which is provided by the exciton model. An alternative explanation might have been possible if a spin-orbital 386 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI perturbation enhancement from some upper state interaction in the composite molecule bad occured. But the near constancy of the triplet state lifetimes ( Table 1) clearly indicates that the spin-orbital perturbation is nearly unaffected by the formation of the composite molecule. Figure 14. Tröger's base as a double molecule, showing vertical twofold axis and symmetric phase relation of transition dipoles for two-fold rotation The aromatic amines are more complex to deal with than are the corresponding aromatic hydrocarbons because another phenomenon complicates the luminescence behaviour of these molecules. In a separate study25 it is shown that the presence of intramolecular charge transfer transitions (t- arr type 26 ) in these molecules leads to enhancement of triplet state excitation in comparison with a related hydrocarbon. Nevertheless, as an overlay there is also dernonstrahle an additional triplet state excitation enhancement in composite molecules made of aromatic amine component molecules. Tröger's base is depicted in Figure 14 as a double molecule, with two covalently bonded N,N-dimethylanilines held in a C 2 geometry. In Figure 15 Figure 15. Triphenylamine as a triple molecule, showing planar conformation with symmetric phase relation of transition dipoles for rotation about normal three-fold axis 387 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY N,N- dimethylaniline 14 Figure 16. Totalluminescence spectrum of N,N-dimethylaniline in EPA rigid glass solution at 77°K. Singlet-singlet emission (fluorescence) on right. Triplet-singlet emission (phosphorescence) on left. Corrected emissivitity curves, ordinate: arbitrary intensity units; abscissa: wavenumbers X 10-a triphenylamine is depicted as a triple molecule, with three phenyls arranged about the N atom in a D 3h geometry. The luminescence spectra of N,N-dimethylaniline, Tröger's base, and o-N,Ndimethyltoluidine are presented in Figures 16, 17 and 18, with corresponding numerical data in Table 2. The luminescence spectra of diphenylamine and triphenylamine are presented in Figures 19 and 20, with data again summarized in Table 2. Tröger's base isarather rigid structure, with the angle between transition moments being approximately 18 degrees for short axis polarization (Figure 14). Qualitatively, the exciton band energy diagram will approximate Tr8ger's base 1·0 14 Figure 17. Totalluminescence spectrum ofTröger's base in EPA rigid glass solution at 77°K· Singlet-singlet emission (fluorescence) on right. Triplet-singlet emission (phosphorescence) on left. Corrected emissivity curves, ordinate: arbitrary intensity units; abscissa: wavenumbers X 10-a 388 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI Figure 1, and a very considerable enhancement oftriplet state excitation may be expected. The data of Table 2 confirm this expectation. Table 2. Intersystem crossing enhancement in composite molecules (aromatic amines) Moleeule Intersystem crossing ratio, (f)pf(f)F N,N-dimethylaniline Tröger's base o-N,N-dimethyltoluidine Diphenylamine Triphenylamine 2·01 18·8 2·38 3·26 8·31 Mean lifetime, Tp (sec) 2·8 1·9 2·3 2·1 0·74 Comparing N,N-dimethylaniline, diphenylamine, and triphenylamine, the data of Table 2 and the corresponding figures indicate a pronounced enhancement of triplet state excitation in this series. A comparison of the data of Table 2 with that of Table 1 shows the enhancement effect for triplet excitation ofthe aromatic aminesrelative to the corresponding hydrocarbon, owing to the intramolecular charge transfer state interaction25 (the small phosphorescence lifetime variations reftect this). However, the composite molecule effect is still clearly evident for the aromatic amine series. The oscillator strengths for the lowest singlet-singlet absorption are 0·027 for aniline, 0·19 for diphenylamine, and 0·25 for triphenylamine (methylcyclohexane solvent, 20°C). As in the case of the corresponding aromatic hydrocarbon series, these data would require a decrease of ftuorescence lifetime, with a corresponding decrease in the phosphorescence{ftuorescence quantum yield ratio for the series. The composite molecule effect through the exciton model seems tobe a necessary explanation in this case also. o-N, N- dimethytoluidine 14 Figure 18. Total luminescence spectrum of o-N,N-dimethyltoluidine in EPA rigid glass solution at 77°K. Singlet-singlet emission (fluorescence) on right. Triplet-singlet emission (phosphorescence) on Lift. Corrected emissivity curves, ordinate: arbitrary intensity units; abscissa: wavenumbers x 10-a 389 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY Diphenylamine 14 Figure 19. Total luminescence spectrum of diphenylamine in EPA rigid glass solution at 77°K. Singlet-singlet emission (ßuorescence) on right. Triplet-singlet emission (phosphorescence) on left. Corrected emissivity curves, ordinate: arbitrary intensity units; abscissa: wavenumbers X 10-a In all ofthe experimental cases studied low temperature (77°K) rigid glass spectroscopy was used. An important point to emphasize is the temperaturedependent nature of the phenomenon we have described. If these had been strong-coupling cases, the absorption spectral effects would have been very conspicuous, and the excitation behaviour would have been relatively temperature independent8 • However, here the absorption spectral effects are virtually unnoticeable. Thus, the two exciton levels (the more strongly allowed upper one, and the relatively forbidden lower one, whose existence facilitates the phosphorescence enhancement) must be relatively close Triphenylamine 14 Figure 20. Total luminescence spectrum of triphenylamine in EPA rigid glass solution at 77°K. Singlet-singlet emission (ßuorescence) on right. Triplet-singlet emission (phosphorcscencP-) on left. Corrected emissivity curves, ordinate: arbitrary intensity units; abscissa: wavcnumbers X 10-a 390 M. KASHA, H. R. RAWLS AND M. ASHRAF EL-BAYOUMI together. Probably, in most of the molecules we have studied, the exciton splitting is of the order of k Tat room temperature. Under these conditions, the triplet state enhancement would become progressively more prominent as one lowered the temperature. A study of such temperature dependence triplet state enhancement in composite molecules could serve to give data on exciton splitting in_ weak coupling cases, a datum otherwise difficult to obtain. As an experimental note, we indicate a few essential points on the data handling for Figures 11-13 and 16--20. The emission spectra were recorded with a Perkin-Elmer Model99 recording double-pass monochromator using fused quartz optics and an RCA lP-28 photomultiplier. A Bauschand Lomb grating monochromator (0·5 m F.L.) with a G.E. AH-6 high-pressure inercury arc or a Hanovia high-pressure mercury-xenon arc were used for excitation. The spectrometer-photomultiplier correction was determined by recording the emissivity from a standard lamp provided by the National Bureau of Standards, with conversion of data to quanta per wavenumber interval. The correction factor so determined was applied to all of the emission curves presented. The data of Tables 1 and 2 were then obtained by graphical integration of the corrected curves. Summarizing our presentation, we emphasize that molecular luminescence studies, by their greater selectivity and sensitivity, may be used to detect weak interactions in molecular composite systems, even when such interactions are not detectable in low-resolution absorption studies. Our demonstration of triplet state enhancement in composite molecules suggests important photochemical applications. Instead of using perturbation methods (e.g., heavy atom substituents, or heavy atom environmental effects), triplet state excitation may be increased significantly by building up a composite molecule whose individual units are of interest for photochemical investigation. The expected temperature dependence for weak coupling cases adds a new experimental parameter. CONCLUSION The molecular exciton model, which deals with the excited state resonance interaction in weakly coupled electronic systems, has been described as an interpretative tool for the study of the spectra and photochemistry of composite molecules. U nder composite molecules are grouped loosely bound groups oflight-absorbing units, held together by hydrogen bonds or by van der Waals forces. Another group of composite molecules included in the study consists of covalently bound light-absorbing units. A skeletal outline of the simplest quantum mechanical framework for the description of the model has been presented. A series of explicit exciton splitting formulae has been given for various geometrical arrangements of double molecules, accompanied by the characteristic exciton splitting diagrams and vector model analogues. As an example of composite molecule effects on molecular excitation, a comparison has been made between the spectral properties of toluene, diphenylmethane and triphenylmethane, with an analogous comparison for aniline, diphenylamine and triphenylamine. It has been shown that in composite molecules a significant triplet state 391 THE EXCITON MODEL IN MOLECULAR SPECTROSCOPY excitation enhancement results from the exciton interaction among excited states of the component molecules. Applications to photochemical interpretations have been discussed. We are pleased to acknowledge with thanks a gift qf some aromatic amines by Professor B. M. Wepster qf the University qf Deljt, Holland, which made the completion qf our study possible. References A. S. Davydov. Theory rif lvlolecular Excitons (tl'anslated by M. Kasha and M. Oppenheimer, Jr.). McGraw-Hill, New York (1962). 2 D. S. McC!ure. Electronic Spectra rif Molecules and Ions in Crystals. Academic Press, New York (1959). 3 H. Kautsky and H. Merke!. Naturwissenschaften 27, 195 (1939). 4 Th. Förster. Naturwissenschaften 33, 166 (1964). 5 G. N. Lewis and M. Kasha. J. Am. Chem. Soc. 66, 2100 (1944). 6 Th. Förster. Naturwissenschaften 36, 240 (1949). 7 G. t. Levinson, W. T. Simpson, and W. Curtis. J. Am. Chem. Soc. 79, 4314 (1957). 8 E. G. McRae and M. Kasha. J. Chem. Pkys. 28, 721 (1958). 9 E. G. McRae and M. Kasha. In Physical Processes in Radiation Biology, p. 23. Academic Press, New York (1964). 10 A. Szent-Györgyi. Science 124, 873 (1956). 11 G. J. Hoijtink. Z. Elektrochem. 64, 156 (1960). 12 M. Kasha. Rev. Mod. Phys. 31, 162 (1959). 13 M. Kasha. In PkYsical Processes in Radiation Biylogy, p. 17. Academic Press, New York (1964). 14 W. T. Simpson and D. L. Peterson. J. Chem. Phys. 26, 588 (1957). 15 D. S. McC!ure. Can. J. Chem. 36, 59 (1958). 16 M. Kasha. Radiation Res. 20, 55 (1963). 17 W. Rhodes. J. Am. Chem. Soc. 83, 3609 (1961). 18 M. Kasha, M. A. El-Bayoumi, and W. Rhodes. J. Chim. Phys. 58, 916 (1961). 19 D. F. Bradley and M. K. Wolf. Proc. Nat. Acad. Sei. U.S. 45, 944 (1959). 2 0 D. S. McClure. Can. J. Chem. 36, 59 (1958). 21 R. Coffman and D. S. McClure. Can. J. Chem. 36, 48 (1958). 22 M. Kasha. Discussions Faraday Soc. No. 9, 14 (1950). 23 P. Ramart-Lucas. In Traite de Chimie Organique (Ed. V. Grignard), Vol. II, p. 72. Masson et Cie, Paris (1936). · 24 G. Kortüm and G. Dreesen. Chem. Ber. 84, 182 (1951). 26 H. R. Rawls and M. Kasha. To be pub1ished. 26 M. Kasha. Light and Life (Ed. W. D. McE1roy and B. Glass), p. 31. Johns Hopkins Press, Baltimore (1961). 1 Note added in proof All of the !uminescence curves were determined at comparable settings of the spectrometer thus excluding simple queuehing as an explanation of the phenomenon described in this paper. S92