J. Phys. Chem. 1986, 90, 1027-1033 and presently the differences shown in Figure 12 cannot be assigned solely to the restricted range of initial conditions associated with the oriented reaction. As stated in the introduction, it is nevertheless quite intriguing that the observed distributions for the oriented/aligned reaction can be interpreted as showing more “dynamical c o n ~ t r a i n t ” ~ ~than , ~ ~their . ~ ~ bulk , ’ ~ ~counterparts. Experiments such as these will continue to improve our quantitative understanding of the molecular dynamics of systems undergoing chemical change on PES’s which encourage complicated nuclear motions. The restricted set of initial conditions provides a means of examining a system’s memory of the initial conditions, for a wide range of experimental conditions. We believe, however, that progress will be greatest when experiments and calculations can be integrated, and this underscores the need for accurate PES’s and dynamics calculations.
IV. Summary The past few years have witnessed a continued maturation of research in the area of molecular dynamics. Distinctions between photodissociation, bimolecular processes, surface scattering, etc. are diminishing, as experiments and computational methods become more refined, and experimentalists and theorists work more closely together than in the past. From our perspective, it seems that this progress is, and will continue to be, due to thinking and probing more deeply into molecular physics, rather than simply the availability of a more abundant data base. The main issue of concern in this paper is elementary processes which can be scrutinized with the aid of statistical models, rather than direct (135) R. D. Levine and R. B. Bernstein, Acc. Chem Res., 7, 393 (1973).
1027
processes which are dominated by specificity and exit channel bias. Toward this end, we have chosen a few examples in which bound PES’s of the type usually associated with statistical behavior are encountered and have discussed the likelihood of nonstatistical behavior in these systems. Following excitation, the initial nuclear motions are inherently nonstatistical, and we peruse nascent product states for hints that nonstatistical behavior is preserved throughout the reaction. Since we are trying to establish a system’s memory for more than just Et and Jo, it is important to restrict the initial conditions of the reaction in order to see if these initial conditions are manifest in the products. A few examples are identified which appear promising, and it is our opinion that continued research will be able to bridge the gap between so-called statistically and dynamically controlled processes, thereby providing a unifying understanding. For the sake of brevity, we have referred mainly to work that is quite accessible and familiar to us, when examining specific issues. Omissions are inevitable, since this is not a compendium or review, and to those thus slighted we apologize.
Acknowledgment. We have benefited from discussions with
H. Taylor, F. Crim, A. Zewail, C. B. Moore, R. N . Zare, E. Gleeson, and A. Gleeson. One of us (C.W.) acknowledges the use of the Oxford and Stoke Newington library facilities during the preparation of this manuscript. This research was supported by The U S . National Science Foundation, ONR, and the Collaborative Research Grants Program of NATO (Grant No. RG. 150.81). Registry No. C F 3 C N , 353-85-5; C N , 2074-87-5; N O , 10102-43-9; N C N O , 4343-68-4; HBr, 10035-10-6; H, 12385-13-6; COz, 124-38-9; OH, 3352-57-6; CO, 630-08-0.
SPECTROSCOPY AND STRUCTURE Electronic Energy Transfer from the Charge-Transfer Excited States of Ruthenium(I I ) Polypyridyl Complexes to the Ligand Field Excited States of Chromium(I I I). Weakly Coupled Small Energy Gap Behavior for Bimolecular Reactions‘ R. Tamilarasan and John F. Endicott* The Department of Chemistry, Wayne State University, Detroit, Michigan 48202 (Received: January 23, 1985; In Final Form: October 7 , 1985)
Interpretation of the rate patterns previously reported for the energy-transfer quenching of (*CT)Ru(bpy)32+and (*CT)Ru(bpy),(CN)* (bpy = 2,2’-bipyridyl) donors by chromium(II1) complexes is generally complicated by appreciable overlap of the donor (*CT ’A,) emission and the acceptor (”T2 4A2)absorbance. To avoid the resulting ambiguities of interpretation, rate patterns have been determined for a series of Cr(II1) amine and cyanoamine complexes for which the spectral overlap is very small and only doublet acceptor states are energetically accessible. The resulting quenching rates are much smaller than the expected diffusion limit, and they tend to increase in proportion to the donor-acceptor energy gap, AE. This is an expected result for AE less than the energies of available acceptor vibrational modes due to the increase of the density of acceptor states with increasing AE. When there is appreciable donor-acceptor spectral overlap, a quartet quenching channel appears t o compete, with the net quenching rate a composite of the doublet and quartet channels.
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Introduction The intermolecular transfer of electronic excitation energy is one of the most fundamental concerns in the study of condensed-phase excited-state These processes can limit ( 1 ) Partial support of this research by the National Science Foundation (Grants 8303202, 80-05497, and GP36888X) is gratefully acknowledged.
0022-3654/86/2090-1027$01.50/0
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the efficiencies of devices for the conversion of photonic to chemical energy, and they are among the most basic of chemical reaction (2) Agranovich, V . M.; Galanin, M. D. “Electronic Excitation Energy Transfer in Condensed Matter”; North-Holland: Amsterdam, 1982. (3) Auzel, F. In “Luminescence of Inorganic Solids”; DiBartolo, B., Ed.; Plenum Press: New York, 1978; p 67.
0 1 9 8 6 American Chemical Society
1028 The Journal of Physical Chemistry, Vol. 90, No. 6, 1986
processes. Yet the principles governing the migration of energy in certain types of systems is not well understood.6 It has been recently proposed7~* that there is a “strict similarity” between the energy-transfer and the electron-transfer processes of transition-metal complexes. Thus, the study of energy-transfer rates would provide a unique perspective for testing the theoretical models of electron-transfer reaction processes, since FranckCondon contributions to the rates are generally smaller for energy-transfer than for electron-transfer processes, and the energy-transfer rates can thus be a sensitive index of variations in the kinetic contributions of purely electronic factors. However, there are a number of difficult mechanistic issues which have not been resolved for energy transfer involving transition-metal complexes.” These mechanistic issues have been of concern to us during the past few years,9 and we have begun to suspect that, for example, differences in the patterns found for the efficiencies of energy ~ * in (2E)Cr(PP),3+ Cotransfer in ( * C T ) R U ( I I ) - C ~ ( I I I ) ~and (III)9-i1 (PP = polypyridyl ligand) systems may originate from some basic difference in mechanism. Three mechanisms have been proposed for the donor-acceptor electronic coupling necessary to allow the intermolecular transfer of electronic excitation e r ~ e r g y : I ~ - ’(a) ~ dipole-dipole; (b) dipole-multipole; or (c) exchange. The first of these requires that the individual electronic transitions of the donor and acceptor be dipole a l l ~ w e d , ~and ~ ~is~ not ’ ~ generally -~~ applicable when these processes are either (or both) spin or Laporte forbidden. However, the first or/and second of these electronic coupling mechanisms could be important in heavy metal systems, where spin-orbit coupling gives the electronic transition in the donor some dipole allowed character. The third, or exchange-coupling mechanism, is important in transition-metal donor-acceptor systems where the individual transitions are spin and/or Laporte forbidden and this is the energy-transfer mechanism most readily related to electron-transfer p r o c e s s e ~ . ~ J ~ The rate constant for energy transfer within a collision complex, (*D,A),can be f o r m ~ l a t e d ’ ~ . ~ ~ where g, is the statistical weight for spin multiplicity changes, KO is an (outer-sphere) association constant describing the encounter of donor and acceptor, ( V ) (the electronic matrix element) is proportional to the electron exchange integral, N is the FranckCondon factor, and p is the density of acceptor states. The Franck-Condon factor is most conveniently discussed in terms of electronic relaxation within a collision complex; thus, for inefficient quenching processes KO
*D + A S (*D,A\
(4) Watts, R. K. In “Optical Properties of Ions in Solids”; DiBartolo, B., Pacheco, D., Eds.; Plenum Press: New York, 1975; p 307. (5) Orbach, R. In “Optical Properties of Ions in Solids”; DiBartolo, B., Pacheco, D., Eds.; Plenum Press: New York. 1975; p 355. ( 6 ) Powell, R. C.; Blosse, G . “Struct. Bonding 1980, 42, 43. ( 7 ) (a) Balzani, V.; Bolletta, F.; Scandola, F. J . A m . Chem. Soc. 1980, 102, 2152. (b) Balzani, F.; Indelli, M. T.; Maestri, M.: Sandrini, D.: Scandola, F. J. Phys. Chem. 1980,84, 852. (c) Scandola, F.; Balzani, V. J . Chem. Educ. 1983, 60. (8) Bolletta, F.; Maestri, M.; Sandrini, D. Inorg. Chim. Acta 1984, 87, 19. (9) Endicott, J. F. Coord. Chem. Reo. 1985, 64, 293. ( I O ) (a) Endicott, J. F.; Heeg, M. J.; Gaswick, D. C.; Pyke, S. C. J . Phys. Chem. 1981, 85, 1777. (b) Endicott, J. F. ACSSymp. Ser. 1982, 198, 227. (c) Endicott, J. F.; Ramasami, T.; Gaswick, D. C.; Tamilarasan, R.; Heeg, M. J.; Brubaker, G.R.; Pyke, S. C. J . Am. Chem. Soc. 1983, 105, 5301. (1 1) Examples of the differences in quenching patterns are illustrated in Figures S-1 and S-2 (supplementary material, see paragraph at the end of the paper). (12) Forster, T. Naturwissenschafen 1964, 33, 166. (13) Dexter, D. L.J . Chem. Phys. 1953, 21, 836. (14) Yardley, J. T. “Introduction to Molecular Energy Transfer”; Academic Press: New York, 1980.
Tamilarasan and Endicott a.
b.
Nuclear Displacement
Figure 1. Qualitative potential energy surfaces for a thermally activated reactant-product surface crossing (a) and for the reactant and product surfaces nested (b).
Step 2 can be treated as a unimolecular electronic relaxation process and two limiting categories of behavior may be disting ~ i s h e d :(1) ~ category 1, the activated surface crossing (or strong couplingi5)limit; and (2) category 2, the nested surface (or weak couplingL5)limit. These categories are illustrated in Figure 1, In the strong coupling limit, N is a function of the difference in energy between the donor and acceptor excited states ( A E ) ,and a sum over the product of force constants V;) and square nuclear displacements (AQ,).2-6,’3-’5Thef, and AQ, are selected on the basis of normal vibrational modes required to describe any differences in bond lengths (angles, etc.) between the electronic excited and ground states of the donor or/and acceptor. In this limit kenwill be temperature-dependent, with E , = ( X / 4 ) ( I &?/A)’, where X is a nuclear reorganizational parameter.’ The treatment employed by Balzani and Bolletta and their co-~orkers’~~ is pertinent only to the category 1 limit. An important intermediate situation, category 3, does arise when E, 0 in cateory 1 systems; namely, under these conditions kenvaries directly as ( V i 2 . This is the situation assumed in the earlier7,*studies of (*CT)Ru(II)-Cr(II1) energy transfer, and it may be an appropriate description of organic triplet-Cr(II1) energy-transfer reactionsL6in the range of Ai? where the (triplet singlet) emission and the (4T2 ‘ A 2 ) absorptions do not ocerlap. When the excited states and the ground states are very similar in geometry, the reactant and product potential energy surfaces can be effectively nested and the rates become dependent on tunnelling rather than surface crossing parameters. For large U, in the weak coupling limit (category 2 behavior), kenis expected to be at most weakly temperature-dependent, and iz’is expected However, when AE is small to decrease as IAEJ increases.2~6~’4~i5 compared to the fundamental frequencies of potential acceptor vibrations, kencan increase in direct proportion with AE since the number of vibrational states, available to accept a single quantum of energy ( p in eq l ) , increases as A E increases.’,6 In view of the above considerations, we have sought to establish the pattern of quenching behavior in (*CT)Ru(II)-Cr(II1) energy-transfer systems in which donor-acceptor spectral overlap is very small. Such systems represent a well-defined limit in which the contributions to the phonon-assisted quenching rates can be explored. The more complex systems, such as those with appreciable spectral overlap, can in principle be better evaluated once the behavior of systems at this limit is established.
+
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Experimental Section Materials. Literature procedures were used for the synthesis of the complexes: Cr(NH,),3+,’7 Cr(en),3+,’8Cr(NH3)5C12+,’9 Cr(NH3)5Br2+,20Cr(NH3)5N32+,2’C r ( N H 3 ) 5 0 H , 3 f , 2 0Cr(15) (a) Englrnan, R.: Jortner, J. Mol. Phys. 1970, 18, 145. (b) Freed, K. F.; Jortner, J. J . Chem. Phys. 1970, 52, 6272. (16) Wilkinson, F.; Tsiamis, C. J . Phys. Chem. 1981, 85, 4 1 5 3 . (17) Oppegard, A. L.; Bailar, J. C., Jr. Inorg. Synth. 1950, 3, 153. (18) Pedersen, E. Acta Chem. Scand. 1970, 24, 3362. (19) Schlessinger, G . Inorg. Synth. 1960, 6 , 138.
Intermolecular Transfer of Electronic Excitation Energy (NH3)SNCS2f,22 Cr(NH3)sCN2+,23 t r a n ~ - C r ( e n ) ~ C I , cis-Cr+,~~ (en)2C12+,2sand trans-Cr( [ 14]aneN4)(CN)2+.26,27The Cr(ND3)63+was prepared by repeated recrystallization of Cr(NH3)63+from D 2 0 . The relative intensities of N H and N D stretching frequencies indicated that the final product was >95% deuterated. [ C ( c h d ~ )C13.H20. ~] This complex was prepared by refluxing Cr(THF)3C1328 with trans-(R)-cyclohexanediamine(chda) in dry DMF: 5 g of chda and 3.5 g of Cr(THF)3C13were dissolved under nitrogen in 100 mL of dry dimethylformamide (DMF). The solution was refluxed for 48 h during which time the crude product precipitated. The crude product was separated, washed with acetone, dried, and recrystallized from water. Two visible-UV absorption peaks were observed for C r ( ~ h d a ) ~352 ~ + ;nm ( e = 56.3 M-I cm-l) and 460 nm ( e = 71.2 M-' cm-I). Anal. Cacld for CrC18N6H44013C13: C, 30.4%; H , 6.24%; N , 11.82; Cr, 7.32%. Found: C, 30.6%; H , 6.46; N , 11.7%; Cr, 7.25%. [Cr(dien),]CI,. A procedure similar to the preceding was used for this complex: 5 g of freshly distilled diethylenetriamine (dien) and 9 g of Cr(THF),CI, were dissolved in 100 mL of dry DMF under N,. The solution was refluxed for 30 min, during which time the product precipitated. The crude product was separated and washed with acetone. The purification of this complex was complicated by the presence of two isomers in comparable amounts: the trans or mer and the cis or fac isomers (identified by comparison to the cobalt analogues; see below). These isomers were separated by means of their differing solubilities in methanol. The crude product was dissolved in the minimum amount of water at 40-45 OC and combined with a saturated solution of LiCl in methanol. The isomer identified as cis precipitated first. The mixture was cooled slowly to room temperature and the cis isomer was separated. The filtrate, containing the other isomer was cooled in an ice-salt mixture until the isomer identified as trans precipitated. The separated isomers were purified by recrystallization from water. The trans isomer had absorption maxima at 460 nm ( 6 = 144 M-I cm-') and 358 nm ( e = 73.6 M-I cm-'; for the cis isomer the absorption maxima were at 455 nm (t = 72 M-' cm-') and at 350 nm ( e = 56.9 M-I cm-I). The identification of the two isomers found for Cr(dien)23+was based on the similar solubility and spectroscopic (visible-UV and infrared properties of the Co(dien)?+ and the Cu(dien)?+ analogues.29 Anal. Calcd for t r a n ~ - C r C , N , H ~ ~ 0 , ~ C, C 117.2; ~ : H, 4.62; N, 15.1; Cr, 9.34%. Found: C , 17.1; H , 4.56; N , 15.2; Cr, 9.24%. Anal. Calcd for c ~ s - C ~ C ~ N ~ H , , OC, , ~ 17.2; C ~ ~H: , 4.6; N , 15.1; land Cr, 9.3%. Found: C , 17.4; H , 4.5; N, 15.2; Cr, 9.2%. Even in acidic ( 1 M) aqueous solutions, ~ i s - C r ( d i e n ) ~is~ + relatively unstable (tl/, < 30 min) while the trans isomer is relatively stable ( t l j z 3-4 h). Consequently we have only used the trans isomer in our quenching studies. The procedure of Demas et aL30 was used to prepare cis-Ru( b ~ y ) ~ ( c N ) The , . [ R ~ ( b p y ) ~ ] was C l ~obtained from J. T. Baker Chemical Co. and recrystallized before use. All other chemicals and solvents were of high purity grades or purified before use. Methods. The bimolecular quenching rate constants were determined from lifetime quenching data. Emission lifetimes were determined by using a nitrogen laser pumped dye laser (Molectron UV 1000 and DL 14, respectively). Signals were detected with an RCA 7 102 photomultiplier coupled to a Gould-Biomation 4500
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(20) Mori, M. Inorg. Synth. 1980, 6, 131. (21) Linhard, M.; Borthhold, W. 2.Anorg. Allg. Chem. 1955, 279, 173. (22) Kirk, A. D.; Wong, C. F. C. Inorg. Chem. 1978, 27, 265. (23) Riccieri, P.; Zinato, E. Inorg. Chem. 1980, 853. (24) Brauer, G. "Handbook of Preparative Inorganic Chemistry", 2nd ed.; Academic Press: New York, 1965; Vol. 2, p 1357. (25) Rollinson, C. L.; Bailar, J. C., Jr. Inorg. Synfh. 1946, 2, 200. (26) Miller, P. K.; Crippen, W. S.;Kane-Maguire, N . A. P. Inorg. Chem. 1983, 22, 696. (27) Abbreviations: [ 14]aneN, = 1,4,8,1l-tetraazacyclotetradecane;chda = trans-(R)-cyclohexanediamine; T H F = tetrahydrofuran; D M F = dimethylformamide; dien = diethylenetriarnine. (28) We are grateful to Professor G . R. Brubaker for providing this compound. (29) Keene, F. R.; Searle, G. H . Inorg. Chem. 1972, 1 2 , 148. (30) Demas, J. N.; Turner, T. F.; Crosby, G. A. Inorg. Chem. 1969, 8, 674.
The Journal of Physical Chemistry, Vol. 90, No. 6 , 1986 2.0
1029
a
A, nm Figure 2. Examples of the variations in spectral overlap between (*CT)Ru(II) ground-state emission and the 4A2 4T2absorption of Cr(II1) complexes: a, Cr(NH3),3t; b, Cr(dien)?+; c, Cr(NH3)5N32t; d, Cr(OH,):+.
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digital oscilloscope. Decay rate constants were obtained from the first-order fit of the decay curves. All quenching experiments were carried out in 1 M aqueous N a C F 3 S 0 3solutions at 15 f 0.1 OC for the ( * c T ) R ~ ( b p y ) ~ , + donor and in M HCF3S03solutions at 15 f 0.1 "C for the (*CT)Ru(bpy)*(CN), donor. Corrections for variations in outer-sphere association constants (Le., for association of donor and acceptor) were based on an extended form of the Debye-Huckel equation3' for the ( * c T ) R ~ ( b p y ) ~donor , + and the preexponential term ( 4 ~ N A - ~ / 3 0 0 0only ) for the ( * c T ) R ~ ( b p y ) ~ ( c Ndonor. ), Mean molecular sizes (averaged over three Cartesian axes)3' were used in these corrections. While the absolute values of the calculated values of KOare somewhat uncertain, variations in KOare small and should represent reasonably well the variations of KO with charge and size. Values of KOare expected to vary slightly as temperature increases. This temperature dependence is expected to be small and within the usual uncertainties in determination of activation parameters. Calculations of Racah and Nephelauxetic Parameters: The Racah parameter, B3s;for the (4T2)Cr(III)excited state was calculated from the energies of the 4T2 4A2and the 4Tl 4A, absorptions using33
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E(4T,) - E(4T2)= 7.5B3j + 5Dq - 1/2[225B3j2 + 100Dq2 - 180DqB3,]1'2 where Dq is the ligand field splitting parameter. The nephelauxetic parameter for the (4T2)Cr(III)excited state was obtained from33 /335= B35/Borwhere the Racah parameter for the free Cr3+ion is Bo = 918 cm-l. The nephelauxetic parameter for the (2E)Cr(III) excited state, pss,was calculated by using calculated values of p3jand the 0-0 energy of the ('E)Cr(III) excited state,33
Evaluation of the Spectral Overlap Parameter ( A ) . The broad (*CT)Ru(II) emissions overlap to varying extents with the (4A2) (4T2)absorptions of the acceptors (Figure 2). The relative overlaps were evaluated by a graphical procedure. The observed absorption spectra were plotted (log e vs. A) along with the
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(31) Robinson, R. A,; Stokes, R. H . "Electrolyte Solutions", 2nd ed.; Butterworths: London, 1959; p 227ff. (32) Brown, G. M.; Sutin, N. J . Am. Chem. SOC.1979, 101, 883. (33) (a) Jargensen, C. K. "Oxidation Numbers and Oxidation States"; Springer-Verlag: West Berlin, 1969. (b) Jargensen, C. K. "Modern Aspects of Ligand Field Theory"; North-Holland: Amsterdam, 1971.
The Journal of Physical Chemistry, Vol. 90, No. 6, 1986
1030
Tamilarasan and Endicott
TABLE I: Rate Constants for the Quenching of (*CT)Ru(II) by Cr(II1) Complexes
(*CT)Ru(bpy)3Z+b quencher Cr(NH3)63+ trans-Cr([14]aneN,)(CN),+ Cr(en),'+ Cr(dien),'+ Cr(chda),'+ Cr(NH3),0H23+ Cr(NH,),CN*' Cr(NH3),C12+ Cr(NH3)sBr2+ Cr(NHJSN3!+ Cr(NH3)sNCS2+ trans-Cr(en),CI,+ cis-Cr(en),Cl,+ trans-Cr(en),CI,+ cis-Cr(en),C12+ tr~ns-Cr(en)~(NCS),+ cis-Cr(en),(KCS),+ trans-Cr(en),F,+ Cr (OH ,) 63+
no.
10-3E00(2E),o cm-!
1 2
15.2 13.9 15.02
3
10-7k 4cor' M-l
14.9 14.8 15.1 14.1 14.8 14.8 14.4 14.5 14.3d 14.4d 14.3d 14.4d 1 3.8d 13.9d 13.1d 14.8
4 5 6 7
8 9
IO 11 12
13 12 13 14 15 16
17
s-l
KO,M-'
