Photoproduct Formation for Cr(en)?+ and Cr(NH3)&12+
The Journal of Physical Chemistry, Vol. 83, No. 16, 1979
Rate of Primary Photoproduct Formation for Aqueous Cr(en):+
2097
and Cr(NH,),CI*+
R. Fukuda, I?. T. Waiters, H. Macke, and A. W. Adamson* Department of Chemistty, University of Southern California, Los Angeles, California 90007 (Received February 22, 1979)
High energy pulsed laser photolysis at 530 nm shows that in the case of aqueous Cr(en):+ there is both a prompt and a delayed appearance of primary photoproduct, Cr(en)z(enH)(H20)4+ (B). The latter grows in with the lifetime of emission from the first doublet thexi state, DlO. Analysis of the variation of the ratio of delayed-to-promptabsorbance change indicates that the first quartet thexi state,,:Q is formed with 70% efficiency and then reacts to give B with a yield of 0.17. DI0is produced with 30% efficiency in a fast intersystem crossing, the~ ~primary +, and then reacts to give B directly with a yield of close to unity. In the case of C T ( N H ~ ) ~ C photoreaction gives C ~ S - C ~ ( N H ~ ) ~ ( H ~ O )The C~~ + (AC). appearance time is 1M in Co(I1) or Fe(II),6and for ones 0.01-0.1 M in hydroxide.' However, the monitoring traces obtained on laser pulse photolysis of such systems were complex in nature, with nonexponential growths or decays in absorbance, and on time scales unrelated to the D,O emission lifetime. Several types of experiments were carried out with alkaline solutions. There is complete emission quenching in 0.1 M sodium hydroxide (and 0.25 M Cr(en)?+), as r e p ~ r t e d . ~ The monitoring traces changed on sequential flashing, however. In a second series, the solution was 0.002 M in hydroxide and 0.09 M in complex, and was prepared with boiled water, nitrogen degassed, and sealed against exposure to air, to avoid any pH change due to absorption of atmospheric carbon dioxide. The emission lifetime was about 60 ns, but lengthened and became complex on sequential flashing. There was still a possibility of carbonate impurity in the reagent sodium hydroxide, and we felt that the effect of carbonate ion should be investigated directly. For this reason, and to minimize any pH change due to photolysis, some experiments were made with a carbonate buffer a t a pH such that hydroxide quenching was negligible. A solution 0.02 F each in sodium carbonate and bicarbonate showed a pH of 10.05, but on making the solution 0.09 F in complex, the pH dropped to 9.4. The effect could be due to displacement of the carbonate hydrolysis equilibrium by ion pairing with the complex. The emission lifetime for this solution was -40 ns, and since the complex was in excess, there must have been dynamic as well as possible static quenching. Similarly, for a solution 0.005 F in carbonate and in bicarbonate, but at essentially the same pH and complex concentration, the
I
'
I
400
1
I
500
I
I
600
Figure 7. (a) Plot of A = (tAC- tC) vs. wavelength, solid line, left from abscissa scale. Points with error bars are for A' = (D, - DO)acU monitoring experiments, right abscissa scale. (b) Plot of A = (eHCeAC) vs. wavelength, full line, letl abscissa scale. Points with error bars - D o h- (0,- Do),,] from monitoring experiments, are for A' = [(Dm right abscissa scale.
emission lifetime was 130 ns. By comparison, the lifetime for the complex in a pH 9.4 solution with no added carbonate or bicarbonate was virtually the unquenched value (1.7 g s a t 21 "C). Because of the number and complexity of these various effects, they were not pursued in detail. It does seem clear that chemical events more complicated than simple hydroxide quenching were occurring, and ones which made unreliable any conclusions from the monitoring traces about the extent of primary photoproduct formation or its appearance rate. Cr(NH3)&t2+. The initial experiments were carried out with unbuffered solutions of Cr(NH3)5C12+ at their natural pH of about 6. Monitoring a t 580 nm showed a prompt absorbance increase, and a slow one with a grow-in time of long nanoseconds. However, in acidic solutions only the prompt absorbance increase was present. Monitoring experiments were then carried out in solutions buffered at various pH's. To anticipate the discussion, we identify the prompt and slow absorbance changes as due to the respective processes Cr(NH3)5C12+-..%cis-Cr(NHJ4(HzO)Cl2+ C AC
(prompt) (2)
C ~ S - C ~ ( N H ~ ) ~ ( H+~BO+ )C~~+ AC Cr(NHJ4(0H)C1+ + HB+ (slow) (3) HC where B and HB+ are the buffer base and acid species, respectively. The hydroxy-chloro complex, HC, is probably the cis isomer, but this was not determined. In acidic media, the total absorbance change in a monitoring experiment, ( D , - Do), should be proportional to the extinction coefficient difference (eAC - ec), while in basic media, the change should be determined by ( e ~ c EC). That this is essentially the case is shown in Figure 7. First, the variation of the total absorbance change on pulse photolysis of a pH 2 solution closely parallels that of ( q c - E C ) , except at the shortest wavelengths. Further, as shown in Figure 7b, [(Dm- DO)base - ( D , - DO)BCidl closely parallels the variation in [eHC - eAC), again with deviation setting in at the shortest wavelengths. This deviation is discussed further below; the rest of the spectral agreements are satisfactory.
Photoproduct Formation for Cr(en);+
The Journal of Physical Chemistry, Vol. 83, No. 76, 7979
and Cr(NH3)&I2+
A second test of the correctness of reactions 2 and 3 consisted of a series of laser pulse photolyses in variously buffered solutions. If the final product is the equilibrium mixture of AC and HC species, then (Dcc - DO)pH - ( D m - D o l a c i d F= (D- - DO)base - ( D , - DO)acid Ka + (H’) Subscripts acid and base are for data at a sufficiently low and sufficiently high pH, respectively, that the photoproduct was entirely in the AC and HC forms, respectively. The values of F obtained from the monitoring data at 580 nm are included in Figure 5. These values were always corrected for any small variations in the laser pulse energy, as determined by the photodiode trace. In alkaline solutions, where it was most apparent, the grow-in of the slow absorbance increase at 580 nm was exponential. That is, the equation [ ( D m- D t ) / ( D , - D i n ) = exp(-ht) was obeyed). The grow-in time, l / h , was 100-130 ns for a solution a t the natural pH and ranged downward in buffered solutions, depending on the buffer and its concentration. These variations were not explored in any detail.
Discussion Cr(en)t+.The various processes to be considered, shown in Figure 1, were described in the Introduction. Those involving Dlo or Q: as reactant can be considered as ordinary thermal reactions obeying, for example, transition state rate theory; D10 and Ql0 are postulated to be good thermodynamic species.27 The reaction kbiw
Di0 ‘ki,&io
(5)
is essentially one of isomerization, albeit with a spin change. Also, the quantity fisccan be written as a ratio of rate constants. However, fpiscis merely a branching ratio during thermal equilibration. We can, for the moment, avoid any assumption as to the relative importance of pisc vs. isc as the route whereby D t is formed, and as to whether product, B, is produced by direct reaction from D t , or results from bisc and reaction from Q .: The kinetic analysis of the monitoring experiment is as follows. Before the laser pulse, there is concentration (A), of complex and, approximating the monitoring beam path length as 1 cm, optical density Do = (A)OtA. Immediately after the laser pulse, we have Din = (A)i,tA (Dl0)incD (B)int~, where ED is the extinction coefficient for ESA (by D t ) . We assume that intersystem crossing is prompt, so that (D,Olin= fZa where Z, denotes the moles per liter of light quanta absorbed by A from the laser pulse, in the volume monitored. The prompt product formation is assigned to a fast reaction from directly formed Q?, (B), = Za(l -f)+Q’, where 4Q’is the fraction of Ql0 exiting by chemical reaction to photoproduct. Finally, (A), = (A), - I , + Za(l - f)(lAt long times, that is, after the complete grow-in of the slow absorbance change, D , = (A),t* + (B),tB, where (A), = (A), -Ia+ Za(l - f)(l - 4 ~ ’ + ) Z j ( 1 - 4D’) and (B), = Za(l - f)4 &I + I& D’; 4 D’ is the fraction of DIo that exits by chemical reaction to photoproduct. From emission studies, (Dl0) = (D?)h exp(-tlr,). Algebraic manipulation shows that (D,- D J / ( D m-Oh) = exp(-t/rp), rp.= 7., That is, the slow absorbance change should grow in with the same lifetime. That this is what is observed is a confirmation of the general correctness of the reaction scheme. Further manipulation of the above relationships gives D m - Din - 4 ~ ( -y 1) + f(1 - 6) R= (6) $Q(Y - 1)- f ( 1 - 6 ) D i n - Do
+
+
2101
where 4 D = f4 D’ and is that portion of the overall quantum yield due to reaction from or through D ;: similarly, 4 Q = (1- fl4 and is the yield due to reaction from directly formed Q1 , Also, 4 = 4 D 4Q.The quantities y and are the extinction coefficient ratios t g / q and C D / q , respectively; 6 is zero if there is no ESA. If y is large compared to unity (or to 6, if 6 > l),eq 6 reduces to R =
Qd,
4D/4
+
Q-
Our results are shown in Figure 6. In the wavelength region 580-610 nm, y is large and R should be independent of wavelength, as observed. We discount the importance of 6 for two reasons. First, 6 should vary with wavelength, and were it large, such variation should make R wavelength dependent, contrary to observation. Second, were 6 large, I , would not be proportional to the laser pulse energy, and neither would the monitored absorbance changes. No such dependence on pulse energy was observed over about a twofold variation. The increase in R at 620 nm is expected since y is now small enough that the f terms in eq 6 cannot be neglected. The solid line in Figure 6 is calculated for f = 0.3, 4 D’ = 0.88, and $&I = 0.15, assuming the literature value of 0.37 for 4 (see ref 1). We conclude that, in the wavelength region 580-620 nm, 6 is not important, and that the above parameters describe the photochemistry. The relatively precise R values at around 580-600 nm give 4 D and 4 Q as 0.26 and 0.11, respectively, to about 5% relative error. Although larger, the error limits in R at 620 nm still place f as 0.33 f 0.09. We can thus conclude that the range of $D‘ is between 0.64 and 1.00 or 0.8 f 0.2 and that of 4Q‘, between 0.14 and 0.19, or 0.17 f 0.03. The ratio 4 D / 4 of 0.70 f 0.03 is somewhat higher than that found in quenching studies but, within our error limits, should be the more reliable. For example, if quenching encounters induce chemical reaction, too low a quenchable yield will be reported. This could be true in the case of OH- as quencher, where for around 530-nm irradiation only about 35% quenchable photolysis is rep ~ r t e d .There ~ are, in addition, the chemical complexities suggested by our monitoring and emission results. The 60% quenchable photolysis found for Co(I1) and Fe(I1) as quenchers (and with shorter wavelength irradiation)6could be in error either because of noninnocent quenching or because the high quencher concentrations needed (>1M) in effect altered the nature of the medium. The present results answer in part the questions posed in the Introduction. First, we have by direct measurement provided an upper limit to the lifetime of Q?;r(Q:) 55 ns in view of the closeness with which the prompt absorbance increase follows the integrated laser pulse. Second, the path of bisc and reaction from Qt cannot be important. This path requires that 4 D ’ be 5 4 i . That is, the efficiency for no path for chemical reaction to products that passes through QIo can exceed the efficiency of reaction from Ql0 itself. Allowing for our error limits, we found that the majority path for disappearance of DI0 is that of direct chemical reaction; this conclusion is confirmed by the quantitative considerations that follow. We thus rule out bisc as a reaction of major importance. This same conclusion was arrived a t on a more general basis, from emission studies.12 Emission rules for Cr(II1) complexes were proposed: Rule 1. For complexes with six equivalent Cr-L bonds, the emission lifetime in room temperature fluid solution decreases with decreasing ligand field strength. Rule 2. If two different kinds of ligands are coordinated, the emission lifetime will be relatively short if that ligand which is preferentially substituted in the thermal reaction
2102
The Journal of Physical Chemistry, Vol. 83,
No. 16, 1979
lies on the weak field axis of the complex. A rationale for these rules is that thermal (as opposed to antithermal) photochemistry likely occurs from D .: In related studies,'l it was specifically proposed that the emission lifetime of Cr(II1) complexes in fluid solution is determined by the rate of chemical reaction from D10 rather than by nonradiative relaxation to the ground state or by the bisc rate. Our results confirm this proposal in the case of C r ( e r ~ ) ~the ~ + ;emission lifetime is mainly determined by the rate of chemical reaction of D10 to photoproduct, k,, = 5.4 X lo5 s-I at 20 0C.12,28 The temperature dependence of the emission lifetime, and hence of k,,, gives the frequency factor A,,, A,, = 5.4 X lo5exp(10000/293R) = 1.6 X 1013s-1,29 This is in the normal range of values. We are not able to give a definitive answer to the question of whether the f value of 0.3 should be attributed to pisc or to isc. If the latter is the case, some rate constant analysis is possible, however. Referring to Figure 1, we know that (km' + k,; + h,,,) k 2 x los s-' since the prompt product formation occurs within the time of the laser pulse. Further, since f,,,is now assigned as 0.3, (km' h,;) N 2.3. k,,, whence h,,, 2 0.6 X lo8 s I. In fact, by using a 5-ns excitation pulse, we can state from the closeness with which the rise in emission intensity follows laser pulse that h,,, 2 1 X lo9 s-'. Further, since q5Q' = 0.17, ( k n i + h,,,) = 4.9kC,',so that k c i = (0.56)k1,,2 lo's-'. Since hblsc 5 lo6 s-' (no greater than 1 / and ~ much less if q5D' is close to unity), K for eq 5 is K , = kblsc/k,,,5 0.02. We also have an estimate for E,,,". In emission studies, extrapolation of the emission decay to time zero after the laser pulse gives an initial oscilloscope reading Vowhich is proportional to Io, the initial emission intensity, which in turn is proportional to fk,. Since k , should not be temperature dependent, that of Voshould be due to f . For C r ( e r ~ ) ~ this ~ + , corresponds to an apparent activation energy of 4.5 kcal mol ',12 which we now assign as E,,,*. The quantity exp(-E,,,*/RT) is 5 X at 25 " C ; so the frequency factor for k,,, becomes A,,, 2 2 X 1OI2 s-'. The lower limit is within the range of normal values for a unimolecular reaction. The actual value of h,,, should perhaps be taken to be near its lower limit, or -1 X l o 9 s-'. This is a rather smaller value than that obtained from the appearance time of excited state absorption in other Cr(II1) complexes.13 These were thiocyanate containing complexes, however, and for two of them, trans-CrtheC respective (en)z(NCS)z+and ~ ~ u ~ ~ - C ~ ( N H , ) , (,N S)~ temperature dependencies of Vo are known, and correspond to El,,* values of 0.0 and -2.3 kcal mol-'. For the same A,,,, k,,,should indeed be powers of ten faster than for Cr(en):+. Returning to the 4.5 kcal mol-l value for E,,,*, one can estimate the energy gap (QIo - Dlo) to be about 14 kcal mol-' (ref 7 and citations therein), so that Eblsc*becomes about 18.5 kcal mol-I. Since E,,*(D:) is only 10 kcal mol it would not be surprising that h,, be much greater than kblsc. Our results thus generate no major inconsistencies i f f is identified as f,,,. The alternative interpretation, f = fplso allows less numerical elaboration. E,,,,* is now 4.5 kcal mol-', attributed to solvation shell effects on the thermal equilibration escape probability of QFc.l2 We now neglect h,,, and conclude that k,; 2 6 X lo7 s-I and kn; k 2 X lo8 s-'~ These are permissible ranges, so again there is no inconsistency. There is evidence, which we accept, that Dlo appears via pisc rather than by ~sc.~O Note that by this interpretation, kbEc should again be small compared to kc,.
+
Fukuda et al.
Returning to Figure 6, we found that R deviates from the calculated values in the case of wavelengths less than 580 nm. The deviations are in the direction expected if ESA is becoming important, and the calculated 6 values are included in the figure. In more detail, we have (wavelength, nm, 6, E * ) : 580: 1.2, 0.1; 570, 4.0, 0.57; 560, 3.9, 1.36. Here, e* is the extinction coefficient for the ESA in M-l cm-'. Qualitatively, it appears that we are observing the long wavelength tail of the first Dlo absorption band, a band that possibly resembles the first ligand field bands of Cr(er~),~+ and of photoproduct and lies between them (see Figure 3). Cr(NH3)5C12+. As noted in the Introduction, this complex was chosen because the principal photoreaction, being antithermal, probably occurs from QlO;it is also a well-studied system in terms of ordinary photochemistry. Initial results were exciting in that both a prompt and a slow absorbance change were observed. From emission studies, the lifetime of Dlo is
