E. D. Sprague, D. Schulte-Frohlinde,and A. J. R . Voss
Energy Commission, under Contract No. At( 11-1)-3221, is gratefully acknowledged.
References and Notes (1) V. H. Fischer. Ber. Bunsenges. Phys. Chem., 71,685(1967). (2) F. Sicilio, R. E. Florin, and L. A. Wall, J. Phys. Chem., 72, 3154 (1968). (3) M. S. Bains, J. C. Arthur, and 0. Hinojosa, J. Phys. Chem., 72, 2250 (1968). (4) V. F. Shuvalov and N. M. Bazhin, Zh. Strukt. Khim., IO, 548 11 969) \ ' - - - I '
(5) G. Czapski, H. Levanon, and A. Samuni, isr. J. Chem., 7, 375 (1969). (6) M. S. Bains, J. C. Arthur, and 0. Hinojosa, J. Amer. Chem. SOC., 91,4673 (1969). (7) A. Samuni and G. Czapski, lsr. J. Chem., 8,563 (1970). (8) A. Samuni and G. Czapski, J. Phys. Chem., 74,4592 (1970). (9) The noncomitant notation 'M-HOp. is used throughout this study emphasizing the undetermined oxidation or complexation state of the complex.
(IO) (a) A. Samuni, J. Phys. Chem., 76, 2207 (1972);(b) G. Czapski, D. Meisel, and A. Samuni, J. Amer. Chem. SOC., 95,4148 (1973). (11) J. H. Baxendale, padiat. Res., 17;312 (1962). (12) M. Simic, P. Neta, and E. Hayon, J. Phys. Chern., 73,3794 (1969). (13) V. K. Stockhausen, A. Fojtik, and H. Henglein, Ber. Bunsenges. Phys. Chern., 74,34 ('1970). (14) J. Rabani,-D. Klug, and?. Liiie,J. Phys. Chem., 77,1169 (1973). (15) D. Klug, J. Rabani, and I. Fridovich, J. B(oL Chem., 247, 4839 (1972). (16) D. Behar and G. Czapski, Isr. J. Chem., 8,699 (1970). (17) (a) H. Levanon and S. I. Weissman, J. Amer. Chem. SOC., 93, 4309 (1971);(b) isr. J. Chem., 10, 1 (1972). (18) G. Czapski, A. Samuni, and D. Meisel, J. Phys. Chem., 75, 3271 (1971). (19) P. S. Rao and E. Hayon, Biochem. Biophys. Res. Commun., 51. 468 (1973). G. G. Jayson, B. J. Parson, and A. J. Swallow, Int. J. Radiat. Chem. Phys., 3,345 (1971). M. L. Kremer, J. Catal., 1, 351 (1962). N. Nord, Acta Chem. Scand., 9,430 (1955). A. Zuberbuhler, Heiv. Chim. Acta, 50,466 (1967). i24j R. D. Gray, J. Amer. Chem. SOC., 91,56 (1969). A, 1902 (1968) (25) I. Pecht and M. Anbar, J. Chem. SOC.
Effects of Photoselection on Decomposition Kinetics in Frozen Solutions Using Unpolarized Light E. D. Sprague,' D. Schulte-Frohlinde,* Abteiiung Strahienchemie, Max-Planck-lnstitut fur Kohienforschung, 0-4330Muiheim a d Ruhr, West Germany
and A. J. R. Voss2 lnstitut fur Strahlenchemie, Kernforschungszentrum D-7500 Karlsruhe, West Germany (Received September 17,7973) Publication costs assisted by Abteilung Strahienchemie, Max-Planck-lnstifut fur Kohlenforschung
Photoselection has been found to be responsible for the deviations from normal kinetic behavior observed in the photodecomposition of the benzenediazonium ion in frozen acidic solutions using unpolarized light. A computer program has been written with which an array of molecules in random orientations can be represented and the process of photodecomposition simulated. Excellent agreement has been found between theory and experiment. In particular, the change in absorbance caused by warming a partially bleached sample to the temperature a t which the molecules become free to rotate is quantitatively accounted for. It has been found that the occurrence of photoselection can result in an error of about 20% in quantum yield determinations.
Introduction In an investigation of the photodecomposition of the benzenediazonium ion in frozen acidic solutions (glasses), kinetic plots were obtained showing curvature such that the apparent quantum yield gradually decreased as the reaction proceeded. Such curvature, however, was not present in similar experiments in the liquid phase. It was further observed that warming a partially bleached, frozen sample above a certain temperature resulted in an increase in the absorbance. These effects are interpreted as being due to the operation of photoselection in the bleaching process. Numerous studies involving photoselection have been carried out in recent years, with sophisticated experiments designed for a wide variety of applications.3 Although essentially all of these measurements involve the use of polarized light, it was recognized from the beginThe Journal of Physical Chemistry, Vol. 78,No. 8. 1974
ning that a beam of unpolarized light is also capable of producing photoselection effects. Theoretical considerations have paralleled the development of experimental techniques but have not yet been presented in a form useful for application to the type of experiment described here. In order to determine the effects to be expected from photoselection, a computer program has been written with which it is possible to represent a system of randomly oriented molecules and simulate the photodecomposition process. The excellent agreement found between theory and experiment strongly supports the interpretation in terms of photoselection. Theory
Before examining the photodecomposition of an assembly of molecules fixed in particular orientations, it will be
783
Decomposition Kinetics in Frozen Solutions
1
useful to consider the case where orientation is unimportant. This is where the absorption is isotropic, either as a result of molecular symmetry or because rotation of the molecules maintains the random distribution of orientations. If i t is assumed that the products of the reaction do not absorb a t the wavelength of interest, the decomposition kinetics are described4 by eq 1, where a is the con-
I ight beam
I
centration of the absorbing species in mol l.-l, t is the irradiation time in sec, 9 is the quantum yield of the reaction, 10is the intensity of the light falling on the sample in einstein 1.- sec- 1, x is the molar extinction coefficient of the absorbing species, related to the natural base e, in 1. mol-I cm-l, and 1 is the length of the light path through the sample in cm. Integration of eq 1 gives eq 2, where c (= 0.434%) is the
atl
+ log (1 - IO-"") = - @ ~ , t +~ t c
(2)
molar extinction coefficient, related to the base 10, in 1. mol- 1 cm- and C is the constant of integration. Substituting A , the absorbance, for at1 gives eq 3. From eq 3 i t is
A
+ log (1 - lo-")
=
- @I,clt
+C
(3)
+
seen that a plot of A log (1 - 1 0 - A ) us. irradiation time should give a straight line with slope - @I&,independent of the value of A . In the present study this equation was seen to hold for experiments in the liquid phase for A values from 4.0 to about 0.05, below which solvent absorption became important. If the absorbance values are small, the exponential term in eq 1 may be expanded in a series which can be broken off after the second term to give eq 4, the familiar firstda - -= @I,Xal (4) dt order decay equation. Integrating eq 4, converting from base e to base 10, and expressing the result in terms of absorbance, gives eq 5. Thus, a t low absorbances, a simple log A = log A, - @I&
(5)
logarithmic dependence of A on t is observed. The situation is somewhat more complex when anisotropic effects must be considered. The following discussion is based on the simplifying assumption that the absorption a t the wavelength of interest corresponds to a transition which has a nonzero transition moment in only one specific direction in the molecule. It is further assumed that the reaction products do not absorb at this wavelength. It is a straightforward matter to remove these restrictions, but this need be of no concern here, since experimental examples meeting these conditions are available for testing the theory. The probability that a given molecule will absorb a photon is proportional to the square of the cosine of the angle between the transition moment in the molecule and the electric vector of the light. The relationship between these vectors is shown in Figure 1. The I, y, and z axes form an orthogonal, laboratory coordinate system, chosen SO that the beam of light comes from the z direction. Since the electric vector, E, of the light must remain perpendicular to the propagation direction, it is confined to the x-y plane. A particular E vector is shown in Figure 1, where p is the angle made with the x axis. Also shown is the transition moment vector, M, for an arbitrarily chosen
X
Figure 1. Coordinate system relating t h e transition moment vector, M, of a molecule in an arbitrary orientation to an arbitrary electric vector, E, of t h e unpolarized light coming along the z
axis.
orientation. It makes the angle 8 with the z axis and its projection in the x-y plane makes the angle $ with the x axis. The angle between the vectors E and M is a. For the orientation illustrated in Figure 1, the extinction coefficient, t p , ~ , $ ,is obtained as a function of the angle a from eq 6, where e o is the intrinsic, or maximum, ex-
cos2 ff
Ed fl $, = 6 ,
(6)
tinction coefficient, observed when a is equal to zero. Simple geometrical considerations yield eq 7 for cos CY.
cos
(Y
= sin 0 cos
4 cos p
+ sin 0 sin 4 sin p
(7)
Since unpolarized light is used, the extinction coefficient must be determined from eq 8, where E is allowed to as-
Lzr%, @
40 =
dP (8)
iZndB sume all possible directions in the x-y plane. The result is given in eq 9, where, as expected, the dependence on the
angle 4 has also disappeared. Averaging this expression over all possible orientations of M, as shown in eq 10, n2n
ta, = -
nli
p2n
pli
J:, J,
sin B dB d$
yields eq 11, the simple relationship between
1 tab
=360
€0
and eaV,
(11)
the average extinction coefficient tav is the molar extinction coefficient used in eq 3 and 5 . Its value may be deterThe Journal of Physical Chemistry, Vol. 78, No. 8, 1974
E. D. Sprague, D. Schulte-Frohlinde,and A. J. R. Voss
704
mined from initial measurements, before decomposibion has occurred. The same value would be observed in the liquid state, where the rotation of the molecules maintains the random distribution of orientations, as long as the shape of the absorption band does not change. As seen in eq 9, the extinction coefficient characteristic of an arbitrary orientation depends only on the value of the angle 0. In order to determine the distribution of extinction coefficients present in a system of randomly oriented molecules, therefore, it suffices to know the distribution of 0 values. A unit vector subtends an element of spherical surface area equal to sin 0 d0 d@, as used in e q 10. This may be rewritten as -d(cos 8) d4, from which it follows that all possible values of cos 8 are equally likely in a random distribution of orientations, that is, when the spherical surface is uniformly covered. This simple result provides the key to the numerical representation of an array of molecules in random orientations. The fundamental idea used in the computer program written for this work involves the visualization of the sample as being divided into many, thin layers, all perpendicular to the light path, and each characterized by a different extinction coefficient value. A set of values for cos 0 are determined by means of eq 12, where n is the number c, = '(i
n
-
i)
( i = 1 , 2,..., n )
of layers assumed in the calculation. The n q values uniformly cover the range from 0 to 1. It is not necessary to consider the range from -1 to 0 because of the squared term in eq 9, which is used, in conjunction with eq 11, to convert the q into extinction coefficient values, e l . The e l are assigned to the layers by means of the following technique. A random number generator5 is used to create labels for the c & . The cI with the smallest label is then assigned to the first layer, and so forth, until the ci with the largest label is assigned to the last layer. The result is a random assignment of the c l values to the n layers. The accuracy with which this corresponds to an array of molecules fixed in random orientations, but also the computing time necessary for subsequent calculations, increases with the number of layers. Each layer is treated as a tiny sample in its own right, and the overall decomposition kinetics result from the simple superposition of the decays in the individual layers. Caution must be exercised in the determination of these individual decays, however, since the intensity of the light reaching a particular layer is a complex function of the irradiation time and the position of the layer along the light path, even for the case of isotropic absorption. Figure 2 illustrates, for example, the occurrence and variation with time of a concentration gradient along the light path through a sample with isotropic absorption. The initial absorbance was chosen to be 1.0, and the curves are equally spaced in time, with the lowest curve corresponding to an overall absorbance of 0.1. It is seen that the chemical changes occur distinctly nonuniformly in the sample as a result of the dependence of intensity on position within the sample. Keeping these difficulties in mind, the following procedure was used to determine the behavior in the individual layers. Since the absorbance in a single layer is only a small fraction of the total absorbance, the values are small enough that eq 5 may be used with essentially no loss in accuracy. This is fortunate, since the detailed calculations require the n individual curves of the absorbThe Journal of Physical Chemistry, Vol. 78, No. 8, 1974
1.0,
I
Z
0 U
z
0.5
0 0
I-
4
ci w
0
t
I
0
I 0.5
I
I
1 .o
DISTANCE FROM FRONT FACE AS FRACTION OF TOTAL DISTANCE Figure 2. Concentration gradients formed during a photochemical reaction in a frozen solution with an initial absorbance of 1.0. The curves are equally spaced in time. See text for explanation.
ance itself us. time, and these are obtained much more easily from eq 5 than from eq 3. The intensity of the light falling on the first layer is not affected by the other layers, so the value of the absorbance is simply calculated from eq 5 for a series of time points. These results for the first layer are then used to determine the average light intensity falling on the second layer during each of the time intervals. The change in absorbance in the second layer during each time interval is then calculated from eq 5, but using the light intensity determined for that time interval. The absorbance us. time data for the second layer are then used to correct the light intensities to give the intensity us. time for the third layer. This process is repeated for the remainder of the layers. Decreasing the size of the time interval, and, therefore, increasing the number of points in time at which calculations are made, increases the accuracy of the results, but, again, increases the necessary computing time. The overall absorbance in the sample at each time point is determined by summing the absorbances in the individual layers a t each time. It was found that these results did not depend on the number of layers or points in time as long as at least 50 of each were used. This applies to calculations with initial overall absorbances in the range 0.5-1.0 and would not suffice for values significantly over 1.0. A running check is kept to find the largest variation observed in the light intensity in any one time interval for any given layer. For the conditions mentioned above, this was normally less than 3%, so the assumption of constant intensity during each time interval, inherent in eq 5 , is justified. Figure 3 shows the results of several sets of calculations. For each of three different initial overall absorbances, two kinetic curves were determined. The first was for the decomposition of an array of molecules in random orientations, and the second was for isotropic absorption, with all cL set equal to ea". The latter calculation is a good test of the method used in the program, since a plot of A + log (1 - 1 0 - A ) us. time must be linear, with a slope independent of Ao. The three accurately linear and accurately parallel
705
Decomposition Kinetics in Frozen Solutions 0.5
I L
t
-2
-1.5
0
0.5
1 .o
1.5
TIME, Io@clt -3
I
I
I
0
1
2
Figure 4. Photodecomposition kinetic curves. Curves a and b are calculated. Curve b is the kinetic curve for anisotropic absorption, and curve a shows the values which should be obtained upon sample warmup. See text for further explanation. The crosses are experimental points from a 0.01 cm thick samM benzenediazonium tetrafluoroborate in 5 M ple of 5 X sulfuric acid glass. Illumination was at 77°K with 254-nm light.
TIME, 1 0 @ c l t
Figure 3. Calculated photodecomposition kinetic curves in a frozen solution as a function of initial absorbance. T h e straight lines are for isotropic absorption, and t h e curved lines are for anisotropic absorption. See text for explanation. straight lines in Figure 3, drawn directly by a Calcomp plotter, remove the possible doubt that a summation of tiny errors in the calculation could result in a serious overall error. It may be assumed with confidence, therefore, that the curvature observed in the remaining three lines in Figure 3 is a direct result of the photoselection process. An effect of the initial absorbance on the amount of curvature in the kinetic plot is seen in Figure 3. The point a t which the two lines cross is shifted to later times for higher initial absorbances. This effect results from the formation of a concentration gradient in the sample, which is itself a strong function of Ao. Below A0 values of about 0.02, the form of the curve remains constant, being simply vertically shifted. For such values of Ao, essentially no gradient is formed, so the kinetic curves in Figure 3 for A0 = 0.02 are independent of this effect. It is seen from these curves that the deviation of the result for randomly oriented molecules from that for isotropic absorption depends on the extent to which reaction has occurred. Since the decomposition is nonuniform when a concentration gradient is formed, the overall deviation observed a t a particular time is the sum of the various deviations present along the gradient. The result is a dependence on the concentration gradient, and, therefore, on the initial absorbance, as seen in Figure 3. The fact that the curved plots in Figure 3 show the type of curvature they do is easy to understand in terms of the preferential decomposition of molecules in favorable orientations. The farther the reaction is carried, the less favorable is the average orientation of the remaining molecules and, therefore, the more slowly the reaction proceeds. It is somewhat surprising, however, that the initial
slopes of the kinetic plots for isotropic and anisotropic absorption are not equal. A careful examination reveals that the initial slope in the case of anisotropic absorption is 1.200 times as negative as that for isotropic absorption, independent of Ao. This apparent inconsistency results from the fact that a function of the absorbance is plotted, rather than a function of the concentration. For isotropic absorption the absorbance remains directly proportional to the concentration a t all times. This is not true, however, for anisotropic absorption. The more strongly absorbing molecules are removed first, giving a larger relative decrease in the absorbance than in the concentration. The actual behavior of the overall concentration during the photodecomposition of randomly oriented molecules can be determined as follows. For each point on the overall kinetic curve, the extent of decomposition in each layer is known. Since the initial concentration is the same in all layers, the overall concentration a t each time point is readily calculated. For purposes of comparison i t is convenient to convert these concentration values into the absorbance values they would represent if all molecules were characterized by an extinction coefficient of ea". The results of such calculations for a particular value of A0 are presented as curve a in Figure 4. Curve b is the usual decomposition curve for anisotropic absorption, as plotted in Figure 3, and the crosses should be ignored for the moment. The fact that the absorbance decreases more rapidly than the concentration in such an experiment is clearly illustrated. The initial slope of curve a in Figure 4 was found to be the same as that of the straight line obtained for isotropic absorption, independent of Ao, so the initial rate of decrease of concentration is the same for isotropic and anisotropic absorption, as expected. Although curve a in Figure 4 cannot be determined directly in a simple experiment, individual points may be accessible to measurement, since each point represents the absorbance which would be observed if free rotation of molecules were suddenly allowed in a sample which had The Journal of Physical Chemistry, Vol. 78, No. 8, 1974
E. D. Sprague, D. Schulte-Frohlinde,and A. J. R . Voss
been decomposed to that point. Under favorable circumstances this can be brought about by warming the sample. In summary, the detailed consideration of photodecomposition kinetics presented here has resulted in theoretical predictions of the magnitudes of the two effects of photoselection which are observable in this type of experiment. The first is the curvature in the kinetic plot, and the second is the increase in absorbance in a partially bleached sample which is warmed until the molecules become free to rotate. These predictions are compared below with the experimental results.
Experimental Section The benzenediazonium tetrafluoroborate used was that prepared for an earlier study.637 It was recrystallized from HBF4 before use. Photolysis was carried out in situ in a modified Cary 14 spectrophotometer. The sample cell, together with the quartz dewar in which it was mounted, could be rotated by 90" to allow irradiation from the side of the instrument. Absorbance measurements were thus made with the same sample axis as the illumination, for which a Hanau Q 81 medium pressure mercury lamp was employed, the appropriate wavelengths being selected with interference filters. Sample cells were of the quartz, cylindrical, loose-window type (Scheiben-Kuvetten, Hellma, Type 124, 201 and 202). Measurements could either be carried out in liquid nitrogen a t 77°K or in a stream of nitrogen gas in the temperature range from 113 to 315°K. The temperature was measured by means of a copper-constantan thermocouple embedded in the cell holder. All calculations were performed on a PDP-10 computer. Determination of the kinetic curves for a particular initial absorbance required typically 10 K storage locations and 10-20 sec of processor time. Results The crosses plotted in Figure 4 are the experimental results for the photodecomposition with 254-nm light of a 5 x 10- M solution of the benzenediazonium ion in a 5 M sulfuric acid glass at 77°K. The initial absorbance in the 0.01 cm thick sample was 0.53. It is seen that the slight curvature of the kinetic plot is well matched by the theoretical line. Similar agreement was observed using 8.7 M phosphoric acid glass or 9 M perchloric acid glass as the matrix. The time in Figure 4 was plotted as I&tlt, since only the form of the decay curve was of interest. In order to determine the quantum yield from such measurements, the light intensity, IO, the average extinction coefficient, t , and the path length, I, must be known or measured. In the experiment in Figure 4 only 1 and were known. An arbitrary value of IO was assumed, and 9 was then varied until the best fit was obtained, as indicated by the occurrence of a minimum in the sum of the squares of the deviations of the experimental points from the theoretical line. The curvature of the kinetic plot resulting from photoselection is not large. A more impressive effect is the increase in absorbance upon warming a partially bleached sample until the molecules become free to rotate. The results of such a warmup experiment are presented in Figure 5. The original absorbance was 0.560 in the 0.1 cm thick sample of 5 M sulfuric acid glass containing 5 X 10-4 M benzenediazonium ion. The sample was bleached The Journal of Physical Chemistry, Voi. 78, No. 8 , 1974
k-
N
60 sec
+-(
0.3 d
N m L
0
I 145 150 155
140
TEMPERATURE,
OK
Figure 5. Absorbance increase on warmup of a 0.1 cm thick
sample of 5
M benzenediazonium tetrafluoroborate in 5
X
M sulfuric acid glass. The sample was bleached at 133°K from an initial absorbance of 0.56 to 0.21 before t h e warmup.
a t 133°K with 254-nm light to an absorbance of 0.210. Warming the sample, as shown in Figure 5, caused the absorbance to increase to 0.257. Separate measurements showed that the shape of the absorption curve does not change as the absorbance increases. The theoretical calculations predict that the absorbance should increase from 0.210 to 0.257, so the effect is quantitatively explained. The increase in the absorbance upon warming can be used to determine the temperature a t which the molecules begin to rotate. For 5 M sulfuric acid glass, the increase 10 sec) a t 145°K and rapidly (T 1 occurs slowly (T sec) a t 149°K. In 8.7 M phosphoric acid glass, the change occurs in the temperature range from 157 to 159°K. It should be mentioned that if a partially bleached sample is warmed and then recooled, subsequent illumination gives a kinetic plot with the same initial slope as the original curve. This is expected on the basis of photoselection, since rotation of the molecules reestablishes the random distribution of orientations.
-
-
Discussion The photodecomposition of the benzenediazonium ion in frozen acidic solution with 254-nm light fulfills the fundamental requirements specified for the calculations described in the theoretical section. The reaction products do not absorb a t this wavelength, and the benzenediazonium ion absorption results from a transition with a nonzero transition moment in only one direction in the molecule. This transition has been assigneds.9 as 1L,with the maximum at 263 nm. The only other absorption in this spectral region is a Ib transition. It has its maximum at 298 nm and is characterized by a much smaller extinction coefficient. This compound is, therefore, well suited for use in testing the theory presented above, and it has been shown that the two observed effects of photoselection are quantitatively accounted for. Strong support is thus provided for this interpretation of these phenomena. It should be noted that, in systems where the assumptions used in these calculations are met, quantum yields determined from the initial slopes of kinetic plots using
787
Decomposition Kinetics in Frozen Solutions
the tangential method will be in error by 20% if photoselection is not taken into account. This is significant in some applications. It might be possible to avoid photoselection effects by choosing some special combination of sample geometry and angle between the light beam causing the reaction and the measurement axis, as has been discussed for luminescence measurements, but this may not be convenient in practice. The conclusions reached here should be of fairly general applicability, since the restrictions imposed in the calculations are very often fulfilled in practice. The calculations could be modified to include those cases where two or more absorption bands with differing polarizations overlap a t the wavelength used. The photoselection effects, however, would be expected to simply decrease in magnitude as the absorption becomes more isotropic in character. It would also be possible to include cases where the reaction products absorb a t the wavelength used. In such cases a much greater curvature in the kinetic plot may be observed. Each system would have to be considered separately, with assumptions being made as to the polarization and extinction coefficient of the transition responsible for the absorption in the product molecule, as well as to the orientation of the product molecule with respect to that of the parent molecule. The behavior of the product absorption upon warmup of a partially bleached sample might provide useful information along these lines. The formation of a concentration gradient in a sample being photobleached, as illustrated in Figure 2, has been d e s ~ r i b e d . The ~ ~ ,results ~ ~ plotted as Figure 2 in ref 13 are in apparent disagreement with Figure 2 here, because the coordinate along the light path was incorrectly chosen in ref 13. Instead of plotting the gradient through the entire sample, only the first 0.4343 of the path is shown. In other words, this figure actually refers to a sample with an initial absorbance of 0.4343 rather than 1.0.
The results in ref 12 and 13 are presented in closed mathematical form, but the orientation of individual molecules is not taken into account. This feature, however, is central to the present work, being of primary responsibility for the observed effects. It must, therefore, be included, and, since the solution of this problem in closed form is probably very difficult, a numerical approach was taken. It has been found that the solvent molecules become free to rotate at 145-149°K in 5 M sulfuric acid glass. It is interesting to compare this result with earlier measurements of the yield of nitrogen during y irradiation of 5 M sulfuric acid containing nitrous oxide.14 A sharp temperature dependence was found in the range 150-170°K, which was concluded to be the range in which the matrix became rigid. It is very reasonable that the molecules should become free to rotate a t the lower end of this transition range.
References and N o t e s Department of Chemistry, University of Wisconsin, Madison, Wis. 53706. National Institute of Oceanography, Wormley, Godalming, Surrey, United Kingdom. For recent reviews see ( a ) F. Dorr in "Creation and Detection of the Excited State, A. A. Lamola, Ed., Marcel Dekker, New York, N. Y., 1971, p 53; (b) A. C . Albrecht, Progr. React. Kinet., 5, 301 (1970); (c) R. Bersohn and S. H. Lin, Advan. Chem. Phys., 16, 67 (1969). 0. Kling; E. Nikolaiski, and H. L. Schlafer, Ber. Bunsenges. Phys. Chem., 67, 883 (1963). PDP-10 Timesharing Handbook, Digital Equipment Corporation, Maynard, Mass., 1970, p 6-37. D. Schulte-Frohlinde and H. Blume, Z. Phys. Chem. (Frankfurt am Main), 59, 282 (1968). D . Schulte-Frohlinde and H. Biume, Z. Phys. Chem. (Frankfurt am Main), 59, 299 (1968). L. Klasinc and D. Schulte-Frohlinde, Z. Phys. Chem. (Frankfurt am Main), 60, 1 (1968). P. Schuster and 0. E. Polansky, Monatsh. Chem., 96,396 (1965). A. H. Kalantar, J. Phys. Chem., 72, 2801 (1968). A. H. Kalantar, J. Chem. Phys., 48, 4992 (1968). E. L. Simmons, J. Phys. Chem., 75, 588 (1971). B. Rabinovitch, Photochem. Photobioi., 17, 479 (1973). F. S. Dainton and F. T. Jones, Radiat. Res., 17, 388 (1962).
The Journal of Physical Chemistry, Voi. 78, No. 8, 1974
