9595
J. Phys. Chem. 1992,96,9595-9597
Rotational DMuslon of Fluorene in Hydroxylic Solvents Yong-Rok Kim and Robin M. Hochstrasser* Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (Received: August 3, 1992; I n Final Form: October 2, 1992)
Rotational diffusion of fluorene was studied by means of fluorescence anisotropy measurements using a time-correlated single photon counting apparatus. The measured rotational relaxation times in various alcohol solvents were compared with hydrodynamic predictions for prolate spheroidal and asymmetric ellipsoidal shapes in the “stick” and “slip”limits. The rotational dynamics of this molecular system was not predicted by slip or stick hydrodynamics assuming the friction which is proportional to the solvents’ viscosities. Some factors that might be responsible for this phenomenon are discussed.
Introduction The rotational correlation times for molecules as solutes in simple liquids or in more complex environments,such as a proteins, are parameters that are often rather straightforward to measure.1*2 There are also in place theoretical descriptions of rotational diffusion that can be compared with such expe~iments.~~ A survey of the literature in this field shows that the relationships between the t h m t i c a l predictions and experiments on real liquids is seldom excellent and often unacceptable.6-’ It appears therefore as if there is a need for further work in this area. In the course of some recent experiments involving energy transfer8 and phot~isomerism~ of bifluorene, we had the need to make a careful study of the rotational dynamics of fluorene as a set of alcohols covering a relatively wide viscosity range. Since fluorene has a well-documented structure,I0 spectroscopy, and photophysics,I1J2it seemed of some interest to compare these results to the theoretical predictions. Such a comparison is the purpose of this letter.
Experimental Method and Results The experimentsconsisted of measurements of the fluorescence anisotropy, r(t) = o.4(P2(@p(f))). The fluorescence excited at 300 nm and detected at 3 15 nm was analyzed by means of a time-correlated single photon counting apparatus that was described earlier in detail.8 The instrument function used in the present experiments was 20 ps. The fluorene concentration was kept below lo4 M to prevent depolarization due to energy transfer or reabsorption. The ‘initial” anisotropies and the rotational relaxation times are presented in Table I. These numbers were obtained from an iterating nonlinear least-squares dtconvolution procedure assuming a single-exponential decay. The xz associated with fits were less than 1.2. The results are also plotted in Figure 1 as relaxation time versus viscosity. The behavior is roughly linear, as expected when viscosity is a good measure of the rotational friction, but shows a noticeable sublinear curvature. Discussion and Comparison with Theory Fluorene is a nonpolar molecule with C, symmetry having a nearly zero dipole moment. It has an asymmetric ellipsoidal shape with the axial ratio, a h , of 1.0:0.7:0.4. Both the absorption and emission transition dipole moments are directed along the longest molecular &.I3 We also considered fluorene as a prolate spheroid with the axial ratio of 1.0:0.5:0.5. Both models were applied to this molecular system to check any differences between them. The modified DebyeStokes-Einstein hydrodynamic model was used to calculate the classical limit of rotational relaxation times for the prolate spheroidal shape under the “stick” boundary c o n d i t i ~ n . ~ - The ~ J ~ rotational relaxation times in the “slip” boundary condition were estimated using the dimensionless frictional ratios calculated by Hu and Zwanzig assuming no fluid can enter or leave the surface of the chromophore molecule and
TABLE I: Rotational Relaxation Time ( T ~ and ) the Corresponding Initial Anisotropy Valuea ( r o )for Fluorene in Alcoholic Solvents
solvent propanol butanol
pentanol hexanol heptanol octanol nonanol
decanol undecanol
I) (CP)
r0
2.1 2.9 3.5 4.6 6.4 8.2 10.2 12.8 15.8
0.34 f 0.03 0.35 f 0.02 0.35 i 0.04 0.34 f 0.04 0.33 f 0.04 0.37 f 0.02 0.37 f 0.03 0.38 i 0.02 0.36 i 0.04
7”.
(Ps)
18 i 3 20 f 2 22 i 3 33 f 3 36 i 4 53 f 5 60 i 4 70 i 5 77 i 6
no tangential force is applied to the surface.IS Since the relevant, probed, transition dipole moment of fluorene is located in the longest axis of the molecule, the anisotropy decay for a prolate ellipsoidal model has a single-exponential form: r ( t ) = ro exp(-t/rl)
(1)
For the prolate model defined above, rl depends only on the rotational diffusion constant Db, which indicates the rotational diffusion is about the axes perpendicular to the long molecular axis TI
1/(6Db)
(2) (3)
where p = a l b and a > b for the prolate spheroid and D is the rotational diffusion constant for a sphere: D = kT/(6tlY)
(4)
Here k, T, V,and TJ represent Boltzmann’s constant, temperature, hydrodynamic molecular volume 4 ~ a b c 1 3of the ellipsoid, and viscosity, respectively. The shape factor S is
With the known bond lengths and angles and van der Waals radii, the molecular axial lengths of fluorene are estimated to be 10.8, 7.2, and 3.8 A. For the molecular shape assumed to be a prolate spheroid there are two different molecular axis lengths of 10.8 and 5.4 A. From the molecular volume of 1.65 X cm3,the rotational diffusion constant is calculated to be 2.74 X lo9 q S-I, which yields the anisotropy decay, r(t) = 0.4 exp[-t/(60.8q)] for the “stick” boundary condition. From the frictional coefficient ratios given by Hu and Zwanzig,ls the anisotropy decay for the “slip” condition becomes r(t) = 0.4 exp[-t/(14.6q)]. In these and subsequent anisotropy equations q is given in centipoise when t is given in picoseconds. When the fluorene molecular shape is considered as an asymmetric ellipsoid, elliptical integrals need to be evaluated to decide on the principal frictional coefficients. The general solution of the diffusion model yields the following equation for the model
0022-3654/92/2096-9595$03.00/0 0 1992 American Chemical Society
9596 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 200
Using the eqs 6 and 9, the anisotropy decay r ( f )is calculated for the "stick" condition as
/
/
Letters
/
+ 0.001 exp[-f/(43q)]
r(t) = 0.399 exp[-t/(63q)]
(10)
In order to obtain the "slip" limit, the values tabulated by Youngren and Acrivos16 are used for the dimensionless frictional coefficients of the asymmetric ellipsoid. The resulting diffusion coefficients are
100
D,' = 2.527
X
lO'Oq-'
D: = 7.823
X
1097-'
3.943
X
10IOq-'
0,'
(11)
0
0
10
20
Viscosily (cp)
Figure 1. Rotational relaxation times of fluorene in alcoholic solvents compared with hydrodynamic calculations. Dashed lines: hydrodynamic calculations in the "stick" and "slip" limits for the appropriate prolate spheroid. Solid lines: hydrodynamic calculations in the "stick" and "slip" limits for the asymmetric ellipsoid. The lines drawn correspond to the individual exponential decay times in the functions given by eqs 10 and 12.
with three different molecular axial lengths and the absorption and emission dipoles along the longes molecular axis4qs
+
r ( t ) = 0.3(2/3 + G) exp[-(6D - 2A)t] 0.3(2/, - G) exp[-(6D
+ 2A)tI
(6)
where D = (D,
+
A = (Dz, Dzb
+ Db + D,)/3
+ Dz, - D,Db - 03, - D&,)'/'
G = (D, - D)/A Here the rotational diffusion constants Di are given by Di = kT/1;.
(7)
The frictional coefficients1;. can be obtained from the following
equation^:^ fa = 16qa(bz + c2)/[3(bZQ+ cZR)]
fb = 16qa(c2+ a2)/[3(c2R + aZP)]
(8)
f, = 16pa(a2 + bZ)/[3(a2P+ b2Q)] where a, b, and c are the semiaxial lengths and P, Q,and R are the elliptical integrals given by P e r r h 3 For the present case we find
P = x m d r / { ( a 2+ r ) [ ( a 2+ r)(bz + r)(cZ+ r)]'/2] = 8.770
X
A-3
Q = Xmdr/{(b2+ r ) [ ( a 2+ r)(b2+ r)(c2 + r ) ] ' / 2 )= 1.495 X lo-'
A-3
R = x m d r / { ( c 2+ r)[(az+ r)(b2 + r)(cZ + r)]'/2] =
3.043 x
A-3
Thus, the rotational diffusion coefficients (in s-I) for each axis are D, = 4.47 x
109~-1
Db = 2.72 x 109q-' D, = 2.60 x
109~-1
(9)
It should be noted that Table I in ref 16 consists of values of X,(4ab/3) and not Xi as stated in the paper. Therefore, the "slip" anisotropy decay is given by r(t) = 0.212 exp[-t/(ll.lq)]
+ 0.188 exp[-t/(5.0q)]
(12)
where t is in picoseconds. The experimental anisotropy data are compared with those calculated anisotropy decays assuming a prolate spheroid or asymmetric ellipsoid model in the "slip" and "stick" limits as a function of the solvent viscosities in Figure 1. The anisotropy calculations for the prolate spheroid and the asymmetric ellipsoid make significantly different predictions of the rotational relaxation times. Particularly in the "slip" limit, the importance of the molecular shape in the hydrodynamic calculations is paramount. From this comparison it is clear that the fluorene molecule rotates significantly faster than predicted by slip hydrodynamics, since the theory gives the greatest weight to the slow (11.1 ps) component in eq 12. This subslip phenomenon could be attributed to the strong hydrogen-bonding association among these alcohol solvent molecules. Extended structures which include hydrophobic regions can be formed in such solvent environments. Presumably fluorene molecules will be located mainly in the hydrophobic regions. This would have two consequences: (1) The solvent friction relevant to rotational diffusion of fluorene would not be given directly by the bulk liquid viscosity which is greatly dependent on the polar interactions. (2) The fluid may not be isotropic for a fluorene diffuser; the fluorene may be confined to lamellar regions facilitating rotation about the perpendicular axis. The calculation (see Figure 1) indicates that the rotational diffusion is close to that expected if the fluorene molecule were to rotate only about an axis perpendicular to its plane, i.e., only the second, low-amplitude "slip" term in eq 12. It is also shown in the table that the initial anisotropy values for this molecular system are close to 0.4, indicating the absence of transition dipole depolarization mechanisms" faster than our time resolution. The calculations for the asymmetric ellipsoid predict a double-exponential decay as shown in eq 12. However, our data were adequately fitted by only one exponential in all solvents. The observed relaxation times were always considerably less than the average decay time (8 ps c P ' ) and close to the shorter decay time (5 ps cP'). Thus, it is concluded that the theory is not predictive for the present experimental situation: The molecule is rotationally relaxing faster than predicted by slip hydrodynamics. Such situations have been found before'*J9and attributed to structures arising from the association of the alcohol solvent molecules. In the present case the solute is a rigid aromatic, and complications concerned with conformational equilibria and chemical associations between solvent and solute are very likely absent. Finally, the hydrophobicity increasing with solvent chain length might account for the slight nonlinearity evident in the T vs q plots. References and Notes (1) Berne, B.; Pecora, R. Dynamic Lighr Scatrering; Wiley-Interscience: New York,1976. (2) Hochstrasser, R. M.; Johnson, C. K. Topics in Applied Physics; Kaiser, W., Ed.; Springer: Heidelberg, 1988; Vol. 60, p 357. ( 3 ) Perrin, F. J . Phys. Radium 1936, 5, 497. (4) Belford, G. G.; Belford, R. L.; Weber, G. Proc. Narl. Acad. Sci. U.S.A.
1972, 69. 1392.
J. Phys. Chem. 1992, 96,9597-9600 ( 5 ) Chuang, T. J.; Eisenthal, K. B. J . Chem. Phys. 1972,57, 5094. (6) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J . Phys. Chem. 1981,85, 2169. (7) Pereira, M. A.; Share, P. E.; Sarisky, M. J.; Hwhstrasser, R. M. J . Chem. Phys. 1991,94, 2513. (8) Kim, Y. R.; Share, P. E.; Pereira, M.; Sarisky, M.; Hwhstrasser, R. M. J. Chem. Phys. 1989, 91, 5775. (9) Lee, M.; Hochstrasser, R. M. Chem. Phys. Lett. 1988, 153, 1. (IO) Dougherty, D.; Llort, F.; Mislow, K.;Blount, J. Tetrahedron 1978, 34, 1301. (11) Minn, F. L.; Pinion, J. P.; Pilipescu, N. J . Phys. Chem. 1971, 75, 1794. (12) Saigusa, H.; Lim, E . C. J . Phys. Chem. 1991, 95, 2364. (13) Bree, A.; Zwarich, R. J . Chem. Phys. 1969, 51, 903.
9597
(14) Fleming, G. R.; Morris, J. M.; Robinson, G.W. Chem. Phys. 1976. 17, 91.
(15) Hu, C.-M.; Zwanzig, R. J . Chem. Phys. 1974, 60,4354. (16) Youngren, G. K.;Acrivos, A. J. Chem. Phys. 1975,63, 3846. SCC also comment by: Sension, R. J.; Hochstrasser, R. M. Submitted to J. Chem. Phys. (17) Hochstrasser, R. M.; Pereira, M. A.; Share, P. E.; Sarisky, M. J.; Kim,Y.R.; Repinec, S.T.; Sension, R.; Thorne, J. R. G.; Iannone, M.;Diller, R.; Anfinrud, P. A.; Han, C.; Lian, T.; Locke, B. Proc. Indian Acad. Sci. (Chem. Sci.) 1991, 103, 351. (18) Canonica, S.;Schmid, A. A.; Wild, U.P. Chem. Phys. Lett. 1985, 122, 529. (19) Courtney, S.H.; Kim, S.K.; Canonica, S.;Fleming, G. R. J . Chem. SOC.,Faraday Trans. 2 1986.82, 2065.
Unusual Spin Density Localization in a Porphyrin ?r Radical. The Octaethyiisobacteriochiorin
?r
Anion Radical of
M. W. Renner,'. E. Fujita,lP*bI. Fujita,laqcA. D. Procyk,ld D. F. Bocian,ld and J. Fajer*Ja Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11973, and Department of Chemistry, University of California, Riverside, California 92521 (Received: August 4, 1992; In Final Form: October 7, 1992)
Isobacteriochlorins (iBCs) are naturally occurring isomers of bacteriochlorins in which two adjacent rather than two opposite pyrrole rings have lost a @-@ double bond. Like the photosynthetic chromophores, biological iBCs transfer electrons, and their iron complexes, sirohemes, mediate the six-electron reductions of nitrite to ammonia and of sulfite to hydrogen sulfide. Intriguingly, the metal-free derivatives, sirohydrochlorins,have also been found to be active in sulfite reduction. The mechanisms of electron transfer by sirohemes or sirohydrochlorins are not established. We have thus considered the possibility that the sirohydrochlorin might act as an electron acceptor, as do the equivalent metal-free pheophytins and bacteriopheophytins in photosynthesis. We report here optical, EPR, and ENDOR results for the T anion radical of a synthetic model, 2,3,7,8,12,13,17,18-octaethyl-iBC, that provide spectral signatures for the putative reduced transient in vivo. The calculated spin profile for the T anion radical that results from one-electron reduction of the iBC macrocycle is highly unusual. Two different computations, iterative extended HUckel (IEH) and self-consistent-fieldPariser-Parr-Pople (PPP) calculations, predict that a single meso carbon atom (C15) would bear from 0.2 (IEH) to 0.4 (PPP) electrons. Experimental EPR and ENDOR results for the anion radical of octaethyl-iBC fall gratifyingly within the two theoretical values: the observed hyperfine coupling constant of 7.7 G for the proton at C15 corresponds to an unpaired spin density of 0.3 electrons for C15, a uniquely high value for a A anion radical of a porphyrin derivative. (Optical spectra and additional ENDOR results for the radical support the T anion formulation.) These results suggest the following: (a) If sirohydrochlorin acts as an electron acceptor in vivo, its anion radical should exhibit a diagnostic EPR signal similar to the one reported here for the synthetic iBC. (b) The high spin density localization at a single carbon renders that position in the radical particularly susceptible to electrophilic attack and opens a novel synthetic avenue for regiospecific chemistry of iBCs via their anion radicals. (c) A considerable effort is now devoted to covalently linked donor-acceptor porphyrin complexes as models of photosynthetic and catalytic electron transfer. Because the unpaired spin density in T radicals extends onto peripheral substituents, the unusually high spin density at C15 in iBC anion radicals should significantly enhance electronic coupling in donoracceptor pairs incorporating iBCs covalently linked at that position.
Introduction Isobacteriochlorins (iBC) are naturally occurring hydroporphyrins in which two adjacent pyrroles have lost a peripheral 0-0 double bond (see Figure 1). Iron complexes of iBCs, sirohemes, medicate the six-elmon reductions of nitrite to ammonia and of sulfite to hydrogen sulfide.2 Intriguingly, the metal-free derivative, sirohydrochlorin, has been found to be active in sulfite reductases depleted of sirohemes.' The facile oxidation of iBCs, compared to porphyrins or chlorins, has focused attention on their 7r cation radicals as possible enzymatic intermediates." Indeed, oxidation of Fe"N0 or FeWO iBC complexes leads to the corresponding T cation radicals whereas oxidation of the analogous porphyrins leads to Fe( 111) The oxidative trends and the unpaired spin density profiles of the resulting r cation radicals of the iBCs agree well with self-consistent-field Pariser-Parr-Pople (PPP) and iterative extended Hackel (IEH)molecular orbital calculation^.^*^ The possible enzymatic role of ~irohydrochlorin~ and the established function of other metal-free hydroporphyrins, such as
the pheophytins and bacteriopheophytins that act as electron acceptors in green plant and bacterial photosynthesi~,8~~ led us to consider the possibility that iBCs may also function via r anion radicals. We report here theoretical calculations and experimental results for a synthetic iBC, 2,3,7,8,12,13,17,18-octaethyl-iBC (H,OEiBC), that reveal a highly unusual spin profile for its 7r anion radical. Both IEH and PPP calculations predict that a single meSO carbon atom (C15) would bear from 0.2(IEH) to 0.4 (PPP) electrons. Experimental EPR and ENDOR results for the anion radical of H,OEiBC fall gratifyingly within the two theoretical values: the observed hyperfine coupling constant of 7.7 G for the proton a t C15 corresponds to an unpaired spin density of 0.3 electrons a t C15, a uniquely high value for a r radical of a porphyrin derivative.1° Optical spectra and additional ENDOR results for the radical support the r anion formulation. These results suggest the following: (1) If sirohydrochlorin acts as an electron acceptor in vivo, its anion radical should display a characteristic EPR signal similar to the one reported here for the synthetic iBC. (2) The high spin density localization at a single
0022-3654192/2096-9597%03.00/0 0 1992 American Chemical Society
