J. Phys. Chem. 1983, 87, 3359-3360
Q
15
1
Flgure 5. Structure of the iodine columns in BILI: (a) molecular geometry; (b) packing of I,-. Ellipsoids are 9 0 % probability surfaces. (From ref 14.)
which may occur in a cooperative fashion along the chains. This mechanism, if operative, cannot explain the properties of the lithium complex BILI which shows very similar cond~ctivity.~In BILI the columns are branched (Figure 5) and consist of 15-species with a bending angle
3359
of 105’ at the central iodine atom. Iodine migration would involve intermediates of asymmetric T-shaped structure. The key to the high conductivity of BILI must be sought in the 7% iodine deficiency which follows for both the analytical results and the X-ray data. This iodine deficiency is equally distributed over the atoms in the column and those in the side chains. The spectroscopic results show only two bands attributed to a bent 1, species (153 and 167 cm-l), but the presence of small amounts of other iodine species may be possible within the sensitivity of the spectroscopic experiment. Unless 15-molecules migrate through the lattice, the iodine species must interconvert during the conduction process if iodine is the charge carrier. The nature of this interconversion cannot be deduced from the evidence presently available. A second potential conduction path is BIKI and BINI (but not in BILI) is provided by the cation columns. Though the presence of solvent molecules in the column rules out any dc conductivity, a small solvent deficiency which seems possible within the analytical results (Table I) would allow hopping of cations between alternative sites and account for one of the frequency-dependent conduction mechanisms. For BINI a linear 1 / T dependence of the conductivity was observed indicating a single activation energy of 0.45 eV.4 Thus, the low activation energy mechanism is not operative in BINI, even though the iodine column structures are identical. This suggests that the low activation energy conductivity which is dominant at low temperature may be cationic and inhibited in the ammonium complex because of hydrogen bonding to the adjacent oxygen atoms. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Foundation, administered by the American Chemical Society, for support of this work. We thank Dr. M. Labes and his co-workers for communicating results prior to publication and Dr. P. Prasad for stimulating discussions. EXAFS measurements were performed at beamline A2 at the Cornell High Energy Synchrotron Source (CHESS). Registry No. BIKI-chloroform, 80894-17-3;BIKI-bromoform, 86163-37-3; BINI-chloroform, 86163-38-4.
COMMENTS Comments on “Polarized Photochemlstry on Bacterlorhodopsln. Dlchrolsm of the Early Photochemical Intermediate K,,,”
Sir: Noting, in the course of their recent investigations of the laser-induced dichroism of aqueous suspensions of light-adapted fragments of the purple membrane, that the dichroic ratio fell with increasing laser intensity, Karvaly and associates1 sought to explain their observations in terms of the following scheme:
Their rate equations read (when allowance is made for a typographical error and, by way of enhancing the clarity, the arguments Q 3 (8, 4) and t are explicitly stated) as follows: dnbR(Q,t)/dt = - l a b R n b R ( Q , t ) cos2 8 + P K , b R n K ( Q , t ) (1) COS2 8 - P K , b R n K ( Q , t ) (2) Equations 1 and 2 imply that nbR(Q,t) + n K ( f l , t ) = nO/4r (3) Karvaly et al. state that the steady-state concentrations of species bR570 and KBlO,immediately after the short pulse (my italics), can be obtained in the following forms:
dnK(Q,t)/dt = l@&nbR(Q,t)
(1) Karvaly, B.; Fukumoto, J. M.; Hopewell, W. D.; El-Sayed, M. A. J.Phys. Chem. 1982,86, 1899. 0022-3654/03/2007-3359$0 1.5010
0 1983 Amerlcan Chemlcal Society
J. Phys. Chem. 1983,8 7 , 3360-3362
3360
no y2 cos2 0 nK(Q,T) = 47T 1 + y2 cos2 0
(5)
where T is the duration of the laser pulse, and y is defined as Y2 =
(6)
(“bR/pK,bR)I
Using eq 4 and 5 to calculate ArL, “the initial polarized absorbances at an observation wavelength different from photolysis, including the contribution of nonphotolyzed bR570 molecules”, they conclude that the dichroic ratio Allbt/Altotdepends on SbR/bK, and go on to consider, as “a refinement of the previous rigid (immobilized) dipole model”, an isomerizationmodel, which allows for “a change in the transition dipole orientation of the photolyzed molecule”. Consider now the instant t = T,at which the laser pulse is extinct and the initial absorbance is measured. At t = T,I = 0 = y (by definition), so that eq 4 and 5 give nbR(Q,r) = no/4r and nK = 0. Referring to the definitions of AFi Allbt =
XZrJr
(BbRnbR + UKnK)
COS2
6 Sin 6 d0 d4
(7)
A,ht =
anisotropy. In this context, it is important to remember that, in flash kinetic spectroscopy, what one measures is not APl but aAl1,*= A;: - A(O), where A(0) = uno/3 is the absorbance before photolysis. One finds aAl, = (a* ~ ) . f -n*p2 ~ l dp, AA, = l/&u* - a)J-lln*(l - p2) dp, where IA = cos 0. When the steady-state approximation holds, the integral involved can be evaluated in closed form, and one gets bill = (a* - ~ ) n o [ l / 3- y-2 + y-3 arctan y ] , aA, = (a* - g)no[’/3 + 1/2(u-2- y-3 - y-l arctan y]. It will not be amiss to add parenthetically that the use of the steady-state approximation will be gainful only if the lifetime 7 of the photoproduct as well as the response time of the monitoring equipment is very much smaller than
T. I conclude by discussing the isomerization model. If the Ke10dipole suffers an average angular displacement of A0 relative to the bR570 dipole, it is not “reasonable to assume that one-half of the photolyzed molecules change the chromophore dipole orientation by +A0 and the other by -A0 with respect to the original direction of the parent molecule”, for the laboratory 2 axis (OZ), the bR570 dipole (OB), and the K,,, dipole (OK) need not be coplanar. If CY denotes the angle between the Gl0 dipole and the 2 axis, one has cos CY = cos 0 cos A0 sin 0 sin A0 cos y
+
one sees that, at t = T,Allbt= 1/3 i?bRnO = ALtot. On the contrary, the experiment shows that Allbt# ALbt at t = T; one must therefore conclude that eq 4 and 5, obtained by using the steady-state approximation, are inapplicable to bacteriorhodopsin, though similar equations do apply to other system^.^-^ As I have latelf15 discussed the problem of calculating, in the rigid (immobilized) dipole model, the intensity dependence of the orientational distribution functions of the unphotolyzed and photolyzed molecules, the details will be suppressed, and only the principal results stated. It will be useful to extend the scope and simplify the notation by introducing the following substitutions: nbR = n, nK = n*, UbR = “0, BbR (TK = (T*, p K , b R = kl, p K , L = 122, and k = (k1 + k2) = 1/T. With CP denoting the quantum yield of the formation of the photoproduct, the rate equations become dn(Q,t)/dt = -CPIuon(Q,t)cos2 0 + kln*(R,t) (9)
+
dn*(Q,t)/dt = cPIuon(Q,t)cos2 0 kn*(Q,t) (10) which can be easily solved if eq 3, or equivalently the relation dn(Q,t)/dt = -(dn*(Q,t)/dt), holds, and this will happen only if k 2 = 0 5 k. The case k = 0 is well approximated by a system (such as that studied by Karvaly and collaborators) for which T > T , one may invoke the steady-state approximation, obtaining thereby
The two-level model embodied in eq 3 leads to very simple expressions for the dichroic ratio and the absorption (2) Eisenthal, K. B.; Rieckhoff, K. E. J. Chem. Phys. 1971,55,3317. (3) Mourou, G.; Denariez-Roberge, M. M. IEEE J. Quantum Electron. 1973, QE-9, 787. (4) Razi Naqvi, K. An. Quim. 1983, 79, 76. (5) Razi Naqvi, K. J. Chen. Phys. 1981, 74, 2658.
where y is the angle between the planes BOZ and BOK. Taking a leaf out of Soleillet’s one can easily show that, so long as eq 3 holds, the anisotropy R = (AA,,AA,)/(aA,, + 2AA,) is given by
-
-
-
where S = 1/2(3cos2 A0 - 1) and R(0;I)is the anisotropy pertaining to the rigid dipole model. In the limit I 0, n*(Q,t)a cos20 n(Q,t)and consequently R(0;I-0) = 2 / 5 . A little calculation shows that, of the two possibilities (for structural rearrangements within bacteriorhodopsin) considered by Karvaly and co-workers,l one can be discarded The maximum value (2.25) of the initial dichroic ratio is too high to be compatible with A0 N 50’; the other, A0 N lo’, can be admitted or excluded only after a careful evaluation, or outright elimination, of the trivial contribution made by instrumental factors, since departures from the theoretical value of 2/5 cannot be attributed entirely to nontrivial causes, such as isomerization or rapid, restricted motion of the photoselected molecules.s (6) Soleillet, P. Ann. Phys. 1929, 12, 23. (7) Pesce, A. J.; RosBn, C.-J.; Pasby, T. L. ’Fluorescence Spectroscopy”; Marcel Dekker: New York, 1971; pp 120-2. (8) Razi Naqvi, K.; Wild, U. P. Chem. Phys. Lett. 1975, 36, 222.
Department of Physics University of Trondheim (NLHT) N-7055 Dragvoll, Norway
K. R a d Naqvl
Received: January 20, 1983
Recalculation of the Rate of Electron Exchange between Cu( I I ) and Cu( I ) in Their 1,lO-Phenanthroiine and 2,2‘-Blpyridlne Complexes in Aqueous Media
Sir: It is now standard practice to use the Marcus relations’ to correlate the rates of electron self-exchange and
0022-3654/83/2Q87-336Q~O~ .50/O @ 1983 American Chemical Society
