Photosynthesis Research 22: 195-199, 1989. © 1989 Kluwer Academic Publishers. Printed in the Netherlands.

Regular paper

The tamper effect: environmental influence on electron tunneling

John Delaney & David Mauzerall The Rockefeller University, 1230 York Avenue, New York 10021, U.S.A.

Received 10 January 1989; accepted in revised form 25 April 1989

Key words: Electron transfer, photochemical electron transfer, solvent effects, zinc porphyrin quinone

Abstract

The time constants for electron transfer from the singlet excited state of the small cavity conformer of the tetrabridged coplanar zinc porphyrin quinone (ZnPQ) average 2.4 times as fast in solvents containing XCC13 group as in solvents of similar dielectric properties. Solvent molecules containing this bulky group cannot fit in the small cavity of conformer ZnPQa. We assign the effect to the increase of the electron wave function in the porphyrin-quinone space by increased exclusion from the electron dense solvent as compared to more usual solvents. We name this property the tamper effect.

Introduction Experimental

The occurrence of quantum mechanical tunneling in electron transfer reactions (Mauzerall 1976) is now well supported by a variety of studies (De- Vault 1984, Kairutdinov and Brickenstein 1986, Mayo et al. 1986, Hush 1987, Mikkelson and Ratner 1987, Eaton and Eaton 1988). Linked porphyrin-quionone molecules have been the object of much interest as models of photosynthetic reaction centers (for a thorough review see Connolly and Bolton 1988). These studies have established that the electron transfer rate is distance dependent (Axup et al. 1988, Closs and Miller 1988, Isied et al. 1988, Joran et al. 1988, Karas et al. 1988, Mclendon 1988) and have provided some evidence for dependance on mutual orientation (Closs and Miller 1988, Mauzerall et al. 1989). Solvent effects have been interpreted within the framework of traditional electrostatics (Seeley 1978), dynamics (Calef and Wolynes 1983, Kakitani and Mataga 1985) and of barriers to tun- neling between donor and acceptor (DeVault 1984). In this communication we present evidence for a novel effect on electron tunneling of barriers external to the donor-acceptor pair. We call this the tamper effect.

Synthesis (Lindsey and Mauzerall 1982) and photophysical properties (Lindsey et al. 1988, Delaney et al. 1989) of the co-planar tetra cyclic porphyrin quinone zinc chelate (ZnPQ) have been described. Electron transfer from the excited singlet state of the porphyrin in ZnPQ was measured via fluorescence lifetimes (Lindsey et al. 1988). Sol- vents were distilled and were deoxygenated with N2 prior to measurement. Lifetimes were obtained from the fluorescence data by iterative convolution (Mauzerall 1985).

Results

The electron transfer time constants in twenty dif- ferent solvents are listed in Table 1. The data is the same as in Delaney et al. (1989) with the addition of information on the electron density of the sol- vents, a parameter described below. There are two electron transfer time constants because the macro- polycycle occurs in two long-lived conformations, ZnPQ, and ZnPQPb (Lindsey et al. 1988). They differ by the average edge to edge separation of the

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Tab le 1. Data on solvents and photophysics of ZnPQ(Ac)4.

Solvent e n 2 d e za, ns z b, ns K

Benzene 2.27 2.24 0.472 1.8 > 50 1.22 Toluene 2.38 2.23 0.467 1.6 > 50 1.40 Hexafluorobenzene - 1.90 0.671 0.9 > 50 0.6 Diethyl ether 4.33 1.82 0.402 1.72 ~ 30 1.38 Ethyl acetate 6.02 1.88 0.488 1.96 10 1.00 Tetrahydrofuran 7.58 1.97 0.493 1.40 8 1.50

Carbon tetrachloride 2.21 2.12 0.763 0.52 6.8 0.35 Pentachloroethane 3.73 2.26 0.806 0.96 6.4 0.37 1,1,2,2,-Tet rachloroethane 8.20 2.22 0.775 0.84 5.4 2.13 1,1,1 ,-Trrichloro ethane 7.53 2.06 0.654 0.66 6.7 0.2 1,1,2-Trichloroethane - 2.16 0.709 1.07 6.3 1.04 1,2-Dichloroethane 10.36 2.08 0.633 0.81 7.4 1.86 Methylene chloride 8.93 2.02 0.862 0.92 6.6 1.78 Chloroform 4.80 2.08 0.543 0.79 6.3 2.03

Sucrose octaacetate - 2.15 1.29 > 50 1.22

Pyridine 12.4 2.27 0.521 0.63 13 4.0 Ethanol 24.5 1.85 0.444 0.63 13 5.7 Acetonitrile 37.5 1.80 0.417 0.63 3.0 1.5 Dimethylacetamide 37.8 2.06 0.758 0.55 13 4.0 Dimethyl sulfoxide 46.7 2.18 0.602 0.63 13 5.7

Averager spacer of PQ 22 2.39 0.559

Solvents constants were obtained from standard sources such as Riddick and Bunger (1970). The electron density, d e is defined as the density times the number ofelectrons divided by the molecular weight o f the solvent. The units are (electron m o l - ] cm 3). The properties of the average spacer were calculated as equimolar mixtures o f 4-methyl-anisole and N-methyl-N-phenylacetamide, except the dielectric constant which is that o f anisole and dimethylacetamide.

o v , -

x 1 [.." 0.8

0.6

0.4

0

o ® ®

I I I I I

io 2'o 3'o 4'o

Fig. 1. The log of the time constant for electron transfer from the singlet excited state of the introverted conformer of ZnPQ, z a, plotted versus log of the solvent dielectric constant. Normal solvents are represented by solid dots and chlorinated solvents by circuled dots. The open circles represent solvents having the XCCI 3 grouping.

function give essentially the same result. The general increase of rate constant with dielectric is explained as the favoring of the polar charge trans- fer state. The constancy of the rate constant of conformer ZnPQa in low dielectric solvents is ex- plained as a local dielectric effect - i.e. the side chains contribute a polarity irrespective of the sol- vent polarity (Delaney et al. 1989). The small mag- nitude of these effects is only consistent with non- adiabatic tunneling. Of interest at present are the points which do not fit on the smooth line. These are all heavily chlorinated solvents containing the X C C 1 3 group. Their increased rate of electron transfer is attributed to the tamper effect.

Discussion

porphyrin and quinone rings, 3.5 and 6.5 A respec- tively. The values of r, are plotted versus log e (static dielectric constant) in Fig. 1. This plot was chosen so as not to favor a particular function of e. Plots of Za versus the Onsager or Mataga-Wel ler

The effect of solvent on the rate of electron transfer has always been discussed in terms of solvation (Seely 1978, Calefand Wolynes 1983, Kakitani and Mataga 1985) and as a barrier to electron tunneling (DeVault 1984). It has been noted that this barrier

has two opposing components: a hindrance caused by the filled orbitals of the solvent, and a help caused by the optical polarizability of the solvent (Mauzerall 1976). While this is so for the media between the donor and acceptor - the classical "barrier" - the opposite is true for the media sur- rounding the donor-acceptor pair. The origin of this effect on the tunneling parameter is the three- dimensional nature of the interaction of the wavefunctions. If the environment, and thus the potential, is nonsymmetric, so will be the wavefun- ctions. As a first approximation the effect will be proportional to the reciprocal of the fractional solid angle subtended by the acceptor onto the donor. The effect is limited because it is only the differential of the electron distribution inside and outside this solid angle that is involved. However, even a factor of two in the tunneling parameter can cause a tenfold change in the rate of electron tun- neling. The effect will increase the rate of tunneling if the outer media has a greater density of filled orbitals (core tamper effect) and lower optical pol- arizability (polarizability tamper effect) than the inner media, and vice versa. We refer to this situ- ation as the tamper effect. Essentially the tail of the wavefunction of the donor is reflected from the outer media and concentrated into the inner media and thus onto the acceptor. We have no direct measure of the lifetime of the putative ionized state P ÷ Q - . However, even if the lifetime were vanishingly short, i.e. purely a charge-transfer channel to the ground state, the same arguments concerning the overlap of the wavefunctions will apply.

We believe an example of this tamper effect is seen in the rate constants for the heavily chlori- nated solvents (XCC13 in Fig. 1). These time constants average 240% less than expected given the solvent static dielectric constants. We have presented evidence that these large molecules cannot fit in the cavity of the more enclosed con- former "a" (Delaney et al. 1989). Essentially the equilibrium constant for the two conformers, K = ZnPQa/ZnPQb, correlates inversely with the molar volume (Vm) of the solvent, being < 1 when Vm > 100 cm 3. This corresponds to a cavity radius of 3.4 A, just that estimated for conformer "a" .

The relevant parameters for the tamper effect are the density of electrons in filled orbitals and the optical polarizability of the solvent versus that of

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the side chains. The parameter de is defined as the solvent density times the number of electrons divided by the molecular weight. It is the reciprocal volume of an electron in a solvent. The density of filled orbital electrons of the chlorinated solvents is so much higher (average de = 0.74) than that of the carbon, nitrogen and oxygen side chains (average de = 0.56) that the tamper effect is maximized. The optical polarizability of these solvents is appre- ciable (average n 2 = 2.06) but is less than that of the side chains (n 2 ~ 2.39), thus also favoring the tamper effect.

The difference between 1,1,1-trichloroethane and its isomer 1,1,2-trichloroethane is particularly striking (Table 1). The conformer equilibrium constant, K, increases 5-fold from 0.2 to 1.0 and ra increases by 60% but Tb increases only by 8% on measurement in the former versus the latter solvent. The parameters r~ and rb are the time constants for electron transfer in photoexcited ZnPQ~ and ZnPQb respectively.

In agreement with this hypothesis, the value of K for the relatively gigantic solvent sucrose octa- acetate is 1.2 (compared to 1.0 in ethylacetate), and decreases to 0.4 as the temperature is lowered (Delaney et al. 1989, Fig. 3C). However, ra remains near 1.3ns, well above that of the chlorinated solvents. The core tamper effect is not expected in this case since the electron density of the atoms of sucrose octaacetate are similar, to those of the bridging groups. However, r~ is one third faster than in ethyl acetate (r~ = 1 ns), possibly reflecting the effect of small polar impurities (see below).

The values of the electron transfer time constant for the large cavity conformer "b" , rb, may support this hypothesis. They are clustered near 6.5 + 0.6 ns for all the chlorinated solvents (Table !). This time constant is near that of tetrahyd- rofuran and ethyl acetate (9 + Ins) but smaller than that of benzene and toluene (> 50 ns). Since all the chlorinated solvents enter the large cavity of conformer "b" , no tamper effect is predicted. It is interesting that hydrogen bond donors and acceptors have Tb about double those of tetrahydro- furan and ethyl acetate in spite of their much higher static dielectric constants. This suggests that they are more rigidly held by hydrogen bonds than the chlorinated solvents and thus less well able to solvate or trap the charged species in the cavity. In fact acetonitrile has an exceptionally low rh (3 ns)

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and alone among these solvents may be able to move freely in the large cavity of conformer "b".

Two objections may be made to the tamper effect. The first is based on the claim that these large chlorinated solvents are too large to fit in the cavity of the conformer "a". The electron may tunnel through a vacuum and this may be faster than in the presence of solvent molecules: all of the cavity space is available for tunneling. However, "nature abhors a vacuum" as seen by the sorptive power of zeolites and the solvents are not pure to the level of < 10- 5 M, the concentration of ZnPQ(Ac)4 present. So small molecules (H20, C2HsOH, etc.) will be expected to enter the cavity. Although this would partially fill the vacuum, it is unlikely that solvent molecules can pack as tightly in the cavity as in bulk solvent: this is the quantized volume or "back pack" problem. The possibility that the internal polar solvent may add a local static polarizability and thus increase the rate constant is ruled out by its non-occurrence with zb (see above). An estimate of the polar impurity effect can be made by com- paring ra in sucrose octaacetate with that in ethyl acetate: there is a decrease of 35% . For com- parison, the average decrease of r~, in the four X C C I 3 solvents over solvents with equivalent static polarizabilities is 240%. Sucrose octaacetate can be assumed to show the same polar impurity effect as the other solvents. However, the polarizability tamper effect would also be rate increasing in this case and larger than in the chlorinated solvent: n 2 = 1.88 for ethyl acetate versus n 2 ~- 2.39 for the side chains and 2.1 for the chlorinated solvents. The core tamper effect is expected to be absent as discussed earlier. Thus we conclude that about 85% of the observed rate increase (205% out of 240%) is caused by the core tamper effect and the remainder by polar impurities and the polariz- ability tamper effect. The core tamper effect may also be present in hexafluorobenzene. Although its dielectric constant does not appear to be listed, it must be in the range 2.5-3. Yet its Ta is only one- half that of benzene. This correlates with its very large electron density, d c = 0.67 versus that of benzene, 0.47. The small value of K, 0.6, supports the view that hexafluorobenzene cannot enter the cavity of the conformer PQa.

The second objection to the tamper effect is that the measured shortened fluorescence lifetime in the heavily chlorinated solvents may be caused by the

heavy atom effect. This has been well studied in molecular spectroscopy (Koziar and Cowan 1978), including the case of direct bonding to the por- phyrins (Solovev et al. 1972). In fact we do observe shorter lifetimes in brominated solvents even in the absence of the quinone in the porphyrin molecule. This effect is proportioned to Z 4, where Z is the nuclear charge of the heavy atom, and thus would be negligible for chlorinated solvents. The lifetime of zinc tetraphenyl porphyrin in the XCCI3 solvents is within 5% of that in acetonitrile (1.85ns, data not shown). Thus the heavy atom effect of the chlorinated solvents can be neglected. Electron transfer to solvent is also precluded.

We conclude that the tamper effect is real and is worth further study. It may play a role in the operation of the Bacterial Reaction Center.

Acknowledgements

This research was supported by the National Science Foundation (Grants DMB83-1673 and DMB87-18078) and by the Rockefeller University.

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