J. Phys. Chem. 1993,97, 13172-13179
13172
Hole Localization and Spin Coupling in a-Mono- and a-Dications of p-Oxoporphyrin Dimers. Relevance to Structure of Oxidized "Special Pair" in Photosynthetic Reaction Centers R. A. Binsteadtit and N. S. Hush'JV**l Department of Theoretical Chemistry and Department of Biochemistry, University of Sydney, Sydney, N.S.W. 2006, Australia Received: July 22, 1993' The antiferromagnetically coupled cofacial p-oxoiron(II1) dimers of octaethylporphyrin (OEP) and a,&y,6tetraphenylporphyrin (TPP) can be oxidized in two one-electron steps to yield a-monocations and a-dications. Hitherto unreported absorption bands are observed in the mid-infrared region in the spectra of the monocations. These are identified as intervalence transitions of dynamically trapped holes. The electron-phonon coupling energies (CH2C12 solution, 295 K) are 0.3 1 f 0.04 eV, and the inter-ring, predominantly through-space, electronic coupling constants J are 0.07 and 0.03 eV, respectively. The small values of J are a consequence of the large mean plane separation of the porphyrin rings (4.53 A). Since it is improbable that the electron-phonon coupling energies will vary greatly between cofacial porphyrin dimers, it is suggested that absorption bands around 1 eV in the r-monocations of "sandwich" compounds such as M"'P2 or MIVP2+,where P is a porphyrin and M are lanthanide, actinide, or transition metals (3-1 2) observed under similar conditions will have electronic ground states that are delocalized on at least the vibrational time scale, with frequency maxima equal to 2 J in the tight-binding approximation. The thermal inter-ring hole-transfer times in the p-oxo dimer monocations are estimated to be approximately 1 ps. The relevance of these results to the problem of the structure of the oxidized "special pair" in the photosynthetic reaction center is briefly discussed. The r-dications exhibit a band in the near-infrared region which is attributed to a transition between antiferromagnetically coupled a-states, from which, using the Hubbard hamiltonian, inter-ring exchange integrals K are calculated to be 0.39 f 0.02 eV, and the singlet-triplet separations SATcalculated to be 0.025 and 0.0024 eV, respectively. The monocations are stable to disproportionation in CH2C12 solution (Kcom(295 K) = 3 X lo5 and 2 X lo4, respectively).
1. Introduction
Electron- or hole-transfer processes involving porphyrins are of widespread biological importance and are currently much studied in model systems. Among these are cofacial porphyrin dimers. The bonding between the porphyrin rings can be achieved in a number of ways. Bonding by means of suitable metal substitution in the ring centers is one such general method. This can be achieved, for example, by forming unbridged metal-metal multiple bonds.192 Alternatively, for metals with suitable ionic radii, complexes of the form M(P)2 can be formed, where P is (formally) a porphyrin dianion and M is a singlemetal ion. When M is a trivalent lanthanide, the complex has unit positive charge and is of porphyrin/porphyrin *-radical type; these and their oxidation products have new near-infrared absorption bands not observed in either the monomeric porphyrin or its monomeric radical cation;3-5 similar behavior is noted for the neutral complexes of tetravalent metals and their (ring) oxidation products; these include transition metals such as ZrIVand HPV 7 Department t Department
of Theoretical Chemistry. of Biochemistry. t Present addrcss: Department of Chemistry, University of North Carolina, Chapel Hill, N.C. 27599, U S A . * My research interests have intersected with those of Gerhard Closs on several occasions, the most recent, from the mid-19809 on, being long-range electron transfer through saturated organic bridges. As I recall, the first, around 1964, was an independent essentially simultaneous interest in the electronic, electrochemical, and spectroscopic properties of the series of ions by successive electron uptake by porphyrin and other tetrapyrrole-type molecules. Our modest contribution to this issue in his honor, dealing as it does with porphyrin radicals and electron transfer, is one I like to think he would have been interested in discussing with us. He and I met at least every two years at the Gordon Conference on Donor-Acceptor Interactions; we were both scheduled as Session Chairmen for the August 1992 meeting, and all participants learned with great sadness of his death just before this. His outstanding originality, and his extraordinary ability to engineer molecules to facilitate crucial tests of theory were universally admired. I shall also greatly miss the valued occasional companionship of a complex and dedicated personality. Abstract published in Advance ACS Absrracrs. November 15, 1993.
(refs 6-10) and actinides such as ThIV and U'v.6JlJ2 The separations of mean plane of the porphyrin rings in these systems, where it is known, is quite small, in the range 2.7-3.4 A. This should permit relatively strong overlap of the porphyrin A systems. (A new type of cofacial porphyrin dimer radical cation in which there is no apparent covalent bond, has also been recently described; this also displays a new infrared band, at 0.65 eV in CH2C12 solution.l3) In general, apart from small differences in the solid state which are probably due to packing forces, no distinction can be made between the porphyrin and porphyrin radical cation moieties in the one-hole dimers, at least on the vibrational time scale. Complete delocalization of the 17 systems has definitely been proposed for some single-hole dimers (e.g., refs 4 and 11); in other cases (e.g., ref 5 ) no decision is reached as to whether the hole is delocalized or dynamically trapped. One type of system which would be particularly useful in throwing light on this general question, and which could also provide information about the microscopic parameters determining hole-transfer dynamics in trapped-hole dimers, is one in which the inter-ring mean plane separation is large enough for electronic coupling to be sufficiently small for the hole to be (at least vibronically) trapped rather than delocalized over the two rings. In this paper, we present experimental results for two systems which we believe to be of this type, namely, the monocations or single-hole states of the pox0 dimers of highspin Fe(II1) porphyrins; these are O(FeIII(TPP))2 and O(FeII1(OEP))2, where TPP is the (formal) dianion of a,@,.y,6tetraphenylporphyrin and O E P is the dianion of octaethylporphyrin. In these, the metal-metal interaction occurs via an oxygen bridge. The two-hole dication states are also studied. In early work on the oxidation of thesespecies,it was concluded that the first one-electron step led to oxidation of one Fe(II1) to Fe(IV).1417 However, it is now well-established that the product of one-electronoxidation is in general an Fe(II1) *-cation radical (refs 18 and 19 and references therein). The interplanar separation in O(FeIII(TPP))2is known from the workof Hoffman,
0022-365419312097-13172%04.00/0 0 1993 American Chemical Society
Hole Localization and Spin Coupling Hoard, et al.20,21to be very large, 4.53 A; the reason for this is that each Fe ion is displaced 0.5 A from its porphyrin ring center. Hoardz1reports similar geometry for the proto-IX DME system. Close similarity of many properties for p-oxo Fe(II1) dimers of variously substituted porphyrins strongly suggests that an interplanar separation close to that observed for the TPPdimer will be general for such systems. We shall assume this to be so for the OEP derivative. The large size of the mean plane separation suggests that electronic interaction between the rings will indeed be quite small. The u-type interaction of the r-systems of the two rings should be essentially of the "through-space" type, involving direct overlap of the *-electron density of each ring. With small electronic coupling, the r-monocations would be expected to exhibit hole trapping, with consequent dynamic transfer of the hole between the two ring systems. Thus, it should be possible to observe intervalencetransfer absorption bands22.23in the r-monocations and, by analysis of their characteristics, to obtain values for the important microscopic parameters determiningthe rates of outerring transfer. The new infrared features of the monohole states of the MP2 systems mentioned above, attributed to transitions between either localized or delocalized states, have frequencies in the range 0.6-1.0 eV, and we would anticipate (and in fact find, contrary to a previous report," bands of very much lower frequencyin spectra of the p-oxo-bridged systems dimers. Studies of the corresponding two-hole dications are expected to yield further information about exchange and spin coupling between Fe(II1) *-cation radicals at large separation. For these purposes, we report the spectroscopy and electrochemistryof the neutral, *-cation, and r-dication states of the above two representative Fe(II1) p-oxoporphyrin dimers.
2. Experimental Section Materials. Tetra-n-butylammonium hexafluorophosphate, TBAH, was prepared by metathesisfrom the bromide salt (Fluka, puriss) and ammonium hexafluorophosphate (Merck, LAB) in distilled water from KMn04and purified by two recrystallization steps from hot, absolute ethanol followed by drying in vacuo at 100 OC. Dichloromethane (Merck, AR) was purified by refluxing over P,Olo for 2 h followed by distillation. The fraction boiling in the range 39.5-40 OC was collected and stored over 3-.& molecular sieveswhich had been predried at 350 OC. Two samples of p-oxo(tetraphenylporphyrin)iron(III) were obtained,one from Strem Chemicals (Danvers, MA) and a second, which was spectroscopically identical to the Strem product, was prepared by Dr. Maxwell J. Crossley in these laboratories. Samples of p-oxo(octaethylporphyrin)iron(III) and monomeric (tetraphenylporphyrin)iron(III) hexafluoroantimonate were also kindly donated by Dr. Crossley. Methods. Electrochemical half-wave potentials, E1p, were obtained by cyclic voltammetry using an operational-amplifierbased potentiostat with positive feedback ZR compensation in conjunction with a Supercycle triangle wave generator24 and a Hewlett-Packard 701SB X-Yrecorder. All measurements were made at room temperature (21-23 "C) in CH2C12/0.1 M TBAH using Teflon-shroudedplatinum disk working electrodes,platinum wire auxiliary electrode, and a Ag/AgNOp (0.01 M in CHpCN) reference electrode in a three-compartment cell fitted with medium-porosity glass frit separators. Controlled potential electrolysis was performed in the same cell using platinum gauze electrodes in conjunction with a Princeton Applied Research Model 173 potentiostat. Solutionsof the *-cations and r-dications of thep-oxo porphyrin dimers were prepared by controlled-potentialelectrolysis in CHzCl2/0.1 M TBAH under argon or nitrogen atmospheres, protected from light. In particular, the dications were found to be highly reactivewith oxygen. Solutionsof (O(FeIII(TPP))2)+,produced by electrolysis at +0.60 V, were relatively stable toward oxygen
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13173 but did decompose slowly if unprotected. However, the corresponding dication had to be prepared and transferred under more rigorous conditions but even so, some decomposition was apparent following reduction to the parent neutral dimer state. Solutions of (O(Fe111(OEP))2)+and (0(Fe111(OEP))2)2+ decomposed more rapidly than their TPP counterparts, so that it proved to be impossible to obtain pure samples of the dication under our experimental conditions. Spectrophotometricmeasurements were made over the range 300&230 nm using a Cary 171 instrument interfaced with a microcomputer system and a digital plotter. Molar extinction coefficients, c (M-1 cm-I), for the neutral p-oxoporphyrin dimers weredeterminedassumingmolecularweightsof 1357.2and 1193.3 for the TPP and OEP species, respectively. In general, spectra were obtained in 1.O f 0.02 mm path length near infrared-grade fused silica cells (NSG), though 10.00 f 0.02 mm cells were also used to confirm Beer-Lambert law behavior for the neutral dimers (7 X 10-5-5 X 1 V M) and to check the calibration of the l-mm cells. Molar extinction coefficients for the spectra of the *-cations and ?r-dicationswere determined by ratio to those of the neutral dimers following chemical or electrochemical reduction of the oxidized species. In the case of (O(FeIIITPP)2)+reduction could be effected by addition of a volumetrically negligible amount of TBA(Br) directly to the sample cell. However, the addition of B r to a solution of the corresponding dication resulted in a chemical reaction with the porphyrin. Hence, reduction was performed electrochemically instead, with about 90% recovery of the neutral dimer. Similarly,solutions of the OEP monocation and dication had to be reduced electrochemically, with recovery of the neutral dimer in about 90% and 70% purity, respectively. The slow degradation of solutions of (O(Fe1110EP)2)2+ was quite evident from the growth of an impurity peak near 1200nm between successive scans and it was not possible to obtain a spectrum free from this impurity. However, corrected spectra of (O(FeII1OEP)2)2+ were obtained by a procedure based on digital subtraction of successive scans. This method, though effective, resultedin a poorer signal-to-noiseratio for thecorrectedspectrum. This was alleviated somewhat by the use of quartic polynomial curve smoothing.25 Similarly,solvent and electrolyte peaks which interfere with the near-IR region of the spectra were removed by digital subtraction followed by curve smoothing. Band-shapeanalysisof the near-IR region of the spectra of the *-monocations, expressed as c/vvs v (cm-I), was performed using a model (eq 1)which assumed a Gaussian line shape for each Z(v) = E A i exp(-ln (2)/(HWS2(v - P,)')
(1)
overlapping component,where A, is the peak amplitude of the ith peak, HWi is the half-width at half-maximum peak height, AVI/Z (cm-l), P,is the peak position (cm-l),and vis theoptical frequency (cm-1). In thecase of the a-dications,thelowest energy transition could be modeled as either a set of overlapping Gaussian componentsor a single Lorentzianband (eq 2),with the remainder
of the spectrum being modeled as Gaussian components. The latter model was preferred as it included most of the observed intensity for the lowest energy transition within a single absorption envelope. To effect these line-shape fits, data were extracted from the smoothed spectra at approximately even cm-I steps in c / v units and stored on disk. These were subjected to nonlinear leastsquares curve fitting, using the Newton-Raphson method. With iterative use of this method excellent fits were obtained for the entire UV-vis-NIR spectra with up to 17 component peaks. The
Binstead and Hush
13174 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993
TABLE I: Oxidation Potentials of the Iron(III) Porphyrins in CHflJO.1 M TBAH vs Ag/AgN03 at T = 23 f 2 OCO Eip, V Eip V wruhvrin EmeCV (AE-mV) (AE., mV) Fc(TPP)(SbF6) +1.155 (67) +0.845 (71) O(Fe11ITPP)z +1.20 +0.760 (66) +0.505 (69) O(Fe"'OEP)2 +1.15 +0.615 (61) +0.295 (60) * Sweep rate = 100 mV/s, Pt disk working, Pt wire auxiliary and Ag/AgNOs (0.01 M in CHaCN) reference electrodes. * Ferrocene/ ferrocinium couple was +0.169 V (AE,= 83 mV) under the same conditions. C Anodic peak maximum, E,, observed for quasi-reversible wave near solvent limit. ~~
,
A
21
~~
initial estimates for the peak parameters and, indeed, selection of the model itself for fitting the spectra were determined first by use of a plotting simulation program. The data were rescaled into t vs Y form (skewed Gaussian) for illustration of the predicted band shapes for the near- and mid-IR transitions. 3. Results
Cyclicvoltammogramsof the pox0 dimers, O(Fe111TPP)2and O(FeIIIOEP)2 in a medium of CHzC12/0.1 M TBAH revealed two reversible oxidation waves in each case (Table I). The peak was 60-70 mV for each wave, independent of separation, Up, sweep rate (u = 50-500 mV/s), while the anodic and cathodic peak currents, 1, and IF, increased linearly with u1i2 and their ratio was close to unity as expected for reversible one-electron waves.26 Thin-layer coulometry at u = 1 mV/s gave peakcurrents for these waves close to those for the ferrocene/ferrociniumcouple at the same concentration,confirming the one-electron nature of the oxidation waves. A third, irreversible oxidation wave was also observed for both porphyrin dimers close to the solvent limit. For comparison the oxidation potentials of the monomeric (FelI1TPP)+ species are also given in Table I. The splitting between the first and second oxidation waves of the p-oxo dimers can be interpreted in terms of the equilibrium
O(Fe"'P),
I
I
l0000
20000
30000
40000
Wavenumber (cm-')
Figure 1. Electronic absorption spectra (e vs v) of the meso-tetra-
-
phenylporphyrin species O(FCI~~TPP)~ (-), (O(Fe111TPP)2)+ (- -) and (O(Fe111TPP)2)2+(* -) inCHZC12solution,withO.l MTBA(PF6)added electrolyte for the cations. I .4
I
l0000
20000
30000
40000
Wavenumber (cm-I)
+ (O(Fe1r1P),)2+* 2(0(Fe"'P),)+
(3) (P = tetraphenyl- or octaethylporphyrin) as a measure of the stability of the mixed-valence ions to disproportionation. The measured potential differencesof 0.255 and 0.32 V for the TPP and OEP dimers, respectively, correspond to equilibrium constants, Kcom,of 2 X lo4 and 2.6 X 105. Thus, solutions of the r-monocations of the dimers are expected to be stable in the absence of chemical reactions with solvent or oxygen. Previous measurements of these oxidation potentials (e.g., ref 19) yield values in approximate agreement with these. As noted above, it was possible to prepare solutions of both the r-monocations and r-dications of the TPP and absorption spectra of the neutral dimers and their oxidized forms are shown in Figures 1 4 , whilethemajorpeaksarelistedinTables1IandIII. Solutions of both (O(Fe111(TPP))2)+and (0(Fe1I1(OEP))2)+in CHzC12/ 0.1 M TBAH exhibit a broad near-IR absorption band (AYIIZ 4000 cm-l) rising to a peak maximum somewhat below the 3333cm-1 lower limit of the Cary 171. These bands are absent from the spectra of the corresponding neutral dimers and r-dication dimers. Unfortunately, it proved to be impossible to define the peak maxima more accurately using infrared spectroscopy owing to the strong interference from solvent bands below 3000 cm-1 coupled with the poorer sensitivityof the IR instrumentsavailable. Consequently, band-shape analysis was employed to extract estimates of the peak positions and half-widths from the near-IR data within reasonable error bounds. For this purpose it was assumed that the spectra,when expressed as t/u, could be modeled empirically as a series of overlapping Gaussian bands. To account for the effects of the visible absorption bands, the entire spectrum was simulated and then curve fitted by nonlinear least-squares
-
Figure 2. Electronic absorption spectra (c VI v) of the meso-octaethylporphyrin species O(Fe11'OEP)2 (-), (O(Fc"'OEP)2)+ (- -) and (O(FeWEP)2)2+(-*-)inCH2Cl2solution,withO01MTBA(PF6)added electrolyte for the cations.
-
-
regression to models with 1 4 1 7 peaks. After achieving a satisfactory fit for the more intense UV-visible region, the broad near-IR absorption envelope was refitted, allowing all parameters for the first three components to vary simultaneously. The fitted near-IR spectra of the r-monocation dimers are shown rescaled as t vs Y in Figure 3. The fits give predicted peak maxima at 2200 f 130 cm-1 (Aulp = 3060 f 100 cm-l) for (O(FeII1(TPP))2)+, and 2800 f 130 cm-l (Au1/2 = 2500 f 160 cm-') for (O(FelI1(OEP))2)+. The spectra of the corresponding r-dications, (0(FelII(TPP))2)2+and (O(FeIII(OEP))2)2+,both display near-IR transitions in the vicinity of 6500 cm-l (AY~/z = 2500-3200 cm-I), which are absent from the spectra of the neutral dimers. In the case of (O(Fe111OEP)2))*+, the spectrum has been corrected for an impurity peak which absorbed at ca. 8300 cm-l, as outlined above. Thesubtraction procedureshould not havegreatlyaffected the band shape of the near-IR transition attributed to the r-dication dimer. The band-shape analysisfor the spectra of the a-dication dimers is considerably more straightforward, since the entire absorption envelope is defined by the experimental data. However, the results of the fits, in particular the line shape of the lowest energy transition, were found to be dependent on the model assumed. With use of a Gaussian line shape for the function t / u vs Y , the lowest energy band for both the TPP and OEP r-dication dimers had to comprise three components for a satisfactoryfit. This requirementcould be eliminated by relaxing
Hole Localization and Spin Coupling
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13175
TABLE II: Electronic Spectral Maxima Data for O(F@TPP)+ (O(FeTPP)d+, and (O(FeTPP)#+ in C H P z Solution
.4
a .3
neutral dimer vx10-3 c x i ( r (cm-I) (M-I cm-I)
.2
-
h
.1
13.11 15.43 sh 16.40 17.57 24.61 28.14 sh 3 1.44 32.26 sh 36.50 sh 40.00 sh
j I
s v
o
0)
2
2 X
1.6
J.!
1.2
0.055 0.139 0.818 1.75 2 1.09 5.152 5.77 5.54 4.78 4.65
r a t i o n dimer
vx10-3 (cm-I)
cxi(r (M-1 cm-l)
0.032
12.94 14.49 sh 15.87 sh 17.51 24.54
0.261 0.533 0.968 1.51 17.72 25.38 7.40
30.57 34.78 sh 40.82 sh
r-dication dimer vx1~3a ~ i ( r (cm-I) (M-1 cm-1)
6.73 12.74sh 14.20sh 16.67 18.18 22.30sh 12.16
0.037 0.501 0.824 1.79 2.18 6.04
4.91 4.79
TABLE IIk Electronic Spectral Maxima Data for O(FeWEP)z, (O(FeWEP)z)+, and (O(FemOEP)z)*+in CHzClz Solution
.8
.4
neutral dimer 0 4000
2000
6000
r-dication dimer
10000
8000
Wavenumber (cm-')
Figure 3. Estimated mid-infrared band profiles
r-cation dimer
I
O. 19
vs v ) for (a) (O(Fe111TPP)2)+and (b) (O(Fe1110EP)2)+in CH2C12/0.1 M TBA(PF6) (a
-
solution, showing the spectral data (-), the fitted curve (- -), and the first three component bands (e-) after subtraction of all fitted bands higher than 10 OOO cm-I, obtained from multi-Gaussian fits of the data as c / v vs v.
15.65 sh 17.06 18-00 26.10 28.90sh 29.94sh 35.09sh 40.32
0.196 1.099 1.283 13.17 8.45 7.72 3.15 3.64
13.66 sh 15.15 sh 17.10 17.67 26.73 29.67 41.32
6.16 9.22 sh 13.67 sh 15.97
0.194 0.374 1.033 1.083 11.13 8.83
17.44 27.78 28.69
3.41
>43.5
0.074 0.323 0.258 0.668 0.952 11.42 11.15 >3.26
TABLE I V Band-ShapeParameters for the Mid-infrared Transitions of (O(FeWPP)z)+ and (O(FeWEP)z)+ in CH2Cl2 - - Solution parameter cm-1 a, M-I cm-l Y-,
3 cm-' x,
cm-1 (eV) J, cm-I (eV)
(0(Fe"'TPP)2)+ 2200 160 390 A 47 2590 120 4.50 2200 (0.27) 200 (0.025)
*
(0(Fe"'OEP)2)+ 2800 & 140 2060 i 110 2330 140 (4.5)b 2800 (0.35) 555 (0.069)
*
See ref 7. Estimated (see text).
4. Discussion
,
0
,
2000
'
4000
'
6000
'
8000
'
10000
Wavenumber (cm-l)
Figure 4. Estimated near-infrared band profiles (e vs v ) for (a) (O(FelI1MTBA(PF6) solution, TPP)2)*+and (b) (O(FemOEP)2)2+inCH2C12/0.1
-
-) ,th efirstcomponent showingthespectraldata(-),thefittadcurve(band (- -),and the sum of the remaining component bands (--) ob tained from multi-Gaussian fits of the data as a/v vs v.
-
the line shape for this band to Lorentzian. In this case most of the experimental profile was contained within a single band, as shown in Figure 4, giving predicted peak maxima for the unsymmetrical function c vs Y at 6670 i 20 cm-I ( A Y ~ = / z 3200 i 45 cm-I) for (O(Fe111(TPP))2)2+ and 6140 i 40 cm-I (Av112 = 2450 i 40 cm-l) for (O(FeIIl(OEP))2)2+.This appears to be the most realistic approach for estimating the intensities of these transitions.
Monocations. We confine discussion of both mono- and dication spectra to that of the mid- and near-infrared region. The peak maxima of the mid-infrared bands of both (O(Fel*I(TPP))2)+ and (O(Fe111(OEP))2)+in CH2C12 solution occur at very low energies, just below the 3333-cm-1 lower limit of the Cary 171 spectrophotometer. Nevertheless, it is possible to estimate the peak positions, half-widths, and intensities for these transitions within reasonable error bounds using the curve-fitting approach above. The results of these fits are shown in Table IV. We make the reasonableassumption that these represent interring transitions. From the data in Table IV we calculate the oscillator strengths f for the TPP and OEP systems, using the Gaussian band-shape approximationf = 4.6 X 10-9cmAv1/2, to be 4.6 X 10-3 and 3.0 X 10-2, respectively. The corresponding transition dipole lengths D1, where D12 is given by 0.9217f X lOS/v,,, are 0.5 and 1.1 A, respectively (units as in Table IV, first entries). If the bands are intervalence transfer bands of dynamically trapped hole systems, these dipole lengths should also be given to good approximation as D I= 0.143 cau1/2vau-1/4 (i.e., JR/x).22 From the data of Table IV, these are D1 = 0.4
13176 The Journal of Physical Chemistry, Vol. 97,No. 50, 1993
and 0.9 A for the TPP and OEP systems, respectively. These are in acceptable agreement with experiment, and there can be no doubt that the singly-oxidized p-oxo-Fe(II1) porphyrin dimer cations are dynamically trapped hole systems, and that the midinfrared bands are indeed attributable to intervalence transfer. A point of general interest for the electronic structures of single r-holecofacial porphyrin dimers can bedrawn from the magnitude of the electron-phonon coupling constant x, which is very similar for both systems, 0.31 k 0.04 eV. In the unbridged single-metal bound dimers of type M(P)2 discussed in the Introduction, there may be a somewhat larger contribution to x from inter-ring stretching modes. However, if the near-infrared bands observed in the systems with energies of the order of 1 eV were to be attributed to intervalence bands of dynamically trapped hole systems, the values of x would have to be larger by 0.7 eV. Such increases would, however, be very highly improbable, and the recognition of the properties of typical dynamically trapped systems such as we discuss leads us to predict that the ground states of all cofacial porphyrin whole systems with near-infrared bands at around 1 eV will be completely delocalized, rather than trapped, on at least the vibrational time scale. The criterion for localization (Hush27) is that 2J/x should be appreciably less than unity; in our systems, this ratio is 0.18 and 0.40 for TPP and OEP dimers, respectively. For the p-oxo-FeIII dimers, the transfer integrals J are sufficiently large (>kBTat 300 K) for the electronic transmission coefficient K of the thermally activated hole-hopping process to be near unity. Thus, the hole transfer at 4.5 A between the porphyrin rings is expected to be close to electronically adiabatic, and this is borne out by calculation. The transmission coefficient K is given by23*29
(4) where P ~isz given by23
A typical value of vcff, estimated by the method of ref 28, is 700 cm-1. Thus the values of K for the hole transfers in the OEP and TPP dimer monocations (CH2C12, 300 K) are 0.98 and 0.54, respectively. These are indeed both close to unity. Assuming an outer-sphere model, and assuming an activation free energy of (x/4 - J),22 hole-transfer times calculated by semiclassical transition-state theory of 1.7 and 0.8 ps are obtained for the OEP and TPP dimer monocations, respectively. In a more complete treatment, the intervalence transfer band envelope would be analyzed to obtain estimates of the relative contributions from high- and low-frequency modes (refs 22 and 30 and references therein), and the semiclassical rate expression modified to allow for vibronic coupling and "scrambling" of the localized states owing to the low-energy barrier. However, the dynamics will be expected to remain in the picosecond region. The above estimate is the more reliable the smaller the high-frequency mode contribution to the electron-phonon coupling energy. The detailed geometries should be mentioned. A single-crystal X-ray structure for O(Fe111(TPP))220*21 has shown that the F e 0-Fe bond angle is 174.5' with an Fe-0 bond length of 1.763 A. The Fe atom is displaced by 0.50 A from the center of the macrocyclic rings, which are almost parallel (dihedral angle = 3 . 7 O ) , resulting in a mean separation of 4.53 A between the ring planes. An important feature of the structure is that the rings are in a staggered conformation (19 = 54.6O) owing the nonbonded repulsions between the bulky phenyl substituents of the two rings, leading to a quasi-& symmetry. While there appears to be no structure yet available for the p-oxo dimer of Fe(II1) octaethylporphyrin, the general features are expected to be similar. The smaller (by a factor of more than l / 2 ) value of the transfer
Binstead and Hush integral J for the TPP dimer system compared with that for the OEP dimer invites comment. Assuming approximate D4h symmetry of the individual rings, it is probable that the orbital symmetriesof the highest filled levels,and hence of the electronic states of the cations, are respectively azu and al,, as established also for the monomeric radical cations," estimated for Ce(TPP)2+ and Ce(OEP)2+(ref 4) and supported by general considerations about the relative ordering of the highest filled *-levels in subs tituted porphyrin^.^^ As suggested by elementary tight-binding theory, in an eclipsed conformation the T--r inter-ring coupling should not depend too strongly on the nature of the (equivalent) molecular orbitals concerned. In a staggered conformation, however, the inter-ring coupling should be more sensitive to the symmetry of the interacting orbitals; it has been suggested4that in this configuration inter-ring ?r coupling will be more efficient via a2,, rather than via alu orbitals. This is qualitatively in agreement with our results. In fact there is good independent evidencethat inter-ring coupling in cofacial monocations is larger for OEP dimers than for the TPP systems; for example, the frequencies of the near-infrared bands in (MIV(P)2)+or (MI1'(P)2),where MIv is a transition metal (Hf, Zr, Ce) or a trivalent lanthanide, which can be set equal to 2 J in these presumably fully delocalized systems, are higher for the OEP (al,) than for the TPP (az,,) isomer' in these staggered dimer systems. The difference is however comparatively small, the OEP coupling strengths being on average only 10%larger. The much larger difference of Jobserved in the trapped-hole p-oxo-Fe(II1) dimer cations may result from a difference of conformation. The staggered conformation of O(Fe111(TPP))2will be retained in the cation, as this is presumably imposed by steric repulsion of the phenyl groups; however, it is possible that the corresponding OEP dimer cation may have an eclipsed ground state, bearing in mind the large inter-ring separation in these dimers, and that the resulting increased overlap may be the main source of the observed much larger coupling strength for this porphyrin. In any case, the observed values are of the order of that obtained from an STO 3G S C F calculation of ethylene-ethylene monocation interaction at 4.5 A, in an eclipsed configuration with a-type overlap of the ?r orbitals, 0.05 eV. It is interesting to note that for a 3.4-A separation, a distance in the vicinity of those found for M(P)2dimers, J f o r the ethylene/ethylene+ dimer is similarly calculated to be 0.5 eV, so that 2 J is of the order of the energies of the inter-ring infrared absorption energies (ca. 1 eV) found in delocalized r-radical dimers such as those mentioned above, where the typical values are 0.65 eV a t 3.20 inter-ring separation (M = Zr) and 0.49 eV (M = Ce) at 3.40 separation.' This of course ignores differences between C and N *-orbitals and strictly applies only to the eclipsed configuration, but it serves to illustrate the sharp dependence of transfer integral on internuclear distance that is both predicted and observed in the r-radical cation dimers. Dications. The results of the spectral fits for the near-infrared bands of the dimer r-dications are summarized in Table V. The band maxima are a t considerably higher energies than those of the monocations (average 0.8 eV), with that of the TPP dimer lying about 0.066 eV above that of the OEP system. A further feature of interest is the relatively low average extinction coefficient. In interpreting these spectra, it will be necessary to consider the exchange coupling between the two porphyrin rings. Calculation of the electronic and especially of the magnetic proper tie^^^-^' of weakly coupled open-shell systems is not straightforward. It is further complicated in the present instance in that in addition to the unpaired a-electron in each porphyrin cation, there is also a high-spin (S= 5/2) iron(II1) ion. It is well-established that for a wide range of complexes in which iron(II1) is bonded to four coplanar nitrogens (e&, 1,lOphenanthroline36 tetradentate Schiff s bases3' and including porphyrins,3*the iron(II1) spins are coupled antiferromagnetically. This has been confirmed for O( FeIII(TPP))2 and related binuclear
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13177
Hole Localization and Spin Coupling
TABLE V: Band-ShapeParameters for the Near-Infrared Transitions of (O(FemTPP)z)'+ and (O(FeWEP)z)z+ in CH2Cl2
Solution
parameter
(O(FeI"TPP)#+
v u , an-'
M-I cm-1 A V Icm-I ~ K12, cm-1 (eV) e,
cm-1 (eV)
*
(O(Fe1110EP)2)2+ 6140 40 690 f 27 2450 f 40 3500 (0.37) 200 (0.025)
6670 20 366 f 2 3200 50 3800 (0.41) 20 (0.0024)
oxebridgediron(II1) porphyrins by study of protonNMRcontact shifts;39 strong antiferromagnetic exchange coupling is found, and the contact shifts are quantitativelyaccountedfor by thermal population of the S = 1 and S = 2 states. This is supported by Mossbaiier studies.40 We assume that this will also be the case for O(FeIII(OEP))2. The simplest model for the dications is thus one in which only the unpaired 17 electrons need to be explicitly considered in discussingthe ground state and the lowest electronic excited states. The magnetic interaction will thus be assumed to lead to spin singlets and triplets, as would be the case for dimers containing closed-shell metal ions. It is assumed that only two one-electron r-levels need be explicitly considered. These are the in-phase and out-of-phasecombinations of the highest-lying r-orbitals & and f#Jb on rings a and b, respectively:
the latter being the lowest lying. In the following discussion, we shall be concerned solely with interaction between the porphyrin ring systems, and the presence of the Fe centers will be ignored, for the reasons discussed above. Assuming antiferromagnetic coupling between the rings (see below) in the ground state, the ground-state wave function for the two-electron representation of the dimer dication system is given, using the Hubbard Hamiltonian41by
(7) where 11) = I+&l and 12) = I+&L This leads to a ground-state energy
EIGZ+)= E l l )
+ 25-
[(2J)'+ (K12)2]
are not too serious underestimates, then at normal temperatures the triplet state would be expected to be significantlypopulated for both the TPP and OEP dimer dications, particularly so for the latter. However, for the dication salt of a substituted TPP dimer, O(FeIII(p-OCH3TPP)z))(C104)~,a magnetic moment at 280 K smaller than that re~ulting3~ from thermal population of the paramagnetic S = 1 and S = 2 states of the antiferromagnetically coupled corresponding neutral dimer was observed.19 The further question of interaction of r and metal spin systems, although probably small, remains to be investigated. We note also that since J
