spectroscopy and structure - Northwestern University

(TTF)C1O4? (TTF)I,,5 (TTF)2Ni(C4H4S4),6 and as well in partially oxidized derivatives of ..... Shift in frequency of v, of band in (TTF)(TCNQ) as a fu...
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J . Phys. Chem. 1986, 90,139-743

739

SPECTROSCOPY AND STRUCTURE Determination of the Extent of Charge Transfer in Partially Oxidized Derivatives of Tetrathiafulvalene and Tetracyanoquinodimethan by Resonance Raman Spectroscopy Richard P. Van Duyne,* Thomas W. Cape, Mary R. Suchanski, Department of Chemistry and Materials Research Center, Northwestern University, Evanston. Illinois 60201

and Allen R. Siedle* Science Research Laboratory, 3M Central Research Laboratories, St. Paul, Minnesota 551 44 (Received: November 28, 1983; In Final Form: October 14, 1985)

A number of tetrathiafulvalene (TTF) compounds with formal oxidation states, p, of TTF less than one (TTFp+)were studied

by resonance Raman spectroscopy. The u j frequencies are intermediate between those in T T P and the cation radical TTF+.. The u3 frequency of TTF, TTFBro,7,TTFI,,7, TTF(SCN)o,52,and TTF' salts was used to demonstrate a linear relationship between p and u j . This was used to determine p for transition-metal salts of TTF. TTFP' compounds were found to undergo laser-induceddecomposition to form species which appear to contain TTP. For the acceptor molecule tetracyanoquinodimethan (TCNQ), a similar relationship obtains between p and v4 in derivatives containing TCNQ-. The resonance Raman spectrum of the conducting complex (TTF)(TCNQ) shows only one band each for u j and u4 of TTF and TCNQ, respectively, from which the degree of charge transfer for both donor and acceptor is 0.58 h 0.06. The total charge for each species is uniformly delocalized over all molecules in the segregated stacks in the solid.

Introduction Partially oxidized derivatives of tetrathiafulvalene (TTF) have attracted considerable attention because of their high, anisotropic dc electrical conductivity.' A pervasive structural motif in these compounds is eclipsed columnar arrays of overlapping T T F molecules as found, for example, in (TTF)HgCl,,* ( T T F ) B T ~ , ~ ~ , , (TTF)C1O4? (TTF)I,,5 (TTF)2Ni(C4H4S4),6and as well in partially oxidized derivatives of bis(ethy1enedithio)tetrathiafulvalene' and tetramethyltetraselenafulvalene.8 This arrangement of thiacarbon units allows effective intramolecular overlap and a continuous pathway for carrier migration. In many of these materials, e.g. (TTF)Bro,79,the T T F molecules exist in formal nonintegral oxidation states and thus these mixed valence compounds are referred to as partially oxidized. In many compounds containing TTF, and in the prototypal organic metal (TTF)(TCNQ), the degree of partial oxidation, p , which corresponds to the average charge on a collection of TTF units, is not obvious from inspection of molecular formulas. A precise experimental determination of p is clearly needed for adequate characterization of compounds derived from TTF. Resonance Raman spectroscopy (RRS) shows considerable utility for this purpose because, as explained by Block, Poehler, Cowan et aL9 for totally symmetric modes, the coupling in the (1) J. S. Miller, Ed., "Extended Linear Chain Compounds", Vol. 1 and 2, Plenum Press, New York, 1982. (2) T. J. Kistenmacher, M. Rossi, C. C. Chiang, R. P. Van Duyne, T. Cape, and A. R. Siedle, J . Am. Chem. Soc., 100, 1958 (1978). (3) S. J. LaPlaca, P. W. R. Corfield, R. Thomas, and B. A. Scott, Solid State Commun., 17, 635 (1975). (4) K. Yakushi, S. Nishimura, T. Sugano, and H. Kuroda, Acta Crystallogr., Sect. B, 36, 358 (1980). (5) R. C. Teitelbaum, T. J. Marks, and C. K. Johnson, J . Am. Chem. SOC., 102, 2986 (1980). (6) J. S. Kasper and L. V. Interrante, J. Am. Chem. SOC.,97, 890 (1975). (7) J. M. Williams, T. J. Emge, H. H. Wang, M. A. Beno, P. T. Copps, L. N. Hall. K. D. Carlson. and G. W. Crabtree. Inorp. Chem.. 23. 2558 (1984). (8) (a) T. J. Kistenmacher, Solid State Commun., 50, 729 (1984); (b) T. J. Kistenmacher, Solid State Commun., 51, 931 (1984). (9) J. S. Chappell, A. N. Bloch, W. A. Bryden, M. Maxfield, T. 0. Poehler, and D. 0. Cowan, J . A m . Chem. Soc., 103, 2442 (1981). I

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Hamiltonian between conduction electrons and intramolecular phonons is proportional to the occupancy of the conduction band, the phonon amplitude u along the normal coordinate, and ( d E / d ~ ) , where ,~ E is the energy of the molecular orbital upon which the conduction band is based. This term effectively mixes electron and phonon states, shifting the frequencies of both. Shifts in the nontotally symmetrical C=N stretching mode have been used to determine the degree of charge transfer in a number of TCNQ complexes9 including that with tetramethylphenylenediamine but in that case the result ( p = 1)'O differs from that (0.7) obtained by analysis of Raman shifts in the acceptor."J2 We have previously employed R R S to characterize metallotetrathiaethylenes in which TTF has the integral oxidation states 1+ and 2+.I3-l5 This paper describes a linear correlation between the frequencies of totally symmetric TTF modes and p in an extensive series of partially oxidized TTF compounds and the determination of p in several new metallotetrathiaethylenes and in (TTF)(TCNQ).

Results The Raman spectra of TTF16'* and electrochemically generated TTF' l 9 have been obtained and their vibrational modes assigned.20 (10) T. J. Kistenmacher, T. J. Emge, F. M. Wiygul, W. A. Bryden, J. S. Chappell, J. P. Stokes, L.-Y. Chiang, D. 0. Cowan, and A. N. Bloch, Solid State Commun., 39, 415 (1981). (11) Z. G. Soos and S. Mazumdar, Phys. Reo. B, 18, 1991 (1978). (12) Z. G. Soos, S. Mazumdar, and T. P. Cheung, Mol. Cryst. Liq. Cryst., 52, 93 (1979). (13) A. R. Siedle, G. A. Candela, T. F. Finnegan, R. P. Van Duyne, T. Cape, G. F. Kokoszka, P. M. Woyciesjes, J . A. Hashmall, M. Glick, and W. Ilsley, Ann. N.Y. Acad. Sci., 313, 377 (1978). (14) A. R. Siedle in "Extended Linear Chain Compounds", Vol. 2, J. S. Miller, Ed., Plenum Press, New York, 1982, p 469. (15) A. R. Siedle, G. A. Candela, T. F. Finnegan, R. P. Van Duyne, T. Cape, G. F. Kokoszka, P. M. Woyciesjes, and J. A. Hashmall, Inorg. Chem.,

20, 2635 (1981). (16) A. J. Berlinsky, Y. Hoyano, and L. Weiler, Chem. Phys. Lett., 45, 419 (1977). (17) R. Bozio, A. Girlando, and C. Pecile, Chem. Phys. Lett., 45, 419 (1977). (18) H. Temkin, D. B. Fitchen, and F. Wudl, Solid State Commun., 24, 87 (1972).

0 1986 American Chemical Society

740 The Journal of Physical Chemistry, Vol. 90, No. 5, 1986

Van Duyne et al.

1.9 1:5 1.4 560 4& Wavenumber CM-I lo3

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Figure 1. Resonance Raman spectrum of TTF(BF4)0,67(band pass, 3.0 cm-'; scan rate, 0.0625 A s-I; counting interval, 5.0 s) over v6, v3, and vj v6 regions obtained with 15-mW 5145-A laser excitation.

45min.at 30MW

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Because the DZhsymmetry of TTF does not change significantly upon oxidation, the same assignments can be used for TTF' and TTFP' (0 < p < 1) as for neutral TTFS2' One vibrational mode of TTF in particular has a large frequency shift upon oxidation: v3 shifts from 1512 cm-l in neutral TTF to 1427 cm-I in electrochemically generated TTF', ranging from 1424 to 1412 cm-' in solid materials containing TTF', to 1323 cm-I in TTF(BF4)?.I5 Another band which exhibits a large frequency shift is v6, occumng and at ca. 510 cm-I in TTF' salt^.'^^^^ at 468 cm-' in TTF16-20 Consequently, one can use the Raman frequency shifts to assess the degree of charge transfer in materials containing T T F (and TCNQ, vide infra). Transition-metal derivatives of T T F are of particular interest because, since the metal can adopt multiple oxidation states, the extent of charge transfer cannot be determined merely from compositional data. The electronic spectra of TTF(SCN)o,52,nF(BF4)0.67, TTFb.71, TTFClo,7,and TTFBro,77,and of TTF[Th(N03)8]0,16, TTF(Coc13)0.42,TTF[C~(N03)21omTTF(PQJo.33, and TTF(CuBr3)o.m are shown in Figures S1 and S2, respectively. (See paragraph at end of text regarding supplementary material.) They demonstrate that partially oxidized TTF salts having either nonmetallic or metal-containing counterions are in resonance when excited with 4579- or 5145-A lasers. Resonance Raman spectra for the v2, v3 region, 1385-1540 cm-', for a number of TTFP' compounds in potassium bromide matrices are shown in Figure S3 (supplementary material). The laser power used was quite low (10-20 mW) in order to minimize sample decomposition. The spectra were obtained with 5 145-A excitation because the intensity of ,the v3 band in partially oxidized T T F derivatives is greater relative to that in T T P with this excitation wavelength than with 4579-A excitation. The bands at 1420 cm-I in these spectra do not appear to be present initially but become relatively more intense after repeated scans of the same spectral region. The resonance Raman spectrum of TTF(BF4)0,67 obtained with 5 145-A laser excitation is shown in Figure 1. This compound is more resistant to decomposition than the halide and thiocyanate analogues and so its spectrum, which offers the prospect of a detailed comparison of TTFP' with TTF', was obtained in segments before significant decomposition occurred. Figure 1 shows that for v 3 and v6, two bands are present. In the case of v3, the 1457-cm-' band is due to TTFP' and that at 1417 cm-l to TTF' Similarly, the 510- and 494-cm-' bands are assigned to the v6 modes in TTF' and TTFP', respectively. Spectra of TTF' compounds obtained with 5145-A excitation typically show the com(19) R. P. Van Duyne, J . Phys. (Paris) Colloq., C5, 239 (1977). (20) R. Bozio, I, Zanon, A. Girlando, and C. Pecile, J . Chem. Phys., 71, 2282 (1979). (21) A complication arises for u2 which, in TTF,could be one of two bands, the other being a Fermi resonance between u2 and (v4 u6). In T T P , there are also two bands potentially assignable to u2 but, because of frequency shifts, (v4 + ua) does not interfere. For the sake of maintaining an assignment consistent with that of other fundamentals in TTF, both of these bands will be referred to as v2. The splitting of u2 represents a lowering of the overall symmetry of the charged TTF moiety but it will be considered an insignificant perturbation for the other fundamentals.

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Figure 2. The effect of exposure to 30-mW 5145-A laser radiation on the Raman spectra of TTF(BF4)067showing the initial spectrum and the

spectrum after 45-min irradiation [3 cm-' band pass; scan rate, 0.05 A s-l; counting interval, 5.0 SI. The lower curve was recorded with 10-mW radiation.

+

bination band v3 v6. The band at 1925 cm-' corresponds to v3 v6 for TTF', for, if it were due to TTF', it should appear at about 1950 cm-'. The absence of this combination band in spectra obtained with 5145-A excitation can thus be diagnostic for TTFP'. The facile decomposition of TTFP' can be another indication that this species is present in solids. The effect of 45 min of 30 mW of 5145-A laser irradiation on the Raman spectrum of TTF(BF4)067in KBr, shown in Figure 2, reveals attenuation of the 1457-cm-I v 3 band and growth of a new peak at 1453 cm-I. Spectra obtained with 10 mW of 5145-A and 8 mW of 4579-A laser excitation showed little decomposition over a period of 2 h. A similar but more pronounced shift in frequency for (TTF)(TCNQ) has also been observed (vide infra). Reduction of the sample temperature to -100 OC has no noticeable effect on the rate of decomposition. The frequency of v3 for TTF' does not change as it gains intensity. The same spectral changes are observed in the spectra of the pure material as well as for the Bro77, I, 71, and SCNo52 salts in KBr, indicating that the matrix does not significantly perturb the spectra. TTF' salts having metal-containing counterions, metallotetrathiaethylenes, have also been studied. Their resonance Raman spectra in the 1385-1540-cm-I region are shown in Figure S4 (supplementary material). As with salts containing halide and pseudohalide anions, the bands at 1420 cm-I are not present initially but appear, along with sample discoloration, after exposure to laser light. Decomposition of TTF(CoCl,), 42 is particularly severe. The compounds TTF(PtcI6), 33 and TTF(CuBr,), 40 are both considered to be salts of TTFP' and both show resonance Raman spectra typical of this species except for weak bands at 1451 and 1441 cm-I, respectively (cf. Figure 3). In both cases, there are strong combination bands between v3 and V g , and between v2 and v6 of TTF' but no combination bands are observed involving either the 1451-cm-I band of TTF(PtC&)o 33 or TTF(CUB~,),~,. At shorter excitation wavelengths, the relative intensity of v3 for TTFP' was smaller relative to v3 of TTF', as in the case of TTF(BF4),67. It is interesting to note that, even at 40 mW of 5145-A laser excitation, v 3 of TTFP' showed no tendency to decrease in intensity relative to v3 of TTF+. This is consistent with the greater stability of TTF(BF4), 67 relative to other TTFP' compounds, and it is possible that TTF' may stabilize TTFP' toward laser-induced decomposition. The resonance Raman spectrum of (TTF)(TCNQ) shows evidence of its decomposition in the laser beam. The spectrum obtained after 10 min of 100-mW 4579-A irradiation, Figure 4A,

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Derivatives of TTF and TCNQ

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Time (hrs.) Figure 5. Shift in frequency of v, of band in (TTF)(TCNQ) as a function of time with 15 mW of 4579-A excitation.

2.0 1.5 1.0 0.5 Wavenumber CM-I lo3 Figure 3. Resonance Raman spectra of (a) TTF(CuBr3),,,a and (b) TTF(PtC16)o,33 obtained with 3.0-cm-' band pass, 0.25 A s-l scan rate, 1.0-scounting interval, and 50-mW 5145-A radiation. -1456

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Figure 4. Resonance Raman spectra of 25 wt %I (TTF)(TCNQ)/KBr [band pass, cm-'1 (A) after 10 min of exposure to 100-mW 4579-A laser radiation [2.0], (B) obtained with 80-mW 4579-A laser power, (C) with 30-mW 4579-A power, (D) with 40-mW 5800-A power. In all cases, a 0.167 A s-l scan rate and 1.00-s counting interval were used.

is dominated by the vibrational features of TCNQO including a strong 1456-cm-] band. Figure 4B shows the spectrum of (TTF)(TCNQ) taken with 80 mW of 4579-A excitation and in it the 1456-cm-' feature is not apparent, indicating that decomposition to TCNQO is dependent on laser irradiation power. Figure 4C shows the spectrum of (TTF)(TCNQ) obtained with 30 mW of 4579-A irradiation. Note that the band at 1448 cm-' in Figure 4B occurs at 1458 cm-l in Figure 4C. Figure 4D displays the resonance Raman spectrum of (TTF)(TCNQ) obtained by using 5800-A excitation. Note the appearance of the v2 C=N stretch of TCNQ at 2213 cm-I and the v6 C-S stretch of TTF at 494 cm-l in this spectrum. At both 4579 and 5800 A, there is significant absorption for both TTF+ and TCNQ- so that scattering from reduced T C N Q or oxidized TTF would be resonance enhanced.

Figure S5 (supplementary material) shows details of the 13501550-cm-' region of the resonance Raman spectrum of nondecomposed (TTF)(TCNQ). On the basis of relative intensity patterns, shifts in band intensities and frequencies with laser-induced decomposition, and comparison with the resonance Raman spectra of other TTFP' compounds, we assign this region of the Raman spectrum as follows: 1458 cm-' to v3 of TTFp'; 1419 cm-' to v4 of TCNQP-; 1474 cm-' to v2 of TTFP'; and 1512 cm-l to vj in TTp.22 These assignments differ somewhat from those of earlier workers who attributed a flO-cm-' variation in Raman line positions to scattering in charge transfer rather than to sample d e c o m p ~ s i t i o n . The ~ ~ weak intensity of the spectra of this compound is made readily apparent by comparison with the broad signal at ca.450 cm-I arising from fluorescence of the glass sample tube. In the resonance Raman spectra of alkali metal TCNQsalts excited at 4579 A, this band is barely evident. The low intensity may be related to the metallic nature of (TTF)(TCNQ), being associated with a decrease in penetration depth of the electromagnetic field in highly conducting materials. The skin depths, calculated from conductivity data on compacted samples, and 2.2 X cm for K'TCNQ- and (TTF)are 4.9 X (TCNQ), respectively. The time-dependent decomposition of (TTF)(TCNQ) has been monitored by using 15 mW of 4579-A laser excitation. The 1419-cm-' band increases in intensity while that at 1458 cm-I first broadens, then shifts to lower frequency, and finally rises in intensity. The peak heights (above background) for these two bands are plotted in Figure S6 (supplementary material) as a function of laser exposure time and are seen to biphasic with breaks occurring at about 2 h for both peaks. The shift in frequency of the 1458 cm-' mode is plotted in Figure 5; although decomposition starts immediately, there is an induction period for the frequency shift. This pattern may be explained by a band at 1448 cm-' growing in while the incompletely resolved 1458-cm-' band decreases. The increase in intensity of the 1419 cm-' could be caused by an increase in skin depth (vide supra). We find that the frequencies of v 3 in TTFP' and v4 in TCNQT are proportional to p. These relationships are shown graphically in Figure 6 in which TTFX refers to fully oxidized TTF' salts in which the counterions are AuC&-, FeC14*-,and SnC16'-. In the latter two compounds, the near-idealized structure and charge in the halometallate anions have been independently established by Mossbauer spectroscopy, leaving little doubt that the T T F cation has unit charge and that it exerts little if any effect on the geometry of the counterion, i.e. there are no significant metal(22) H. Kuzmany and H. J. Stolz, J . Phys. C, 10, 2241 (1977). (23) Additional details may be found in T. Cape, Ph.D. Thesis, Northwestern University, Evanston, IL, 1979.

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, , C , % , , , , I ,

1460 r

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Figure 6. Dependence of frequency of u3 for TTF derivatives (top) and of u4 for TCNQ compounds (bottom) on p .

sulfur bonding interactions. The MTCNQ charge-transfer standards contain univalent alkali metal cations (Li', Na', K+) and analysis of their Raman spectra follows that of other workThe limit of uncertainty for both v4 of TCNQ and v3 of TTF is f 2 cm-I. The uncertainty in p should reflect this error as well as possible frequency shifts due to counterion effects. The dotted lines in Figure 6 represent error limits in assessment of associated with counterion variation. When the linear relationship between v3 and in TTFP" and v4 and in T C N P is used, p for TTF and TCNQ in the crystalline complex (TTF)(TCNQ) are found to be 0.58 f 0.07 and 0.58 f 0.1 1, respectively, and thus, the degree of donor-acceptor net charge transfer is 0.58 f 0.06 (the uncertainty is lowered because the two determinations of are independent). The degree of charge transfer in (TTF)(TCNQ) determined by Raman spectroscopy is in good agreement with values obtained by other spectroscopic Further, since v,(TTF) and v,(TCNQ) are single vibrational bands whose frequencies are intermediate between those in the neutral and radical ion species, the exchange rate of electrons along the donor and acceptor stacks must be fast on the Raman time scale, viz. 1 0 - ~ ~ - 1 0 -S.' ~

Figure 7 shows a plot of the frequency of v3 in TTFP+ over a narrower range of p , 0.5-0.85, using as standards TTFBro,, TTFI,,,,, and TTF(SCN),,,,. In these compounds, p is fixed by stoichiometry. A linear relationship again obtains, indicating that resonance Raman spectroscopy can be used to characterize the degree of oxidation or charge transfer in new TTF derivatives. We have applied this technique to materials in which the counterion contains a transition metal. In these, p is not at all obvious merely from compositional data since both the metal and TTF may assume more than one oxidation state. For example, in T T F ( C U B ~ ~ ) u3 , , ~is, 1441 cm-' so that p is 0.76 f 0.08. Since earlier X-ray photoelectron spectroscopic measurementsL5indicated that copper in this compound is present as CUB^,^-, a value of 0.80 is expected and found. Similarly, from the 1451-cm-' u3 peak in TTF(PtC16),,,, p is found to be 0.65 f 0.07 in accord with the ~~

(24) R. Bozio, I. Zanon, A. Girlando, and C. Pecile, J . Chem. Soc., Faraday Trans. 2, 74, 235 (1978). (25) A. Girlando and C . Pecile, Spectrochim. Acta, Part A, 29, 1859 (1973). (26) I . Zanon and C. Pecile, J . Phys. Chem., 87, 3657 (1983). (27) C. K. Chi and E. R.Nixon, Spectrochim. Acta, Parr A, 31. 1739 (1975) -,. (28) S. Matsuzaki, R. Kuwata, and K. Toyoda, Solid State Commun., 33, 403 (1980).

Expansion of u3 vs. u curve for (1) TTF(SCN),,,,, (2) (TTF)(TCNQ), (3) TTF(BFAa7, (4)TTFCIO..I,( 5 ) TTF(P~CI~)O.~J, (6) TTF[Th(NOJslo.,6,(7) TTFIo.7, (8) TTF[Cu(NO,),Io 33. ( 9 ) TTF(CuB ~ J O and , ~ ~(10) , TTFBro.77.

Figure 7.

expectation that platinum is present as Pt(1V) in PtC1,2-. u3 for TTF in TTF[Th(N03)8]o,,6occurs at 1448 cm-' from which p is 0.69 f 0.08, indicating that thorium remains in the formal 4+ oxidation state, behavior entirely consistent with the solution-phase chemistry of this element. The cobalt complex TTF(CoC13),,,, is subject to relatively rapid laser-induced decomposition and characteristic TTP peaks are not observed in the initial resonance Raman spectra. The TTFP" v3 band occurs at 1456 cm-' from which p is calculated to be 0.60 f 0.07. This result is inconsistent with a single oxidation state because p must be 0.84 for pure C O C I ~and ~ - 0.42 for a species containing only C0C13-. For this reason, we consider that TTF(COC~~),,.,~ is a mixed valence material containing both Co(1) and Co(II1). Resonance Raman spectroscopy is less well adapted to quantitative analysis of materials containing both TTF' and TTFp". The former, present as an impurity or because of laser-induced decomposition in samples of (TTF)(TCNQ) and TTF(BF4),,6,, gives rise to a combination band between v3 and v6. This indicates that either u3 or v6 is much more in resonance than the same modes in TTFP'. Since resonance enhancements on the order of IO6 are possible, relative intensities of the two u3 peaks should not be used to estimate relative amounts of TTF' and TTFP' in a sample. We conclude that there exists a linear relationship between v3 and p in TTFP" and between u4 and p in TCNQP-. These correlations allow resonance Raman spectroscopy to be used as a valuable characterization technique for new compounds containing TTF and TCNQ provided that the potential for laser-induced decomposition is taken into account. Presumably, similar correlations between normal-mode frequencies and the degree of charge transfer obtain in other partially oxidized materials, for example those containing tetraselenafulvalene and its analogues, and have been applied to determine p in the neutral and ionic phases of the novel TTF-chloranil charge-transfer complex.29 Further, it appears that Raman spectroscopy may be useful for probing interactions between thiacarbon acceptors and surfaces and, indeed, vibrational spectra of TTF adsorbed on silver and gold surfaces have recently been observed by surface-enhanced Raman spectroscopy (SERS). On these metals, significant electron transfer occurs and the TTF was shown from measurement of the u3 frequency to exist primarily as TTFt.30

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(29) A. Girlando, F. Marzola, C. Pecile, and J . B. Torrance, J . Chem. Phys., 79, 1075 (1983).

Derivatives of T T F and TCNQ

Experimental Section Resonance Raman spectra of all compounds were obtained with excitation from a Coherent Radiation Model CR-8 Ar' laser or a Coherent Radiation Model 490 CW dye laser containing rhodamine 6G pumped all lines by the CR-8 source. Spectra were collected with a 0.75M Spex Model 1400-11 double monochromator equipped with a cooled RCA C31034 photomultiplier tube and standard low-level threshold photocounting detection electronics. Spectra were obtained with rapidly spinning solid powder sampled sealed under vacuum in 5-mm 0.d. Pyrex tubes in order to minimize sample decomposition in the laser beam. Focusing and alignment of the samples were done quickly (