J . Phys. Chem. 1988, 92. 6456-6460 I
I
+
.
+*
I
LIOUID WATER
.+
++
**
w .L
.
++
++
*++ i t
1
1.5
2
2.5
ENERGY (eV)
Figure 3. DOS-vs-energy comparison between the two sets of calculated (+) and measured ( 0 )data shown in Figure 2 for liquid water. The zero of energy corresponds to the energy of the bottom of the conduction band at V,,.
reasonably well into two straight lines whose inverse slopes Eo are equal to 0.81 eV below, and to 0.27 eV above, an energy in the region of 1.6 eV. This two-exponential band-tail behavior seems to be rather unusual and might suggest that there exist two different types of electron trapping sites in liquid water. We note, however, that the DOS distribution found here differs from that of Thompson et a1.,I6 who reported in a short abstract a single conduction band tail in water decaying exponentially below Vo with a characteristic energy near 0.2 eV. A molecular dynamics simulation study aimed a t identifying microscopic electron localization sites in pure liquid water has recently been published by Schnitker et al.” These authors calculated the energy distribution of preexisting traps for a scattering quasifree electron. Figures 2 and 3 compare their results (16) Thompson, J. C.; Antoniewicz, P. R.; Bennett, G. T. Bull. Am. Phys. SOC.1985, 30, 600. (17) Schnitker, J.; 1986, 85, 2986.
Rossky, P. J.; Kenney-Wallace, G. A. J . Chem. Phys.
to the DOS obtained here. As we can see from Figure 2, the DOS obtained from the simulation can also be decomposed into two straight lines whose inverse slopes are almost identical with the values reported above. However, in order to have the calculated and the measured sets of data coincide, we had to shift, by about 1 . 1 eV to higher energies, the energy scale of the calculated electronic trap distribution. In our opinion, the striking agreement between the two sets of data (see Figures 2 and 3) seems to support the existence of two different types of microscopic electron localization sites in liquid water. The shift in the energy scale, however, remains a problem. In fact, this shift cannot be. explained by a Voeffect since the origin of the energies should be the same in both cases and corresponds to the bottom of the conduction band. One possible explanation could be that the calculation was performed with a finite-size simulation system consisting of 216 water molecules; that is, the importance of long-range interactions could have been underestimated.’* In summary, the main conclusions of this work are as follows: (i) it is possible to interpret the incompletely relaxed electron absorption spectrum in polar liquids as a direct measure of the density of localized states below the conduction band edge;19 (ii) for the studied liquid alcohols, this density of states tails off exponentially into the forbidden gap; and (iii) liquid water seems to behave in a peculiar way in that the energetic gap-state distribution below Voshows a two-exponential behavior. This result could help to bring a new insight into the understanding of the structural properties of this liquid.
Acknowledgment. We thank Drs. C. Tannous and B. Hickel for valuable discussions and Profs. G. R. Freeman and C. Ferradini for useful comments on the manuscript. The work reported here was supported by the Medical Research Council of Canada and the Natural Sciences and Engineering Research Council of Canada. One of us (C.H.-L.) benefited from a grant from the France-Quzbec (INSERM-FRSQ) exchange program in health sciences. This support is gratefully acknowledged. Registry No. Ethanol, 64-1 7-5; I-propanol, 7 1-23-8; 2-butano1, 7892-2. (18) Schnitker, J.; Motakabbir, K.; Rossky, P. J.; Friesner, R. Phys. Rev. Lett. 1988, 60, 456. (19) As a consequence, the incompletely relaxed electron molar absorptivity r(X) at a given wavelength X should be regarded as proportional to the preexisting trap-state DOS of the considered liquid at the corresponding energy E [ E (eV) = 1240/X (nm)]: a(X) = a DOS(E), where a is a constant characteristic of the absorbing trapped electron only.
Relation between Geometry and Charge Transfer in Low-Dimensional Organic Salts Timothy C. Urnland,? Sharon Allie,+ Tom Kuhlmann,+ and Philip Coppens* Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14214 (Received: April 7, 1988) The Cambridge Data Base has been used to examine the relation between charge transfer and geometry in salts containing the TCNQ (tetracyanoquinodimethanide)anion and the TTF (tetrathiofulvalene), TSF (tetraselenofulvalene), and BEDT-TTF [bis(ethylenedithio)tetrathiofulvalene]cations. The correlation is based on either a bond length ratio or a bond length difference function and is calculated both for an extended data set, including charge transfers based on stoichiometry, and on a more restricted set based on neutral molecules and experimentally measured charge transfers. A two-parameter linear least-squares fit is found to be adequate; inclusion of a third (quadratic) coefficient does not give a significant improvement with the data available. The bond length difference function tends to give somewhat smaller standard deviations in predictions based on the derived equations. The curves for BEDT-TTF are not significantly different from those for the larger TTF set of entries. Introduction Low-dimensional solids containing planar organic cations and/or anions can have remarkable electrical transport properties, in particular when the ions are arranged in homogeneous stacks with Undergraduate Research Participants.
0022-3654/88/2092-6456$01.50/0
intermolecular overlap of valence molecular orbitals. Partial filling of the resulting electron band leads to an electronic stabilization of the homogeneous stack structure. The conductivity is particularly high when charge transfer between the donor and acceptor molecules is less than complete, so that a mixed valency exists in each off the stacks, which increases the electron mobility. The
0 1988 American Chemical Society
Geometry and Charge Transfer in Organic Salts
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988
6451
TABLE I: Abbreviations Used in This Paper BEDT-TTF DMTCNQ HMM(TCNQ),
bis(ethy1enedithio)tetrathiafulvalene 2,5-dimethyi-7,7,8,8-tetracyanoquinodimethanide monomethylmorpholinium
bis(7,7,8,8-tetracyanoquinodimethanide)
N
N
HMTSF HMTTF MPh(TCNQ), MPM(TCNQ), TCNQ TMTSF TMTTF TSF TTF
Figure 1. Definition of bonds.
early prototype of the low-dimensional conducting solids is TTF-TCNQ (tetrathiofulvalene tetracyanoquinodimethanide), in which the charge ranges between 0.59e at 53 K and ambient pressure and Z/3ea t pressures above 14-18 kbar a t 10-20 K.1-5 More recently superconductivity has been found in the Bechgaard salts of TMTSF (tetramethyltetraselenofulvalene),6 and in salts of BEDT-TTF (bis(ethylenedithi~)tetrathiofulvalene).~~~ The magnitude of the charge transfer from the HOMO of the donor molecule to the L U M O of the acceptor is related to the ionization potential I of the donor, to the electron affinity A of the acceptor, and to the gain in Madelung energy M of the solid upon formation of an ionic s t r u ~ t u r e . Partial ~ charge transfer, which is typical for the highly conducting phases, occurs for moderately negative values of I - A.' In other classes of conducting salts, such as salts of a radical cation and an acceptor molecule or a donor molecule and a radical anion, charge transfer is closely related to the stoichiometry of the solids. Comparison of bond lengths between, for example, neutral TCNQiOand the sodium salt Na+TCNQ-" shows that the geometry varies with the electron population of the MO's, as is to be expected. In general a larger electron population leads to a lessening of the quinoid character of the T C N Q molecule, with the C-C bonds becoming more nearly equal. Similar changes occur in T T F in which the bonds between sulfur and the central carbon atoms and the centeral C=C bond are particularly affected. Since the bond length variation is considerably larger than the experimental accuracy achieved in the better studies, it is possible to obtain an estimate of the molecular charge from the experimental geometry. Systematic attempts to this effect have been made for T C N Q by two groups of authors, based on a linear interpolation between neutral T C N Q dimensions and those for the T C N Q R b salt. Flandrois and Chasseaui2used a difference ( I ) Comes, R.; Shapiro, G.; Garito, A. F.; Heeger, A. J. Phys. Reo. Lett. 1975, 35, 1518.
(2) Comes, R.;Shirane, G.; Shapiro, S. M.; Garito, A. F.; Heeger, A. J. Phvs. Reo. B Solid State 1976, 14,2376. (3) Pouget, J. P.; Khanna, S. K.; Denoyer, F.; Comes, R.; Garito, A. F.; Heeger, A. J . Phys. Reo. Lett 1976, 37, 437. (4) Kagoshima, S.; Ishiguro, T.; Anzai, H. J . Phys. SOC.Jpn. 1976, 41, 206 1. (5) Megtert, S.;Comes, R.; Vettier, C.; Pynn, R.; Garito, A. F. Solid State Commun. 1979, 31, 977. Megtert, S.; Comes, R.; Vettier, C.; Pynn, R.; Garito, A. F. Solid State Commun. 1981, 37, 875. (6) Bechgaard, K.; Carneiro, K.; Rasmussen, F. B.; Olsen, M.; Rindorf, G.; Jacobson, C. S.; Pederson, H. J.; Scott, J. C. J . A m . Chem. SOC.1981, 103, 2440. (7) Vagubskii, E. B.; Shchegolev, I. F.; Laukhin, V. N.; Kononovich, P. A.; Kartsovnik, M. B.; Zvarykina, A. V.; Buravov, L. I. Pis'ma Zh. Eksp. Teor. Fiz. 1984, 39, 12 (JETP Lett. 1984, 39, 12). (8) Crabtree, G. W.; Carlson, K. D.; Hall, L. N.; Copps, P. T.; Wang, H. H.; Emge, T. J.; Beno, M. A.; Williams, J. M. Phys. Reo. B Condens. Matter 1984, 830. 2958. (9) Saito, G.;Ferraris, J. P. Bull. Chem. SOC.Jpn. 1980, 53, 2141. ( I O ) Long, R.E.; Sparks, R. A.; Trueblood, K. N. Acta Crystallogr. 1965, 18. 932. ( 1 I ) Konno, M.; Saito, Y. Acta Crystallogr., Sect. 8:Struct. Crystallogr. Struct. Chem. 1974, 86,1294. (12) Flandrois, S.; Chasseau, D. Acta Crystallogr., Sect. 8: Struct. Crystallogr. Struct. Chem. 1977, 833, 2744.
hexamethylenetetraselenafulvalene hexamethylenetetrathiafulvalene N-methylphthalazinium bis(7,7,8,8-tetracyanoquinodimethanide) methylphenylmorpholinium
bis(7,7,8,8-tetracyanoquinodimethanide) 7,7,8,8-tetracyanoquinodimethanide tetramethyltetraselenafulvalene tetramethyltetrathiafulvalene tetraselenafulvalene tetrathiafulvalene
between bond lengths in their work, while Coppens and Guru used a dimensionless ratio of bond lengths sums as the geometric parameter. The two expressions are given by q = 7.25(b - c) - 8.07(c q = 22.43 - 23.81(a
d) - 1 (ref 12)
+ c)/(b + d)
(ref 13)
(1) (2)
where q is the charge transfer and a, b, c, and d a r e bond lengths defined in Figure 1. Since the number of known crystal structures has vastly increased over the last decade, and the Cambridge Data Base is available for their examination, it seemed appropriate to survey this new information in order to obtain a broadly based expression, which would allow a rapid estimate of charge transfer from molecular dimensions. Reliable values for the charge transfer in a number of salts are available from the reciprocal-space positions of 2kF satellite reflections, which are determined by the occupancy of the one-dimensional conduction band.14 Values based on stoichiometry are more controversial, as formal charges in salts such as Na-TCNQ or (BEDT-TTF)zN03 may not correspond to the actual charge distribution in the solid. We have therefore performed calculations with two different sets of structural data as input. In the first, referred to as set 1, charge transfers based on stoichiometry are included, while the second set (2) only contains data for the neutral molecules and those for which charge transfer has been derived from 2kF scattering.
Method The Cambridge Data Base was used to generate files containing low-dimensional salts with known crystal structure. A bond length ratio r and a bond length difference 6 were calculated and their standard deviations obtained from bond length standard deviations retrieved from the original literature. The coefficients of a polynomial in the charge transfer q were fitted to the observed bond length ratio r, or bond length difference 6, by minimization of CwA', where w = l/02, A = row - raid (or 6ow - Bald), and rcalcd= a , + a2q + n3q2. A locally modified version of the least-squares fitting routine LFITIS was used. In several cases more than one experimental bond length ratio is available for one charge transfer. Values for which a(r) > 3amin(r)were rejected. Their influence in the weighted leastsquares minimization would in any case be minimal. In addition, some points that clearly deviated from the curves, possibly because of unrecognized experimental errors, were omitted. Fits were performed for the donor molecules TTF, TMTTF, TSF, TMTSF, and BEDT-TTF and for the acceptor T C N Q (see Table I for abbreviations used). For the donor molecules the ratio a / b was used, where a is the central C=C bond length and b the length of the adjacent C-S bond (Figure 1). For T C N Q the ratio used was ( a + b ) / ( c+ d ) . In order to test the dependence of the results on the function selected, calculations were also (13) Coppens, P.; Guru Row, T. N. Ann. N.Y. Acad. Sci. 1978, 313,244. (14)Pouget, J. P. Highly Conducting One Dimensional Solids; Conwell, E. M., Ed.; Pergamon: New York, in press. (15) Press, W. H.;Flannery, B. P.; Teukolsky, S. A.; Vettering, W. T. Numerical Recipes; Cambridge University Press: Cambridge, U.K., 1986.
6458
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988
Umland et al.
TABLE 11: Charge Transfer and Bond Functions Used in Curve Fittings set __ r 6, 8, ct 1 2 ref Tetracyanoquinodimethanide -0,116 (7) -0.59 x x u TMTSF-DMTCNQ TTF-TCNQ (100 K) 0.9595 (22) -0.099 (7j -0.59 x b TCNQ 0.9653 (24) TTF-TCNQ -0.59 x c Na-TCNQ (low temp, -0.134 (6) TTF-TCNQ (45 K) 0.9533 (19) -0.140 (13) -0.59 x x c form I) 0.9512 (43) TTF-TCNQ (60 K) Na-TCNQ (low temp. -0.111 (17) -0.59 x x c TTF-TCNQ (53 K) 0.9612 (57) d form 11) 0.9625 (117) -0.107 (34) -0.57 x TMTTF-TCNQ Na-TCNQ (353 K) -0.72 x x e -0.096 (8) H MTTF-TCNQ 0.9663 (28) 0.9710 (239) -0.083 (30) -0.57 x TMTSF-TCNQ f MPh(TCNQ), K-TCNQ (black metallic form) (24) (93) (53) (64) (73) (53) (49)
-0.227 -0.355 -0.366 -0.337 -0.360 -0.390 -0.337
(4) (17) (IO) (12) (10) (14) (8)
TMTT F-( C104) 2 (TMTTF),NO, (TMTTF)2CIO4 (TTF)IC~~ (TMTTF),SCN (TMTTF),Br TTF-I,
0.8638 0.7957 0.7874 0.8041 0.7938 0.7757 0.8029
(TMTSF),AsF, (TMTSF),SiF, (125 K) (TMTSF),SiF3 HMTSF-TCNQ TMTSF-DMTCNQ
0.7151 (41) 0.7111 (26) 0.7080 (43) 0.7372 (43) 0.71 5 1 (42)
-0.551 (8) -0.493 (9) -0.529 (9)
BEDT-TTF (B-BEDT-TTF),CI,I (120 K) (P-BEDT-TTF),CI2I
0.7509 (68) 0.7855 (15)
-0.439 (14) -0.373 ( 2)
0.7890 (15)
-0.367 (2)
-0.536 (61
-0.526 (5j
2.00 0.50 0.50 0.67 0.50 0.50 1.00 0.50 0.50 0.50 1.00 0.50
x x x x
x
x x
Tetrathiafulvalene m TTF-CI04 n TTF-CIO, o TTF R TTF-TCNQ (I00 K) TTF-TCNQ r TTF-TCNQ (53 K) s TMTTF-bromanil
b
Tetraselenafulvalene w TMTSF-TCNO x (black metallic form) x TMTSF x TSF (dimer) x x y x x z TSF x
Bis(ethylenedithio)tetrathiafulvalene x dd (6-BEDT-TTF),BrCII 0.50 x ee (120 K) (P-BEDT-TTF),BrCII 0.50 x ee (BEDT-TTF),(MnCI,),
0.00
set r
6 , 8,
ct
1
2 ref
0.9633 (41) 0.9420 (20) 0.9800 (56)
-0.105 (12) -0.169 (7) -0.057 (16)
-0.50 0.00
x x
x x
g h
-1.00
x
x
i
0.9688 (5)
-0.089 (16)
-1.00
x
x
i
0.9753 (21) 0.9589 (29) 0.9838 (31)
-0.070 (6) -0.117 (8) -0.046 (5)
-1.00 -0.50 -1.00
x
x
j
0.8218 0.8196 0.7684 0.7836 0.7854 0.7865 0.7807
-0.305 -0.314 -0.407 -0.377 -0.374 -0.403 -0.381
(89) (89) (19) (30) (24) (25) (57)
k
x
x
x
I
(15) (14) (4) (6) (5) (14) (10)
1.00 1.00 0.00 0.59 0.59 0.59 0.52
x
x
x x x x x
0.7094 (110)
-0.550 (20)
0.57
x
x
uu
0.7146 (54) 0.7086 (41) 0.6801 (41)
-0.540 (12) -0.553 (8) -0.612 (8)
0.00 x 0.00 x 0.00 x
x x
bb
x
cc
0.7836 (29)
-0.376 (6)
0.50
x
0.7839 (29) 0.8493 (30)
-0.375 (5) -0.254 (20)
0.50 2.0
x
ee
x
ff
t t
x x
x x
x
u
u u c
gg
cc
ee
Blessing, R. H.; Coppens, P. Solid State Commun. 1974, 15, 215. bKistenmacher, T. J.; Phillips, T. E.; Cowan, D. 0. Acta Crystallogr., Sect. E: Struct. Crystallogr. Cryst. Chem. 1974, 30, 763. cSchultz, A. J.; Stucky, G. D.; Blessing, R. H.; Coppens, P. J . Am. Chem. SOC.1976, 98, 3194. dPhillips, T.E.; Kistenmacher, T. J.; Bloch, A. N.; Ferraris, J . P.; Cowan, D. 0. A c f a Crystallogr., Secr. B: Struct. Crystallogr. Cryst. Chem. 1977, 33, 422. CChasseau,D.; Comberton, G.; Gaultier, J.; Hauw, C. Acfa Crysfallogr.,Sect. 8: Sfruct. Crystallogr. Crysr. Chem. 1978, 8 3 4 , 689. (Bechgaard, K.; Kistenmacher, T. J.; Bloch, A. N.; Cowan, D. 0. Acta Crystallogr., Sect. B Struct. Crystallogr. Cryst. Chem. 1977, 8 3 3 , 417. CAnderson, J. R.; Bechgaard, K.; Jacobsen, C. S.; Rindorf, G.; Soling, H.; Thorup, N. Acta Crystallogr., Sect. B Struct. Crystallogr. Cryst. Chem. 1978, 8 3 4 , 1901. *Long, R. E.; Sparks, R. A,; Trueblood, K. N. Acta Crystallogr. 1965,18,932. 'Konno, M.; Saito, Y . Acta Crystallogr., Sect. B Struct. Crystallogr. 1965, 18, Chem. 1975, 8 3 1 , 2007. JKonno, M.; Saito, Y. Acta Crystallogr.,Sect. B: Struct. Crystallogr. Crysf. Chem. 1974, 8 3 0 , 1294. 'Gao, Y.; Coppens, P. Acta Cryst. 1987, C43, 1610. 'Konno, M.; Ishii, T,; Saito, Y. Acfa Crysfallogr.,Sect. 8: Sfruct. Crysfallogr.Crysf. Chem. 1977, B33, 763. "Shibaeva, R. P. Kristallografa 1984, 29, 480. "Liautard, B.; Peytavin, S.; Brun, G.; Maurin, M. Acta Crystallogr., Sect. B: Strucf. Crystallogr. Cryst. Chem. 1982, 8 3 8 , 2746. OLiautard, B.; Peytavin, S.; Brun, G.; Chasseau, D.; Fabre, J. M.; Giral, L. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1984, C40, 1023. p Williams, J. M.; Ma, C. L.; Samson, S.; Khanna, S. K.; Somoano, J. J . Chem. Phys. 1980, 72, 3781. qGaligne, J. L.; Liautard, B.; Peytavin, S.; Brun, G.; Maurin, M.; Fabre, J. M.; Torreilles, E.; Giral, L. Acta Crystallogr.,Sect. B: Struct. Crystallogr. Cryst. Chem. 1979, B35, 1129. 'Galigne, J. L.; Liautard, B.; Peytavin, S.; Brun, G.; Fabre, J. M.; Torreilles, E.; Giral, L. Acta Crystallogr., Sect. B: Struct. Crysfallogr.Crysf. Chem. 1978, 8 3 4 , 620. 'Teitlbaum, R. C.; Marks, T. J.; Johnson, C. K. J . Am. Chem. Soc. 1980, 102, 2986. 'Yakushi, K.; Nishimura, S.; Sugano, T.; Kuroda, H.; Ikemoto, I. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1980, B36, 358. "Cooper, W. F.; Edmonds, J. W.; Wudl, F.; Coppens, P. Cryst. Struct. Commun. 1974, 3, 23. "Kistenmacher, T. J.; Phillips, T. E.; Cowan, D. 0. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1974, 830, 763. "Wudl, F. J . Am. Chem. SOC.1981, 103, 7064. XEriks,K.; Beno, M. A,; Bechgaard, K.; Williams, J. M. Acta Cryst. Struct. Commun. 1984, C40, 1715. YEmge, T. J.; Cowan, D. 0.;Bloch, A. N.; Kistenmacher, T. J. Mol. Cryst. Liq. Cryst. 1983, 95, 191. 'Anderson, J. R.; Bechgaard, K.; Jacobsen, C. S.; Rindorf, G.; Soling, H.; Thorup, N. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1978, 8 3 4 , 1901. ""Kistenmacher, T.J.; Emge, T. J.; Bloch, A. N.; Cowan, D. 0. Acta Crystallogr., Sect. B: Strucf. Crystallogr. Cryst. Chem. 1982, 8 3 8 , 1193. bbKistenrnacher, T. J.; Emge, T. J.; Shu, P.; Cowan, D. 0. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1979, 8 3 5 , 772. Weidenborner, J. E.; La Placa, S. J.; Engler, E. M. ACA Meeting Abstract, University of Michigan, August 1977. ddKobayashi, H.; Kobayashi, A,; Sasaki, Y.; Saito, G.; Inokuchi, H. Bull. Chem. SOC.Jpn. 1986, 59, 301. ccEmge, T. J.; Wang, H. H.; Leung, P. C. W.; Rust, P. R.; Cook, J. D.; Jackson, P. L.; Carlson, K. D.; Williams, J. M.; Wangbo, M.-H.; Venturini, E. L.; Schriber, J. E.; Azevedo, L. J.; Ferraro, J . R. J . A m . Chem. SOC.1986, 108, 695. ffTori, T.; Inokuchi, H., to be published, as quoted in: Mori, T.; Wang, P.; Imaeda, K.; Enoki, T.; Inokuchi, H. Solid S f a t e Commun. 1987, 64, 733. ggKagoshima, S.; Pouget, J. P.; Yasynaga, T.; Torrance, J. B. Solid State Commun. 1983, 46, 521. Mayerle, J. J.; Torrance, J. B. Acta Crystallogr., Sect. B Struct. Crystallogr. Cryst. Chem. 1981, 837, 2030
performed using the difference function, which was defined as 6 = a c - b - d for T C N Q and as 6 = a - b for the cations. As initial calculations showed that methyl and hexamethylene substitution did not significantly alter the q-r relation, TTF, TMTTF, and H M T T F salts were treated as one group, with a parallel combination for the selenium analogues of the TSF family. BEDT-TTF salts, in which the outer ring sulfur atoms are conjugated to the central fulvalene moiety, were treated separately. With the set-2 fit for the T C N Q molecule, alkali-metal salts were found to be fully ionic. Data for these salts were therefore added to the input to extend the range in q. For BEDT-TTF only one input set was used as no diffuse scattering information is available.
+
Results Results of the fits are given in Table IV and illustrated for some of the two-parameter fits in Figure 2. The three-parameter fit
is in general not justified as it leads to coefficients of the same magnitude as the standard deviations. When the predicted charge transfers (ct) (Table V) are compared, there is very little difference between the values based on the bond length ratio and those from the bond length difference function, in particular when the uncertainty represented by the standard deviations is taken into account. In most cases the standard deviations obtained with the difference function 6 are somewhat smaller. This may be due to better linearity of the bond length difference as a function of charge transfer. A choice between the set-1 fit (measured ct plus stoichiometry values) or the set-2 fit (mostly measured ct values as described above) may be based on possible differences in the predictions and on the standard deviations of the predicted values. For TCNQ the differences between the two sets are negligible; as the set-I set gives somewhat smaller standard deviations, it should be preferred. For TTF differences are more pronounced; in particular
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 6459
Geometry and Charge Transfer in Organic Salts
TABLE 111: Coefficients in the Exmession for (A) rand (BI 8 a
09T
TCNQ
BEDT-TTF
0.940 0.942 0.940 0.942 0.762 0.768 0.768 0.768 0.697 0.698 0.699 0.765
TCNQ TTF TSF BEDT-TTF
-0.179 -0.418 -0.575 -0.415
TTF
TSF
0931
-10
1
I
-06
-08
-02
-04 Charge Tronsfer
(3) (3) (3) (3) (3) (1) (1) (6) (7) (9)
-0.024 -0.036 -0.023 0.049 0.026 0.029 0.024 0.035 0.037 0.023 0.043
(3)
(11) (4) (12) (3) (7) (2) (6) (11) (15) (62) (4)
I
I
I
(A) r = a, + a2q (3) -0.036 (4)
0
079r
(B) 6 = a , (10) (5) (12) (10)
+ a3q2 +0.89 0.010 (10) +0.84 0.012 (12)
2 2
-0.73 0.011 (3) -0.79 0.089 (96)
-0.8 1 -0.63 0.015 (64) -0.82
+
a2q -0.117 (14) 0.093 (5) 0.081 (24) 0.089 (19)
0.88 -0.75 -0.83 -0.98
TABLE IV: 9 as a Function of (A) rand (B) 8 for Two-Parameter Fits4 molecule
TCNQ TTF TSF BEDT-TTF 076 1
I
I
020
010
0
030
040
I
I
050
060
Charge Transfer
c
075r
A, (A) q = A , 26.24 26.28 -15.55 -26.88 -20.20 -18.72 -17.92
(B) TCNQ TTF TSF BEDT-TTF
= A, -1.531 4.490 7.059 4.681
A2
set
+ A2r -29.92 -27.94 20.42 34.98 29.00 26.81 23.43
1 2 1 2 1 2 1
+ A26 -8.545 10.748 12.284 11.273
1 1 1
1
Or is the bond length ratio; 6 is the bond length difference. 073
the second set gives unrealistically large values for large ct, as for example for TMTTF(C10J2. This can be attributed to the lack of large ct values in the input set 2 for this complex. For T S F the number of compounds in set 2 is quite small. W e conclude that, in general, the number of entries in the more restricted sets 2 is too small for the present purpose. Inverse equations for the two-parameter case, giving q as a function of r (and 6) are listed in Table IV. The expression for u(q) can be derived by using standard statistical methods.I6 One obtains
071
0 70
0691 0 68f 067;
I
I
I
I
040
020
080
060
1
100
Charge Tronsfer
where a(r), u(al),and u(a2)are the standard deviations in the bond length ratio (or difference function) in a, and a2,respectively, and y(al,a2)is the covariance between u1 and a2. The last three of these are listed in Table 111 for each of the fits performed.
d 074
1
I
I
I
050
100
150
zoo
Further Discussion It is of interest to analyze predictions made with the equations described above. A first observation is that the coefficients for BEDT-TTF are not significantly different from those of the broader based T T F fit, notwithstanding the difference between the molecules. The latter may therefore be used for BEDT-TTF also, to give more precise values (Table VB). A number of conclusions may be drawn from the predicted values listed in Table V. For example, the two T C N Q molecules in HMM(TCNQ), have significantly different charges, while those in MPM(TCNQ), are identical. The charge transfer to the
Charge Transfer
Figure 2. Examples of fits to set-2 data. Numbers correspond to sequence of entries listed in Table 11. (a) TCNQ; (b) TTF; (c) TSF; (d)
BEDT-TTF.
(16) Eadie, W. T.; Drigard, D.; James, F. E., Roos, M.; Sadoulet, B. Statistical Methods in Experimental Physics; North-Holland: Amsterdam, 1982.
6460 The Journal of Physical C h e m i s t r y , Vol. 92, No. 22, 1988
Umland et al.
TABLE V: Predicted Values of Charge Transfer Based on (A) Bond Length Ratio and (B) Bond Length Difference, Based on Two-Parameter Curves (A) Predicted Values of Charge Transfer Based on Bond Length Ratio (a
set
+ c)/
(b + d) 0.9748 (40) 0.9785 (60) 0.9412 (30) 0.9487 (40) 0.9562 (40)
compound S-methylthiouronium-TCNQ Se-methylselenouronium-TCNQ phenazine-TCNQ TMTSF-TCNQ (red form) NMP-TCNQ (triclinic)
-0.98 -1.09 -0.05 -0.26 -0.47
set 2 -0.96 (13) -1.06 (19) -0.02 (11) -0.23 (13) -0.44 (1 1)
I
(13) (19) (12) (12) (I I)
ref
compound
( b + 6)
a
MPht(TCNQ), HMM(TCNQ),
0.95950) 0.9657 (30) 0.9522 (40) 0.9660 (10) 0.9622 (20)
a
b c
MPM(TCNQ),
d
2 -0.56 -0.73 -0.35 -0.74 -0.63
(8) (10) (11) (6) 16) set
~~
set
alb
compound
1
TTF-chloranil TTF-fluoranil (TTF),CI (TMTTF),SCN (TMTTF),Br
0.7739 (32) 0.7775 (25) 0.8041 (64) 0.7938 (73) 0.7757 (53)
(TMTSF),AsF, (TMTSF),SiF,
0.7151 (41) 0.7080 (43)
(BEDT-TTF),(NOj)l a phase, molecule 1 (BEDT-TTF),Hg,Br, I molecule A molecule B molecule C
0.7822 (74) 0.786 (7) 0.754 (7) 0.749 (7)
0.25 0.32 0.86 0.65 0.28
(8) (7) (14) (15) (12)
2
ref
0.19 (11) 0.32 (09) 1.25 (23) 0.89 (26) 0 26 (19)
g
J
0.46 (20) 0 26 (9)
compound
a/b (49) (54) (93) (24)
k I
(19) (10)
0.7111 (25) 0.6917 (38)
-0.14 (23)
0.35 (17) -0.17 (27)
a phase, molecule 2
0.7629 (90)
-0.05 (22)
molecule D molecule E molecule F
0.786 (7) 0.851 (7) 0.834 (7)
o p
(TMTSF),SiFS (125 K) TMTSF-TCNQ (red)
0.41 (18)
r
0.50 (17) -0.25 (18) -0.37 (18)
S
(11) (12)
compound TTF-chloranil TTF-fluoranil (TTF),CI (TMTTF),SCN (TMTTF),Br (TMTSF)ZAsF6 (TMTSF)2SiFS
-0.536 (6) -0.551 (8)
comDound (BEDT-TTF)j(NOj), a-phase, molecule 1 (BEDT-TTF)5Hg,Br,l molecule A molecule B molecule C
a-b.8,
set 1
set 1. TTF
ref
-0.378 (13)
0.42 (15)
0.43 (15)
r
-0.370 (1) -0.430 (1) -0.440 (1)
0.51 (3) -0.17 (14) -0.27 (17)
s
o
(TMTSF),SiF, (125 K) TMTSF-TCNQ (red)
p
0.51 (4) -0.13 (6) -0.24 (7)
p 4
-0.526 ( 5 ) -0.589 (7)
ref
1
e f
(4) 14) (5) (3) (4)
0.60 (12) -0.18 (21)
a - b, 8,
set 1
set 1. TTF
a-phase, molecule 2
-0.414 (16)
0.01 (21)
0.04 (18)
molecule D molecule E molecule F
-0.370 (1) -0.250 (1) -0280 ( 1 )
0.51 (3) 1.86 (29) 1.53 (22)
0.51 (4) 1.80 (7) 1.48 ( 5 )
comvound
m n
0.50 (17) 2.02 (20) 1.62 (18)
a+c-b-d.A
0.47 (11) 0.29 (13)
f ref
1
0.84 0.52 0.69 2.08
(B) Predicted Value of Charge Transfer Based on Bond Length Difference set1 ref comDound a+c-b-d.8, set -0.072 (12) -0.92 ( 5 ) a MPht(TCNQ), -0.116 (7) -0.54 -0.061 (18) -1.01 (5) a HMM(TCNQ), -0.098 (1 1) -0.69 --0.169 (9) -0.09 (8) b -0.137 (11) -0.36 -0.147 (12) -0.27 (6) C MPM(TCNQ), -0.097 (4) -0.70 -0.125 (11) -0.46 (4) d -0.108 ( 5 ) -0.61 a-b,A set 1 ref compound a-b,8, set 1 -0.396 ( 5 ) 0.23 (7) g TTF-13 -0.337 (8) 0.87 (9) -0.389 ( 5 ) 0.31 (7) g (TMTTF),CIO, -0.366 (10) 0.56 (9) -0.338 (12) 0.86 (13) h (TMTTF)zNOI -0.355 (17) 0.67 (19) -0.360 (10) 0.62 (1 1) I TMTTF(C104), -0.227 (4) 2.05 (9) -0.390 (13) 0.30 (15) J
comDound S-methylthiouronium-TCNQ Se-meth ylselenouronium-TCNO phenazine-TCNQ TMTSF-TCNQ (red form) NMP-TCNQ (triclinic)
e
f f f
2
0.8029 0.7874 0.7957 0.8638
I
ref (8) (10) (11) (6) (6)
1.21 (18) 0.67 ( i 9 j 0.96 (33) 3.34 (23)
TTF-1, (TMTTF)2C104 (TMTTF),NO, TMTTF(CIO4),
g h
-0.53 -0.70 -0.33 -0.71 -0.61
j. f f ref
k 1 m n
p q
ref
'Abashev, G. G.; Vlasova, R. M.; Kartenko, N. F.; Kuzmin, A. M.; Rozhdestvenskaya, I. V.; Semkin, V. N.; Usov, 0. A.; Russkikh, V. S. Acta Crystallogr., Sect. C: Crysf. S f r u c f .Commun. 1987, C43, 1108. bGoldberg, I.; Shmueli, U. Acta Crystallogr., Sect. E Sfruct. Crystallogr. Crysf.Chem. 1973, B29, 440. CKistenmacher, T. J.; Emge, T. J.; Bloch, A. N.; Cowan, D. 0. Acta Crystallogr., Secf.B: Sfruct. Crystallogr. Cryst. Chem. 1982, B38, 1193. dFritchie, C. J. Acta Cryslallogr. 1966, 20, 892. 'Gao, Y . ;Coppens, P. Acfa Crystallogr., Sect. C: Cryst. Strucf.Commun. 1987, C43, 1610. fVisser, R. J. J. Thesis, University of Groningen, 1984. SMayerle, J. J.; Torrance, J. B.; Crowley, J. I. Acta Crystallogr., Sect. B Struct. Crystallogr. Cryst. Chem. 1979, 835, 2988. *Williams, J. M.; Ma, C. L.; Samson, S.; Khanna, S. K.; Somoano, J . J . Chem. Phys. 1980, 72, 3781. IGaligne, J. L.; Liautard, B.; Peytavin, S.; Brun, G.; Maurin, M.: Fabre, J. M.; Torreilles, E.; Giral, L. Acta Crystallogr., Sect. E : Struct. Crystallogr. Cryst. Chem. 1979, 835, 1129. JGaligne, J. L.; Liautard, B.; Peytavin, S.; Brun, G.; Fabre, J. M.; Torreiles, E.; Giral, L. Acta Crystallogr., Secr. B: Strucf.Crystallogr. Crysf. Chem. 1978, 834, 620. 'Teitelbaum, R. C.; Marks, T. J.; Johnson, C. K. J . A m . Chem. SOC.1980, 102, 2986. 'Liautard, B.; Peytavin, S.; Brun, G.; Chasseau, D.; Fabre, J. M.; Giral, L. Acfa Crystallogr., Sect. C: Crysf. Sfruct. Commun. 1984, C40, 1023. '"Liautard, B.; Peytavin, S.; Brun, G.; Maurin, M. Acta Crystallogr., Sect. 8: Sfruct. Crystallogr. Cryst. Chem. 1982, B38, 2746. "Shivaeva, R. P. Kristallografia 1984, 29,480. 'Wudl, F. J . Am. Chem. SOC.1981, 103, 7064. PEriks, K.; Beno, M. A.; Bechgaard, K.; Williams, J. M. Acta Crystallogr., Secf C: Cryst. Struct. Commun. 1984, C40, 1715. qKistenmacher, T. J.; Emge, T. J.; Bloch, A. N.; Cowan, D. 0 . Acta Crystallogr.,Sect. B: Struct. Crystallogr. Cryst. Chem. 1982, B38, 1193. Weber, A,: Enders, H.; Kelier, H. J.; Gogu, E.; Heinen, I.; Bender, K.; Schweitzer, D. Z . Naturforsch., Teil B 1985, 40, 1658 'Mori, T.; Wang, P.: Imaeda, K.; Enoki, T.; Inokuchi, H. Solid State Commun. 1987, 64, 733
T C N Q molecules appears to be slightly larger than one in the latter case. The charge transfer in phenazine-TCNQ is essentially 0, while it is about OSe in the triclinic phase of NMP-TCNQ. The largest variation within one crystalline phase is found in the recently studied crystals of (BEDT-TTF),Hg,Br,,, in which the charges on the BEDT-TTF molecules range from essentially 0 to +1.80 (7), with intermediate values of +0.51 (4) and +1.48 (5). In many cases such differences have been noticed in the original literature. However, the present work allows a more systematic evaluation and derivation of standard deviations based on both the errors in the coefficients of the equations used and
the experimental errors in the bond length functions. It should be kept in mind, however, that the relation between charge transfer and geometry is approximate and ignores other effects, such as a certain influence of molecular packing on intramolecular geometry. Acknowledgment. Support of this research by the donors of the Petroleum Research Fund, administered by the American Chemical Society, is gratefully acknowledged. Computations were performed on a VAX computer acquired with support from the National Science Foundation (CHE8406077).
