2 0 1 t h G. Soos Princeton University, Princeton, New Jersey 08540
Electronic Structure of Organic Conductors and Semiconductors
High electrical conductivity, comparable to that o f poorer metals, is occasionally Once we accept the possibility o f organic found in organic molecular solids. solids whose molecular components are free radicals, the electronic structure o f organic conductors and semiconductors can be understood.
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Organic molecules usually fonn Van der Waals solids, with weak intermolecular forces and essentially uncharged molecules in the crystal. Such solids have low melting or suhlimation points. They are electrical insulators, with room temperature conductivities 15-20 orders of magnitude smaller than that of tvnical metals. Hieh electrical conductivitv. .. comparable to that of poorer m;:tals, is nevertheless occ$: sionally found in urganic molecular solids. This mexpectcd hehavior has heen intriguing both chemists and physiviits for thr last two drcndes (1-51. Organic conductors and iemicunductors illt~strnte11 new class (31of organic molecular solids in which the molecular building blocks are frw radicals, with an odd number of electrons, one of which clearly cannot be paired. Once we accept the possibility of organic solids whose molecular components are free radicals, the electronic strncture of organic conductors and semiconductors can be understood qualitatively by the same methods used for the far more common organic solids based on molecules with an even number of electrons. The Durnose . . of this article is to discuss frec-radical orgnnir conductors i~nilsemict~ndurtorsand t,, contrast them \r,ith iuch familiar classes of solids as metals. magnetic insulators, and molecular solids. Covalent bonds, with pairs of electrons between two atoms, are predominantly found in organic molecules. It follows that most organic molecules contain an even number of electrons, Free radicals, with an odd number of electrons, are reactive species involved in many chemical reactions. Two free radicals R R often react to form an additional covalent hond in R-R. The formation of Hp from two H,atoms or of ethane (CHT-CH~) . " ". from two methvl radicals (CH?) . ". illustrates the reactivity of radicals with each other even in the.ahsence of anv other reaeent. The recombination reaction 2R R? can be"suppressei in several ways: (1)Molecular sieves provide unreactive channels or mazes which effectivelv orevent the radicals from finding each other. (2) The radicafcan he stabilized by distributing the odd electron over several atoms as shown in Figure 1for tripheuylmethyl, an important radical identified in 1900 with three benzene rings replacing the H
+
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Supported by NSF-GR-CHE 76-07377
DPPH Figure 1. The neutral triphenyimethyi and DPPH (diphenylpicryl hydrazyi) free radicals. me unpaired electron in both cases is delocalized over the reiectran nelwork of the rnolacuies. Triphenyimethyl dimerizes. but DPPH farms a true free-radical solid. 546 1 Journal of Chemical Education
atoms of CH3. (3) Radical ions of the type A- or D+ clearly have less possibility for reacting with themselves, since like charges repel. Molecular sieves cannot he used to Droduce a solid where the radicals are next to each other. stabilization of R by various suhstituents can be used to produce free radical solids such as DPPH (Fig. I), which is widely used as a standard in calibrating electron paramagnetic resonance (epr) spect r o m e t e r s r ~ seen s in Figure i, stable, neutral, free radicals tend to have bulky substituents which prevent close contact of the molecnles.~~hese solids are consequently poor conductors. The search for more compact neutral radicals, which nevertheless do not react t o form Rp, has so far not produced any organic conductors. The wav to oreanic conductors and semiconductors has consequenky been through ion radicals. Molecules with large electron affinity are electron acceptors (A) and form stable anion radicals A-. The TCNQ and chloranil molecules shown in Fieure 2 are acceotors with an even number of electrons. Their anions have an odd numhrr of electrons, as emphasized bv thr sliahtl\rt~dundantnuration A-. Conversel\., niolecult:i with small ionization potentials are electron dono& (D). Both TMPD and T T F in Figure 2 are donors with even number of electrons that readily form cation radicals D+. TCNQ is a particularly versatile acceptor which forms ion-radical solids with many metals or organic bases (2), while TMPD and TTF form ion-radical solids with halides or inorganic anions ( I ) . The crystal structure ( 6 )of these solids contains planar ionradicals in stacks along a specific crystal axis. The face-to-face se~arationbetween adiacent ion-radicals is small. in the ranee 3.i - X S a. There is noiovalent twnd (which would rcqoirL< 2A1, but thew is significant contact between the radicnls. Klectriral conducriun is, not too unexpectedly, far greater along the direction of the molecular stack than perpendicular This paper is fifth in a series of Resource Papers intended primarily for college and university teachers. Their publication is supported in part by a grant from the Research Corporation. Zoltin G. Soos was born in Budapest, Hungary, in 1941. A 1962MCL graduate of Haward with a major in chemistry and physics, he earned a PhD in Chemistry at the California Institute of Technology in 1965. After apostdoctoral year at Stanford, he joined the Princeton faculty in 1966and is currently an Associate Professor of Chemistry. His research interests are primarily theoretical and focus on the elec-
The unusual properties o f organic conductors and semiconductors are primarily associated with the unpaired electron in the highest occupied a-MO.
to it. The point here is that ion-radirnl orgmic solids prwide a versatile method fur supprriing the reaction of radicals with each other, without relyi& on bulky groups that prevent close contact between the radicals. Delocalized *-Electron Radicals We first examine the orbital of the odd electron responsible for the unusual physical properties of organic conductors and . . . . semirunrlurtors. Slnrr ;my electrol~icenergy level accommodatrsn pnir ~~Ielectrons, the odd rlertron will necessarily he in the highest energy, or least binding, occupied molecular orhital. This orbital and the next higher, which is the lowest unoccupied molecular orbital (LUMO), are the "frontier orhitals" that play major roles in the chemistry of both even and odd electron molecules. 'I'he highest occupied molerular orhital (HOMO) in free radicals can I w investizated in some detail I N taking- ad\,anrage of the intrinsic magnetic moment g, or spin, of the unpaired electron. The two possible orientations a and 0 of an electron spin S = '12 in a static magnetic field H, lead to an energy separation of w H o 10'O sec-' a t H , = lo4 Gauss. Now a ra;lid'requenc~ymagnetic field at 10" sec-' can induce rransitions between n and ,(, thus flipping the unpaired spin. Enere\, ahsor~~tion frwn the radiofreoumcv . - field is the haais for electron paramagnetic resonance (epr) which was invented in the 1950s and has been a powerful tool for studying free radicals (7,8). Paired electrons in covalent bonds have cancelling intrinsic moments and thus no epr spectrum. The D and A molecules in Figure 2 are planar. They have covalent bonds based on rr-orbitals, or electronic wavefunctions which are even under reflection in the molecular plane. In addition, if 2 is taken to he perpendicular to the molecular plane, the 2p, atomic orbital (AO) of each C or N has a node in the molecular plane. Linear combinations of such AOs nroduce a-orbitals. which are delocalized over the entire molecule and have a nodal surface in the molecular plane. Delocalized 7-MOs are important in understanding aromatic organic solids such as benzene or chloranil, etc., which have an even number of electrons, since both the HOMO and the LUMO are often a-MOs. For example, the HOMO to LUMO transition is the lowest electronic excitation and is induced - E H O ~h arcurd~ , by photons w ~ t hfrequency u = I#.'I.IIMO inp tco the Rohr frequency rule.
-
-.
a
- Donors
TMPD
7
- Acceptors
Figure 3. Spin densities for TCNW and TMPD+ radical ions based on solution hyperfine data and on theoretical computations.The Iota spin density is unity and is the same on symmetry-related atoms.
TCNQ C! CI
if b TTF
The epr spectrum orn-electron radicals in solution has Itern rxtcnsivcls analsled (71. 'l'he tart that the HOMO is over the entire moiecule-can he established by observing additional splittings, called hyperfine structure, due to the nuclear spin of the protons. Epr spectra with 10-100 byperfine lines are seen in carefully deoxygenated solutions (8).The splitting due to each proton is proportional to the probability that the unpaired electron is in the 2p, A 0 of the atom bonded t o the proton. In other words, the linear combination of AOs making up the HOMO can be directly related to epr spectra. The HOMO can also he computed approximatelv using quantum mechanics. The analys& of hyperfine interaction; and their theoretical interpretation is a separate topic (7). The point here is that the spin densities of TCNQ- and TMPD+ shown in Figure 3 are representative results. Spin densities at atoms that are not bonded to a proton are based on theory. The sum of all spin densities adds up to unity for one unpaired electron and, asexpected, the spin densities at symmetry-related atoms are equal. The central assumption in Van der Waals, or molecular, solids is that weak intermolecular forces do not perturb the molecules. This conceot (3)can be aoolied .. to ion-radical organic solids, whose crystal structure clearly shows molecules or molecular ions at standard Van der Waals separations, except for some small shortening of the face-to-face separation along the stack axis. The occurrence of many unpaired elec-
Chloranil
Figure 2. The strong r-electron acceptors TCNQ (tetracyanoquinodimethan) and chlaranil and the strong rr-electron donors TMPD (NNN'N'-tehamethyl-p phenylenediarnine)and TTF (tetrathiofulvalene).
Stock Axis
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Figure 4. Schematic drawing of a regular stack of planar r-electron radicals with lanice spacing R. The region of overlap between adjacent r-electron HOMOS is along the stack. Volume 55, Number 9, September 1978 / 547
The MO approach works for small separation between the radicals, while the V B method becomes valid at large separations. The VB approach perhaps offersa more useful startingpoint because there are far more organic semiconductors than organic "metals."
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trons spoils the rich hyperfine structure observed in solution, hut enr sDectra of ion-radical crvstals nevertheless indicate that the belocalized HOMO of the unpaired electron is essentially unchanged on .. zoine.. to the solid state. Vibrational and opticnl spectra are also consistent with this conrlusiun, which iurther h n o n s t r a t e s thr molecular nature o i %did organic free radicals. Ion-radicals also involve electrostatic forces typical of inorganic salts like NaC1, but the delocalization of the charge over aromatic molecules reduces the importance of electrostatic binding. Indeed, several different contributions (9) to the binding energy of ion-radical solids are comparable and thus complicate quantitative analysis. MO and VB Approach to Free Radical Stacks The unusual . moperties of oraanic conductors and semi. conducu~rsare primarily nsswiated \r,ith the unpaired elcitron in the hirh(.it o r r u ~ i e ds-hlO. Stackiclr such 1)Ianarmolrculr.; face-to-face a-electron overlap alodg the stack only and suggests hiehlv anisotropic, one-dimensional interactions. varioustypes of ibn-radical stacks are in fact the principal structural motif in these solids (6). Without attempting to rationalize the observed crystal structure, we consider in Figure 4 the interactions of unpaired electrons in adjacent radicals A and B separated by 3.1-3.5 A. Although qnite different quantitatively, the problem is analogous to two H atoms a t a separation R. The reaction H H H produces a coThe behavior valent bond of 110 kcal/mole a t Ro = 0.74 near R 1.5-2.0 A is more representative of the far weaker interaction and almost Van der Waals contact in ion-radical solids. There are twoapproximnte starting pointsf~mHZ,themoleculnr nr1)ital I M O I and valence bond ( V H J methods ( 1 0 ) They are almost eqially successful a t R = 0.74 A and, as has lone been known. they converae in more elaborate auantum meihanical treatken&. Such computations becomeprohihitive in manv electron svstems such as the a-radicals in Figure 2, where even calculations for a single radical entail semiempirical methods. The radicals A and B in Figure 4 have normalized r-electron HOMOS $A and cPB,which for two H atoms would simply he the 1s AO. A and B are usually, but not always, the same chemical species. The intermolecular separation R in Figure 4 will he varied, hut would be known from the crystal structure in specific cases. The MO approach is to ignore the interaction between the two electrons that will eventually occupy and $B and to construct linear combinations of $A and For Hz, the even combination i s A 1 s is~a bonding MO, while the odd combination i s A - IsB is antihonding, with a nodal plane perpendicular to the int,ernuclear separation. We can always construct a normalized bonding MO of the type x = CA$A C B $ in ~ which the phases of $A and $B interfere constructively. The MO prescription for the ground electronic state of the radical pair is, consequently
+
-
- 1.
mB.
+
+
&(I.
2) = x ( ~ ) x ( ~ ) ( ~P ID I ~s
~VV'~
(1)
The two electrons are spin paired in the honding MO. For large R, the "bond" is weak and electrons can he thermally excited t o the antibonding MO; X* = -CB$A C A ~Such . excited states have unpaired spins and thus give an epr 0 corresponds, for Hz, to spectrum. The opposite limit R the He atom and eqn. (1) goes smoothly over to x 1s for He. On the other hand, the two electrons are never on the same radical in the VB function
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+
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&dl,2) = N[ba(l)b~(Z) + '$~(2)h3(l)l(0182- @laz)V'3 (2)
548 1 Journal of Chemical Education
We again have spin-paired electrons and either electron can he on either radical. The VB fnnction for Hz becomes exact for large R and it correctly predicts that Hz dissociates into twoH alums, whereas the MO function in eqn. (1) gives a 50% chance of dissociating into H+ H-. The MO approach is superior for smallR, the VB approach a t large R. For Hz a t R o = 0.74 A the twoare comparable. The MO method neglects correlations between the motion of the t w 112. The 1:l TCNQ complex with M 2 P also has a mixed stack, hut is largely neutral (r < 112) at room temperature. The 1:l complex with the neutral radical N-ethylphenazine (EP), on the other hand, leads to mixed stacks featuring an unusual a-bonding of TCNQ- ion radi,cals from adjacent chains (30).The recombination reaction 2R Rz is evidently not suppressed here even for charged A- radicals, and an unusually long carbon a bond of about 1.65 A is produced between two TCNQ- radicals. The C atoms involved are, perhaps not too unexpectedly, those with the maximum u n p a ~ r r delectron spin dmsities in Figure 3. Any detailed u n d e r s t a n d i n g of these widely difiwent structures of e s a r n t i a l l y s i m i l : t r ( q a n i r molecules p t w s prohlems t h a t far exced our current knowledgr t ~ l ' i n t e r m n l e r u l ~l'urc~s. ~r The V H ideas i n w l \ , i n g the highest wcupirri MOs merely p r o v i d c a r o n \ , e n i e n t starting point, based on t h t , ~ ~ l ~ s r r structure, ved tor correlating variuus physical pruperties.
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Summary
121 Melhy, I.. R.. Harder, R. J., Herder. W. R.. Mahler. W., Benmn. R. E., and Mochel, W. E . , J Amer. Chem. Sm.. 84,3374 (1962).TheverrstiUty ofTCNQ mion radicals d U and their unusual physical propertier are intmduced in this key paper. Siomons. W. J.. Biemtedt. P. E.. and Kepler, R. G.. J. Chem. Phys, 39.3523 (19631. The first syitematicrtudy ofelectrical propertiesufTCNQsaltr.Chesnut, D.B..and Phillips, W. D., J. Chem Phya, 35,1002 (19611. The firstepr spectra of tripletspin oicitona in TCNQ salts.
interpretations are pmaihlehepcnding on what data are emphasized Speeulationa about making oven better organic eunductors mnsequently tend to difior. (5I MiFer, J. S., and Rysfein, A. J., l'iog. Inor8 Chemilry, 20.1 (19761 Theempharir here 1s on the physical propwties of one-dimensional inorganic systems, and especially on tho partly oxidized K ~ P ~ ( C N I I B ~ O . S . ~ with ~ Hface-to-face ~O. stacks of PtICNI. camplaxer The nimi1arities between organic and inoqanie conductors were noted byShchegulev,Phvs. SrolusSdidi ( a ) , 12.4 (19721. It remainsto beseenwhether more quantitative treatment. of solid state prapertiea will empha~ile.imi1aritios or differences rtr inorganic and organic systems. (61 Holbetein. F. H.. in "Perrpectiues in Structural Chomistry,"Vol. IV., (Editors: Dunik, 1.D., and lbers. J. A.1 John Wiley B Suns. Inc., New York. 1971 pp. 166395. A mmprehenaive review of crystal structures containine.TCNQ.. Chlorsnil and TMPD. Ref. (11 hasmF-basadst;~~tures. (71 Carrington. A., and Mckchlsn, A. D.,"lntroduction toMagnnicR~aonance."Harper and Row. New Yurk. 1967. This excellent introductory text summarizes solution hyperfine qlittinm and their interpretation in Ch.6, the epr oftriplet states inch. 8, and magnetic detection of molecular rate processes in Ch. 12. 18) Turkeuieh, J..Phys. Today, 26. [July 19651. A briofhistoricalaemunlofepr,solution DPPH spectra at various stages of roaalution. and discussion of the interpretation af hvoerfine m1ittin.r.
119771. Far a review, see Mehger. H. M., N. Y. Acod. ~ c i e h e (to s be publiihed.
The synthesis, experimental characterization, and theoretical understanding of one-dimensional conductors, of paramagnetic semiconductors, and of charge-transfer salts is a young, hut rapidly growinp, area of research in both chemistryand phy& As a new class of solids, these crystalline organic free radicals resemble metals in sometimes having partly filled hands; they resemble magnetic insulators based on transition-metal complexes in sometimes having localized unpaired electrons; they resemble molecular crystals in having essentially unperturbed molecular species in the solid state: and thev resemble inoreanic salts in havine electrostatic cbntrihutibns to the lattiLe binding. All of these features can he understood qualitatively by considering crystals of organic ion-radicals. Ions hinder the recombination reaction 2R R 2 and radicals produce partly filled hands for the odd electrons. The relatively poor overlap and small bandwidth of the HOMOS of adjacent a-electron radicals in a stack then suggest a VB approach in which the electrons are strongly correlated by excluding double occuD a n c v in anv HOMO. in contrast t o the band or MO descri~. tion of uncorrelated electrons in metals. These general electronic features have been illustrated by a hypothetical chain of H atoms which can also be used to extract the magnetic ~ . r o. ~ e r t iofe sdimerized stacks. the behavior of .~ a r t.l vfilled s t : ~ ( : k s , and the inherent instat;ilitws of one-dimensio~~d arrays. The electronic structure of these unusual frrr-radical solids t h u s reflects familiar honding a r g u m e n t s , once appropriate mngnitudes fnr such parameters as t h e b a n d w i d t h nr t h c c o r r e l a t i o n energy are intr
