摘要:

CHEMICAL SOCIETY REVIEWS VOLUME 5,1976 0 Copyright 1976 LONDON THE CHEMICAL SOCIETY CONTENTS PAGE N.M.R. AND THE PERIODICTABLE. By R. K. Harris 1 GROUP SELECTIVITY REDUCINGTHE FUNCTIONAL OF COMPLEX HYDRIDE AGENTS. By E. R. H. Walker 23 PROPERTIESELECTRONIC OF SOME CHAIN AND LAYERCOMPOUNDS. By A. D. Yoffe 51 CHEMICAL OF MOLECULAR By A. Hinchliffe INTERPRETATION WAVEFUNCTIONS. and J. C. Dobson 79 CONDUCTIVITY IN POLYMERS.AND SUPERCONDUCTIVITY By E. P.Goodings 95 MELDOLA MEDAL LECTURE. MOLECULAR AND THE SEMI-COLLISIONS CLASSICAL APPROXIMATION.By J. N. L. Connor 125 INGOLD LECTURE. FOUR-MEMBEREDRINGSAND REACTION MECHANISMS. By P. D. Bartlett 149 INTENSITIES TRANSITIONS.VIBRATIONAL IN ELECTRONIC By M. Roche and H.H. Jaffe’ 165 SYNTHETIC TO 8-LACTAMS.By N. S. Isaacs 181ROUTES ON THE PHILOSOPHYSOMECONSIDERATIONS OF CHEMISTRY. By D. W. Theobald 203 THE EFFECT OF ISOTOPICSUBSnTUnON OF DIFFUSION IN LIQUIDS. By R. Mills and K. R. Harris 215 ABSORPTION IN THE SPECTRA OF STARS; A CRYSTAL FIELDBANDS APPROACH.ByP. G. Manning 233 CHANGE,NYHOLM MEMORIAL LECTURE. GROWTH, AND CHALLENGE.ByD. J. Millen 253 PYRO-COMPOUNDSINORGANIC Ma[(X@,)b]. By G. M. Clark and R. Morley 269 SPECTROSCOPIC OF SOLUTE-SOLVENT By C. N. R. Rao,STUDIES INTERACTIONS. S. Singh, and V. P. Senthilnathan 297 1976 PRESIDENTIAL ADDRESS. CHEMISTRYAND THE NEW INDUSTRIAL REVOLUTION.By F. A. Robinson 317 SOLUTIONS SOLVATEDOF METALS: ELECTRONS.By M. C. R. Symons 337 MULTISTABILITY REACTIONIN OPEN CHEMICAL SYSTEMS. By L. J. Aarons and B. F. Gray 359 ROBERT ROBINSON LECTURE. POST-B,, PROBLEMS IN CORRINSYNTHESIS. By A. Eschenmoser 377 CONFORMATIONAL ANALYSIS AND AMINES:OF SOME ALCOHOLS A COMPARISON OF ORBITAL THEORY, ROTATIONAL MOLECULAR AND VIBRATIONAL SPECTRO-SCOPY. By D. R. Truax and H. Wieser 411 ENVIRONMENTAL : AN INTERNATIONAL VIEWREGULATION &-BRITAIN.By T. W. Hall 431 11-EUROPEAN ECONOMIC By S. P. Johnson 441COMMUNITY. 111-UNITED STATES. By J. B. Ritch, jun. 452 IV--AN INDUSTRYVIEW. By R. C. Tincknell 463

ISSN:0306-0012    

DOI:10.1039/CS97605FP001

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

The Functional Group Selectivity of Complex Hydride Reducing Agents By E. R. H. Walker ICI LTD., PHARMACEUTICALS DIVISION, MERESIDE, ALDERLEY PARK, MACCLESFIELD, CHESHIRE, SKlO 4TG 1 Introduction Sodium borohydridel and lithium aluminium hydride2 have been known for over twenty years, and their use has revolutionized the procedures utilized for the reduction of functional groups in organic chemistry. However, despite their great convenience, these reagents suffer from certain deficiencies. As is well known, lithium aluminium hydride is an exceedingly powerful reagent, capable of reducing many functional groups, and is thus of little value for selective reductions, while sodium borohydride is a mild reducing agent, reacting readily only with aldehydes, ketones, and acid chlorides, and is thus only useful for the selective reduction of these relatively reactive groups.Much work has been conducted over the past few years to discover new reagents with reduction power intermediate between those of lithium aluminium hydride and sodium borohydride, and there is now available a wide range of reagents for selective reductions. In this review the nucleophilic reducing agents sodium borohydride and lithium aluminium hydride are taken as starting points, and the effects on their reducing power of solvent, change of cation, and change of substituent are described. The electrophilic reducing agents diborane and aluminium hydride have, as expected, a quite different pattern of selectivity, and the effect of substituents on the re- ducing power of these reagents is examined.The majority of the reagents dis- cussed are commercially available or are readily prepared from commercially available materials, and the review concentrates on the functional group select- ivity of each reagent. The reactivity of each reagent towards twelve different functional groups is summarized in tabular form in Section 7 (p. 49), using a format introduced by H. C. Brown.3a The table indicates the reactivities of reagents towards sample representative groups and must be interpreted with caution, because the reactivity of many functional groups can be greatly modified by the molecular environment in which the group is placed. At the beginning H. I. Schlesinger, H.C. Brown, H. R. Hockstra, and L. R. Rapp, J. Amer. Chem. SOC., 1953,75,199. A. E. Finholt, A. C. Bond, and H. I. Schlesinger, J. Amer. Chem. SOC.,1947,69, 1199. (a) H. C. Brown, ‘Boranes in Organic Chemistry,’ Cornell University Press, New York, 1972, p. 209; (6) G. M. L. Cragg, ‘Organoboranes in Organic Synthesis,’ Marcel Dekker, New York, 1973, p. 319; (c) E. Schenker, ‘Newer Methods of Preparative Organic Chem- istry’, Vol. IV, ed. W. Forest, Academic Press, New York, 1968, p. 196; (d) H. 0. House, ‘Modern Synthetic Reactions,’ 2nd. edn., Benjamin, Manto Park, California, 1972, p. 45. Functional Group Selectivity of Complex Hydride Reducing Agents of each section is given a list of solvents in which each reagent has been used. Several recent books3 have reviewed the subject of hydride reducing agents and have formed a source for some of the data given here.2 Sodium Borohydride(Solvent:water, alcohols, or 2-methoxyethyl ether) Sodium hrohydride is a very mild reducing agent and can be used to reduce aldehydes, ketones, and acid chlorides in the presence of a wide variety of functional groups. For example, the nitro-ketone (1) can be readily reduced to the nitro-alcohol (2). In some systems saturated ketones can be selectively reduced4 in the presence of @-unsaturated ketones [equation (l)]. Sodium borohydride is a nucleophilic reagent. Thus reduction occurs by attack at the centre of lowest electron density, which in the case of (3) is the carbon atom of the saturated ketone, C-1.Delocalization renders the unsaturated system less susceptible to nucleophilic attack. In the case of the electrophilic reducing agent diborane the reverse selectivity occurs (see Section 4).Although esters are not usually reduced by sodium borohydride, 4nitrophenyl and 2,4-dinitrophenyl esters, e.g. (4) (systems in which the electron-withdrawing effect of the nitro-groups has increased the susceptibility of the ester carbonyl 4 J. D. Cocher and T. G. Halsal1,J. Chem. Soc., 1957, 3441. Walker to nucleophilic attack), are reduced5 very rapidly at room temperature to give the corresponding alcohol, e.g. (5). Thus it shouId be possible to reduce a 2,4dinitrophenyl ester selectively in the presence of a methyl ester. Sodium borohydride has a number of disadvantages as a reducing agent.Thus, although alkyl esters are reduced only very slowly, because of the basicity of the reagent, transesterification can be rapid [equation (2)]. The reduction of enones is invariably accompanied by some double-bond reduction to yield the corresponding saturated alcohol. For example, sodium borohydride reduction6 of the prostaglandin intermediate (6) yields 10-20 "/,of the saturated alcohol (7). Double bonds conjugated to esters, nitriles, amides, aromatic rings, and nitro- groups can also be reduced' by sodium borohydride [equation (3)]. 6COAr 0 (6) NaI3H410 + (7) 10-20% 80 -90% Ar = PhC6H4 A. Effect of Solvent.-Sodium borohydride has a great advantage over lithium aluminium hydride in that it can be used in a wide range of solvents.S. Takahashi and L. A. Cohen,J. Org. Chem., 1970,3S,1505. * J. Bowler, K. B. Mallion, and R. A. Raphael, Synrh. Comm., 1974,4, 211. A. Hassner and C. Heathcock,J. Org. Chem., 1964,29,1350. Functional Group Selectivity of Complex Hydride Reducing Agents (i) Water. Sodium borohydride is very soluble in water, reacting with it slowly to evolve hydrogen. These aqueous solutions can be stabilized by the addition of alkali.1 Such aqueous solutions readily reduce aldehydes and ketones in two-phase systems even where the solubilities of the compounds in the aqueous phase are quite limited. The rate of reduction is increased in the presence of phase-transfer catalysts.8 (ii) Alcohols.Sodium borohydride is very soluble in methanol and ethanol. It reacts rapidly with methanol, but only slowly with ethanol, and therefore for most purposes ethanol is the preferred solvent, possessing the advantages of homogeneous solution together with little loss of reducing agent through side- reaction with the solvent. (iii) Ethers. Sodium borohydride has a very low solubility in diethyl ether and THF, and is not used in these solvents. In 2-methoxyethyl ether9 sodium borohydride is an exceptionally mild reducing agent, reducing aldehydes but not ketones. In this solvent it may be possible to reduce an aldehyde selectively in the presence of a ketone.* (iv) Dimethyl Sulphoxid~-Tetrctmethylene Sulphone. Sodium borohydride has been used in dimethyl sulphoxide-tetramethylene sulphone mixtures to reduce alkyl halides10 in the presence of acids, esters, lactones, and nitro-groups.B. Effect of Cation.-(i) Lithium Borohydride (Solvent:tetrahydrofuran). Lithium borohydride is a stronger reducing agent than sodium borohydride and is ideal for the reduction of esters [equation (4)], particularly in the piesence of func- tional groups that are readily reduced by lithium aluminium hydride, e.g. amidesll [equation (5)]. (ii) Zinc Borohydride (Solvent : dimethoxyethane). Zinc borohydride is readily prepared from sodium borohydride and zinc chloride in dimethoxyethane.12 It has the same reducing power as sodium borohydride but is Iess basic, and is *Sodium borohydride has been used in the presence of 3 equivalents of acetic acid for the selective reduction of aldehydes in the presence of ketones (G.W. Gribble and D. C. Ferguson, J.C.S. Chem. Comm., 1975, 535). C. M. Starks, J. Amer. Chem. SOC.,1971,93, 195. H. C. Brown, E. J. Mead, and B. C. Subba Rao, J. Amer. Chem. SOC., 1955,77, 6209; ref. 3a, p. 216. lo R. 0.Hutchins, D. Hoke, J. Keogh, and D. Koharski, Tetrahedron Letters, 1969, 3495. l1 R. W. Jeanloz and E. Walker, Carbohydrate Res., 1967,4, 504. lDW. J. Gender, F. Johnson, and A. D. B. Sloan, J. Amer. Chem. Soc., 1960, 82,6074. Walker LiBH4 Me(CH2)14C02(CH2)3CH3 Me(CH2)14CH20H (4) Me MeI I HO OCHC02Me HO OCHCHzOH OH LiBH4’ (5)d-)Me di;?; NHCOMe NHCOMe particularly suitable for the reduction of alkali-sensitive compounds12 [equation (@I.NaBH4 OH C. Effect of Substituent.-(i) Alkyl and Aryl Borohydrides. Many alkyl- and aryl-subs tituted borohydrides have been recently described in the literature, a few of which are shown here. Borohydrides (8),13 (9),14 and are com- mercially available, being named respectively Superhydride and 1, and K Selectride. Compounds (11),16 (l2),17 and (13)18 have been prepared for use as stereoselective reducing agents. The borohydrides (8)-( 13) can be prepared from the corresponding boranes by reaction uith either lithium hydride or t-butyl-lithium.17 l3 H. C. Brown, and S. Krishnamurthy.J. Amer. C hem. SOL, 1. 73,95 1669. l4 H. C. Brown and S. Krishnamurthy,J. Arne,, c‘hern.SOL’.,1972, 94.7’59 l5 C. A. Brown, J. Amer. Chem. SOC.,1973,95 4100. H. C. Brown and W. C. Dickason, J. Amei Chem. SOC.1970,92,709. l7 E. J. Corey, S. M. Albonico, U. Koelliker, T. K. Schaat, and R. K. Varma, J. Arner. Cherrr. SOC.,1971, 93, 1491. J. Hooz, S. Akiyama, F. J. Cedar, M. I. Bennett, and R. M. Tuggle, J. Amer. Chem. SOC., 1974,96,274. Functional Group Selectivity of Complex Hydride Reducing Agents (a) Lithium triethylborohydride (Superhydride) (Solvent: tetrahydrofuran). Lithium triethylborohydride has a selectivity for functional groups (Section 7) that is similar to that of lithium borohydride. However, the inductive effect of the alkyl substituents makes lithium triethylborohydride an extremely nucleo- philic species,l3 being 20 times more nucleophilic than thiophenoxide ion and 10O00 times more nucleophilic than lithium borohydride.Lithium triethyl- borohydride readily reduces alkyl halides by an sN2process but does not reduce Br Walker aryl halides [equations (7a and b)]. Thus this reagent can be used for the selective removal of an alkyl halide in the presence of an aryl halide. Lithium aluminium hydride reduces both alkyl and aryl halides.19 Epoxide (14) is readily opened in an sN2 process by lithium triethylborodeuteride, also commercially available, to give the stereochemicallypure deuterio-alcohol (15). (b) Lithium and potassium tri-s-butylborohydride14J5 (L and K Selectride) (Solvent:tetrahydrofuran). Lithium tri-s-b~tylborohydridel~has approximately the same functional group selectivity as lithium triethylborohydride. It is, however, an exceedingly stereoselectivereducing agent, owing to the bulk of the s-butyl substituents.Thus the ketone function of PGEz (16) is stereoselectively reduced, the reagent approaching exclusively from the least hindered /.%face of the cyclopentane ring to give PGFza (17); none of the epimeric PGF~B(18) is formed.20 The substituted cyclohexanones (19) and (20) are also reduced14 OH; I dH bH H. C. Brown and S. Krishnamurthy, J. Org. Chem., 1969,34,3918. E. R. H. Walker, unpublished result. 29 Functional Group Selectivity of Complex Hydride Reducing Agents 00-4OH + +OH 0.7% 1 96.5% 3.5% But with a very high degree of stereoselectivity.At -78 "C the ketone group of the enone (21) is selectibely reduced20 to the mixed epimers of the allylic alcohol (22). At ambient temperatures, however, reduction of the lactone and ester functionalities occurs to yield a complex mixture of products, showing that lithium tri-s-butylborohydride is a powerful reducing agent.* h.t. mixture Ar =PhC6 H4 (ii) Cyanoborohydrides. Sodium cyanoborohydride,21 lithium cyanoboro-hydride,22 and tetrabutylammonium cyanoborohydrideZ3 have been used as reducing agents. The electron-withdrawing effect of the cyano-group (23) makes these reducing agents weaker than their borohydride equivalents. H I-H-B+cNI H *It has recently been shown that L Selectride will convert a/3-unsaturated esters into satu- rated ester (B.Ganem and J. M. Fortunato, J. Org. Chem., 1975, 40, 2846). 21 R. F. Borch, M. D. Bernstein, and H. D. Durst, J. Amer. Chem. Soc., 1971,93,2897. ra R. F. Borch and H. D. Durst, J. Amer. Chem. SOC.,1969,91,3996. 43 R. 0.Hutchins and D. Kandasamy, J. Amer. Chem. SOC.,1973,9S, 6131. Walker (a) Sodium cyanoborohydride (Solvent: water, methanol, hexamethylphos- phoramide, or dimethyl sulphoxide). Sodium cyanoborohydride is an extremely selective reagent, reducing only aldehydes, ketones, alkyl halides, and iminium salts. By careful choice of the solvent media used, both alkyl halides and iminium salts can separately be reduced in the presence of aldehydes and ketones. Sodium cyanoborohydride is stable in aqueous acidic media.Under neutral conditions aldehydes and ketones are nut reduced2I by the reagent [equation @)I, and this NzIBH~CN,PhCIlO \/ > PhCH2OH PH 7 important property gives rise to its high degree of selectivity as a reducing species. Under acidic conditions (pH 34) aldehydes and ketones are readily reduced [equation (9)] via the corresponding protonated species (24). Under neutral PhCI-IO PhCH2 OH pH 3-4, NaBH3CN or or (9)HCI-MeOH Me3C Me3C Me Me conditions in hexamethylphosphoramide sodium cyanoborohydride will reduce24 primary alkyl halides in the presence of aldehydes [equations (10) and (1l)]. In principle, any double bond (25) which can be sufficiently polarized [e.g. that in (24)] should be reducible by sodium cyanoborohydride. When A and B are carbon and nitrogen respectively, (25) represents the iminium moiety (26), 24 R.0.Hutchins, B.E. Maryanoff, and C. A. Milewski, Chem. Comm., 1971, 1097. 31 2 Functional Group Selectivity of Complex Hydride Redimkg Agents which can readily be reduced by sodium cyanoborohydride. Since (26) can be generated from an aldehyde and amine at near neutral pH (conditions under which aldehydes and ketones are not reduced), the iminium intermediatean be reduced in the presence of the parent carbonyl group, leading to a facile method of reductive amination21 [equation (12)]. This reaction is best carried out in the presence of 3A molecular sieve, and it can accommodate a wide range of func- tionality.Replacement of the amine used above [cj; equation (12)] by toluene-p- sulphonyl hydrazide leads to a method of deoxygenation of ketones and aldehydes25 [equation (13)] employing the same general principles outlined above. Again, a wide range of functionality can be accommodated. The generality of the rtduction is demonstrated for the recently published26 sulphoxide to sulphide transformation, where A and B in (25) are S and 0, respectively. The sulphoxide is reduced after methylation with methyl fluoro- sulphonate [equation (14)], and the reaction can be carried out in the presence of a ketone. (b) Lithium cyanoborohydride.22 For most purposes lithium cyanoborohydride and sodium cyanoborohydride are interchangeable.(c) Tetrabutylammonium ~yanoborohydride~~ (Solvent: hexamethylphosphor-amide, methanol, or benzene). Tetrabutylammonium cyanoborohydride in 0.1N hydrochloric acid solution has been used for the selective reduction of an aldehyde in the presence of a ketone23 [equation (15)]. (iii) Sulphurated Sodium Borohydride (Solvent :tetrahydrofuran). When sodium borohydride and sulphur are allowed to react at room temperature in tetra- hydrofuran there is a rapid evolution of hydrogen, and sulphurated sodium borohydride27 is formed. Sulphurated sodium borohydride is a mow powerful reducing agent than sodium borohydride, and reductions of functional groups containing nitrogen are particularly facile. Aromatic nitro-compounds are reduced in high yields to the corresponding amine~,~~ and this reaction can be selectively carried out in the presence of ortho-, meta-, or para-substituted hal- ogen, ester, nitrile, olefin, or ether groups [equation (16)]. In the case of aliphatic nitro-compounds the structure of the substrate governs the course of the 25 R.0.Hutchins, B. E. Maryanoff, and C. A. Milewski, J. Amer. Chem. Soc., 1971,93, 1793. +aE H. D. Durst, J. W. Zubrick, and G. R. Kieczykowski, Tetrahedron Letters, 1974, 1777. 27 J. M. Lalancette, A. Freche, J. R. Brindle, and M. Laliberte, Synthesis, 1972, 526. Walker .u N I I Functional Group Selectivity of Complex Hydvide Reducing Agents Me(CH2)8CH0 BuqNBH3CN Me(CH2)8CH20H (15a) 0 R = Hal, COzR', CN, A,or OR' NaBH2S3 Ph PhC 5N (1 7) reaction.Primary nitro-derivatives, e.g. phenylnitromethane, are converted into the corresponding nitriles [equation (17)] and secondary nitro-compounds yield a mixture of the corresponding ketone and oxime, but tertiary nitro-compounds are inert. In the absence of the more reactive nitro-groups, aromatic nitriles are reduced to the corresponding amines [equation (1S)]. Although aldehydes and ketones are normally reduced by sulphurated sodium borohydride, sterically hindered ketones such as camphor are not reduced [equation (19)]. It should thus be possible with this reagent to reduce an aldehyde or unhindered ketone selectively in the presence of an hindered ketone. Walker 3 Lithium Aluminium Hydride (Solvent: tetrahydrofuran, diethyl ether, or methylene chloride) Lithium aluminium hydride is a very powerful reducing agent, reducing a wide range of functional groups to their lowest oxidation state.Selective reductions of functional groups are rarely possible. A. Effect of Solvent.-Lithium aluminium hydride must be used in aprotic solvents and is usually used in diethyl ether or tetrahydrofuran. In all the solvents used it is a very powerful reducing agent. The cyclic carbonate (27) has been reduced28 by lithium aluminium hydride in a mixture of diethyl ether and methylene chloride to give the trio1 (28). The use of methylene chloride as solvent extends the range of lithium aluminium hydride as a reducing agent to those substrates that are insoluble in ether solvents.One partial reduction which can be achieved with lithium aluminium hydride is the reduction of an acid to the corresponding aldehyde via the irnida~olide~~ [equation (20)]. B. Effect of Cation.-Sodium aluminium hydride30 has the same reducing power as lithium aluminium hydride and offers no majoi advantage as a reducing agent. 28 D. Y. Curtin, J. A. Kampmeier, and M. L. Farmer, J. Amer. Chern. Soc., 1965,87,874. 29 H. A. Staab and A. Mannschreck, Chem. Ber., 1962,95,1284. 30 A. E. Finholt, E. C. Jacobson, A. E. Ogard, and P. Thompson, J. Amer. Chem. SOC.,1955, 77,4163. Functional Croup Selectivity of Complex Hydride Reducitig Agents C. Effect of Substituent.-(i) Alkoxy Substiruents. (a) Lithium tri-t-butoxy- aluminium hjdride (Solvent : tetrahydrofuran).The steric and electronic effects of the t-butoxy-groups render lithium tri-t-butoxyaluminium hydride a very mild reducing agent, and in terms of its selectivity for functional groups (Section 7) it resembles sodium borohydride much more than lithium aluminium hydride. One of the key reactions of lithium tri-t-butoxyaluminium hydride is the reduc- tion of acid chlorides to aldehydes,31 which can be carried out in the presence of a wide range of different functional groups [equations (21), (22), and (23)32]. ap-Unsaturated systems undergo 1,2-rather than 1 ,4-attack [equation (22)]. LiAl H(OBut), OzN -78'C,THF ' 02N Lithium tri-t-butoxyaluminium hydride will also reduce imidazolides to aldehydes33 and offers an advantage over lithium aluminium hydride in that a wide range of functionality can be accommodated [equation (24)].The imidazo- lide is derived from the corresponding and equation (24) represents a selective method for the conversion of acids into aldehydes. To demonstrate the selectivity of the reagent, a ketone can be red~ced3~ in the presence of a formate [equation (25)]. (b) Sodium bis-[2-methoxyethoxy]alurninium hydride (RED-AL) (Solvent : benzene, toluene, xylene, diethyl ether, or tttrahydrofuran). RED-AL35 is commercially available as a 70 :< solution in benzene and has approximately the same reducing capability as lithium aluminium hydride. The reagent claims the following advantages over lithium aluminium hydride: (1) It is safer; it does not ignite in moist air or oxygen.(2) It is stable in dry air. (3) Tt is very soluble in aromatic solvents and ethers. (4) It is stable at 200 "C. RED-AL is therefore a safe, soluble reagent that is equivalent in reducing power to lithium aluminium hydride. It can rarely be used as a selective reagent because of its high reducing power. 31 H. C. Brown and B. C. Subba Rao, J. Amer. Chem. SOC.,1958, 80, 5377. 32 E. D. Bergmann and A. Cohen, Tetrahedron Letters, 1965, 1151. 33 T. C. McMorris, J. Org. Chem., 1970, 35, 458. 34 J. Fajkos, Coll. Czech. Chem. Comm., 1959,24,2284. J. Malek and M. Cerny, Synthesis. 1972, 217. Walker AcO LYP -&AcO 0 OH HCO An @-Unsaturated system, e.g. (29), can be reduced by RED-AL to give the corresponding allylic alcohol, e.g.(30), in contrast to lithium aluminium hydride, which yields the corresponding saturated alcohol. Under forcing conditions RED-AL can cause hydrogenolysis of benzyl alcohols. Thus the alcohol (32) formed by reduction of the ester (31) in refluxing benzene undergoes hydro- genolysis in refluxing xylene to give p-cresol (33). Because of its great solubility, OHCOZEt NaH2Al(OCH CH,OMe)PhH, A, T>6X -88-OH OH OH (31) (32) (33) RED-AL can be used at low temperature, and some partial reductions can be achieved. For example, the ester (34) has been reduced in ether to the aldehyde (3336 by RED-AL at -78 "C. a6 J. Vit, Org. Chem. Bull., 1970, 42, (3), 1. Functional Group Selectivity of Complex Hydride Reducing Agerzts RED-AL > s+CHO -7 8 OC (34) (35) Cii) Alkyl Substituents.(a) Sodium diethylulumirzium hydride (Solvent: toluene). Sodium diethylaluminium h~dride~~ is commercially available as a 25 % solution in toluene. It has a similar reducing power to that of lithium aluminium hydride, and like RED-AL it is soluble in aromatic hydrocarbons. 4 Diborane (Solvent:tetrahydrofuran, methylene chloride, or dimethyl sulphide) Whereas the nucleophilic reducing agent sodium borohydride attacks a molecule at the centres of lowest electron density, the electrophilic reducing agent diborane initiates its reactions by attack at the centres of highest electron density. Ex-cellent examples of the consequence of these differing modes of reaction are the reductions of trimethylacetaldehyde (36) and chloral (37).The electron-with- drawing effect of the halogen atoms of chloral (37) increases the susceptibility of the aldehyde to nucleophilic attack. Sodium borohydride therefore reduces chloral (37) far faster than trimethylacetaldehyde (36). This same electron- withdrawing effect results in a decreased susceptibility to electrophilic attack. Thus diborane reduces trimethylacetaldehyde (36) but does not reduce chloral (37). Similarly, acetyl chloride (38) is also not reduced by diborane. (36) (37) Diborane can be conveniently prepared in methylene chloride,38 using sodium borohydride, a phase-transfer catalyst, sodium hydroxide, and an alkyl halide.Diborane is commercially available as a 1 molar solution in tetrahydro- furan or as a more stable 10 molar solution in dimethyl sulphide. While the tetrahydrofuran and methylene chloride solutions have equal reactivity in most reactions, the dimethyl sulphide solution is less reactive. The spectrum of reducing activity (Section 7) of diborane is quite different to that of sodium borohydride. One of the key reactions is the reduction of car- boxylic acids,39 which can be carried out in the presence of a wide range of different functional groups [e.g. equations (26)-(28)]. Acids are reduced via the corresponding triacylboranes (39), in which the resonance interactions between the acyl oxygen and boron (40) render the carbonyl group much more susceptible 37 H.J. Sanders, Chem. Eng. News, 1972, June 19, p. 29. 38 A. Brandstrom, U. Junggren, and B. Lamm, Tetrahedron Letters, 1973, 3173. s.0 N. M. Yoon, C. S. Pak, H. C. Brown, S. Krishnamurthy, and T. P. Stocky, J. Org. Chem., 1973,38,2786. Walker C02Me (28)Ho2YYo2h*e '''0 to reduction. An acid can be protected from diborane reduction by making an acid salt. Reduction of the salt is prevented because the triacylborane [e.g. (39)] can no longer form. The reduction of an acid with diborane in dimethyl sulphide occurs rather slowly, presumably because of the strength of the borane-dimethyl sulphide complex, but can be catalysed40 by the addition of trimethyl borate, which reacts with the acid to form an acyl dimethyl borate (41), equivalent to the triacylborane (39).This derivative then undergoes rapid reduction to the required alcohol. Diborane will reduce amides to amines41 [equation (29)] and electron-rich RC /OMe b-B \OMe C.F. Lane, H. L. Myatt, J. Daniels, and H. B. Hopps, J. Org. Chem., 1974,39,3052. 41 M.J. Kornet, P. A. Thio, and S. I. Tan, J. Org. Chem., 1968,33,3637. 39 Functional Group Selectivity of Complex Hydride Reducing Agents ketones to the corresponding methylene compounds42 [equation (30)]. It is possible to reduce an enone selectively43 in the presence of a ketone [equation (31)]. Sodium borohydride has the opposite selectivity (see Section 2). I, %l r I 1 Esters are not usually reduced by diborane. However, hydroboration of olefinic esters often results in ester reduction,44 indicating the important influence of chemical environment on the reactivity of a functional group.For example, hydroboration-oxidation45of the olefinic ester (42) gives the expected hydroxy- W. J. Wechter, J. Org. Chem., 1963, 28, 2935. 43 M. Stefanovic and S. Lajsic, Tetrakedroti Letters, 1967, 1777. 44 H. C. Brown and K. A. Keblys, J. Amer. Chem. Sac., 1964, 86, 1795. 45 D. Varech and J. Jacques, Bull. SOC.chim. France, 1969, 3505. 40 Walker ester (49, together with the alcohols (44)and (46), in which the ester has been reduced via the cyclic intermediate (43). I I. CIIO (42) (43) (44) + @OHI *OH +C02Mc A. Borane-Amine Complexes.46-(Solvent : water, methanol, diethyl ether, hexane, methylene chloride, or toluene).The commercially available borane- ainine complexes shown here have a wide range of physical properties and can \ I\ JT 1 Liquids Solids be used in many solvents, including water. The complexes have a very different reactivity to that of diborane (e.g.acids are not reduced) and are essentially very similar to sodium borohydride except for their reaction with carbon-carbon double bonds (see Section 7). Borane-amine complexes thus represent a ‘safe’ source of diborane for the hydr~boration~~ a carbon-carbon double bond of [equation(32)]. 16 C. F. Lane, ‘The Borane-Amine Complexes,’ Aldrich Chemical Company Reviews, Vol. 6, No. 3. 37 L. T. Murray, Ph.D. Thesis, Purdue University, Lafayette, Indiana, 1963.Functional Croup Selectivity of'Complex Hydride Reducing Agents n OWNPh B. Effect of Substituent.-2-Methylbut-2-ene reacts with diborane to give the commercially available dialkyl-borane disiamylborane (47). Thexylborane (48) and 9-borabicycIo[3,3,1 Inonane (9-BBN) (49), an air-stable white solid, are also commercially available. B 1-1 (i) Bis-3-methyl-2-butylborane (Disiamylborane) (Solvent: tetrahydrofuran). Dialkylboranes have a modified reduction power (see Section 7)compared with that of diborane, the most notable difference being that acids are not reduced by the reagents. The most useful reactions of dialkylboranes are the partial reduc- tion of lactones to lactols48 and of tertiary amides to aldehydes49 [equation (33)] and the hydroboration50 of a carbon-carbon double bond in the presence of an acid [equation (34)].* *Brown has shown that 9-BBN can be used to convert up-unsaturated aldehydes and ketones into corresponding allylic alcohols in excellent yields.The transformations can be carried out selectively in the presence of an isolated carbon-carbon double bond, a nitro-group, or an ester group (S.Krishnamurthy and H. C. Brown, J. Org. Chem., 1975, 40,1864). 48R.E. Ireland, D. A. Evans, D. Glover, G. M. Rubottom, and H. Young, J. Urg. Chem., 1969,34,3717. 4D H. C. Brown, D. B. Bigley. and N. M. Yoon, J. Amer. Chem. SOC.,1970,92,7161. so H. C. Brown and D. B. Bigley, J. Amer. Chem. SOC.,1961,83,486.Walker 5 Aluminium Hydride (Solvent : tetrahydrofuran or diethyl ether) Aluminium hydride is a powerful reducing agent similar in activity to lithium aluminium hydride, and it is therefore of little value as a selective reducing agent. A recent reports1 gives details of the preparation of a stable ethereal solution of aluminium hydride. Aluminium hydride has one major advantage over lithium aluminium hydride and diborane in that it reduces an u/hnsaturated system, e.g. (50), to the corresponding allylic alcohol52 (51) ;lithium aluminium hydride gives the saturated alcohol (52) while diborane hydroborates the double bond. The preferred AlH3Ph+CHo > LiA 1H4I PI1-OH reagent for the transformation of (50) into (51) is, however, di-isobutylaluminium hydride (see below).Aluminium hydride can cause hydrogenolysis of acetals and ketals. A. Effect of Substibent.-(i) Di-isobutylaluminiurn Hydridel(So1vent :toluene or dimethoxyethane). Di-isobutylaluminium hydride (DIBAL) is commercially available either as the neat liquid or as a 20% solution in toluene. The reagent which can also be used in dimethoxyethane, is more selective than aluminium hydride (see Section 7) and is a very useful and versatile reagent. DIBAL is the preferred reagent for the reduction of lactones, esters, amides, and nitriles to the corresponding aldehydes. For example, the lactones (53)53 and (55)54 are reduced to the lactols (54) and (56), respectively, by DIBAL at -70 "C.The nitriles (57)55 and (59)56 are reduced to the corresponding aldehydes 61 E.C. Ashby, J. R. Sanders, P. Clavely, and R. Schwartz, J. Amer. Chem. SOC.,1973, 95, 6485. 6a M. J. Jorgenson, Tetrahedron Letters, 1962, 559. 63 E. J. Corey, N. M. Weinshenker, T. K. Schaaf, and W. Huber, J. Amer. Chem. SOC.,1969, 91,5675. O4 J. Schmidlin and A. Wettstein, Helv. Chim. Actu, 1963,46,2799. 65 J. A. Marshall, N. H. Andersen, and J. W. Schlicher, J. Org. Chem., 1970, 35, 858; J. A. Marshall, N. H. Andersen, and P. C. Johnson, ibid., p. 186. 6s S. Trofimenko,J. Org. Chem., 1964, 29, 3046. Functional Group Selectivity of Complex Hydride Reducing Agents 0 otIoA-70°C QIpyvvv4 c-3*lUAL ~THP OTHP ATHP OTl11' (53) (54) THP == tetrahydropyran-2-yl ether (58) and (60) by DIBAL at room temperature.The lactone (53) can be reduced to the lactol (54) in the presence of a nitrile20 (61). Esters are also readily reduced5' to the corresponding aldehydes by DIBAL at -70 "C,e.g. (62) to (63). Another key reaction of DIBAL is the 1,2-reduction of up-unsaturated systems, Thus the enedione58 (64) is cleanly reduced to the enediol(65) and the enone (66) reduced58 to the allylic alcohol (67). DIBAL reacts with acetylenes to give on work-up a cis-substituted ~lefin~~ [equation (35)], but an ester can be selectively reduced60 in the presence of an acetylene [equation (36)]. 6 Miscellaneous Reagents A. Lithium n-Buty1copperhydride.-(Solvent : diethyl ether). Masamune has recently described61 the preparation and properties of the readily accessible lithium copper hydride reagent (68 ).Primary, secondary, and tertiary halides and mesylates are reduced with this reagent to the corresponding alkanes. The reduction can be carried out in the presence of esters and the reagent forms an attractive alternative to the use of sodium borohydride in dimethyl sulphoxide- 67 C. Szantay, L. Toke, and P. Kolonits, J. Org. Chem., 1966,31, 1447. 68 K. E. Wilson, R. T. Seidner, and S. Masamune, Chem. Comm., 1970, 213. gD G. Wilke and H. Muller, Chem. Ber., 1956, 89,444. O0 E. J. Corey and R. A. Ruden, Tetrahedron Letters, 1973, 1495. S. Masamune, G. S. Bates, and P. E. Georghiou, J. Amer. Chem. SOC.,1974, 96, 3686. Walker qCN Functional Group Selectivity of Complex Hydride Reducing Agents +?0 Et -5-Et EtuEt(35)ii, MeOH Et*O CuH f BuLi LiCuHBun -4OOC ’ (68) tetramethylene sulphone.For example, the halide (69) and mesylate (71) are conveniently reduced to the alkane (70) and ester (72), respectively, by lithium n-butylcopperhydride in diethyl ether. Aldehydes and ketones are reduced by lithium n-butylcopperhydride while an enone suffers 1,4-reduction to give the saturated ketone [equation (331. (KCuH& has also recently been described.62 It has approximately the same reducing specificity as lithium n-butylcopper- hydride and appears to offer no significant advantage. m T.Yoshida and E. Negishi, J.C.S. Chenr. Comm., 1974, 762. Walker-CO2Et C02EtMeS020U (71) (72) -(37) 0 0 B.Polymethylhydrosiloxe (PMHS).63-(Solvent : diethyl ether, toluene, ethanol, or dioxan). PMHS is a commercially available polymeric hydrosiloxane which can be used either for the selective reduction of aldehydes and ketones in the presence of all othei functionality or as a source of hydrogen for the reduc- tion of a double bond. The reduction of aldehydes and ketones is mediated by a catalytic amount of a tin oxide, which is converted into a tin hydride in situ. Thus, for example, the enone [equation (38)] and aldehyde [equation (39)] are reduced to the corresponding alcohols by PMHS in the presence of 2 mole% of dibutylacetyltin oxide. Under these conditions no other functional groups are reduced.If the quantity of the tin oxide is increased to 1equivalent, nitro-groups, nitriles, and carbon-carbon double bonds are reduced. 2 mole% (Bu2AcSn)20, PMHS, EtOH (38)0 OH PhCHO > PhCH20H (39) PMHS can be used for the in situ generation of tributyltin hydride from tri- butyltin oxide, and this has been used for the reductione4 of the iodo-prosta- glandin intermediate (73) to give the dimethyl acetal (74) in high yield. Jn the presence of palladium on charcoal PMHS will reduce63 cis-carbon-carbon double bonds whereas trans-carbon-carbon double bonds are not reduced [equa- tion (40)]. Under these conditions aromatic nitro-compounds are reduced to amines63 [equation (41)]. 63 J. Lipowitz and S. A. Bowman, J. Org. Chem., 1973,38,162. 61 G.Robinson, personal communication. Functional Group Selectivity of Complex Hydride Reducing Agents c1__3 ?4 &me OCOAr OMC (73) Ar = PhCBHI (74) The author wishes to thank Dr N. S. Crossley for helpful discussions and Mrs K. Hurley for typing the manuscript. 7 Functional Group Selectivity Table* RCHO J J ti \' JJJ J JJJdJJd ho JdJJJJJdJdddJJJ RCOCl JJdJJ x RCHO J v/ x J x d Lactone V.sl0w J x JJXJX JJX Lactol J Lactol v. slow J J x J X J J d X J/o\R1COzR2 v.slow J Jxx R2=Ph, X J RCHO -+RICH0 RCOzH xx X X Jx RCOzM X X X dx RCON: X X RCHO J RCHO RCN X X X J RCHO RN02 X X X X X X xx xx X J X XX RHal X X alkyl: J aryl : x xx 3* J indicates that the functional group is reduced, while x indicates that it is resistant to reduction.Where appropriate the structure of the reduction P product obtained is indicated in the Table. (b\o Functional Group Selectivity of Complex Hydride Reducing Agents 8 Index of Reagents* Reagent Aluminium hydride Bis-3-methyl-2-butylborane Borane-amine complexes Diborane Di-iso bu tylaluminium hydride Lithium aluminium hydride .Lithium borohydride Lithium n-butylcopperhydride Lithium cyanoborohydride Lithium tri-t-butoxyaluminium h ydride Lithium tri-s-butylborohydride Lithium triethylborohydride Polymet hylhydrosiloxane Potassium tfi-s-butylborohydride Sodium aluminium hydride Sodium bis-(2-methoxyethoxy)- aluminium hydride (RED-AL) Sodium borohydride Sodium cyanoborohydride Sodium diethylaluminium hydride Sulphurated sodium borohydride Tetrabutylammonium cyano- borohydride Zinc borohydride Page No.43 42 41 38 43 35 26 44 32 Li(But0)3A1H 36 LiBus3BH 29 LiEt3BH 28 MesSiO( MeHSi0)35SiMe3 46 KBus3BH 29 NaAIH4 35 NaHzAl(0CH2CH 20Me)~ 36 NaBH4 24 NaBH3CN 31 NaEt 2A1H2 38 NaBH2S3 32 32 26 *The names of the reagents used in this review are those in common use among organic chemists, and are not necessarily correct inorganic nomenclature.

ISSN:0306-0012    

DOI:10.1039/CS9760500023

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Electronic Properties of Some Chain and Layer Compounds By A. D. Yoffe CAVENDISH LABORATORY, UNIVERSITY OF CAMBRIDGE, MADINGLEY ROAD, CAMBRIDGE, CB3 OHE Solids having chain- or layer-like structures may in certain circumstances approximate to ‘one-’ or ‘two-dimensional’ solids. The chains or layers can be separated by relatively large distances, of the order of the van der Waals atomic radii, and this results in extreme anisotropy in the electronic, vibrational, and mechnical properties. These properties to a large extent correspond to those appropriate for single chains or layers, and the interaction between the chains or layers can be treated as a perturbation. The materials are of considerable interest at present and their physical and chemical properties are being intensively studied in many laboratories throughout the world.The results obtained with the metallic members are particularly exciting and sometimes very puzzling. It was a theoretical paper by Little1 in 1964 that caused renewed interest in the so-called ‘one-dimensional conductors’. This paper was concerned with the possibility of high-temperature superconductivity, particularly in long-chain organic molecules. The theory was based on electron-phonon (vibrational) interactions, and it was greeted with some criticism and scepticism. In 1973, Heeger and his colleagues at the University of Pennsylvania published some spectacular results on the electrical conductivity found in a few of their crystals of the organic charge-transfer complex TTF-TCNQ (1,4,5,8-tetrathiafulvalene-tetracyanoquinodimethane).z These crystals, which are extremely anisotropic in their physical properties, behave as metals at room temperature when the conduc- tivity is measured along the stacks of molecules.At low temperatures, however, there is a change in behaviour, and the variation in conductivity with tempera- ture corresponds to a small band gap semiconductor. There was some talk of super-conducting fluctuations in the crystals, and there is little doubt that the pub- licity associated with these experimental findings stimulated the wide interest and excitement in this class of materials. Chain-like solids have been studied for some time now, and the ‘Krogmann type’ solids3 such as the mixed-valency planar complexes of platinum have received attention from a number of groups, including that associated with Zeller at the Brown Boveri laboratories in S~itzerland.~A typical solid is KzPt(CN)4Bro.3,3HzO, sometimes abbreviated as KCP(Br), and here we have linear chains of platinum atoms in the crystal. The W.A. Little, Phys. Rev. (A), 1964, 134, 1416. L. B. Coleman, M. J. Cohen, D. J. Sandman, F. G. Yamagishi, A. F. Garito, and A. J. Heeger, Solid State Comm., 1973, 12, 1125. K. Krogman, Angew. Chem. Znternat. Edn., 1969, 8, 35. H. R. Zeller, in ‘Festkorper Probleme’, ed. H. J. Queisser, Pergamon, Oxford, 1973, Vol. 13, p. 31. Electronic Properties of’Soine Chain and Layer Compounds most important result, however, was reported in 1975 when a group working in the I.B.M.laboratories in California on the sulphur-nitrogen polymer (SN)% announced that they had found superconducting behaviour.5 The transition temperature was quite low, in the region of a quarter of a degree Kelvin, but this is the first polymer and also the first pseudo ‘one-dimensional’ solid to behave in this way. It is not intended in this review to give an exhaustive account of all this work since this can be found in books and published articles.6 The subject is developing at an astonishing rate where many of the ideas are contro- versial to say the least, and it is possible only to give trends, and to mention some of the phenomena encountered. Turning to the layer-type solids, there are many distinct classes and we should mention graphite and its compounds;7 the metal halides such as PbI2, C0c12;~ the arsenic and antimony chalcogenides such as AszSe3, Sb&; the gallium chalcogenides Gas, GaSe ;g the ‘inverse structure’ silver subflouride AgzF; and the transition-metal dichalcogenides based on MoS2.The physical and chemical properties of many of these solids have been discussed in reviews.1° The last group consists of the sulphides, selenides, and tellurides of metals such as Ti, Zr, Hf, V, Nb, Ta, Mo, and W. Some of these layer materials are wide band gap semiconductors, e.g. HfS2; some such as NbSez are metals and superconductors; while others such as MoTe2 are relatively small band gap semiconductors. The most interesting features of these materials are associated with the width and occupation of relatively narrow ‘d’ bands. The physical topics which have been studied in these layer materials include electron transport in narrow ‘d’ bands; excitons, including anisotropy effects, thickness effects, and screening by free carriers; metal--non-metal transformations; superlattice formation including Peierls distortions, Kohn anomalies, and charge-density waves; superconduc- tivity and possible ‘two-dimensional’ superconductivity associated with a single layer or sandwich; and intercalation studies with a variety of metals and organic molecules.An extension of this work to ternary compounds such as PbzMo,SZ has recently been made. These solids are related to the transition-metal chalco- R.L. Greene, G. B. Street, and L. J. Suter, Phys. Rev. Letters, 1975, 34, 577. (a) ‘Low-Dimensional Cooperative Phenomena’, ed. H. J. Keller, Plenum Press, New York, 1975; (b)‘One Dimensional Conductors’, ed. H. G. Schuster, Springer, Berlin, 1975. ‘See, for example, A. R. Ubbelhode, Proc. Roy. SOC., 1972, A327, 289, and references therein; J. E. Fischer, T. E. Thompson, and F. L. Vogel, Phys. Rev. Letters, 1976, in press; M. E. Vol’pin, et al., J. Amer. Chem. SOC.,1975,97, 3366; E. L. Evans and J. M. Thomas, J. Solid State Chem., 1975, 14, 99. See, for example, M. R. Tubbs, Phys. Stat. Solidi (B), 1972, 49, 11; 1975, 67, 11; G. Harbeke and E. Tosatti, R.C.A. Rev., 1975, 36,40. See, for example, E. Mooser, I. Ch. Schliiter, and M.Schluter, J. Phys. and Chem. Solids, 1974,35, 1269. loJ. A. Wilson and A. D. Yoffe, Adv. Phys., 1969,18, 193; A. D. Yoffe, in ‘Festkorper Prob-leme’, ed. H. Queisser, Pergamon, Oxford, Vol. 13, p. 1 ; Ann. Rev. Muter. Sci., 1973, 3, 147; ‘Proceedings of the 12th International Conference on the Physics of Semiconduc-tors’, ed. M. H. Pilkuhn, Teubner, Stuttgart, 1974, p. 61 1. There will also be a book series called ‘Physics and Chemistry of Materials with Layered Structures’, managing editor E. Mooser, Reidel Publishing Co., to appear shortly, and a review by J. A. Wilson to appear in Rev. Mod. Phys.; V. L. Kalikhman and Ya. S. Umanski, Soviet Phys. Uspekhi, 1973, 15, 728. Yofe genides but are not layer materials. They have relatively high superconducting transition temperatures, but more important the highest superconducting critical fields yet determined.We can in fact expect a good deal of activity in all these areas. 1 Chain Compounds :Pseudo One-dimensional Systems A variety of solids fall into this category and the reader is referred to reviews by Thomas and Underhill, Krogman and Day.6 In addition, the A15 or p-tungsten-type solids11 such as NbsSn, V3Si, and NbsGe, which are high-tempera- ture superconductors having transition temperatures of 18, 17, and 23 K, respectively, may also be considered in this category, since the structure shows three interpenetrating orthogonal arrays of parallel chains of metal atoms. In this review we concentrate mainly on the conducting solids which are built up from metal-like strands or chains separated by relatively large distances, and there can be extreme anisotropy in many of the transport properties parallel and perpendicular to the chains.For some materials the anisotropy can reach values of the order of 104-105 at room temperature. Table 1 lists the electrical conductivity of some selected materials.12 It is apparent from the values for the room-temperature conductivity that these materials are good conductors. Further, if the effective conductivity per strand is considered, then the values are similar to those for typical metals such as copper (a N 106 Q-I cm-l). Simple structures for TTF-TCNQ, KCP(Br), and (SN)s are shown in Figures 1-4. In TTF-TCNQ negative charge is transferred from the TTF molecule to the TCNQ molecule.The planar TCNQ- ions are stacked face to face as linear chains and in Figure 1 the chains would emerge out of the paper. The TCNQ- chains are separated by similar chains of TTF+ cations. The highest electrical conductivity is along the chain direction, i.e. along the b-axis. Recent work suggests that the charge transfer is not complete and values quoted lie in the range 0.5-0.8 electrons per TTF molecule.13 The sketches in Figures 1-4 are idealized drawings and in the real structures there are subtle deviations which can influence the physical properties. Thus in KCP(Br) the successive atoms are not in equivalent positions and the CN groups are not planar. For (SN)2 polymer two models of the structure are at present available.14 The helical chain structure proposed by Boudeulle is given in Figure 3 but this differs in many respects from that of the Pennsylvania group, and further work, probably involving neutron diffraction or soft X-ray absorption, is needed to resolve this point.A. Conductivity Measurements.-The electrical conductivity along the chain direction in crystals of TTF-TCNQ increases markedly on cooling, and some results are given in Figure 5. For a very few crystals the effect was more spec- l1 See, for example, J. Ranninger, J. Phys. (F).1975, 5, 1083, and references therein. l2 See, for example, J. S. Miller, J. Amer. Chem. Soc., 1974, 96, 7131, and references therein. l3 P. Coppens, Phys. Rev.Letters, 1975, 35, 98.l4 M. Boudeulle, 1974, PhD. Thesis, Lyon; M. Boudeulle and P. Michel, Acta Crpf.,1972. A28, S199; A. G. MacDiarmid, C. M. Mikulski, P. J. Russo, M. S. Saran, A. F. Garito, and A. J. Heeger, Bull. Amer. Phys. SOC.,1975, 20, 360; J.C.S. Chem. Comm., 1975,476. wl P Table 1 Some represeiitative ‘metal-like’ chain solids Compound Colour Metal-metal Efective radius Room Calculateda separation along of metal atom temperature conductivity, chain/A in chainlA conductivity, o*/n-1 cm-1 o/n-1 cm-1 Organic charge-transfer complexes TTF-TCNQ black 103 2 x 103 HMTSF-TCNQ 2 x 103 N(TTF)da 4 x 102 Planar complex systems KzPt(CN)4Bro.s, 3H20 polished copper N 2.89 1.31 3 x 102 5.5 x 103 Ir parent compounds 9 KzPt (CN)4,3 H2O -3.5 1.31 5 x 10-7 10-5 9 Pt -2.77 1.39 9.4 x 104 9.4 x 104 Sulphur-nitrogen polymer (SN)% polymer brass -1.05 1.7 x 103 Hgz.sshFa Alchemists’ gold 2.84 1.5 8 x 103 Ni0.25Pt304 -2.80 1.31 3 x 103 1.8 x 104 h(co)2.93c11.07 -2.85 1.33 0.2 1.87 au* calculated for a single strand.Yofe L I I I $ C cc NN TTF TC NQ Figure 1 Simplified sketch of TTF and TCNQ molecules arranged according to theposition of their ions in the crystal laitice. The planar TCNQ-ions are stacked face to face in linear chains (emerging out of plane of the paper along the c-axis) separated by similar chains ofTTF-ions tacular and the conductivity above 60 K seemed to approach values of the order of 106 0-1cm-1, comparable with copper at room temperature.This result caused quite a stir in the scientific community. Below 60 K, however, the conductivity decreases and the solid behaves as a semiconductor. We shall return to this point later. In the case of KCP(Br) there is a change in the slope of the conductivity curve at 120 K. The sulphur-nitrogen polymer on the other hand remains metallic below liquid helium temperatures and becomes super- conducting at 0.33 K. This material is the first linear or polymeric system to be shown to be a superconductor, and it is certain that this result will have important consequences. The superconducting transition temperature does increase with pressure and has nearly doubled (0.54 K) in value by cu. 9 kbar.15 B. Optical Properties.-Further evidence for metallic behaviour along the chains comes from experiments on optical reflectivity and from n.m.r.spectroscopy, including measurements of Knight shifts, magnetic susceptibilities, and specific l5 W. D. Gill, R. L. Greene, G. B. Street, and W. A. Little, Phys. Rev. Letters, 1975,35, 1732. Electronic Properties of Some Chain and Layer Compounds NC CN Figure 2 Idealized sketches of a Pt(CN)42-group, and of the stacking of Pt(CN),2-groups in a KCP(Br) crystal, showing the overlap of the d,r atomic orbitals based 011 the Pt atoms. The CN groups are staggered to reduce Coulomb repulsion heats. Figure 6 gives reflectivity spectra using polarized light.16 In all cases when the electric vector of the incident light is parallel to the chain direction, we find typical metallic (free carrier) reflection which can be described by the Drude theory, and from these results it is possible to obtain the dielectric constant, the electron relaxation time, and the plasma frequency. Perpendicular to the chains the solids behave as transparent dielectrics or semiconductors.C. Peierls Distortions.-We have to ask why the conductivity of TTF-TCNQ, and less obviously KCP(Br), decreases at low temperatures (Figure 5), since the reverse is expected for metaIs. Many ideas have been put forward but the simplest is that we are concerned with a Peierls distortion of the lattice. The original idea of Peierls was simply that a one-dimensional solid with, for example, l6 For TTF-TCNQ see A.A. Bright, A. F. Garito, and A. J. Heeger, Solid State Comm., 1973, 13, 943; for KCP(Br) see H. R. Zeller, ref. 6(u), p. 215; for (SN), see P. M. Grant, R. L. Greene, and G. B. Street, Phys. Rev. Letters, 1975, 35, 1743. Yofe 0 0 Figure 3 The structure of (SN)%showing parallel arrangement of the helical polymer strands (after Boudeulle14) Figure 4 Representations of the two structures at present available for (SN), showingbond lengths and bond angles [(a) after Boudeulle,14 (b) after MacDiarmid et a1.14] Electronic Properties of'Some Chain and Layer Compounds I 0 100 200 T,K I 100 2 00 T/K Figure 5 Temperature dependence of the electrical conductivity for single crystals, normali- zed to room temperature (RT).(Left) TTF-TCNQ, after Heeger and co-workers;g and KCP(Br) after ZelIer and co- workers. The change from metallic to semiconducting behaviour around the maximum on the curve is clearly seen for TTF-TCNQ. (Right)(SN)%.This curve is for one of the better crystals, where ORT = 1730 0-l cm-l. The crystal is metallic at all temperatures; (after V. V. Walatka, M. M. Labes, and J. H. Perlstein, Phys. Rev. Letters, 1973, 31, 1139. See also G. B. Street, H. Arnal, W. D. Gill, I?. M. Grant, and R.L. Greene, Mater. Res. Bull., 1975, 10, 877) a half-filled energy band (i.e.a metal) would spontaneously undergo a transition to an insulator. The 'one-dimensional' solids are particularly prone to this kind of distortion. For a linear chain of equally spaced 'one-electron' atoms (e.g.H, Na, etc.) separated by a distance L?, the simple energy band structure is as shown in Figure 7(a). We have a half-filled band and metallic behaviour. It is energetically favourable for the lattice to distort, for example in the manner shown in Figure 7(b), SO that the unit cell doubles. This is equivalent to halving the Brillouin zone, and an energy gap is opened at the edge of the new zone for wave number k = krn/2ain the manner discussed in elementary texts on solid- state physics and chemistry. All the occupied electron states are then in the lower energy band, while the upper band of higher energy contains only empty states. In this way there is a lowering of the kinetic energy of the electrons, but this must be set against an increase in elastic energy due to the structural dis- tortion.It turns out that the balancing favours the opening up of a gap for quasi one-dimensional metallic systems and is ProbabIy still favourable for two- dimensional (layer-type) metals, but not for three-dimensional (normal) metals. In the discussion above the distortion leads to formation of a superlattice. Yofe 0---\ (W, ----(KCP)Br\ €11 *.* ** TTF-TCNQI I I Photon energy Figure 6 Reflectivity spectra from single crystals of TTF-TCNQ, KCPPr), and (SN)s,using polarized light.le When the electric vector of the incident light is parallel to the chains in the crystal (Ell) we see typical metallic free carrier reflection and interband transition regimes.For the other plane of polarization (El), the free carrier region is absent in this range of photon energies When an energy gap opens up at the zone boundary, we have a small band gap semiconductor and a metal-semiconductor transition. The Peierls theorem suggests then that at the absolute zero a truly one-dimensional system will not be metallic. In Figure 7(c), which is another way of illustrating the Peierls distortion, we can see that the Brillouin zone boundary of the distorted insulating phase coincides with the wave vector k~ at the Fermi level of the undistorted metallic structure. In other words the new period in reciprocal space is now 2kF along the chain direction. The new superlattice period is now 27r/2k~.This is also the wave vector where the Kohn type of anomaly17 inbolving soft phonon (vibrational) modes is expected.* In a sense the Kohn anomaly is a precursor of the Peierls distortion, since the phonons of wave vector 2k~become increas- ingly soft as the temperature is lowered, until the static distortion or superlattice prevails.The experimental approach then is to look for a decrease or softening in the phonon frequency on cooling to temperatures where the Peierls distortion or metal-semiconductor transformation takes place. Many experiments on *The ‘Kohn anomaly’ may be described theoretically as a singularity in the dielectric screening function and is observed experimentally as a softening (frequency w -+ 0) of certain phonon modes q in a metal whose Fermi surface is just spanned by the wave vector y.See for exampleH. Rietschel, Solid State Comm., 1973, 13, 1859. 17 See, for example, treatment by J. M. Ziman. in ‘PrincipIes of the Theory of Solids’, 1965, Cambridge University Press, p. 129; also ref. 6(6). Electronic Properties of Sonze Chain and Layer Conlpouiicls H---2n/2k, __+i #-4+:+--, 5 *+-+;+ P-0-i ( b) Figure 7 Energy (E) wave vector (k) diagrams for u lineur chain of one-electron atoms separated by a distance ‘a’. Figure 7(a) is for an undistorted chain resitlting in a half-filled band, and the Fermi energy EFis marked. When the lattice is distorted as shown in Figure 7(b) from the old, 0,to the new $ ,positions, the unit cell now has a periodicity 2‘a’ and a ‘Peierls’ gap opens up at fkF, resulting in a small band gap semiconductor, Figure 4(c).The electron energy band for occupied states has been drawn as a thick line in both Figure 7(a) and Figure 7(c) diffuse X-ray scattering and inelastic neutron scattering have shown that this does occur with KCP(Br), and that this material does go through a Peierls transition. On the other hand the evidence in the case of TTF-TCNQ is not conclusive. Since KCP(Br) appears to be a good example of a solid in which a structural distortion leads to a small energy gap of the order of 0.2 eV, we look a little further into the electron energy scheme for this solid. This treatment is very qualitative, and in Figure 8 the energy bands are set out.l8 The general ordering of the energy bands is surprisingly simple.In the simple [Pt(CN)#+ system the crystal-field splitting of the d bands is such that the upper valence band is a full d band formed by the overlap of essentiallydzz orbitals on the Pt atoms (d2con-figuration) along the chain direction, and this has been confirmed by e.p.r. measurements. The conduction band, which is empty, is thought to come from the overlap of metal pz orbitals. The introduction of Br atoms to give KCP(Br), la M. J. Minot and J. H. Perlstein, Phys. Rev. Letters, 1971, 26, 371. Figure 8 Simplified sketch of energy bands near the Fermi level EFfor KCP(Br). The relevant metal (Pt) atomic orbitals forming the bands are shown on the left. The Br-energy lies below the dza band.As a result of the removal of electrons the dta band is roughlv 516 full, giving a ‘hole’ type metal with one Br atom for every three Pt atoms, results in the removal of electrons from the ‘&z’ band so that it is now only 5/6 full (assuming 1.7 electrons per Pt atom). Since the band is now only partly filled, the solid is now a metal. The Fermi wave vector kF now is kF = 0.85 T/C, and the Peierls theorem suggests that an energy gap should open up at this wave vector and a superlattice should be formed. Experiments have shown that the energy gap 2d fr: 0.2 eV and that the lattice distortion has a periodicity of 6-7 Pt atoms as predicted. The band scheme outlined in Figure 8 is very diagrammatic and elementary and there have been attempts to map out reliable band structures for KCP(Br).lg There are, however, problems associated with the structure of KCP(Br) and it would appear that this is not as simple as was originally supposed.The treatment of the results associated with the Peierls distortion has also been simplified. There are in fact a number of associated phenomena connected with the regime where the semiconductor-metal transformation takes place, and where the transport properties as a function of temperature are anomalous. These phenomena include Kohn anomalies, charge-density waves of the kind postulated by Overhauser in 196g20 involving dynamic lattice distortions which are connected with a divergence in the static dielectric functions of the electronic system at some wave vector, and Frohlich-type superconductivity21 where because of strong electron-phonon interaction an ideal one-dimensional system can become superconducting in the Peierls distorted condition.In this situation superconductivity is thought to be due to travelling lattice waves (electrons + phonons) rather than electron pairs as in the normal Bardeen-Cooper-Schriefer (BCS) theory. These topics, however, would require lengthy treatment and this is not possible in this review. Another factor which is important is the presence l9 D. M. Whitmore, Phys. Letters (A), 1974, 50, 55; L. Fritsche and M. Rafat-Mehr, ref. 6(b), p. 97; K. P. Messmer and D. R. Salahub, Phys. Rev. Letters, 1975, 35, 533. aoA.W. Overhauser, Phys. Rev., 1968, 167, 691; Phys.Rev. (B), 1971, 3, 3173. alH. Frohlich, Proc. Roy. SOC.,1954, A223, 296; C. Mavroyannis, J. Low Temp. Phys., 1975, 20, 285. Electronic Properties of Some Chain and Layer Compounds of defects, for example interrupted strands in the crystal, which can introduce the problem of disorder into the system. There is fairly good evidence for a Peierls-type distortion in KCP(Br). The situation for TTF-TCNQ is somewhat confused, and there is no clear evidence from structural work for such a distortion. It has been argued that a two-chain model is appropriate for this material. There are two separate potentially conducting chains and it is thought that above 60 K the TTF+ chains are metallic but the TCNQ- chains remain insulating in some kind of Peierls state.Below 60 K where the transition from a metal to a semiconductor takes place there is strong interchain coupling and as a result of this interaction the solid will behave more as a three-dimensional system with a small energy gap develop- ing. These conclusions are, however, speculative and reliable band structures are required. Some progress has been made in this direction.22 The electron energy bands which arise from the overlap of n-electron wavefunctions of nearest neighbours in the stacks of anion and cation radicals give a conduction band which can be thought of as a n-electron-type system with a bandwidth of 0.5 eV. One interesting development in the synthesis of organic charge-transfer complexes has been the preparation of HMTSF-TCNQ (see Table 1; HMTSF = hexamethylene-1,4,5,8-tetraselenafulvalene)by Bloch et al.23This solid re- mains metallic even below 1 K, although superconductivity has not yet been found.It shows, however, that it is possible to synthesize organic solids which are pseudo one-dimensional but which resist Peierls-type distortions. The possibility remains that an organic solid will be synthesized which is a superconductor in the spirit of the Little theory. D. Band Structure of (SN)2Polymer.-It is fortunate that (SNzpolymer crystals are metals even at low temperatures and do become superconducting at ca. 0.3 K. On the application of hydrostatic pressure in the region of 9 kbar the transition temperature is doubled. There have been speculations as to why this material does not undergo a Peierls distortion.No less than six band structures are now a~ailable.~4 Broadly speaking these can be classified into two groups. One of these considers a single chain of the (SN)% polymer as a metal. From the helical structure and stacking of the SN groups in the unit cell it is shown that two overlapping bands cross the Fermi level. Perturbation theory can then be used to derive a three-dimensional band structure, since the chains are thought to be weakly coupled in the sense that they are linked by van der Waals’ forces. Observation of crystals of (SN)s in a high-resolution scanning electron micro- zz I. P. Batra, B. I. Bennett, and F. Herman, Phys. Rev. (B), 1975, 11,4927; G. Stollhoff, ref.6(b),p. 257. zs A. N. Bloch, D. 0. Cowan, K. Bechgaard, R. E. Pyle, R. H. Banks, and T. 0. Poehler, Phys. Rev. Letters, 1975, 34, 1561. a4 (a) D. M. Parry and 5. M. Thomas, J. Phys. (C), 1975, 8, L45; (b) W. I. Friesen, A. J. Berlinsky, B. Bergerson, L. Weiler, and T. M. Rice, J. Phys. (C), 1975, 8, 3549; (c) V. T. Rajadand L. M. Falicov, Phys. Rev. (B), 1975,12,1240; (d)H. Kamimura, A. M. Glazer, A. J. Grant, Y. Natsume, M. Schreiber, and A. D. Yoffe, J. Phys. (C), 1976, 9, 291; (e) M. Schluter, J. R. Chelikowsky, and M. L. Cohen, Phys. Rev. Letters, 1975, 35, 869; W. E. Rudge and P. M. Grant, Phys. Rev. Letters, 1975,35, 1799. Yofe scope clearly shows the fibre-like character of the crystals and the fibres are readily separated. The dispersion of the energy levels in a direction perpendicular to the chains is therefore small.One such band structure and a sketch of one of the Fermi surfaces are shown in Figure 9. In the one-dimensional model there are two kalues for the Fermi wave vector kF which are not a simple fraction of r/b,although kpl + kp2 = r/band it is suggested that this is a possible reason for the absence of a Perierls distortion. There are of course other possible explanations. This band structure is consistent with the pronounced aniso- tropy in the electrical, optical, and mechnical properties. In the second approach the proposed band structure for a single chain shows a degeneracy at the edge of the Brillouin zone in the manner well known for graphite, and the solid should be a semi-metal.However, for a single chain the system would undergo a Peierls distortion which would lift this degeneracy to form a semiconductor. It is argued that this does not happen because of the strong three-dimensional character of the solid. Essentially the difference between the two models is the degree of s-p mixing. Small s-p mixing gives two over- lapping conduction bands. Strong s-p mixing results in the complete separation of the two bands giving the single conduction band of the second model. Only time will tell which of these two approaches is correct. E. Conclusion.-The most important development in the work on metallic chain-like solids has been the synthesis of materials which do not undergo Peierls distortions at low temperatures.These include the organic charge- transfer solids such as HMTSF-TCNQ and the inorganic polymer (SN)s, which is a superconductor. There are other possibilities including the use of odd alternant hydro~arbons,~5 and the synthesis of new organic and inorganic polymers. For example, it should be possible to replace sulphur and nitrogen by different atoms in (Swzpolymer. The electrical conductivity of (SN)2 can also be modified by the addition of electron donors and acceptors to give intercalates.26 It is already known that acceptors such as the halogens (Cla, Br2, 12) increase the electrical conductivity in a temporary fashion. What is clear is that a good deal of interesting and important physics and chemistry is coming out of this work, and many challenging problems remain to be solved.Some of these are concerned with the anisotropy of the crystals, with the mechanism of electron conduction and superconductivity along and normal to the chains, and with the metal-non-metal transformation often seen at low temperatures. 2 Layer Compounds:Pseudo Two-dimensional Systems It is impossible in a review of this length to discuss all layer-type solids, and in this section we will concentrate on the transition-metal dichalcogenides having the general formula MX2. However, many of the phenomena to be discussed are common to the other layer materials as well. We also restrict the discussion to compounds formed from the metals M belonging to the Groups IV, V, and 'ti R.C.Haddon, Nature, 1975, 256, 394. 28 F. Levy, 1975, unpublished results, Cambridge. 63 3 hk6I I I I I I f2-25h1 r k Figure 9 (Above left) The Brillouin zone of (SN)zpolymer corresponding to the primitive monoclinic Bravais lattice. (Right) The calculated energy band scheme for a single chain of SN polymer, showing the two Fermi wave vectors kF1 and kFz for the two conduction bands. This model predicts metallic behaviour for a single chain at all temperatures.(Below left) A possible three-dimensional Fermi surface for the upper conduction band of for a three-dimensional band structure. The shape is biconcave. This model assumes weak interaction between chains in the three-dimensional band structure calculations Yofe VI elements Ti, Zr, Hf; (V) Nb, Ta; (Cr) Mo, W; and with X =S,Se, or Te.Typical materials would then be ZrS2, NbSe2, and MoS2. The dichalcogenides formed from other transition metals often form distorted structures within the layers and their properties can be more complicated. It turns out that the most interesting features of these materials are associated with the ‘d’ bands, and to determine the electron energy levels it is necessary to make measurements on the various optical and electrical properties. A material such as MoS2 with a layer structure can be cleaved to give very thin crystals and it is relatively easy to obtain crystals severalhundred kqptroms thick over quite large areas. Frindt has in fact made measurements on crystals a unit cell thick which is of the order of 12A and this correspondsto two layers.27 Cleavage of the crystals along the layers takes place between sheets of sulphur atoms which are held together only by weak van der Waals’ forces, and the structure for MoS2 is based on the trigonal-prism configuration as shown in Figure 10.The other configuration frequently met is octahedral, for example with the Group IV compounds ZrSz and HfS2 and with some members of the Group V compounds such as 1T-TaS2. @.. .., . ... . .. ..... .. Figure 10 Stacking arrangement for ~H-MOS,,2H-NbS2,and CdI, (equivalent to ZrS,and 17’-TaS,) layer poIytypes A. Optical Properties and Band Structure.-The apparatus used to measure optical absorption in transmission is fairly straightforward. It is also possible to work in reflection, and the various polarization dependences are shown in Figure 11.The kind of optical absorption spectrum obtained for MoSz at helium temperatures in the visible and ultraviolet when the electric vector of the incident light is parallel to the layers (E I_ c) is shown in Figure 12. There is a good deal of structure here and this is used to build up a model of the electron energy levels. Peaks A and B are ground-state exciton peaks, and on careful examination of the spectra it is possible to see the higher-order excitons as well.* *Excitons in solids are excited states which result from the Coulomb interaction between electrons and holes, analogous to a hydrogen atom.The excitation can be produced by the absorption in the solid of a photon of appropriateenergy, usually just less than the band gap.R. F. Frindt, J. Appl. Phys., 1966, 37,1928. Electronic Properties of Some Chain and Layer Compounds C Figure 11 Schematic diagram showing the three possible configurations of polarizationand incident directions for normal incident reflectivity of light 7.0 a C -I D Ix 16%m-’ 1 G .O 5.0 *\4.0 3.0 B I 2 .o 1 .o 0 2.0 2.5 3.0 3.5 4.0 t?V Figure 12 Transmission spectrum of 2H-MoSa at 4 K showing the strong exciton peaks A andB Yofe These are seen more clearly in modulation experiments. The excitons are delocalized or Mott-Wannier-type excitons with a binding energy for the ground state of the order of 0.05eV.The effective Bohr radius of the ground-state exciton (n = 1) is of the order of 30 A, while for n = 2 it is in the region of 120 A. This is quite large and can become comparable with the thickness of some of the crystals used, and as will be shown later this can have some interesting effects. There is now detailed information available from a wide variety of optical and electrical measurements. These include the use of synchrotron radiation, photo- emission (both U.V. and X-ray photoelectron spectroscopy and angular-depen- dent photoelectron spectroscopy), and electron energy loss measurements. Using these results it is possible to propose an electron energy band scheme for the Group IV, V, and VI compounds and this is shown in Figure 13.dx2-y? xy dxz,y.? B=-=. ( 4 P -ME) ZrS2 NbS2 MoS2 c v Octahedral Trigonal prism Figure 13 Suggested schemes for the electron energy (E) versus density of states N(E),for the Group VI (MoS,), Group V(NbS,), and Group IV (ZrS,) transition-metal dichalco- genides. The atomic orbitals involved in the bands are listed, and the number of electron states per band is given. Undistorted 1T-TaS, would have a scheme similar to ZrS, but with the dza band halfflled, but the presence of superlattices causes minor changes to the energy bands and the Fermi surface For the Group VI compounds we have a full dz2 band formed by the overlap of essentially dz2 orbitals based on the Mo atoms within the layers, and we obtain a semiconductor with a band gap of the order of 1 eV.Moving down to the Group V compounds with a dl configuration on the metal atom, the dza band is now half filled, giving a metal and a superconductor. For NbSez the transition temperature for superconductivity is 7.3 K. There are similarities Electronic Properties of Some Chain and hyer Compounds between these systems and the chain compound KCP(Br) since in both the conduction band is based on the dzz orbitals. For the Group IV compounds with a do configuration on the metal atoms, the dzz band is now empty and we again have semiconductors or insulators with many interesting electrical proper- ties. Because the co-ordination is octahedral for the Group IV dichalcogenides the crystal-field splittings will be somewhat different from those of the Group V and VI compounds with trigonal-prism co-ordination. These model band structures are idealized representations.There will be mixing of the orbitals forming the bands, and layer-layer interactions are important. Fairly reliable band structures are now available for many of the transition-metal dichalcogenides,28 and in the case of the metals such as NbSez and TaSz the shape of the Fermi surface has been calculated (see Figure 14). Figure 14 Schematic representation of the Fermi surface of 2H-NbSe, unfolded into the double Brillouin zone. The shaded sections are electron-occupied states. A hole 'barrel shaped' Fermi surface is apparent along the centre of the zone TAT'.The narrow necking regions are also important for considering possible Kohn anomalies, Peierls distortions, and charge density wuves (after Wexler and Wooleys8) It turns out, however, that the overall ordering of the energy bands is not very different from those shown in Figure 13, and for the purposes of this review these model band structures will be sufficient. B. Excitons and Screening.-Both experimental and theoretical work has been carried out concerning the anisotropy of the excitons (orbits, dielectric constants, I*See, for example, L. F. Mattheiss, Phys. Rev. (B), 1973, 8, 3719; G. Wexler and A. M. Wooley, J. Phys. (C), 1976, in press. Yofe and effective masses) and whether the excitons should be considered as two- or three-dimensional excitations.The effect of crystal thickness on exciton energies has also been considered. Using a particle-in-the-box idea it can be argued that the energy of the excitons should increase as the thickness is decreased, and this dependence should go as the inverse of the square of the crystal thickness. In addition, as the crystal thickness is reduced, scattering of the excitons at the surface should result in the disappearance of the higher-order excitons. Both these effects have been observed. Figure 15 shows results obtained by Frindt THKNJESS /i 52 39 19.5 13 11 I I --4-----I--L,eo--I I 1 I I I 0 20 40 60 1t2-x 10-'2/cm-2 Figure 15 Variation in the energy of the ground-state exciton with crystal thickness (t) for WSe, (after Consadori and Frindt2g) for WSZwhere the relation is linear down to a thickness in the region of 40 A.Below this there is an unsurprising departure from a straight line.29 It is also possible to observe and follow experimentally the screening of excitons by free carriers. If a semiconductor such as WSz which has sharp exciton features at low temperatures similar to those shown in Figure 12contains impurity atoms of Nb or Nay then free carriers (holes or electrons) are present and these screen out the electron-hole interactions which normally give rise to excitons. This is an example of Thomas-Fermi screening. As a result the excitons are no longer stable and the sharp features in the spectra disappear.This phenomenon is associated with the metal-insulator transition. F. Consadori and R. F. Frindt, Phys. Rev. (B), 1970,2,4893. Electronic Properties of Some Chain and Layer Compounds C. Metal-Non-metal Transformation in 1T-TaSz.-A Group V metal dichalco- genide such as TaSz is a metal and a superconductor when the structure is based on the trigonal-prism configuration (see Figure 10). It is also possible to prepare crystals of TaSz with the octahedral co-ordination, lT-TaSz, and in the undistorted structure this compound should also be a metal, having a half-filled ‘d’ band. The electrical measurements on 1 T-TaS2, however, show very unusual behaviour when the temperature3O or pressure is varied. A resistance-temperature plot is shown in Figure 16.Above 350 K (region 1T1)we have the Figure 16 Resistivity versus temperature plot for 1T-TaS2, showing the three regimes, 1TI, 1 T,, and 1 Ts (after Tidman and Frindt30) lowest resistivity (apparent metallic behaviour) with a discontinuous 50% increase at 350 K to the 1T2 region. Here the resistivity-temperature slope resembles that for a semiconductor, but the magnitude of the conductivity corresponds to a semi-metal or a poor metal. On further cooling to 190 K another discontinuity (with. hysteresis) to the semiconducting 1T3 form can be seen. Careful electron diffraction (Figure 17),31 X-ray diffraction, and neutron diffraction measurements32 on this material as a function of temperature have led to a possible interpretation of these results in terms of charge-density waves.30 A. H. Thompson, F. R. Gamble, and J. F. Revelli, Solid State COM~.,1971, 9, 981 ;J. P. Tidman and R. F. Frindt, 1975, to be published. 31 J. A. Wilson, F. J. Di Salvo, and S. Mahajan, Adv. Phys., 1975, 24, 117; P. M. Williams, G. S. Parry, and C. B. Scruby, Phil. Mag., 1974, 29, 695; 1975, 31, 255. 32 See analogous experiments by D. E. Moncton, J. D. Axe, and F. J. Di Salvo, Phys. Rev. Letters, 1975, 34, 734, and unpublished work. 140K 295K 400K 1 T3 1T2 1Jt 1 T-TaS, Figure 17 Transmission electron difraction patterns for the three diferent temperature regimes shown in Figure 16. The pattern in the 1T2 regime corresponds to an incommensurate charge-density wave, but on passing to the 1T3 regime there is a first-order transition and the period changes to being commensurate with the lattice (after Williams, Parry, and %ruby3') 3 2 3 Electronic Properties of Some Chain and Layer Compounds This concept was developed in 1968 by Overhauser and we have already referred to it in the section on chain materials. A charge-density wave can be a lower energy state and is a sinusoidal variation in the electron density with a certain wave vector.This can result in a Coulomb attraction between the regions of electron concentration built up by the charge-density wave and the ions in the lattice, and a periodic structural distortion of the lattice is formed which has the same wave vector as the charge-density wave.This is a kind of superlattice. The periodicity of the charge-density wave, however, can be shown to be determined by the shape of the Fermi surface of the metal, and there does not need to be a simple relation between the distortion and the periodicity of the underlying lattice. It can be incommensurate with the lattice. Referring to Figure 6, for 1T-TaS2 in the 1T1 phase the distortions are not seen at all and we have the most metallic-like state. As the crystal is cooled to the 1T2 phase, the incommensurate distortions appear, while in the 1 T3 phase, the superlattice wave vector has become a commensurate multiple* of the reciprocal lattice vector, and the crystal then forms a commensurate superlattice. When a com- mensurate superlattice is formed small energy gaps open up in certain regions of the Fermi surface and these no longer contribute to metallic conductivity.In this way it is possible to interpret the curves shown in Figure 16 in terms of a de-crease in the extent of the Fermi surface. This behaviour is not unlike that discussed under Peierls distortions in ‘one-dimensional’ systems where we considered metal-insulator transitions. Peierls distortions were originally used only in discussions of one-dimensional systems, and for commensurate superlattices. The arguments used were based on energetic grounds in terms of a lowering of the electron kinetic energy versus expenditure of strain energy. The other approach of Overhauser based on charge-density waves comes from electronic considerations in which a many-body formalism is devel- oped.The periodic lattice distortion follows formation of the charge-den- sity waves, but it is also necessary to have strong electron-phonon coupling. The theory can predict the nature of the superlattice whether incommensurate or commensurate, once the detailed shape of the Fermi surface for the un- distorted lattice is known, and to some is the more satisfying approach. There is thus a strong inter-relation between charge-density waves (and spin-density waves), soft phonon modes, Kohn anomalies, and Peierls distortions. These experiments have provided the strongest direct evidence of charge- density waves, and they have led to considerable interest in their possible role in other phenomena, for example in superconductivity.D. Transport and SuperconductingProperties.-2H-NbSez is a metal and a type 2 superconductor with a transition temperature 7‘’ in the region of 7.3 K. Many *The superlattice wave vectors for a commensurate superlattice in the case of the ‘one- dimensional’ solids are integral multiples of the reciprocal lattice vectors, for example a two-times superlattice. For ‘two-dimensional’ systems the situation is different. For 1T-TaS, at low temperatures the commensurate superlattice is Ejl3 by Jl3 times the reciprocal lattice vector. For 2H-NbSe, it is nearly 3 x 3. The reason for this is that in the layer-type solids the superlattice wave vector may be in a different direction than the reciprocal lattice vector. Yofe experiments have been made to determine the effect of magnetic fields on Tc with the field perpendicular and parallel to the layers, and on the superconducting energy gaps by i.r.and tunnelling measurements. In the early work on 2H- NbSez, 2H-TaSz, and 2H-TaSe2, the resistivity, magnetic susceptibility, and Hall constant behaved in an unusual ways3 as the crystal was cooled to temperatures approaching T.(Figure 18). For example, on cooling, the Hall constant changed Figure 18Idealized sketch of results ana!ogous to those obtained by Lee et aP3for the Hall coeficient RE, the resistivity p, and magnetic susceptibility x, for crystals of 2H-TaS,.Anomalous behaviour takes place at temperatures below that shown by the dotted line.Tc is the superconducting transition temperature. Tois the onset temperature for the charge- density wave sign from positive (hole conduction) to negative (electron conduction) and the conductivity deviated from linear behaviour. More recently it has been shown that in 2H-NbSez there are anomalies in the heat capacity34 at the same tempera- ture as the start of the Hall reversal and the departures from linear behaviour in resistivity with temperature, around 32 K. Again careful electron diffraction and neutron diffraction measurements show the formation of superlattice distortions for Nbse~.~~ The superlattice is approximately 3 x 3 but is not quite commensurate with the lattice. A number of suggestions have been made to explain these results.One argument is that the anomalies in the transport and heat capacity measurements result from the stabilization of an incommensurate charge-density wave at around 35 K. When the charge-density wave is formed, however, it has only a minor effect on the shape of the Fermi surface and for this reason the anomalies in the electrical conductivity are of a minor character. The 83 See H. W. S. Lee,M. Garcia, H. McKinzie, and A. Wold, J. Solid State Chem., 1970, 1, 190. *‘J. M. E. Harper, T. H. Gaballe, and F. J. Di Salvo, Phys. Letters, 1975, 54A,27. aa P. M. Williams, C. B. Scruby, and G. Tatlock, Solid Stute Comm.,1975, 17,1197; also the chapter by P. M. Williams on charge-density waves in the series edited by E. Mooser (see ref. 10).Electronic Properties of Some Chain and Layer Compounds other argument is based simply on lattice contraction and the effect on the details of the ‘d’ band formation. There are similarities in the fluctuations seen in the transport properties of 2H-NbSez and 2H-TaSez and many of the chain-like solids already discussed. Charge-density waves have also been shown to have an important bearing on the superconducting properties of NbSes and NbS2. In particular the magnitude of the pressure dependence of the superconducting transition temperature appears to be directly related to presence of a ~uperlattice.~~ In NbSe2, where a superlattice has been observed, the superconducting transition temperature increases with pressure from 7.3 to 9 K at ca.30 kbar. It is thought that at this pressure the superlattics is no longer stable and the lattice reverts to the undistorted structure. At higher pressures the transition temperature does not vary appreciably with increase in pressure. Two important factors which can influence the super- conducting transition temperature are the density of electron states at the Fermi level and the electron-phonon interaction. These pressure experiments suggest that the density of states is more important. The charge-density wave and the coupled superlattice will result in a reduction in the density of states at the Fermi level, in a manner analogous to that discussed for Peierls distortions. As the superlattice is eliminated by the application of pressure the density of states at the Fermi level will increase, resulting in an increase in Tc.These are speculations, however, and there is a need for experimental support for these ideas.E. Intercalation with Organic and Inorganic Atoms and Molecules.-It has been known for some time that it is possible to introduce organic and inorganic molecules and atoms between the layers in a variety of layer-type solids. This is the process of intercalation. Perhaps the best documented are graphite37 and the clays,38 and more recently new materials have been synthesized by reac- tion of the constituent compounds following intercalation between the la~ers.3~ In the case of the transition-metal dichalcogenides, a number of research groups have been active in this field.40 Essentially three different types of impurity have been studied in some detail.They can all be classified as electron donors, since there is no clear evidence that impurities which act as electron acceptors can be introduced in the van der Waals gap. ae P. Molinie, D. Jerome, and A. J. Grant, Phil. Mag., 1974, 30, 1091; also J. Friedel, J. de Phys., 1975, 36, L279 37 See, for example. W. Rudorff and E. Schulze, Z. anorg. Chem., 1954, 277, 156; and also ref. 7. 38 See, for example, R. E. Grimm, ‘Clay Mineralogy’, McGraw Hill, New York, 2nd edition, 1968; D. T. B. Tennakoon, J. M. Thomas, M. J. Tricker, and J. 0.Williams,J.C.S. Dalton, 1974, 20, 2207, 2211. 39 See review by J. M. Thomas, Phil. Trans. Roy. SOC.,1974, 277, 751.40See, for example, F. R. Gamble and T. H. Geballe, ‘Solid State Chemistry Series’, ed. N. B. Hannay, Plenum Press, New York, Vol. 3; R. Schollhorn and A. Lerf, J. Less Conrmon Metals, 1975, 42, 89; J. V. Acrivos, J. Phys. Chem., 1974, 78, 2399; G. V. Subba- Rao, M. W. Shafer, and J. C. Tsang, J. Phys. Chem., 1975, 79, 553, 557; J. Cousseau, L. Trichet, and J. Rouxel, Bull. SOC.chim. France, 1973, 872. Yofe (i) Organic molecules such as amines. These are Lewis bases (electron donors) and include aniline, pyridine, cyclopropylamine, octadecylamine, and tetrathioful- vene. Some of this work has been reviewed by Gamble and Geballe. It is a rela- tively simple matter to intercalate a solid such as TaSz with an organic amine. The solid is introduced into the hot liquid or vapour, and the crystal can swell in a dramatic and spectacular way.The separation between the layers in some circumstances can reach values in the region of 60 A, where the thickness of a single layer is only of the order of 6 A. Figure 19 shows the probable orientation of some of the molecules with respect to the MX2 layers and the position of the lone-electron pair on the nitrogen atom. There is, however, some controversy on this p0int.~0~ It is argued that some charge transfer takes place from the organic molecule to the host lattice although there is not complete agreement on this point. What is interesting is that these solids after intercalation remain superconductors, and it is tempting to argue that we are concerned here with superconductivity associated with the single layers themselves.There is some experimental support for this idea from experiments on superconductivity as a function of crystal thi~kness.~lHowever, a number of theoreticians are opposed to this view, and require that the superconductivity of the intercalated solid be truly three- dimensional. (ii) Alkali-metal andpseudo alkali-metal atoms, Atoms such as Nay K, Rb, Cs, Ca, Sr, Bay Ga, Ge, Cu, Ag, Sn, Pb, Hg (also Eu, Yb) can be introduced between the layers of solids such as MoSz or NbSez from metal-ammonia solutions or by electrolysis. Another method is to use molten alkali halides. There is an increase in the ‘c’ spacing after intercalation and for the metal-ammonia solutions some ammonia also enters with the alkali-metal atoms.Ionization K -K+ + e is more complete than for the organic molecules, and the intercalate KzMoSz becomes metallic and a superconductor, with Tcfor KoAMoS~being 6.5 K.42In the system MoS2 + xK -KzMoS2 semiconductor + metal -metal and superconductor we can follow the transformation from a semiconductor to a metal by optical43 and electrical techniques. If we begin with 2H-NbSe2, which is a metal, and intercalate with alkali-metal atoms then we find NbSe2 + xK -KzNbSe2 metal + metal 3 ‘semiconductor’ to form a semiconductor. These findings can be readily explained if we look at the model given for the electron energy IeveIs in Figure 13. Intercalation of 40u F. R. Gamble and B.G. Silbernagel, J. Chem. Phys., 1975, 53, 2544. 41 R. F. Frindt, Phys. Rev. Letters, 1972, 28, 299. 42 A. M. Hermann, R. Somoano, V. Hadek, and A. Rembaum, Solid State Comm., 1973, 13, 1065. 43 J. V. Acrivos, W. Y. Liang, J. A. Wilson, and A. D. Yoffe, J. Phys. (C). 1971, 4, 418. EIectronic Properties of Some Chain and Layer Compounds I i I I 0 I2 0 I I U u I I I w C t a .- d I I I i o=o U I I I TaS2 with hydrogen44 gives HzTaS2 and with x <0.1 Tcrises from 0.8 to 4.2 K. For the Group IV intercalate Li0.3Til.iS2, Tcis fairly high in the region of 13 K.45 Here Tcis the superconducting transition temperature. New types of complex involve the use of the metallocenes of cobalt and chromium which appear to act as pseudo alkali metal~,~6 and the orientation of the molecule between the layers is thought to be as shown in Figure 20.There S Ta S cocp2 tc Figure 20 Sketch of an intercalation complex between a transition-metal dichalcogenide (e.g. TaS,) and a metallocene (e.g. CoCp,, where Cp is cyclopentadien.yl). 46 The metallo- cene appears to act as a pseudo-alkali metal have also been many studies on the complex molybdenum-sulphur systems47 such as Pb0.5Mo3S4, Pb1.0Mo5.1S6, and SnPbMoS5. These are not layer materials, but have very interesting properties. The superconducting transition tempera- tures are in the region of 13 K, but the critical fields Hcz(0) can reach tre- mendous values in the region 500-700 kG, probably the highest yet attained.We can expect a good deal of activity on this topic. (iii) Transition-metal atoms. Intercalates formed from the 3d transition-metal atoms Ti, V, Cr, Mn, Fe, Co, and Ni have many interesting magnetic properties. It has been shown by a number of investigators that compounds such as Mnlp- NbSez or CrlpNbSez are ferromagnetic at low temperature^.^^ The Mn and Cr sit in the van der Waals gap in specific sites, e.g. octahedral in the case of CrlpNbSes. It is argued that the ferromagnetic coupling between the Cr3+ ions in the van der Waals gap is by superexchange through Cr-Se-Cr units, and by interaction with conduction electrons. F. Conclusions.-The electronic properties of layer materials and their inter- 44 D. W.Murphy, F. J. Di Salvo. G. W. Hull, J. W. Waszczak, s. F. Mayer, G. R. Stewart, S. Early, J. V. Acrivos, and I". H. Geballe. J. Chern. Phys., 1975, 62, 967. 4rH.E. Burz, A. S. Cooper, E. Corenzwit, M. Marezio, B. T. Matthias, and P. H. Schmidt, Science, 1972, 175, 884, 1465. 48 M. B. Dines, Science, 1975, 188, 1210. 47R.Odermatt, Q. Fischer, H. Jones, and G. Bongi. J. Phys. (0,1974, 7, L13;S. Foner, E. J. McNiff, E. J. Alexander, Phys. Leften, 1974, 49A, 269; B. T. Matthias, I.E.E.E. Trans., 1975, 11 (magnetism volume), 154. 48See,for example, I. M. Verhoeve and R. C. Sherwood. J. Phys. and Chem. Solids, 1971, 32, 167; J. Rouxel, A. Le Blanc, and C. A. Royer, Bull. Suc. ckim. France, 1971,2019. Electronic Properties of Some Chain and Layer Compounds calates are highly anisotropic, and in many circumstances the solid can be considered as a stack of quasi ‘two-dimensional’ layers.As we might expect, the layer materials exhibit a number of properties which lie between the ‘one-’ and ‘three-’ dimensional types of solid. To take one example, charge-density waves are most pronounced in ‘one-dimensional’ systems, weaker in ‘two- dimensional’ systems, and weakest in the ‘three-dimensional’ systems, The same is true of Kohn-type anomalies. Many important topics have of necessity been omitted from this discussion. These include phonon energies, angular-dependent photoemission experiments, the effects of pressure, and the mechanical proper- ties. Because of space limitations we have also concentrated on the transition- metal dichalcogenides.There is, howevei, a great deal of interest in the other layer materials, and in particular graphite and the graphite intercalates are being studied in many laboratories throughout the world. The intercalates formed from graphite with the so-called super-acids HF + SbF5, and possibly 2HF + HfF4, are highly conducting solids,49 with a conductivity approaching that of copper. On the practical side there are possible applications and some of these have already been mentioned. These include for example their use as catalysts, i.r. detectors, superconducting quantum interference detectors (SQUIDS) for the detection of small magnetic fields,5* computer components, and as possible switching materials.They are also of course important lubricants. Systems such as Ti& + Li are being used as model solids in the study of the ‘super ionic’ or ‘fast ionic’ conductors,51 and indeed some of the layer solids based on the transition-metal trichalcogenides coupled with alkali-metal atoms are them- selves candidates for use in high current density batteries. They are also being studied as possible electronic switching materials. The related alloy systems such as lead-molybdenum-sulphur have important magnetic properties in the super- conducting state. Solids such as PbIz have potential applications as holographic materials.52 Many fundamental problems remain to be solved, and other systems such as the antistructures Hf2S and AgzF need to be examined. These studies will require experimental and theoretical work of considerable skill and ingenuity.49 J. M. La Lancette and J. La Fontaine, J.C.S. Chem. Comm., 1973, 815; S. Loughin, C. Y. Yang, and J. E. Fischer, Appl. Optics, 1976, in press; see also ref. 7. ‘OF. Consadori, A. A. Fife, R. F. Frindt, and S. Gygax, Appl. Phys.Letters, 1971,18, 233; commercial SQUIDS based on 2H-NbSe2 are now available. 51 Unpublished work by Dr. B. C. H. Steele and his co-workers at Imperial College, London. 5a H. J. Tolle and R. Memming, Appl. Phys. Letters, 1975, 26, 349.

ISSN:0306-0012    

DOI:10.1039/CS9760500051

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Chemical Interpretations of Molecular Wavefunctions By A. Hinchliffe and J. C. Dobson CHEMISTRY DEPARTMENT, UMIST, MANCHESTER M60 1QD 1 Introduction The calculation of reasonably accurate wavefunctions for moderately large-sized molecules is now completely routine. For many authors the primary aim of performing such wave-mechanical calculations is to evaluate physical properties such as the dipole moment of a molecule, the electric field gradient at a nucleus, spectroscopic constants, and the like. However, from the early days of quantum mechanics others have repeatedly attempted to ‘interpret’ the wavefunction !#‘ (or to be rigorous Y2:the reader will recall that whilst !?’ itself has no direct physical meaning, y/z d Y is taken to represent a probability). When Yis a many-electron wavefunction, Y2dV becomes yzdrl dsl dr2 ds2 .. . dr, dsn (where r and s indicate space and spin variables of the n electrons) and gives the probability of an instantaneous configuration of all electrons. The most common physical properties, however, depend on the probability per unit volume of finding a single electron (no matter which) at a given point r in space: this is given1 by The factor n arises because the n electrons are indistinguishable. The quantity P is often referred to as the ‘electron density’ since for many purposes the electron distribution may be treated as a smeared-out charge of density P (electrons per unit volume). The aim of such an investigation is to try to recover chemically useful infor- mation from Y,to see why it takes a particular form for a given molecule, and to rationalize how y/ changes from molecule to molecule; in other words, to obtain by reliable techniques answers to the questions posed by elementary descriptive valence theory.In this review we shall describe some of the more popular methods available for such an investigation, and then show by means of two examples what sort of chemical information wave-mechanical calculations can give. We could mention here that some methods lead to information that can be directly compared with experiment (such as electron-density maps) whilst others, such as population analysis, do not. In general there is no single ‘best’ method of analysis: the different methods tend to be complementary. R.McWeeny and B. T. SutcIiffe, ‘Methods of Molecular Quantum Mechanics’, Academic Press, New York. 1971. Chemical Interpretations of Molecular Wavefunctions 2 Techniques Density Maps.-For a preliminary survey of the electron density in a molecule one can make a pictorial representation of the calculated electronic charge density. The most common choice is a contour diagram (a map with lines joining points of equal electron density), although such diagrams do not usually give much information; Figure 1 shows a contour map calculated from a Self Consistent Field Molecular Orbital (SCF-MO) wavefunction for the tetrahedral molecular ion LiNHs+; this shows the electron density surrounding the Li H \ LiH--2NH' Figure 1 Total SCF-MO electron density map for the molecular ion H,NLi+ drawn in a plane containing N, Li, and one of the H atoms.Contours are drawn corresponding to values of the electron density as follows: A = 0.002, B = 0.004,C = 0.008, D = 0.020, . . ., N = 20.000 electrons Hinchtifle and Dobson nucleus overlaps relatively little of the electron density surrounding the N; thus the Li-N bond is weak. The H nucleus, on the other hand, is closely embedded in the contour rings surrounding the N atom. A qualitative examination of the diagram therefore reveals that it is difficult and probably pointless to attempt to identify a fragment corresponding to a free H atom, but an Li+ fragment can be identified quite readily. These electron-density maps provide a theoretically calculated quantity which can be compared with the results of X-ray diffraction.A whole volume of the Transactions of the American Crystallographic Association2 is devoted to reporting a symposium on the subject. Among other papers, Cade discusses the probable accuracy of quantum-mechanical calculations and Coppens gives alternative choices of theoretical and experimental quantities to compare. MO Density Diagrams.-Many molecular wavefunctions are currently calculated using the SCF-MO scheme, where the total electron density is the sum of the densities in the occupied MO’s. Thus one can attempt to understand the total electronic density by examining density diagrams for the individual MO’s. A good example is the discussion by Buenker and Peyerimhoff3 of the geo- metries of Ha molecules.They were testing the theory of Walsh,4 according to which the apex angle and bond length of such molecules can be predicted by considering the variation of a loosely defined theoretical quantity often referred to as an ‘orbital energy’ with the apex angle. Walsh’s arguments are based on simpIe concepts pertaining to the effect of atomic orbital (AO) mixing on the energy of the MO; conclusions about the geometry are then made easily on the basis of which orbitals are occupied in a particular electronic configuration. The theory dues give gross features correctly but cannot explain, for example, why the isoelectronic molecules BH2-and NH2+ should have very different bond lengths.By looking at the orbital density plots (amongst other things) Buenker and Peyerimhoff were able to rationalize the experimental facts much more convincingly. Obvious disadvantages of this kind of approach are (i) the number of orbitals can quickly become unmanageable, many MO’s often being involved in the bonding with even inner shells having to be considered, and (ii) MO’s are often delocalized over the entire molecule, making conclusions about particular bond- ing regions difficult to obtain unless one is prepared to transform such MO’s into localized MO’s. Density Difference Maps.-The electronic rearrangement which takes place when atoms combine to form molecules is rather subtle. It is natural to attempt to depict this rearrangement by subtracting the superimposed free-atom electron densities from the molecular density.Bader, Keaveny, and Cade5 have developed a Trans. Amer. Cryst. ASSOC.,1972, 8. R. J. Buenker and S. D. Peyerimhoff, J. Chem. Phys., 1966,45,3682. 4A. D. Walsh, J. Chem. SOC.,1953, 2260. R. F. W. Bader, I. Keaveny, and P. E. Cade, J. Chem. Phys., 1967,47, 3381. Chemical Interpretations of Molecular Wavefunctions this technique in a large number of systematic applications, but there is a major conceptual difficulty in the not-infrequent case that one or more of the atoms has a partially filled shell in its electronic ground state. A typical example is NF3; the N atom has a unique 2Sground state but the F atoms each have orbital configurations s2p5which give spatially degenerate 2Pstates.Apart from the spin degeneracy there is thus a 33-fold spatial degeneracy. Which combination of these spatial wavefunctions should one take as reference states in evaluating the atomic densities? Figures 2a and 2b, which show two density difference maps for NF3 in a plane Figure 2a SCF-MO density diflerence map for NF, (with pyramidalgeometry) drawn in n pbne containing the N and one of the F atoms. This map is the eleclron density of the mdecu 'e minus that of 'spherically averaged' atoms. Contours are drawn corresponding to values of the electron density as follows: A = -0.800, B = -0.400,C = -0.200,D = -0.800,.. .,J = 0,. . ., S = +0.800 electrons Hinchlifle and Dobson Figure 2b As for Figure 2a, except that this map is the electron density of the molecule minus valence states containing the N and one F atom (F1) illustrates the problem; the top map has as reference state a ‘spherical average’ of the PI,PO,and P-1 states for each F whilst the bottom map has a ‘valence state’ in which thepo orbital on each F is singly occupied (we should mention that a valence state is not necessarily a true spectro- scopic state, rather the state of an atom ‘in the molecule’).Chemical Interpretations of Molecular Wavefunctions The top map shows how electron density is built up in thep, orbital on Ff at the expense of the pg orbitals, the bottom map telling a very different story as there is now a substantial build-up of electron density between N and FI.The two maps are thus quite different and the decision as to which reference state to use is clearly subjective: it depends on one’s preconceived ideas about the bonding in a molecule. One obvious class of compound for which this choice is rather more objective is ionic molecules such as LhS, when one naturally compares the molecular density with that of the superimposed ions, Li+ and S2-in this case. Integration over a Region of Space.-Our qualitative discussion of Figure 1 suggested that in favourable circumstances, one might expect to identify spatial regions corresponding to atomic fragments. Several recent attempts to achieve this quantitatively deserve mention: Bader and BeddallY0 for example, divide up the total electron density into atomic regions in which the Virial Theorem (V} = -2(T> is satisfied by the kinetic T and potential V energy operators over the region.They have reported results for LiF, LiO, and LiH, together with their positive ions, the aim being to find atomic ‘invariants’ such as an atomic charge density and potential which can be transferred from molecule to molecule. Ransil and Sinai’ have suggested two ways in which the electron density can be partitioned numerically: in the first, contours enclosing one nucleus only (see for example Figure 1) are taken as defining ‘atomic’ regions, those enclosing two or more nuclei regions of ‘delocalization’. In their second scheme regions are classified according to the density difference map and the population in each region is found by numerical integration. Such techniques are not widely used presumably because of the difficulty of performing the numerical integrations.Another method, which avoids such integrations, will now be described. Population Analysis.-The aim of population analysis is to divide up molecules into ‘atoms’ and ‘overlap regions’ which can be easily characterized by the amount of electronic charge density they contain. If the wavefunction was calculated using a set of atomic orbitals (a so-called basis set) which are well localized in space on atoms A, By... then it is useful to split up the charge density P into atom and overlap terms P(r) = cpw + c cpmw (2)A A<B where PA is the net density of atom A and PABthe overZap density of the atoms A and B.These densities are defined in terms of the atomic orbitals and a matrix P which readers familiar with the Hiickel treatment of n-electron molecules will recognize as the matrix of charges and bond orders, with the sums running only R. F. W. Bader and P. M. Beddall, J. Chem. Phys., 1972,56,3320. B. J. Rand and J. J. Sinai, J. Chem. Phys., 1967, 46,4050. Hinchlife and Dobson over those AOs @Z which are centred on atom A. There is a related formula for Pm.To obtain the amounts of electronic charge in the atom and overlap regions these densities are integrated to give the corresponding populutions pA and pAB. Given a MO wavefunction and the values of the overlap integrals between the AO’s (which have to be calculated anyway, as part of the SCF-MO procedure) it is an easy matter to calculate the populations PA and pm.The three basic assumptions of population analysis are as follows: (i) the partitioning described by equation (2) is chemically useful ; (ii) useful information is retained when the densities are integrated to give populations; (iii) it is valid to divide the overlap population pm into parts and assign the parts to the two atoms contributing For a given atom A the sum of the fractions UA~,VAAC, . . . with reference to all other atoms ByC, . . . is called the valence population VA, the sum of VA and the atom population PA being the gross population 4~.In the Mulliken scheme,sa which is the most widely used, the fractions of equation (4) are assumed equal: i.e.the electron density in a given overlap region is allotted equally to the two atoms involved. (It is interesting to note that this approximation was used in 1952 by McWeeny,*b in a crystallographic application; he showed that X-ray scattering from an aggregate of bonded atoms could be dealt with in exactly the same way theoretically as when no interactions were present by replacing the atomic scattering factor by ‘effective’ scattering factors. In the example given, H2, the effective scattering factor related to a charge distribution characterized by the Mulliken gross population of each H atom). Figure 5 (p. 92) shows a contour map of the overlap density function PLiF(r) for LiF.It can be seen that the Mulliken assumption is not very realistic for such a molecule, as the overlap density is very unequally shared. There are, however, alternative schemes such as one we will refer to as the Lowdin-Daudel schemesc in which the overlap population is divided up according to the bond dipole -the bigger the bond dipole the more unequal the sharing of pAB. Population analysis tends to be used in two main ways and the relative importance of assumptions (i), (ii), and (iii) is different in either case. Often the ‘atomic charges’ ZA-qA, where ZAis the nuclear charge number and qA the gross population, of atom A are taken as a succinct description of the major features of the charge distribution and in particular its polarity.A good example is the study by Veillard9 of lithium acetylene, LiCCH, where the gross populations of the CT-and w-electrons are presented separately and compared with those in acetylene. The molecule is predicted to be highly ionic with no definite Li-C bond but rather an ionic association between the Li+ ion, carrying a positive charge of 0.78, and the CCH- ion. There is also a small back-donation of electron (a) R. S. Mulliken, J. Chem. Phys., 1955, 23, 1833; (b) R. McWeeny, Acta Cryst., 1952, 5, 463; (c) P.-0. Lowdin, J. Chem. Phys., 1953, 21, 374; (d) R. Daudel, A. Laforgue, and C. Vroelant, J. Chim. phys., 1952, 49, 545. @A.Veillard, J. Chem. Phys., 1968, 48, 2012. Chemical Interpretations of Molecular Wavefunctions density from C to Li via the nelectrons.When population analysis is used in this way assumption (i) is less important than (ii), e.g. it is impossible from the gross populations to distinguish an atom whose electron density is approximately spherical (e.g.Li+ in Figure 1) from one that is not: population analysis can say nothing about the lone-pair in ammonia. The second main use of population analysis is to discuss the nature and strength of bonding, pABbeing taken as a measure of how the strength of a bond can be attributed to contributions from atoms A and B. An example is the study by Cruickshank et al.1° on KrFz where the overlap populations pKrFand some component MO populations are discussed. In this use of population analysis assumption (iii) is not required but (i) and (ii) are vital.Population analysis is a particularly simple process to perform but the indices calculated depend directly on the atomic orbitals used in the calculation, as equation (3) shows. This can give rise to the problem of basis set dependence. It sometimes happens that two basis sets give strikingly different population indices but otherwise give results in good agreement with each other. Mullikenll has discussed this problem and given criteria for choosing basis sets which are likely to lead to ‘reasonable’ populations. A basis set is said to be physically balanced if it has sufficient flexibility to describe all parts of the molecule well, and formally balanced if each atom has an adequate number of atomic orbitals centred on it.Only formally balanced basis sets are likely to lead to numerical populations that are meaningful (thus a wavefunction for HF calculated using only F atomic orbitals could be physically balanced if enough atomic orbitals were used, but it is not formally balanced and one would not attach much importance to the resulting gross populations of 10 for F and 0 for H). There are, however, examples in the literature of bad disagreement between calculations on the same molecule using rather similar basis sets of AO’s.12 As an alternative to dividing up the overlap population between two contri- buting atoms one can reject assumptions (ii) and (iii) and just investigate the net and overlap densities PA and PAB directly rather than their integrals.Bader and Henneker13 have used this approach to study the degree of ionicity in LiF: a ‘classical’ model of the ionic bond was taken as two charged spheres each slightly polarized by the electric field of the other, this electron density distribution then being compared with an SCF-MO one by calculating the forces exerted by the two distributions on the nuclei. Again, Roby14 argues that it is not very useful to attempt to split up the electron density in the bonding region at all :the electron density is genuinely shared by the participating atoms. Thus he is able to give a very different definition for the atomic charges etc., which seem to have none of the disadvantages of the Mulliken-type schemes. ’” G. A. D. Collins, D.W. J. Cruickshank, and A. Breeze, Cham. ComM., 1970, 884. l1 R. S. Mulliken, J. Chem. Phys., 1962, 36, 3428. la R. S. Mulliken and P. Politzer, J. Chem. Phys., 1971, 55, 5135. l3 R. F. W. Bader and W. Henneker, J. Amer. Chem. SOC.,1965, 87, 3063. l4 K. R. Roby, Mof. Phys., 1974, 1, 81. Hinchlifle and Dobson Summary.-The methods discussed can be conveniently classified into those which investigate electron densities directly (total densities, difference densities, and the like) and those methods which attempt to characterize regions of space numerically, usually by the amount of electron density contained within the regions. Population analysis is probably the easiest method to use as the cal- culation is rather simple, For this reason it is almost certainly the most widely used method; it can give useful information when applied to a series of related molecules or when used in conjunction with other methods of analysis, but its predictive value is small when used in isolation on a single molecule.In Section 3 we show how the different methods are used together to give information about the bonding in LiF, then in Section 4 the differences between the electronic structures of NH3 and LiNH3+ are discussed, 3 How Ionic is LiF? Throughout this section all calculations refer to an isohfed LiF molecule, i.e. LiF(g) and not LiF(c). Before giving any quantitative results it is useful to discuss what might be expected, in line with the general aim of the review. Clearly LiF will be strongly ionic, approximating to LifF-, and so to get any insight into its bonding it is necessary to compare LiF with Li+ and F-ions since a comparison with the neutral atoms would show a predominant charge transfer from Li to F and consequent expansion of the fluorine L shell, which would mask any more subtle effects.We could imagine then a ‘zero-order’ description of LiF comprising two undistorted (spherical) ions at their equilibrium distance: a better approximation would result if polarization of the charge clouds were admitted, i.e. the spherical ions would distort owing to their mutual repulsions. In orbital language the AO’s of Li+ would be allowed to vary owing to the nearby F-ion and vice versa, but no MO formation would be allowed at this stage.Finally a covalent interaction could be allowed in which MO’s were formed. We can summarize this as follows 1 spherical Li+ and F-ions (at equilibrium separation) J. polarization 2 distorted Li+ and F-ions+ covalence 3 LiF molecule However, the problem of basis set dependence (see p. 86) must be remembered : if the Li+ and F- basis sets were sufficiently large the zero-order wavefunction would be a rather good approximation and we would ascribe nearly all improve-ments on going from 1 to 3 above to polarization and few to covalence. On the other hand, if we had used a very small basis set of AO’s comprising Is orbitals on Li and F with 2s and 2p on F we would find no polarization effects whatever. This qualitative discussion suggests a number of questions: (i) how closely does a good SCF-MO wavefunction for LiF resemble the ‘zero-order’ model? (ii) is the polarization of Li+ and F-ions the same as one would find from clas- sical electrostatics? (iii) is it possible to distinguish between polarization and Chemical Interpretations of Molecular Wavefunctions covalence effects? With these questions in mind we now examine the various methods of analysis.Ransil and Sinai7 have calculated an electron-density map for LiF using an accurate SCF-MO wavefunction and by numerical integration over the closed contours around the Li and F nuclei (i.e.those contours which only encircle one atom) obtained the amounts of electron density in each atomic region.A com-parison with the free-atom values shows that there has been a substantial amount of charge transfer on forming the molecule from F and Li atoms. An SCF-MO density difference map of the molecule minus undistorted ions is shown in Figure 3. Bader and Henneker13 have discussed a similar map, together with one F Li Figure 3 Total SCF-MO density difference mapfor LiF with respect to free ions. Contours as Figure 2a of the molecular density minus that of the free atoms. On comparing the two maps it turns out that the contours of Figure 3 are very much smaller than those on the (molecule -atoms) map, showing that LiF is much more nearly ionic than covalent. It should be remembered that Figure 3 is a density diflerence map Hinchliffeand Dobson and so a large positive contour around the F is not due to the initially greater amount of charge on that centre.It can be seen that electron density has been removed from the region in front of the Li+ ion (i.e. the region close to Li and in between Li and F)and increased in the region behind it. We call this a dipole polarization. Overall the F electron density is slightly more contracted than that of a free F-ion as the outer parts of the F density are negative, and is polarized towards the Li nucleus. The Li approximates very closely to a Li+ ion slightly polarized away from F-. It is interesting to examine the density difference map for the n-electrons separately (Figure 4). Comparing Figures 3 and 4, and noting that both the shape F Figure 4 SCF-MO density diference map for the n-electrons of LiF with respect to the a-parts of the density in the free ions.Contoursas for ,Figure 2a Chemical Interpretations of Molecular Wavefunctions of the positive contours stretching out from F to Li and also the n-map contours are very similar in magnitude to the total, one might guess that the n-orbitals are more important than the a-orbitals in moving electron density into the bonding region. Some of the more significant statistics from population analysis studies of LiF with the SCF-MO wavefunctions used to calculate Figures 3 and 4are shown in Table 1. Clearly, LiF is rather close to Li+(ls2) F-(ls22s22p6)as the gross popu-Table 1 Some indicesfrom apopulation analysis study of an SCF-MO wavefunction for LiF low din-Daudel Mulliken (a) Overall indices pLi” a 0.059 77-0.088 total 0.147 valence population of Li with respect to F a -0.009 0.030 0.034 0.044 valence population 0.123 0.074 gross population 9.922 9.873 valence population 0.025 0.074 Li gross population 2.078 2.127 atomic charge 0.922 0.873 (b) Gross populations 3.992 3.970 1.971 1.956 >Pn 3.953 3.942 0.001 0.001 0.004 0.004 1.984 2.014 Li PU 0.050 0.060 0.044 0.053 lations show.The d-orbital gross population is very small but this does not mean that such polarization functions are unimportant. The overlap population pLiF is small at 0.147when compared with more typical values of ca. 0.7for covalent molecules like NH3; the u contribution (0.059)turns out to consist of a negative term (due to overlap of Li s with Fp, orbitals) close to Li and a positive term (mainly Lip,:Fp,) rather polarized towards F.In the Mulliken scheme this overlap population is divided equally between Li and F as shown, but when the Lowdin-Daudel scheme is used, the a-valence population of Li is negative (-0.009).Because of this very unequal sharing of the overlap density one would Hinchlife and Dobson hesitate to ascribe to it any ‘covalent’ interaction: it represents rather a reorgani- zation within the electron density of the F-ion. On the other hand, the overlap density is more nearly equally shared on the Lowdin-Daudel scheme with a valence population of F of 0.054 and Li 0.034, so one might tentatively suggest that there is evidence for a weak n-bond.To re-emphasize the point regarding the allocation of overlap dmsity between two atoms by equation (4), Figure 5 is a contour map for the overlap density PFLi(r). It shows that the electron density in the bonding region is really very unequally shared: there is a region of negative overlap near the Li nucleus and a smaller one near F. The region of positive overlap is well towards the F end of the bond and extends some distance from the internuclear axis as one might expect from the relative importance of the n-contribution. By studying the gross populations in Table 1 of the individual atomic orbitals on F and comparing with similar quantities for a free F-ion one can show that the outermost part of the F charge density has contracted considerably in going to LiF, both for 2s and 2p orbitals.On the other hand, the inner 1s orbital is not significantly affected. To conclude, very good agreement between the descriptions of LiF is given by the various methods and the following points can be made. The electron density is reasonably well approximated by the superposition of ions but there are considerable distortions from the spherical shape. The polarization of the F-ion is not exactly what one would expect classically, since the o-and T-parts need to be considered separately and, whilst the distortion of the o-density is essentially a polarization towards Li+and contraction, that of the n-density can best be described as a weak covalent bond.4 How does LiNH3+differ from NH3? l5 We have already discussed the total electron-density map (Figure 1) caIcuIated for LiNH3+ from an accurate SCF-MO wavefunction (see p. 80),and decided that to a good approximation the molecule can be regarded as a combination of NH3 with Li+. The dipole moment p calculated for the molecule at the par- ticular geometry chosen for the SCF-MOcalculation is 2.591 atomic units and if we write p(LiNH3) = p(NH3) + ccR(Li-N) (5) where R(LI-N) is the Li-N bond distance, then u would be exactly 1 if no charge transfer or polarization had taken place. In fact u = 0.872, showing that there has been a substantial charge transfer to Li from N. The atomic charges are calculated from a Lowdin-Daudel population analysis to be 0.937 (1 .O), -0.345 (-0.187), and 0.136 (0.062) for Li, N, and H, respectively, with the corresponding free Li+ and NH3 values in parentheses.This shows the polarization of the NH3 fragment, whilst the overlap population in the NH bond hardly changes, being 0.702 in LiNH3+ and 0.733 in NH3. Again, the valence population of H is almost l5 A. Hinchliffe and J. C.Dobson, Theor. Chim.Acfa, 1975,39, 17. Chemical Interpretations of Molecular Wavefunctions Hinchlife and Dobson constant at 0.569 as compared with 0.594 in NH3. That the Li-N bond is weak is shown by the overlap population of 0.108. A density difference map calculated from the same SCF-MO wavefunction of molecule minus (NH3 + Li+) fragments is shown in Figure 6; like Figure 1 it is Li Figure 6 SCF-MO density difference map of the molecular ion H,NLi+ with respect to NH, and Li+, drawn in the same plane as Figure 1.Contours as for Figure 2a Chemical Interpretations of Molecular Wavefunctions drawn in a plane containing Li, N, and one of the H atoms. It can be seen that the Li+ exhibits the same dipole polarization as the Li in LiF (see Section 3), since electron density is removed from ‘in front’ of the Li nucleus as demon- strated by the dotted contours, and redistributed behind the nucleus. The N atom, on the other hand, shows a quadrupolar polarization :electron density is removed from the regions on either side of the nucleus and transferred to regions above and below.Such a polarization turns out to be common for atoms which bond mainly through p-electrons,Is and a closer examination of the density difference map for LiF shows the same feature. The zero-contour line (J on the map) is rather close to the N-H bond, supporting the assertion that the overlap density in the N-H bond hardly changes on molecule formation. 5 Conclusions In this review we have tried to show how useful chemical information can be recovered from wavefunctions. There is no ‘best’ method of analysis. The use of density difference maps can draw attention to electronic rearrangements different from those expected on preconceived ideas of bonding, whilst Lowdin-Daudel population analysis is, we believe, a useful guide for intepreting the density difference maps.In conjunction with a knowledge of the polarity of atomic densities, population analysis helps in an understanding of the origin of dipole and yuadrupole moments. The authors thank Dr. R. F. Weaver for Figure 2. Professor Ashmore, Professor Cruickshank, and Dr. McDougall are thanked for their helpful comrr,ents on the manuscript and the University of Manchester Regional Computer Centre (UMRCC) for the computing facilities. la R. F. W. Bader, I. Keaveny, and G. Runtz,Canad. J. Chem., 1969,47, 2308.

ISSN:0306-0012    

DOI:10.1039/CS9760500079

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Conductivity and Superconductivity in Polymers* By E. P.Goodings JCI LTD., CORPORATE LABORATORY, THE HEATH, RUNCORN, CHESHIRE, WA7 4QB 1 Introduction If an electrically conductive polymer is to find technical applications it should be flexible and capable of being shaped by normal processes. The first conductive polymers were mostly refractory pyropolymers resembling graphite, but more recent work has shown that conduction can be obtained in other structures which are more amenable to plasticization. Some of these enjoy modest commer- cial success, but dramatic improvements to produce polymers with metallic conductivity and even superconductors depend on our gaining a greater under- standing of conduction mechanism in polymers. To economize in our use of polymers we need to tailor them mcre closely to our requirements. This is particularly true of polymers which, by conducting electricity electronically, do not become exhausted in use like ionic conductors and yet are more flexible and lighter in colour than the conductive mixtures of carbon black with conventional polymers.Thus an electrically conducting polymer should conduct electronically like a metal, have good mechanical properties, and be normally processable. No such polymer has yet been made but the way is gradually becoming clear and one or two useful conducting polymers are just appearing on the market. Progress in this field depends on understanding how organic materials conduct. We shall say a little about this, then consider the two broad classes of conductors and finally discuss superconduction.No really satisfactory theory of organic conduction has yet emerged but the picture is taking shape and we see that it is the molecular nature of organic solids which dictates their electrical properties. 2 Molecular Conductivity Semiconductors fall between metals and insulators (Figure 1) and have con- ductivities ranging from 10-10 to 10+2 ohm-1 cm-1. The conductivity (0) depends on the concentration of charge carriers (n),their charge (e), and mobility (p) according to equation (1). The concentration of carriers (electrons), and hence the semiconductivity, increases with temperature according to a Boltzmann- type distribution with activation energy EA[equation (2)].Thus semiconductivity with a positive activation energy is distinguished from metallic conductivity which falls as the temperature rises. * This review is an extension of the talk given by the author at the Annual Chemical Congress, York, 1975. Both the talk and the review are based on an article published by the author in Endeavour (1975,34, 123) and he thanks the Editor for permission to use the material. 4 95 Conductivity and Superconductivityin Pobmers -INSULATOR SEMI CONOUCTOR +coNwcToR SUPERMETALLIC-COPJOUCTOR -20 -15 -I0 -5 0 5 .. 24 Pb AT 4K -METAL COMPLEXES --PYROPOLYMERS -Figure 1 Conductivity ranges of various types of material. The scale gives the log of the conductivity (ohm-' cm-l) at 300 K cr = nep (1) a = noepexp(-EA/kT) (2) Two distinct transport mechanisms are often considered : band conduction and hopping conduction.In a solid with long-range order and closely packed atoms, as in a metallic semiconductor, the energy levels form conduction and valence bands separated by an energy gap. An electron on excitation into the conduction band leaves a hole in the valence band which also acts as a charge carrier and as the carriers move freely in the bands they have high mobilities. This is occasionally the case with close-packed molecular solids such as anthra- cene which, with a mobility of ca. 1 cm2 V-1 s-1 Cp N l), is almost a band-type conductor but, having no charge carriers, is an insulator. Most organic mole- cules are widely separated, being held together by weak van der Waals forces.Hence the electronic coupling between organic molecules is poor and herein lies the major obstacle to conduction as it is difficult for an electron to pass between them. Electrons then move by thermally activated hopping and because they spend a long time on each molecule mobility is low. Generally, mobility increases with long-range order and is highest in single crystals so that polymers start with a handicap. Thus poly-(N-vinylcarbazole), (PVK), has a low hole mobility (10-6 cm2 V-l s-l) whereas the monomer model, N-isopropylcarbazole, as a single crystal has a high hole mobility (0.3 cm2 V-1 s-l).l Mobility is the parameter which has received least attention in studies of conducting polymers.Charge carriers are most readily formed by activation of non-bonding or n-bonded electrons, and if they are delocalized in a conjugated system they form an internal conduction path of high mobility. Thus long conjugated systems D. L. Stockman, in 'Current Problems in Electrophotography', ed. W. F. Berg and K. Hauffe, de Gruyter, Berlin, 1972, p. 194. Goodings form one class of organic conductors. Also w-bonded electrons give better intermolecular orbital overlap than o-bonds. Hence we find that planar aromatic molecules which can stack like cards with an interplanar spacing no greater than that in graphite (0.335 nm), provide a conduction pathway normal to the molecular planes. Thus the second major class of organic conductors comprises the stacked planar n-electron systems.3 Conjugated Molecules In a polyene chain, -(CH)n-, welectron delocalization tends to make all the G-C bonds of equal length. By treating the system quantum mechanically as a particle in a box we find that the energy required to excite an electron from the ground to the first excited state is given by EA =19(n +l)/n2 Thus as n increases the activation energy for carrier formation decreases and conductivity should increase with chain length. This is seen in a series of measure- ments on thiophenylene-ethylenes made by Kossmehle2 (Figure 2); the slight -7 -7t T-8 tf Figure 2 Dependence of Conductivityon the length of the conjugated system decrease in conductivity on passing from crystalline oligomer to partly crystalline polymer at n >5 can also be seen.For values of n typical of a polymer (ca. IOOO), EAbecomes equal to the value of kT at room temperature (0.025 eV) and so the excited levels should become thermally populated. Thus we might expect metallic conduction in a *M. Hartel, G. Kossmehl, G. Manecke, W. Willie, D. Wohrle, and D. Zerpner, Angew.Makromol. Chem., 1973, 29/30,307. Conductivity and Superconductivity in Polymers true polyene such as polyacetylene; however, it is found that only highly crystal- line, stereoregular polyacetylenes show appreciable conductivity. The highest known conductivity (a = ohm-1 cm-1) is found in trans-polyacetylene which Shirakawa3 made by Ziegler-Natta polymerization in a thin film.P~lyphenylacetylene~is an insulator (a = 10-l6 ohm-l cm-I) and the conduc- tivity of polymethinimine, -(CH=N),-, recently made by the zinc chloride- catalysed polymerization of 1,3,5-triazine,5 is little better (a = 1.3 x 10-11 0hm-l cm-I). There are three reasons for this poor conductivity in polyencs: (i) the large intermolecular barrier; (ii) the bonds are not all equal in length but alternate. (This Jahn-Teller effect stabilizes the polymer but it restricts electron delocalization); (iii) rotation of the chain interrupts conjugation particularly where coplanarity of substituents is prevented by steric interaction, as in polyphenylacetylene, lnterrupted conjugation is overcome by locking the bonds in a planar polyacene structure as is found in pyropolymers and ultimately in graphite, but these are very intractable materials which must be fabricated before pyrolysis, as in the case of carbon fibres6 which have a conductivity of 3 x 10f2 ohm-l cm-l.The polyacene quinone radical (PAQR) polymers are also very intractable substances. They are made by condensing pyromellitic anhydride with various aromatic compounds to form planar conjugated ladder polymers up to SO00 8, long (Figure 3). Poh17 found evidence of high intramolecular conductivity in the extraordinarily high dielectric pennittivities shown by these polymers. Values of up to 300 0oO were measured, compared with normal values of 2-7. TYPICAL PAQR POLYMER (PROBABLE STRUCTURE) c 0.-PoLARism . INTERMOLECULARC -'-' EXCITON ( RP.DI C AL ,c -.\ IONS)F.-/1 1 ELECTRIC FIELD Figure 3 Lander and layer structures of PA QR polymers, showing hyperelectronic polarizabiliry H. Shirakawa and S. Tkeda, Polymer J., 1971. 2, 231; Jap. Pat. 73 32 581. A. G. Hankin and A. M. North. Trans. Faraduy SOC.,1967, 63, 1525. D. Wohrle, Mukromol. Ch~m.,1974, 175, 1751. R. W. Cahn and B. Harris, Nuturf, 1969. 221, 132. R. D. Hartman and €4. A. Pohl, 1.Polymer Sci., Part A-I, Polymer Chem., 1968, 6, 1135; H. A. Pohl, J. Biof. Phys., 1974, 2, 113. Goodings The carriers slam to the ends of the molecules producing full polarization in weak fields. This effect Pohl calls 'hyperelectronic polarizability' and the uninterrupted conjugation he calls 'eka conjugation'.It is not certain that the bond length alternation in polyenes can be avoided by using planar polyacenes.8 Polyacetylenes are paramagnetic and Byrd et al.9 showed that the conductivity of substituted polyphenylacetylenes is proportional to the electron spin concen- tration (Figure 4). Thus the carriers can be identified as unpaired electrons -I NHeCHO --I E U-' -I E -L 0 b (3s -I -I 1 I I t 5 17 18 19 20 , LOG (ELECTRON SPINS. GRM-'1 Figure 4 Conductivity and unpaired electrons inpolyphenylacetylems which are probably formed by electron transfer from an excited triplet to a singlet molecule. The resulting intermolecular exciton ionizes to give radical- ions as the charge carriers, and it is probable that radical-ions are the carriers in the majority of organic molecular systems (cf: Figure 3).a M.R.Boon, 77teor. Chim. Acta, 1971,23, 109. N.R. Bytd, F. K.Kleist, and D.N. StamiteS, J. Polymer Scf., Part A-2, PoIymer Phys., 1972, 10,957. 99 Conductivity and Superconductivity in Polymers In polyenes the first step towards carrier generation probably involves chain rotation to break double bonds,1° and this can be prevented by locking the chain in a crystal lattice. There is one example of this in the polydiacetylenes made by Wegnerll using solid-state polymerization in a single crystal (Figure 5). These 1~1~10~(300 K) 70 1.4~10~(22 K) 4x10-4 1.2~10~(10 K) GOLD METALLIC LUSTRE Figure 5 Conductivitiesof poZydiacetyZene,ll made by solid-state polymerization, and of poly(sukhur nitride)14 polymer crystals are 1-15 cm long, have a metallic lustre, and are macro- scopically free of defects.X-Ray analysis12 shows that the polymer is planar and perfectly conjugated with bond alternation. Thus carriers cannot be readily formed by chain rotation. In agreement with this Bloor has now shown13 that the polymer has no measurable electron spin, which also shows that the mole- cules are probably as long as the crystal and the intermolecular barrier to conduction must be negligible. So we see that charge carriers are probably generated by thermal excitation ofn-electrons but that this is made difficult by bond alternation because the electrons are localized, thus explaining the high activation energy and low conductivity which probably occurs by hopping. In spite of bond alternation, poly(su1phur nitride) as single crystals has metallic conductivity (Figure 5).14 We shall return to this later.To summarize, conjugated polymers can give fairly high conductivity but at the expense of poor mechnical properties, refractory behaviour, and dark colour. Fortunately an alternative electronic conduction pathway is found in the stacked planar n-electron systems. Charge-transfer complexes and certain radical-ion salts are of this type. lo G. M. Holob, P. Ehrlich, and R. D. Allendoerfer, Macromolecules, 1972, 5, 569. l1 W. Schermann and G. Wegner, Makromol. Chem., 1974, 175, 667; 1972, 15435. l2 E. Hadicke, E.C. Mez, C. H. Krauch, G. Wegner, and J. Kaiser, Angew. Chem. Internat. Edn., 1971, 10, 266. l3 D. Bloor, D. J. Ando, F. H. Preston, and G. C. Stevens, Chem. Phys. Letters, 1974,24,407. l4 C. H. Hsu and M. M. Labes, J. Chim. phys., 1974, 61, 4640; A. A. Bright et al., Phys. Rev. Letters, 1975, 34, 206. Goodings 4 Charge-transfer (CT) Complexes Partial formation of radical-ions occurs in the donor-acceptor interaction lead- ing to CT complexes which form rigid stacks, * * -DADADA * * ., and these determine the mechanical properties of solid complexes. Conductivity is highly anisotropic and occurs by radical-ion disproportionation, as suggested by Eley.15 t-Formation D -+ A -+- D' A' Transport Dt A'J - A0~~~ D+ A0 A;D'- A' A' A' Dt Df Quite high conductivities are found, e.g.in the perylene-nickel maleonitrile-dithiolate complex.l6 -NC NC CN per) Ienr nickel nialeonitriledit hiolnte 020 OC= 50 ohm-l cm-l Many polymeric CT complexes have been made, usually with the donor species carried on a vinyl polymer. However, this often results in the conductivity being lower than that of the equivalent monomeric complex, e.g. in the pheno- thiazine-DDQ system (Figure 6).17 Littls attributes this to the small spacing of the donor repeat units and finds that by taking polyethyleneimine as the backbone the repeat spacing of methylmercaptoanisole donor units (0.635 nm) in the crystalline polymer is the same as the repeat distance of most CT complexes (0.64-0.68 nm).If 2,4,5,7-tetranitrofluorenoneis used as acceptor, the conduc- tivity of the polymeric complex is greater than that of the monomer by lo3. Although the conductivities are low this is an important observation because it shows that the polymer can be tailored to give the correct geometry to facilitate sandwich stacking. The polymers are soluble and more tractable than the conjugated systems as the stiff rod-like stacks are plasticized by the flexible a-bonded polymer matrix. D. D. Eley, J. Polymer Sci.,Part C,Symposia, 1967,17,78. l6 L. Alcacer and A. H. Maki, J. Phys. Chem., 1974,78,215. l7 R. Knoesel, B. Gebus, J.-P. Roth, and J. Parrod, Bull. SOC.chim. France, 1969, 294. la M.H.Litt and J. W. Summers, J. Polymer Sci.,Polymer Chem., 1973, 11, 1339.Conductivity and Superconductivity in Polymers 0 (ohm-1crn-l) MONOMERIC 1 POLYMERIC I 0-4 ' ~xIO-~ I x lo-" Figure 6 Polymeric charge-transfer complexes Complexes formed from polymeric donor and polymeric acceptor species, such as that based on PVK and shown in Figure 7, are claimedlg to form films with conductivities as high as lO+3 ohme1cm-1. I co \NH 111 Figure 7 Charge-transfer complex of donor and accceptor polymers Generally these polymeric CT complexes are brittle materials, however. They are of value where mechanical properties are not important, as in the case of the poly-(2-~inylpyridine)-iodinecomplex which is used as a cathode in the miniature Li-I2 primary cell made by Wilson Greatbatch Ltd20 for implantable cardiac pacemakers (Figure 8).The complex serves a dual function as a source of iodine for the cell reaction 2Li + I2-2LiL and as electronic conductor carrying the current to the collector. The conduc- l8 H. Naarmann, Ger. Pat. 1 953 898, 1 953 899; Angew. Chem., 1969,81,871. 2o A. A. Schneider, W. Greatbatch, and R. Mead, 9th International Power Sources Sympo-sium, paper No. 30, 1974. 102 Goodings CELL REACTION 2 Li +I2 -2 LiI Q CURRENT COLLECTOR WT. 809 C-T COMPLEX CATHODE VOLTAGE 2.8V O.C. CAPACITY 4 amp h LB ELECTROLYTE FORMED IN SlTU ENERGY DENSITY 120 Wh kg -I Li ANODE --1.4--cm C T COMPLEX PVP:12 = I :7-24 (BY WT) CT = ohm-' em-' AT 9O-7S0/o 12 PVP = POLY (2-VINYLPYRIDINE ) lin= 13000 Figure 8 Charge-tramfer complex as cell electrode tivity of the complex is constant at 10-3 ohm-1 cm-1 as the iodine concentration falls from 90 to 75% on discharging the cell.This solid-state cell with the LiI electrolyte formed in situ has a very high energy density (120 w h kg-l) compared with the best lead acid battery (30 w h kg-1) and a service life of ten years. It illustrates the use of one commercially valuable conducting polymer. 5 Radical-ions The classical radical-ion conductors are based on TCNQ, which forms the redox system shown in Figure 9. The system is characterized by the com- proportionation constant K, which is a measure of the energy difference between the oxidation Ievels in terms of the redox potentials El and E2.TCNQ forms charge-transfer complexes and simple and complex salts such as those of quinoline. A complex salt usually has a higher conductivity than a simple salt, but simple salts can also have high conductivity if they are associated with a polarizable cation21-23 as in N-methylphenazinium tetracyanoquinodimethanide, NMP-TCNQ (Figure 10) The TCNQ species form a homogeneous sta~k~**~~ and in NMP-TCNQ they are all equally spaced at 0.324 nm so that the unpaired electrons can delocalize into a conduction band to give metallic conductivity which falls as the temperature is increased. However, most simple salts are not band but hopping conductors,26 in which the TCNQ species are unequally spaced as dimers on which the electrons are localized (0.324 nm between mole- cules in a dimer and 0.332 nm between dimers). This might be caused by steric s1 A.F. Garito and A. J. Heeger, Phys. Rev. (B), 1972, 5, 952. J. R. Melby, Canad. J. Chem., 1965, 43, 1448. a3 D. W. Bonniface, M. J. Braithwaite, D. D. Eley, R. G. Evans, R. Pethig, and M. R. Willis, Discuss Faraday Soc., 1971,51, 131. D4 C. J. Fritchie, Acta Cryst., 1966, 20, 892. 96 H. Kobayashi, Bull. Chem. SOC.Japan, 1975, 48, 1373. as 0. II. LeBIanc, jun., J. Chem. Phys., 1965, 42,4307. 103 Conductivity and Superconductivity in Polymers NC OX SEM RED OX + RED 2 SEM log K = €1 -€2 0.059 (OHM CM)' El = 0.127V 10-5 E2= -0.291V 2 109 K = 7.I 140 Me Figure 9 The 7,7,S, 8-tetracyanoquinodirnethaneredox system \\\ ' \\\ i;" 0 (ohm-' cm-')N-rnethylphenazinium+TCNO' 1-4 x 1O2 N-ethylphenazinium+TCNQ7 lo-@ N-methylphenazinium+(TCNQ;) 7.1 x 'lo-' Figure 10 Crystal structure of N-rnethybhenazinium TCNQ, and conductivities of this and related sal ts Goodings -n--Sit)lJ)ICsalt -> 0 2-energy barrier (TCNQ radical-ion (ncutral (TNCQ d i mer) TCNQ) dianion) Conlpl~~s --tsah -r 0 0 -no energy barrier (radical-ion) (neutral (neutral (radical-ion) m 01.) mol.) effects in the case of N-ethylphenazinium TCNQ simple salt which has 10l1 times lower conductivity than NMP-TCNQ. Thus uniformity of the band system is destroyed and the salt is a semiconductor, although carrier mobilities might be quite high.27 The problem here is that for electrons to move along the stack, Coulomb forces have to be overcome in forming the dianion and so conduction is poor.If neutral TCNQ is added, however, it is not necessary to form a dianion and this is the reason why complex salts have a higher conductivity.28 Sometimes this fails because electron transport from radical-anion to neutral TCNQ is hindered by the Coulombic attraction of the counter cation which is fixed in the solid alongside the radical-anion. However, this can be avoided by using lower concentrations of neutral TCNQ. These complex salts can be regarded as mixed valence conductors. Although NMP+TCNQ*- has metallic conductivity it differs from metals because on cooling it becomes a semiconductor as shown in Figure 11.First c (ohm cillt G SEMKXNMICTOR I I I -D METAL -‘I4oobNMPTCNQ. =380(ohmcm‘r)-MAX I00 /-I I (Walatka 197312ool ‘1,!I I 1 I00 200 300 4 00 TEMPERATURE /K Figure 11 The temperature dependence of the conductivity of’metallic’ TCNQ salts p7 G. J. Ashwell, D. D. Eley, S. C. Wallwork, and M. R. Willis, Proc. Roy. Soc., 1975, A343, 461. V. Hadek, Phys. Status Solidi, 1968, 30,275. Conductivity and Superconductivity in Polymers the conductivity reaches quite a high maximum (4 x lo2ohm-l cm-l) and then undergoes a transition to a semiconductor.29 There are several theories explaining this tran~ition.~~ It is possible that reorganization of the TCNQ stack is induced by asymmetry in the cation, and that the one-dimensional metal becomes a three-dimensional semiconductor because of radical-ion pairing.31 -S3 This Peierls or metal-insulator transition, which is a form of the Jahn-Teller effect, results in a change in crystal structure.34 Many TCNQ salts of polymeric cations have been made and two examples are given in Figure 12.35036 The highest conductivities are ca.ohm-l cm-l. I x lo-*CH2&(CH3) -TCNQ-(5O/oTCNQ ) AT 800/0 EXTENSION 1.66 x E= -C~H~OOCNH NHCC+H~CHM~-O -),OCNH Figure 12 Twoexamples of TCNQsalts ofpolymeric cations Mostly they are dark-coloured materials but owing to the plasticization of the rigid TCNQ stacks by the flexible a-bonded polymer backbone they have better processability than the conjugated systems. Thus they are soluble in organic solvents and form brittle films.The conductivity of the TCNQ salts of poly-(24nylpyridine) seems to depend on polymer crystallinity23 but not on ta~ticity.~~ We see here an example of maximum conductivity being achieved with a reduced concentration of neutral TCNQO. The elastomeric salt with 5% by weight of TCNQ has a low conductivity (a = 10-8 ohm-1 cm-l) which nevertheless is 29 M. J. Cohen, L. B. Coleman, A. F. Garito, and A. J. Heeger, Phys. Rev. (B), 1974,10,1298. 30 I,. L. van Zandt and J. M. Honig, Ann. Rev. Muter. Sci., 1974, 4, 191. s1 M. J. Cohen, L. B. Coleman, A. F. Garito, and A. J. Heeger, Phys. Rev. (B), 1974, 10, 1298. 3a P. A. Lee, T. M. Rice, and P. W. Anderson, Ph-vs. Rev. Letters, 1973, 31, 462.33 A. F. Garito and A. J. Heeger, Accounts Chem. Res., 1974, 7,232. F. Denoyer, F. Comts, A. F. Garito, and A. J. Heeger, Phys. Rev. Letters, 1975, 35, 445. 36 E. P. Goodings. Discuss. Faraday Soc., 1971, 51, 157. 86 A. M. Hermann, S. P. S. Yen, A. Rembaum, and R. F. Landel, Polymer Letters, 1971, 9, 627. Goodings much higher than that of the same polymer with 5% carbon black (a = ohm-1 cm-1). Moreover, the polymer retains its elasticity and on stretching by 80% the conductivity rises whereas that of the carbon composite is halved. Unfortunately polymeric TCNQ salts gradually decompose in air and lose their conductivity. 6 Radical-cations Radical-cations are also electronic conductors. Some of the earliest examples were the polyaniline radical ions3’ (Figure 13), which form stacked structure^.^^ 1-I’ i-i-+I +2 10 -to (HYDRATED) EMERALDINE pN=0=Na3&aNH2 -S04H Sx I 0‘2 (HYDRATED) 4O/O EMERALDINE-POLY(p -AMINOSTYRENE) GRAFT Figure 13 Some polyaniline radical-cations, and their conductivities They are closely related to aniline black which, if carefully prepared as the linear emeraldine, has a high condu~tivity3~ but is a refractory substance.However, Labarre and Jozefowicz40~41 grafted 4 % emeraldine onto poly(p- aminostyrene) to give a polymer of conductivity 5 x 10-2 ohm-1 cm-1 which could be compaction moulded; attempts have been made to use it as a battery electrode. Here again the mixing of stiff molecules with flexible chains gives improved polymer properties.87 J. Honzl.K. Ulbert, V. Hadek, and M. Tlustakova, Chem. Comm., 1965,440. 88 J. Huml. Acta Cryst., 1967, 22, 29. 39 M. Jozefowicz, L. T. Yu. G. Belorgey. and R. Buvet, J. Polymer Sci.. Part C,Symposia, 1967. 16, 2943; R. Buvet. M. Guillon, and L. T. Yu, Ion Exchange Sofvenr Eurracrion, 1973.4. 181 ;M. Jozefowicz. L. T. Yu. J. Perichon. and R. Buvet. J. Pol-vrner Sci., Part C, Symposia. 1969.22, 1187: M Doriomedoff. F. H. Cristofini, R. De Surville, M. Jozefowicz,L. T. Yu, and R. Buvet. J. Chim. phys.. 1971. 68, 1055. 40 D. Labarre and M. Jozefowicz. Compr. rend., 1969, 269, C,964. X. Gerbaux, A. Hadni, M. Heider, M. Jozefowicz, D. Labarre, and J. Nkl, J. Chim.phys., 1970, 67, 684. Conductivity and Superconductivity in Polymers Heterocyclic radical-cations which are even polyenes, like TCNQ, are particu- larly stable and form the fulcrum of the violene redox systems42 (Figure 14) in -e .f.-eX+CH=CH.f;iX = XfCH=CHkX X=ICH-CH%X te +e RED SEM ox CT (ohm-’ cm” 1 RED I SEM I ox -1 2 1.0 3.7 (cl-l -(I)=<:) (TTF) YELLOW DKPURPLE YELLOW 1.3 IO-’4.3 10 -5 -(CI OJ GREEN GREEN BLUE Figure 14 The violeneredox system which the reduced form is usually much paler in colour than the radical-cation. The radical-cation of 1,4,5,8-tetrathiafuIvalene(TTF) has a much higher con- ductivity than the neutral material. The radical-cation of benzothiazolidin-oneazine (BTA*+)has been incorporated by Manecke43 into a polymer which probably combines both radical-ion and conjugated-chain type conductor classes, as both oxidation levels have higher conductivies than the corresponding monomers. Here, as there are no flexible chains present, the stiff molecules give a refractory solid.The complex salt BTAOBTA*+ BF4- has a much higher conductivity (10-3 ohm-1 cm-1) than either component, as would be expected. But the effect of traces (6 p.p.m.) of radical-cation on the conductivity of neutral BTA is remark-able in increasing the conductivity by lo4or 105 (Figure 15).44 This is analogous to the doping of Ge by In to give a p-type semiconductor and renders doubtful many recorded values of conductivity in radical-ion systems. Although polymeric TCNQ salts partly solve the problem of refractory 42 S.Hunig, Pure Appl. Chem., 1967, 15, 109. 43 G. Manecke and J. Kautz, Makromol. Chem., 1973, 172, I. 44 W. A. Barlow, G. R. Davies, E. P. Goodings, R. L. Hand, G. Owen, and M. Rhodes, 4th International Symposium on Organic Solid State, Bordeaux, July, 1975; to be pub- lished. Goodings c3 5-8- > 0-9- z 0 " BTA' BTA+ -I o ) ; r - properties in organic conductors they are strongly coloured and sensitive to air. The use of lightly coloured neutral violenes doped with traces of radical-cation means that a solution to these problems is in sight. 7 Photoconduction Radical-ions can also be generated by photoprocesses and this leads to photo- conduction. It is the most complex aspect of conduction but must be mentioned in this survey as it is the basis of the electrophotographic industry annually worth some E600M.45 In xerography (Carlson,46 1954) a photoconductor coated on a metal drum is negatively charged in ths dark by a corona discharge (Figure 16).The image to be copied is projected onto the photoconductor, thereby discharging the light areas. Black positively charged toner powder coated with resin is sprayed onto the latent image where it is held and subsequently transferred to negatively charged paper. The image is finally fixed by heating to sinter the resin. The photoconductor formerly used was AszSe3 but this is difficult to manipu- late as it is applied by vacuum sublimation and is brittle. It is now being replaced by materials based on poly-(N-vinylcarbazole) (PVK)47which is a good dark insulator whose photoconductive properties were discovered in 1957 by H0eg1.~~ 45C.H.L. Goodman, in 'Electronic and Structural Properties of Amorphous Semi- conductors', ed. P. G. LeComber and J. Mort, Academic Press, 1973, p. 549. 4B A. A. Newmann, Brit. J. Photogr., 1964, Sept. 25, 784. 47 G. Weiser, J. Appl. Phys., 1972, 43, 5028. 48 H. Hoegl, 0.Sus, and W. Neugebauer, Ger. Pat., 1 111 935; 1 068 115. 109 Conductivity and Superconductivity in Polymers CORONA /DISCHARGE 111111I -L =c CHARGING EXPOSURE .CORONA * * . DEVELOPMENT -TRANSFER P -PHOTOCONDUCTOR C -CONDUCTIVE SUPPORT Figure 16 The stages in the eZectrophotographic process It absorbs U.V. light (360 nm) forming an exciton state which ionizes in an electric field49 (Figure 17), and the electron is stabilized in trapping levels of low potential (carbazole dimer units)50 leaving only the radical-cations, PVK*+, to -CH2-CH -I (PVK 1& POLY ( N-VINYLCARBAZOLE)-16 -I -I0 DARK 5x10 ohm cm SENS lTlS AT1 ON PHOTO It 11 kVK?+;]+TNF y--PVK’ + TNF’ PERSISTENT P HO TOCO NDUCTl VITY 02N&N02 NO^ (TNFI PVK+TNF + CC13 COOH 2,4,7 -TRINITROFLUORENONE. hv_ PVK ? &C.CCl, +TNFH Figure 17 Thephotoconductivity of poZy(N-vinykarbazole) *O I(.Knto, T.Nogami, M. Yokoyama, and H. Mikawa, Chem. Lerters, 1974, 1097; R. R. Chance and C. L. Braun. J. Chem. Ph.vs., 1973, 59, 2259. &OH.Bauser and W. Klopffer. Chem. Phys. Lertrrs, 1970, 7.137; H. Meier, W. Albrecht, and U. Tschirwitz. in ‘Current Problems in Electrophotography’, ed. W. F. Berg and K. Hauffe, de Gruyter, Berlin, 1972, p. 163. Goodings act as charge carriers (U360m = 10-13 ohm-1 cm-1). Indirect evidence for the formation of radical-cations comes from studies of photoconduction in anthra-cene-1 and also the increase in photoconductivity of various compounds on introducing substituents which reduce the ionization potential.52 In visible light PVK remains an insulator (cr550nm = 10-16 ohm-' cm-1) but can be sensitized with an electron acceptor, 2,4,7-trinitrofluorenone(TNF), which by forming charge-transfer states shifts the absorption into the visible53 and renders it photoconductive ((3550m = 10-13 ohm-1 cm-l).PVK is solely a hole conductor but the TNF creates electron carriers and the mobility increases. The radical- anion TNF*-contributes to the conductivity, and the amorphous nature of PVK is important in giving the chain the flexibility necessary to accommodate the PVK-TNF sandwich complex in the polymer matrix.54 Support for this mechanism comes from Williams,55 who found that addition of tnchloroacetic acid protonated the radical-anion thus preventing recombination with the radical cation, PVK*+. The salt PVK-+ -0OCCCb is fairly stable and so results in persistent dark conductivity of several days duration. Thus PVK is another commercially important conducting polymer and for this reason its charge transport properties have been studied in greater detail than those of any other polymer.8 OrganometallicPolymers The introduction of metal atoms into a polymer can inmase the conductivity. This usually arises from (i) improved intermolecular orbital overlap due to the more diffuse metal d-orbitals and (ii) extension of the intramolecular conduction path by conjugation of the d-orbitals with then-electron system of the polymer so that the path passes through the metal atoms even if they form the sole links in the polymer chain. The effect of chelating metal ions onto a conjugated polymer is seen in the structure (l), which has a higher conductivity (1.4 x 10-10 ohm-' cm-I) than that of the unmetallized form (4.5 x lO-'3 ohm-1 cm-'1.2 If the polymer chain is not conjugated then improved conductivity is still possible becaure with a transition metal a mixed-valence state system can 61 B. J.Mulder and J. de Jonge. Solid State Comm., 1967, 5, 203. J. Rochlitz, Chem. Zrp., 1972, 96, 561. 63 H. Hoegl. G. Barchiet'o, and D. Tar, Photochcm. and Photohiol., 1972,16,335; M. Lardon, E. Lell-Doller, and J. W. Weigl, Mol. Crystals, 1967, 2, 241. 64 W. Klopffer. J. ChPm. Phys., 1969. 50, 2337. 66 I).J. Williams, G. Pfister, and M. Abkowiu, Tappi, 1973, 56, 129. Conductivity and Superconductivity in Polymers transport electrons by redox behaviour. This is illustrated by the ferrocene- ferricenium polymers (Figure 18), which conduct by metal to metal hopping with- Figure 18 Mixed valence ferrocene-ferriciniurn polymer out participation by the organic framework.56 Although the unoxidized ferrocene polymer is practically an insulator, the partly oxidized form has a conductivity of ohm-1 cm-1.Moreover, Pittman et aZ.b7 have now shown that a doping effect is observed analogous to, but less marked than, that which has been found with radical-ions. The addition of 5% of the ferricenium (FeIII) form to the reduced (FeII) form of both unconjugated and conjugated ferrocene polymers d CH, -CH -'-. Fe Fe6'-. n It poly(ferroceny1ene) poly(ethyny1ferrocene) poly-(3-vinylbisfulvalenedi-iron) increases the conductivity by about lo3.A maximum increase of 107 to 108 fold is reached in poly(ferroceny1ene) with 35-65 % FeIII using tri-iodide as counter anion (0 = 10-7 ohm-' cm-1).The hopping mode dominates the conductivity even when a conjugated system is present as in poly(ethyny1ferrocene). By super- imposing the TCNQ radical-ion system even higher conductivities can be 56D.0. Cowan, J. Park, C. U. Pittman, Y. Sasaki, T. Mukherjee, and N. A. Diamond, J. Amer. Chem. SOC.,1972,94,5110. 67 C. U. Pittman, Y. Sasaki, and T. K. Mukherjee, Chern. Lerrers, 1975, 383. 112 Goodings realized. Poly-(3-vinylbisfulvalenedi-iron)with 71 % of the iron in the ferri- cenium form as the TCNQ (probably complex) salt has a conductivity of 9 x 10-3 ohm-1 ~m-1.5~ This is a rather refractory black powder but attempts to improve the polymer properties by copolymerization with 72 mol % styrene reduced the conductivity to 2.5 x 10-5 ohm-1 cm-1.Some of these polymers are soluble but as usual no mechanical properties have been reported. In the hopping mixed-valence systems the metal atoms have a different geo- metry according to their oxidation state and any constraints on a change in geometry could lower the condu~tivity.~~ It is interesting that those biological conducting polymers which transport electrons through metalloproteins with metal sites 2.5-5.0 nm apart avoid this problem because the geometry of the metal complex is a compromise between those of the reduced and oxidized states.6o 61 The metal is more effective if it forms square-planar complexes with conjugated ligands. Thus the CuII complex of 1,5-diformy1-2,6-dihydroxynaphthalene dioxime (2), although a refractory solid, has a conductivity of 4 x 10-5 ohm-1 cm-1.62 If a mixture of transition-metal ions is used in this type of polymeric complex the conductivity can be in~reased.~3 OH OH II I OH In these planar complexes the molecules are usually linked by metal d-orbital bonds perpendicular to the plane, and thus the carrier mobility tends to increase.An excellent example of this is copper phthalocyanine, which has the highest mobility of any organic compound (75cm2V-1 s-964 although the conductivity is low (ca. 10-14 ohm-1 cm-9.65~66 Here the copper dzz orbitals overlap with the azamethine nitrogen 3d orbitals of the neighbouring molecules with an inter- 58 C. U. Pittman and B. Surynarayanan, J. Amer. Chem.SOC.,1974,96,7916. 69 D. 0.Cowan, C. LeVanda, J. Park, and F. Kaufman, Accounts Chem. Res., 1973, 6, 1. R. J. P. Williams, Biochem. SOC.Trans., 1973, 1, 1. 61 J. R. McKellar, J. A, Weightman, and R. J. P. Williams, Discuss. Faraday SOC.,1971, 51, 176. 62 M. J. S. Dewar and A. M. Talati, J. Amer. Chem. SOC.,1963, 85, 1874; 1964, 86, 1592. 63 Y. Akiyama and H. Mizutani, J. Phys. SOC.Japan, 1969, 26, 1128. e4 G. H. Heilmeier and S. E. Harrison, Phys. Rev., 1963, 132, 2010. 65 B. S. Wildi and J. E. Katon, J. Polymer Sci.,Part A2, Polymer Phys., 1964,4709. 66 C. Hamann and H. Schmidt, Pluste u Kuut., 1969, 16, 85. Conductivityand Superconductivity in PoZyrners planar distance of 0.338 nm.64 On extending the conjugation by polymerization the conductivity is increased by a factor of 10'2 to 5 x ohm-1 cm-I in copper polyphthalocyanine (Figure 19)which is made from pyr~mellitonitrile.~~~~~ Figure 19 Copper polyphthalocyanine However, the mobility then falls to 10 cm2 V-1 s-1.67 As might be expected copper polyphthalocyanine is an insoluble, infusible solid and the only effect of introducing ether or sulphide links appears to be a reduction in conductivityto10-6-10-11 ohm-' cm-1.66 Polymerization can also occur through the metal atom66*6* but in poly-{oxy(phtha1ocyanine)silandiyl } (3) the resultant separation of the phthalo- cyanine planes by oxy-groups, although resulting in lower conductivity (6 x lo-' ohm-' cm-1) does not give an insulator.Substitution of the oxy by the bigger -0C2H40-group further reduces the conductivity to 3.7 x ohm-1 cm-1.Polymeric porphyrin-like metal con-.plexes have been made from various tetranitriles and have conductivities of up to 10-1 ohm-1 cm-1.2s65Although @?A. Epstein and B. S. Wildi. J. ChPm. Phys.. 1960, 32. 324. G.Meyer and D. Wohrb, Makromol. Chem., 1974, 175, 714. Goodings they have high thermal stability and can either be fabricated by forming in situ on heating a mixture of metal and nitrile or be deposited as a film on the metal69 they have found no technical application so far. The copper polyphthalocyanine type structure exemplifies both conjugated and stacked planar conduction systems. Transition-metal complexes with planar ligand systems also can form a mixed-valence structure which is different from the ferrocene-ferricenium system where the metal atoms are in integral oxidation states.These are the Krogmann salt~~~9~1 which are square-planar complexes of d8 transition-metal ions such as those of Pt and Ir. In potassium cyanoplatinate (Figure 20) the weak dudu metal-metal bonds are strengthened by removing pt2.3 +Pt2+ M-I TRANSITION -100 K “VCN K2Pt (CN}4 %K2Pt (CN)4 Bro.3-2.3H20 (5 =5x10-’RT ohrn-lcm’i Figure 20 Potassium cyanoplatinate and its bromine oxidation to a fractional oxidation level one third of the electrons from the dzaantibonding orbitals by bromine oxidation. This results in a fractional oxidation level of 2.3 giving the compound K2Pt(CN)4 Br0.3, 2.3H~0(KCP), with equivalent Pt atoms.In effect this is a polymerization as the decrease in interplanar distance from 0.335 to 0.289 nm gives a bonded chain of metal atoms which now forms a conduction band 5/6 full. The con- ductivity, which increases on oxidation from 10-7 to ohm-1 cm-l, is metallic and highly anisotropic, being lo5times greater parallel to than perpendicular to the metal-metal chain. Thus KCP is a one-dimensional metal and like NMP- TCNQ it shows a metal-insulator transition at ca. 100K below which the conduc- tivity is very low. In this case the phase change72 might be due to an asymmetric S. D. Levina, K. P. Labanova, A. A. Berlin, and A. I. Sherle, Dokludy Akud. Nuuk. S.S.S.R.,1962, 145, 602. 70 K. Krogmann, Angew. Chem. Internat.Edn., 1969, 8, 35. 71 M. J. Minot and J. H. Perlstein, Phys. Rev. Letters, 1971, 26, 371. 7a R. Comes, M. Lambert, H. Launois, and H. R. Zeller, Phys. Rev. (B), 1973,8, 571; Phys. Status Solidi (B), 1973, 58, 587. Conductivity and Superconductivity in Polymers location of the potassium or bromide ions in the lattice.73 They are very brittle solids. Few organometallic polymers with covalent metal-metal bonds have been described. A unique example is the homoatomic ladder polymer bis( catena-polymethylarsenic) (4). It forms a purple crystalline insoluble solid which can be sublimed to give thin films. It appears to be a band-type conductor with a high mobility estimated to be 1 cm2 V-1 s-l. With an energy gap of 1.2 eV the con- ductivity is low (5 x 10-lO ohm-' cm-') but increases in photo~onduction.7~ Me Me Me Me A 'IA ' 0.29nm ---AS -AS -AS-AS-- - -0.24nm I A 'I 'I Me Me Me Me The ladders are coplanar, forming a two-dimensional metallic arsenic species, and the polymer probably represents the closest known approach to the structure of an inorganic semiconductor.Although its electrical properties probably could be adjusted by doping, its mechanical properties would restrict its use to specialized applications. Indeed this is true of all the organometallic polyniers. It is possible that a superconductor might be found in the organometallic class but otherwise the most likely outlet for these polymers would be as photo-conductors in optoelectronic devices.We see then that organometallic polymers include examples of both conjugated and stacked planar systems. The mixed-valence polymers find analogies in the semiconducting radical-ion salts and the Krogmann-type structures fall in the same class as the metallic conductor radical-ion systems. As with their purely organic counterparts, the organometallic polymers must have better mechanical properties before they become generally useful as conductors. We will now discuss the use of both conjugated and stacked planar systems in the search for room temperature superconduction. 9 Superconduction Metals such as lead superconduct at around 4 K because the conduction 73 J. H. Perlstein, M. J. Minot, and V. Walatka, Muter. Res. Bull., 1972,7,309; J.M. Williams, S. W. Petersen, J. L. Petersen, H. M. Gerdes, and F. K. Ross, Chem. Eng. News, 1974, Aug. 19, 23. 74 A. L. Rheingold, J. E. Lewis, and J. M. Bellama, Znorg. Chem., 1973, 12, 2845; J. E. Lewis and M. Edris, Bull. Amer. Phys. SOC.,1975,20,695; Phys. Rev. (B), 1975,11,4033. Goodings electrons pair together in an attractive potential developed by the polarization of the positive metal ions (the electron-phonon mechanism). The resistivity is then zero but above a critical temperature, Tc, conduction reverts to that of an ordinary metal. The value of Tc is inversely proportional to the square root of the atomic mass of the metal and the highest value is likely to be 25 K. A value of 23.2 K has been recorded for Nb3Ge.75 Hence sophisticated refrigeration techniques will always be necessary in order to use these electron-phonon superconductors.In 1964, Little76 suggested that the attractive potential needed to pair the conduction electrons should be created by polarizing a system of auxiliary electrons rather than heavy-atom cores, and because of the low electron mass he predicted transition temperatures above 1000 K. He proposed using a polyene chain as the conduction path (Figure 21) and cyanine dye side-groups CH3 CH3 Figure 21 Typical model for an organic superconductor according to Liftle76 with their highly polarizable auxiliary electrons to provide the polarization 'well', thus giving the famous Little superconducting polymer. So far no-one has made this polymer, the nearest approach being that of Liepins77 who used the conjugated polymaleonitrile backbone (5), but none of his structures showed superconductivity.r (5)I< . dyc \irlc-gt.oup 75 L. R. Testardi, J. H. Wernick. and W. A. Royer, Solid State Comm., 1974, 15, 1. 78 W. A. Little, Phys. Rev. (A), 1964, 134, 1416.''R. Liepins, C. Walker, H. A. Fairbank, P. Lawless, and C. Moeller, Amer. Chem. SOC., Polymer Preprints, 1970, 11, Sept., 1048. Conductivity and Superconductivity in Polymers As an alternative to the conjugated system a stacked planar one-dimensional metal might function as the conducting spine, and so TCNQ salts of cyanine dyes have been studied but without success.78 One obstacle is the metal-insulator transition which converts the metallic TCNQ conductor into an insulator on cooling down in the search for superconductivity.In NMP+TCNQ*- the transi- tion has been blamed on the asymmetric cation and so the symmetrical small and highly polarizable tetrathiafulvalene radical cation (TTF) was examined (Heeger79). The salt TTF-+ TCNQo- as single crystals showed (Figure 22) highly CU METAL ALONG CHAIN +-----------------(ohm-& m-I ) 0300K= 103 D58K =1.5~10~ "3 x~~-7O4 K CTINORMAL TO CHAIN O300K o r 0 58 100 200 300 TEMPERATURE /K Figure 22 Superconducting fluctuations in TTF.'TCNQ--anisotropic metallic conductivity which increased from lo3at room temperature to a maximum of 1.5 x 104 at 66 K, the highest value recorded for an organic material.Then at 58 K it underwent a metal-insulator transition. However, the transition temperature had been lowered considerably compared with NMP- TCNQ (220 K). But the remarkable feature was that in a few samples, just before the transition there was an enormous increase in conductivity to above 106 ohm-1 cm-1. This exceeds the conductivity of copper at room temperature and has been attributed to fluctuations that herald superconductivity. Heeger79 thinks that electron pairing is occurring by the usual phonon mechanism and not according to Little's mechanism, but the system is unstable and on further cooling the peak collapses. Moreover, the samples are not reproducible and no other worker has observed these giant conductivity peaks.True superconduction might be realized if the metallic state could be stabilized J. H. Lupinski, K. R. Walter, and L. H. Vogt,Mid. Crystals, 1967,3,241;E. B. Yagubsky,M. L. Khidekel, I. F. Shchegoleyev. L. I. Buravov, R. B. Lynbovsky, and V. B. Strynkov,Zhur. obshchei Khim., 1968, 38,992. L. B. Coleman, M. J. Cohen, D. J. Sandman, F. 0.Yamagishi, A. F. Garito, and A. J Heeger, Solid State Comm., 1973,12, 1125. Goodings above the Peierls transition. It has now been found that the non-planar hexa- methylene-l,4,5,8-tetraselenafulvalene(HMTSF) (6) forms a CT salt with TCNQ (HMTSF-TCNQ, (T300 K = 2 x 103 ohm-1 cm-l) which does not undergo a metal-insulator transition.80 But although it remains metallic down to 0.045 K neither giant peaks nor superconduction were found.@genSe Se Moreover, although it has been shown that in the solid state TTF-TCNQ is essentially a CI'salt, consisting of segregated stacks of TTF-+ and TCNQo- radical-ions as in Na+ TCNQe- and NMP+ TCNQ=- where electron transfer is complete,81~8*the precise degree of electron transfer is not known. It is possible82 that the TTF and TCNQ molecules, respectively, are not all equivalent and both neutral and ionic (closed and open shell) forms contribute to the structure. Recent work82983 suggests that small amounts of neutral TTFO and TCNQO are present and consequently they could function as dopants in the radical-ion stacks. Hence TTF-TCNQ probably behaves as two sets of doped conducting chains with the expected high conductivity, and the lack of reproducible behaviour could be due to the variable composition sometimes found on recrystallizing a CT complex.In fact, the giant peaks might be unrelated to superconduction and the use of stacked planar systems might be the wrong approach. It might be easier to achieve long-range order in a conjugated polyacene system so that Little could be right and we shall have to face the problem of making his model. To support this view comes a very recent report from Greene et aZ85 at IBM that they have found superconduction in poly(su1phur nitride). The polymer does *O A. N. Bloch, D. 0 Cowan, K. Bechgaard, R. E. Pyle, R. H. Banks, and T. 0. Poehler, Phys. Rev. Letters, 1975, 34, 1561. s1 L.B. Coleman, J. A. Cohen, A. F. Garito, and A. J. Heeger, Phys. Rev. (B), 1973,7,2222; T. E. Phillips, T. J. Kistenmaker, J. P. Ferraris, and D. 0. Cowan, J.C.S. Chem. Comm., 1973, 471 ;J. C. Scott, A. F. Garito, and A. J. Heeger, Phys. Rev. (B), 1974, 10, 3131. 82 Y. Tomkiewiez, J. B. Torrance, B. A. Scott, and D. C. Green, J. Cheni. Phys., 1974, 60, 5111; W. D. Grobman, R. A. Pollak, D. E. Eastman, E. T. Maas, jun., and B. A. Scott, Phys. Rev. Letters, 1974, 32, 534. 83 P. Coppens, Phys. Rev. Letters, 1975, 35, 98, F. Denoyer, F. ComBs, A. F. Garito, and A. J. Heeger, Phys. Rev. Letters, 1975, 35, 445; W. T. Wozniak, G. Depasquali, M. V. Klein, R. L. Sweany, and T. L. Brown, Chem. Phys. Letters, 1975, 33,33. 84 P.Nielsen, D. J. Sandman, and A.J. Epstein, Solid State Comm., 1975, 17, 1067; B. H. Schechtman, S. F. Lin, and W. E. Spicer, Phys. Rev. Letters, 1975, 34,667; P. Nielsen, A. J. Epstein, and D. J. Sandman, Solid State Comm., 1974, 15, 53; A. J. Epstein, N. 0. Lipari, P. Nielsen, and D. J. Sandman, Phys. Rev. Letters, 1975, 34, 914; A. J. Epstein, N. 0.Lipari, D. I.Sandman, and P. Nielsen, Phys. Rev. (B), in the press. 85 R. L. Greene, G. B. Street, and L. J. Suter, Phys. Rev. Letters, 1975, 34,577. Conductivity and Superconductivity in Polymers not show a metal-insulator transition and remains metallic at low temperatures (Figure 23) with a conductivity of 5000 ohm-l cm-l at 1 K. All resistance is Hi FIBER AXIS 1.0-d -0.5 -0 0.2 0.3 0-4 0.5 Figure 23 Superconductivity in poly(suZphur nitride) (Reproduced by permission from Phys.Rev. Letters, 1975,34,557.) lost at 0.26 K and this is proved to be superconduction by the depression of the transition temperature to 0.1 K by a magnetic field of 335 G (the Meissner effects6). This then is the first superconducting polymer but it is inorganic and far from being a room-temperature superconductor. It is a crystalline fibrous material but fully oriented epitaxial thin films of the polymer have been prepared on polyethylene and poly(ethy1ene terephthalate) which should make the material more easily adaptable to useful applications.87 We have seen that certain organometallic polymers can provide a conducting spine and much of the intense interest in KCP and related Krogmann salts has been in search of superconductivity.Indeed platinum complexes of the mixed-valence type bearing cyanine dye ligands have been made but neither these nor truly covalent catenated heteroatomic organometallic systems (Figure 24) have shown superconductivity88 possibly because steric repulsion of the ligands reduces the intermetallic interaction and so reduces carrier mobility.89 Biological polyniers must also be considered. They are well known as semi- J. M. Blatt, ‘Theory of Superconductivity’, Academic Press, 1964, p. 357. A.F. Garito, Physics Todzy, 1975, 28, 17. W.A. Little and J. P. Collman, Final Technical Report AD-769630, 1973. R. Aderjan, D.Baumann, H. Breer, H. Endres, W. Gitzel, H. 5. Keller, R. Lorentz, W.Moroni, M. Megnamisi-Bilombb, D. Nothe, and H. H. Rupp, in ‘Extended Interactions between Metal Ions in Transition Metal Complexes’, ed. L. V. Interrante, Amer. Chem. SOC., Symposium Series No. 5, 1974, p. 314. Goodings Et MIXED VALENCE TYPE (OC)Re -G eM e2-G e Me2-Fe(C0)-Ge Me2-GeMe2-Re(CO)55 4 TRUE COVALENT TYPE Figure 24 Mefal-metal bonded systems conductors90 and it is possible that some are superconductors. Deoxyribonucleic acid (DNA) has a structure resembling Little’s superconductor model but although the poly(sugar phosphate) backbone is periodic, the pendant pyri- midine and purine bases are placed aperiodically. Nevertheless Ladikgl considers from a study of a periodic DNA model that the delocalizedn-electrons from the bases might pair if they interact with the a-electrons functioning as the polariz- able side-chain electrons of Little’s model.Moreover, in the case of the DNA double helix he thinks that the polarization of thew anda-electrons in one chain might give an attractive interaction between the .rr-electrons of the other chain and result in electron ~airing.~~,~~ Thus Ladik believes that it is possible for enhanced conductivity to occur in some regions of DNA at room temperature although this will not amount to normal superconductivity. There is support for the view that certain parts of nerve fibre which have a high concentration of cholesterol are superconductive at physiological tempera- tures.93 Halperng4 found that the diamagnetism of the sodium salts of cholic, desoxycholic, lithocholic, and cholanic acids changed abruptly at 30, 60, 130, and 277 K, respectively, and these are thought to be superconductive transitions in small domains dispersed in the bulk insulating matrix.Goldfeing5 has now D. D. Ely, in ‘Organic Semiconducting Polymers’, ed. J. E. Katon, Edward Arnold, London, 1968, p. 259; E. 0. Forster and A. P. Minton, in ‘Physical Methods in Macro- molecular Chemistry’, ed. B. Carroll, Dekker, New York, Vol. 2, 1972. s1 J. Ladik, G. Biczo, and J. Redly, Phys. Rev., 1969, 188, 710. 92 J. Ladik and A. Bierman, Phys. Letters, 1969, 29A,636. n3 F. W. Cope, Physiol. Chem. and Phys., 1971,3,403; 1974, 6,405. 94 E. H. Halpern, ‘High Temperature Non-metallic Superconductors’, Naval Shipyard R.and D. centre, Annapolis, Maryland, 1973, report 3917. 95 S. Goldfein, Physiol. Chem. and Phys., 1974, 6, 261. Conductivity and Superconductivity in Polymers shown that the transitions are electronic in nature because there is no change in the atomic lattice structure. He also finds that the four bile acid salts obey the empirical rule of MatthiasS6 which applies to superconducting transition-metal alloys, i.e. that Tc is proportional to the average number of valence (outer shell) electrons per atom. This indicates that high-temperature superconducting regions are present in these compounds. Proteins are well known to show semiconductivity, which increases dramatical- ly with the degree of hydration, but the mechanism of conduction is not known.Evidence is now appearing to suggest that proteins also may show super- conductivity. Frohlichg6 has found that a magnetic field of 600 G increases the diamagnetic susceptibility of a 0.01% aqueous solution of lysozyme by a factor of lo4times that expected for ordinary diamagnetic material. An increase in field to 800G destroys the effect by what appears to be a room-temperature Meissner effect. Frohlich thinks that small superconductive regions attached to each enzyme molecule are formed by some process involving water. These regions cluster together and lead to the enormous increase in diamagnetism. These observations hold out the promise that room-temperature super- conductivity will be realized.In biopolymers it is probably restricted to localized domains and so far no high or superconductivity has been observed as a bulk property. But biopolymers may hold the clue to the specification for a true superconducting polymer. Thus so far no organic superconductor has been discovered. The emphasis is on achieving perfect long-rahge order for superconduction but how this could be embodied in a useful polymeric structure is not clear. However, ordered polymer structures exist and even if they are not perfect enough for super- conduction it is certainly possible that they could provide sufficient organization to give metallic conductivity. 10 Conclusions We have seen that polymers with high conductivity can be made. The main problem is to combine this with good processability and this is where stacked- planar systems are superior to conjugated polymers.But even then good mech- anical properties have yet to be achieved. In some way the rigid n-bonded systems must be combined with a conventional a-bonded polymer without destroying its flexibility and tensile properties. The structure will contain a radical-ion system to provide charge carriers but we do not know how to design the polymer structure to give high carrier mobility. Conductive polymers might be expensive to make but this is less important in special applications. There is no doubt that a room-temperature super- conducting polymer would be worth its weight in gold if it provided us with loss-free power transmission and friction-free magnetic bearings.The work on organic superconduction has not failed. It has succeeded in showing that the first step forward must be to understand the organic metallic O6 N. A. G.Ahmed, J. H. Calderwood, H.Frohlich, and C. W.Smith, Phys. Letters, 1975. 53A,129. Goodings state. The second step comes as a challenge to polymer physicists to unravel the relationship between charge-carrier mobility and the supermolecutar structure of polymers. This is most important as without it we cannot progress. Then as the third step chemists will have the opportunity to make a polymer with metallic conductivity and good mechanical properties. That achieved an organic superconductoris more likely to follow. But sciencemust come before technology.

ISSN:0306-0012    

DOI:10.1039/CS9760500095

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

MELDOLA MEDAL LECTURE* Molecular Collisions and the Semiclassical Approximation By J. N. L. Connor DEPARTMENT OF CHEMISTRY, UNIVERSITY OF MANCHESTER, MANCHESTER M13 9PL 1 Introduction An understanding of atomic and molecular collisions is fundamental for gas- phase chemistry. Only binary collisions are important when the gas is not too dense.l They involve the collision of one atom or molecule with a second atom or molecule. Three types of collision can occur in a binary collision, as shown in Figure 1. molecular collisions elastic inelastic reactive Figure 1 Elastic, inehstic, and reactive molecular collisions. The simplest collision process is elastic scattering; it involves a change only in the translational motion of the colliding partners. IneZastic scattering changes the internal state of a particle as a result of the collision and reactive scattering results in a change in chemical species as well.The experimental observables for binary collisions are elastic, inelastic, and reactive collision cross-sections. From them, macroscopic properties of the gas can be calculated such as transport coefficients and reaction rate constants.lv2 The theoretical framework underlying gas-phase chemistry is shown in Figure 2. The starting point involves nuclei, electrons, Coulomb’s Law, and the fundamental constants. From them intermolecular curves and surfaces can be calculated by *Delivered 24 September, 1974 at the Autumn Meeting of the Chemical Society, University of Leicester. R.D. Levine and R. B. Bernstein, ‘Molecular Reaction Dynamics’, Ciarendon Press, Oxford, 1974. a R. E. Weston and H. A. Schwarz, ‘Chemical Kinetics’, Prentice Hall, Englewood Cliffs, 1972. Molecular collisions and the semiclassical approximation the techniques of molecular quantum ~hemistry.~-~ These intermolecular interactions determine the dynamics of the colliding particles.1~7 Next, molecular collision theory is used to calculate collision cross-sections. In favourable cases, theory can be compared directly with experiment at this point. This is the case for collisions of Li+ with H2 for example.8 The final step in Figure 2 involves statistical mechanics to calculate macroscopic properties of the gas. nuclei, electrons, R, e, me molecular quantum chemistry 1 intermolecular potentials collision theory 1 elastic, inelastic, and reactive collision cross-sections statistical mechanics i macroscopic rate phenomena Figure 2 Theoretical framework of gas-phase chemistry.The most direct means for studying the dynamics of molecular collisions are molecular beam,g-l5 laser,16J7 and chemiluminescencels experiments. These experiments have provided a wealth of information and insight that is inaccessible H. F.Schaefer, tert., ‘The Electronic Structure of Atoms and Molecules: A Survey of Rigorous Quantum Mechanical Results’, Addison-Wesley, Reading, Mass., 1972. J. Goodisman, ‘Diatomic Interaction Potential Theory’, Academic Press, New York, 1973 (2 vols.).C. Thomson, Ann.Reports, (A), 1974, 71, 5. G. C. Maitland and E. B. Smith, Chem. SOC.Rev., 1973, 2, 181. M. A. D. Fluendy and K. P. Lawley, Essays in Chem., 1973, 5, 25. J. P. Toennies, Chem. SOC.Rev., 1974, 3, 407. J Schaefer and W. A. Lester, J. Chem. Phys., 1975, 62, 1913. R.J. Cross, Accounts Chem. Res., 1975, 8, 225. loJ. L. Kinsey, in ‘Chemical Kinetics’, ed. J. C. Polanyi, [M.T.P. International Review of Science, Physical Chemistry (Series One), Vol. 91, Butterworths, London, 1972, Ch. 6; J. M. Farrar and Y.T. Lee, Ann. Rev. Phys. Chem., 1974,25,357. l1 M. A. D. Fluendy and K. P. Lawley, ‘Chemical Applications of Molecular Beam Scattering’, Chapman and Hall, London, 1973. la ‘Molecular Beam Scattering’, Faradav Discuss. Chem. SOC.,1973, No.55. l3 J. P. Toennies, ‘Physical Chemistry, An Advanced Treatise’, Vol. VIA, ‘Kinetics of Gas Reactions’, ed. H. Eyring, W. Jost, and D. Henderson, Academic Press, New York, 1974, Ch. 5. See also Vol. VIB. l4 M.A. D. Fluendy, Contemp. Phys., 1975,16, 147. l6 Adv. Chem. Phys., 1975, Vol. 30. 18 ‘Chemical and Biochemical Applications of Lasers’, ed. C.B. Moore, Academic Press, New York, 1974, Vol. 1. l7 K. L. Kompa, Topics Current Chem., 1973, 37, 1 ; M. J. Berry, Ann. Rev. Phys. Chem., 1975, 26, 259. 18 T. Carrington and J. C. Polanyi, in ‘Chemical Kinetics’, ed. J. c.Polanyi, [M.T.P. Inter- national Review of Science, Physical Chemistry (Series One), Vol. 91, Butterworths, London, 1972. Ch. 5. Connor to the traditional kind of ‘test tube’ experiment, since the latter necessarily involves some kind of statistical average of molecular properties, an average that obscures the information being sought (see Figure 2 again).It is well known, for example, that reaction rate-constant data provide weak constraints on any model of the collision itself. Collisions between atoms and molecules are dynamic phenomena and are more difficult to treat theoretically than static properties.19 Consequently theoretical collision dynamics has not achieved the same level of accuracy that is now possible for static chemical properties (such as those of spectroscopy). Nevertheless, important advances have been made in recent years, and inter- pretative and predictive ability is considerable.Theories of molecular collisions can be classified in many ways. A classification suggested by Marcus20 is shown in Figure 3. Dynamical theories involve a solu- molecular collision theories dynamical statistical -dynamical statistical theories theories theories Figure 3 Molecular collision theories. tion of Schrodinger’s equation (quantum dynamics) or Hamilton’s equations (classical dynamics). In contrast, statistical theories avoid the solution of a dynamical problem by statistical assumptions. Transition State Theory as usually formulated is an example of a statistical theory.21 Statistical-dynamical theories treat some degrees of freedom by a statistical approach and the remainder by dynamical models. Dynamical models can be further divided into exact and approximate ones, as shown in Figure 4.dynamical collision theories exact approximate(quantum, classical, (quantum, classical, semiclassical) semiclassical) Figure 4 Dynamical collision theories. l9 A. C. Wahl and C. W. Wilson, ‘Computers in Chemical Research and Education’, Proc. Internat. Conf. Ljubljana/Zagreb, 12-17 July 1973, ed. D. HadZi, Elsevier, Amsterdam, 1973, Vol. 2, p. 41133. 2o R. A. Marcus, Faraday Discuss. Chem. SOC.,1973, No. 55, p. 9. 21 R. A. Marcus, ‘Techniques of Chemistry, Investigation of Rates and Mechanisms of Reactions’, ed. E. S. Lewis, Wiley, New York, 1974, Vol. 6, Part 1, Ch. 2. Molecular collisions and the semiclassical approximation Approximate theories make dynamical approximations, in contrast to exact theories, which do not.Quantal and classical theories solve Schrodinger’s equa- tion and Hamilton’s equations, respectively. The solutions can be analytic or numerical. An exact quanta1 treatment22-24 is always correct but is not feasible in most cases. A purely classical treatment, on the other hand, is feasible for many collision systems.25-29 However, a purely classical calculation can be highly inaccurate with regard to certain features of the scattering. For example, a purely classical treatment cannot account for important tunnelling and interference effects that occur in atom-atom colli~ions.3~-~~ A semiclassical treatment33 constructs an asymptotic or short (de Broglie) wavelength solution to the Schrodinger equation with the help of real-and complex-valued solutions of Hamilton’s equations.Although it uses classical trajectory data as input, semiclassical theories can account for essentially all the ‘quantum effects’ such as diffraction, interference, quantization, quasi-bound states, resonances, selection rules, and tunnelling that purely classical theories miss. This technique of using real- and complex-valued classical trajectories in such a way that quantum effects are correctly accounted for is aptly described by the phrase ‘Sewing quantum flesh on classical bones’.=-37 Complex-valued classical trajectories were introduced into short-wavelength theories in a systematic way by Keller in 1958 in his ‘Geometrical Theory of Diffra~tion’.~~They have subsequently been used in numerous wave-propagation problems.39 The important role of classical trajectories in semiclassical elastic Ira Methods Computer Phys., 1971, Vol.10. as D. J. Kouri, ‘The Physics of Electronic and Atomic Collisions.’ Invited Lectures and Progress Reports, VIII’th ICPEAC, ed. B. C. cobid and M. V. Kurepa, Institute of Physics, Beograd, 1973, p. 529. 24 D. A. Micha, Adv. Chem. Phys., 1975,30, 7. P. J. Kuntz, ‘The Physics of Electronic and Atomic Collisions’. Invited Papers and Progress Reports, VII’th ICPEAC, ed. T. R.Govers and F. J. de Heer, North Holland, Amsterdam, 1972, p. 427. a0 D. L. Bunker, Methods Computer Phys., 1971, 10, 287. J. C. Polanyi and J. L. Schreiber, ‘Physical Chemistry -An Advanced Treatise’, Vol.VIA, ‘Kinetics of Gas Reactions’, ed. H. Eyring, W. Jost, and D. Henderson, Academic Press, New York, 1974, Ch. 6. 28 M. Karplus, ‘Collision Dynamics of Chemical Reactions’, 16 mm Colour Sound Film, Harper and Row, London. R.N. Porter, Ann. Rev. Phys. Chem., 1974, 25, 317. so Sir Harrie Massey, Contemp. Phys., 1973, 14, 497. 31 E. E. Nikitin and M. Ya. Ovchinnikova, Uspekhi jiz. Nuuk, 1971, 104, 379 (Soviet Phys. Uspekhi, 1972, 14, 394). 33 U. Buck, Adv. Chem. Phys., 1975, 30, 313. Some theories treat the internal motion quantum mechanically and the translational motion classically. These ‘classical path theories’ are included in the quantum category in this review. They are sometimes also called ‘semiclassical theories’. 34 B.E. Kimber, adapted from a quotation in refs. 35-37. s6 Yu. A. Kravtsov, Izvest. V.U.Z. Radio&., 1967, 10, 1283. (Radio. Phys. Quanr. Elec-tron., 1967, 10, 719). 3* Yu. A. Kravtsov, Akust. Zhur., 1968, 14, 1 (Sovier Phys. Acoust., 1968, 14, 1). a7 M. V. Berry and K. E. Mount, Reports Progr. Phys., 1972, 35, 315. 118J. B. Keller, Proc. Symp.Appl. Math., 1958, 8, 27. See for example ‘Special Issue on Rays and Beams’, Proc. Z.E.E.E., 1974, 62, No.11. 128 Connor scattering was emphasized by Smith40 and Berry,41 following on from the pioneering researches of Ford and Wheeler in 1959.42 Applications to inelastic and reactive molecular collisions started in 1970 due to the efforts of Millel”13 and Marcus.& This review will describe some recent applications of semiclassical mechanics to elastic, inelastic, and reactive molecular collisions.One example of each type of collision will be described, believing that this is more valuable than a discussion of many examples in a more cursory manner. No derivations of equations will be presented; instead, some important features will be pointed out. Of particular note will be the way the theory depends on the topological structure of families of real- and complex-valued classical traje~tories.~~ For further information on semiclassical mechanics the book by Childg6 and the reviews referred to below are recommended. A large number of references on semiclassical collision theory can be found in some recent literature surveys.47-49 Asymptotic approximations are commonly used in physical calculations (often without realizing it).They are usually very accurate, frequently more so than one would expect. As an example, consider Stirling’s asymptotic approximation for the Gamma (factorial) function9 r(x) N (277)f xz-* e-z widely used in statistical mechanics. Table 1 shows that this approximation is valid for x % 1, but even for x = 1 or 2 (which are not usually thought of as large numbers) it compares favourably with the exact result. A similar situation holds in semiclassical theories of molecular collisions.51 A general condition for the validity of short-wavelength theories is S % k, where S is a classical action variable, but in practice good results are often ob- tained when S z k, and in some cases the exact answer is pr0duced.~2 Action variables were used in the Old Quantum The~ry,~~-~~ for example the Bohr-40 F.T. Smith, J. Chem. Phys., 1965, 42, 2419. 41 M. V. Berry, Proc. Phys. Soc., 1966, 89,479. 48 K. W. Ford and J. A. Wheeler, Ann. Phys., 1959, 7,259, 287. 4s W. H. Miller, J. Chem. Phys., 1970, 53, 1949. 44 R.A. Marcus, Chem. Phys. Letters, 1970, 7, 525. 46 M. V. Berry, Sci.Progr., 1969, 57,43. 48 M. S. Child, ‘Molecular Collision Theory’, Academic Press, London, 1974. 47 T. F. George and J. Ross, Ann. Rev. Phys. Chem., 1973, 24,263. 48 D. Secrest, Ann. Rev. Phys. Chem., 1973, 24, 379. IsJ. N. L. Connor, Ann. Reports (A), 1973, 70, 5. 6o F. W. J. Olver, ‘Asymptotics and Special Functions’, Academic Press, New York, 1974, p.88. s1 I. C. Percival, ‘Atomic Physics’, Vol. 2, ed. P. G. H. Sandars, Plenum Press, New York, 1971, p. 345. 63 A. Norcliffe, Case Studies Atom. Phys., 1973, 4, No. 1. 63 M. Born, ‘The Mechanics of the Atom’, translated from the German by J. W. Fisher and revised by D. R. Hartree, Ungar Publishing, New York, 1960. O4 M. Jammer, ‘The Conceptual Development of Quantum Mechanics’, McGraw-Hill, New York, 1966. 66 F. Hund, ‘The History of Quantum Theory’, Harrap, London, 1974. Molecular collisions and the semiclassical approximation Table 1 Stirling’s approximation for the Gamma function as an example of an asymptotic approximation X 1 m)1.00000 x 100 (277)*xz-* e-2 0.92214 x 100 2 1.00000 x 100 0.95950 x 100 3 2.00000 x 100 1.94540 x 100 4 6.00000 x 100 5.87654 x 100 5 2.40000 x 101 2.36038 x 101 6 1.20000 x 102 1.18346 x lo2 7 7.20000 x 102 7.11485 x 102 8 5.0400o x 103 4.98780 x 103 9 4.03200 x 104 3.99485 x 104 10 3.62880 x lo5 3.59870 x 105 20 1.21645 x 1017 1.21139 x 1017 30 8.84176 x 1030 8.81724 x lO3O 40 2.03979 x 1046 2.03554 x 1046 50 6.08282 x 10c2 6.07269 x 1062 Sommerfeld quantization condition which is the basis of the very accurate Rydberg-Klein-Rees method of molecular spectro~copy,~~ and other examples of action variables are described in the following sections.In the development of molecular collision theory, an important role has been played by certain canonical models of the collision process.49 These replace the actual (complicated and possibly unknown) intermolecular potential by a simpler one. In addition, the three-dimensional space in which the collision occurs is often reduced to two dimensions (planar) or one dimension (linear).This removes some degrees of freedom from the problem and simplifies the theoretical treat- ment. Table 2 lists a few of these canonical models for collisions involving a single potential energy surface (electronically adiabatic approximation). The three examples of semiclassical mechanics considered in the following Sections make use of the canonical models in Table 2. This is so that some important features of the collision are established as clearly as possible. Section 2 considers quasi-bound states in the elastic scattering of two atoms and the topic of complex eigenvalues.In Section 3, the interaction of a Morse oscillator with an atom is considered as an example of an inelastic collision, whilst Section 4 is devoted to reactive scattering and the definition of tunnelling. In every case the semiclassical results are compared with exact quantum ones to illustrate the good agreement that can be obtained (typically within a few per cent). It should be noted that exact quantum results are, in general, only available for simple systems of the kind in Table 2. Conclusions are in Section 5. 2 Elastic Collisions: Quasi-bound States and Complex Eigenvalues Quasi-bound states arise in the elastic scattering of two atoms in the following way.Consider the radial Schrodinger equation for the collision :37s46 E. A. Mason and L.Monchick, Adv. Chem. Phys., 1967, 12, 3B. Connor Table 2 Canonical models for molecular collisions Collision process Canonical model Elastic scattering Lennard-Jones (12, 6) potential Vibrationally inelastic collision Collinear collision of atom and a harmonic oscillator with exponential repulsion Rotationally inelastic collision Atom-rigid rotator collision with a Lennard-Jones (12, 6) and ~z(cos6) interact ion Reactive collision Collinear atom-molecule collision on the Porter-Karplus potential- energy surface where I is the orbital angular momentum quantum number, p is the reduced mass of the system, and E is the collision energy.Typically, the potential- energy curve V(r) has a long-range attraction and a short-range repulsion; a well known example is the Lennard-Jones (12, 6) potential (see Table 2): where rm is the distance at which the well depth is E. Now for a certain range of I values, the effective potential Vz(r) defined by: V&) = V(r)+ h21(1 + 1)/2pr2 (3) can have a barrier in addition to a well. This is illustrated in Figure 5. The barrier may support quasi-bound states; these states have a finite lifetime because they can decay by tunnelling through the barrier, unlike true bound states which have an infinite lifetime. Other names for quasi-bound states are ‘shape resonances’ (from the shape of the effective potential) and ‘orbiting states’ because classically the particles orbit around each other when the collision energy is close to the barrier maximum.Quasi-bound states play an important role in a number of phenomena. These include : (a) rotational predissociation of diatomic molecule~~~~~8 (b) long-range interatomic forces59 G7 M. S. Child, ‘Molecular Spectroscopy’, ed. R. F. Barrow, D. A, Long, and D. J. Millen (Specialist Periodical Reports), The Chemical Society, London, 1974, Vol. 2, Ch. 7. Is W. C. Stwalley, J. Chent. Phys., 1975, 63, 3062 69 R. J. Le Roy, ‘Molecular Spectroscopy’ ed. R. F. Barrow, D. A. Long, and D. J. Millen, (Specialist Periodical Reports) The Chemical Society, London, 1973, Vol.1, Ch. 3. Molecular collisions and the semiclassical approximation Figure 5 Origin of quasi-bound states in the elastic scattering of two atoms. a, b, and c are classical turning points. (c) elastic and inelastic scattering e~periments~0-~3 (d) three-body recombination reaction~~t~~ (e) low-temperature transport property of gases66 (f)Penning ionization67 (g)pressure-induced absorption spectra of gases68 A quasi-bound state can be characterized by the boundary conditions:69 *CO) = 0 N$(r) outgoing wave only (4) r+m 6o J. P. Toennies, W. Welz, and G. Wolf, J. Chem. Phys., 1974, 61, 2461. 61 A. Schutte, D. Bassi, F. Tommasini, and G. Scoles, J. Chem. Phys., 1975, 62, 600. 6B J. G. Maas, N. P. F. B.Van Asselt, and J. Los, Chem. Phys., 1975,8, 37. O3 P. D. Gait, Chem. Phys. Letters, 1975,35, 72. 64 R.T.Pack, R. L. Snow, and W. D. Smith, J. Chem. Phys., 1972, 56,926. P. A. Whitlock, J. T. Muckerman, and R. E. Roberts, J. Chem. Phys., 1974, 60, 3658. R.A. Buckingham and E. Gal, Adv.Atom. Mol. Phys., 1968, 4,37. O7 R. J. Bieniek, J Phys. (B), 1974,7, L266. G.E.Ewing, Accounts Chem. Res., 1975,8, 185. 'CIV. de Alfaro and T. Regge, 'Potential Scattering', North Holland, Amsterdam, 1965. Connor The outgoing wave at infinity, with no incoming wave, is in accord with the idea of a quasi-bound state decaying by tunnelling through the barrier. The boundary conditions (4) have the important mathematical consequence that they give rise to a complex eigenvalue problem.69 When 1 is restricted to (physical) integer values, the energy becomes complex- valued, and its eigenvalues can be written: En = 8,-i&rn, &'n > 0, rn> 0;n = 0,1,2,.. . (5) where 8n is the resonance energy and rnthe resonance width. The physical interpretation of rnfollows from the time evolution factor for the wavefunction: lexp(- iEnt/h)(Z = exp(-rnt/h) (6) Equation (6) shows that the system decays exponentially in time, with a 'life- time' 7%= h/T'n. A long-lived state corresponds to a small r,and a short-lived one to a large rn. Equation (5) gives the complex eigenvalues for the Schrodinger equation (1) that satisfy boundary conditions (4). An alternative possibility consistent with these boundary conditions is to keep E real and allow the angular momentum to become complex-valued. Its eigenvalues can be written : In = In(') + ilnci), In(') > 0, > 0;n = 0,1, 2, .. . (7) The complex eigenvalues (7) are called 'Regge Poles' (so called because the Scattering matrix takes the form: S = m/(l -Zn) close to a pole Zn, where m is its residue).69 The physical interpretation of follows from the fact that the system decays exponentially with scattering angle 8 according to exp(- In(i) 8). The quantity l/ln(i)can be defined as the 'angular life' of the system.69 For a long-lived state which orbits many times before decaying ln(i)is small whereas for a short-lived one Zn(i) is large. It can be seen that complex angular momentum and scattering angle are conjugate variables analogous to complex energy and time.When the Schrodinger equation (1) is solved semiclassically, the solution is of the form:37946 where 2pr (9) The appearance of (I + *)2 instead of &I + 1) in equation (9) is the Langer substitution.37.70 Provided h(Z + 4) is identified with the classical angular 7e R. E. Langer, Phys. Rev., 1937, 51,669. Molecular collisions and the semiclassical approximation momentum, p(r) is the classical radial momentum, except that it can take on complex values instead of being restricted to being purely real. It can be seen that the semiclassical wavefunction (8) possesses the important property that it is composed of (real-or complex-valued)classical dynamical quantities.The semiclassical approximation (8) is clearly not valid close to real or com- plex points where P(r>= 0 (10) because there the solution ‘blows up’. Points satisfying equation (10) are usually called ‘turning points’ or ‘transition points’ (see Figure 5). A major problem in semiclassical mechanics is to connect the solution valid on one side of a turning point with the solution valid on the other side. Figure 5 is an example showing three turning points. To overcome the connec-tion problem mentioned above, the semiclassical wavefunction in the neighbour- hood of turning point ‘a’ can be mapped onto the solution of the Schrodinger equation for a linear potential (the solution involves the Airy function).37.46971 The turning points ‘b’ and ‘c’ can come close together or coalesce, and a unforrnly valid treatment requires that the semiclassical wavefunction be mapped onto the solution of the Schrodinger equation for a parabolic barrier (the solution involves Weber parabolic cylinder functions this time).37*46*71 In this way, the semiclassical wavefunction for equation (1) that satisfies boundary conditions (4) can be constructed.The semiclassical eigenvalue equation is found to be:72-77 a(E,Zn) = (n + 8)~ i [ r(8-ic) 1+ &[E -cln(-c)] -iln (27r)* exp(m/2) (1 1) where fia(E,In) = p(E,In ;r) dr1 is the classical action integral associated with the well and C -fin~(E,ln) = i Jr p(E, In; r) dr b is the one for the barrier. Equation (11) is also valid for the complex energy eigenvalues provided the replacements E -En and In -I are made.The quantization formula (1 1) again involves only classical dynamical quanti- 71 S. C. MilIer and R. H. Good, Phys. Rev., 1953, 91, 174. 78 J. N. L. Connor, Mol. Phys., 1968, 15, 621; ibid., 1969, 16, 525. 73 J. N. L. Connor, Mol. Phys., 1972. 23, 717. 74 J. N. L. Connor, Mol. Phys., 1973, 25, 1469. 7s J. B. Delos and C. E. Carlson, Phys. Rev. (A), 1975, 11, 210. 7* C. V. Sukumar and J. N. Bardsley, J. Phys (B), 1975, 8, 568. 77 C. V. Sukumar, S. L. Lin, and J. N. Bardsley, J. Phys. (B), 1975, 8, 577. Connor ties, namely the two complex-valued action integrals ha and hm. The form of equation (11) is characteristic of two turning points (which may be nearly co- incident), both of them being well separated from the third one.Limiting cases of equation (1 l), when all three turning points are well separated from each other, are of interest. When ~TEis large in magnitude (in terms of Figure 5 this corresponds to the energy being well above the barrier), equation (1 1) simplifies to : C a This is a Bohr-Sommerfeld quantization condition for the positions of the Regge Poles fn. The simpler form of equation (14) compared with the more general equation (1 1) reflects the simpler turning-point distribution in this case. Table 3 compares equation (14) with exact quantum results for the Lennard- Jones potential (2).78The parameters approximate elastic scattering of K by HBr.79 The agreement is seen to be excellent.Table 3 Exact quantum and semicIassicaI Regge Pole positions for a Lennard- Jones (1 2, 6) potentiala Quantum@ Semiclassicalb I \7I n Re fn Im In Re ln Im In 0 180.012 21.219 180.015 21.218 1 179.239 24.035 179.242 24.034 2 178.522 26.890 178.526 26.889 3 177.866 29.780 177.869 29.779 4 177.272 32.700 177.275 32.699 5 176.742 35.645 176.745 35.644 6 176.277 38.609 176.279 38.608 7 175.877 41.588 175.880 41.587 8 175.544 44.576 175.547 44.575 9 175.276 47.568 175.279 47.567 a Parameters in equations (1) and (2) are E = 2.0 x lO-*O J, p = 4.377 x g, E = 4.0 x J, rm = 4.0 x m. These values correspond approximately to K + HBr elastic scattering.See R. B. Bernstein and R. D. Levine, J. Chem. Phys., 1968, 49, 3872;b J. N. L. Connor, W. Jakubetz, and C. V. Sukumar (unpublished results). The semiclassical results are calculated from equation (14). Another interesting limiting case arises when the energy in Figure 5 is well below the barrier maximum. The quantization formula (11) simplifies to (for the complex energy eigenvalues this time) :72-74 J. N. L. Connor, W. Jakubetz, and C. V. Sukumar (unpublished results). '@R. B. Bernstein and R. D. Levine, J. Chern. Phys., 1968,49, 3872. 135 Molecular collisions and the semiclassical approximation and Equation (15) is a Bohr-Sommerfeld quantization formula for the resonance energy gnin which 4is a small term giving rise to a level shift In equation (16) for the resonance width, w is the classical angular frequency of oscillation in the well.In deriving equations (15) and (16), advantage has been taken of the fact that rnis small (corresponding to a long-lived quasi- bound state), with the consequence that the action integrals become real-valued. Table 4 shows some resonance energies and widths calculated from equations Table 4 Some exact quantum and semiclassical resonance energies and widths for a Lennard-Jones (12, 6) potentiala-Quantumb SerniclassicaIC 7 I 1 1 118 gn 0.31004 r, 1.2 x 10-17 gn 0.31003 rnd7e 1.21 x 10-17 197 0.31008 9.6 x 0.31007 9.36 x 25 0.34862 6.0 x 10-4 0.34846 6.00 x 10-4 77 0.34935 6.9 x 10-8 0.34938 6.89 x 10-8 128 0.35007 2.0 x 10-11 0.35007 2.02 x 10-11 123 0.3896 1 8.4 x 10--5 0.38962 8.64 x 10-5 87 0.39009 4.2 x 10-4 0.39008 4.22 x 10-4 137 0.40233 3.4 x 10-3 0.4025 3.20 x 10-3 a The potential parameters are given by R.B. Bernstein, C. F. Curtiss, S. Imam-Rahajoe, and W. T. Wood, J. Chem. Phys., 1966,44,4072; b R. A. Bain and J. N. Bardsley, J. Chem. Phys., 1971, 55, 4535; C A. S. Dickinson, Mol. Phys., 1970, 18, 441. The semiclassical results are calculated from equations (15) and (16); Resonance energies and widths are expressed as a fraction of the well depth; e These values are more accurate than in the original paper of A. S. Dickinson, Mol. Phys., 1970, 18, 441 and are reported by M. S. Child ‘Molecular Spectroscopy’, ed.R.F. Barrow, D. A. Long, and D. J. Millen (Specialist Periodical Reports), The Chemical Society, London, 1974, Vol. 2, Ch. 7. (15) and (16) for the Lennard-Jones (12, 6) potential (2) compared with exact quantum result^.^^^^^ The agreement is again seen to be excellent. Equation (16) for the widths is based on the approximation that rnis small. Table 5 compares equation (16) with exact quantum res~lts5~381 for the broad quasi-bound states of ground-state H2. (These calculations use the very accurate A. S. Dickinson, Mol. Phys., 1970, 18, 441. a1 R. J. Le Roy and R. B. Bernstein, J. Chenz. Phys., 1971, 54, 51 14. Connor Table 5 Exact quantum and semiclassical resonance widths for the Hz ground statea n 1 Qaantum r,,blcm -1 Semic Iassicald r, C/cm-l 11 14 17.9 19.2 8 21 39.4 38.2 7 23 30.4 31.6 6 25 26.5 27.8 5 27 25.1 26.4 4 29 24.7 25.8 3 31 23.6 24.5 2 33 20.4 21 .o 1 35 14.1 14.3 0 38 80.O 64.4 a Adapted from M.S. Child ‘Molecular Spectroscopy’, ed. R. F. Barrow, D. A. Long, and D. J. Millen (Specialist Periodical Reports), The Chemical Society, London, 1974, Vol. 2, Ch. 7; b R. J. Le Roy and R. B. Bernstein, J. Chem. Phys., 1971, 54, 5114; c Calculated from equation (16); Less accurate values were reported in Table 2 of ref. 49. potential -energy curve of Kolos and Wolniewicz82). There is good agreement even though the widths are relatively large, and equation (16) might be thought to be invalid.To summarize this section: it has been shown how quasi-bound states can be characterized by complex energy or complex angular-momentum eigenvalues. The semiclassical eigenvalue equations involve only real- or complex-valued classical dynamical quantities. The agreement with exact quantum results is very good. 3 Inelastic Collisions: Collinear Collision of an Atom with a Morse Oscillator An inelastic collision is the next example of semiclassical mechanics to be considered. The model is that of a collinear collision of an atom with a Morse 0scillator~3-~~(cf Table 2). An exponential repulsion between the atom and the end of the molecule is assumed. The oscillator is initially in quantum state n and the problem is to calculate the probability that the oscillator is in a quantum state rn after the collision.In the quasi-bound system discussed in Section 2, the distribution of classical turning points played an important role in the semiclassical analysis. It is instructive to consider the turning-point distribution in the present case. An inelastic collision is more complicated than the previous example because, sB W. Kolos and L. Wolniewicz,J. Chem. Phys., 1964, 41, 3663; ibid., 1965, 43, 2429; ibid., 1968, 49, 404. 83 A. P. Clark and A. S. Dickinson, J. Phys. (B), 1973, 6, 164. J. N. L. Connor, Mol. Phys., 1974, 28, 1569. R. Schinke and J. P. Toennies, J. Chem. Phys., 1975, 62,4871. *6 J. W. Duff and D. G. Truhlar, Chem. Phys., 1975,9,243. Molecular collisions and the semiclassical approximation in addition to the radial co-ordinate R, the oscillator co-ordinate q must also be considered.The classical Hamiltonian for the collision (in reduced units) is :a H = (2P)-'pR2 f ipq2 4-vM(q) 4-v(R,4) (1 7)=E where p~ and pq are the classical momenta conjugate to R and q, respectively, and E is the total energy. VM(q) is the Morse oscillator potential: Vidq) = D (exp[-q/(20)*]-1 l2 (1 8) and V(R,q) is the exponential interaction between the atom and the oscillator: V(R,q) = exPL:-4R -dl (19) Figure 6 shows some classical trajectories in (R, q) space for the Hamiltonian (17) calculated by numerical integration of Hamilton's equations on a computer.84 The collision starts and finishes at a value of R sufficiently large that the inter- action V(R,q) is negligible.The parameters for the collision correspond approxi- mately to a collision between He and H2.83-86 I 1 1 II Connor The turning points of the oscillator (q motion) and that of the incoming atom (R motion) can be seen clearly. Figure 6 implies that, in a semiclassical analysis, using (pq,q) as variables for the oscillator will cause difficulties because of the singular behaviour of semiclassical wavefunctions at turning points [see equa- tion (S)]. Another important problem that arises in a semiclassical calculation of a transition probability Pmenis ‘What is the classical equivalent of a quantum number?’. These problems can be overcome by using action-angle variablesa7(J, w) for the oscillator instead of (pq,9).Figure 7 shows the same collision as in Figure 6 1 1 II I -2 0 2 4 6 8 10 R Figure 7 Same collision as in Figure 6, but plotted in (R, w) space. The Hamiltonian for the collision is defined by equations (21)--(23). but plotted in (R, w) space.84 It is immediately clear that the turning points in the oscillator motion have been eliminated, and only one in the R motion remains. The connection between action variables and quantum numbers is found by applying the Bohr-Sommerfeld quantization relation to the oscillator [cf. equa-tions (14) and (IS)]. Because of this relation, it is convenient to repiace J by a (continuous) classical variable ii (the ‘quantum number variable’) defined by:ug88 H.Goldstein, ‘Classical Mechanics’, Addison-Wesley, Reading, Mass., 1950, p. 288. R. A. Marcus, J. Chem. Phys., 1971, 54, 3965. 139 Molecular collisions and the semiclassical approximation In terms of (ii, w), the classical Hamiltonian for the collision becomes:84 H = (2pI-l p~~ + E(E) + V(R,q) (21)=E where the Morse oscillator energies are: €(ii)= (ii + 4) -(40)-1(ii + g)z (22) and q is related to w by: q = (2W {h[l + (E/D)+cos(~~~)]-ln[l -(~/0)]} (23) It is interesting to note that in the Old Quantum Theory action-angle variables were called 'uniformizing variable^'.*^ Table 6 summarizes the main properties of action-angle variables that are useful in semiclassical calc~lations.43@~~~ Table 6 Properties of action-angle variables useful in semiclassical calculations 1. Use of action-angle variables removes singularities in the unperturbed semiclassical wavefunction for the internal states.2. The action variables bear a simple (Bohr-Sommerfeld) relation to quantum numbers. 3. Initial angle variables occur in [0, 11. A transition probability Pm,-ninvolves the oscillator initially in a state n and finally in a state m. Now the final value of the quantum number variable ii depends on the initial value of the angle variable (phase) of the oscillator wo. This is illustrateds4 in Figure 8 for the collision already shown in Figures 6 and 7. The final 5 versus initial w0 plot is seen to have a simple sinusoidal shape. Consider now the elastic transition 4 -4.It is clear from Figure 8 there are two values of wo (called wl0 and w2O) such that the final value of ii is 121 = 4. The two values of w0 occur where the horizontal line tn = 4 intersects the Fz(wo) curve. The simplest semiclassical approximation for the transition probability is :43,44,84,88 pgy5 = p1 + p2 where is the classical probability associated with each individual trajectory contribut- ing to the transition n --t m and is found from the slope of the curve in Figure 8. The primitive semiclassical approximation is an asymptotic one that assumes that the two contributing trajectories are well separated from one another :43,44,88 N. Bohr, 'On the Application of the Quantum Theory to Atomic Structure', Supplement to Proc.Cambridge Phil. SOC.,1924, p. 4. I I I 1 I p2Pr;ive = pi + p2 + 2(pip2)+sin(Az -Ai) (26) where the classical phase: dt -I R(t)pR(t)dt + &T (27) tb rb is evaluated along each contributing trajectory from initial time to to a final time t. The last term in equation (26) gives rise to an interference effect. Since the average of this term is zero, the primitive approximation (26) oscillates about the classical result (24). This interpretation of equations (24) and (26) is the same as that for the famous ‘two slit’ experiment often discussed in books on quantum mechanics. O0 R. P. Feynman and A. R. Hibbs, ‘Quantum Mechanics and Path Integrals’, McGraw-Hill, New York, 1965, Ch. 1. Molecular collisions and the semiclassical approximation The primitive approximation (26) breaks down when the two contributing trajectories come close together because pi -co.This catastrophic behaviourgl can be removed by using a uniform Airy approximation that is valid regardless of whether the trajectories are close together or far apart :92993 )Pzrff = dpi* + pzi)2 x3 Ai(-x) + r(pli -~2 x-*~Ait2(-~x) (28) where x = CHd2 -A1113 (29) and Ai is the regular Airy function (already mentioned in Section 2).When the trajectories are well separated, equation (28) reduces to the primitive approxima- tion (26).92993 Finally, equation (28) requires for its validity that the amplitude of the E versus w0plot be large. When the amplitude is small, a uniform Bessel approxima- tion can be derived for this case:94 CcOse+ &r(pl+ -p2*)2~k/2(5) <lcOs~PE:;~ = +r(pl* + p23)2~k2(5) (30) where (52 -k2)+ -kcos-l(k/<) = +(A2 -dl) and cod = [l -(k/L32]i , k = Im -n1 (31) Equation (30) reduces to the Airy approximation (28) when the amplitude in the E versus w0 plot becomes large.94~95 The structure of equations (24)-(3 1) is interesting.Their validity increases in the order classical -primitive ---f Airy -Bessel for the results discussed below, but so does the complexity of the equations. In each case, however, they involve only (real-valued) classical dynamical quantities, namely the pi and Ar. Consider next the transition 4 -+3 in Figure 8. It is clear there are no real values of wosuch that the equation: E(w0) = 3 (32) is satisfied.Thus the transition is dynamically forbidden in classical mechanics even though it is energetically allowed. The 4 -3 transition is an example of a ‘classically forbidden’ transition, in contrast to the 4 -4 one which is ‘classically allowed’.43.44 The classical approximation for this transition would be simply zero : The use of the word ‘catastrophic’ is deliberate. Application of ‘Catastrophe Theory’ to the classical and semiclassical mechanics of molecular collisions leads to a deep under- standing of their inter-relationship (J. N. L. Connor, ‘Catastrophes and Molecular Col- lisions’, Mul. Phys., in the press). 92 J. N. L. Connor and R. A. Marcus, J. Chem. Phys., 1971, 55, 5636. 93 J. N. L.Connor, Mol. Phys., 1973, 25, 181. O4 J. R. Stine and R. A. Marcus, J. Chrm. Phys., 1973, 59, 5145. O6 J. N. L. Connor, Chem. Phys. Letterb, 1974, 25, 61 1. Connor pizqsical --0 In semiclassical mechanics, however, complex values of wo satisfying equation (32) must also be considered. Such complex solutions of equation (32) do indeed exist, and can be used to integrate Hamilton’s equations, in which the co- ordinates, momenta, and time become complex-valued during the collision. Figure 9 shows a plot of Re E against Im ii for the transition 4 -+ 1 of Figure 8.84 1 Im 7i 0 Re 6 I-1 -2 -3 -4 Figure 9 Plot of Re ii against Tm ii for the transition 4 + 1 of Figure 8. The collision parameters are the same as in Figures 6-8.The expressions for the transition probabilities for classically forbidden transi- tions are the appropriate extensions of equations (25)-(31) in which the pi’s and di’sbecome complex-valued84 [cf. equations (11)-(14) of Section 21. Table 7 compares a few exact quantum results83 with the various semiclassical appro~imations.8~The uniform Bessel approximation (30) is generally in very good agreement with the quantum results, although the Airy approximation (28) is of comparable accuracy for inelastic transitions. The primitive approxima- tion is generally less accurate than either the Airy or Bessel approximations. More advanced reviews of the semiclassical mechanics of inelastic (and reac- tive) collisions have been written by Miller96-gs and Child,99 where further 98 W.H. Miller, Adv. Chem. Phys., 1974, 25, 69. 9i W. H. Miller, ‘The Physics of Electronic and Atomic Collisions.’ Invited Lectures and Progress Reports, VIII’th ICPEAC, ed. B. C. CobiC and M. V. Kurepa, Institute of Physics,Beograd, 1973, p. 503. g8 W. H. Miller, Adv. Chem. Phys., 1975, 30, 77. M. S. Child, ‘Modern Theoretical Chemistry’, Vol. 3, ‘Dynamics of Molecular Col- lisions’, ed. W. H. Miller, Plenum Press, New York, 1976. 4 z%' Table 7Some exact quantum and semiclassical transition probabilities for collinear He-H2 collisions when E = 6a gQ&Transition Classicalbsc Primitiveb Airyb Besselb Quantum6 5mn-tm 4-4 0.504 x loo 0.985 x 100 0.892 x 100 0.818 x 100 0.818 x 100 !i4+3 0 0.173 x loo 0.122 x 100 0.117 x 100 0.117 x 100 4-2 0 0.634 x 0.584 x 10-2 0.566 x 10-2 0.564 x 12h 4-1 0 0.141 x 0.135 x 10-3 0.132 x 10-5 0.138 x 10-3 0' '5.5-5 0.828 x 100 1.402 x 100 1.124 x 100 0.925 x 100 0.925 x 100 85-6 0 0.155 x 10-1 0.142 x 10-1 0.130 x 10-1 0.130 x 10-1 35-+4 0 0.762 x 10-1 0.634 x 10-1 0.597 x 10-1 0.597 x 10-1 5-3 0 0.220 x 10-2 0.207 x 10-2 0.199 x 10-2 0.198 x s.5-2 0 0.461 x 0.445 x 10-4 0.433 x 10-4 0.456 x Pg aJ. N. L. Connor, Mol. Phys., 1974,28, 1569; Semiclassical results are calculated from equations (24)-(31) when the transition is classically allowed. For equations in the classically forbidden case see the reference in footnote (a);C Classical transition probabilities that are identically zero are classically forbidden transitions; d A.P. Clark and A. S. Dickinson, J. Phys, (B), 1973, 6, 164. Connor references can be found together with those in the literature surveys of refs. 4749. To summarize this section: it has been shown how action-angle variables play an important role in applying semiclassical mechanics to inelastic collisions. Classically forbidden transitions can be treated with the help of complex-valued solutions of Hamilton’s equations. Very good agreement with exact quantum results can be obtained. 4 Reactive Collisions: Collinear H + H2 Reaction The final example of semiclassical mechanics to be considered is the collinear exchange reaction : H + H2 (n = O)+Ha (m= 0) + H (33) in which the reactant and product molecules are in their ground vibrational states. The potential-energy surface used for the reaction is the one of Porter and Karplus100 (cf.Table 2). This has a barrier height of z 38 kJ mol-l, and since the zero-point energy of H2 is z 26 kJ mol-l there is a barrier of z 12 kJ mol-1 to reaction. The system can tunnel through the barrier to form reaction products in a way similar to the decay of a quasi-bound state discussed in Section 2. This tunnelling region is an interesting one because it dominates the thermal energy kinetics. In a semiclassical framework, tunnelling is a classically forbidden process that can be treated by complex-valued classical trajectories. Since the semiclassical theory is similar to that for the non-reactive inelastic collision of Section 3, only the results will be described.The calculations discussed below were carried out by Miller and co-workers.101-103 Figure 10 shows the semiclassical reaction transition probability PRoc o together with the exact quantum results.lM The agreement between the two over ten orders of magnitude is impressive. Figure 11 shows the same results on a linear scale, together with the transition probability obtained in a classical Monte-Carlo (real-valued) trajectory calcula- tion.lO5 Figure 11 is useful for discussing the concept of tunnelling in systems with many degrees of freedom.101J02 It is necessary to have a procedure that defines tunnelling, since in an exact quantum-mechanical calculation no distinction is made between it and non-tunnelling processes.From the examples discussed in Sections 2 and 3, it should be clear that, in semiclassical mechanics, tunnelling is a classically forbidden process that uses complex-valued classical trajectories in its description. loo R. N. Porter and M. Karplus, J. Chem. Phys., 1964, 40, 1105. lol T. F. George and W. H. Miller, J. Chem. Phys., 1972, 56, 5722. lo2 T. F. George and W. H. Miller, J. Chem. Phys., 1972, 57, 2458. Io3 S. M. Hornstein and W. H. Miller, J. Chem. Phys., 1974, 61, 745. lo* See J. W. Duff and D. G. Truhlar, Chm. Phys. Letters, 1973, 23, 327, and references therein. IoG D. J Diestler and M. Karplus, J. Chem. Phys., 1971, 55, 5832. Molecular collisions and the semiclassical approximation 10-4 lo-' 10-l0 5 10 15 20 E&J mol-' Figure 10 Reaction probability P&, for the ground-state to ground-state H + Ha --+ H2+ H coilinear reaction on the Porter-Karplus surface as a function of the relative collision energy Eo.The solid line (QM) is the exact quantum mechanical result (see J. W. Duffand D. G. Truhlar, Chem. Phys. Letters, 1973, 23, 327) and the dotted line (SC) is the semiclassical result (S. M. Hornstein and W. H. Miller, J. Chem. Phys.,1974, 61, 745). For the transition probability curves in Figure 1 1, complex-valued trajectories occur up to an energy of z 22 kJ mol-1. There is thus a considerable amount of tunnelling in this system. Another definition of tunnelling compares the results of a classical Monte- Carlo calculation with the exact quantum ones.From Figure 11, the Monte-Carlo threshold is z 21 kJ mol-1, so again there is a considerable amount of tunnelling, though less than in the semiclassical definition. There is a difficulty with the Monte-Carlo definition, however. The usual 146 Connor 0.6 0.5 0.4 /PRO+O 0.3 0.2 0.1 0 14 16 18 20 22 E,-,/kJ mol-I Figure 11 Same as Figure 10 except that the ordinate is shown on a linear scale. The dashed line (CL) is the classical Monte-Carlo result (D. J. Diestler and M. Karplus, J. Chem. Phys., 1971,55, 5832). Monte-Carlo method assigns an initial quantum number to the oscillator and averages over its initial phase. This results in a continuous range of E values for the products (cf.Figure 8). To quantize these classical trajectories, they are assigned to ‘boxes’ labelled by the closest integer value of ii. Although reasonable, this method of ‘quantizing’ classical trajectories is nevertheless an arbitrary one, 147 Molecular collisions and the semiclassical approximation and other ‘quantization’ methods1°6-108 produce different thresholds for the reaction and hence different amounts of tunnelling. These difficulties do not arise in the semiclassical theory, where quantization is unambiguous and tunnel- ling is associated with complex-valued classical trajectories. The definitions discussed above are dynamic ones, i.e. tunnelling is defined as something that does not occur according to (real-valued) classical dynamics.In contrast, an energetic definition can be used. According to this, tunnelling occurs if the collision energy is less than the barrier height. As already mentioned, the barrier to reaction on the Porter-Karplus surface is z 12 kJ mol-1, so from Figures 10 and 11 there is a very small amount of tunnelling if this definition is used. The dynamic and energetic definitions are identical for systems with one degree of freedom: if the system has sufficient energy to go over a barrier, then classical dynamics will also take the system over that barrier. However, this need no longer be the case in systems with more than one degree of freedom because certain processes may be energetically allowed but dynamically forbidden (cf.Figure 8). To summarize this section: it has been shown how semiclassical mechanics can be applied to reactive molecular collisions, and that good agreement with exact quantum results can be obtained. The definition of tunnelling has also been discussed. 5 Conclusions This review has discussed the application of semiclassical mechanics to elastic, inelastic, and reactive molecular collisions. Simple examples were considered to illustrate some important features of each type of collision as clearly as possible. In addition, comparison with exact quantum results showed the semiclassical approximations to be numerically very accurate. However, the semiclassical approach can be applied to more complicated (yet realistic) systems where the standard quantum mechanical techniques are not applicable or converge very slowly.The difficulty of solving a problem by semiclassical methods is related to the complexity of the structure of classical trajectories. In all cases, however, the semiclassical formalism involves h and real- or complex-valued classical quanti- ties. The semiclassical approach allows a clear distinction between quantum effects, which a purely classical theory cannot describe, and dynamical effects, which are common to both classical and quantum descriptions. The semiclassical approach thus allows a broad understanding and physical insight that is fre- quently lacking in the usual quantum theories, as well as often being numerically very accurate. I am grateful to the Society of Maccabaeans and the Royal Institute of Chemis- try for the award of the Meldola Medal.I would also like to thank my teachers of theoretical chemistry: A. D. Buckingham, P.W. Atkins, M. S. Child, and R. A. Marcus. lo(R. A. La Budde and R. B. Bernstein, J. Chem. Phys., 1975, 59, 3687. lo’ W. H. Miller, J. Chem. Phys., 1974, 61, 1823. J. M. Bowman, G. C. Schatz, and A. Kuppermann, Chem. Phys. Letters, 1974, 24, 378.

ISSN:0306-0012    

DOI:10.1039/CS9760500125

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

INGOLD LECTURE Four-membered Rings and Reaction Mechanisms By P. D. Bartlett DEPARTMENT OF CHEMISTRY, TEXAS CHRISTIAN UNIVERSITY, FORT WORTH, TEXAS 76129, U.S.A. 1 Introduction By the time I entered the chemical profession, C. K. Ingold had written about one-third of his eventual 443 publications, and had established the style and tempo that left such an important mark on the chemistry of our time. His work, entwined with the conviction that intimate details of structure and mechanism were knowable, was important from the start in my own approach to chemical research. Ingold’s first paper on four-membered rings was in 1922. His last publication, the second edition of his great book in 1969, contains a review and perceptive discussion of [2 + 21 cycloaddition to yield four-membered rings.As far as our research group is concerned, the novelty and excitement in the field of four- membered rings today centres about singlet oxygen, which appears to be the only known reagent that reacts vigorously and stereospecifically both in the Diels-Alder manner and in [2 + 21 addition to the double bond. Ordinary oxygen does not behave like ethylene, but is extremely reactive toward free radicals. This behaviour is associated with its existence in a triplet ground state, with unpaired electrons in two equivalent n orbitals. In the longest-lived singlet state of oxygen (lAs), 22.5 kcal mol-1 higher in energy than the triplet, these two electrons are paired and the properties of this species are those of a very reactive olefin.The higher singlet state, lCg+, is so short-lived as to undergo no chemical reactions in competition with quenching. It is now recognized1 that the photosensitized oxygenations, produced when oxygen is bubbled through an irradiated solution of reactant and a light-absorbing substance such as methylene blue or a porphyrin, are reactions of singlet oxygen (lAg) produced by energy transfer from the excited dye. 2 Four-membered Rings from Singlet Oxygen Two of the modes of reaction of singlet oxygen-l,4-addition to dienes or anthracenes [equations (l), (2)], and ‘ene’ reaction [equation (3)] with alkenes having allylic hydrogen-are normal reactions of the double bond distinguished for their extraordinary speed; a third mode, observed with enol ethers, enamines, (a) C.S. Foote and S. Wexler, J. Amer. Chern.SOC.,1964,86,3879; (6) C.S. Foote, Accounts Chem. Res., 1968, 1, 104; (c) E. J. Corey and W. C. Taylor, J. Amer. Chern. Soc., 1969, 86, 3881. Four-memberedRings and Reaction Mechanisms and alkenes with hindrance to ene-reaction, is the [2 + 21 addition to yield 1,Zdioxetans [equations (4), (S)]. - ‘c=c Me / Me 10, Me’/ ‘Me EtO, 7 c-0 I1 EtO The first obvious problem of mechanism raised by this behaviour is the exceptional position of singlet oxygen with respect to the orbital symmetry rules.? Why does not singlet oxygen, like other dienophiles that react con- certedly in [2 + 41 cycloaddition, yield its [2 + 21 products by way of open intermediates which rotate internally and lose configuration ?8 G.0.Schenck and K. Ziegler, Nuturwiss., 1945,32, 157. A. Willemart, Compt. rend., 1937,205, 866,993. G.0.Schenck and K. Schulte-Elte,Annulen, 1958,618,185. P. D. Bartlett and A. P. Schaap, J. Amer. Chem. Soc., 1970,92,3223,6055. (a)P. D. Bartlett and M. S. Ho, J. Amer. Chem. Soc., 1974, 96, 627; (b) M. S. Ho, Thesis, Harvard University, 1974. ‘I R. B. Woodward and R. Hoffman, ‘The Conservation of Orbital Symmetry’, Academic Press, New York, 1970; Angew. Chem. Internat. Edn., 1969, 8, 781. * P. D. Bartlett and R. Wheland, J. Amer. Chem. SOC.,1970,92, 3822. Bartlett Rationalizations for the apparent concertedness, though forbidden, of singlet oxygen’s [2 + 21 cycloadditions closely resemble those offered earlier7 for the behaviour of keten.In both cases dipolar ions are ruled out as intermediates by the absence of polar solvent effects to the degree always accompanying important charge separation at the transition state.9 One of the remaining possibilities is antarafacial approach of the keten, as in (l), or singlet oxygen, as in (2), to the R2 H RH ‘C’ olefin, leading to favourable correlation of the orbitals in reactants, transition states, and products. Ketens and oxygen have in common a linear character which removes the serious substituent hindrance presumably responsible for the rarity of antarafacial participation of simple olefins. There is, of course, no direct way of verifying antarafacial approach of a double bond that has no configuration, as is true of both these reagents. It is noted, however, that toward ketens a cis-alkene is often much more reacthe than a trans-alkene, which is suggests a geometry of the kind shown for (1).It is also observed that aldo-keten cycloadditions to cis-alkenes lead preferentially to the product with all three substituents (R1,R2, R3) cis,in specific agreement with the implications of (l).lo The crossed geometry of the transition state (l),with only minute modification, is also consistent with the second unique capability of the keten molecule pointed out by Woodward, namely its resemblance to a vinyl cation. Keten in the carbonyl-polarized form readily leads in an allowed [2 + 11 cycloaddition to the stage (3), which by analogy to known cases should retain configuration as it re- arranges internally to the adduct (4).The geometrical requirements of (3) and P. D. Bartlett, Quart. Rev., 1970, 24,473. lo (a)W. T. Brady, E. F. Hoff, R. Roe, jun., and F. H. Parry, jun., J. Amer. Chem. Suc., 1969, 91,5679; (b)T. DoMinh and 0.P. Strausz, J. Amer. Chem. Suc., 1970,92,1766. Four-membered Rings and Reaction Mechanisms (1) are so similar that it is suggested that the actual reaction occurs in simultaneous response to the driving forces for both processes. For singlet oxygen there is also a much-discussed mechanism analogous to (3), although the suggestion in this case arose independently.1l It has been pointed out that a perepoxide, or peroxiran, (3,could be formed in a symmetry-allowed, stereospecific fashion and might serve equally well as a precursor of the dioxetan (6) or of the allylic hydroperoxide (7), generally produced from alkenes having (5) (6) (7) [formed from (6;R2= Me)] allylic hydrogen atoms.Again it is possible to believe that with singlet oxygen as with keten, the factors predisposing to the approach (2) would also be com- patible with the formation of (5); recent conclusions from MJND0/3 calcula-tions12 indicate (5) as lying on the favoured path. Although much of the concern with the perepoxide has centred about its intermediacy in the oxygen ene-reaction, it may be noted that the ene-reaction can proceed over a low-strain, symmetry-allowed direct path, and must do so in the best-known cases with enophiles like maleic anhydride, where no reasonable analogue of the perepoxide is available.On the other hand, it is for the concerted, stereospecific cycloaddition of singlet oxygen to the double bond that the perepoxide mechanism provides a needed rationalization for this reagent's unique position in terms of orbital symmetries. Only indirect evidence has been generated for the intermediacy of perepoxides in reactions of singlet oxygen, and in some cases modifications have been necessary in the original inter~retati0ns.l~ However, in the related case of an episulphoxide,14 an analogous compound has been prepared at -30 "C and rearranged at 25 "Cto the allylic sulphenic acid (8) which is the sulphur counter- part of a singlet oxygen ene product.Work with the special compounds biadamantylidene (9)15J6and binorborny- lidene (10),6 in which Bredt's Rule hindrance prevents the occurrence of an ene l1 D. B. Sharp, Abstracts 138th National Meeting, American Chemical Society, New York, September 1960, No. 79 P. Is M. J. S. Dewar and W. Thiel, J. Amer. Chem. Soc., 1975, 97, 3978. l3 K. Gollnick, D. Halsch, and G. Schade, J. Amer. Chem. Soc., 1972, 94, 1747. l4 J. E. Baldwin, G. Hofle, and S. C. Choi, J. Amer. Chem. SOC.,1971,93,2810. l6 J. Strating, J. H. Wieringa, and H. Wynberg, Chem. Comm., 1969, 907; H. Wynberg,E. Boelema, J. H. Wieringa, and J. Strating, Tetrahedron Letters, 1970, 3613. J. H. Wieringa, J. Strating, H.Wynberg, and W. Adam, Tetrahedron Letters, 1972, 169. Bartlet t reaction, has shown that carbon, as well as nitrogen or oxygen substituents, can activate the double bond toward dioxetan formation with singlet oxygen. The first unusual observation about the products was that the resulting dioxetans were extraordinarily stable, withstanding temperatures more than 150 "C higher (9) than tetramethyldioxetan does. It is also characteristic of these olefins, as of other highly hindered ones,17 that ozonization leads simply to epoxide without the formation of an ozonide and without cleavage at the double bond. This behaviour would be compatible with endwise approach of the ozone molecule to the double bond, the trailing pair of oxygen atoms coming off as singlet oxygen.By analogy to a literature report later shownlS to be in error, in which pina- colone was considered to have the special property of stripping a single oxygen atom from an ozonization intermediate, Schaap and Faler conducted the photo-oxidation of biadamantylidene in pinacolone as solvent.lg The oxidation product, in addition to the dioxetan, included 19% of the epoxide, assumed to be due to deoxygenation of an intermediate perepoxide by a Baeyer-Villiger reaction with the solvent. In the related case of binorbornylidene, however, all solvents tried yielded mixtures of dioxetan and epoxide, benzene yielding more epoxide than pinacolone, and no solvent (including pinacolone) being detectably oxidized in the process.6 A series of comparable experiments showed that the same was true of biadamantylidene.20 Jefford and Boschung21 later observed that the photo-oxidation of norbornene in several solvents also yielded dioxetan l7 J.J. Backer, Chem. Weekblad., 1939, 36, 214; P. D. Bartlett and M. Stiles, J. Amer. Chem. SOC.,1955,77, 2806. K. R. Kopecky, P. A. Lockwood, J. E. Filby, and R. W. Reid, Canad. J. Chem., 1973,51, 468. l9 A. P. Schaap and G. R. Faler, J. Amer. Chem. SOC.,1973,95,3381. M. J. Shapiro, unpublished work at Texas Christian University. *l C. W. Jefford and A. Boschung. Helv. Chim. Acta, 1974,95,3381. Four-membered Rings and Reaction Mechanisms and epoxide in proportions which reflected the same solvent order as for other olefins. Table 1 summarizes the results for these substrates.Table 1 Epoxid~]dioxetanfromphoto-oxidation Biadamantylidene Norbornenea Binorbornylidenec l02, CHzClz 0.09d - 0.66 l02, MeCN - 0.64 0.85 102, pinacolone 0.23b 1.1 2.9 0.19d 102, benzene 0.53d - 4.5 l02, MeCOMe - 1.86 5.1 =Ref.21;bref. 19; Cref. 6b;“ref. 20. Despite the failure to find evidence of uptake of an oxygen atom by the solvent in any of these cases, reagents exist that are able to perform this function. Tetracyanoethylene was shown by Criegee and Gunther22 to remove the terminal oxygen atom from a carbonyl oxide in the cleavage of an initial ozonide. Dr. Ho has found that in the presence of two equivalents of tcne in acetonitrile the ratio of epoxide to dioxetan in the photo-oxidation of binorbornylidene is increased from 0.76 to 15.9.6bCyanide ion in tenfold excess in methanol had a similar but much smaller effect.Since the nature of the terminal oxygen in a peroxiran is expected to be similar to that in a carbonyl oxide-co-ordinately bonded to another oxygen-this result is compatible with the involvement of a peroxiran in the formation of the epoxide in singlet oxygen reactions. But what is the oxygen-removing reagent which is common to all the reaction media of Table 1, but is not in any case the solvent ? A potential oxygen acceptor always present in singlet oxygen reactions is singlet oxygen itself, which might, if present under conditions of sufficiently long life, react with the perepoxide to yield epoxide and ozone in an approximately thermoneutral reaction.Since binorbornylidene and biadamantylidene are themselves epoxidized by ozone, presumably with singlet oxygen as the other product, the reaction of perepoxide with singlet oxygen can be treated as a chain process leading on each occurrence to two epoxide molecules without diminishing the singlet oxygen concentration. Treatment of this kind leads to the equation below in which ke/kdis the ratio of rate constants for the first-order rearrangement of the perepoxide and its second-order conversion into epoxide. This equation predicts that the relative importance of the epoxidation will be proportional to the steady-state d(epoxide) ke d(dioxetan) = 2g(102) concentration of singlet oxygen, hence to the light intensity and, in dilute solution, to the sensitizer concentration, and inversely proportional to the olefin 22 R.Criegee and P. Giinther, Chem. Ber., 1963,96,1564 Bart left concentration and the quenching power of the solvent for singlet oxygen. Variation of the conditions in these respects does indeed shift the product ratio in the predicted direction. A few examples are given in Table 2. Likely as this mechanism appears for photo-epoxidation of binorbornylidene and biadamantylidene under dye ~ensitization,~~ it is by no means general for photo-epoxidation. Many olefins are epoxidized by photosensitization with benzil or with biacetyl under conditions where singlet oxygen, if present, would lead either to no reaction or to products entirely different from those found.24 Table 2 Efect of conditions on epoxideldioxetan ratio in photo-oxidation sensitized by tetraphenylporphin Olefin Conc.Sensitizer Conc. Solvent Epoxidel Ref. 110-5 moll-1 dioxetan (9) 0.0037 1.6 benzene 4.5 6b (9) o.Ooo19 1.6 benzene 14,19 6b (8) 0.0011 1.o benzene 0.53 20 (8) 0.0011 1.o CHzClz 0.09 20 3 Opening of the Dioxetan Ring 1,2-Dioxetans cleave thermally to two carbonyl-containing fragments. Such a cleavage, if concerted and suprafacial, is required by the orbital symmetry rules to produce one of these fragments in an excited state. In good agreement with this expectancy, the decomposition of 1 ,Zdioxetans leads generally to chemi- luminescence, although the emission directly observable from the product ketones represents a very low apparent quantum yield.Careful studies have shown that the losses are due to quenching of the excited molecules formed, and that the excitation energy can be accounted for by recovery with suitable calibrated fluorescers.25 Thus in the thermal decomposition of dioxetans, unlike their thermal formation, there is no reason why a direct, concerted mechanism cannot be assumed. There is a problem, however, with respect to the conservation of spin multi- plicity. Rapid intersystem crossings between singlet and triplet states are well known, but it is general experience that the time of passage over a transition state does not allow an intersystem crossing to be part of a concerted reaction mechanism.The best known exceptions involve atoms heavier than those of the first row of the periodic table, such as the reaction of 3P sulphur atoms with the carbon-carbon double bond,26 or the excitation of 9,lO-dibromoanthracene to a singlet state by energy transfer from an excited triplet ketone.25 It was therefore unexpected that the thermal decomposition of tetramethyl-1 ,Zdioxetan leads 23 Theoretical calculations (M. J. S. Dewar, A. C. Griffin, W. Thiel, and I. J. Turchi, J. Amer. Chem. SOC.,1975, 97, 4439) support the perepoxide as an intermediate both in dioxetan formation and, through reaction with a second singlet oxygen molecule, in epoxidation. 24 N.Shimim and P. D. Bartlett, J. Amer. Chem. SOC.,1976, 98, in press. 86 (a)V. A. Belyakov and R. F. Vasil’ev, Phorochem. and Photobiol., 1970, 11, 179; (6) T. Wilson and A. P. Schaap, J. Amer. Chem. SOC.,1971,93,4126. 86 H. E. Gunning and 0.P. Strausz, Adv. Photochem., 1966,4,143. Four-membered Rings and Reaction Mechanisms directly to excited acetone in which the triplet molecules outnumber the singlets by about 250 to 1. Evidence that this is so comes from several directions. First, the singlet excited ketone can be assayed by the intensity of fluorescence it induces in 9,lO-diphenyl- anthracene, which can yield induced fluorescence only from singlet states. Fluorescence in 9,10-dibromoanthracene, on the other hand, is induced by energy transfer from either singlet or triplet excited ketone.25 In the decom- position of tetramethyl-1 ,Zdioxetan the relative intensities of luminescence seen with these two fluorescers indicate that the excited acetone is mainly triplet.Second, fumaronitrile reacts with singlet excited acetone by cycloaddition, whereas triplet acetone only induces trans-cis-isomerization about the double bond. 'Chemical titration' of thermally decomposing tetramethyldioxetan with fumaronitrile [equations (6) and (7)] yields isomerization, indicating mainly CN Me Me CN (7)6"-Me NC Me / CN triplet acetone as the excited species directly formed.27 These two methods agree in indicating that triplet acetone is produced, not as a later but as a primary product in the thermal decomposition of tetramethyldioxetan.In addition, two other methods which could not have ruled out the initial formation of singlet acetone giving rapid intersystem crossing, nevertheless confirm the presence of triplet. Thermally decomposing tetramethyldioxetan produces, from benzoyl peroxide in carbon tetrachloride, chlorobenzene showing the kind of chemically induced dynamic nuclear polarization (CIDNP) signal characteristic of triplet radical pairs.28 Triplet acetone is also indicated by the hydrogen abstraction reactions performed on 1,4-~yclohexadiene by the excited product from the dioxetan decomposition, a type of chemistry characteristic of nn* excited triplet states.29 In the case of dioxetan decomposition it is not necessary to assume that the thermal cleavage is a completely concerted process, since there is no observation corresponding to retention or loss of configuration to afford evidence on this point.The prevalent formation of triplet acetone would be less exceptional if, as t7 N. J. Turro and P. Lechtken, J. Amer. Chem. SOC.,1972,94,2886. 18 P.D. Bartlett and N. Shimizu, J. Amer. Chem. SOC.,1975,97,6253. SOT. Wilson, M. E. Landis, A. L. Baumstark, and P. D. Bartlett, J. Arner. Chem. SOC., 1973,95,4765. Bartlett proposed by O'Neal and Richardson30 (Scheme 1) the 0-0 bond breaks reversibly and the change of multiplicity occurs in an intermediate biradical. By this view the triplet is the preferred product because it best accommodates the energy change in the cleavage, the singlet formation being endothermic and c the formation of two ground-state molecules liberating an amount of energy not so efficiently disposable.Turro, on the other hand, proposes that the comrnon feature of concerted processes with intersystem crossing is the presence of a torque tending to rotate the spin vector and arising from a change in orbital angular momentum inherent in the reaction. A picture of dioxetan ring-cleavage is proposed31 (Scheme 2) which is expected to provide such a torque32 and to make singlet-triplet conversion a normal accompaniment of this reaction. Me \t/c=otMe MeIMe-C-0 11 + +Me-C-0I MeMe \/c=o Me Scheme 2 Neither of these mechanisms of dioxetan cleavage leaves much room for catalytic effects by ordinary polar solvents.When, therefore, it was observed33 that in methanol the decomposition of tetramethyldioxetan was as much as 100 times as fast as in benzene, competing mechanisms were suspected. Richardson34 noted that the chelating agent ethylenediaminetetra-aceticacid (edta) in many cases greatly reduced the rate of dioxetan decomposition; by following this lead 3O H. E. O'Neal and W. H. Richardson, J. Amer. Chem. Sac., 1970,92,6553. 31 N. J. Turro and P. Lechtken, J. Amer. Chem. Sac., 1973,95,264. 3* L. Salem and C. Rowland, Angew. Chem. Internut. Edn., 1972, 11, 92. s3 N. J. Turro and P. Lechtken, J. Amer. Chem. Sac., 1973,95,264; Pure Appl. Chem., 1973, 33,363. 34 W H. Richardson, private communication, 1973.Four-membered Rings and Reaction Mechanisms it was possible to show29 that (i) the uncatalysed rate is much the same in benzene, ethanol, and methanol; (ii) only this uncatalysed reaction gives rise to chemiluminescence and to reactions of excited ketone triplets; and that (iii) the catalysis can be simulated by addition of a number of metal salts, whether in benzene or in an alcohol. Table 3 Catalysis of tetramethyldioxetan decomposition in methanol at 57 OC3= Additive 105 ki S-1 moll-1 ( x 105) without with kz(apparent) I mol-l s-1 CuCl2,2H20 0.83 52-88 1150 1280 1.64 12-17 2200 1290 CUCl 0.83 52-88 150 75 ? 4.77 52-88 1050 200 ? FeC13 3.6 52-88 140 14 SnC12,2H20 1.07 52-88 85 none 5.1 12-1 7 9 none Dipped aluminium foil Dipped copper wire 40 8.3 250 200 + + It appeared, moreover, that small traces of catalysts in common solvents affected the rate of tetramethyldioxetan decomposition to an important extent.In subsequent experiments all hydroxylic solvents were treated with 5 x 10-4 mol 1-1 edta to obtain the uncatalysed rate of tetramethyldioxetan ring opening. Even so, the uncatalysed rates varied with the history of the sample. In the experi- ments reported in Table 3 the uncatalysed rate was determined each time before adding the catalyst, and the catalytic rate constant was determined by difference. Cupric, cuprous, and ferric chlorides appear in descending order of catalytic power, with stannous chloride appearing to react little, if at all, faster than the uncatalysed ring opening. The sensitivity of the dioxetan to trace contaminants is dramatized by the fact that dipping a piece of clean aluminium foil, or stirring the sample with copper wire, increased the rate of decomposition by factors of 5-24.All catalysts, added intentionally or unintentionally, were rendered ineffective by a sufficient amount of edta. The cupric salts of acetic acid, tropolone, and citric acid in methanol form a series in which the catalysis decreases, approaching the inactivity of the fully chelated edta complex (Table 4). In view of the importance of orbital-symmetry considerations in the previous thinking about the formation and cleavage of dioxetans, it is natural to ask whether the catalysis of dioxetan ring opening is a matter of insertion of a metal ion between the oxygen atoms to produce a metallocycle whose fragmentation is symmetry-allowed.Indeed, complexes of rhodium and iridium, known for their ability to undergo oxidative additions with hydrogen chloride and with hydrogen, rank high among the catalysts for ring opening of tetramethyl-158 Bartlett Table 4 Eflect of added anions on catalysis of dioxetan destruction at 51 "C inMeOHa (ref. 37) Anion [Anion] [CU2+]b 104 (klcat -kluncat) s-l - - 860 Acetate 2.1 260 Troponoxy 2.0 14 Citrate 2.0 4 Edta 1.2 0 UTreated with dry Chelex 100 and vacuum distilled at 0 "C; b[CuCI,] = 7 x mol I-'.dioxetan.35 Table 5 provides some examples of the effect of changes of metal, and of one component at a time of the complex, upon the rate of this catalysed reaction. These changes are not inconsistent with an oxidative addition mechanism for the rhodium and iridium complexes. Table 5 Cleavage of tetramethyldioxetan in benzenea Complex Relative rate Rh(Ph3P)Kl 1.o Rh(CO)(Ph3P)aCl 1.5 Rh( CO)(Ph3P) 21 2.9 Rh(CO)(PhsAs) aC1 6.2 [Rh(CO)aC1]2 31 Ir(CO)rPh3P)2CI 62 [Rh(nbd)Cl]z 185 Ir/Rh 41 I/Cl 2 PhsAs/PhsP 4.1 CO/Ph3P 1.5 =Reference 35. Nevertheless, oxidative addition-implying a ready change of valence on the part of the metal ion from x to x+ 2-cannot be a general mechanism by which metal salts catalyse the opening of tetramethyldioxetan.The series of effective metal salts for this reaction includes some which are oxidized with difficulty and some that are not oxidized at all. Cupric ion, with no available higher oxidation state, is a much better catalyst than cuprous ion. The property of this series of metal ions that correlates well with their catalytic power is, instead, their Lewis acidity. The Figure shows the catalytic rate constants for dioxetan ring opening plotted, on a log scale, against their association equilibrium constants with malonate ion, one of the few series of such associations for which measurements are available.~6~37 It would appear that this ring opening J. McKennis, unpublished work at T.C.U. 36 J. E. Prue, J. Chem. SOC., 1952, 2337; M.L. Bender, 'Mechanisms of HomogeneousCatalysis from Protons to Proteins', John Wiley, New York,1971, p. 218. 37 P. D. Bartlett, A. L. Baumstark, and M. E. Landis, J. Amer. Chem. SOC.,1974, 96, 5557. Four-membered Rings and Reaction Mechanisms 3.0 2.0 log K cat 1.o 0 I I I 4.0 5.0 6.0 log K malonate Figure Relation between association equilibrium constants of bivalent metal ions with malonate ion3 and their catalytic constants for cleavage of tetramethyldioxetan to acetone3' must be initiated by an unsymmetrical electrophilic attack of the catalyst ion upon one of the oxygens of the 0-0 bond. In the dioxetan complexed with the Lewis acid, (ll), fission of the ring by a polar process takes precedence over apparent homolytic cleavage in the uncatalysed reaction.Me,C=O : Cu"' -t Me& =O If this is so, tetramethyldioxetan should be subject to attack by simple, non- reducing Lewis acids like boron fluoride. Table 6 shows that indeed boron fluoride etherate cleaves the dioxetan in four halogenated or aromatic solvents. Bartlett Competing with the cleavage, however, is a molecular rearrangement of which the isolated product is pinacolone. In CFC13 as solvent, a four-fold excess of boron fluoride etherate causes the entire product to be pinacolone, with no cleavage detected. Table 6 Tetramethyldioxetan and BF3 etherate39 Solvent % Pinacolonea % Acetone 0.8 CFC13 41 59 4 CFC13 100 - 1 cc14 90 10 1 PhH 36 64 1 PhBr 40 52 aNo t-butyl acetate formed.The formation of pinacolone from tetramethyldioxetan represents a net reduction, with loss of one oxygen atom, and is reminiscent of the problem of the missing oxygen in photo-epoxidation with molecular oxygen. A careful check revealed no oxidized solvent molecules, and no tertiary butyl acetate formed by Baeyer-Villiger attack of an oxidizing intermediate upon pinacolone. The most likely alternative to cleavage in the co-ordinated intermediate (12) might be a 'perpinacol rearrangement' yielding the carbonyl oxide of pinacolone, (13). Such intermediates, in the absence of methanol, which converts them into methoxyhydroperoxides, are known to dimerize to cyclic bis-per~xides,~~ which are thermally unstable.In an experiment carried out at -78 "C,gaseous boron fluoride was bubbled into a methylene chloride solution of tetramethyldioxetan for 10 s and methanol was added after the mixture had been allowed to stand for 30 minutes. In addition to 28 % recovered dioxetan the main product was still pinacolone (47 %), along with 5 % of acetone. There was found, however, 22%of (14), the dimeric peroxide of pinacolone, and the mother liquor showed a peroxide titre corresponding to a further 60-80 % of the pinacolone. This result is consistent 38 R. Criegee, A. Kerckow, and H. Zinke, Chem. Ber., 1955,88,122. 161 Four-memberedRingsand Reaction Mechanisms Me"0-0 Me,3 with rapid hydrolysis of the dimeric pinacolone peroxide by traces of water present in the solvents, powerfully catalysed by the boron fluoride.Stannic chloride in deuteriomethanol or deuterioacetonitrile, followed by n.m.r., brought about complete cleavage of tetramethyldioxetan to acet0ne.3~ Thus Lewis acids that are not insertion reagents produce dioxetan cleavage. What happens with insertion reagents that are not Lewis acids? Triphenylphosphine in benzene at 6 "C reacts with tetramethyldioxetan to yield the insertion product (15), which at 55 "Cundergoes cleavage to triphenyl- phosphine oxide and tetramethyloxiran, (1 6).*O The relative reactivities shown in the insertion of several phosphorus com- pounds into tetramethyldioxetan can be correlated with the preference of phosphoranes to be formed with the most electron-attracting groups situated at the apical positions of the trigonal bi~yramid.~~ In the case of the stannous ion we have a reagent that is both a Lewis acidand capable of a two-unit valence increase, hence a candidate for oxidative addition.As shown in Table 7 stannous chloride in various solvents shows competitive cleavage of dioxetan and reduction to pinacol. The pinacol formation involves hydrolysis of stannic pinacolate, but is totally prevented only in solutions of the complex material diphenyltin in dry benzene. Stannic pinacolate, once formed, neither fragments to acetone and stannous tin nor rearranges to pina-colone. Evidently therefore the cleavage seen is the result of the stannous compound acting in the Lewis acid mode, like boron fluoride, in competition with oxidative addition.39 A. L. Baumstark, Thesis, Harvard University, 1974. 40 P. D. Bartlett, A. L. Baumstark, and M. E. Landis, J. Amer. Chem. SOC.,1973,9§, 6486. *l P. D. Bartlett, A. L. Baumstark, M. E. Landis, and C. L. Lerman, J. Amer. Chem. SOC., 1974,96,5267. Bartlett Table 7 Tetramethyldioxetan and stannous catalysts: fragmentation vs. reduc-tion, room ternperat~re3~ Reagent Solvent % pinacol % acetone SnCl2 CD30D ‘wet’ 37 63 SnCl2 CD30D:DzO (1 :8, v:v) 68 32 SnCl2 CD3CN ‘dry’ 21 79 SnCl2 CD3CN:DzO(1:8,v:v) 68 32 SnC12 [2H6]DMS0 ‘wet’ 31 69 ‘PhzSn’ PhH, dry 0 100 Sn(0Ac)z CD30D ‘wet’ 33 67 The new work reported here was supported by the Robert A. Welch Founda- tion at Texas Christian University, and by the National Science Foundation and the National Institutes of Health at Texas Christian and Harvard Universities.

ISSN:0306-0012    

DOI:10.1039/CS9760500149

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Vibrational Intensities in Electronic Transitions By M. Roche and H. H. Jaffe DEPARTMENT OF CHEMISTRY, UNIVERSITY OF CINCINNATI, CINCINNATI, OHIO 45221, U.S.A. 1 Introduction The electronic spectra of atoms are known to consist of single lines, each corresponding to the single transition between two electronic states1 The electronic spectra of molecules, on the other hand, are usually seen as broad regions of absorption with more or less detailed structure. However, recent technological advances have led to the observation of much more detail in these broad regions. In general, each of these regions of absorption corresponds to one, or possibly a superposition of two or more electronic transitions. Molecular electronic transitions cover rather broad areas, because electronic excitation is accompanied by changes in vibrational and rotational energy which are not present in single atoms.The increase of interest in medium- to high-resolution spectroscopy makes worthwhile a summary of what is well known2 about the distribution of intensity among these various vibrational structures in an electronic transition. Most of the treatments readily available are rather specific to special cases or to specific small molecules. We have chosen here to outline the theory of the intensity distribution among the different vibronic components of electronic transitions, allowed or symmetry forbidden, with special attention to absorption. Thus, we have not examined fluorescence, or, more generally, ‘the fate of the excited state’,3 in any detail; also, we have omitted any reference to the rotational fine structure which further subdivides the vibronic bands and can be very useful in the interpretation of electronic spectra.We must first describe a molecular state involving both electronic and nuclear motion. We will assume that we can apply the well-known Born-Oppenheimer (BO) approximation,4 in which one separates the motion of the electrons and of the nuclei. Therefore, we will write the total wavefunction as the product (l), where #I(e,q), the electronic wavefunction, depends explicitly on the co-ordinates of the electrons, represented by e, and parametrically on the co-ordinates of the nuclei, represented by q: Le., is different for each set q.It is given as a solution of the electronic Schrodinger equation of the molecule [equation (2)]; G. Herzberg, ‘Atomic Spectra and Atomic Structure’, Dover Publications, New York, 1944. G. Herzberg, ‘Electronic Spectra of Polyatomic Molecules’, Van Nostrand Reinhold Co., New York, 1966, Chapter 2. M. Orchin and H. H. Jaffk, ‘Symmetry, Orbitals, and Spectra’, Wiley Interscience, NewYork, 1971, Chapter 11. F. L Pilar, ‘Elementary Quantum Chemistry’, McGraw-Hill, New York, 1968, p. 414. Vibrational Intensities in Electronic Transitions me, 4)#I@, 4) = EI(d$I(e, 4) (2) X/(q) is the vibrational wavefunction, solution of the nuclear equation (3), which is the Schrodinger equation for a set of nuclei a moving in a potential field V,(q).We see that a different nuclear equation holds for each different electronic state I, which is the reason why the vibrational (or nuclear) wave- functions have to be specified by the two quantum numbers Z and ,LThe set (I,)defines a vibronic state, of energy EIF. VI(q)has as many dimensions as there are vibrational degrees of freedom in the molecule (3N -6 for a non-linear molecule, 3N -5 for a linear molecule, if N is the number of atoms of the molecule). The BO approximation is only valid if the state I is well separated from all the other states: otherwise a strong coupling occurs between diferent electronic states and the nuclear motions (Jahn-Teller and Renner effects5); throughout this review we shall assume the states with which we deal to be sufficiently well separated so that such couplings can be ignored.Let us now consider an one-electron transition between two electronic states I and F. A priori there is nothing to indicate that the electron cannot jump from any initial vibronic state Ip to any final vibronic state Fv,so that the spectrum corresponding to the electronic transition FtI could be composed of an infinity of lines (some of which might actually be superimposed). In this review we shall attempt to show qualitatively how the intensity of the absorption (or emission) of light may be distributed among these lines, or bands (because of the rotational structure, each line is in fact a band consisting of many lines and will be referred to as a vibronic band). First let us recall how we can determine theoretically the intensity of an electronic transition.Virtually all such transitions known from observation are electronic dipole transitions, and for the sake of simplicity we restrict ourselves to this case although the discussion can be extended to magnetic dipole and electric quadrupole transitions. The intensity of the transition Fv tIp may be expressed through the oscillator strength (4) where IdEIp,Fvlis the difference in energy between the two vibronic (4) -+ ru give the position (5) of electron i and nucleus 0,respectively, and 2,the charge of nucleus 0.The difference dE,,,,, can be expressed as the sum of an electronic difference dEIF G. W. King, 'Spectroscopy and Molecular Structure', Holt, Rinehart, and Winston, New York, 1965, pp.410-418. Roche and Jaflc! (for example between the energies of the states I and F at their respective equilibrium positions) and of a vibrational energy dEpv,[equation (ti)]. AEI,,F" = AEIF + AEPV (6) We shall see that usually the most intense vibronic bands arise from transitions between vibronic states having vibrational quantum numbers ,u and Ywhich are not very different: taking into account that a quantum of vibrational energy is much smaller than one of electronic energy, we can neglect dEpyin equation (6) and write fKlAEZFl IGZ8l2 For two definite electronic states I and F the intensity distribution thus -+ depends only on ]MI$yI . Using the product form for thes, equation (l), we obtain equation (7).The second term on the right of this equation contains the 3 + operator cZ,r,, which depends only on the nuclear co-ordinates ; consequently, 0 we can integrate first with respect to the electronic co-ordinates. $I(e,q) and $d,e,q) are orthogonal at any q since they are different solutions of the same electronic Schrodinger equation, and thus the second term vanishes. Accordingly, we have equations (8) and (9). The latter can be rewritten as equation (lo), 3 where the electronic transition moment M&) is given by equation (11) and MZF(q) = J $Z(e,q)zra#F(e,q) de (11)i depends only parametrically on the nuclear configuration q. Let us now consider all the transitions from the initial state I, to the various vibrational levels vof the final electronic state F.One can easily derive equation (12) by use of the so-called 'closure relation'.6 This equation means that the Vibrational Intensities in Electronic Transitions total intensity of all the transitions Fu cZp depends only on Xf(q) and not on the actual form of the vibrational wavefunctions of the final state F. However, this total intensity still depends on the form of the potential surface VFthrough+ MIF(4. 2 Harmonic and Condon Approximations Harmonic Approximation.-To try to gain some insight into the intensity distribu- tion we must now introduce some approximation. A priori we do not have any idea of the form of the X, which depend on the form of the potential surfaces; our first approximation will thus concern the shapes of V, and VF.Let us consider the potential surface V, as an example. If t,are the Cartesian displacement co-ordinates of the nuclei in a local axis system centred on the nuclei, we can expand V, around the equilibrium geometry of the state I as a series (13). This series contains no linear terms because we assume the state Z to be stable, i.e., (aV,/afj)~= 0 for allj. We now introduce the assumption that the potential surface is harmonic, i.e. that all terms in equation (13) above second order may be neglected; thus VI = C'aijtctj i./ With this assumption, it is always possible to find a transformation which allows us to transform the ti into a new set of co-ordinates Q, such that VI can be expressed as equation (14).In other words, the cross-terms are eliminated from the expression for V,. In these co-ordinates, the nuclear Schrodinger equation may be rewritten' as equation (15). Then a section through V, along any Q, is a parabola, the concavity of which is proportional to ha. The Q, are ortho-normalized linear combinations of the mass-weighted Cartesian displacement co-ordinates mitt,and are called the 'normal co-ordinates' of the state I. We see that the nuclear Hamiltonian is now a sum of one-dimensional Hamil- tonians [equation (16)], and we thus write Xf(q) as a product of functions See ref. 4, p. 417. Roche and Ja@ xIPa(Qa).The p on XIc now stands for the collection of pa,and the nuclear Schrodinger equation splits into 3N -6 (or 3N -5) equations (17).This is just the equation of the one-dimensional harmonic oscillator, the solutions of which are well known. We thus have equation (18), where pa refers to the vibrational quantum number and pa refers to the corresponding frequency. We do not need the exact expression of theXp=(Qa,&), but it must be remembered that these functions form an orthonormal set, i.e. where 6 is the Kronecker symbol. Analogous equations hold for the state F; XFv=n;x”~(Q,’,)(,?, where the normal co-ordinates Q,’ of F are distinguished by a prime from the Q, of I: EFv = E’V, = IfiC,(v, + +) (19) a a Note that EFvis the energy above the minimum of VFwhile Ere is the energy above the minimum of V’.The difference EFv-EIprepresentsdEpvof equation (6).Condon Approximation.-We now introduce a second hypothesis in order to --* simplify equation (10). As we have seen, MI&) depends on the configuration of --f the nuclei. We assume that MI&) can be approximated by a quantity indepen- --+ --t -+ dent of q: kfIF((I) X MIF(0),where MIF(0)is the electronic transition moment Bf%hESqU%b~UR3nWk3 EOI&~U3PfiOR0Of $?C!E3$P$EI.Thk JS EP%d $hE‘cCEdO3l approximation’. Then 3 Franck-Condon Factors and Vibrational Intensities in Allowed Transitions + Next we assume that MIF(0) # 0, i.e. we consider only allowed electronic transi- tions; the case of forbidden transitions will be treated later. With the Condon approximation the intensity distribution for allowed transitions depends only on the quantities Vibrational Intensities in Electronic Transitions Introducing the Condon approximation in equation (12) leads 4 r where the relationship (22) holds.At this point we have reduced the problem of xspv2= 2cpv= 1 (22) V V the intensity distribution of the vibronic components of an allowed electronic transition to an evaluation of the integrals Spv.The relative magnitudes of these depend on the relative shapes and positions of the potential surfaces VI and V,, and we can now investigate the different possible situations. In any case, we notice that because of our harmonic hypothesis, sections of V, and V, by vertical planes (assuming the energy axis to be vertical) are parabolas.The simplest situation arises when not only the normal co-ordinates Q, and Q,' of initial and final states are the same, but also the associated ha[LJequation (14)] are the same. This implies that the force constants for the various vibraions do not change upon excitation, and that the potential surfaces V' and V, are identical, except for displacement along the energy axis. This case is illustrated in Figure l(a) where V, and V, are shown for a hypothetical case involving only two normal co-ordinates. In this situation (Case 1) Cpv can be factored into 3N -6 components, equation (23), one for each normal co-ordinate. The CPavaare called the Franck- cpv = naCpava= naspav2 (23) Condon factors. It follows that the vibrational Schrodinger equations, and consequently the vibrational eigenvalues and eigenfunctions, are identical for the states I and F.As a consequence, the xva and xpa are functions belonging to the same orthonormal set, Spa.== Spava, and the only vibronic components of the transition Fc I having non-zero intensity are those in which the sets of vibra- tional quantum numbers (p and v) are identical. Since the vibrational energy spacings are also identical, the spectrum will consist of a single vibronic band, which represents the superposition of all the degenerate transitions Fp f-Ip. A more complicated situation (Case 2) exists when, although the Q, and Q,' are the same, one or more of the concavities ha of equation (13) differ between states I and F. This case is illustrated (again in the two-dimensional case), in Figure l(b).Again, equation (23) holds. In this case the vibrational Schrodinger equations, although of equal form, are no longer identical, and different eigen- values Epaand Eva' result. Consequently, the overlap integrals Spava# 8&va and new vibronic bands become allowed. However, a selection rule arises from the nature of the vibrational wavefunctions in the harmonic approximation used here. These functions xFa(Q,,h,), are even or odd functions of Q,, depending on whether ,u, is even or odd, and similarly for xva(Q,',A,'). Consequently Spava vanishes unless pa and va are of the same parity, and we obtain the selection rule (24). 170 Roche and Jafb +"t Figure 1 The relative shapes and orientations of potential surfaces (two-dimensional) for pairs of electronic states, (a) Case I, (b) Case IT, (c) Case 111, (d) Case IV dv, = pa -va = 0, +2 (24) The electronic spectrum of the molecule in the initial state Ip should now be composed of various progressions of bands, each progression corresponding to a vibration 01 for which the surfaces are distorted (a single band corresponds to all the other Q, for which no distortion occurs).At elevated temperatures, where a number of vibronic states Ipare populated, a separate progression should appear for each significantly populated state. Since the spacing of vibrational levels is not the same in the two states, the progressions do not coincide but are offset from one another by Pa -[in units of ti: cf.equations (18) and (19)]. A study of the algebraic form of the Franck-Condon factors for diatomic Vibrational Intensities in Electronic Transitions molecules* shows that the band for which Av, = 0 is by far the most intense and then the intensity decreases sharply with increasing Idv,l. In absorption at room temperature or below, most of the molecules are in the vibrational ground state (all pa = 0) so that the most intense bands will result from transitions F,, clo (cold bands; Fvtlp for some pa > 0 give the so-called hot bands). It can be shown that the Franck-Condon factor COOfor the 0-0 band is given by COO= 2,/pz/(p, + Pa). Even if v, = 3 pa, which corresponds to a strong distortion, COO= 0.94, and the 0-0 band is most prominent among the cold bands.In summary we can say that the distortion of the potential surfaces has a small effect on the spectrum, and generally speaking this spectrum will show the dv = 0 bands very prominently and no clear progressions. In a third situation [Case 3, Figure l(c)] the potential surfaces are displaced relative to one another along one (or more) of the normal co-ordinates Q, (as well as along the energy axis) by an amount dQ,. Cpyis still the product of 3N -6 CPKyK for two displaced [equation (23)],so that we have to examine CpKv= harmonic oscillators. There is no distortion, so that CPavK moreover= CyKpa; whenp, = 0, Coy,takes the simple form (25),where y, the displacement parameter coy,= yYae-Y/va ! (25) is given by (26).The main feature is that all dv, are now allowed. The ratio of y = .J&AQ,2/2A (26) two successive Franck-Condon factors is given by (27). Since y can take any positive value, we see that the maximum value of CPKy,does not necessarily it will be so only if y .c 1. For y = 1, COI= COO,occur at COO: and for y = 2, COZ = COl = 2coo. For any normal co-ordinate Q,, for which the minimum of VFis displaced relative to the minimum of VI,we then expect to see a progression of vibronic components; usually the progressions are not very long, since the Coy,decrease rapidly for large values of v,. The maximum intensity in such a progression then occurs usually not at v, = 0, but at some relatively small value of this quantum number.The appearance of these progressions is the rationale for the statement frequently found in the literature that those vibrations appear prominently in the vibronic spectrum which transform the molecule from the equilibrium geometry of its ground state to that of the excited state. In actual molecules, of course, we usually do not encounter any of these first three limiting cases in pure form. Thus the deformations of Case 2 usually accompany the distortions of Case 3, and we have to deal with Case 4 where we find both distortion and displacement along one (or more) of the normal co- C.Manneback, Physica, 1951, 17, 1001. Roche and Jafk ordinates [Figure l(d)]: equation (23) is still valid and it is possible to evaluate the ctava.As indicated above, the deformations of the potential energy surface usually have relatively little effect on the Franck-Condon factors, so that Case 4 is very similar to Case 3. Often, the displacement of VFrelative to Vr occurs along several normal co-ordinates. Since the total Franck-Condon factor CPvis the product of individual CPavafor individual vibrations, the effects are readily predicted, and mixed progressions (corresponding to combination bands in the i.r.) between the displacing normal co-ordinates are expected to show weakly in absorption or emission. In all the above situations of Figure 1, we have assumed that the normal co-ordinates remain unchanged upon excitation, although their origin may have been displaced.To provide a general treatment, we must consider changes in going from the Q, to the Q,‘. Since the vibrational degrees of freedom are the same in the ground and excited states, it is always possible to express the normal co-ordinates Q,’ as linear combinations of the Q,: Q,’ = CA,BQp + B, = 1,2,. . . ,3N -6 We may now distinguish two basically different situations: if all AaB (except A,,) vanish, the co-ordinate axes in the two states are parallel. If any Aa8 (a # p) is non-vanishing, some Q,’ axes are rotated with respect to the Q, axes; this situation is referred to in the literature as the Duschinsky effe~t.~ The difference between these two situations is illustrated in Figure 2 where again we suppose that there are only two normal co-ordinates (a,/i?1, 2).We note that = the sections of V, and V, by horizontal planes are ellipses with principal axes directed along the axes of the normal co-ordinates; such ellipses are represented in Figure 2. In Figure 2(a), with no Duschinsky effect, Ql‘ = QI + B1 and Q2’ = Q2 + B2; ,GI = fil but ii2 # v”. This corresponds to Case 3 of the previous discussion for Ql, and to Case 4 for Q2. On the other hand, Figure 2(b) represents the same surfaces, but in addition to displacements and distortions, there is a rotation of Ql’ and Q2‘ with respect to Ql and Q2. The factorization of equation (23) is not possible when a Duschinsky effect is present, and the calculation of the intensity distribution requires the evaluation of more involved integrals than simply the overlap between two displaced and/or distorted harmonic oscillators.A Duschinsky effect is probably present in many actual spectra and is likely to alter significantly the vibrational intensities if the rotation of the normal co-ordinates is important. Although it has been studied in some particular F. Duschinsky, Acta Physiochim. U.R.S.S., 1937, 1, 551. Vibrational Intensities in Electronic Transitions E (a> (b) Figure 2 Potential surfaces illustrating the Duschinsky eflect cases,lOJ1 it has not yet been fully investigated; apparently most spectra can be understood with sufficient accuracy without taking it into account. We have thus examined the different cases and seen why more than one band appears in the electronic spectra of molecules; observation of only a single band would correspond to the ideal Case 1of identical potential surfaces, a case which is virtually never encountered.lo B. Sharf and B. Honig, Chem. Phys. Letters, 1970, 7, 132. l1 G. J. Small, J. Chem. Phys., 1971, 54, 3300. 174 Roche and Jaflk The above discussion presupposed a knowledge of Vr and V,. Unfortunately, theoretical calculation of potential surfaces, even for ground states, although in principle feasible, is not yet a practical reality. While information about ground- state potential energy functions is readily available from i.r. and Raman spectro- scopy, and other physical measurements, the vibronic structure of electronic transitions is about the only experimental avenue to excited-state potential functions, We are now in a position to apply the above arguments to obtain information about the relation of VFto Vzfrom the vibronic structure of spectra.For example, if no progressions are observed, implying that all bands correspond to dv = 0, this strongly suggests that Vr and V, are practically not displaced with respect to each other. On the other hand, the appearance of progressions in one or several frequencies shows that the surfaces are displaced along the corresponding normal co-ordinates. The intensity distribution depends on the extent of the displacements. If one knows the normal co-ordinates, one can calculate approxi- mately the displacements by fitting the bands with calculated Franck-Condon factors. In absorption at low temperatures we expect, for each displaced co- ordinate Q,’, a progression of band with maximum intensity generally occurring at some dv, > 0; i.e.the most intense band generally is not the 0-0 band (all the p, and all the va equal to zero). At higher temperatures, several new pro- gressions of weaker intensity may appear, their intensity increasing with temper- ature (hot bands). At sufficiently high temperatures, the cold bands may even noticeably lose intensity. The spacing of the successive terms is a measure for the vibrational frequencies va of the excited state in absorption andpa of the ground state in emission. Such simple rules form a useful tool for the analysis of experimental spectra and the study of the potential surfaces of excited states.Symmetry arguments can also serve as a powerful tool in the analysis of experimental spectra and the study of excited states. The reader is referred to standard texts for the use of group theory in spectroscopy.12 Let it suffice here to say that the transition Fv+-Ipcan have non-vanishing intensity only if xzp(q)xFv(q)[cf. equation (20)) is invariant under all symmetry operations of the molecule; in other words, if the product of the X is totally symmetric. This requirement immediately elimin- ates many vibronic transitions but never the 0-0 band: the 0-0 band is always present in an allowed transition. It is now time to look back to our two basic approximations, the assumption of a harmonic potential surface and the Condon approximation.In particular, the discussion of the Condon approximation will lead us to the consideration of symmetry-forbidden electronic transitions. Harmonic Approximation.-Potential surfaces are not in reality harmonic except in a small region around the equilibrium geometry. The anharrnonicity becomes important for high vibrational excited states, and these in turn are important l* See for example: M. Orchin and H. H. Jaff6, ‘Symmetry in Chemistry’, Wiley, New York, 1967, Chapter 5, section 5.3. Vibrational Intensities in Electronic Trairsitions when the potential surfaces are largely displaced; in such rather rare cases dramatic changes in the spectrum can occur for which the above discussion is totally invalid.Such a case is, e.g., the phenomenon of dissociation upon excita- tion.l3 In a rigorous treatment it is to be noted that, with the introduction of higher-order terms in Vz(and/or V,), the nuclear Schrodinger equation cannot be factored into 3N -6 unidimensional ones and consequently the normal co-ordinates do not exist as such. However, for small translations of the potential surfaces, only those levels appear in the spectrum for which paand v, are small, and therefore anharmonicity will have little effect ; under these circumstances anharmonicity can be treated as a perturbation. + Condon Approximation.-So far we have assumed that M,,(y) is approximately 3 constant and we have replaced it by Mz,(0), where 0 stands for the equilibrium + geometry of I. In a better approximation we can expand MIF(q)in a series around 0 [equation (28)].Substitution in equation (10) leads to equation (29). Q,+ .... 0 4 Perturbations due to Vibronic Coupling 3 + The derivatives M, = [aM,fl(q)/aQ,]~do not generally all vanish and hence the second term on the right of equation (29) generally makes some contribution + to MzFpv.This second term appears because the electronic wavefunctions vary with q, and will be referred to as the 'vibronic coupling' term or simply 'perturb- -+ ing' term; in turn we call MIF(0)Spvthe 'Condon term'. Again group theory provides rigorous symmetry selection rules for the perturbing term in symmetrical molecules, and an important remark can be made similar to the one we have made for the Condon term: for the perturbing term to be non-zero, XzpQ,X,' must be totally symmetric.Now if Q, is totally symmetric, this means that XI"XF' must be totally symmetric; in other words if Q, is totally symmetric, the same vibronic transitions are allowed for the Condon term and the perturbing term. On the other hand, if Q, is not totally symmetric, XzpXF"must not be totally symmetric: in other words, if Q, is not totally symmetric the vibronic transitions allowed for the Condon terms art: forbidden for the perturbing term, and some of the vibronic transitions forbidden for the Condon term can be made allowed by the perturbing term. We will keep this remark in mind in looking at the possible effects of the l3 See ref.2, p. 445. Roche and Jaffi vibronic coupling terms in electronic transitions. First we rewrite equation (29) in a more convenient way as equation (30),assuming as before that the harmonic approximation is valid and that there is no Duschinsky effect. It can be shownl* that the recurrence relationship (31) holds for the harmonic functions xva. With the use of this relation, equation (29) then takes the form (32), where a and b are constants; in equation (32) we have the same type of integrals S as in our previous discussion of the Franck-Condon factors. Perturbing terms due to Q, which are not totally symmetric give rise to bands which are forbidden in the Condon approximation. In the cases of potential surfaces illustrated by Figures l(a) and (b) (Cases 1 and 2), the coefficients of + Maare very small unless ,u, = v, k 1 ; in these cases no progressions in 01 will be observed, but only the 0 -1 bands in the cold, and 1 +-0 and 1 -2 as hot bands.Thus we may expect progressions in any vibration /3 for which V, and V, are strongly displaced relative to one another. In the cases of Figures l(c) and (d) (Cases 3 and 4) we may expect progressions in a.The effect of these perturbing terms due to non-totally symmetric Q, differ depending on whether the electronic --+ + transition is allowed [MIF(0)# 01 or symmetry forbidden [MIF(0)= 01. In the allowed case, the perturbations cause new weak bands to appear in addition to the much more intense Condon term allowed bands.In the forbidden case these perturbation bands are the only bands appearing in the spectrum, as will become apparent from the following argument: a totally symmetric distortion, by definition, does not change the symmetry of the molecule or of the electronic --t state of this molecule; consequently, if MIF(0)= 0 for symmetry reasons + MIF(Q,) vanishes for any value of Q, if Q, is totally symmetric; as a result, vibronic coupling by totally symmetric vibrations vanishes, and only non-totally symmetric vibrations can bring intensity to symmetry-forbidden transitions. From what we have said before, we can then conclude that the vibronic bands that would be allowed in an allowed transition are forbidden in such a symmetry-forbidden transition; in particular, the 0-0 band is forbidden.The absence of the 0-0 band along with the weak intensity of the spectrum is characteristic of symmetry-forbidden transitions (another feature is a distinct vibrational structure in the spectrum, even in solution, due to the fact that in general only a few l4 E. B. Wilson, J. C. Decius, and P. C. Cross, 'Molecular Vibrations', McGrnw-Hill, New York, 1955, p. 38. Vibrational Intensities in Electronic Transitions bands are allowed). In many molecules, there is no change of symmetry upon excitation, which means that V’ and V, may only be displaced along totally symmetric vibrations. These do not contribute to the intensity but may show up as progressions.On the other hand, the transitions which make the transition allowed generally do not show up as progressions. The perturbing terms due to totally symmetric vibrations contribute intensity in allowed transitions. The effect of such terms is not readily observable since the intensity they contribute is much smaller than typical Condon terms on which they are superimposed; thus they only result in a change of the intensities of the Condon term bands. It has been shown that such perturbation may be respon- sible for a lack of ‘mirror symmetry’ between absorption and fluorescence, even when such a symmetry would be expected according to the Condon approxi- mation.15 5 Example of Symmetry-forbidden Transitions We shall conclude this elementary review with a discussion of some of the most prominent features of the absorption band system of benzene vapour near 260 nm.The overall weak intensity and pronounced vibrational structure, even in solution, suggest a symmetry forbidden transition. From its energy it appears obvious that it is a 7~ -+n* transition. We shall limit ourselves to two of the numerous progressions exhibited by the real spectrum :the progression A which is by far the most intense of all, and the progression B of weaker intensity. The intensities of A and B have been estimated by Sponer et aZ.,16 and are presented in Figure 3. Both progressions are in the same vibration 18 (frequency 925 cm-l). A progression :x 00 --+ 1.1 B progression : io-too fio-+oi 10402 io-+o3 00-00 (0-0) (38 100cm -) Figure 3 Two progressions in the absorption spectrutn of betizene vapour The vibronic bands are represented by ab -+ a’b’ where a and a’ are the quantum numbersof thevibrationa (see below) in the ground and excited states, respectively, l6 D.P. Craig and G. J. Small, J. Chem. Phys., 1969, 50, 3827. l6 H Sponer. G. Nordheim, A. L. Sklar, and E. Teller, J. Chem Phys., 1939, 7, 207. Roche and Jafb and b and b’ are the corresponding quantum numbers for the vibration fl. The intensities of the B bands are found experimentally to increase with temperature: they are thus hot bands. The rather long progressions in v8 show that VI and V, are displaced along the corresponding normal co-ordinate Qp. The vibrations of the ground state I are known17 from i.r.and Raman spectra but not the vibrations of F, and in order to identify Qb we have to make some reasonable hypotheses and see whether the experimental spectrum is in agreement with them. We will assume that, at equilibrium, I and F have the same symmetry (&). Then Qs has to be totally symmetric; benzene has only two totally sym- metric vibrations, one involving mostly the carbon ring at 993 cm-1, the other involving mostly the C-H bonds at 3073 cm-l. Now a T -T* transition will certainly affect primarily the C-C bonds so that we can assume that Vr and VF are distorted and displaced along the ‘ring-breathing’ totally symmetric normal co-ordinate. The distortion is not significant (993 cm-1 -925 cm-l); the displacement has been estimated to correspond approximately to an in- crease of 0.04 A in the C-C bond distances;18 this is enough to make the dvB = 1 bands more intense than the dv, = 0 bands.Next, we shall try to understand the 1126 cm-1 separation between the A and B bands. Since the first are cold bands, and the second hot bands, the frequency would have to correspond to one of the vibrations of the ground state; however, no such vibration exists in benzene. This is another argument to assign the band system to a forbidden transition, which is then made allowed by some non- totally symmetric vibration. In this case, we have seen that the cold bands will correspond to a 0 -1 transition in a and the hot bands to a 1 40 or 1 --+ 2 transition in a;in fact, two systems of hot bands, one for 1 -+ 0 and one for 1 --t 2 are expected to show with comparable intensities, the second being displaced with respect to the first toward the highfrequencies by 2Ta: a more detailed analysis of the spectrum shows that there is another progression of hot bands similar to the B progression at higher frequencieP and we will then assign B to the 1 ---t 0 transition in a.If this is so, Figure 4 shows immediately that the separation between the A and B bands is pa + .”,. Let us attempt to find among the vibrations of benzene the vibration a which can contribute the most to the intensity. An out-of-plane vibration will not significantly change the T wavefunctions involved 4 in this T -+T* transition, and the derivatives Ma will be small for such a vibra-tion. Therefore, we have to look for a among the in-plane vibrations, Examina- tion of the corresponding frequencies shows that the only reasonable choice for a is the 606 cm-l vibration (Ezs);hence va = 1126 -606 = 520 cm-1 in the excited state.The frequencies of all the other in-plane non-totally symmetric vibrations lie above lo00 cm-l, which would lead to an estimate of less than 150 cm-1 for Pa, and would imply a tremendous and very unlikely distortion of VF with respect to V.. The 606 cm-l vibration is mainly a ring vibration, the most likely to affect the T electrons and the intensity of the spectrum. With this l7 G. Varsanyi, ‘Vibrational Spectra of Benzene Derivatives’, Academic Press, New York, 1969, pp.70-71. F. M. Garforth, C. K. Ingold, and H. G. Poole, J. Chem. Soc., 1948, 406. Vibrational Intensities in Electronic Transitions -1 To I I I I I I I I I I I I +1 I I I I.f1 0 Figure 4 Vibronic transitions from ground to excited state in benzene choice for a, we see that V, and V, are only slightly distorted and not displaced along Q,, so that there is no progression in a.The 0-0 band is of course absent, and, if allowed, would be situated at 38 100 cm-1 (Figure 3). In summary, we have given a satisfactory interpretation of the spectrum as a symmetry-forbidden transition and have identified the vibronic bands. We have at the same time gained some insight into the shape of the potential surface of the excited state.

ISSN:0306-0012    

DOI:10.1039/CS9760500165

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Synthetic Routes to /3-Lactams By N. S. Isaacs DEPARTMENT OF CHEMISTRY, UNIVERSITY OF READING, WHITEKNIGHTS, READING. BERKS. The four-membered p-lactam (2-azetidinone) ring system (1) has for many years been of great practical significance as the centre of reactivity of the penicillins (2) and cephalosporins (3). Much effort has been put into the synthesis of simpler 4 3 RCONJH CH2-CH,I I, U \ k0,H (1) penicillin G (2) R = PhCH, l-IO,CCH(CH,),CONH NH: CH,OCOMeI p>0 CO,H cephalosporin c (3) /3-lactams for testing as antibiotics, antidepressants, sedatives, etc.,l.2 and great interest has been aroused by their conversion into linear polymers. Numerous routes to these compounds have been devised over the years, although much of the information is to be found in the patent literature, and a wide variety of structural types is now available by rational syntheses.A review of the earlier literature by Sheehan and C~rey~~ contains representative synthetic procedures. Other aspects of synthesis have been reviewed more re~ently.~~J 1 E. Testa, L. Fontanella, G. F. Cristiani, and F. Fava, Annulen, 1958, 614, 158; E. Testa, A. Bonati, G. Pagani, and E. Gatti, ibid., 1961, 647, 92; E. Testa, L. Fontanella, and L. Mariani, ibid., 1963, 660, 135; E. Testa, L. Fontanella, and M. Bovara, ibid., 1964, 671, 97; E. Testa and L. Fontanella, ibid., 1964, 671, 106; E. Testa, L. Fontanella, and V. Aresi, ibid., 1964, 673, 60. E. Testa, L. Fontanella, and F. Fava, Furmuco Ed. Sci., 1958, 13, 152; E.Bellasio, A. Vigevani, G. F. Cristiani, and E. Testa, ibid., 1970, 25, 347; L. Fontanella, G. Pifferi, ibid., 1972, 27, 527; L. Fontanella, G. Pifferi, E. Testa, and P. Consonni, ibid., 1973, 28, 105. "(a) J. C. Sheehan and E. J. Corey, in 'Organic Reactions', Wiley, New York, 1957, Vol. 9, Chap. 6; (b) P. G. Sammes, Chem Rev., 1976, 76, 113; (c) A. K. Mukerjee, and R. C. Srivastiva, Synthesis, 1973, 328; K. Hensler, Helv. Chim. Acru, 1972, 55, 388. Synthetic Routes to /%Lactams 1 Ring-closures of C3N Systems In principle, it is possible to construct the 2-azetidinone ring by cyclization at each of the four bonds, and examples of at least three of these four possibilities are known. A. Cyclization of 3-Aminopropanoic Acid Derivatives.-The obvious synthesis of a @-lactam, dehydration of 3-aminopropanoic acid, is not readily achieved owing to the ring strain engendered on lactamization. Few examples of this method are known,4 though heating in DMSO at 150°C has recently been claimed5 to yield the parent compound satisfactorily. Two versatile methods of this type have been developed and extensively used by Testa, Fontanelli, and co-workers in a long series of papers and patents recording the syntheses of hundreds of examples.The first approach, pioneered by Holley and Holley,G consists of treating a 3-aminopropanoate ester with a Grignard reagent, forming the /?-lactam in one operation (Scheme 1). Yields were originally very low,6 Me Me MeI I CH2-+Et ,CH, -6,.Et/ \ NH MeMgI Y Scheme 1 but under optimum conditions 50-90 % conversion may be achieved.1~2.7~8 This method is capable of yielding a wide variety of alkyl and aryl derivatives with up to five substituents at N, C-3, and C-4. Acetic anhydride,Q acetyl ~hloride-PCls,~~and alanesll have been proposed as cyclizing agents. The second classical approach uses thionyl chloride or a similar reagent in the presence of a weak base. A @-aminopropanoyl chloride is formed which spon- taneously cyclizes. Again, this approach is very versatilegJ2-14 for alkyl- and aryl-substituted @-lactams. Both these methods permit the retention of stereo-chemistry at the a-and /3-carbons and the incorporation of chiral centres at C-3 and C-4of the lactam ring.12 The principal disadvantages lie in the limitations on certain functional groups, e.g.hydroxyl and carbonyl, which would react * E. Jucker, A. Ebnoether, E. Rissi, A. Vogel, and R. Steiner, Chem. Abs., 1963.59, PI 1 425c. R. W. Holley and A. D. Holley, J. Amer. Chem. SOC.,1949, 71, 2124, 2129. 'T.V. Stezhko, S. Y. Skachilova, and M. G. Pleshkov, Zhur. org. Khim., 1974, 10, 1556. 'E. Bellasio, A. Vigerani, and G. F. Cristiani, Farmaco Ed. sci., 1970, 25, 409. B. I. Kurtev, N. M. Mollov, E. M. Simova, and Y. Stefanovski, Compt. rend. Acud. bulg. Sci., 1960, 13, 167. A Dobrev and C. Ivanov, Chem. Ber., 1971, 104,981. loE. Testa and L. Fontanella, Chem. Ah., 1962, 56, P1429f. l1R. B. Woodward, Chem. Abs., 1971, 75, P140833.1) K. D. Kampe, Chem. Abs., 1970,73, P45 313. lS L. Fontanella and E. Testa, Annzlen, 1959, 622, 117. F. F. Blicke and W. A. Gould, J. Org. Chem., 1958, 23, 1102. Isaacs with the Grignard reagent or thionyl chloride, and also in the lengthy synthesis of the appropriate starting materials. For example, the route shown in Scheme 2 R2 R2 CONH, R'vcozEt R2/ \CH2NH2 Reagents: i, OEt-, RlCI; ii,OEt-, RTI; iii, OH-; iv, SOCI,; v, NH8;vi, H,, catalyst Scheme 2 has been extensively used by the Italian workers. Alternatively, Michael addition of a carbanion to an irninel5 or of an amine to an acrylatel6J7 will yield the p-aminopropanoates more directly (Scheme 3). H Ph NH C0,EtPh" ObC'OEt /Ph Me H Me \/CH--CH2\ COzR0 FH MeN H /NH2MeNH Scheme 3 Some instances are known in which the addition of a primary amine to a /%halogenopropanoyl halide leads directly to the fl-lactam.One supposes that initial attack occurs at the @carbon rather than at the carbonyl group18otherwise E. Simova and B. Kurtev, Munatsh., 1965, 96, 722. l6 N. P. Zapevalova, T. A. Sokolova, N. M. Bazhenov, and A. 1. Kol'tsov, Doklady Akad. Naitk S.S.S.R., 1963, 150, 551. T. A. Sokolova and L. A. Orsyannikova, Doklady Akad. Nauk S.S.S.R., 1962,143, 140. B. J. R. Nicholaus, E. Bellasio, G. Pagani, and E. Testa, Gazzetfa, 1963, 93, 618. 183 Synthetic Routes to ,&Lactams a p-halogenoamide would result, and these are known to need strong base to effect cyclizat ion. 199 20 B.Cyclization of 3-Halogenopropanoamides.-Internal displacement of halide by aide nitrogen is not energetically favourable unless the amide is first converted into its conjugate base. The latter conversion requires a strong base. This type of synthesis has been developed by Knunyants21 using alkali-metal amide as base (Scheme 4).22~~~ Other bases which may be used include lithium carbonate,24 /CH2-cH2'c CHS-CHZBr IN-CHN I I\0 I Ph/ I % Ph Ph Scheme 4 sodium hydride and sodium hydro~ide,~~~~~ amines in dimethylformamide,27 dimsyl sodium,2* and weak bases at high temperature^.^^ The method is versatile for alkyl- and aryl-substituted p-lactams and no doubt involves inversion of configuration at C-4. C. Ring-closure at C-3-C4.-Bond formation between the a-and /%carbons can be accomplished if there is a nucleophilic leaving group at one and a potential carbanionic centre at the other.It is difficult to generalize, but the examples in Scheme 5 may illustrate the application of this prin~iple.~~-~~ D. Ring-closure at C-2-C-3.-While no examples of this type of synthesis are known to the reviewer, a possible approach might be via the urethane (4), although the necessary basic conditions would probably induce some reaction other than cyclizat ion. E. Bellasio, G. F. Cristiani, and E. Testa, Ann. Chim. (Italy), 1969, 59, 1122. zo E. Testa, L. Fontanella, and V. Aresi, Annalen, 1964, 673, 60; E. Testa, B. J. R. Nicolaus, E. Bellasio, and L. Mariani, ibid., p. 71. a1 I.L. Knunyants, E. E. Rytslin, and N. P. Sambaryan, Izvest. Akad. Nauk S.S.S.R. Odtel Khim Nauk, 1960, 527. ea M. S.Manhas and S. J. Jeng, J. Org. Chem., 1967, 32, 1246. z3 E. Testa, L. Fontanella, and V. Aresi, Annalen, 1964, 673, 60. z4 Chem. Abs., 1970, 73, 45 314. as D. Greiciute, J. Kules, and L. Rosteikeine, Zhur. org. Khim., 1974, 10, 436. za J. E. Baldwin, A. Au, M. Christie, S. B. Haber, and D. Hesson, J.Amer. Chem. SOC.,1975, 97, 5957; S. Nakatsuka, H. Tanino, and Y. Kishi, ibid., pp. 5008, 5010. F. Merger, Chem. Abs., 1972, 76, P3683. S. D. Levine and V. L. Narayanan, Chem. Abs., 1971, 74, P87 810. za R. F. Abdullah, S. K. Lataivi, T. A. Crabb, and R. Cahill, Z. Naturforsch., 1971, 26, 95 A. K. Bose, G. Spiegelman, and M. S. Manhas, Tetrahedron Letters, 1971, 3167.*l E. Ziegler and G. Kleineberg, Monatsh., 1965, 96, 1296. as B.G. Chattergee and P. N. Moza, J. Medicin. Chem., 1966, 9, 259. Isaacs C1 Ph H Ph \‘CH \CH -CH =CH~ NEt, ‘CH -CH -CH= CH,1 I + It N-Cc\ Ph” ‘0 Ph’ NO Scheme 5 \c-r-0 ,N-CC lrOEt 2 Non-concerted Cycloaddition Reactions Several useful syntheses of p-lactams which have been developed consist of the addition of a C-N to a C-CO component to form the ring in a single operation with a stepwise mechanism. Substituted acetyl chlorides with electron-withdrawing substituents and at least one hydrogen at the a-carbon add to imines in the presence of amine bases.33 The mechanism is probably as depicted in Scheme 6. The acyclic intermediate amide may on occasion be isolated.This method is particularly suited to the preparation of 3-X-azetidinones, where X is an acid-strengthening group such as -N3,34 -0R,3oJ3p35J6 -ha1,33~37-3~ -COC1.30~40 This addi- tional functionality at C-3 is valuable by virtue of the further transformations which are possible (see Section 7). Some typical examples are shown in Scheme 6. Some workers have reported stereospecificity between C-3 and C-4,30*35939 33 R. Lattrell and G. Lohaus, Chem. Ah., 1972,77,P48 199. 34 A. K. Bose, B. Anjaneyulu, S. K. Bhattacharya, and M. S. Manhas, Tetrahedron, 1967,23, 4769. 36 A. K.Bose, B. Lal, and B. Dayal, Tetrahedron Letters, 1974, 2633. R.Lattrell and G. Lohaus, Annalen, 1974, 87. 37 D.A.Nelson, J.Org. Chem., 1972,37, 1447. 38 A. K.Mukerdzhi and N. N. Savarov, Khim. geterotsikl. Soedinenii, 1970, 1626. A.K.Bose, B. Dayal, H. P. S. Chawla, and M. S. Manhas, Tetrahedron Letters, 1972,2823. 4oA.K.Bose, J. C. Kapur, B. Dayal, and M. S. Manhas, J. Org. Chem., 1974, 39, 312; Tetrahedron Letters, 1973, 1811, 2563. Synthetic Routes to /&Lactams c1 H CI Ar, ,H C1 I H Ar H C1 I HCB Ar I C1 C ‘C’ Et,N ‘i;Q’ c1 , ‘cI -c’ ~II I-Ph )N -C\O phHN-C\\O 0 PhC‘H S PhCH,S‘CH ‘CH -CH Et3NII + II R,N-c, RAN o”c‘cl ‘0 Scheme 6 while others have obtained mixtures of cis-and trans-pr0ducts.3~ The degree of stereospecificity has been sh0wn3~ to depend upon the conditions used, mainly trans resulting from addition of base to the other reagents and cis from addition of acyl chloride to the mixture of imine and base.3-Aminoazetidinones have been thus prepared by reduction of the azido-cornpo~nds~~ and by hydrolysis of an amidoazetidinone generated from an a-amidoacetyl chloride such as phthalyl 186 Isaacs glycyl chloride41 or phthalimidoacetyl chloride (5);3*~42*~3the latter eventually yields (6) on transamidation with hydrazine. If the imine component in these reactions is a Schiff base or an N-arylimidic acid derivative (7), then 4-alkoxy- azetidinones are produced.42 The sulphur analogues, thioimidates, give the corresponding 4-alkylthiol compounds,43 including cyclic systems with the penam structure (8).39J4 The reactions may be carried out in many cases by treating a mixture of the imine and, for example, dichloroacetic acid, with P0C13.37*45 It is possible that the acid chloride is formed as an intermediate, though it has been suggested that the phosphorus halide participates as an electrophilic catalyst (Scheme 7).Anhydrides can also be used;46 Yoshida and coworkers have extensively investigated the use of dichloroacetic anhydride in the production of 3,3-di~hloroazetidinones.~~ c-Ph Ph </H c1 'CH CHCI, 0 'CH CClz 11-I -!-cl -'N112 IN -C, p-An' OH/C"o C1"CI p-Ad I OPOClZ OH C1 Ph I Cl'CH-C' I1 p-*n/ "-C*o Scheme 7 41 L. Paul, A. Draeger, and G. Hilgetag, Chem. Ber., 1966, 99, 1957 48 L. Paul and K. Zieloff, Chem. Ber., 1966,99, 1431. 43 M. D. Bachi and 0.Goldberg, J.C.S. Chem. Comm., 1972, 313. 44 R. A. Firestone, N. Maceijewicz, and B. Christensen, J. Org. Chem., 1974, 39, 3384. 45 E. Ziegler, T. Wimmer, and A. Mittelbach, Monatsh., 1968, 99, 2128. 46 A. K. Bose, J. C. Kapur, S. D. Sharma, and M. S. Manhas, Tetrahedron Letters, 1973,2319. 47 G. Sunagawa and N. Yoshida, Yakugaku Zasshi, 1962, 82, 826, 835, 846; N. Yoshida, Sankyo Kenkyusho Nempo, 1966, 18, 38. 3 187 Synthetic Routes to /%Lactams A second method of this type is the Reformatsky reaction between imines and a-bromo-esters in the presence of zinc, which was first discovered by Gilman and S~eeter.~SThe method has recently been extensively developed in France and by Bose and associates in New Y0rk.49-5~ Ana-(bromozinc) ester forms and provides a nucleophilic centre for C-3-C-4 bond formation (Scheme 8).Some control of N-C, IEt Ico Ph’ ‘0 ph\ CH-C6 Et IINH C=O Ph’ I OEt (9) Scheme 8 the stereochemistry at these centres can be obtained as the cis:trans ratio is sensitive both to the solvent51 and to the size of the 3-substituent.50~55 In some instances, yields are appreciably reduced by the formation of ,&amino-esters (9) which fail to cyclize because of competitive displacement of the zinc by a pr~ton.~~~~~However, as shown above, these compounds can be converted into the p-lactam by addition of a Grignard reagent. The Reformatsky method is versatile in giving a wide range of alkyl- and aryl-azetidinones; because of their greater availability, diarylimines have been most used and consequently 1,4-diaryIazetidinones are the commonest products. Unactivated esters will also condense with imines under the influence of strong bases (Scheme 9).57 It is uncertain whether this reaction is a nucleophilic addition H.Gilman and H. Speeter, J. Amer. Chem. SOC., 1943, 65, 2255. 49 E. Cuinget, D. Poulain, and M. Tarteret-Adelban, Bull. SOC.chim. France, 1969, 514. H. B. Kagan, J.-J. Basselier, and J.-L. Luche, Tetrahedron Letters, 1964, 941. 61 J.-L. Luche and H. B. Kagan, Bull. SOC. chim. France, 1969, 3500. 52 F. Dardoize, J. L. Moreau, and M. Gaudemar, Compt. rend., 1969, 268,2228. 63 M. S. Manhas, J. Jeng, and A. K. Bose, Tetrahedron, 1968, 24, 1237. 54 S. Mohan, P. S. Sethi, and A.L. Kaloor, J. Indian Chem. SOC., 1971, 48, 685. 56 F. Dardoize, J. L. Moreau, and M. Gaudemar, Bull. SOC.chim. France, 1973, 1668. 66 F. Dardoize, J. L. Moreau, and M. Gaudemar, Bull. SOC. chim. France, 1972, 3841. b7 E. Simova, M. Mladenova, and B. I. Kurtev, Izvest. Ost. Khim. Nauk Bulg. Akad. Ncuk, 1970,3, 497. Isaacs PhCH=NPh Phi-IC yC,Me, PhRN 1 “0 11 II\--C‘ + CH -CMe,Ph, I I - PhCH -CMe, N--C Ph’ I I *O OBut Scheme 9 of ester enolate, or whether an intermediate keten is formed, these species being known to add to imines. 3 12 + 23 Cycloadditions The /?-lactam ring may be synthesized in one step by the cycloaddition of component halves of the ring, each initially containing a double bond. Two well documented possibilities are an isocyanate with an olefin, and a keten with an imine.These reactions may occur by concerted processes, in which case the restrictions of orbital symmetry conservation necessitate an orthogonal approach of the reagents (a ,2s + ,2a co&guration).58 However, in some instances at least there is strong evidence that a two-step mechanism operates via a zwitterionic intermediate. A. The Addition of Isocyanate to Ole6n.-Chlorosulphonyl isocyanate has been found to be very reactive towards a great variety of olefinic species, leading to /?-lactams directly in moderate to high yield (Scheme 10).59-62 The initial product, a 1-chlorosulphonylazetidinone,is thermally unstable but is readily hydrolysed to the parent /?-lactam.In this way, a wide variety of C-3 and C-4 substituents may be introduced. As byproduct, spy-unsaturated amide (10) may be obtained, in agreement with the proposed intermediate zwitterion (1 1); the proportions of the two products depend upon the number and type of substituents on the olefin used.60 This mechanism also explains the regiospecificity which invariably leads to the isomer of (11) with the most stable distribution of positive charge. One might expect some loss of stereochemical integrity in the olehic moiety since rotation in (1 1) is possible. However, frequently this does not occur to any great m N. S. Isaacs and P. Stanbury, J.C.S. Perkin 11, 1973, 166. s9 C. Ivanov and V. Dryanska, Doklady Bolg. Akad. Nauk, 1969, 22,423.*O R. Graf, Anmlen, 1963, 661, 111. H. Bestian, H. Biener, K. Clauss, and H. Heya, Annalen, 1968, 718, 94. T. Haug, F. Lohse, K. Metzger, and H. Batzer, Helv. Chim. Acta, 1968, 51,2069. Synthetic Routes to p-Lactams 7Me2C=CH2 Me26-CH2 I C CIS02N= C=0 ClS02N4z~0 \ N-C ClSO,/ +O HN-Scheme 10 extent though higher temperatures favour products of lower ~tereoselectivity.~~ This observation, together with the more rapid addition of cis-than trans-oleh~s,~~has led to the interpretation of these reactions as concerted cyclo- additions. However, the regiospecificity and the large rate-enhancing effects both of alkyl substituents on the olefin and of solvent polarity conclusively demon- state the presence of a polar intermediate.Thus 2,2-disubstituted ethylenes react ca. lo4 times faster than alk-l-enes,64 and solvent effect values such as kMeNo,: khexane Z lo5 are observed. Conjugated dienes undergo 1,2-addition, though the 1-chlorosulphonyl-4-vinyl-azetidinones subsequently rearrange, even at room ternperat~re,~5 to the 1,4- adducts63966-70 or to 2-pyridones.71 As expected, nucleophil ic subst ituen t s activate the olefin; vinyl ethers readily yield 4-alkoxyazetidinones72-76and vinyl esters the 4-acetoxy-analogues,77 from which 4-hydroxy-/3-lactams may be obtained on careful hydroly~is.~~Enamines similarly give 4-aminoazetidi- none~.~~,~*Allenes also add to give 3-methylene derivatives (12).79 Cyclopropanes O3 H. J. Friedrich, Tetrahedron Letters, 1971, 2981.O4 K. Clauss, Annalen, 1969, 722, 110. O6 R. W. Hoffmann and H. Diehr, Tetrahedron Letters, 1963, 1875. 66 E. J. Moriconi and W. C. Meyer, Tetrahedron Letters, 1968, 3823. O7 E. J. Moriconi and W. C. Meyer, J. Org. Chem., 1971, 36,2841. 68 P.Goebe and K. Clauss, Annalen, 1969, 722, 122. 6s T. Haug, F. Lohse, K. Metzger, and H. Batzer, Helv. Chim. Acta, 1968, 51, 2069. 'O M. Fischer, Chem. Ber., 1968, 101, 2669. 71 H. Koichi, H. Matsuda, and Y. Kishida, Chem. and Pharm. Bull. (Japan), 1973, 21, 109C. 72 F. Effenberger, P. Fischer, G. Prossel, and G. Kiefer, Chem. Ber., 1971, 104, 1987. 73 J. C. Martin, J. L. Chitwood, and P. G. Gott, J. Org. Chem., 1971, 36,2228. 74 R.Lattrell, Annalen, 1969, 722, 132, 142. 76 F. Effenberger and R.Gleiter, Chem. Ber., 1964, 97, 1576. 76 F. Effenberger and R. Gleiter, Angew. Chem., 1963, 75,450. 77 H. Bestian and D. Grimm, Chem. Ah., 1969, 73,P98 777. G. Opitz and J. Koch, Angew. Chem., 1963, 75, 167. Is E. J. Moriconi and J. F. Kelly, J. Amer. Chem. SOC.,1966, 88, 3657; J. Org. Chem., 1968, 33,3036. Isaacs Ph Ph H\: I,..CH-CII HN -C take part in the reaction, apparently following initial isomerization to the olefin caused by the electrophilic isocyanate.80 Chlorosulphonyl isocyanate is the most reactive, but other isocyanates have also been widely used; rates of olefin addition are greatly diminished by the presence of groups less electron-withdrawing than C1, e.g. kc1so,Nco :~M~OSO,NCO = 1 :10-4.64 Trichloroacetyl isocyanate adds to dienes,73?81 phenyl isocyanate to vinyl ether^,^^^^^ enamine~,~~and dienes,68 and p-nitrophenyl isocyanate to ~tyrene.~OVarious aroyl and arenesulphonyl isocyanates have been shown to add to alkenes85lS6 and vinyl ethers87988 and even to acetylene~8~~90 (to give 2-azetinones).Alkyl isocyanates have been little examinedg1 and would be expected to be somewhat unreactive. B. The Additions of Ketens to 1mines.-Staudinger, investigating the chemistry of diphenylketen in 1911, added p-nitrosodimethylaniline and obtained the p-lactam (13). He interpreted this as an initial cycloaddition to the nitroso-group, loss of C02 (to give an imine), and a second cycloaddition to the imine.92 This interpretation has been recently c0nfirmed.~3 There are many examples of the E.J. Moriconi, J. F. Kelly, and R. A. Salomone, J. Org. Chem., 1968, 33, 3448. B. A. Arbuzov, N. N. Zabova, and E. G. Yarkova, Zzvest. Akad. Nauk S.S.S.R.,Ser. khim., 1969, 1114. R.W.Hoffmann, U. Bressel, G. Juergen, and H. Haeuser, Chem. Ber., 1971, 104, 873. 8a R. W. Hoffmann, Angew. Chem. Internat, Edn., 1972, 11, 324. 84 M. Perelman and S. A. Miszak, J. Amer. Chem. SOC.,1962,84,4988. F. Effenberger and W. Podszun, Angew. Chem. Internat. Edn., 1969,8,976;F.Effenbergerand 0. Gerlach, Chem. Ber., 1974, 107, 278. 86 B. A. Arbuzov and N. N. Zobova, Doklady Akad. Nauk S.S.S.R., 1967,170, 1317. 87 M. Seefelder, Chem. Abs., 1968,69, P106 257. I. Ojiwa, S. Inaba, and Y. Nagai, Chem. Letters, 1974, 1069.B. A. Arbuzov and N. N. Zobova, Doklady Akad. Nauk S.S.S.R.,1967,172, 845. v0 R. Lattrell and G. Lohaus, Chem. Abs., 1971, 74, PI2 982. s1 K. D. Kampe, Annalen, 1971,752, 142; Chem. Ah., 1970, 73, PI20 136. va H. Standinger and S. Jelagin, Chem. Ber., 1911,44, 373. ma R.C.Kerber and M. C. Cann, J. Org. Chem., 1974,39, 2552. Synthetic Routes to /%Lactams Ph Ph Me,N (13) formation of a fl-lactam by cycloaddition of diphenylketen to a preformed imine, e.g. (14) (Scheme 11).94-96 Dimethylketen reacts analogo~sly.~~~~* Many R', ,R2C II/-! phu:0 Me' (14) R' = R2 = Ph R' = Me, R2 = H Scheme 11 other ketens are known only as transient species and are generated in situ by a nitrogen base and a substituted acetyl chloride (Scheme 12).It is clear that this H C1 'c1 Scheme 12 94 J. M. Decazes, J.-L.Luche, and H. B. Kagan, Tetrahedron Letters, 1970, 3561, 3665. 95 R.Huisgen, B. A. Davis, and M. Morikawa, Angew. Chem. Internut. Edn., 1968, 7, 826. 96 M. Sakamoto and Y.Tomimatsu, YakugakuZusshi, 1970, 90, 1386. 97 J. Cuthbert, K. C. Brannock, R. D. Burpitt, G. P. Gott, and V. A. Hoyle, J. Org. Chem., 1971, 36, 2211. 98 J. C. Martin, R. D. Burpitt, P. G. Gott, M. Harris ,and R. M. Meen, J. Org. Chem., 1971, 36, 2205. 192 Isaacs reaction is precisely that described in Section 2 as a dipolar cycloaddition initiated by attack of the imine nitrogen on the carbonyl group of the acyl chloride. The keten mechanism is frequently assumed to be the correct one for the analogous additions to alkenes,99 since here no nucleophilic species is available to add to the carbonyl group and no reaction occurs until the addition of base.It is apparent, therefore, that there remains uncertainty as to the true nature of the additions to imines which will here be treated as occurring via the keten. As a preparative route to p-lactams the additions of chloro-,100-102 fluoro-,lo0 dichloro-,102~103 bromo-,104 azid0-,44,105 and phenyl-ketensl06 or their equivalents are easy and efficient, leading to the appropriate 3-substituted compounds (Scheme 11). The stereochemistry at C-3-C-4 is not unambigously defined, but aldoketens tend to react with monosubstituted imines to give trans-products,lo7 though as much as 50 % cis product has been obtained from o-nitrobenzaldehyde anill01 (the rn-and p-isomers giving only trans) for reasons which are not clear.A high &:trans ratio was also obtained from the reaction of this anil and preformed methylketen, which tends to substantiate the keten mechanism for the former process. Few additions of keten itself have been observed, although it forms a lactam with (CF&C=NPh.lO* 4-Iminoazetidinones (1 5) are readily prepared from the keten and a ~arbodi-imide,~03~~05~106~109whereas the addition of amidines gives 4-aminoa~etidinones.110~~~~Ketens can result from the photo- lysis of, e.g. diazo-ketones (1 6),112 or the thermolysis of oxazolium-5-olates (17)113 and be trapped as a /3-lactam by imine. 4 Ring Expansions Several routes to azetidinones are known which involve expansion of a three- membered ring, either a cyclopropane or an aziridine.Addition of a primary amine to cyclopropanone followed by N-chlorination of the resulting hydroxyamine (18) and treatment with silver ion produces the lactam (Scheme 13).l14 A similar synthesis may be achieved using a benzoate leaving group or tosyl hydroxylamine.ll5 Oxidative ring-expansion of a cyclo- 99 R. Montagne and L. Ghosez, Angew. Chem. Znternat. Edn., 1968, 7, 221, 643. looW. T. Brady and E. F. Hoff, J. Amer. Chem. SOC.,1968, 90, 6256. lolD. A. Nelson, Tetrahedron Letters, 1971, 2543. F. Duran and L. Ghosez, Tetrahedron Letters, 1970, 245. Io3 R. Hull, J. Chem. SOC. (0,1967, 1154. looW.T. Brady, E. D. Dorsey, and F. H. Parry, J. Org. Chem., 1969,34,2846. lobM. S. Manhas, S. Jeng, and A. K. Bose, Tetrahedron, 1968, 24,1237. lU6P. G. Bird and W. J. Irwin, J.C.S. Perkin Z, 1973, 2664. lo' J.-L. Luche and H. B. Kagan, Bull. SOC. chim. France, 1968, 2450. lo8Y.V. Zeifman and I. L. Knunyants, Doklady Akad. Nauk S.S.S.R., 1967,173, 354. log C. Metzger and J. Kurz, Chem. Ber., 1971, 104, 50. 110 M. Sakamoto and Y. Tomimatsu, Yakugaku Zasshi, 1970, 90, 1386. A. K. Bose and I. Kugajevsky, Tetrahedron, 1967, 23, 957. Ila W. Kirmse and L. Horner, Chem. Ber., 1956, 89, 2759. 113 E. Funke and R. Huisgen, Chem. Ber., 1971, 104, 3222. 114 H. H. Wasserman, W. H. Adickes, and 0. E. de Ochoa, J. Amer. Chem. SOC.,1971, 93, 5586. lib H.H. Wasserman, E. A. Glazer, and J. Hearn-Michael, Tetrahedron Letters, 1973, 4855. Synthetic Routes to /%Lactarns Me Ar IMe /BuOCl+xR’ ‘Cl RNHB / propanone tosylhydrazone by MnO2 gives the p-lactam with retained stereochemistry at C-3-C-4.ll6 Dichlorocarbene addition to the azirine (19) leads, presumably, to the aza- bicyclobutane (20) which opens to the chloroazetine (21); this, in turn, can be readily hydrolysed to the p-lactam (Scheme 14).l17 The aziridinecarbonyl chloride (22) spontaneously rearranges to the 3-chloroazetidinone (23) (Scheme 14).11S It has been reported that diphenylcyclopropanone reacts with ammonia in one step to give 3,4-diphenylazetidinone (cis + trans).ll9 5 Ring-contraction Methods /%Lactams can be generated by the expulsion of a carbon, oxygen, or nitrogen atom from several types of five-membered ring.Photolysis of pyrazolidones (24) brings about isomerization to 1-aminoazetidinones (Scheme 15).120-122 Oxopyr- roline oxides have also been reported to give 1-acetylazetidinones among the F. D. Greene, R. L. Camp, V. P. Abegg, and G. 0.Pierson, Tetrahedron Letters, 1973, 4091. 117A.Hassner, J. 0. Currie, A. S. Steinfeld, and R. F. Atkinson, Angew. Chem. Internut. Edn., 1970, 9, 731 ;J. Amer. Chem. SOC.,1973, 95, 2982. 11* J. A. Deyrup and S. C. Clough, J. Amer. Chem. SOC.,1969, 91,4590 llSF.Toda and T. Mitote, Bull. Chem. SOC.Japan, 1969, 42, 1777. lSo J. C. Sheehan and G. D. Lambach, J. Amer. Chem. SOC.,1951,73,4752. lS1S.N.Ege, J.Chem. SOC.(C), 1969, 2624. la*C. E. Hatch and P. Y.Johnson, Tetrahedron Letters, 1974, 2719. 194 Isaacs Me PhHwN Me *Meu: aq. f---HCl Me hu __I) PhCHzCONH (24) 5% Scheme 15 products of phot~lysis,'~~and oxazolium salts give p-lactams on treatment with diethyl-P-a~etylphosphite;~~~however, these methods are of limited value because the reagents are not readily available and yields are poor. Among the most useful ring-contractions is the application of the photo-Wolff rearrangement to 2-diazocyclopentane-1,5-diones(25). Starting materials are available by lSs D. A. Black and A. B. Boscacci, J.C.S. Chem. Comm., 1974, 129. 124 A. Takamizawa and H. Sato, Chem. and Pharm. Bull (Japan), 1974,22, 1526.Synthetic Routes to /3-Lactams standard routes (Scheme 16), and the method can be adapted to the synthesis of a precursor of the cepham nucleus (26).125-127 (25) Scheme 16 PhCH,CONH CO,R 6 Miscellaneous Methods The one reported direct oxidation of an azetidine to azetidinone was catalysed by R1~0g.l~~The addition of copper phenylacetylide to diphenylnitrone leads to cis-l,3,4-triphenylazetidinonein good yield,129 though nothing is known for certain of what must be a complex sequence of events. On photolysis, diazoacetic diethylamide gives cleanly a mixture of 1-ethyl-4-methylazetidinone and l-ethylpyrrolidone;130 presumably an intermediate carbene inserts into the methyl and methylene groups to form the two products (Scheme 17).Diazo- 57% 43 % Scheme 17 G. Lowe and D. D. Ridley, J.C.S. Chem. Comm., 1973, 328. lP6 G. Lowe and D. D. Ridley, J.C.S. Perkin I, 1973, 2024. la’ G. Lowe and H. Wing Yeung, J.C.S. Perkin I, 1973, 2907. lP8J. C. Sheehan and R. W. Turley, J. Org. Chem., 1974, 39, 2264. lss M. Kinugasa and S. Hashimoto, J.C.S. Chem. Comm., 1972, 466. 130 R. R. Rando, J. Amer. Chent. SOC.,1970, 92, 6706. Isaacs methane reacts over a prolonged period with phenyl isocyanate giving a 20% yield of l-phenylazetidinone. It is to be supposed that a double methylene insertion occurs forming an intermediate aziridinone.l3l Radical decompositionor photolysis of N-bromoaziridinones can give alkyl isocyanates which react in situ with an olefin to give a more complex aziridinone (Scheme 18).g1 Scheme 18 7 Modification of the /?-LactamRing The synthetic scope of the preceding methods is considerably widened by the transformations which may be carried out upon substituent groups while leaving the lactam ring intact.The amide link in monocyclic /?-lactams appears to be little more reactive than in acyclic analogue~l~~J33 so that even hydrolytic procedures may be carried out, e.g. hydrolysis of l-chlorosulphonyl derivatives (see Section 3A, Scheme 10). N-Acylation,l34 alkylation (by NH2- followed by alkyl halide)23J35 amino- methylation and hydroxymethylation (Mannich rea~tion),l~~J~~ and nitro- sation137 have been widely reported, and all appear to be easier with p-lactams than with acyclic amides.Possibly the lactam nitrogen is more basic than its acyclic counterpart, though no quantitative information is available. The protonated lactam appears to be stable in acetic-sulphuric acid.138 Other reactions at nitrogen include halogenationg1 and Michael addition to form lactim ethers.139 Nucleophilic substitution at C-4 is possible. Acetate may be displaced by a wide variety of oxygen, nitrogen, and sulphur nucle~philes.~~~-~~~ Inversion of configuration results following displacement of sulphonate, and this may be used to build up fused ring systems (Scheme 19).143J44 Low-temperature 131 J. C. Sheehan and P. T. Izzo, J. Arner. Chem. SOC.,1948,70,1985. 13s R.J. Washkuhn and J. R. Robinson, J. Phurm. SOC.,1971, 60,1168. 13s G.M.Blackburn and J.D. Plackett, J.C.S. Perkin ZZ, 1972, 1366; 1973, 981. 134 E.Testa, G. Pifferi, L. Fontanella, and V. Aresi, Annalen, 1966,696, 108. 135 D.Bormann, Annalen, 1969, 725, 124. 136 C.Cignarelli, G. F. Cristiani, and E. Testa, Annulen, 1963, 661, 181. 13' G.Pifferi, P. Consonni, and E.Testa, Gazzettu, 1967, 97, 1719. 138 P. A. Petyunin and G. P. Petyunin, Zhur. org. Khim., 1972, 8, 373;(Chem. Abs., 1972,77, 153 448). 139 D. Bormann, Chem. Ber., 1970, 103, 1797. I4O K.Clauss and D. Grimm, Chern. Abs., 1971,74, PI41 500. 141 R.Lattrell and G. Lohaus, Chem. Abs., 1972, 77, 48 201. lg8 R.Lattrell and G. Lohaus, Annalen, 1974, 901. 14s H.W. Schnabel, D. Grimm, and H. Jensen, Annulen, 1974, 477. D. Bormann, Annalen, 1974, 1391; Chem.Abs., 1975,82, PI71 004,P171 005. Synthetic Routes to p-Lactams AcO H H H OH COMe Me X Y'bo X = RS, ROYN3,hal, SCN Y = RCO,R,NO,RZNCHg, HOCHg Z = hal, N3,NO, Scheme 19 bromination of the 4-thiolate leads to the Calkoxy-derivative with retention ofconfiguration.145 3-Substitution may be accomplished by electrophilic displacement, taking advantage of the acidic a-hydrogen. 3-Nitroazetidinones are formed by the action of strong base followed by alkyl nitrite on the azetidinone.146 Acy- lation,147J48 alkylati0n,1~*91~9 and halogenation may be carried out at the 3-position, and 3-azidoazetidinones generated by reaction of the enolate ion with tosyl azide.150 If a suitable leaving group is present nucleophilic substitutions may also be carried out at C-3.1479151 Oxidative cleavage of a wide variety of alkyl and aryI substituents on nitrogen may be accomplished by ozonolysis~52 and de-S- B45 A.K. Bose, J. C. Kapur, S. G. Amin, and M. S. Manhas, Tetrahedron Letters, 1974, 1917 141 H.Jensen and P. Wegener, Chem. Abs., 1971,75, P63 589. K. Kuehein and H. Jensen, Annalen, 1974, 369. rreT.Durst and M. J. Labelle, Cunud.J. Chem., 1972,50, 3196. IrrT.Durst, R.Van den Elzen and R. Legoult, Canad, J. Chem., 1974,52, 3206. w0 Chem. Abs., 1975,82, PI71 001-P171 005. m K. R. Henery-Logan and V. V. Rodricks, J. Amer. Chem. SOC.,1963,85, 3521, 3524. *6a R. B. Woodward, Chem. Abs., 1967,70, P28 91 1 ;R.Lattrell and G. Lohaus, Chem. Abs., 1971,74, P12 982. Isaacs alkylation by silver153 and mercury154 compounds. 3,4-Elimination produces the $-unsaturated la~tam.15~ Modification of naturally occurring p-lactams can be the most economical route to certain azetidinones. The penicillins and cephalosporins are the most accessible natural products of this type, and several methods have been devised whereby the thiazolidine or dihydrothiazine rings may be cleaved leaving the p-lactam system intact.155 6/3-Aminopenicillanic acid (27) may be readily converted into the 6,6-dibromo-derivative (28).Treatment of (28) with sodium hydride and methyl iodide (Scheme 20) gives the lactam (29).156 This type of cleavage appears to be restricted to penam derivatives with no 6-hydrogen, or at least a non-acidic 6-hydrogen, in which case elimination leading to lactam ring- opening occurs.6-Tritylamino- or 6-amido-derivatives will undergo alkylation and elimination in an analogous fa~hi0n.l~~ The ‘secopenicillins’ thus obtained can be used to build up the cepham ring system. From the penicillin derivative (30), Barton and co-workers obtainedl58 the corresponding sulphoxide which on pyrolysis to a sulphinic acid was trapped as the dihydropyranyl derivative (31) (Scheme 21). Furthermore, a method for the removal of the isopentene residue on the nitrogen was found; 1,3-dipolar cycloaddition of diazomethane to the double bond yielded the pyrazoline (32) which, on cleavage by zinc and acetic acid, gave the cis-3-amino-4-thioalkylazetidinone(33), a most promising inter- mediate for the elaboration of novel penicillins and cephalosporins.15g Cleavage of the thiazolidine ring may also be accomplished using diazoalkanes, and it has been reported160 that the remaining nitrogen side-chain may be removed using 153 R.Lattrell, Annulen, 1974, 1361. A. K. Bose, B. Dayal, J. C. Kapur, and M. S. Manhas, Tetrahedron Letters, 1974, 3135. ls5 M.S. Manhas and A. K. Bose, ‘Synthesis of Penicillin, Cephalosporin C, and Analogs’, Marcel Dekker, New York, 1969;‘Cephalosporins and Penicillins’, ed. E. H. Flynn, Academic Press, New York, 1972. ls8J. P. Clayton, J. H. Naylor, M. J. Pearson, and R. Southgate, J.C.S. Perkin I, 1974,22. J. P. Clayton, J. H. Naylor, M. J. Pearson, and R. Southgate, Chem. Abs., 1971, 74, PI41 499; Chem.Abs., 1964,61,PlOS 255; Chem.Abs., 1973,78,111335;E.G.Brain and N. F. Osborne, Chem. Ah., 1974, 81, P120654. 15* D.H. R. Barton, D. G. T. Greig, G. Lucente, P. G. Sammes, M. V. Taylor, C. M. Cooper,G. Hewitt, and W. G. E. Underwood; J.C.S. Chem. Comm., 1970,1683;R.D. G.Cooperand F. L. Jose, J. Amer. Chem. SOC.,1970,92,2575. 159 D. H. R. Barton, D. G. T. Greig, P. G. Sammes, and M. V. Taylor, J.C.S. Chem. Comm., 1971, 845. ld0N.Soma, M. Yoshimoto S. Ishihara, and E. Nakayama, Chem. Ah., 1975, 82, P43 164. Synthetic Routes to p-Lactams (30) R' = PhCH,CONH (31) R2= CO,CH,CCI, \CH"' (32) Scheme 21 zinc and acetic acid. Ring-opening with desulphurization can be brought about by the action of Raney nicke1le1a or mercuric acetate (Scheme 22).161b The PhCHzCONH SHgOAc H C0,-K+ H C0,HgOAc1AcOH 0 (34) Scheme 22 lol (a) A.K. Bose, M. S. Manhas, J. S. Chib, H. P. S. Chawla, and B. Dayal, J. Org. Chem., 1974, 39, 2877;(b) R. J. Stoodley and N. R. Whitehouse, J.C.S. Perkin I, 1974, 181 Isaacs trans-3-amino-4-acetoxylactam(34)is potentially capable of yielding the correct cis-relationship of a penicillin upon displacement with a sulphur nucleophile. New routes to such potential antibiotic precursors are still being sought.ls2 8 Uses of p-Lactams The most important uses of compounds containing a p-lactam ring are undoub- tedly as antibiotics related to penicillin (2) or cephalosporin (3). Innumerable modifications of the 6-side-chain have been carried out with the objects of increasing the range of organisms susceptible, e.g. to include Gram-negative bacteria, increasing the potency of the drug, and countering the resistance developed by certain organisms which can mobilize a lactamase system.Structures (35) illustrate some of the useful semi-synthetic derivatives of (2) prepared by chemical or microbiological acylation methods.ls3 With the ability to remove and replace the thiazolidine ring, new prospects open for the synthesis of an even greater variety of structures. Recently,some monocyclic /%lactams have been shown to have bactericidal activity, including the naturally occurring norcardicin (36) and some 1,4-diaryl-3-methoxyazeti-RCONH 0n$ NOH COzH ampicillin: R = PhCHNH2 carbenicillin: R = PhCHC02H methicillin: R = o,o-(MeO),C6H, dicloxacillin: R = (36) R = (CH&CHCOZHI NH, N-0 CI dinones which have been claimed to be active against both Gram-positive and Gram-negative organisms.ls4 Other biological activity which may be associated with simple p-lactams includes inhibition of aspartate oxidase165 and other enzymesls6 and antidepressant activity.la*T. Kamiya, T. Teraji, M. Hashimoto, 0. Nakaguchi, and T. Okei, J. Amer. Chem. Soc., 1975, 97,5020; P. W.Wojkowski, ibid., p. 5628; S. Kukolja and S. R. Lammert, ibid., p. 5582. lo3K. E. Price, Adv. Appl. Microbiol., 1969, 11,17. 16' A. K. Bose, M. S. Manhas, J. C. Kapur, S. D. Sharma, and S. G. Amin, J. Medicin. Chem., 1974, 17,541.166 A. Guidetta and G. Di Prisco, Biochem. Biophys. Acta, 1963, 77,394. lB6 L. Gasola, A. Guidetta, and E. Rocca, Arch. Biochem. Biophys, 1964, 107,57. Synthetic Routes to P-Lactams Linear polyamide formation from simple alkyl azetidiriones has attracted a lot of attenti~n.l~~J~*The conversion is effected by strong base and useful polymers can be obtained. These may be chiral,l6Q and vinyl substition may give rise to mixed vinyl and polyamide materials which are highly cr0ss-1inked.l~~ The potential of the p-lactam ring to react with a nucleophilic entity and yield a free amine function makes these species likely to be of use in a variety of industrial situations if economic considerations prove favourable. 167 T. Kodaira, H. Mikake, K. Hayashi, and S.Okamura, BUN.Chem. SOC.Japan, 1965,38, 1788. l6* Chem. Abs., 1966,65, P7347; 1969,71, P4427. E. Schmidt, Angew. Makromol. Chem., 1970, 14, 185. 170 J. Walter and C. Beermann, Chem. Abs., 1967,66, P76 541.

ISSN:0306-0012    

DOI:10.1039/CS9760500181

出版商:RSC    

年代:1976

数据来源: RSC

摘要:

Some Considerationson the Philosophy of Chemistry By D. W. Theobald DEPARTMENT OF CHEMISTRY, UNIVERSITY OF MANCHESTER INSTITUTE OF SCIENCE AND TECHNOLOGY, MANCHESTER M60 1QD. I consider then that to render a reason of an effect orphaenomenon, is to deduce it from something else in nature more known than itselfl. and that consequently there may be divers kinds of degrees of explication of the same thing. For although such explications be the most satisfactory to the understanding wherein it is shewn how the efect is produced by the more primitive and catholick affections of matter, namely, bulk, shape and motion; yet are not those explications to be despised, wherein particular effects are deduced from more obvious and familiar qualities or states of bodies.For .. . . every new measure of discovery doth instruct andgratify the understanding. R. Boyle, ‘Certain Physiological Essays’, 1772. Precision is not to be sought for alike in all discussions ... . It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits. Aristotle, ‘Nichomachaean Ethics’. 1 Introduction In this review I try to raise some philosophical points about the position of chemistry in relation to other natural sciences. Chemistry is a physical science with some similarities to physics and some to biology. But there are differences of emphasis and style worth recording. No-one questions that biology has many differences from physics, a fact reflected in the style of explanations found in the two sciences.But the position of chemistry in relation to biology and physics is perhaps not so clear. There is a need for some philosophical discussion of this as soon as one asks questions such as-What is it that identifies the science of chemistry? Does the subject matter of chemistry set it apart from physics or biology? Is there something peculiar to the style and procedures of explanation chemists use? Or is the description ‘chemical’ merely a matter of administrative convenience in government, universities, and industry? These matters are worth considering if only to come to terms with those philosophers and scientists who would have us believe in a simple-minded way that the subject matter of chem- istry, and indeed of all the other sciences, is ultimately the subject matter of physics, at least in principle, even if not now in practice.4 203 Some Considerations on the Philosophy of Chemistry To some it may seem eccentric to concentrate upon the science of chemistry when most currently published work in the philosophy of science is in fact in the philosophy of physics, and when such philosophy is quite commonly believed to contain all there is of importance in the philosophy of science. And yet the science of chemistry has a history at least as long, complicated and interesting as that of physics. Indeed the chemical activity of mixing A with B and seeing what happens is probably older than the more physical activity of trying to discover why it happens.Why then is the philosophy of science focussed so much upon physics? The answer I think lies in the general concern of chemistry with things at what might be called an ‘intermediate level of physical complexity’. That is to say, it deals with molecules, not atoms, and (this is the important point) it deals with things supposedly more ‘complicated’ than atoms, and so with things sup- posedly less ‘fundamental’ than atoms. On the other hand, it deals with things less ‘complicated’ than, and therefore more ‘fundamental’ than the genes, organ- isms, cells, species and genera of the biological sciences. So the motive behind concentrating upon the philosophy of physics probably originates in the feeling that this is the philosophy which has to do with ‘fundamental’, ‘simple’ things.Now if this claim had any clear meaning, one could at least decide for or against it. But what meaning can we in fact give to these predicates, ‘fundamental’ and ‘simple’? Does it make proper sense to suppose that the sciences can be arranged along a scale of esteem according to some notion derived from physics of what is or is not ‘simple’ and ‘fundamental’? If a clear and unprejudiced meaning could be given to the terms ‘fundamental’ and ‘simple’, then indeed the plurality of sciences as we know it at present would arguably be a phenomenon of intel- lectual convenience rather than a reflection of reality, and those philosophers who argue for reduction to a unified science would have a much more persuasive case to present.My own view, however, is that no such meanings can sensibly be given to terms like ‘simple’ or ‘fundamental’ in science, and that therefore proposals about the unity of science cannot do justice to the principles and prac- tice of at least one science, chemistry, and are therefore best ignored. To discuss these points, I shall first say something about the alchemical background of modern chemistry, because the philosophy of alchemy has something in common with the philosophy behind a good deal of chemistry, and then I shall go on to discuss the character of explanation in chemistry, and compare it with that in the sciences of physics and biology. 2 Alchemy, and its Relation to Madem Chemistry Chemistry as a science of material change is often considered a natural develop- ment from alchemy, a view which usually assumes that the philosophy of chem-istry is in all important respects the same as that of alchemy.But I think this is too simple as it stands. For we must remember that alchemy was not a physical science as we understand it. It was not simply primitive chemistry, but rather an attempt (usually sincere) to produce a truly natural philosophy. In fact alchemy is an admirable illustration of the proper meaning of the term ‘natural philo- sophy’, indeed perhaps the only one there is. I have argued this at some length D. W.Theobald elsewhere,l but some of the main points I made are worth repeating in this re- view. A physical science is a matter of explaining or rationalising (a difference to which I shall refer later) observable material changes in terms of material causes and effects.This requires some carefully formulated conservation principles. Those of matter, as historically understood up to the middle of the nineteenth century, or of some other extensive physical quantity such as energy, electric charge or momentum, are the most familiar. Conservation principles define the boundaries of physical change by defining the term ‘physical system’ both con- ceptually and operationally for a given set of circumstances. Without such boundary conditions, physical explanation which can be checked becomes im- possible, because there is then no limit to the field of causation which may be invoked.2 Alchemy was not a physical science within this definition, for it had no physical conservation principles whatsoever.No causally significant physical .observations were, could, or even needed to be made by alchemists in the way that scientists today make what they consider to be causally significant observa- tions. For this is the crucial point. Alchemy was, I believe, a serious attempt to understand the philosophical apparatus of Aristotle’s metaphysics by seeking its illustration in the directly observable properties of material bodies, such as colour, fusibility, and crystallinity. By such a phenomenological method, al- chemists hoped to clarify such important Aristotelian (and later mediaeval) philosophical categories as ‘change’, ‘matter’, ‘form’, ‘good’, ‘perfection’, ‘actuality’, and ‘potentiality’.Of course we now see this whole undertaking as something of a muddle, although it was a reasonable and certainly understand- able muddle given the state of philosophy and physical science before the six- teenth and seventeenth centuries. For it is a commonplace that science and philosophy did not begin to draw apart until perhaps the sixteenth and early seventeenth century, when in the study of nature, quantity replaced quality, and moral neutrality a certain moral involvement. The transmutation of one material into another no longer exemplified impermanence, imperfection, or moral strife: it revealed nothing but a certain aseptic, material, causal pattern.Alchemy was not replaced by something superior, namely chemistry, doing the same job; for it was not replaced by anything. It is, I think, more correct to say that alchemy declined quite naturally in importance as the Aristotelian philosophy upon which it was parasitic was gradually rejected as an acceptable philosophy in Western Europe, and as philosophers and scientists became aware of their proper roles. The new Cartesian and Newtonian philosophy made the familiar Aristotelian categories seem obscure and even irrelevant, and as a result alchemy was left without its raison d’6tre. As I have indicated, explanation in alchemy was not quantitative and predic- tive in the sense we find in modern physics, but rather qualitative, philosophical and rationalising, and I believe that something of this difference has been D.W. Theobald, ‘Alchemy-a Philosophical Reappraisal’ The Technologist, 1965, 2, 135; for a different interpretation of alchemy see B. J. T. Dobbs ‘The Foundations of Newton’s AIchemy’, Cambridge University Press, 1975. Y,Elkana, ‘The History of the Conservation of Energy’, Hutchinson, London, 1974. Some Considerations on the Philosophy of Chemistry carried over into the methodology of modern chemistry, helping to give it a somewhat different philosophical outlook from physics. It is possible to see now why I do not think that physics has had such a profound involvement with philosophy as has chemistry, since it has never been so directly phenomeno- logical as chemistry.Certainly over the years physics has been provided with a philosophical basis, namely that formulated initially by Locke and others, but it was not generated from such a basis as were alchemy and some early chemistry from Aristotelian metaphysics. I do not find it surprising, then, that to under- stand the philosophy of physics is not wholly to understand the philosophy of chemistry. Both sciences are concerned with the properties of matter, but I hope to show that the differences between the two are suffcient to make the assimila- tion of chemistry to physics simpliciter, a philosophical error which does a dis- service to the practice of chemistry. 3 The Differing Characters of Explanations in Chemistry and in Physics We can often approach questions about the differences between sciences by con- sidering what can be said about explanation in those sciences, bearing in mind that no science is committed to a single explanatory procedure.Scientific ex- planations take on a wide range of forms from the highly formal and quantita- tive explanations encountered in physics, to the informal qualitative explana- tions of everyday life. This variety is inevitable because explanations often have to serve very different purposes-showing why something is not so surprising as it seemed at first sight, spelling out detailed causes, rationalising extensive arrays of superficially disparate observations, etc. Whereas any given science may at times make use of different sorts of explanation, a science is usually character- ised by its preference for explanations of a certain character-either formal and quantitative on the one hand, or informal and qualitative on the other.It is these preferences I shall describe. A. Explanations in Physics.-These usually aim at more or less precise quantita- tive prediction, following closely the model of deductive explanation much dis- cussed by HempeP and subsequently others. This, at its simplest, is as follows. Given a set of universal premises T, which will usually mention some theoretical concepts, be highly formalised mathematically, and which will materially con- nect being an X with being a P,where X and P are observables characterised precisely by numbers, then it can be logically deduced, or predicted, that for any particular X,X’, X‘ will be P.Alternatively given that this X,X’is observed to be P, then the universal premises T explain that fact. Of course X’s may have other properties Q, R,but these are ignored by T. So strict Hempelian explanation is a selection procedure for choosing predicates which are conformable to a certain logical and numerical manipulation. Now if an explanation T models itself upon this pattern, that is if it aims at precise predictions, the concepts which clothe the logical skeleton of T will Inter ah, C. G. Hempel, ‘Aspects of Scientific Explanation and other Essays in the Phil-osophy of Science’, Free Press, New York, 1965. D. W. Theobald have to be ‘simple’ in the sense of being able to be characterised by numbers only.The argument then runs that this can be achieved satisfactorily only by the progressive dissection of matter. Explanations, it is argued, must be framed in terms of concepts referring to ever smaller pieces of matter because it is only such concepts which are ‘simple’ enough to be describable in all respects exactly by numbers, so enabling predictions to be made about larger, so-called more ‘complicated’ systems. Physics then tries to tell us why something behaves as it does by referring to its constitution. But, of course, there are other questions which may be asked, e.g. is this pattern of behaviour unique? What is the purpose behind it behaving in this way? Why is it behaving like this now ? etc.The answers to these questions will not necessarily require the reductive ‘in- nards’ approach of physics just outlined. We can now recognise precisely therefore what is involved in thinking smaller particles are ‘simpler’ than larger particles of which they are allegedly con- stituents. I mentioned earlier that physics was held to be about ‘fundamental’ things in contrast to chemistry and biological sciences. This is usually taken to mean that physics is about ‘simple’ things in contrast to chemistry and biology. But in what way is an atom ‘simpler’ than a molecule, or a molecule ‘simpler’ than a bulky material sample? The answer to this question is not something independently demonstrable about the world, for epithets such as ‘simple’ and ‘fundamental’ can have sense only from a certain point of view, in this case that of physics.In other words the ‘simplicity’ of physics and the ‘complexity’ of chemistry and biology arise because we impose a certain logical and numerical requirement upon our interpretation of causal connection. In practice this means we opt for the Hempelian model for explanation. But the question now urgently arises-is this the only way we can deal with matters of explanation, understanding, and causality ? I think history and chemical practice show that it is not. Should we aim in science at a more tho- rough reductionist approach to explanation, with the conduct of physics in mind, or should we be prepared to recognise limitations to such a philosophy for science? I believe that the science of chemistry throws some interesting light on these questions.B. Explanations in Physics.-Thackray in a recent book ‘Atoms and Powers’4 has discussed at length some of the methodological differences between Newton- ian chemistry and Daltonian chemistry, that is between the chemistry of the sixteenth and seventeenth centuries and that of the early nineteenth century. We find that Newton and his contemporaries vainly tried to understand material change in terms of point particles and inverse power laws, in terms of the forces of physics in fact, whereas Dalton and his successors saw as their objective the rationalisation of material change in terms of units of phenomenological mass. The Daltonian atom was such a unit of phenomenological mass, and this was successfully used to interpret the relative weights of reactants and products in a chemical reaction (one is reminded here of the function of the Mendelian A.Thackray, ‘Atoms and Powers’, Oxford University Press, London,1970. Some Considerations on the Philosophy of Chemistry gene in the biology of reproduction). Dalton avoided any physical specifications for the atom, for as he probably realised, such Newtonian detail would not have been relevant at that moment in the development of chemistry. Indeed it can be argued that scientists’ preoccupation with Newtonian theory delayed the start of serious chemistry for nearly 150 years. What seems clear from Thackray’s book is that progress in chemistry, and I imagine in science generally, is not necessarily linked with an uncritical pre- occupation with quantitative reductive analysis.There is almost certainly what might be called an ‘optimum epistemological level’ for the concepts of a science at a given moment in its history, and to try to force a more ‘fundamental’ character upon them may be to divert that science from its proper course at that time. In other words, perhaps the Hempelian model for explanation is not right for all the sciences all of the time.5 Some scientific explanations do undoubtedly have the Hempelian form I have outlined above. At least a great deal of explanation in physics and some in chemistry conforms to it; there is a lot to be said for this after all.It ought to be easy to work with, and it does enable one to make predictions. But perhaps we should not be preoccupied with prediction at the expense of explanation which does not have prediction as a primary function. After a11 there are many in- stances where a perfectly acceptable explanation does not enable one to predict like events with any degree of assurance. I think of the connection between drinking and dangerous driving as an example. The reason is that explanation is not purely a matter of logical structure, of events being conformable to some logical scheme. This point is clearly shown by the various published discussions of Hempel’s Paradox of the Ravens.6 Explanations have to be rational, and enable us to understand the events at issue.But this condition is satisfied in explanations by analogy and precedent, such as we have in legal, biological, and geological argument, and in many areas of chemical argument. Predictive power is not relevant in these instances. Rationality is admittedly a logically weaker imposition upon acceptable explanation than conformity to any logical model, but then it is methodologically and epistemologically richer. Rationality means no more than that explanations have to be commonly reasonable in the circumstances, and this alone guarantees our understanding. A simple formulation of rational explanation would go something like this. X’s are usually P,but this particular X,X’, turns out not to be P.A reasonable explanation for this may be given in terms of the absence or presence of some special condition, Q.Spelling out such an explanation will not in general involve appeal to highly formalised theoretical premises, for prediction is not involved here. We are concerned with a special case, and a special condition Q. Indeed such an explanation is much more likely to involve appeal to analogy and pre- cedent, rather than to quantitative laws and theories; it is an integrating explana- 6 M. Hocutt, ‘Aristotle’s Four Becauses’, Philosophy, No. 190,1974,49,385 ;M.Mandelbaum, ‘The Problem of Covering Laws’, in ‘Philosophy of History’, ed. P. Gardiner, Oxford Uni-versity Press, 1974. a D. W. Theobald, ‘Introduction to the Philosophy of Science’, Methuen, London, 1968, and refs.cited. D. W. Theobald tion. To take an example from organic chemistry, suppose that an acid and an alcohol fail to react to form an ester under conditions when esterification usually does occur, then we may be able to explain it by referring to some peculiar structural feature Q of the acid or the alcohol involved. We confidently expected them to react-in fact we were in no position to predict that they would not-and yet we can still explain their failure to react. Our explanation is not likely to carry precise predictive implications either, because we may not meet another case exactly like it, such is the abundance of experimental results in chemistry. But it is nonetheless a rational explanation which may serve our future purposes as precedent or analogy.To put the matter otherwise: it is possible to argue ‘no esterification E because Q’, without being committed to any predictive law-like generalisation of the form, ‘whenever Q, then no E’. We are committed to the logical ‘if Q, then no E, but that is a logical, not an empirical, corollary of our explanation. In chemistry we are often setting out to understand what has actually occurred rather than deliberately contriving to fulfil predictions. We are, so it has been said, telling ‘likely stories’ rather than hazarding and testing prophecies. As we shall see, it is this difference of temporal emphasis which aligns chemistry with biology as much as with physics. The sorts of explanations chemists use are often looser and less analytical then the full Hempelian model of parts of physics.But this does not mean to say that chemistry is a primitive science compared to physics. It reflects a frequent and real difference between the character of some of the concepts used in chemistry and the character of concepts used in more formalised sciences such as physics. 4 Concepts Used in Chemistry First consider some of the concepts chemists use every day; the following list is of course far from exhaustive: substance equilibrium molecule bond functional group bond strength reactivity solvation steric interaction valency stability transition state symmetry Now these concepts are static, organising and descriptive concepts more like concepts in biology than the dynamic causal concepts of so much of physics.Consider now these biological concepts : organism genus organ evolution gene natural selection function natural balance PWO* life behaviour death Species environment Some Considerations on the Philosophy of Chemistry There is a temptation to see some striking analogies between some of these con- cepts and some of the chemical concepts listed previously: for example, between molecules and organisms; between atoms and genes as the unitsof inheritance in chemical reactions and biological evolution; between a functional group in a molecule and an organ of an organism; between death and decomposition; between the chemical equilibrium between molecules and the ecological balance of competing organisms.There are of course striking disanalogies, but that is to be expected between a science of the living and a science of the dead. But it is worth recalling briefly here what was said earlier about alchemy, when it was argued that alchemy was an attempt to illustrate Aristotelian philosophical argument in material terms. Aristotelian philosophy as we know was man- centred and biologically conceived, and the analogies mentioned previously be- tween certain biological and chemical concepts are perhaps no more than a con- tinuation of the involvement of alchemy and some early chemistry with such philosophy. The chemical concepts I have listed are, like the biological concepts mentioned, organising concepts. They are not vulnerable to vulgar testing, for they are designed to make sense of large and timeless ranges of experience rather than to explain the details of particular individual cases.No doubt these and other chemical concepts could be given a reductive and analytical interpretation. But do they need to be? Would such an analysis be relevant to the chemists’ require- ments. Is a molecular biological analysis of the Mendelian gene always relevant to the biologist ? Is a physical analysis of the chemical molecule always relevant to the chemist? For that is the question-relevance. To the chemist it is not a question of what is or is not comprehended by the science of physics, but of what is or is not relevant and necessary to understanding the chemical problem in hand.The fundamentals of chemistry have nothing necessarizy to do with the fundamentals of physics. Let us return to the familiar chemical reaction already referred to, namely the esterification of alcohols by acids. The variety of recorded reactions is too vast to allow a Hempelian account based upon highly formalised physical theory to be anything but useless, because this is inordinately cumbrous. Instead we use some of the general organising concepts of chemistry as listed, to bring out the pattern which runs through the different examples. The chemist is not always interested in detail, but often in the general scheme of things chemical, in the way that a biologist is interested in the general scheme of living things and their interactions.5 Differences in Interpretations arising from Chemistry and Physics The chemist usually does not need to look further than the molecule, atom, and electron to understand chemical phenomena. However, his is not the atom and electron conceived as putative historical (and so causal) precursors of molecules, but the atom and electron construed as parts of molecules, i.e. conceived from a molecular point of view. The statement ‘the purpose of these electrons is to hold this molecule together’ may be compared as an explanation with ‘the purpose of D. W.Theobald this organ is to allow this organism to survive’. But neither the organism nor the molecule is logically derivative upon the organ or the electron. Nor are they empirically derivative.A part of an organism may give us some information about the structure of the organism from which it comes and also may tell us what role that part plays, but it will not tell us how that organism behaves as a whole. Similarly an analysis of molecules into atoms can tell us nothing extensive about the parent molecule. For the atoms in a molecule only have significance within the molecule, in relation to the other atoms. It is the society of atoms which matters, that is the whole molecule, rather than the separate atoms them- selves. To the question ‘what is an electron?’, there will be many answers which will reflect many different physical interests, for example, the quantum theory and the band theory of solids and metals, as well as the theory of chemical bonding.These answers are not necessarily relevant to one another. The chemist should not therefore automatically be preoccupied with adjusting his picture of the electron devised for chemical interpretation to the demands of other areas of physical science. In short the chemists’ atom and electron ought not to be identified simpliciter with the physicists’ atom and electron. It might be countered that the properties of a molecule or of a bulk material sample are predictable in principle, if not in practice, in the Hempelian way from a knowledge of the atom and electron in physics as premise. But are they, in fact? There is always some disagreement between the experimental parameters and such predictions of them.Moreover this might not be solely due to ex-perimental error, but to the fact that molecules conform to diferent laws from the physicists’ atoms and electrons; or to put it another way, to the fact that molecules follow chemical laws different from those to be obtained by an extra- polation of the physical laws of physics. Chemical laws may not be the simple Cartesian push-pull laws of physics, and perhaps even a non-Cartesian formula- tion of them will have to be devised.’ The only condition one can specify in advance is that molecules must conform to those most fundamental laws of energy, the laws of thermodynamics, which provide the boundary conditions of all physical change. But these say nothing of the time scale or the path of change, and nothing therefore follows from them about the forces operative in molecular or chemical reactions.So there is no a priori physical reason why these forms should be the same as those we recognise in physics. Most philosophers re- cognise that individual human behaviour follows patterns which are not to be obtained by an extrapolation of the laws of neurophysiology; and that the behaviour of collections of individuals is not predictable from the behaviour of the individuals comprising those collections. There are indeed real differences here. What conclusive argument is there that there is not such a difference be-tween the behaviour of atoms and the electrons and the behaviour of those col- lections of atoms and electrons we call molecules? I do not believe that the philosophical doctrine of ‘emergence’ is to be rejected out of hand in pursuit of ’D.Bohm, ‘Classical and Non-Classical Concepts in Quantum Theory’, British J. Phil. Science, 1962, 12, 265. 211 Some Considerations on the Philosophy of Chemistry a single chimerical Truth. The recognition of emergent properties, far from re- stricting the course of scientific research as some advocates of the unity of science argue, provides challenging new material for scientific thinking. It is dficult indeed, because it challenges old habits of thought. But it is perhaps a more honest recognition of the variety of an evolutionary universe. A different perspective upon this philosophical point is gained by considering levels of organisation in matter. Consider for a moment what we mean when we say that chalk is made up of molecules, and that these molecules are made up of atoms, and so on.Now whereas we can talk of the systems of molecules which make up the chalk, we cannot meaningfully talk of systems of atoms making up this substance. An analogy would be as follows. We can appreciate the arrange- ment of bricks which make up a house, but we do not thereby imply recognition of any arrangement of grains of sand and lime which make up the bricks of the house. So quite properly one does not speak of houses as being built of sand and lime because houses to those concerned with them are built of bricks and not sand and lime. Likewise in chemistry, where we are dealing with the properties of sub- stances like chalk, we ought not to think of them as being composed of arrange-ments of atoms, but properly as systems of molecules, because it is of such things that substances are composed.The molecule is the chemical brick, and is a quite proper terminus for chemical inquiry. This is not to say that the make-upof the molecule should not be explored by those theoreticians whose proper concern it is. But the builder who selects a brick because he knows what sort of properties it has does not need to know the detailed properties of sand and lime from which it was made. The matter can be put another way. Membership of a class or system is not transitive, whereas membership of a collection or aggregate is. Thus an indivi- dual plant is a member of the class called the ‘species‘, but is not properly a member of the ‘genus’ to which that species belongs, though it is a member of the aggregate called the ‘plant kingdom’.Now what of atoms, molecules and substances? I do not think that substances can be said to be heaps, aggregates, or collections of molecules, nor yet that molecules can be said to be heaps, aggregates, or col- lections of atoms. I would argue that the formula ‘H2O’ refers to that class of molecules every member of which is composed of H and 0 atoms related in a certain way, whereas the term ‘water’ refers to that class of substances each member of which has ‘H2O’ molecules as members related in a certain way. So whereas molecules are properly said to be parts of water, and atoms properly parts of molecules, atoms are not properly speaking parts of water. I would be prepared to contend therefore that there are certain levels of organisation to be recognised in the study of matter, and that these cannot be short-circuited with- out talking nonsense.6 The Special Role of Chemistry in Science What does all this amount to? I think it may go some way towards persuading (and it is only persuading) chemists that their alter ego need not be a physicist. D. W. Theobald Chemical science has not so far been infected by mathematico-physical methods to the extent of some other sciences. Whereas physics has been forced to abandon the familiar concept of substance, chemists so far have not.During the height of Newtonian fashion in the seventeenth and eighteenth centuries, Boyle was not- able in predicting the fruits of Newtonian method, namely, no concept of sub-stance and an immaterial universe. Some of the great analytical and synthetic successes of chemistry would not have been possible if Newtonian method had been adopted in the eighteenth and nineteenth centuries. For chemistry is the science of a substantial universe with observable qualities. The chemist is traditionally the scientist who first and foremost wants to know what happens when X is mixed with Y. He may wish to rationalise what he observes, but initially his is a species of idle, natural curiosity. Chemical curiosity is much less disciplined than physical curiosity, and it is this element of indiscipline in chemistry which makes it particularly easy to exploit technologically.Many more things have been discovered in chemistry than have been rational- ised, and this is because chemical work has never been quite so dependent for its impetus on theory as has work in the more mathematical sciences. In physics it is sometimes dil€icult to find enough observations to test a theory (for example in cosmology) but this could never be said of chemistry. Theories are rarely highly controlled by observation in chemistry, since theories are, as I have explained, generally rationalising constructions covering vast arrays of experi- mental data, rather than precise mathematical formulations vulnerable to a single quantitative misfortune.There is a further point which adds to this difference. Whereas it is possible to talk about the electron (a highly specified particle), it is not possible to talk about the ester, the salt, and so on, because no one ester or salt is exactly like another. For these are types, representing a classification of individuals. These explanatory descriptions SN~and SN2 given by organic chemists to certain substitution reactions in organic chemistry are no more than classifications in terms of extreme types. The biological parallel is obvious. And this has its effect upon the character of mechanistic descriptions of chemical reactions which are, as I have said, rationalising rather than predictive. Chemistry then stands between physics on the one hand and biology on the other, as an area in which rationalising, pattern explanations rub shoulders with Hempelian, deductive explanations to a greater extent perhaps than in any other science.This is, in my view, the principal value of chemistry as the basis of a scientific education. But chemists will continue to enjoy this stimulating position only if they resist the temptation to model their science exclusively on either physics or biology. This would be methodologically indefensible, besides being a severe limitation upon the chemical imagination. There is more in heaven and earth than can be comprehended by the philosophy of any single science. Of course I cannot prove this point, but then I am consoled by the fact that the converse cannot be proved either. Chemists must not fall into the trap of Tristram Shandy’s father (together with modern reductionists)-‘who like all systematic reasoners would move heaven and earth, and twist and torture every- thing in nature to support his hypothesis’.

ISSN:0306-0012    

DOI:10.1039/CS9760500203

出版商:RSC    

年代:1976

数据来源: RSC