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QUARTERLY REVIEWS RECENT ADVANCES IN SESQUITERPENOID CHEMISTRY By D. H. R. BARTON D.Sc. F.R.S. and P. DE MAYO M.Sc. PH.D. (THE UNIVERSITY G LSSGOW W .2) THE chemistry of terpenoid compounds has long been an inspiration to the creative endeavours of the organic chemist. The field of study ranges through mono- sesqui- di- and tri-terpenoids and includes carotenoids and steroids. Even a penta-terpenoid solanesol from flue-cured tobacco has recently been isolated. Apart from their intrinsic interest terpenoid compounds have provided impetus for theoretical and mechanistic studies and for synthetic investigations. The best definition of a terpenoid is that it is a compound whose carbon skeleton is either ( a ) theoretically constructed from isoprenoid units (1) or ( b ) has at some stage in its biogenesis had a carbon skeleton so constructed (cf.ref. 2). In the case of sesquiterpenoids the great majority of compounds can be regarded as built up from the union of three isoprenoid residues joined in hesd-to-tail order (2). (1) (2) ( 3) (4) (5) Within the field of sesquiterpenoid chemistry one finds a wide range of oxygenated function of ring size and of mechanistic change. If no other type of organic compound were known organic chemistry would still be a rich and varied field for investigation. The purpose of the present Review is to deal briefly with established sesquiterpenoid chemistry and treat in more detail the advances of the last decade. First the extent of the subject is already too large for adequate description in a short review; secondly earlier work has already been summarised adequately elsewhere.Sesquiterpenoids can be classified into groups of related compoundf 1 Rowland Latimer and Giles J . Amer. Chem. SOC. 1956 78 4680. 3 Simonsen and Barton " The Terpenes " Cambridge Univ. Press Vol. 111 1952 ; The reason for this approach is twofold. Ruzicka Experientiu 1953 9 357. see also Haagen-Smit Foi*tschi*. Chem. org. Nuttrrstoffe 1955 12 1. N 189 190 QUARTERLY REVIEWS according to their carbon skeletons. The simplest compounds are aliphatic. Two well-studied and important groups afford respectively cadalene (3) and eudalene (4) on dehydrogenation. A further large group gives on such treatment azulenes (as 5) indicative in most cases of a system of fused five- and seven-membered rings. We can also recognise an interesting group of sesquiterpenoids with rings of medium size (9-1 l-membered).* In recent years many sesquiterpenoids of lactonic character have been investigated ; these it is convenient to discuss separately although most of them have decalin- or azulene-type carbon skeletons.Tricyclic sesquiterpenoids are common and often present laborious structural problems. Aspects of relative and absolute stereochemistry must also be considered. Sesquitmpenoids lacking Carbon Rings.-Farnesol (6) which is widely distributed in Nature is the most important member of this small group. Farnesol and its isomer nerolidol (7) are related in the same way as are geraniol and linalool. 5 Farnesol was the first sesquiterpenoid to have its constitution eIucidated.6 In recent years it and its derivatives have been the subject of interesting cyclisations.7 In so far as cyclic terpenoids may arise in Nature from acyclic or other simpler precursors such experiments are also of considerable biogenetic interest .* Simple carbonium-ion theory 9 predicts satisfactorily the products of such cyclisation reactions.The stereochemistry of cyclisation can be discussed along the following lines. lo Concerted cyclisation of a triene such as (8) should afford a trans-fused decalin (9 ; X = anion). Non-concerted cyclisatian to a monocyclic inter- mediate (10) followed by a concerted ring closure (or its equivalent) should furnish a cis-fused decalin (1 1 ; X = anion). Several convincing examples of the latter process are known.11 1 2 In the laboratory the cyclisations proceed to give products of mixed stereochemistry and the processes are Prelog J.1950 420 ; Brown Fletcher and Johannesen J . Amer. Chem. Soc. 1951 73 212 ; Heck and Prelog Helv. Chem. Acta 1955 33 1541 ; Brown and Ham J . Amer. Chem. SOC. 1956 78 2735. Simonsen and Owen " The Terpenes " Cambridge Univ. Press Vol. I 1947. Inter al. Zobrist and Schinz Helv. Chim. Acta 1949 32 1192 ; Caliezi arid Schinz ibid. p. 2556 ; 1950 33 1129 ; 1952 35 1649 ; Collin-Asselineau Lederer and Polon- sky Bull. SOC. chim. Prance 1950 715 ; Stoll and Commarmont Helv. Chim. Acta 1949 32 1836 ; Kappeler Eschenmoser and Schinz ibid. 1953 36 1877 ; Kappeler StaufYacher Eschenmoser and Schinz ibid. 1954 37 957 ; Gamboni Schinz and Eschenmoser ibid. p. 964. Inter d. Bloch and Rittenberg J. Biol. Chem. 1945 169 45 ; Langdon and Bloch ibid. 1953 200 129 ; Woodward and Bloch J .Amer. Chern. SOC. 1953 75 2023 ; Clayton and Bloch J. Biol. Chem. 1956 218 305 319 ; Dauben Abraham Hotta Chaikoff Bradlow and Soloway J . Arner. Ghem. SOC. 1953 75 3038 ; Corn- forth and Popjak Biochem. J . 1954 58 403 ; Popjak Arch. Biochem. Biophys. 1954 48 102. Ingold " Structure and Mechanism in Organic Chemistry " Bell London 1953 ; Wheland " Advanced Organic Chemistry " Chapman and Hall London 1949. ti Kerschbaum Ber. 1913 46 1732. lo Stork and Burgstahler J . Amer. Chem. SOC. 1955 77 5068. l1 Inter al. Eschenmoser and co-workers ref. 7 ; also Eschenmoser Ruzicka Jeger and Arigoni Helv. Chim. Acta 1955 38 1890. l2 Linstead Wang Williams and Errington J. 1937 1136 ; Linstead Millidge and Walpols J. 1937 1140; Burnop and Linstead J. 1940 720. BARTON AND DE MAY0 SESQUITERPENOIDS 191 not in general fully concerted.For example,1° treatment of farnesenic acid (12) in benzene solution with boron t'rifluoride-ether complex affords (yy- c y y x (-yy- qJx G+ (10) (I I) I4 H4- t \ k ' (8) (9) the monocyclic derivatives (13) and (14). Cyclisation of the latter a t higher temperatures gives three cis-decalin derivatives (15) (16) and (17). Com- parable cyclisation processes in Nature appear to be fully c0ncerted.1~ Their imitation still presents therefore a challenge. Amongst more recently investigated non-carbocyclic sesquiterpenoids we may mention ngaione (18) and its enantiomer ipomearnarone.l4 Ngaione comes from the essential oil of Myoporum acuminaturn ipomeamarone is found in black-rotted sweet potatoes. The structure (18) is of course built LIP from the usual chain of three isoprenoid residues.Cadalene-type Sesquiterpen0ids.-The chemistry of these substances has for the most part already been adequately reviewed. A number of sesquiter- pene hydrocarbons affording cadalene (3) in high yield on dehydrogenation and giving cadinene dihydrochloride (19) on addition of hydrogen chloride have been reported.l5 The compound known simply as cadinene (from oil of cubebs) has the constitution (20).l6 We may also include in the cadalene l3 Tchen and Bloch J. Arner. Chern. SOC. 1956 78 1516. l4 Kubota and Matsuura Chern. and Ind. 1956 521 ; see also Birch Massy-Westropp Wright Kubota Matsuurat and Sutherland ibid. 1954 902. l 5 Inter al. Herout and Santavy Coll. Czech. CTLem. Comm. 1954 19 118. l6 Campbell and Soffer J.Amer. Chem. SOC. 1942 64 417 and references there it may still be cited. inhomogeneous. This refers to material recorded from the dihydrochloride; 192 QUARTEJXLY REVIEWS group a number of monocyclic sesquiterpeuoids which afford the cadalene- type skeleton on cyclisation or are structurally closely related. Esainples A (20) are zingiberene (21),17 y-curcumene (22),18 and lanceol (23).19 Also we niay mention the cadalene-type dimer gossypol the pigment of cotton aeed.*O The interesting seaquiterpene dcohol carotol (24) 21 giving on dehydro- genation the naphthalene (25) may be a member of the cadalene group in which methyl migration has occurred in the last step of the biosynthesis of the carbon skeleton. The skeleton of carotol can be constructed from three iaoprenoid residues but not if these are linked as in the conventional farnesol chain.An alternative possible biogenesis may be through a spiranic intermediate (see acorone below). Laserpitin the bitter principle from Laserpitium htifolium has recently been shown to have the same skeleton as carotol.22 Ledol isolated from marsh tea oil was formerly assigned the formula (26) or (27).23 Recently this compound and its considered diastereo- isomer palustrol have been investigated by Kiryalov z4 and the new constitution (28) has been proposed. The known degradations of ledol e3 2 4 could only be explained on the basis of formula (28) if non-Markownikoff opening of the cyclopropane ring be postulated. In so far as all known cyclopropane compounds in the terpenoid series undergo Markownikoff rupture with acid the validity of formula (28) may be doubted.25 Definite l7 Eschenmoser and Schinz Helv.Chim. Acta 1950 33 171. I* Batt and Slater J . 1949 838 ; Birch and Mukherji ibid. p. 2531. l9 Eschenmoser Schreiber and Keller Helv. Chim. Actcc 1951 34 1667 ; Birch and Murray J . 1951 1888. Adams Morris Geissman Butterbaugh and Kirkpattrick J . Amer. Chem. SOC. 1938 60 2193 ; Edwards and Cashaw ibicl. 1956 78 3224 and references there cited. *l 8orm and UrbBnek Coll. Czech. Chem. Comm. 1948 13 49 420 ; 8orm and Mleziva 1949 14 98. 2 2 ,qorrn Holub and Herout Chem. and Ind. 1954 965. 23 Komppa cited in ref. 3. 2 4 Kiryalov Doklady Akad. Nut& S.S.S.R. 1948 61 305. g 5 de Rlayo Perfumery Essent. Oil Record 1957 18. BARTON AND DE MAP0 SESQUITERPENOIDS 193 evidence against structure (28) has been provided by Cole and Lahey 26 who were unable to find in the infrared spectrum of ledol t'he band a t 3060 cm.-l characteristic of a niet51iylene group in a three-membered ring.27 Eudalene-type Sesquiterpenoids.-These are sesquiterpenoids which afford eudalene (4) on dehydrogenation. Some typical examples are eudesmol(29) from eucalyptus oil ~ ( 3 0 ) and /I-cyperone (31) from the tubers of Cyprus rotzmdus,28 and the related carissone (32).2g The carbon skeletons of these compounds can be constructed from a farnesol chain. woHm (29) (30) O R (3 I) moH (32) OH - - & - & - 4 & The position of the angular methyl group in these compounds has been established rigidly by degradation 30 and by synthesis.31 The most interesting non-lactonic sesquiterpenoid of the eudalene type i s eremophilone (33),32 for in this compound the angular methyl group occupies an apparently non-isoprenoid position.The constitution of eremophilone can be reconciled with the normal eudalenoid pattern if its Me QAc Me -C' d'+ 'C' (33) (36) (37) la- (3 8' biogenesis involves migration of a methyl group .33 Similar migrations are by now a familiar feature of the chemistry of the higher terpen0ids.3~ Eremophilone (33) occurs in the wood oil of Eremophila rnitchelli together 2 8 Lahey and Lamberton Austral. J. Chem. 1956 9 431. 27 Cole J. 1954 3807 3810. 28 Bradfield Gillam Hedge Rao and Simonsen J. 1936 667 ; Bradfield Pritchard 2b Mohr Schindler and Reichstein Helv. Chirn. Acta 1952 37 462 ; Barton and and fiimonsen J. 1937 760; McQuillin J . 1955 528. Tarlton J.1954 3492. Plattner Fiirst and Hellerbach Helv. Chirn. Acta 1947 30 2158. 51 Howe and McQuillin J. 1955 2423. 32 Simonsen et nl. citsed in ref. 3. 33 (Sir) Robert Robinson cited in ref. 3. 31 Barton Chem. and Ind. 1948 638 ; Velluz Muller Petit and Mathieu Bull. SOC. chim. Prance 1952 401 ; Subluskey and Sanderson J. Arner. Chenz. SOC. 1954 76 3512 ; Barton and de Mayo J. 1953 3111 ; Allnn Fayez Spring and Stevenson J. 1956 456 and earlier papers iii t h i a series. 194 QUARTERLY mVIEWS with hydroxyeremophilone (34) 35 and dihydrohydroxyeremophilone (35). One of the most interesting reactions of these compounds is the conversion of eremophilone oxide (36) by digestion with sodium acetate and acetic anhydride followed by hydrolysis with alkali into hydroxyeremophilone (34).A possible mechanism is indicated iii the formulae; the conversion of the postulated intermediate (37) into (34) by rearrangement of the a-ketol system etc. is conventional. The constitution assigned to dihydro- hydroxyeremophilone has recently been confirmed by X-ray analysis. 36 The sesquiterpene alcohol elemol obtained from Manila elerni oil is st monocyclic derivative (38) of the eudesmol carbon skeleton.37 It will be noted however that elemol is not a cyclisation product of farnesol although its skeleton is divisible into isoprenoid residues. that elemol may be formed in Nature by ring fission of a eudesmol-type precursor. The sesquiterpenoid components of sandal wood oil a- (39) and /?-santalene (40) and their derivatives can also be regarded as belonging to the eudalene group.3 It has been suggested (40) (39) Azulenic Non-lactonic Sesquiterpen0ids.-Most of the natiirally occurring non-lactonic perhydro-azulenic sesquiterpenoids are related (41).A typical example is guaiol whose constitution (42) to guaiazulene was elucidated HO (43) (44) by Plattner and his collaborators. 38 The most significant reaction sequence was that indicated in the formule which afforded cadalene (3) and the naphthol (43). It could have been objected to the constitution (42) that the tertiary hydroxyl group might also have been placed as in (44). The correctness of Plattner’s formula (42) has been confirmed by pyrolysis of the phenylazo- The identity of the latter was established by synthesis. 35 See also Geissman J . Amer. Chem. SOC. 1953 75 4008. 36 Grant and Rogers Chem.and I n d . 1956 278. 37 Sy’kora Herout Pliva and Sorrn Coll. Czech. Chem. Comm. 1954 19 124; 38 Plattner and Lemay Helv. Chim. Acta 1940 23 897 ; Plattner and Magyar Lifkora Cernf Herout and gorm ibid. p. 566 ; 1955 20 220. ibid. 1941 24 191 ; 1942 25 581. BARTON AND DE MAY0 BESQUITERPENOIDS 195 phenylurethane of guaiol to give a hydrocarbon (45),39 the presence of the isopropenyl grouping being established by the infrared spectrum. The guaiazulene derivative aronindendreue the characteristic sesquiter- pene of eucalyptus oils 1im 1)een related t o t,he alcohol globulol froin EucaZyptus gZobuZus by pyrolysis of the 3 5-dinitroben~oate.~~ Recent work on aromadendreiie 41 has led to the proposal of two plausible structures (46) and (47) for the hydrocarbon and to the corresponding saturated tertiary alcohol formulations for globulol.Patchouli alcohol a crystalline constituent of Patchouli oil was the subject of preliminary investigations in the last century. It is however only recently that structural formulx have been advanced. Treibs 4-2 proposed the formula (48) mainly on the basis of two important experiments carried out on ‘‘ patchoulene ” (49) the hydrocarbon mixture obtained by acid-catalysed dehydration of the alcohol. Dehydrogenation gave guaiazu- lene (41) whilst ozonolysis followed by oxidation with potassium perman- ganate furnished homocamphoric (50) and camphoric acid. Further investi- gation by Buchi and Erickson 45 has shown that whilst “ patchoulene ” is correctly formulated as essentially (49) patchouli alcohol itself has structure (51 ) its conversion into the hydrocarbon mixture involving a rearrangement.The acetate of patchouli alcohol prepared by reaction with keten was pyrolysed and the resulting hydrocarbon oxidised to the nor-ketone (52). (51) (52) (53) (54) Further oxidation of the ketone gave a substituted glutaric acid (53) with loss of one carbon atom. Further degradation of the acid (53) furnished the ketone (54) whose infrared spectrum showed the keto-group to be contained in a five-membered ring. The size of ring B is therefore also established. The orange agaric Lactarius deliciosus contains a number of interesting This establishes the size of ring c. 38 O’Brien Penfold Sutherland and Werner Austral. J. Chem. 1954 7 298. *O Blumann Cole Thiebei-g a.nd White Chem. and Ind. 1954 1426. 4 1 Treibs and Barchet Anfinalen 1950 566 89 ; Birch and Lahey Austral.J. Chem. 4 3 Buchi and Erickson J. A n ~ r . Chenz. rs’oc. 1956 78 1262. 1953 6 379. 4 2 Treibs Anfialen 1949 564 1-41. 196 QUARTERLY REVIEWS guaiaziilene derivatives. Of these t8he more important are lactaroviolin (55) and lactarazuleiie (56).44 Lactaroviolin (55) is converted into lactarazu- leiie (56) on Wolff-Kishner reduct ion wliilst qii partial hydrogenation the xznlenc affords guaiazulene (41 ). Ozoiiolysis of lactarazulene gives forinalde- hyde. This evidence establishes the constitution (56) and only leaves unplaced the aldehyde group in lactaroviolin. The correctness of forniiila (55). suggested 1,y physical data has been confirmed hy conversion of the aldehyde group into -CH( OH)*Mo followed by partial hgclrogenntjion.This (55) (5 6) 671 selectively reduced the isopropenyl group and removed the hydroxyl group by hydrogenolysis thus affording 1 -ethyl-4-methyl-7-isopropylazulene (57). Asahina and Nakanishi 45 isolated from the rhizomes of Valeriana oflcincclis L. var. Zutifolia Miq. a sesquiterpenoid ester which afforded two mols. of acetic acid and a glycol kessoglycol on hydrolysis. This glycol and the related alcohol kessyl alcohol have been the subject of extensive inve~tigation.~G Kessoglycol is a derivative of guaiazulene ; it has two secondary hydroxyl groups a t positions 3 and 6. The remaining structural feature is the position of the ether bridge. Formulze (58) and (59) have been accepted for some time as representing kessoglycol and kessyl alcohol respectively. Recently the transformations carried out by Ukita 46 have been re-appraised and the structures (60) and (61) proposed for the glycol and its derived alcohol respectively.The new formuk are in bettler mechanistic accord with the available e~idence.~' Of the remaining guaiazulene derivatives partheniol which occurs as the cinnamate in guayule has been formulated as (62),48 whilst linderene from the oil of Linderia strychnifolin is formulated as (63).49 The latter structure a t least is not however firmly established in its finer details. 4 4 Inter al. Willstaedt Ber. 1935 68 333 ; $orin Benegova and Herout Coll. Czech. Chem. Cornm. 1954 19 357 ; gorm Benegova KrupiEka Sneberk Dolej#. Herout and Sicher Chew. and Id. 1954 1511 ; Plrtttner and Heilbronner Ezperientia 1915 1 233 ; Plattner Heilbronner Schmid Sandrin and Furst Ghem.nnd Ind. 19.54 1602 ; Heilbronner and Schmid Helv. Chim. Acta 1954 37 2018. 4 5 Asahins and Nakanishi J . Piharm. SOC. Japun 1929 49 135. 4 6 Uliita ibid. 1914 84 285 ; 1945 65 458 ; Treibs Annalen 1960 570 166. 4 7 de Mayo Perfumery Essent. Oil Record 1957 18. 48 Haagen-Smit and Fong J . Amer. Chem. SOC. 1948 70 2075. 48 Takedu Negata and Kubota Phwrrn. Bull. ( J w p m z ) 1053 1 211 ; Takeda ibid. p. 24.1. RARTON AND DE MAT0 SESQUITERPENOIDS 197 Other guaiazulene derivatives of uncertain structure are germacrol 50 the gurjunenes himbaccol 51 and a-chigndmarene. 5 2 I Oil of vetiver contains two stereoisomeric ket,oncs N- md p-retivone. Degrndntioiral studies have mainly heen concerned with /l-vetivone ( 64).3 Dehydrogenation of suitable derivatives affords vetivazulene (65).The carbon skeleton of this azulene is also based on the farnesol chain. Recently a tricyclic sesquiterpene hydrocarbon tricyclovetivene (SS) has been isolated from the same essential and on dehydrogenation tjhis also affords vet ivnzulene. ' (64) (6 6) A new type of azulene skeleton has been detected in t>he ketone zierone.54 Dehydrogenation of a derived hydrocarbon affords tjhe novel zierazulene (67) the constit,iition of which has bekn confirmed by synthesis. A possible expression for zierone is (68). 'l'lie carbon skeleton of this coinpound can be constructed from isopreiioid residues but not froin a farnesol chain. Medium-ring Sesquiterpen0ids.-Few cornpoiintis of this class are as yet known. The most important and most int'eresting is the sesquiterpene caryophyllene the chemistry of which was extensively investigated by 8irnonseii,3 Ruzicl~a,~ and their colleagues before the war (1939).Other compounds to be mentioned here are the crystalline zerumbone and the liquid humulene the final details of whose structure still await elucidation. The crystalline lactorre pyrethrosin with its ten-inenrbered carbon ring is conveniently considered along with lactones of' the decaliii class (see below). The sesquiterpene fraction of oil of cloves is the main source of caryo- phyllene. In the older literature the terms cc- ,!I- and y-caryophyllene have been used to designate specific hydrocarbons froin this source. Since a-caryophyllene is identical with huniulene and y-caryophyllene is possibly 50 Treibs Annalen 1952 576 116.61 Birch and Mostyn Austral. J . Chem. 19.55 8 550. j2 Rao Dutt Dev and Guha J . Indian Ghem. SOC. 1982 29 604 (i02. 5 3 Chiurdoglu and Tullen Chesn. and Ind. 1956 1094. 6 4 Bradfield Penfold and Ximonsen J . PTOC. Roy. L!OC. New South Wales 1933 67 200 ; Birch Collins and Penfold Chetn. and Ind. 1955 1773. 198 QUARTERLY REVIEWS an artefact arising from thermal isomerisation it is now customary to refer to the main hydrocarbon p-caryophyllerie simply as caryophyllene and to use the rational name isocaryophyllene instead of y-caryophyllene. Caryophyllene is principally remarkable for the ease with which it and its derivatives undergo cyclisation. It has the molecular formula C1,H, and contains two ethylenic linkages ; it is therefore bicyclic. Oxidative degradation affords three cycZo1)utnne acids norcaryophyllenic acid (69 ; n = 0 ) caryophyllenic acid (69 ; n = l ) and homocaryophyllenic acid (69 ; n = 3) all of which have been synthesised.j5 One of the two ethylenic linkages is present as ;C-=CH, the other is trisubstituted and from the degradations shown in the annexed formulae 56 is contained in the system -CH,-C=CH-.I CH3 The size of the second ring in caryophyllene was for many years a matter of doubt. Evidence on this point was finally forthcoming from two sources. Caryophyllene is smoothly oxidised by hydrogen peroxide to a crystalline J epoxide. This compound retains the >C=CH of caryophyllene for on further attack by potassium permanganate it affords a crystalline C, epoxy-ketone. 57 The infrared carhonyl frequencies of the epoxy-ketone 5 5 Rydon J .1936 593 ; 1937,1340 ; Campbell and Rydon J. 1953,3002 ; Dawson and Rainage J . 1950 3623; 66 Ruzicka and Wind Heh. Chinz. Actn 1931 14 410. 57 Treibs Chew. Ber. 19-17 80 56. 1951 3382. EARTON AND DE MAY0 SESQUITERPENOIDS 199 and of suitable derivatives are best interpreted in terms of a nine-membered ring for caryophyllene. 58 Decisive chemical evicience has been adduced 59 by the reaction sequence outlined where (A) represents the eposy-ketone. I n the formult-e on p. 198 the C,H, fragment must contain the dimethyl- cyclobutane ring. Allowing for this and recognising that the dicarboxylic acid froin this sequence is ditertiay shows t,hibtt tfhe formula for c;wyophyllene (70) (71) (7 2) must be either (70) or (71). The constitutions of caryophyllenic and homo- caryophyllenic acids exclude (71) leaving (70) as a formula adequate to explain all the known facts.The exact nature of “ y-caryophyllene ” now known as isocaryophyllene has been elucidated in the following way.6o isoCaryophy3lene is a hy-product in the preparation of caryophyllene nitrosite (73) and is formed when the latter is heated in ethanol. On treatment with per-acid isocaryophyllene affords a crystalline oxide isomeric with that (see above) from caryophyllene. (73) (74) (75) (76) .... OH (7 7) (78) (79) Under mild acid conditions caryophyllene oxide (73) gave a crystalline diol (74) which when oxidised with chromic acid afforded first the ketol (75) and then the diketone (76). Similar cyclisatiori of isocaryophyllene oxide gave a stereoisomeric diol(78) oxidised via the ketol(79) to the same diketone (76).These experiments show that the two eposides must be stereo- isomerides and that therefore caryophyllene and isocaryophyllene are simply geometrical isomerides about the endocyclic et,hylenic linkage. All the evidence goes to show that caryophyllene is less stable and more reactive 58 Sorm DolejS and Pliva CoZZ. Czech. Chem. Conznz. 1950 15 186. 69 Barton and Lindsey J. 1951 2988. 60 Aebi Barton and Lindsey J . 1953 312-1 ; see also Ramage and Whitehead J. 1954 4336. 200 QUARTBRLB REVIE\VS towards electrophilic reagents than its isomer. Caryophyllene is therefore the trana-isomer (80) The constitution of the diketoile (76) has been rigidly established G 3 by the degradational sequence shown leading finally to p-cymene. The con- figurations of the epoxide rings are based on conformational analysis 60 6 2 and isocaryophyllene the cis-derivative (81).(76) -!+ 2 4 Reagents 1 CrO ; 2 ReO ; 3 H,O,-OH- ; 4 heat ; 6 CH,N then SeO ; of the secondary liydroxyl groups in (74) and ( 7 8 ) and upon other con- siderations. A number of acid-catalysed cyclisations of caryophyllene are of consider- able interest. The major cyclisation products are clovene (82) and caryolan- 1-01 (83 ; R = OH) (formerly known as /3-caryophyllene alcohol). The constitution and stereochemistry of clovene have been firmly established by relating it to the diol (74).629 6 3 The constitution of caryolan-1-01 (83 ; R = OH) was proposed on chemical evidence 64 and established beyond 6 H,O,-OH-; 7 Pd-C. question by the very important X-ray studies of J.Monteath Robertson and Todd 6 5 on caryolanyl chloride (83 ; R = Cl) which is formed from the alcohol with retention of constitution and ~onfiguration.6~ The X-ray studies were especially important in elucidating the stereochemistry of the tricyclic derivatives of caryophyllene and of the ring junction in caryo- phyllene itself.66 The conversion of the bridgehead alcohol (83 ; R = OH) 61 Inter ul. Prelog Schenker and Kiing H e h . Cl~im. Acta 1953 36 471 ; Prelog 6 2 Aebi Barton Burgstahler and Lindsey J. 1954 4659. G3 Lutz and Reid J. 1954 2265 ; see also Esrhenmoser and Gunthard Helv. 6 * Barton Rruun and Lindsey J . 1952 2210. 6 5 Robertson and Todd J. 1956 1254. 6 6 See also Sorm Jarolim Streibl aiicl Dolejg Chen?. and Ind. 1956 154. Rchenker and Gunthard ibid. 1952 35 1598.Chim. Acta 1951 34 2338. RARTON AND DE MAY0 SESQUITERPENOIDS 201 into thc chloride is of some mechanistic interest 6 7 since the change requires the formation of a bridgehead carbonium ion. Presumably the required ion with its flatt,eiied (trigonal) geonietry is not seriously impeded in the 4 3 1 system (83). With rnaleic anhydridc caryophyllene forms an adduct which is not of the usual Diels-Alder type 3 its constitution has been shown to be (84). The adduct cyclises with electrophilic reagents (X = Br or H) to furnish yet another type (85 ; X = Br or H) of tricyclic caryophyllene derivative.68 Humulene (a-caryophyllene) from oil of hops is closely related to caryophyllene but differs in being monocyclic in containing three ethylenic linkages and in being optically inactive.Hexahydrohumulene (humulane) is undoubtedly 1 1 4 8-tetramethylcycloundecane (86) and it has been synthe~ised.~~ The exact locatim of the three ethylenic linkages within the framework (86) is stir a matter for final decision.'O Zerumbone is an interesting ketone isolated from wild ginger.71 Its structure (87) has recently been elucidated and its relation to humulene made apparent.72 On treatment with alkali zerumbone is cleaved to give ethyl methyl ketone as the sole volatile fragment. This fact together with the conversion of zerumbone into humulane and ozonolysis to give as-dimethylsuccinic and lzvulic acid serve to establish the constitution. Miscellaneous Non-lactonic Sesquiterpenoids.-We discuss here several compounds not conveniently considered in the previous sections.The sesquiterpene cedrene from cedar-wood oil is a good example of the difficulties of structural work when no useful dehydrogenation products can 67 Applequist and Roberts Chem. Rev. 1954 54 1065 ; Doering Levitz Sayigh Sprecher and Whelan J . Amev. Chem. SOC. 1953 75 1008 ; Fawcett Chefm. Rev. 1950 47 219. 68 Nickon J . Amer. Chem. SOC. 1955 77 1190. 69 germ Mleziva and Arnold Coll. Czech. Ghem. Comm. 1949 14 693 ; Sorm Mleziva Arnold and Pliva ibid. p. 699 ; Herout Streibl Mleziva and Sorm ibid. p. 716 ; Sorm Streibl Pliva and Herout ibid. 1952 16 639 ; germ Streibl Jarolim Novotny Dolejs and Herout ibid. 1954 19 570 ; Clerno and Harris J. 1951 22 ; 1952 655 ; Harris J. 1953 184. 'O Harris ref. 69 ; Fawcett and Harris J. 1954 2669 2673 ; Clarke and Ramage J. 1954 4345. 71 Varier Proc.IrLdian Acad. Sci. 1944 20 A 257. '2 Dev Ghem. and l n d . 1956 1051 ; see also Balakrishnan Razlan and Bhattrt- charyya Perfumery Essent. Oil Record 1956 274. 202 QUARTERLY REVIEWS be obtained. Cedrene is tricyclic and contains one ethylenic linkage present as the grouping -CH=CMe-.3 The related terticrry alcohol cedrol con- taining the system -CH,*CMe( OH)- occurs along with cedrene. A key degradation product in the cheinistry of cedrene was norcedrenedi- carboxylic acid obtained-with loss of two carbon atoms-by various oxidation procedures. For some years this acid was regarded as a succinic acid but eventually critical interpretation 7 3 based on the extensive work of Plattner and his collaborators 74 showed that this compound must be c- COXt COCH 43- H H (88) (90) (89) of the glutaric acid type (88) and thus made possible the deduction of the expression (89) for cedrene.All structural arguments have been decisively confirmed by the brilliant synthesis of cedrol (go) and hence cedrene (89) carried out by Stork and Clarke 75 along the lines illustrated. The possible biogenetic relation between cedrol and the cadalene group of sesquiterpenoids (see above) is indicated by rewriting formula (90) in the form (91). An interesting transformation in the chemistry of cedrene which initially led to difficulties of intcrpretation,3 is the dehydrobromination with rearrangement of monobronionorcedreiiedicarboxylic acid (92) in alkaline solution to give the acid (93). The reaction is essentially a neopentyl solvolysis. Longifolene from Indian turpentine is another tricyclic sesquiterpene with only one ethylenic linkage.The compound was studied extensively 73 Stork and Breslow J . Amera. Chem. SCC. 1953 75 3291 3292. 7 4 Plather Kusserow mid Klaiui He/?*. C ’ h h . Actcc 1912 25 1345 ; Plattner Fiirst EEcjc‘lieninoser Keller Klaui Meyer. and Rosner ibid. 1953 36 1845 and references there cited. 7 5 Stork arid Clarke J . Au2~r. C’hen~. SOC. 1955 77 1073. BARTON AND DE MAY0 SESQUITERPENOIDS 203 by Simonsen and his collaborators 76 and later by others.77 However it proved difficult to break down the ring system and the correct constitution (94) was only elucidated by the excellent X-ray work of Moffett and Rogers 78 on the longifolene hydrohalides (95 ; X = halogen). It is still desirable of course that the proposed structure should be confirmed by further chemical evidence.Recently Sorm and his collaborators 79 have elucidated the constitution of acorone a diketone isolated from sweet flag oil. This has been shown to be a carbocyclic spiran (96) ; the discovery is especially important since 0 W-qf- (96) ' it is the f i s t example to be found in Nature. wz$ The spiran character of the diketone is strikingly revealed by the formation i f both cadalene and 1 7-dimethyl-4-isopropylnaphthalene on dehydrogenation of a suitable derivative. The same point is illustrated in the transformations formalised here. Lactonic Sesquiterpenoids based on Decalin.-The most important com- pound of this type is santonin (97). This has been the subject of investiga- tion for more than a century and even now provides the basis for much interesting research.One of the most characteristic reactions of santonin is its ease of aromatisation under acid conditions to desmotroposantonin (98). It was this 'rearrangement which impeded the recognition of the correct santonin structure for many years.*O The constitution of santonin has been 76 Simonsen J. 1923 2642 ; Bradfield Francis and Simonsen J. 1934 188. 7 7 Dupont Dulou Naffa and Ourisson Bull. SOC. chim. France 1954 1075 ; and Ourisson ibid. p. 1115; Zeiss and Arakawa J. Amer. Chem. SOC. 1954 76 1653. 78 Moffett and Rogers Chem. and I n d . 1953 916. 79 Sykora Herout Pliva and Sorm Chem. and I n d . 1956 1231. 80 Clemo Haworth and Walton J. 1929 2368 ; 1930 1110 ; Clemo and Haworth J . 1930 2579. 201 QUARTERLY REVIEWS confirmed by synthesis 81 and the stereochemistry almost completely elucidated 8 2 as in (99).In the space available only two of these can be discussed. On prolonged trentinent with alkali santonin is converted into santonic acid (100) by the internal Michael rearction indicateci.83 Treatment with acetic acid followed 11-y heating at Santonin undergoes many reactions of theoretical interest. 260-300 O gives santonide and parasantonide. Both compounds have the formula (101) and differ in configuration at C,,.82y 83 A mechanism for this interesting rearrangement has been proposed.83 Santonin like other cyclohexadienones is sensitive to light. Amongst the many irradiation products described in the earlier literature the mostl important are photosantonic acid whose constitution is still under investiga- tion and the so-called isophotosantonic acid.The latter which is produced from santonin in yields of up to 35% on irradiation with ultraviolet light in aqueous acetic acid contains an ap-unsaturated cydopentenone ring and has the constitution (lO2).8* Ozonolysis affords acetic acid and with loss of water a bis-y-lactone. The carbon skeleton has been confirmed by conversion of a derivat,ive into charnaz~lene.~~ Amongst other lactones of fhe decalin type there should be mentioned artemisin (103) 39 8sa and y-santonin ( 104).33 85b Although y-santonin is not a cydohexadienone nevertheless with 55% sulphuric acid it is readily aromatised to desmotropo-y-santonin (105) the reaction proceeding through the diene (106) and the conjugated dienone (107) as indicated. The hydroxyl 81 Abe Harukawa Ishikawa Miki Sumi and Toga Proc.Jap. Acad. 1954 30 116 119; J . Amer. Chem. SOC. 1953 75 2567; 1956 78 1416. 8 2 Inter al. Woodward and Yates Chem. and Id. 1954 1391 ; Abe Miki Sumi and Toga ibid. 1956 953 ; cf. also Miki J . Pkarm. SOC. Japan 1955 75 416. 83 Woodward Brutschy and Baer J . Amer. Chem. Soc. 1948 70 4216 ; Woodward and Kovach ibid. 1950 72 1009. 8 4 Barton de Mayo and Shafiq J. 1957 929. *ja Sumi Proc. Jap. Acad. 1956 32 684. 8 G b C'hopra Cocker Cross Edward Hayes and Hutrhison J . 1955 588 ; Chopra Cocker Edward McMurry and Stuart J . 1956 1828 and references there cited; Dauben and Hance J . Arne?. C'iiem. Soc. 1955 77 2451 ; Dauben Ilance and Hayes ibid. p. 4609 and references there cited. BARTON AND DE MAY0 SESQUITEKPENOIDS 205 group double bond and lactone group of y-santonin have been inter-related by oxidation of y-santonin to the corresponding diketoiie (lOS) which on mild treatment with a base gives the conjugated dienone (10'3).The allylic-lactone character of y-santonin is demonstrated by its ease of hydro- genolysis to the acid (110). The interesting sesquiterpenoid lactone pyrethrosin was first isolated in 1891 from Chyysanthemuna cinerarizfobium. It has recently been shown to represent a new type of monocarbocyclic sesquiterpenoid.86 Pyrethrosin contains two ethylenic linkages (one of which is conjugated with a y-lactone grouping) an acetoxyl group and a cyclic ethereal oxygen atom. It is therefore monocarbocyclic. When heated with acetic anhydride and (I 13) toluene-p-sulphonic acid pyrethrosin is converted into cyclopyrethrosin acetate (1 1 l) the structure of which has been proved inter al.by conversion into the diketone (109). The acid-cntnlysed forinntion of cyclopyrethrosin acetate from pyrethrosin necessarily involves fission of the ethereal ring. The conciihions of the reaction are however so drastic that it would be unwise to make definite 8 6 Earton and de Mayo J . 1957 150. 0 206 QUARTERLY REVIEWS structural proposals for pyrethrosin itself on this evidence alone. Fortun- ately pyrethrosin is also cyclised under the very mild conditions of oxidation with sodium dichromate in aqueous acetic acid at room temperature. Two products (112) and (113) are formed in the oxidation. The former of these has been related to cyclopyrethrosin acetate in the manner indicated. Now if one considers the mechanism of the chromic acid oxidation this must surely be electrophilic attack upon the ethereal ring with participation of the n-electrons of the non-conjugated ethylenic linkages in the formation of the new carbon-carbon bond thus producing the carbonium ion (114).By proton loss the latter would afford the unsaturated ketone (112) whilst by reaction with the water present in the medium it would afford the tertiary alcohol (113). The ketone group of the ion (114) therefore indicates one end of the ethereal ring and the positive charge one end of the ethylenic linkage. These considerations allow only three possible formulze (1 15) (116) and (117) for pyrethrosin. The first two can be rejected since pyre- throsin contains only one grouping of the type (;C=CH,). The correct formula for pyrethrosin must therefore be (117).The ring structure of pyrethrosin may well be of some biogeiietic signi- ficance since if one unites a ten-membered ring as in (118) it is possible by establishing different bonds across the ring to construct the carbon skeletons of most of the bicyclic sesquiterpenoids. The cyclisation reactions of pyrethrosin itself already illustrate this point experimentally. The lactones so far discussed have been derivatives of eudalene or in the case of pyrethrosin could be cyclised to such a skeleton. Recently an interesting lactone has been discovered which although a decalin deriva- tive belongs to a different series. Iresin (119) from Iresine colosioides is an unsaturated lactonic glycol giving a benzylidene derivative. Dehydro- genation afforded 1 5-dimethylnaphthalene and 1 5-dimethyl-2-naphthol.Ozonolysis of iresin furnished an internal acetal (120). On the basis of this and other evidence the constitution (119) was proposed. Djerassi and his colleagues 87 have however been careful to point out that an alternative structure with the angular methyl a t C(5) instead of C(lol is also possible on the evidence so far adduced. In any case iresin is an important compound Djerassi Sengupta Herran and Walls J . Amer. Chem. SOC. 1954 76 2966 ; Djerassi Rittel Nussbaum Donovan and Herran ibid. p. 6410 ; Djerassi and Rittel ibid. 1957 79 3528. We thank Professor Carl D jerassi for his kindness in sending us a copy of the last paper before its publication. BARTON AND DE MAYO SESQUITERPENOIDS 207 since it represents a sesquiterpenoid chain cyclised in a manner characteristic of the first two rings (see 121) of the di- and tri-terpenoids.If the Me i s at C,, this would be the result of a trivial migration after cyclisation. Lactonic Sesquiterpenoids based on Perhydroazu1ene.-The chemistry of these interesting compounds has only recently received serious attention. One group of azulenic lactones can be described as " chamazulene-pre- cursors ". This is because of the facility with which they afford chamazuIene ( 122) g8 even under such mild conditions as steam-distillation. Wormwood has been extensively investigated 89 and the blue szulene of oil of wormwood identified as chamazulene (122). The oil also contains an interesting yellow dihydrochamazulene known as chamazulenogen which is converted into chamazulene merely on exposure to air.The original chamazulene precursor in wormwood is artabsin ( ~ 3 ) . ~ * On steam-distillation particularly in the presence of a trace of acid this is changed into chamazulene. The proposed constitution is supported by inter al. conversion by hydrogenation into the hydroxy-lactone (124) obtained earlier from arborescin (see below). Sorm and his colleagues 89 have also investigated the chamazulene pre- cursors of oil of chamomile. From this source matricin (125) was isolated. I n faintly arcid solution a t about 50" this lactone afforded guaiazulenic acid (126) obtained earlier by Stahl 91 from yarrow and later also from chamomile. At somewhat higher temperatures this is decarboxylated to chamazulene. HO QoAc 0 (1 22) 88 Meisels and Weizmann J .Amer. Chem. Soc. 1053 '75 3865; germ Herout and Takeda Chem. Listy 1954 48 281 ; Novak germ and Sicher ibid. p. 1648. b r m Vonaselr and Herout, Coll. Czech. Chern. Coinrn. 1019 14 91 ; Herout and Sorm &id. 1053 18 854 ; Cekftn Herout and &orni ibid. 1954 19 798 ; &xm Novotnjl and Herout Chem. crnd Ind. 1955 569 ; cf. Schenclr and Schuster Arch. Pha~m. 1956 289 1. Herout Dolej3 and Sorm Chern. and Ind. 1956 1236; Cekan Herout and Sorm ibid. p. 1234. 91 Stahl Chem. Ber. 1954 8'7 202 505 1626. 208 QUARTERLY REVIEWS The bitter principles of Artemesia absinthium have recently 9 2 been isolated and characterised as anabsinthin C15H2003 and absinthin a sub- stance having the composition C1,H2,03,~H,0. Tenulin and helenalin are the bitter principles of various Heleniuin species.The early work on tenuling3 has recently been e~tended.~4 Tenulin affords acetic acid on alkaline hydrolysis. It is also a y-lactone and contains an a,8-unsaturated cyclopentenone system. Since tenulin has the formula C1,HZ2O5 these facts would appear to account for all the oxygen atoms. However other evidence discloses the presence of a hydroxyl function and the molecule does not afford acetic acid on acid hydrolysis as does a true acetate. Under very mild alkaline conditions tenulin is isomer- ised to isotenulin which does have a true acetate residue but lacks the hydroxyl group. On the grounds of this and other evidence the masking of the acetate function has been explained g4 as illustrated. On digestion with sodium hydrogen carbonate solution teiiulin and isotenulin are converted into deacetylneotenulin.The latter contains the system -CO*CMe:C< since on ozonolysis it affords acetic acid. This and other work has led to formulation of tenuliii as (127) isotenulin as (128) and deacetylneotenulin as (129). Recently Braun Herz and Rabindrau 95 (128) 8 0 9 0 H (129) oq-$ OQ HO&Q (130) (I3 I) (132) co2H have made the interesting observation that deacetyldihydrodehydroisolerlulin (130) is cleaved with alkali to a dicarboxylic acid containing an a/j-unsaturated ketone grouping. This reaction is possibly explained better by the formula- tion (1 31) for deacetyldehydrodihydrodsotenulin the dicarboxylic acid being g2 Soim Novotny niitl Herolit, C'hem. and Tnd. 1956 569. Qa Clark J . Anze~. C'Aenx. Soc.. 1039 61 1836 ; 1940 62 597 ; Urignacle and Hend- st Barton a8nd de Mayo J .1956 142. 9 5 Braun Herz and Rdindrau J . Anto.. C'Jwm. Soc. 1956 78 4433. leg' ibid. 1948 '70 3921 ; Ungnnde Hendley and Dunkel ibid. 1950 7'2 3818. BARTON AND DE MAYO SESQUITERPENOIDS 209 (132). If this is correct then the tenulin formula (127) simply requires revision to (133). The modified formula for tenuliii (134) advanced by Braun Herz and Rabindrau 95 does not explain the properties of neotenuiin ; other evidence of these workers however tends to support the position of the lactone ring as in (127). A Helenalin also obtained from Helenium species is a lactone showing inany similarities to deacetylisotenulin. Earlier work by Adams and Herz 96 had established the presence of a y-lactone and a secondary hydroxyl group and an $-unsaturated cyclopentenone system.Evidence was also provided for the presence of a grouping >C=CH and for an azulenic carbon skeleton. Further work by Biichi and Rosenthal 97 has completed the evidence for constitution (135). An isomer of helenalin isohelenalin was also isolated in these studies and shown to have structure (136). The position of the orp-unsaturated ketone moiety in these formulae was based on nuclear magnetic resonance spectra. The position of the secondary hydroxyl group was deduced mainly from the action of base on dehydrotetrahydrohelenalin (137). This afforded a dicarboxylic acid (138) t’he formation of which can be rationalised as the cleavage of a vinylogous P-diketone system.97 It is however clear that further evidence as to the position of the lactone ring is desirable both for tenulin and for helenalin.Arborescin isolated from Artemisia m4orescens is nn isomer of artabsin ( 123).98 A relation between these two conipouncls has already been referred to in the text above. The proposed constitution (139) for arborescin 98 contains the unusual feature of a trimethylene oxide ring. Whereas the position of the ethyleiiic Ijiiknge and one terminus of tlhe oxide ring appear 9 6 Adams and Hwz J . Anzer. Ghein. Xoc. 1949 71 2546 2551 2554. 98 Mazur and Mciscls C’herrb. und Ind. 105G 402. Buchi and Rosenthal ibid. 1956 78 3860. 2 10 QUARTERLY REVIEWS to be well established some dubiety is attached to the other terminus. Structures such as (140) and (141) still reniain to be excluded. Other sesquiterpenoid lactones for which structures have been proposed are dehydrocostus lactone 99 (142) from costus oil carpesia lactone loo (143) from Carpesium abrotanoides and geigerin lol (144).The constitution for carpesia lactone may require some revision as to the position of the ketonic function. Relative and Absolute Stereochemistry of Se3qUiterpenoids.-Stereo- chemical investigations have not been pursued so intensively in sesquiter- penoid compounds as in di- and tri-terpenoids. The methods are however the same and we can mention degradation to compounds of known orientation ring formation and conformational analysis lo2 as important techniques for the solution of these stereochemical problems. The first method also of course provides information on absolute configuration. Where degradation is not convenient molecular-rotation correlations are often of great help lo3 the basic idea being that like structures embedded in like stereochemical environments make like contributions to molecular rotations.We may use the stereochemistry of zingiberene (21) as an illustration. The adduct (145) of zingiberene and dimethyl a'cetylenedicarboxylate affords the (+)-diene (146) as well as the dimethyl methylphthalate (147) 99 Romanuk Herout and germ Coll. Czech. C'henb. Comn. 1956 21 894. loo Kariyone and Naito J. Pharm. Sac. Japan 1955 75 39 ; Kariyone Naito and lol Rimington Onderstepoort J . V p t Xci. 1936 7 485 ; Perold I . 1957 45 ; Bnrt!on I o 2 Barton and Cookson Quad. Rev. 1956 10 44. lo3 Mills J. 1952 4976 ; Hlyne J. 1952 2916 ; 1953 3072 ; Klyne and Stokes Chatani Pharm,. Bull. (Japan) 1954 2 339. and Levisalles unpublished work.J . 1954 1979. BARTON AND DE MAYO SESQUITERPENOIDS 21 1 on pyrolysis. lo5 The absolute configuration of fhe diene (146) is known from its relation to citronellal the (+)-form of the latter affording the ( -)-diene.lo6 The complete absolute configuration of zingiberene as (148) w-as then deduced by comparing the molecular rotations of zingiberene and ( - )-or-phellandrene ( 149) whose absolute configuration is known. In the eudalene group of sesquiterpenoids trans-fusion of the rings is general except for dihydrohydroxyeremophilone 36 the stereochemistry of which is depicted in (150). The absolute configuration of this compound is based on molecular-rotation considerations. l o 4 Eudesinol has been related to the steroids which are of known absolute configuration through an intermediate in the Woodward steroid synthesis.lo7 In this way eudesmol has been shown to have the absolute structure (151). The relationship of‘ eudesmol to cc- and 8-cyperone and to carissone lo8 shows that these com- pounds also have the same type of absolute configuration. Saiitonin has been converted into /3-cyperone thus establishing its absolute stereo- chemistry as already indicated in formula (99).109 Nothing is as yet known about the stereochemistry of the perhydro- azulenic sesquiterpenoids but the known relation of santonin to “ isophoto- santonic acid ” must eventually prove helpful. The stereochemistry of cedrene (89) was established interestingly enough by synthesis; ‘ 5 the absolute configuration is not known. The absolute configuration of caryophyllene (80) is based on extensive molecular-rotation correlations.l10 The stereochemistry of longifolene already given (94) is based on the X-ray work and for the absolute configuration on molecular- rotation arguments lo4 Djerassi Riniker and Rinilmr J. Ainer. C‘hem. Soe. 1966 78 6362 and earlier Io5 Eschenmoser and Schinz Helv. C’him. Actu 1950 33 171. lo6 Arigoni and Jeger ibid. 1954 37 S81. lo’ Riniker Kalvoda Arigoni Fiirst Jeger Gold and Woodward J. Amer.. Chcria. lo8 Ayer and Taylor J. 1955 3027 ; McQuillin J. 1956 628 ; Howe and McQuillin log Bruderer Arigoni and Jegor Helv. Chim Actu 1956 39 858. 110 Barton and Kickon J. 1954 4665. ll1 Ourisson Bull. Xoc. chim. France 1955 895. papers. SOC. 1954 76 313. J . 1955 2423.

ISSN:0009-2681    

DOI:10.1039/QR9571100189

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

THE INBSITOLS By 8. J. ANGYAL PH.D. (NEW SOUTH WALES UNIVERSITY OF TECHNOLOGY SYDNEY) 1. Introduction ONLY two decades ago the chemistry of the inositols (cyclohexiriiehexols) was in the same state as that of the simple sugars a t the advent of End Fischer only a few naturally occurring isomers were known and their configurations had not been established. By now thanks mainly to the excellent work of T. Posternak and of H. 0. L. Fischer and to recent advances made in Sydney all the isomers predicted by theory are known their configurations have been established and methods have been developed for their interconversion. The study of the inositols is of interest) and import,ance for two reasons. First one of the isomers myoinositol is a compound of outstanding bio- logical interest it is of widespread occurrence in both plants and animals and it may have nutritiona.1 significance.Despite a large amount of work however there is still no definite knowledge of its biologicaJ function or of its biosynthesis or its metabolism. This Review does not deal with the biochemistry of the inositols. Secondly the inositols offer unique opportunities for stereochemical studies. They form the only set of hexnsubstituted cyclohexanes in which every possible isomer is known. (The all-cis-isomer is yet unknown amongst the hexachlorocyclohexanes.) As derivatives of cyclohexane the inositols can be used to study the applications of conformational a n a l y ~ i s . ~ As polyhydroxy-compounds closely related to the sugars they can serve as useful models for the study of some carbohydrate reactions ; the behaviour of secondary hydroxyl groups can be examined without the disturbing effect-steric and electronic-of a ring-oxygen atom and without the possi- bility of ring-opening.Thc present Review discusses mainly the reactions of inosit,ols and related compounds from the stereochemical point of view. in 1850 from muscle tissue (i'g ivdg = sinew). The name inositoi has since come to be used for the designation of all the isomers which are differentiated by prefixes. The original inositol has been known for many ycars as mcso- or i(in:tctive)- 1 For work tip to 1'3.17 see the review by Fletclisr Adz]. Gtrrbolrycli*tcte Cltem. 1'328 3 43. Other reviews Dangschnt in Paecli and Trstcey " Moderne Methoden der Pflanzenanalyse " Springer Berlin 1955 p. 64 (analytical methods) ; Postern& Bull.Soc. Chim. hid. 1961 33 1011 (naturally occurring ryclitols). 2 E'oy 1'evi~ws oi llrp 1)iochemist ry of ~n?yoinositol. see ,Schopf~r ?lt//l. #oc. C'hinz. hiol. 1951 33 1113 T\'eicllc% ' * The I3iocliemistry nf Tnositol -' Mellon Inrtitute Rihliographic Series IZullet iii lu 0. 6 10.5 1 . The first iiiositol was isolated by Scherer 3 Barton and Cookson Quait. Rev. 1936 10 44. 1 scllcrcr AtLtLUle& 1850 '73 322. 212 ANGPAL THE INOSITOLS 213 inositol; these unspecific prefixes have now been replaced by nzyo (puv”~ = muscle) but the compound is often referred to particularly by biochemists simply as inositol. The convenient term cyclitol is used to describe all polyhydroxycycbhexanes. Quercitol and inosose are thc generic 3 /- - - i oo W I / \- \ names for cyclohcxanepentols and ~ ) e n t ~ h y d ~ ~ ~ ~ ~ ~ c Z ~ l i e x ~ i i o ~ respectively ; the individual isomers are distinguished by prefixes .* Fletcher Anderson and Lardy J.O q . Chon. 1951 16 1238. Anggal and Macdonald J . 1952 086. * The nomenclature of the cyclitols is in a confused state several different systems being nseci by various authors (see refs. 5 6 49 70). In this Review the cyclitols are named and numbered according to Angyal and Macdonald ; more controversial fcaturos of noinenclature such as the designation of enantiomorphs have been avoided. 214 QUARTERLY REVIEWS For the inositol structure theory predicts the existence of eight diastereo- isomers of which only one is racemic ; the seven meso-forms and the two optically active isomers are shown with their prefixes by formulze (I)- (VIII).The preparation of the rarer ones from the common isomers is also shown ; the reactions involved are discussed below. The inositols are-for polyhydroxy-compounds-surprisingly stable. They withstand the action of alkalis and acids even of concentrated hyciriodic acid of reducing agents and of heat up to about 350". They are only slowly oxidised by concentrated nitric acid. They all melt above 200" and some above 300". 2. Configuration and synthesis of the inositols 2.1. wyoInositol.-The structure of any inositol is easily established by its oxidation with nitric acid to a mixture of hydroxy-ketones which in alkaline solution isomerise and are oxidised t o hexahydroxybenzene tetrahydroxy-p-benzoquinone and rhodizonic acid ; the last gives a characteristic red ba'rium salt.Since every oxygen and carbon atom of the inositol is preserved this transformation proves the cyclohexanehexol structure ; as a characteristic qualitativc test for inositols it is known as 0-GMe2 OH OH H O&*.COy OH OH (XVI) the Scherer reaction.8 Surprisingly under the vigorous conditions of the oxidation the cyclohexane ring is not opened whereas the quercitols (cyclo- hexanepentols) are cleaved by nitric acid at the methylene group under much milder conditions. The configuration of myoinositol presented a more difficult problem because degradation by permaiigannte oxidation designed to split the cyclohexane ring gave too many products owing to random fission. Little progress was made towards a solution and indeed generally in the chemistry of inositols until stereospecific reactions were developed for producing changes a t one or two of the secondary hydroxyl groups only Two such reactions were introduced in the thirties and both led independently to the configuration of myoinositol.Posternak lo used enzymic dehydrogenation 7 Gelormini and Artz J . Amel.. C'hem. SOC. 1930 52 2483 ; I-Ioglnn and Bartow ibid. 1920 62 2397 ; Preisler and Bergcr ibiil. 1942 64 67. * Scherer Aiznnlen 1832 81 375 ; Ralkowski Z. physiol. Chena. 1910 69 406 Fleury Courtois and Jouanrie t BuK Soc. Chirn. biol. 1951 33 1889. Kiliani and Scheibler Ber. 1889 22 517. lo Postcrnak Helv. Chirn. Aclu 1942 25 746 and references there cited. ANGYAL THE INOSITOLS 215 by Acetobacter suboxydans (5.1 ; this and similar designations refer to sections of this Review) first described by Kluyver,ll to produce scylloinosose (IX) ; this was oxidatively split a t the keto-group to yield saccharic acids which were identified.In 1942 Dangschat l2 described the preparation (5.2) of 1 2-0480- propylidenemyoinositol (XIV) ; acetylation of its free hydroxyl groups and removal of the isopropylideiie group gave the tetra-acetate (XV) which was cleaved by lead tetra-acetate in one specific position. The production of ( & )-idosaccharic *acid (XVI) established the configuration of myoinositol as (11). myoInosito1 is produced commercially from maize steep liquors but it has also been synthesised by two methods both of which are of considerable interest. In 1914 Wieland and Wishart l3 made the remarkable claim that hydrogenation of hexahydroxybenzene with a palladium catalyst gave the biologically important myo-isomer alone amongst all the possible isomers in high yield and purity.With the establishment of the configura- tion of myoinositol-many years later-the stereospecificity of the hydro- genation has become even more remarkable and has still not been satis- factorily explained; A recent re- investigation l4 has shown that the hydrogenation produces a complex mixture in which myoinositol in a yield of about 20% is indeed the pre- dominant product ; several other inositols as well as quercitols and cyclo- hexane-tetrols and -triols have been isolated from the mixture by chroma- tography on cellulose powder a method particularly useful in cyclitol chemistry.15~ l6 This method is suitable for the preparation of (uniformly) Many attempts have been made to cyclise hexose derivatives to inositols thereby emulating Nature which presumably produces inositols in this way ; 18 but only one was successful.Grosheintz and Fischer l9 cyclised 6-deoxy-6-nitro-~-g~ucose (and its L-idose epimer) to a mixture of deoxynitro- inositols from which the all-truns-isomer (XVII ; R = NO2) was isolated. Presumably this isomer is readily formed because it is the most stable one having all substituents in equatorial positions ; the stereochemistry of the other nitro-compounds or the synthesis of isomeric ones by the use of different deoxynitrohexoses has not been investigated. Reduction l9 of the nitro-group gave scyZEoinosamine (aminodeoxyscyEZoinosito1) (XVII ; R = NH,) which has been also prepared 2O from scylloinosose (IX).The it has indeed often been doubted. 4C - la belled myoinositol. 17 l1 Kluyver and Boezaardt Rec. !L'rav. chim. 1939 58 956. lP Dangschat Nnttcrtoiss. 1942 30 146. l 3 Wieiand and Wishart Ber. 1914 47 2082. l4 Angyal and McHugh J . 1957 3682. l5 Anderson and Ballou J . Arner. Chem. SOC. 1953 75 648. l6 Angyal Gilham and Macdonald J . 1957 1417. l7 Weygand and Sehulze 2. Nuttirforsch. 1960 l l b 370. l 9 Grosheintz and Fischer J . Amer. Chem. SOC. 1948 70 1479. Z o Carter Clark Lytle and McCasland J . Biol. Chem. 1948 175 683 ; Anderson Fischer Harvey Lectures 1945 40 1%. and Lardy J . Arrt,er. Chem SOC. 1950 72 3141. 216 QUARTERLY REVIEWS final step was carried out by Posternak z1 who obtained myoinositol by treatment with nitrous acid in poor yield ; the yield is much improved if tlie penta-0-acetyl derivative of the inosainine is used.22 In t'his case as in wll others z 2 23 known so far in cyclitol chemistry t,he amino-group is replaced l ~ y a hydrosyl group mainly with inversion ; such behaviour is not in accordance with experience in other fields.2.2. The Other Inositols-Only two optically active inositols (IIIa and I I I b ) can exist both have long been known to occur in numerous plants as nionomethyl ethers. The most convenient source of quebrachitol %O-methyl-( -)-inositol is the latex of the rubber tree Hecea brasiliensis ; 24 that of pinitol 3-O-methyl-( +)-inositol is the sugar pine Pinms larnbertictn~.~~ [ (+)-Pinit01 has been found in nearly 300 plant species ; its enantiomer has recently been isolated from one plant.26] In each case the methyl group is readily removed by concentrated hydriodic acid.The configuration of (-)-inositol has been established 27 as (IIIb) by the isolation of D-gluco- snccharic acid from its permanganate-oxidation products. scyZZoInosito1 (scyllitol) (I) has been isolated from several plants and but it is more conveniently prepared 28 by reduction of scyZZoinosose (IX) with sodium ama,lgam ; this reaction proves its configuration since that of the inosose had already been established by Posternak.lo The other inositols have not been found in Nature and are prepared by synthesis from myo- or the optically active inositols. Oxidation of myoinositol by nitric acid if interrupted a t an early stage gives epiinosose (X) in no more than 20% yield.29 It is not known whether this dehydro- genation is stereospecific (which i t niay well be owing to the " 3-alkyl effect " 30) or whether epiinosose is isolated because it is less soluble than its isomers.Its configuration was established by permanganate oxidation to DL-talomucic and DL-glucosaccharic acid ; hydrogenation gives epiinositol (V) whose configuration is thereby defined. 31 21 Posternak Helv. Chim. Actu 1950 33 1597. 22 L. Anderson personal communication ; cf. Wintersteiner and Klingsberg 2 3 Patrick Williams Waller and Hutrhings i6id. 1956 78 2652 ; Jlann and 2 4 van Alphen l n d . Eng. CIicrrb. 19.51 43 141 ; for tlio structure uf quebrachitol 2 5 Anderson Ind. Eng. Cham. 1953 45 593 ; for tlic structure of 1hitol see Angj-nl 2 6 Plonvier Cotupf. ?wjd. 1 !fTtfi 243 1913. z7 Yosternal< Heltq.~ ' A i i t . A r t ( / 1933 19 1007. 28 I c ~ P ~ ihkl,. 1941 24 10-15. 2q Idem ihid. 1936. 19 1333. 30 Kiyne Expcrienlia 1956 12 119. 31 Postcrnuli l i c l u . C ' l ~ i i i ~ . d c l u 1946 29 19'31. J. Amer. Chem. SOC. 1951 73 2917. iVoolf' ibid. 1967 79 120. see Posternak Heli2. Clzirn. Acta 1952 35 50 and ref. 6. Jincdonald and Mathcqon J . 19.53 3321. ANGYAL THE INOSITOLS 217 allo- and mum-Iiiositol were first prepared by hydroxylation of con- duritol (XVIII) a naturally occurring cyclohexenetetrol 32 the configuration of which was established by its oxidation to mucic acid The two inositols were distinguished by oxidation of suitable derivatives to allomucic and inucic acid respectively. More recent preparations from the naturally occurring inositols are illustrated by the sequences (I1 -+ XI1 -+ VIJ) aiicl neoInositol (IV) has been made 33 by epoxide opening (5.7) of 1 2- anhydroalloinositol (XIX) a reaction which proves its configuration.cisInosito1 (VI) was isolated,14 in 4% yield from the cyclitol mixture produced by hydrogenation of hexahydroxybenzene (2.1) with palladium ; the yield could Be increased to about ZO% and cisinositol made the major product by the use of a palladium-carbon catalyst. cidnositol was the last of the possible isomers to be isolated; hence its configuration can be deduced but has not been proved ; however its chernical beliaviour particularly its reaction with boric acid (5.5) and periodic acid (5.4) is in accordance with the all-&-configuration. (111 + XI11 -+ VIII). 3. Compounds related to inositols 3.1.The 1nososes.-The inososes have not been found in Nature but they are important intermediates in the synthesis of inositols. They are formed in the dehydrogenatiou-catalytic or enzymic (Ti.l)-of inositols. Chemically they resemble the sugars much more closely than the inositols since they form phenylhydrazones and osazones and reduce Fehling's solution and sodium hypoiodite in the cold. In the presence of bases the inososes and particularly their esters aromatise very easily ; thus on treatment with sodium acetate and acetic anhydride 1 2 3 &tetra- acetoxybenzeiie (XXIlI) is formed. 29 Isbell 34 proposed the mechanism (XX) + (XXIII) in which each step is thought to be preceded by enolisation When a pent.a-ester of an inosose is hentccl to 150" in contact with soda- 33 Dangschat and Fischer Nahrzuiss.1939 27 756. a 3 Angyal and Matheson J . Amer. Chem. SOC. 1055 77 4343. 31 Isbell Ann. Rev. Biochem. 1043 12 213. 218 QUARTERLY REVIEWS glass (but not with Pyrex glass) it loses one mol. of acid and is transformed 35 into an unsaturated ketone presumably (XXI). Before this behaviour was discovered 36 the esters were believed to be dimorphous. On reduction with sodium amalgam 29 the inososes give mixtures of epimeric inositols the keto-group being reduced mainly to an equatorial hydroxyl group. Catalytic hydrogenation on the other hand gives mainly the axial epimer.29 Sodium borohydride yields both epimers when the keto-group is unhindered but only the axial one when hindered by an axial hydroxyl group. 37 3.2. The Quercito1s.-Theory predicts the existence of ten diastereomeric yuercitols of which four are symmetrical and the others represent six pairs of enantiomorphs.Only about half of these are known but with our present knowledge it would be possible to prepare most of the unknown ones if required. Two have been found in Nature (+)-protoquercitol (XXIV) originally known as d-quercitol which was discovered in acorns in 1849 and ( -)-viboquercitol (XXV) originally described as E-quercitol. The others were synthesised by the catalytic hydrogenolysis of the corre- sponding inososes in dilute sulphuric acid solution an interesting method introduced by Posternak 28 for the complete reduction of the keto-group. HO HO HO (XXVI) (XXVI I> (X XVI I I) 3.3. The 1nosamines.-The discovery of ~treptamiiie,~~ 1 S-diamino- 1 3-dideoxyscyEEoinosito1 (XXVI) as a degradation -product of strepto- mycin has directed attention to the amino-derivatives of the inositols.Inosamines (aminodeoxyinositols) can be synthesised by hydrogenation of the oximes or phenylhydrazones of inososes,20 by opening the epoxide ring of anhydroinositols with ammonia 39 and by reaction of bromodeoxyinositols with arnmonia.*O Recently 2-amino-2-deoxyneoinositol (XXVII) has been obtained as a fragment of the molecules of two new antibiotic^.^^ Amongst other compounds related to inositols mention may be made 35 Mrs. E. Smith Ph.D. Thesis Sydney 1956. 36 Fleury Lecocq and Posternak Bdl. SOC. chim. France 1964 1107. 37 Roymond Helv. Chim. Acta 1957 40 492. 38 Lemicux and Wolfrom Adv. Carbohydrate Chem. 1948 3 337 ; €or synthesis by ring-closure of a nitro-sugar (2.1) see Wolfrom Olin and Polglase .T.Amer. Chem. Roc. 1950 72 1724 and by catalytic dehydrogenation (5.1) see H o p s and Pnulsen G h . Ber. 1056 $9 1152. Anderson Ahs. Papers 129th Meeting Amer. Chem. SOC. 1956 p. 2 7 ~ ; Allen J . Amer. Chem. SOC. 1957 79 1167. 4o Wolfrom Radell Husband and McCasland ibid. p. 160. ANGYAL THE INOSITOLS 219 of the C-methylinositols of which two have been found in Nature mytilitol,41 which is C-methylscylloinositol (XXVIII) and laminitol 4 2 of a configuration yet unknown. 4. The conformation of the inositols It has generally been assumed that the inositols in accordance with the tenets of conformational analysis exist predominantly in that chair con- formation which has the smaller number of axial hydroxyl groups. These conformations-shown in formulae (1')-( VIII' )-have not been directly proved (as has been done for the pyranose sugars by Reeves 43) but analogy with other polysubstituted cyclohexanes and with the sugars leaves little doubt about them.The reactions discussed below are all in accordance with this assumption." It is to be noted that the two possible chair forms are identical in the case of cis- and muco-inositol each with three axial hydroxyl groups. And in the case of alloinositol the two chair forms are mirror-images of each other alloinositol is therefore an inseparable racemic mixture of rotational isomers. Every hydroxyl group in cis- muco- and allo-inositol has an equal chance of being axial. scylloInosito1 (I) is the most stable isomer. The equilbrium constants of complex formation with boric acid ( 5 .5 ) allow the approximate calcula- tion 45 of the free-energy difference between the isomers ; thus myoinositol (one axial OH) is estimated to be less stable by 0.9 kcal./mole epiinositol (two on the same side) by 2.8 kcal./mole and cisinositol (three axial groups on the same side) by 5-7 kcal./mole than scylloinositol. Unfortunately no method is known whereby inositols can be equilibrated amongst them- selves and thereEore these figures have not been experimentally verified ; nor have the heats of combustion of the isomers been determined. At an elevated temperature hydrogen halides in acetic acid partially convert 41 Posternak Helv. Chim. Acta 1944 27 457. 4 2 Lindberg and McPherson Acta Chem. Scund. 1954 8 1875 ; 1955 9 1097. 4 3 Reeves Adv. Carbohydrate Chem.1951 6 107. 4 4 Kuhn J . Amer. Chem. Xoc. 1952 74 2492 ; 1954 76 4323. 45Angyal and McHugh Chem. and Id. 1956 1147. * These conclusions are not incompatible with Kuhn's observation 4 4 that in dilute solution in a non-polar solvent cis-cyclohexane- 1 3-diol shows evidence (infrared spectrum) of internal hydrogen bonding so that the diaxial conformation is present. The energy of the hydrogen bond is sufficient t o compensate for the diaxial interaction. In hydroxylic solvents (the only ones in which inositols are soluble) intermolecular hydrogen bonding occurs and cis-cyclohexano- 1 3-diol would be expected to exist in the diequatorial conformation. 220 QUARTERLY REVIEWS myo- scyllo- or (-)-inositol into (3:)-inositol ; 46 but it is not known if this reaction is an equilibration (mono- and di-halogenated deoxyinositols are also formed in these reactions 47).An interesting correlation has been noted 48 between the natural occur- rence of the cyclitols and their conformational stability. Inositols which have a high interaction energy owing to two axial hydroxyl groups on hhe same side (epi allo muco cis) have not been found in Nature whereas all the other configurations occur in Nature either as inositols (myo scyllo active) or inosamine (neo). The two naturally occurring quercitols are also free from l a 3a-interactions. An inositol methyl ether will be conformationally more sta8ble if the methoxyl group is equatorial rather than axial. The axial 2-methyl ether of myoinositol has not been found in Nature but all the equatorial isomers occur,16 a t least in one enantiomorphous form the inactive 5-methyl ether sequoyitol ; the dextrorotatory 4-methyl isomer ononitol ; and the l-methyl ether bornesitol of which both enantiomers were found in plants.Similarly the axial l-methyl ether of the optically active inositols has not been found in Nature but quebrachitol and pinitol represent the 2- and the $isomer respectively.* The two methoxyl groups in clambonitol 1 3-di- O-niethylmyoinositol are also equatorial. 16 One is tempted to suggest that the final stage in the biosynthesis of inositols and their methyl ethers may be thermodynamically controlled. 5. Reactions of configurational or conformational interest 5.1. Dehydrogenation.-Much study has been devoted to the dehydro- genating action of Acetobacter suboxydans (the organism used for the produc- tion of L-sorbose from sorbitol) on cyclitols.The reaction is highly stereo- specific cyclitols are dehydrogenated to ketones according to t,he rule first announced by Magasanik and Chargaff 49 and established by many examples that only axial hydroxyl groups are dehydrogenated. No excep- t,ion is known to this rule i t is valid also for cyclohexanetetrols but not for all the triols,50 but it is possible that another enzyme is responsible for these dehydrogenations. 51 Thus scylloinositol :and scylloquercitol devoid of axial hydroxyl groups are unattacked ; myoinositol and vibo- yuercitol are converted into monoketones ; the active inositols 49 and neoinositol,52 each with two axial hydroxyl groups give 1 2- and 1 4- 4 6 Posternak Helv. Chi,,?.Actcl 1948 31 2242 ; Fletcher J . Anaey. Chem. SOC. 1948 79 4050 ; Contardi and Ciocca Gazzetta 1949 79 694. 47 McCasland and Horswill J . Amer. Ghem. SOC. 1953 75 4020 ; 1954 76 2373 48 Angyal and Mills Rev. Pure Appl. Chem. (Australia) 1952 2 185. 49 Blagasanik and Chargaff J. Biol. Chem. 1048 174 173. Posternak and Ravenna Helv. Chim. Acta 1947 30 441 ; Posternalc and Friedli ibid. 1953 36 251 ; Posternak and Reymond ibid. 1953 36 260 ; 1955 38 195. 51 Anderson Tomita Kussi. and Kirkwood J. Biol. Chenz. 1953 204 769. 5 2 Anderson Angyjal McHugh and Takedn unpublished work. * One may note that the active inositols though dksymmetrical have a two-fold axis of symmetry ; positions 1 and G 2 and 5 3 and 4 are therefore equivalent and only three different monosubstitution products are possible.ANGYAL THE INOSITOLS 221 diketones respectively. epilnositol with its two axial hydroxyl groups in 1 3-position however gives only a mon0ketone.4~ This instance and some other cases led to postulation of a second rule,53 namely that an equatorial hydroxyf group is required in the " rneta "-position to the carbon atom carrying the axial hydroxyl group in counterclockwise direc- tion when viewed from the axial hydroxyl group (XXIX). However cdsinositol and cisquercitol which do not conform to this rule are dehydro- genated albeit only The group in '' para "-position to the axial hydroxyl group also has some effect the reaction rate decreasing as the group is varied according to the sequence e-OH > = 0 > H > a-OH > e-OMe. L4 methoxyl group in nearly every position inhibits the dehydrogenation (-+)-bornesitol and (-)-pinit01 being the only known exceptions.52 Similar stereospecificity is shown in the plnt<inum-catalysed dehydro- genation of inositols in aqueous solutioh a reaction introduced by Heyns and P a u l ~ e n .~ ~ Inososes are produced albeit in a yield somewhat lower than in the bacterial reaction and again only axial hydroxyl groups arc affected ; 55 scylloinositol remains unchanged myoinositol gives scyllo- inosose etc. In two respects however this method differs from Acetobacter dehydrogenations the reaction usually stops at the monoketone stage enabling the preparation 56 for example of neoinosose (XXX) not obtainable by the use of Acetobacter ; and methyl ethers are also dehydrogenated 559 j7 if they have a free axial hydroxyl group.The stereospecificity of these two reactions is probably due to the direction of adsorption on the (catalyst or enzyme) surface. It is worth noting that the catalytic dehydrogenation is reversible whereas only axial hydroxyl groups are converted into keto-groups the latt'er are hydrogenated over the same catalyst to axial hydroxyl groups. 5.2. isohropylidene Derivatives. - Cyclitols which possess adjacent hydroxyl groups in cis-relation react with acetone in the presence of acidic catalysts to form isopropylidene derivatives.6 This is in accordance with general experience in carbohydrat,e chemistry and with the case of the cyclohexane-1 2-diols of which only the cis-isomer reacts with acetone.* Accordingly scylloinositol and scylloquercitol remain unchanged myoinositol vibo- and proto-quercitol sequoyit~ol .57 and quebrachitol give nionoisopropylidene compounds and the optically active inositols arid 53 Magasanik Franzl and Chargaff J .Arner. Chem. Soc. 1962 74 2618. 54 Heyns and Paulsea Chem. Bey. 1953 88 833 ; 5 5 Angyal and Pitman unpublished work. 5 6 Allen <J. Amer. Chem. SOC. 1956 78 6601. B7 Anderson Delucn Bieder and Post, ihid. 1957 79 11'71. 5s Fenton Salcedo and Franz Ahs. Papers 130th Meeting Amer. Chem. Sac. * Both isomers give isopropylidene derivatives on reaction with acetone diethyl 1966 89 1152. 1956 p. 7-0. a ~ e t a l . ~ ~ P This reaction has no6 yet been applied to cyclitols. 222 QUARTERLY REVIEWS epiinositol form diisopropylidene derivatives,6 The reaction with the other inositols has not yet been described.In an ideal chair form the distance between 1 2-cis-substituents is the same as between truns-substituents when these are equatorial. One might therefore expect cyclisations involving these substituents to take place with equal ease. However attachment of a five-membered ring involves some distortion of the cyclohexane molecule in order to bring the 1 S-sub- stituents into a more nearly coplanar position.59 In case of cis(e,a)-groups the distortion flattens the ring somewhat and moves the axial groups further apart (XXXI) little resistance is offered to such distortion. On the other hand when trans(e,e)-groups are forced nearer to each other (XXXII) the axial groups are compressed and the ring is more strongly puckered and therefore more energy is required. This explanation is supported by the interesting observation that (+)- or (-)- and epi-inositol form triiso- propylidene derivatives as well as the diisopropylidene compounds ; a trans-pair of hydroxyl groups has also reacted.The formation of each cis-isopropylidene ring has moved two axial groups away from their axial neighbours and thus the way has been opened for the remaining axial groups to undergo the distortion indicated in (XXXII). myoInositol is more resistant than the other cyclitols to the action of acetone and conditions for a reproducible reaction have only recently been worked out.16 The difficulty is probably due to the resistance of the axial hydroxyl group to the movement indicated in (XXXI) since it is forced to approach two neighbouring equatorial hydroxyl groups. isoPropylidene derivatives being partially substituted are useful inter- mediates.Thus toluenesulphonylation 33 of the 1 2-5 6-di-O-isopropyl- idene derivative of (-)-inositol-in which the two free hydroxyl groups are equivalent-gives the monotoluenesulphonyl derivative (XIII) the intermediate in the synthesis of neo- and do-inositol. Acetylation of 1 2-O-isopropylidenemyoinositol (XIV) followed by removal of acetone by mild acid hydrolysis gives a tetra-acetate (XV) from which the 1-0- monotoluenesulphonyl compound (XII) the intermediate in the synthesis of mzccoinositol is prepared. 5.3. Steric Hindrance.-The presence of six oxygen atoms attached to a cyclohexane ring results in congestion which is particularly accentuated if some of the hydroxyl groups are acetylated. Under these conditions the usual reluctance of axial hydroxyl groups to take part in reactions involving replacement of the hydrogen atom becomes very marked.Thus it was found impossible to methylate the free axial hydroxyl group of 1 3 4 5 6- pent,a-O-acetylmyoinositol (XXXIII) ; under vigorous conditions acetyl migration occurred and the equat!orial 1 - hydroxyl group thus uncovered 59 Hassel and Ottar Acta Chern. Scand. 1947 1 929. ANGYAL THE INOSITOLS 223 was mc hhylated.60 Only the equatorial 5-hydroxyl group but not the 6-axial group could be koluenesulphonylated 5 5 in 1 3 4-tri-O-acetyl- quebrachitol (XXXIV). (XXXIII) A c 6 i)Ac (XXXIV) 5.4. Oxidation with Periodate.-Oxidation of inositols with periodate is anomalous ; more than the expected 6 mol. of reagent are consumed and less than 6 mol.of formic acid are formed. Over a mol. of carbon dioxide is also produced and glyoxylic acid has keen identified as an intermediate.G1# 62 The initial reaction presumably consists in the splitting of a 1 2-glycol group to give a dialdehyde. The rate of the initial reaction depends on the relative positions of the hydroxyl groups,63 and considerations similar to those concerning the formation of isopropylidene derivatives will apply. A cis-diol is split faster than a trans-diol ; the reaction of scylloinositol (relative rate R 1) is slower than that of any other isomer ; myoinositol which has three contiguous cis-hydroxyl groups is oxidised more slowly (B 2-2) than cyclitols with only two adjacent cis-hydroxyl groups such as viboquercitol (R 3-8) and protoquercitol (R 5-3) owing to the unfavourable effect of an axial group flanked by two equatorial ones (p.222). The reaction rates of aZZo- (B 120) epi- (R ca. ZOO) and cis-inositol (R ca. ZOO) which all have two axial hydroxyl groups on the same side are particularly high ; e 3 this may be due either to release of compression energy in the transition state of the reaction or to mutual repulsion of the axial hydroxyl groups which brings them nearer to their neighbours than they would otherwise be. Once past the initial fission the reaction with periodate becomes complex. The dialdehyde probably forms cyclic tautomers (cf. the reaction of glucose 6*) and their further cleavage coupled with hydroxylation (" over- oxidation " G5) may account for the observed results The reaction has been discussed by Fleury et aLG1 and by Schwarz.G2 5.5.Borate Complexes.-Another reaction of glycols which depends on the steric arrangement of the hydroxyl groups is the formation of complexes with boric acid. The behaviour of the cyclitols on ionophoresis in borate buffers has been studied 63 66 and has led to the discovery of a new type of complex. In many cases the ionophoretic mobility showed no direct relation to the number of cis-1 2-dial groups ; however the 1 3 54s- trio1 arrangement usually caused high mobility and it was postulated 6 3 6o Anderson and Landel J. Amer. Chem. Xoc. 1954 76 6130. 61 Fleury Poirot and Fievet Compt. rend. 1945 220 664 ; Arm. Phavm. frang. O 2 Schwarz Chem. and Tnd. 1955 1388. Angyal and MeHugh J. 1957 1123. 6 4 Schopf and Wild Chern. Ber. 1954 87 1571. 6 5 Huebner Ames and Rubl J.Amer. Chclm. SOC. 1946,68 1621. e6 Foster and Stacey Chem. und fnd. 1953 279 ; Foster ibid. p. 591. 1947 5 209; Fleury and Dizet Bu.11. SOC. China. hiol. 1955 37 1099. 224 QUARTERLY REVIEWS that ‘‘ tridentate ” complexes of type (XXXV) were formed. Thus the mobility of myoiiiositol (11) was not substantially changed by inethylation in the 2- and the 4-position t1hough the former left no free cis-1 2-diol group ; but it was inuch reduced by methylatioil at position 1 or 5 though adjacent cis-hydroxyl groups were left inta.ct. More information on complex formation was obtained by studying the pH changes caused by addition of cyclitols to a borax solution (the com- plexes being strong acids). It was found that when a cis-1 3 5-tlriol grouping was present the complex was formed from the cyclitol and boric acid in a 1 1 ratio and the equilibrium constant K = [Complex-]/[Cyclitol] [Borate-] could be determined.cisInosito1 with three axial 1 3 5- hydroxyl groups in either chair conformation has a remarkably high equilibrium constant ; the other cyclitols have to change into the less stable of the chair forms to achieve the requisite arrangement of three axial hydroxyl groups ; their equilibrium constants are smaller and fall into the order predicted by conformational analysis .63 From the equilibrium constants values of the various steric interactions in cyclitols have been calculated. *5 Tridentate borate complexes are also formed by appropriate acyclic polyhydroxy-compounds e.g. by pentaerythritol and probably by some sugar derivatives.5.6. Reactions of Toluenesulphonyl Derivatives.-Solvolysis of toluene- p-sulphonyl esters in the absence of bases a commoii reaction of simpler coiiipounds has never been observed with carbohydrates. Some 0-mono- toluene-p-sulphonylinositols however are solvolysed smoothly in boiling 95% acetic acid.67 Thus 3-O-toluene-p-sulphonyl-( - )-inositol [formed from (XIII) by removal of the two isopropylidene groups] gives aEEoinositol (VIII) in good yield the reaction occurring with complete inversion. In other cases e.g. 1 - or 6-O-toluene-p-sulphonylepiinositol inversion is accompanied by considerable retention. Some toluenesulphonyl compounds like (XI) react very slowly under the same conditions. Insufficient examples are yet known to allow conclusions about the stereochemistry of the reaction.It is well established in carbohydrate chemistry that tolixeiiesiilphoiiyIoxIy-gro~~ps are removed by iodide ion with of a doolde bond but only if m e of the groups is primary.G* 67 Angyal Gilhaiii and Pitman unpublished work. 68 Tipson ddu. C’cwbohydmte Cheitz. 1953 8 108. two adjacent tjhe formation However two ANQYAL THE INOSITOLS 225 secondaxy groups have been eliriiiiiated from i~iositols,~~ e.g. the 3 4-di-O- toluene-p-sulphonyl derivative (XXXVI) of ( -)-inositol yiclds t'he cyclo- hexenetetrol (XXXVII). By following a suggestion by Tipson,68 it was (XXXVI) (xxxv I I) found that p-iiitrolmizenesulphonyl groups react faster and give a better yield. In the examples so far studied the two sulphonyl groups are in trans-relation but this is not believed to he an essential requirement for the react'ion.5.7. Anhydroinosito1s.-Inositols caiinot bc dehydrated directly but 1 2-anhydroinositols are readily prepared by the action of bases on toluene- sulphonyl derivatives in which an adjacent hydroxyl group is free and trans-situated. 70 Thus the 1 2-5 6-di-O-isopropylidene-3-O-toluene-p- sulphonyl derivative (XIII) of ( -)-inositol gives after the subsequent removal of the isopropylidene groups 1 2-anhydroalloinositol (XIX). These epoxides are useful intermediates because they yield inositols by acid- or base-catalysed hydration inositol inethyl ethers with sodium inethoxide inosamines with ammonia,39 etc. Hydration of 1 2-anhydro- alloinositol (XIX) provides the synthesis 33 of moinositol (IV). The anhydroinositols have provided an opportunity for study 70 of the " epoxide migration " i.e.opening of an epoxide ring by rear attack of ail adjacent trans-situated hydroxyl group with formation of another epoxide ring. This rearrangement has often been postulated in carbohydrate chernistry 71 but no clear-cut example has previously been described. All the anhydroinositols in which there is an adjacent trans-hydroxyl group undergo epoxide migration in alkaline solution a t room temperature. 1 2-Anhydroalloinositol (XIX) gives 1 2-anhydroneoinositol (XXXVIII) ; the reaction is reversible. The position of the equilibrium is in accordaiice with conformational considerations the isomer with fewer alxial hydroxyl groups (for the half-chair conformation of cyclohexene oxide 7 2 ) being the more stable. The anhydride (XIX) has two axial (or quasi-axial) hydroxyl groups but (XXXVIII) only one; in the equilibrium mixture they were found in a ratio of 1 9.Because of epoxide migration the reaction of sulphonyl compounds with strong bases often yields a rearranged instead of the expected anhydritlc. For example I -O-tolizerie-p-snlrli~i~~l~~~~~ii~~sitol (XI) gives Angyal and Gilham J . . 19.37 in t 1 1 ~ pres?. 70 Angysl and Gilham J. 1957 3691. 71 %'!'or a discussion see NewUi J. 1956 4-11. 76 Cf. ref'. 3. 226 QUARTERLY REVIEWS 1 2-anhydromyoinositol (XL) via the less stable (-j)-l 2-anhydroinositol (XXXIX) in the cold and (&)-inositol (111) in hot alkali.73 (All the compounds in this sequence are racemic the formulae showing only one enantiomer.) Epoxide migration can be niinimised by the use of weaker bases ; thus rnucoinositol (VII) can be prepared froin the sulphonyl corn- pound (XII) by heating it with a strong-base ion-exchange resin (Deacidite FF) in the carbonate form.’ (Vll) ’ (I I I) The direction of ring-opening of epoxides in the carbohydrate field is not clearly understood despite considerable discussion ; 7 4 75 inductive effects particularly that of the ring-oxygen atom complicate the picture. ?%‘it h the anhydroinositols only conformational effects need to be considered and the prevalent direction of ring-opening can be predicted. 7 5 Electro- philic or nucleophilic opening occurs in such cz way as to place the new groups-at least initially-into axial positions according to the Purst- Plattner rule 76 (XLI * XLII) ; subsequently the molecule may invert into the other chair form.Eaoh half-chair form of the epoxide can undergo diaxial opening; the proportion of the products will depend on the pro- portion of and that in turn on the relative energies of the two half-chair forms. In 1 2-anhydrodoinositol (XIX) both half-chair forms have two axial (or quasi-axial) hydroxyl groups and are therefore of similar stability the two possible products neo- and (-)-inositol are formed in approximately equal amounts. In the other anhydroinositols mentioned here one half-chair form has fewer axial hydroxyl groups t h m the other and the inositol derived from this forin (by diaxial opening) predominates. 1 2-Anhydroneoinositol (XXXVIII) gives mainly alloinositol ; the innin products of the hydration of the other anhydrides have already been indicated. Angyal and Curtin unpublished work. 7 4 Cookson Chem. mid Id. 2954 223 2512 ; Overend ihitl. 1955 995. i 5 Aagyal ibid. 1954 1230. 7 6 Furst and Plattner Abs. Papers 12th Intornat. Congr. Pure Appl. Chein. New York 1951 p. 405; see also Earton J . 1953 1027.

ISSN:0009-2681    

DOI:10.1039/QR9571100212

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

By PETER J. FENSHAM M.Sc. PHB. (DEPARTMENT OF CHEMISTRY MELBOURNE UNIVERSITY) Introduction ONE of the main impetuses to the fundamental study of heterogeneous catalysis in the past decade has been the repeated suggestion that semi- conductivity and catalytic activity are related phenomena. Not only have these two properties been qualitatively linked but the hope has also been raised that one may be quantitatively predicted from the other. The purpose of this Review is to outline the main findings upon which these assertions have been based and to examine critically the present state of the suggested relation. It is largely through the developments in the theory of the solid state that these two phenomena have been considered as related. This theory has made possible models of the structures and properties of solids on the scale at which chemical reactions occur.Hitherto the main interest in heterogeneous catalysis had centred on the kinetics of the reactions rather than on their mechanisms ; now it is the catalyst itself and in particular its surface which is the focus of attention. I n considering the action of the catalyst and its surface two particular factors have been explored and established as participatory. One is the geometrical factor on which Balandin and Beeck 2 have made notable contributions. More recently the experiments of Gwathmey and his co-workers and Sosnovsky on chemi- sorption and catalysis on the various faces of single crystals have helped to define the r81e of this factor. The second factor is the r61e of electrons in the catalytic process.As early as 1928 Roginskii and Schulz hinted at this in explaining the catalytic decomposition of solids. Further development of this idea a t this stage was hindered by the inadequacy of the atomic theory of solids. This electronic factor in reactions on semiconducting catalysts is the subject- matter of this Review It is now reasonably established that heterogeneous catalysis implies that one or other of the reacting species is adsorbed on the catalyst. Hence an understanding of adsorptive processes on solids has become a prerequisite to the elucidation of catalytic reactions. I n a. series of classical experiments Langrnuir showed that gas molecules could be adsorbed on solid surfaces Balandin 2. phys. Chem. 1929 2 B 289 ; Trapnell Adv. Catalysis 1931 3 1. Beeck Rev. Mod. Physics 1945 17 61.Gwathmey et al. J. Anter. Chem. SOC. 1954 76 390; J . Chim. phys. 1956 Sosnovsky J. Chem. Phys. 1956 23 1486. Roginskii and Schulz 2. phys. Chem. 1928 138 A 21. 53 667. ti Langrnuir J. Amer. C'hem. SOC. 1916,38 2221 ; Trans. Furaday SOC. 1922,17,607. 227 22s QUARTERLY REVIEWS and that the forces involved were similar in character tlo those which existed in the solid itself. These adsorptive forces were gradually differentiated into two types. When hydrogen had been adsorbed on zinc and chromium oxide catalysts a t 100" c and above Garner and Kingman found that this adsorption was irreversible and that attempts t o remove it by further heating resulted in the production of water vapour. For similar adsorptions on manganous oxide and MnO-Cr20, Taylor and Williamson found that increase of temperature led to an increase in the amount of adsorption.Such experiments involving what Taylor called " activated adsorption *' clearly involved different forces from experiments where reversi bility was maintained and in which no such high energy of activation was required. In this way the distinction between physical adsorption and chenii- sorption was drawn. The forces in the former are van der Waals in char- acter non-specific and involve energies of the order of a few kcal./mole so that the adsorption occurs rapidly even a t low temperatures. In chemi- sorption however the forces are specific and approximate more to electro- static or covalent ones with appropriately higher energies giving rise to slower adsorption which is temperature-dependent like other activated processes.In 1932 Lennard-Jones l o gave these conpepts a theoretical foundation when he showed that a gas molecule in adsorption on a solid may have to overcome a potential barrier. The early adsorption experiments also showed that the heah of adsorption of a gas on a solid varied with the extent of coverage.ll This led Taylor l2 t o postulate that solid surfaces are not homogeneous with respect to adsorption or catalysis but that they contain in fact certain '' active centres " for these processes. The " active centres " were thought of as specific points edges or positions on the surface which were capable of adsorption and initiating reaction both energetically and geometrically. The two concepts of (' activated adsorption " and " active centres " have been very substantlially modified in recent years but they have played most important parts in establishing the relation between semiconductivity and catalysis." Activated adsorption " brought out the electronic factor which is common to both phenomena while the "active centre" was peculiarly able to accommodate in models of catalytic surfaces many o€ the structural units that were appearing in the modern theory of solids. Recently the place of the electronic factor in cheniisorption and catalysis has become firmly established and Trapnell 1 3 has reviewed it for metallic catalysts. The contributions of Beeck,2 Eley,14 and Dowden arid Reynolds l5 7 Gamer :md Kinginan Trcuas. E'aiudgy Soc. 1931 2'5 322. 9 Taylor ibid. p. 575. lo Lennard-Jones Trans. Faraday SOC. 1932 28 333. l1 Garner and Rlenrh J.1924 1288. l 3 Trapnell Quart. Reuiews 1954 8 404. l5 Dowdon and Keyiiolds J . 1960 242 263. Taylor and Williamson J . Amer. Chent. Xoc. 1'331 53 3168. Taylor PI'OC. ROY. SOC. 1955 A 108 10:. Eley Discuss. Pnvadriy Soc. 1950 8 31. FENSHAM SEMICONDUCTIVITY AND CATALYSIS 229 have clarified much earlier work l6 on catalysis by metals and alloys. Stone has also reviewed catalytic processes in terms of the electronic factor and lie has included in his field the large group of semiconducting catalysts.17 Such catalysts have been in use and under investigation for many years especially the mixed-oxide catalysts of Huttig and his co-workers l8 who found that the catalytic activity could often be correlated roughly with various physical changes in the state of the catalyst such as the structure colour absorptive properties and magnetic susceptibility.It is now clear that the electronic state of the solid was the dominant factor both in the physical changes in the catalyst and in its activity. Semiconductivity and the theory of solids The Band Approach.-Semiconductors are substances which exhibit electronic conductivity a t high temperatures and whose conductivity tends towards zero as the temperature falls. For solid semiconductors the theory of the solid state which involves a model of a regular lattice of ions or atoms has been used extensively to explain the observed properties. Two theoretical approaches have been applied to semiconductors. l9 The first is analogous to the molecular-orbital method in molecular theory and in it each electron is described by a wave function extending throughout the lattice.The outermost electrons are thus assumed to be free to move in the periodic field of the atomic cores and the other electrons. The second approach is analogous to the Heitler-London treatment of molecules and the atoms or ions of the solid are treated as individual entities which interact with each other. The first or collective-electron approach leads to a separation of the energy states of the free electrons into bands which may overlap or be separated by gaps of forbidden energy. Wilson *O applied this approach to semiconductors and described them as having a filled band of bound electrons a t absolute zero which is separated by an energy gap from a conduction band empty a t absolute zero but able to accommodate electrons of suitable energy at other temperatures.Insulators appear as substances in which the energy gap between the filled band and the empty conduction band is so wide that a t normal temperatures electrons have insufficient energy to bridge it. Imperfections in the crystal lattice have the effect of introducing additional discrete levels in the gap between the filled and conduction bands. These imperfections may be due to any of a grea't variety of causes some of which are discussed in more detail below but the presence of impurity atoms in the lattice is a typical case which illustrates the general effect of these discrete energy levels on the conductivity. The impurity atom imy have electrons associated with it which are available for excitation into the conduction band more easily than the electrons in the filled band.l6 Rienacker 8. Elektrochem. 1941 47 805. 17 Stone. " Chemistry of the Solid State " Butterworths London 1965 chap. 15. ** Huttig J. Chinz. phys. 1939 36 81. l9 Mott " Semiconducting Materials " Butterworths Lon on 1951 p. 1. 20 WiIson " Mexiiiavnduotord and Metals " Cambridge Unrv. Press 1939. 5' 230 QUARTERLY REVIEWS Alternatively the impurity atom may give rise to empty energy levels to which electrons from the filled band can be excited more easily than they could be to the conduction band. Types of Semiconductor,-We can now appreciate that the theory of semiconductivity distinguishes between three types of semiconductors the energy levels of which are indicated schematically in Fig. 1. hi these figures the ordinate represents energy and the abscissa represents.a dimen- sion of distance through the crystal. The first type (Fig. l a ) is called intrinsic semiconductivity and examples of materials exhibiting it are germanium lead sulphide and silicon. Here the forbidden energy gap is of such a width that a t various temperatures a reasonable number of electrons are excited across it. This excitation places an electron in the condnction band and leaves R vacancy in the filled band of electrons. Movement of the. conduction electron and of the electrons in the no-longer-filled band by means of the vacancy can now both contribute to the conduction. The latter conkribution is referred to /Conduction € I filled band (a> (6) (C) FIG. 1 Types of senLicorLductivity. (u) Intrinsic ( b ) n-type extrinsic ( c ) p-typo extrinsic.as " positive hole '' conduction and is equivalent but of opposite sign to the movement of an electron. The other two types of semiconductor are both extrinsic in that they depend for their conduction on the existence of energy levels arising froin imperfections in the lattice. In n-type (normal or excess) concluehors (Fig. l b ) the levels associated with the impurity are close to the conduction band into which electrons associated with the impurity atoms are excited or donated. Zinc oxide exhibits conduction of this type. In p-type (abnormal or deficit) conductors (Fig. lc) the impurity levels are empty and close to the filled band and electrons from it are excited into or accepted by these discrete impurity levels. This leaves positive holes in the filled band which give rise to the conduction.Cuprous oxide is n p-type conductor. Fowler 21 has derived a relation for the variation of conductivity with absolute temperature ( T ) by using Fermi-Dirac statistics where E is the energy required to make the nppropriatk electron excitat'ion in Fig. 1 . 0 = A exp (- Z / 2 k T ) . * ( 1 ) 2 1 Fowler " Statistical Mechanics " Cambridge Univ. Press 1036. FENSHAM SEMICONDUCTIVITY ANT) CATALYSIS 23 1 It will be clear from the above that for a particular substance a t one temperature one type of conduction may predominate but at other tempera- tures the other types may also contribute appreciably. The conductivity is then better represented by a sum of terms similar to that in equation (1). The electrical conductivity (a) is thus a measure of the number of free electrons or positive holes in the semiconductor where e is the electronic charge n and p are the number of free electrons and positive holes and ,un and ,up are their respective mobilities.Conductivity data are insufficient to give either n or p alone but by also measuring another property of semiconductors the Hall effect these quanti- ties can be isolated. A conductor carrying a current has an electric field induced across it when it is placed CT = e(np72 + PP,) - . (3) This property was discovered in 1879. Flu. 2. Hall-effect arrangement. in a magnetic field. is given by the vector relation where I is the current per unit area H is the magnetic field and BH is the Hall constant. The effect is usually measured by arranging a thin strip of $he substance in such a way that the magnetic field is normal to the surface and passing the current along it as in Fig.2. Equation (3) becomes for this arrangement The direction and magnitude of the induced field V V=R,I x H . - (3) V = R H I H / d . . (4) For semiconductors use of the model outlined above gives the Hall constant 22 Rkl as 3n R - P H - * ( 5 ) - * co - *(; ;)m - where c is the velocity of light and pH is the Hall mobility. 1950. 2 2 Shockley " Electrons and Holes in Semiconductors " Van Nostrand New York, 232 QUARTERLY REVIEWS Measurement of the conductivity and the Hall constant of a semi- conductor thus serves to give both the number of free electrons or positive holes and the nature of the conduction electronic or positive-hole. It should be pointed out that despite the success of the band theory in explaining the properties of many semiconductors the approach breaks down for some substances of which nickel oxide is an example.This oxide has a cubic structure and on the band theory a crystal would have its 3d electrons split into two bands with four and six states per atom each. Ni2* has eight 3d electrons which would mean that both these 3d bands could not be completely filled. On this model then NiO should be a metallic conductor whereas it is in fact an insulator when pure and a semiconductor when it contains impurities. In such cases where non-conductors have partially-filled bands Mott 23 has suggested that a Heitler-London approach must be applied. In intrinsic semiconductors the effective values of n and p will depend on the temperature. However in extrinsic semiconductors though their actual effect on conductivity is again temperature-dependent the potential values of n and p are determined by the history of the semiconductor and ca8n vary immensely.For example zinc oxide prepared in various ways had free-electron densities which ranged from 1015 ~ m . - ~ to 1019 cm.-3.24 The density of zinc atoms in zinc oxide is - 5 x loz2 cm.-3 so that a very pure sample would have a concentration of lattice imperfections-say inter- stitial zinc atoms as donor impurities-as low as 1 in lo7. Greenwood and Anderson 25 have very tentatively calculated densities for acceptor impurity centres and actual free positive holes in cuprous oxide. At room temperature their values are of the order of 1012 ~ r n . 1 ~ and 1O1O ~ m . - ~ respectively.Lattice Imperfections.-The imperfections which can exist in crystal lattices can be classified as reversible or irreversible. Reversible imperfec- tions exist in all crystals to minimise the total free energy a t temperatures above absolute zero. They consist of Frenkel defects-interstitial units occurring in the la'ttice with or without vacant sites-or Schottky defects- vacaiit lattice sites. The particular type of reversible defect will depend on the respective energies of formation for the substance concerned. The theory of these reversible imperfections has been developed by Schottky 26 and Frenkel 27 and recently reviewed together with lattice imperfections of all types by Stone.28 Irreversible imperfections which also form discontinuities in the periodic lattice depend however primarily on the history of the sample.They include flaws and strain-relieving Smekal cracks as well as the surfacc of the crystal and grain boundaries in polycrystalline material. Another type of irreversible imperfection which is becoming of increasing interest ill solid chemistry is the dislocation. Dislocations involve the displacement from 23 Mott Proc. Pkys. Soc. 1949 62 416. " Hnlin J . Appl. Php. 1951 22 855 ; 2 5 Greeiiwood and Anderson Proc. Roy. Soc. 1952 A 215 353. 2 6 Schottky Z. phyls. Chem. 1930 11 B 163. 27 Frenkel is. Physik 1926 35 652. 28 Stone " Cheiiiistry of the Solid State ' ' 9 LSuttori+-orths London 1953 chap. 2. Schfirowslii E . Phpsik 1953 135 318. FENSHAM SEMICONDUCTIVITY AND C:STALYSIS 233 thoir normal position of some of the planes of the crystal lattice.There are two main types edge and screw dislocations and their general propertlies have been admirably discussed by C ~ t t r e l l . ~ ~ Dislocations are inobi le through .the crystal and unlike other internal imperfections their movement in the interior is reflected on the surface by a small mobile area of atoms where the dislocation emerges. This emergence a t the surface has been used successfully by Frank 30 to explain crystal growth. Derry Garner and Gray 31 have also suggested that dislocation ends in the surface layers play an important part in removing vacancies during chemisorption and so facilitating the incorporation of the adsorbed oxygen on p-type semi- conducting oxides. Dislocations are able to act as sources and sinks of vacancies and interstitial ions by niechanisms suggested by Seitz.32 The looping or curving of dislocations or their mutual annihilation may provide the thermal pulses that are required for the formation of these reversible imperfections. Mitchell and his co-workers 33 a t Bristol have beautifully demonstrated some of these mechanisms with respect to photographic processes. While the theory of crystal growth would only require a few dislocations in each crystal the &location densities that have been inferred for ordinary crystals are at least of the order of lo* cm. ~111.1~. Such densi- ties of imperfections must be expected to affect the semiconductivity appreciably although as yet only Read Pearson and Morin 34 have reported directly on this factor. They found that dislocation densities 8,s low as lo6 cm.~111.1~ had a pronounced influence on the conductivity and the Hall effect in pure germanium As well as these irreversible imperfections of a physical nature others inay arise from more chemical origins. These may be non-stoicheiometric compositions or the presence of actual foreign-ion impurities in interstitial or lattice positions. For these chemical imperfections appropriate re- arrangements of charge occur to maintain overall electrical neutrality. Some examples of these imperfections are shown in Fig. 3 overleaf. When attention is turned to the surface of 8 solid a's it must be when catalysis is considered theory and existing knowledge are much less certain than has just been outlined for bulk properties. The electrical state of the bulk may be reflected in the surface layers as has usually been assumed in the past but this is by no means necessary.At least it can be said that new possibilities must be considered through the very nature of the surface imperfection itself. For example Tamm 35 showed that the discontinuity in a perfect lattice at its surface can give rise to energy levels in the forbidden gap. Electrons in these levels could then move freely on the surface but not in the bulk. As yet there The surface of semiconductors. Cot,trell " Progress in Metal Physics ") Butterworths London 1949 vul. 1. 30 Frank Discuss. Paraday Xoc. 1949 5 49. 31 Derry Garner and Gray < J . China. pliys. 1954 51 670. 32 Seitz Adu. Pkysics 1952 1 91. 3 3 Evans and Mitchell " Report on Bristol Conference on Defects in Crystal Solids " 8 4 Read Pearson and Morin Phys.Rev. 1954 93 666. 35 Taiiitn Yhysikul. %. Sovietunion 1933 1 733. Physical Society London 1955. 234 QUARTERLY REVIEWS has been no convincing evidence that these levels have a significant r61e in conductivity. However the surface of a crystal also has possibilities for physical and chemical imperfections which are inore varied than can exist in equilibrium in the bulk. Thus crystal surfaces are unlikely to maintain the regularity of the bulk lattice and they may contain steps and plateaux. Tolansky 36 has given much evidence of such irregularities on so-called " smooth " surfaces and Rhodin 37 has discussed the difficulties of obtaining even metal single crystals that are atomically plane. Similarly foreign atoms adsorbed on the surface or occupying lattice positions in the surface layers are possible when they could not be accommodated in the bulk without complete break- down and recrystallisation of the lattice.All these imperfections may give FIG. 3. Crystal imperfections of chenaicul origin. Znz+ 0 2 - Zn2-t. 0 2 - cu+ 0 2 - cu+ 0 2 - cu+ 0 2 - 0 2 - znz+ 0 2 - Znz i- CU 4- CU+ CU+ (u) Excess of zinc in zinc oxide. ( b ) Excess of oxygen in cuprous oxide. Ni2f 0.2- Ni2-j- 0 2 - 0 2 - Li+ 0 2 - Niz+ NiZ+ 0 2 - Ni+t-@ 0 2 - 0 2 - NiZ+ 0 2 - NY2 + (c) Solution of Li+ in nickel oxide e = quasi-free electron @ = quasi-free positjive hole u = cation vacancy rise to energy levels in the surface which enable the electrical character of the crystal surface to differ radically from that of the bulk. The existence of such surface levels was postulated by Bardeen 38 in an attempt to explain certain electrical properties of germanium.He suggested that a double or barrier layer occurs on the crystal surface which raises the surface energy levels above those in the bulk of the crystal. The effect of such a barrier layer in chemisorption has been discussed by Aigrain and D u g a ~ ~ ~ Hauffe and Engell,40 and W e i ~ s . ~ l It can be illustrated for the case of chemisorption of oxygen on a donor or n-type semiconductor. When the gas molecules are adsorbed electrons are trans- ferred from donor sites near the surface of the semiconductor thus reducing the conductivity. As more gas is adsorbed a negative charge is built up 36 Tolnnsky PYOC. Roy. SOL 1945 A 184 51. 37 Rhodin J. A m e r . C'hem. SOC. 1930 72 6691. 3 8 Barcieen Phys. Rev.1947 71 71'7. 39 Aigrain and Ihgas Z. Blelitrochmn. 1952 56 363. 4o Hauffe and Engell ibid. p. 366. Weiss J . Chern. Phys. 1953 21 1531. FENSHABI SEMICONDUCTIVITY AND CATALYSIS 23 5 on the surface which is compensated by a positive charge extending some distance below the surface because of the low density of donor sites. This electric field across the space between the adsorbed layer and the lower surface levels raises the potential of the electron energy levels near the surface. This means that adsorption as it proceeds requires more and more energy for the required electron transfer and the concentration of electrons in the boundary layer decreases. For a p-type semiconductor when oxygen is adsorbed on its surface the electrons are transferred from the full band of the semiconductor.The ready availability of such electrons in the Surface - Distunce (electrons) (a1 (6) FIG. 4 Adsorption of oxygen on (a) an n-type senuiconductor and ( b ) a p-type semiconductor. immediate surface layers means that the space across which the induced field builds up is less with an appropriately lower barrier to further adsorp- tion. In this case the adsorption increases the concentration of positive holes in the double layer. Iiauffe has called these two types of barrier layer " exhaustion " and " inundation " ,regions respectively. 4 2 The resulting energy levels are shown in Pig. 4. Conversely adsorption on n- and p-type conductors can also occur in which inundation of electrons and depletion of positive holes follow respectively. For example many authors have observed that the adsorption of oxygen on cuprous oxide increases t)he conductivity 25 and 4 2 Hauffe Aclv.Cccttclysis 1955 7 213. 236 QUARTERLY REVIEWS Brauer 43 has found that adsorption of water vapour decreased the con- ductivity. The barrier layer predict's that adsorpt'ion reaches a point a t which the potential barrier prevents further electron transfer and adsorption. In exhaustive adsorption this point will correspond with low surface coverages and the results for hydrogen on cuprous oxide 44 and oxygen on zinc oxide 45 bear this out. On the other hand inundative adsorption should make possible much greater surface coverages ; the adsorption of oxygen un cuprous oxide 46 and nickel oxide47 and of hydrogen 48 and carbon inonoxide 49 on zinc oxide have this character.The importance of boundary layers arising from chemisorption is inmediately apparent for catalysis. The number of electrons available for a chemical reaction on the cata,lyst surface is determined by the potential in the boundary layer. In order therefore to understand one of the controlling factors in catalysis on semiconductors it is necessary to have some nieans of observing boundary phenomena in the surface layers. The obvious property for this is the conductivity in the surface layers since this is directly related t o the density of current carriers which is in turn controlled by the barrier potential. Measurement of the Surface Conductivity.-Examination of the literature on semiconductivity indicates that the distinction between bulk and surface conduction has not always been clearly drawn nor are there simple techniques for their independent ineawrement.Much of the work on conduction has been done on compressed powders and the difficulties in interpreting such measurements have recently been discussed by Gray.50 Even under the best conditions the results are not easy to interpret €or it is often found that the conductivity varies with the frequency at which it is measured. One way of interpreting this variation is to identify the bulk conductivity with the high-frequency values and to explain the lower conductivity at lower frequencies in terms of high intergranular contact resistances and surface effects. With the notable exceptions of Verwey 51 Miller 52 and Morrison 4 5 most authors have largely ignored such intergranular effects and this makes many of the isolated studies of semiconductivity of doubtful value for correlation with chemisorption and catalytic data on the same substances.In making use of these isolated data on semiconductivity it must be remembered that the Hall effect is usually measured on single crystals or slabs of compressed powder. The Hall constant in such cases is an indication 3 3 Urituer A ~ ~ Y L Physik 1936 25 60'3. 3 4 Garner Gray and Stone Y r o c . Roy. Soc. 1949 A 197 294. 35 Morrison Adv. Cataly.sis 1955 7 259. Garner Stone and Tiley Proc. Roy. SOC. 1952 A 211 472. 47 Dell and Stone Trans. Fc/raduy h'oc. 1954 50 501. 4R Taylor and Linng J . Am~r. C'hevn. ~Soc. 1917 69 1306. 49 Garner and Maggs Trcins. Farcidmy Soc. 1936 32 1744. 50 Gray. " Chemistry of the Solid Slate" Butterworths London 1953.5 1 Verwey " Semiconducting Materials " Butterworths London 1951 p. 151. 5 2 Miller ibid, 1'. 172. BENSHAM SEMICONDUCTIVITY AND CATALYSIS 237 of the average number of current carriers and in general reflects the pro- perties of the bulk. That these electrical properties in the same sample can be dominated by different regions of the crystal has been strikingly demonstrated by Morrison. *5 He observed the Hall voltage and the conduc- tivity of a sintered zinc oxide sample as a function of time at constant temper- ature. The result is shown in Fig. 5 and indicates that the Hall effect reflecb- ing the bulk properties is largely insensitive to considerable changes which occurred in the conductivity presumably arising from surface phenomena. II FIG. 5 Variation with time of the conductivity and Hall eflect of zinc oxide at 100" ( f r o n b 23") x U Conductance (left-hand scale in arbitrary units) @ KN = ineasure (left-hand scale) of number of carriers = l / V H whero VH is the [Reproduced by permission o f The Academic Press h c .New YorB froin ief. 42.1 Hall voltage in arbitrary units. Morrison has further calculated that particles with diameters of 10p or less can be expected to exliibit conductivities which are largely indicative of the surface. Moreover although sintered powders often consist of particles larger than this size the fusion " necks " may well be of this order so that at low frequencies the observed conductivities will again be surface dominated. For exaniple Bevan and Anderson 53 found that the effect of adsorbed oxygen on the conductivity of siiitered zinc oxide was reversible down to temperatures as low as 500".Since the melting point of zinc oxide is 2100° bulk diffusion rates a t 500" would be far too low to affect such reversible equili1)riuiii in anything but the surface layers. Semiconducting films with their very sins11 particle sizes in general are likewise found to be predominantly surface-controlled as far as conduction is concerned. 31! 50 5 3 Bevan and Anderson Discuss. Faradny SOC. 1950 8 238. Q 238 QUARTERLY REVIEWS In this light it appears that conduction nieasurernents can be used to produce precise information about boundary-layer conditions but only when the physical conditions of the system are rigorously controlled. Models of Adsorbing Surfaces.-Taylor’s early model of an adsorbing surface consisted of static centres of varying energy content some of which were particularly active in adsorption.Kwan 54 and others have found that this hypothesis is unnecessary for some adsorption data and have suggested a heterogeneity induced by the adsorption itself rather than the inherent “ active centres ” to explain some of Taylor’s experimental resixlts. Nevertheless some adsorption results on semiconducting oxides do seem to require heterogeneous surfaces. The variation of the heat of adsorption on semiconductors may in part be explained by interaction between the adsorbed species or by differential energies of special adsorption sites. However such explanations cannot deal with the whole range of surface coverages over which the heats vary. A new approach to semiconducting surfaces was inade by Volkenstein 55 and later by B o ~ d a r t .~ ~ They both treated the surface as essentially dynamic in character. Volkenstein considers imperfections of all the types discussed above to be the adsorption centres. These then have mobility on the surface and can interact with each other and their number is temperature-dependent. With such assumptions he has shown that the amount of adsorption and the variation of the heat of adsorption can be predicted from the nature of the reversible and irreversible imperfections which are present. Boudart treats the surface as a two-dimensional semiconductor with possible properties which differ markedly from the bulk conditions as has been discussed earlier. The energy levels are controlled by impurities and adsorbed species thus presenting a surface model similar to the intermediate states in inter-oxide mixtures which Huttig l8 has described.Such a sur€ace has an induced heterogeneity in which all the sites are active for part of the time. These dynamic models were indirectly the forerunners of the boundary- layer theory for adsorption systems which has been outlined above. Examples of semiconducting catalysts Some illustrative systems of various types in which the catalysis- conductivity relation has been cxplored will now be discussed in terms of the above theory and limitations. Non-stoicheiometric Oxides.-(i) p- Type cuprous oxide. During several years Garner and his co-workers a t Bristol have extensively studied cuprous oxide as an adsorbent and catalyst for the oxidation of carbon monoxide and the decomposition of nitrous oxide.31’ 447 46 *‘ Unfortunately the conductivity measurements have all been made on films and the main 5 4 Kwan Adv.Catalysis 1954 6 67. 5 5 Volkenstein Zhur. $2. Khim. 1949 23 917 ; Uspekhi fiz. Nauk 1953 50 253. 5 6 Boudart J . Amer. Chem. Xoc. 1952 74 1531. FENSIIADS SEMICONDUCTIVITY AND CATALYSIS 239 adsorption studies on powdered samples. This difference in state of the catalyst in the various sets of measurements immediately int,roduces the uncertainties which have been outlined. Adsorption of oxygen on oxidised copper films was found to increase the conductivity while carbon monoxide and hydrogen decreased it. If a mixture of carbon monoxide and oxygen was placed over the film the conductivity indicated that the surface was saturated with carbon monoxide.When oxygen was adsorbed at room temperature on a cuprous oxide layer supported on powdered copper metal it was found to be available for reaction with carbon monoxide. Carbon monoxide was itself adsorbed an the oxide surface and only some of it could be removed reversibly. On a surface previously exposed to oxygen carbon monoxide was rapidly adsorbed and carbon dioxide was slowly liberated followed by further adsorption of the monoxide. Mixtures of carbon monoxide and oxygen over the oxide powders gave rapid adsorption of the monoxide followed by slow oxidation liberating carbon dioxide. Garner Gray and Stone 44 interpreted these results by assuming that oxygen adsorption involves electron transfer from the oxide leaving positive holes which increase the conductivity.Conversely the carbon monoxide adsorption decreases the positive hole concentration reducing the conductivity. Tiley 46 refined these adsorption observations when he found that oxide layers up to 150 A thick on copper powder can adsorb more than a monolayer of oxygen a t room temperature. This suggests that a t this temperature the oxygen can penetrate into the lattice and that in such oxide layers copper atoms from the bulk metal must be free to diffuse. Surface pheno- mena must therefore involve a t least 20-30 lattice layers. More detailed observations of the conductivity changes during the adsorption of oxygen on oxide films indicated that the rate-determining step is the dissociation of oxygen 57* 3l where 0 represents a positive hole. incorporation reaction However the difference between newly-adsorbed oxygen and lattice oxygen suggests that 0- ads ions are stable a t room temperature and magnetic- susceptibility measurements have lent tentative support to this suggestion.58 The nature of the adsorbed carbon monoxide became clearer when Tiley found that carbon dioxide did not adsorb on a clean oxide surface at room temperature but did so on an oxygenated surface in a way which depended on the time interval between the two adsorptions.The following reactions were postulated for these adsorptions 0 2 $ 2oads $ 20- ads + 2 0 This reaction is then followed by the @ads 02- + @ Cogas + COad + e toads + 20- ads co ads + 20 Go2 -k 0- ads -+ co ads f e toads -k 0 -+ co ads ~- _____ _ _ _ _ -~ ~ _ _ ~ ~ _ _ _ __ 5 7 Gray and Savage Discuss. Faraday SOC.1950 8 250. 68 Fcnsham Ph.D. Thesis €3 ristol University 1952. 240 QUARTERLY REVIEW% The oxidation reaction is then These results indicate that at room temperature the course of this reaction over cuprous oxide depends on the p-type character of the catalyst and they illustrate how conductivity measurements can be used to elucidate the reaction mechanism. Turning to the kinetics of this reaction Stone l7 considered the efficiency of various semiconducting catalysts. Despite the lack of uniformity in their physical and chemical state in the different experiments he was able to generalise that p-type oxides are better than n-type oxides. In the p-type oxides like cuprous oxide the reaction can proceed without the diffusion of ions owing to the adsorption and subsequent reactivity of oxygen.However on n-type oxides adsorption of carbon monoxide is readily achieved but the subsequent steps given above require diffusion of lattice oxygen. Hauffe Glang and Engell 59 have found that Stone’s order of catalyst efficiency holds for the decomposition of nitrous oxide but these generalisations remain qualitative and no quantitative statement is yet possible. Gray and Darby 6o have recently discussed the development of such a relation for the kinetics of adsorption of oxygen on oxide semiconductors. In 1938 Wagner and Hauffe61 observed that the conductivity of zinc oxide was changed by the adsorption of hydrogen. Bevan and Anderson found that the activation energy of the conductivity of sintered zinc oxide powders varied with both temperature and ambient oxygen pressure.53 This immediately suggested that the active energy levels were surface ones associated with adsorption and not Tamm levels or foreign- atom levels which would be independent of temperature. These authors also found that the conductivity was reversible at temperatures a t which equilibrium between the bulk and the surface is most unlikely. These findings have been confirmed by Morrison and Miller ; 62 other authors have 011 the contrary found that a t low temperatures the Hall and conductivity results on powdered zinc oxide were indicative of similar bulk mechanisms and independent of atm~sphere.~~ Morrison suggests that during the pre- paration of the samples in the latter studies adsorption on the surface greater than the low-temperature equilibrium values had already occurred.This would set up a barrier potential which would make the surface insensitive to further ambient pressures. Miller 52 has found that the mobilities in sintered zinc oxide a t high frequencies agree with those observed in single crystals supporting the analysis of the powder measurements given above. To explain these conductivity results Morrison has postulated a model of the zinc oxide surface in which surface levels involving both Q3- and 0- ions can exist. This model also explains various anomalous findings for hydrogen adsorption on zinc oxide and the need for hydrogen activation of zinc co ads -k COads 2c0 gas (ii) n-Type zinc oxide. Hauffe Glang and Engell Z. phys. Chenz. 1932 201 223. 6O Gray and Darby J . Pkys. Chem. 1956 60 201. 61 Wagner and Hauffe 2. Elektrochem.1938 44 172. 6 2 Morrison and Miller Univ. Penn. Tech. Report 1952 no. 6. 63 Harrison Phys. Rev. 1954 93 5 2 ; Fritsch Ann. Physik 1955 23 375. FENSHAM SEMICONDUCTIVITY AND CATALYSIS 241 oxide catalysts for hydrogen-deuterium cxchange. Residual 0 - and 0 2 - ions on the surface from the preparation of the oxide are the main sites responsible for hydrogen adsorption and hence two types of adsorption occur depending on the proportions of these sites which in turn depend on the history of the sample. Hydrogen activation removes the residual oxygen ions from the surface and a boundary layer inundated with elec- trons is restored which facilitates the electron transfer in the desorption of the H+ and D+ ions-the rate-determining step in the reaction. In support of this model Voltz and Weller 64 found that the p-type conductor chromic oxide has maximum activity for hydrogen-deuterium exchange when it is in a reduced state with minimum conductivity and positive-hole density in the surface.A qualitative generalisation can thus be made that n-type conductors are superior hydrogenation catalysts to p .type conductors ; but again quantitative statements await detailed information about the nature of the surface. Some refinement of these generalisations has been attempted for semiconductors of the foreign-atom impurity type. Controlled-valence Semiconductors.-The developments of the theory of impurity semiconductivity led to a method of producing semiconductors with controlled conductivity. In a series of careful studies Verwey and his co- workers G5 showed that the incorporation of foreign ions into a nickel oxide lattice altered the semiconductivity.They fired mixtures of nickel and lithium oxide in air a t 1200" and then investigated the conductivities and compositions of the resulting oxides. Up to 10 atoms yo of lithium the mix- tures appeared to be homogeneous with compositions LisNi,-,,2 + N i p O . The conductivity increased by a factor of lo5 as the lithium content was raised from 0 to 10 atoms yo. Hauffe and Vierk 66 conversely found that the conductivity of nickel oxide was decreased by additions of chromic oxide. The first use of these controlled-valence semiconductors to elucidate catalytic behaviour was by Wagner 67 in 1950. He showed that dissolution of gallium oxide in zinc oxide increased the conductivity and simultaneously the converse decreasing effect of lithium oxide additions was demonstrated.66 However Wagner was unable to find any difference in the catalytic activity of pure or gallia-containing zinc oxide for the decomposition of nitrous oxide.This is not now surprising in view of the fact that p-type character has been found to be the operative feature for efficiency in this reaction and the gallia merely increased the n-type conductivity of the zinc oxide. A more fruitful investigation of this catalyst was that of Parravano and Molinari 68 who studied the hydrogcn-deuterium exchange reaction which is catalysed by n-type oxides. They prepared their catalysts by firing them in air at 800" for three hours Vor comparable surface areas the relative conver- sion rates a t 160" were ZnO $- Li,O < ZnO < ZnO -I- A1,0 < ZnO 4- Ga,O ; 64 Voltz and Wellel..J. Amer. Chem. SOC. 1933 '75 522'7. 6 5 Verw-eg et ((I. Chern. Weehblad 1948 44 705 ; Phillips Res. Report 1930 5 173. 66 Hauffe and Vierk 2. phys. Ghem. 1950 196 160. 67 Wagner J . Chern. Phys. 1950 18 6. 6a Parravnno and Molinari J . Amer. Chem. SOC. 1953 75 5233. 242 QUARTERLY REVIEWS this was exactly the order of the n-type conductivities. These findings showed a direct relation between reaction rate and electron density or activation energy of conduction. The correlation does indicate that donor- level electrons are involved in the exchange reaction but uncertainty about the surface state of the catalysts prevents any further statement. Similar series of experiments have been made on nickel oxide catalysts.Parravano 69 prepared a series of catalysts by firing the mixed oxides in air a t 600" for three hours. Between 100" and 180" the activation energy for the oxidation of carbon monoxide was similar to that over pure nickel oxide. From 180" to 250" however the activation energies had the following values NiO + 0.01 mole yo of Cr203 < NiO $- 1 mole yo of NiC1 < NiO + 0.01 mole 76 of Ag,O < NiO + 0.01 mole yo of Li20. Again the catalytic activity in the reaction appeared to correlate with the electronic state of the catalyst. Shortly after this study Schwab and Block 7O found quite opposite effects in the same system. Lithia-containing catalysts showed a lower activation energy than pure nickel oxide which in turn was lower than the catalysts containing chroniia. In this case the catalysts were fired at 830" for three hours and the reaction was studied between 250" and 450".Very recently a third set of conflicting results on this same system has been reported. 71 Boudart and Parravano 72 have attempted to explain this discrepancy in terms of an inversion of the properties of nickel oxide in which the foreign atoms first occupy actual thermal vacancies in the cation lattice and then a t a certain concentration begin to expand the lattice by substituting for Ni2f ions. The evidence for this seems to be doubtful and the physical changes could equally reflect the appearance of other phases in the crystal. Another explanation of the discrepancy between the above results suggests that in Parravano's case the catalysis was predominantly a t surface dis- continuities while in Schwab and Block's experiments the electronic state leading to irreversible adsorption of carbon monoxide was dominant .17 Thus in the latter case the degree of p-type conductivity would be correlated with increased activity as observed.Experiments on the effect of sintering temperature and ambient atmosphere on the preparation of these oxide solu- tions lend considerable support to such an explanation.73 It is most unlikely that the overall concentration of the foreign atoms in an oxide fired a t only 600" (m.p. of NiO is 2100") is any indication of the concentration in the surface layers which are operative in the catalysis. At this temperature solution by diffusion into the bulk would be very slow. This means that the concentration in the surface may be a t least an order higher than has been assumed in the catalytic studies.The concentrations would certainly be different from those in Verwey's samples prepared as they were a t temperatures where bulk diffusion occurs. With such surface conditions 69 Parravano J. Amer. Chein. SOC. 1953 75 1448. 70 Schwab and Block Z. phys. Chem. Frankfurt 1954 1 42. 7l Keier Roginskii and Sazonova Doklndy Akad. Nauk S.S.S.R. 1956 108 859. 7 2 Pa,rravano and Boudart Adv. Cutulysis 1955 7 47. 7 3 Fcnsha,m J . Anker. Chem. Soc. 1954 76 969. FENSHAM SEMICONDUCTIVITY AND CATALYSIS 243 two phases probably exist or at least a homogeneous lalttice is most unlikely. Much further work on the formation of semiconductors of the controlled- valence type is necessary before tlhe catalytic activity of the surface can be considered directly in terms of its known and reproducible electrical state.Germanium.-Although germanium was listed earlier as exhibiting intrinsic semiconductivity it also displays all the impurity effects which have been discussed for oxides. For example if an element of valency other than four is substituted into the lattice the foreign atoms can operate as electron donors or electron acceptors.22 Hence boron impurities produce p-type conduction and arsenic impurities lead to n-type behaviour. Physical imperfections such as dislocations 34 and lattice vacancies have also been shown to influence the conductivity. Morrison 7 4 and Bardeen and Brattain 75 found that the electrical properties of germanium were sensitive to the ambient atmosphere. Oxygen was found to produce acceptor levels on the surface 76 and Morrison actually observed a p-type surface on an n-type conductor during his adsorption experiments.Because of it's importance in transistor electronics germanium has been very extensively studied as a semiconductor and more quantitative information is available about its beha+iour than for any other semiconductor. I n order to make use of these data in exploring the catalytic behaviour of semiconductors a series of experiments have recently been undertaken by Taylor and his co-workers a t Princeton.77 The decomposition of germanium hydride was found to be heterogeneous over a germanium surface produced by previous thermal decomposition of the hydride and the mechanism is known to involve the following reaction GeH -++ GeH3ads + Hads As yet these experiments have not been completed and in particular no simultaneous measurements of conductivity and reaction rate have been made.Nevertheless Tamaru has been able to show that the presence of traces of arsine in the system accelerates the decomposition ratc. This result can be explained if arsenic atoms from the arsine enter the germanium lattice producing donor levels with available electrons which increase the dcsorption of the Hf ads the rate-determining step in the decomposition. Evaporated germanium films are invariably p-type conducting owing to their high concentrations of vacancies a'nd other lattice imperfections which seem to be inevitable in such situations of high thermal non-equilibrium. Becker and Lark-Horovitz 78 found that films produced by thermal decom- position at 600" were more crystalline than evaporated films although at room temperature d l were still p-type.However they did induce n-type conduction in such films by additions of arsenic antimony and bismuth. The films in the catalytic experiments described above were slowly produced 7 4 Morrison J . Plzys. Chem. 1953 57 8GO. 7 5 Bardeen and Brattain Bell System Teclznol. J . 1953 32 1. 7 6 Clarke Phys. Rev. 1953 91 75G. 77 Fensham Tsmaru Boudart a,nd Taylor J. Phys. Chein. 1955,59 806 ; Tamaru 78 Becker and Lark-Horovitz Proc. Natl. Electronics Cohf. 1952 8 506. Boudart and Taylor ibid. p. 801. 244 QUARTERLY REVIEWS a t teiiiperatures below 300" under conditions of thermal equilibrium and it would be of great interest to know more of their electrical properties.If indeed it is possible to control the electronic state of such films in the way that is possible for single crystals of germanium then further experiments on the above lines give promise of greatly increasing our knowledge of the conductivity-catalysis relationship. Mixed Oxides.-A final class of semiconductors which have been investi- gated in terms of the general relation are Huttig's classical mixed oxide systems. In these the catamlysts cover the whole range of compositions of the component oxides and not only low concentrations of one in the bulk of the other. It is to be expected therefore that all the complexities of a multiphase system which existed in Huttig's work make the inter- pretation of the basic electronic mechanisms in these catalytic reactions difficult. Garner Dowden and Be la Banda 79 studied the activity of a complete series of ZnO-Cr,O catalysts for the decomposition of isopropyl alcohol.Catalysts rich in zinc oxide were found to catalyse dehydrogenation to acetone whereas those rich in chromia favour'ed dehydration to propene. The conductivity of the catalysts was not followed during these reactions but separate measurements showed that the activation energy of their semiconduction (in hydrogen) increased parallel with the increase in the proportion of dehydration to dehydrogenation. These authors tentatively suggest that the rate-controlling step in the dehydrogenation is favoured by the electron-donor properties of the ZnO-rich catalysts. It is clear that in such a system the results cannot justify any more definite statement about the general relation.The importance of measuring conductivity and cntalytic activity simul- taneously in such systems has been shown by Weisz Prater and Ritten- house.8* They found that chromia-alumina catalysts changed from p - type to 12-type conduction during the catalysis of' the dehydrogenation bf cycbo- hexaiie and butane. Organic semiconductors A quite different class of semiconductors is the as yet small group of organic compounds. In 1941 Szent-Gyorgi 81 suggested that some bio- chemical mechanisms may be better approached by considering that protein molecules and extended systems of proteins have common energy bands similar to those which appear in the collective-electron approach to crystalline solids. He postulated this model to account for the transfer of energy and electrons during oxidations and fermentations catalysed by insoluble enzynies bound to insoluble proteins.The observed semiconductivity of some protein films provided meagre evidence for such a model. 50 B 35. Garner nowden and de la Rnncln Anciles reed SOC. EspuiL. Pis. Qdm. 1951 60 Weisz Prater and Rittenhouse J . C'hein. Phys. 1953 21 2236. 81 Szent-Gyorgi Ncltzrie 1941 148 167 ; 1946 157 875. FENSHAM SEMICONDUCTIVITY AND CATL4LYSIS 245 In 1948 Eley 8 2 and Vartanyan 83 revived interest in these ideas when they showed independently that phthalocyanines-structurally related to the porphyrins-were semiconductors. Since then Eley 84 and Inokuchi 85 and their co-workers have found semiconductivity in a number of other organic compounds including some protein molecules. Eley has also recently detected impurity semiconduction in phthalocyanines.The con- ductivity in many of these cases is found to be associated with then electrons of the aromatic nuclei. Most of these studies have used only direct-current techniqu-es and contact resistances have been a confusing factor. The relatiion between biochemical catalysis and semiconductivity remains unexplored but this field holds great possibilities for many more refined experiments of the type which have already proved successful in inorganic ca.talysis. 8 2 Eley Nature 1948 162 819. 83 Vartanyan Zhur. j i z . Kl~im. 1018 22 763. 8 4 Eley et al. Trans. Faraday SOC. 1953 49 7 9 ; 8 5 Inokuchi et al. J . C'hern. Phys. 1950,18 810 ; J . C'hern. SOC. Japm 1951 24 242. 1955 51 1529.

ISSN:0009-2681    

DOI:10.1039/QR9571100227

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

THERMAL TRANSFORMATIONS IN SOLIDS By A. R. UBBELOHDE M.A. D.Sc. F.R.S. (IMPERIAL COLLEGE LONDON) Introduction The hadequacy of Classical Phase Relations €or describing Transitions between Condensed Phases.-The classical approach to the phase rule was based on the concept of independent phases in equilibrium. On this basis separate equations of state can be attributed to each phase the propertics of which can be summarised in the molar free energy fuiictions. For the purposes of this Review which is concerned primarily with one- component systems the free-energy function G takes thc form G = f(p T) where p T are chosen as independent variables. This is thc equation of a surface. When two independent phases are in equilibrium their molar free energies are equal so that transitions between phases are located thermodynamically on the intersections between surfaces.Much of the classical discussion of phase transitions was presented in terms of geometrical conclusions about the intersections between independent free-energy surfaces.1“ It is con- venient to consider sections of these surfaces by the planes p constant and T = constant. Of particular importance are the derivatives since these refer to readily observable experimental quantities such as the entropy X the molar volume V the specific heat C, the isothcrma,l com- pressibility x and the thermal expansion a. According to the classical geometrical concepts of a transition between two independent phases 1 and 2 the G curves intersect a t a sharp angle and the differences between the slopes of the tangents represent the change in molar entropy and in molar volume respectively.1 ( a ) See Findlny “ The Phase Rtule and its Applications ” Longmans Green London 1938 8th edn. and earlier textbooks ; ( b ) Lumsden “ Thermodynamics of Alloys ” Monograph Institute of Metals London 1952. 246 UBBELOHDE THERMAL TRANSFORMATIONS IN SOLIDS 247 These are interrelated by the classical Cllausius-Clapeyron equation as proved in standard textbooks of thermodynamics. Various lines of inquiry have led to the conclusion that for certaiii transi- tions between phases the classical phasc relations arc inadequate. This is particularly evident for transitions between condensed phases such as solid-solid solid-liquid and anisotropic liquid-isotropic liquid though it also applies to some extent around the critical temperature for liquid-vapour transitions.Well away from the critical temperature the classical phase rule can still be applied for solid-vapour and liquid-vapour transitions. ~ h o u g h some of what follows also applies in modified form to transitions I I I 220 2 30 240 250 Temp (OK) FIG. 1 Heat capacity of unzrnoniu?rL chloride. [Reproduced from Ubbelohde “ Modern Thcriiiodynainical Priuciples ” Oxford Unh. Press 1952 p. 81.1 involving liquids 3 this Review dcals specifically only with solid-solid transformations. The most direct thermodynamic evidence about the inadequacy of the classical phase rule in describing certain transformations in solids arises from experimental measurements of specific heats and specific volumes. For example many ammonium salts (see p. 269) show a marked anomaly in the specific heats which rise to a peak value around - 31 * c and fall back at still higher temperatures to values more characteristic of normal crystal lattices.The fancied resemblance of such curves t o the Greek capital letter A (lambda) has led to the description of such phenomena as ‘‘ lambda-point anomalies ” . Measurements of specific volumes show a corresponding Ubbelohde Brit. J . AppZ. Phys. 1956 7 313. Idem Quart. Rev. 1950 4 350. 248 QUARTERLY REVIEWS aiioinalous increase spread over a temperature interval so that coefficients of thermal expansion also pass through a peak before returning to more iiorinal values. This kind of hehaviour which is now known in many classes of crystal obviously suggests that the classical abrupt change in heat content or specific volume a t a transition point which corresponds with a discontinuous change in tangent slopes to the two free-energy curves has in some way been spread over a narrow range of temperatures.Contrary t o the hypo- thesis of wholly independent phases actual observations show that the free energy of the low-temperature structure 1 exhibits to varying degrees a “ forewarning ” of the transformation which likewise modifies the trend -Ji-.5 -31.0 -30-S -30.0 Temp. (%) F I G . 2 .JIolcir volume f o r sccblinied crystals of arnmoniurrL chloride. of free energy of structure 2 near a transformation. For various geoiiietricad aspects of ‘‘ forewarning ” which will not ba detailed here see refs. 3 and 4. ,4 second fundamental criticism about the application of the classical phase rule to solids arises from the consideration that when a change of structure has occurred in a solid contributions from strain energy 5 or iiifernal surface energy ‘1 to a certain extent play the part of additional degrees of freedoin in the free-energy eyuatioiis.When these terms are iniportaiit in cquatioiis such as G = f(p T c 1 1 ) . . (3) F = ( C + 2 ) + L - P . - (4) a inociified phase rule has to be applied where Xn refers to the additional ‘‘ degrees of frcedom ” introduced. These Jaffmy Ann. Phglsique 1948 3 5. Ubbelohcle PYOC. Boy. Xoc. 1037 A 159 301, UBBELOHDE THERMAL TKANSFOKMATIONS I N SOLIDS 249 are particularly important in the phenoirienon of hysteresis discussed later which modifies the conventional significance attributed to a '' degree of freedom ".Mathematical Theories of Phase Transformations of " Higher Order ".- Early attempts to interpret '' smeared or diffuse transitions " followed the classical approach of the phase rule in being fundamentally mathematical theories that pay no regard to t,he structural changes taking place. It was pointed out by Ehrenfest that if two free-energy curves made contact this corresponded mathematically with an intersection of higher order. Standard mathematical theory about curves shows that intersections of the second or third order correspond with contact of the first or second order respectively. When intersections between curves are of order higher than unity one mathematical consequence is that instead of a discontinuity in the first derivatives of the G functions as in equations (1A and IR) dis- continuities are only found in the second.or third or higher derivatives. according to the order of intersection encountered. The most important matheinatical outcome of this theory is that the Clausius-Clnpeyron equation (2) which applies for discontinuous transitions of the first order niust be replaced by equations involving differentials of higher order. The precise form these take depends on assumptions about t,he '' order " of contact which may not be realistic structurally (see 1'. 261). For cxarnple Ehrenfest derives the relations where cc is the thermal expansion x is the compressihility arid C the specific heat a t constant pressure. For more detailed discussions about these and other relations for continuous transitions see refs. G and 7. Ehrenfest's theory is not quite satisfactory even from a purely formal standpoint since in an intersection of the second order the G curves for '.phase " 2 lie wholly below those of ' * phase " 1 throughout the diagram ( i t s in Fig. 3 b ) so that 1 would never be stable relative to 2. This formal difficulty was obviated by Justi and von Laue who suggested that lambda- point transitions were in fact of the third order so that crossing as well as contact of the G and G curves was implied as in Fig. 3 (x. I n order not to prejudice interpretation transformations which behave experimentally broadly in accordance with classical thermodynamics will be termed discontinuous in what follows. Even discontinuous transforrna- tions may show forewarning to a varying extent (see p. 24s). 'l'ransforma- lions which show no classical discontinuity are described i&s continuous.Whcrc there is evidence that " continuity * ' arises t'hrougli a coexistence of two distinct structures over a narrow range of temperature in a hybrid single crystal in ways more fully discussed below such '. continuous " Ehrenfest, Pim. Amstrrclcm Aknd. 1933 36 153. ' (Symposia) (a) " Phase Transformations in Solids " Wiley New York 1951 ; (b) " Changements de Phase " Socikte de Chimie physique Paris 1952. * Justi and von Laue 2. tech. Phys. 1934 15 521 ; Phys. Z. 1934 35 9-15. 250 QUARTERLY REVIEM'S transforniations are best described as " smeared " transforniations from one structure into another. This terminology is further- discussed later. In spite of its great influence on the development of research in thernial transitions the mathematical theory of Ehrenfest Laue has serious defects.These arise from their important features of crystal structure and crystal be briefly summarised as follows (i) Studies of crystal structure have shown that transformation is found any change of structure transformation is only small. This fact is not in mathematical the structural and of Justi and von complete disregard of' behaviour which may whenever a continuous above and below the contradiction with the theories but its full significance only emerges when all aspects of continuous transformations are considered. / ? \ 2 F I G . 3 (ii) It is very important to determine whether apparent cont4iiiiiity of transformation only arises when the properties of polycrystalline samples are studied or whether continuity is also found in the properties of single crystals taken through a transformation cycle.This distinction is irrelevant in the classical phase rule in which a '( solid " was assumed to be in " equili- brium " at every stage of the transformation. Actually however it is of great significance in " smeared ' ' transformations where the averaging of behaviour in a polycrystalline sample may simulate a smoothness of change which need not apply to individual single crystals. (iii) Consideration of the structural aspects of a transformation brings out the importance of hysteresis which is often associated with continuous transformations. Hysteresis can be an essential part of a smeared trans- formation when this takes place by way of hybrid single crystals in which two closely similar structures coexist over a narrow range of teniperature.Crystal structure and thermodynamics of transformations in solids. Discontinuous Transformations.-At 0" K the crystal structure with the lowest lattice potential energy has the highest stability. Subject to the limitations indicated by valeiicy theory more than one type of crystal Cf. Ubbelohde and Woodwarcl Nature 1945 155 170 ; 1945 156 20; Proc. Roy. Soc. 1946 A 185 448; 1947 A 188 357. UBBETdOHDE THERMAL TRANSFORMATIONS I N SOLIDS 25 1 lattice can often be formulated for example for ionic crystals or for metals. But the difference of lattice energy between such structures is usuaJly quite large so that there is no difficulty in predicting which form will be stable at 0" K and zero pressure. Crystals whose force fields are primarily deter- mined by van der Waals forces and hydrogen bonds frequently exhibit a diversity of structures with about the same lattice energy since the various forces are all of the same order.Under increased pressures the changing contribution of repulsion forces to the lattice energy is often quite different for different crystal polymorphs ; transitions are theoretically possible a t 0" K for this reason. Effects of increased pressure on crystal transformations will not be discussed in detail in this Review.lO At ordinary pressures when there is a comparatively large difference of lattice structure between two polymorphic forins of a substance the existence of a transformation temperature above 0" K arises when the two polyrnorphs have sufficiently different rates of increase of entropy with temperature.Fornially the conditions required are [Gllo - [G,] < 0 ; 1 stable at 0" ii ; and dG,/dT > dG2/dT. These conditions permit a transformation temperature T such that J o J o In changes of G with temperature the difference in heat content between two polymorphs usually does not change much with temperature. The main factor leading to transformation is the increasing divergence of crystal entropies. One highly important origin of entropy differences between polymorphs leading to a thermal transition arises from vibrational entropy. Alternative crystal forms of the same substance all have zero entropy at O " K if they obey the Neriist heat theorem as may usually be assumed in t'he absence of special evidence to the contrary. At higher temperatures the entropy difference 8 - X = (Cp2 - Cp,)d ln T 1 eventually compensates for the difference in lattice energies and a trans- formation 1 + 2 results.Fig. 4 illustrates lb t)he thermodynamic functions for the two crystal forins of tin. The curves of AH and TAX intersect at the transition temperature where AG = 0. Grey tin has four nearest neighbours a t 2-80 A and a cubic structure. White tin has four nearest neighbours at 3.016 A and two at 3.175 A and a tetragonal structure. At the transformation temperature of -292" K direct calorimetry shows that the heat of transformation is about 522 cal.(g.-atom)-l and is compensated by the entropy difference. So far as is known this transformation is discontinuous although anomalous structural changes in tin l1 may imply some " forewarning ".This can 10 See Bridgman " The Physics of High Pressures " Bell London 1949. 11 Arlman and Kronig Physica 1943 10 795 ; Prasad and Wooster Acta Cry$t. 1956 9 36. 252 QUARTERLY REVIEWS be given a structural interpretation to niatch the t hermod,ynaniic de- scription. Froni the crystallographic standpoint in a discontinuoils transforniation between independent phases a single crystal of one form changes into a random assemblage of (smaller) crystallites of the other form. If n single crystal is studied by one of the standard X-ray techniques siich as the obtaining of Laue photographs then when it is taken round a cycle of teniperatures including tjhe transformation temperature there should be no persistence of crystal axes. l2 Specific tests for persistence of axes have not in fact yet been made for many interesting transformations which are apparently discontinuous theriiiodyiiamically.It can be predicted with sonic confidence that randoni- i3ation of the crystallites of the new structure formed from the parent single cq-slal must be quite marked for a discontinuous transforimtion to appear. Nevert,heleas absolutely complete randomisation of axes must be rare. The number of nuclei of the new form which grow into crystallites at the expense o f a parent single crystal must be limited for kinetic and energetic reasons. Depending on the rnechaiiisni of crystal growth the probability of formation of such nuclei rnay often show some preferred orientation with respect to thc parent crystal lattice. Proin the structural point of view. randoinisation of new crystallites is only complete in a polycrystalline assembly where avcraging over many parent crystals can be made.A further consideration is t>hat when a polycrystsllinc assembly is talien repeatedly through a t’hermal cycle tmversing a transition the new crystallites will ultimately 1)econie so srnull that their atoins become sufficiently mobile to exhikit grain growth. A ‘‘ natural ” lower limit for crystallite size in polycrystalline l 2 Kennedy Ubbelohde and Woodward PYOC. Roy. Xoc. 1033 A 219 303. UBBELOHDE THERMAL TRANSFORNIATIBNS I N SOLIDS 253 transformations can be foreseen on these grounds. So far the only evidence for a natural limit arises for metals. By way of an example of raiidoinisa8tion in :t transformation Plate 1 illustrates X-ray rotation photograplis of crystallites of the stable polymorph a resorcinol which gradually appeared when a single crystal of resorcinol was studied during many months at room temperature.If the 0 crystallites were completely randomised they would give perfect powder rings. Actually marked preferred orientations are observed though so far as is known the reversible transition o! to p is thermodynamically discontinuous.13 Up to the present structural studies on discontinuous transformations have seldom been correlated with thermodynamic considerations. A sug- gestive general discussion has been given by Buerger.7a Some of the few examples for which there is both structural and thermodynamic information will now be considered. (i) The transformation a t 469" of czesium chloride from body-centred cubic to face-centred cubic has been studied l4 by means of measurements on thermal expansion intensities of X-ray reflections as a function of temperature electrical conductance and differences of heat content.(ii) The transformations of rhombic into monoclinic sulphur at 9M0 of cc into p o-nitroaniline and of yellow into red mercurous iodide have been studied by measurement of rates of evaporation and rates of movement of boundaries between phases as well as by measurement of thermodynamic parameters .I5 (iii) X-Ray powder studies of the transforniation of rubidium and potassium halides from face- to body-centred cubic under pressure have been made.16 Transformations occur at around 5000 atm. for the rubidium salts and subdivision of grains is observed in tlhe transformation indicating that it is structurally discontinuous.(iv) X-Ray studies have been made on transitions of silver iodide under pressure.l7 A general discussion of transitions in silver halides has been given by Huggins.'" (v) A variety of techniques has been applied for transitions in refractory metals .I8 Continuous Transformations.-By contrast with the limited studies that combine structural with thermodynamic information for discontinuous transformations a very large body of work has been carried out on trans- forinations in solids which are or appear to be continuous. In order to obtain some perspective it is convenient to group methods of study. Many purely thermoclyriamic methods involve measurements of heat content specific heat or specific volume a t different temperatures. Much less abundant information has Thermodynamic methods of study.13 Robertsoii and Ubbelohde PTOC. ROY. SOC. 1938 A 167 136. 1 4 (a) Menary Ubbelohde and Woodward ibid. 1951 A 208 158 ; l5 Hnrtmshor.ne Discuss. Fnrriday XOC. 1040 5 149. IF Jacobs I'hys. Reu. 1938 54 466. 18 Jaeger Proc. Ic. netl. Aknd. Wetenschuy,. 1940 43 762. ( b ) Harper and Ubbelohde ibid. 1955 A 232 310. Idem ibid. p. 326. R 254 QUARTERLY REVIEWS been obtained on compressibilities on shifts of transformation temperature under pressure or on shifts of transformation temperature due to impurities. Polycrystalline samples have been used of somewhat indeterminate micro- structure in practically all experiments though the most recent work shows that the microstructure should be carefully specified in smeared transitions.I n certain experiments the influences of crystal size and crystal perfection have been studied on phenomena such as hysteresis.lg Attempts have also 1)een made 20 to influence nucleation by ultrasonic vibrations in the trans- formation of solid hydrogen bromide without perceptible effect (cf. Pig. 5). Stiidies of specific volumes have the important practical advantage that prolonged observat'ions can be made. This can be particularly significant in view of observations that near a trmsformation rates of change in solids W 81 86) 8 9 90 91 92 Temp (OK) FIG. 5 Change o j heat content of solid hydrogen bwmide around T,. The curves are conventional hysteresis curves and the points were determined in experiments with ultrasonic vibrations. [Modified from Euchen Z . ICZeLtrocheaz.1939 45 126.1 are frequently very slow.21 Volume changes suffer however from the dis- advantage that in many interesting transformations they are small and are in any case difficult to correlate with other thermodyiianiic or structural changes. Techniques of study include diln tometric measurements on thermal transforniations based on linear coefficients of thermal expansion determined either by optical comparators or by mechanical or optical interference methods and have been applied to tra,nsformations in tungsten iron and nickel metals and in ammonium chloride.4 Very numerous experiments have been made by using polycrystallinc samples and a confining fluid and transforniations in sulphur and in amnionium and tetradeutero- ammonium halides sodium nitrate copper sulphnte pentahydrate ani- l9 Thomas and Staveley J.1951 1420 2572 ; Thomas Staveley and Cullis J . 1952 1727. 2o Eucken 2. Elektrochem. 1930 45 126. 2 1 Teniperley " Changes o i State " Cleaver-Hume Press 1956 pp. 33 41. UBBELOHDE THERMAL TBANSFORMATIDNS IN SOLIDS 255 monium dihydrogen phosphate and ammonium dichromate ; also in resorcinol 1 2 and ammoniuni chloride. 22 Suitable confining fluids are how- ever difficult to find especially for use a t temperatures above about 250" C. X-Ray niet,hods have been increasingly used to evaluate the thermodynamic parameters at both high and low temperatures for polycrystalline samples and for single crystals ; applications include transformations in nickel sodium nitrate animonium chloride bromide and iodide and in M,H,IO where M = Ag or NH4.23 Calorimetric studies if t,hey involve the conventional electrical heat- input calorimeter may give artificially smoothed specific-heat curves becausc of the slowness of certain changes in crystals and the difficulty of t8esting for equilibrium especially near the peak temperature T of a thermal transformation.This fact makes mathematical arguments about the precise shape of a specific-heat curve near T difficult to test in reality. Nevertheless plots of the excess of specific heat AC in an anomaly over the normal value for crystal vibrations give basic thermodynamic information about the transformation since they permit estimates of the total entropy change involved. Usually the integral need only be taken over a quite narrow range of temperature AStransf. = JI:ACD d In T Calorimetric studies of transformations have been made for niany solids in the course of evaluation of standard entropies by means of the Nernst heat theorem.Many examples up to 1948 have been collected in ref. 4; transformations studied in other ways mentioned in this Review have generally also been studied by calorimetry ; individual references are not given where no new points of major significance arise. In certain instances attempts have been made to analyse the specific- heat curves in detail. For example entropy changes for the ellipsoidal and tetrahedral molecules quoted below have been carefully evaluated in a number of cases.24 These support the view that the transformations involve at most hindered rotation above T with potential barriers separating minima of potential energy.There is little real evidence for free rotation in most crystals. Computations of the increase in entropy in some of the transformations leave no doubt that some form of randomisation of structure is taking place on passing from low to high temperatures. For example in ammonium chloride above T, C - OR. Subtracting the contribution to the specific heat due 24 to lattice vibrations Cvib. = BR this leaves (Cv)orient. = 3R above T,. If there were free rotation C' 3R/B ; librations about equilibrium orientations in the crystal are indicated by this evidence. For hydrogen and deuterium chloride bromide and iodide determination of the entropies of transformation 24 gives a value of n in the Boltzmann Z2Mitsui and Furuchui Phys. Rev. 1963 90 193; 1954 95 558. 2 3 Baertschli Helv. Phys.Acta 1945 18 267. 2 4 Zimm Oriani and Hoffman Ann. Rev. Phys. Chern. 1953 4 219. 256 QUARTERLY REVIEWS expression AXtransf. = R Inn for these halides of n - 4.6 except for hydrogen bromide where it is near 3.2. Here n refers to the number of alternative orientations above T,. In a body-centred cubic lattice as assumed by the hydrogen halides above T, the molecules may occupy six alternative positions so that the maximum value for AStransf. = R ln 6. Reasons why the computed value lies somewhat below tlie maximum have not been found. Structural origins of entropy increases in transformations in solids The principal types of randomisation that have been suggested to account for the anomalous entropy increases in crystals include the structural changes now discussed. Positional Randomisation in Solids.-In certain crystals consisting of spherical or almost spherical units in close packing the continuous trans- formations observed can be attributed to randomisation of position of certain units of structure with regard to the ideal crystal lattice.One example in ionic crystals is the transformation of /3 into cc silver iodide. Above 146" X-ray and conductance evidence indicates that the Ag+ cations have their positions randomised. 25 In addition to occupying sites in the ideal lattice the Ag+ cations occupy alternative sites a t random. Various other silver salts which exhibit transitions have been reviewed.l79 26 Con- ductance and X-ray evidence suggests 27 that analogous randomisation of Na+ and F- occurs in cryolite above about 880°.27 In metals randomisation of position is observed with a critical temperature T, in various order- disorder transformations in alloys.Below T the atonis of the alloy occupy specific positions on a superlattice ; random positions with respect to the same lattice points are assumed above Tc.28 Orientational Randomisation in Solids.-In many crystals polyatomic units of structure can become randomised in orientation with respect to neighbouring groups above a critical temperature T which depends on the crystal forces. It was originally suggested 29 that above T these polyatomic groups were rotating freely thereby acquiring effective rotational point symmetry about one or more axes. Thermodynamic evidence quoted above and various structural studies have shown that alternative orientations with different minimum potential energies U, U, 77 .. . are present in many crystals. As the temperature rises the orientation of the asymmetric units becomes randomised with respect to these alternative positions (cf. Frohlich ref. 7 b ) . Many solids in which the units of structure have approximately ellipsoidal shape show transforniations involving randomisation of orientation. Transformation temperatures are generally higher tlie higher the lattice forces but even for the halogen acids PoZyatomic groups of ebZipsoidaZ symmetry. 2 6 Krieger and James J. Chem. Phys. 1954 22 796. 2 6 Pitzer J. Amer. Chern. SOC. 1941 63 512. 27 Landon and Ubbelohde Proc. Roy. Xoc. 1957 A 240 160. 28 Elcock " Order-Disorder Phenomena " Met,hixen London 1956 ; see also other 29 Pauling Phys. Rev. 1930 36 430. discussions i n refs.4 and 7. UBBELOHDE THERMAL TRANSFORMATIONS IN SOLIDS 257 quite complicated relations are found. 349 26 Many other diatomic molecules whose crystals exhibit " randomisation of orientation " are quoted in ref. 3. A great variety of non-thermodynamic methods of study have been applied in the attempt to elucidate what is happening to anomalous thermal transformations in solids. Tetrahedral molecules exhibit transformation temperatures T which rise as the crystal potential barriers opposing randomisation of orientation increase. Thus for molecules interacting with van der Wads forces in the Randomisation of orientation of tetra,hedral molecules. /O I5 a 20° 25 T tnp. (OK ) FIG. 6 Effect on the lumbdu-point anomaly of dilution of solid methane by kwypton. A 3-70XKr; B 7-45%Kr; C 50.22%Kr and above.[Reproduced from Ubbelohde " Modern Thermodynamical Principles " Oxford Univ. Press 1952 p. 83.1 crystals though there is some uncertainty about the nature of the transition for the larger rnolec~les,7~ the sequence of T found is methane 20" K ; silane 63" K ; carbon tetrafluoride 77" K ; neopentane 140" K. For com- parable transformations in ionic lattices for ammonium salts containing tetrahedral groups there is a jump to higher temperatures around 240" K. One significant way of experimenting with potential barriers opposing randomisation of orientation in crystals is to dilute the crystal lattice with more symmetric;tl ~noleculcs or atoms so as to reduce the barrier. Por example Fig. 6 illustrates the effect on the specific heat anomaly of bringing progressively more krypton into solid solution in methane.30 The steepness of the co-operative change rapidly decreases with increasing dilution of 30 Eucken and Veith 2. phys. Chem. 1938 38 B 393. 258 QUAKTERLY IZEVIEWS the non-spherical methane molecules. A corresponding effect has been studied for the " rotation " of bcnzene in its crystals below their melting point An interesting shift of transforniation temperature occurs on substituting isotopes ; effects can be particularly striking when deuterium is substituted for hydrogen in the crystals. When hydrogen bonds are present the sub- stitution of deuterium for hydrogen alters zero-point energies and affects the overlap of alternative structures in the crystals. The shift of trans- formation temperature is often quite large ; it is difficult to predict quanti- tively but the general qualitative influences can be understoocl.33 When hydrogen bonds are ahsent the principal effect of substituting deut,erium for hydrogen is to raise the moments of inertia of rotators and the reduced masses of vibrators in the crystals by amounts which can be readily calculated.The repulsion envelopes of the deuterium-substituted molecules also undergo a small shrinkage owing to a decrease 33 in the zero-point energies of the valency bonds. In the absence of otlier complicating factors this shrinkage should lead to effects on the transformation parameters comparable with those of increasing the external pressure on the hydrogen compounds but no complete tests of such effects can yet be made. In the case of crystalline methane it is interesting to note that substitution of deuterium for hydrogen leads to a doubling of the lambda peaks with a general shift of the upper peak to higher temperatures thus methane has one value of T a t 20.4" K and monodeuteromethane and tetradeuteromethane have double peaks at 15*5" 22.6" K and 21.4" 26.3" K respectively.Increasing the pressure on crystalline methane also leads to a doubling of the lambda pealis in con- formity with the general ststemeiit,s made above.34 The appearance of more than one lambda peak is strong evidence that the transforma- tion involves orientational randoinisation but not free rotation in the crystals. In solid solutions of methane in tetradeuteroiiiethane the upper peak varies in a regular way as the mole fraction of CH increases but the lower peak is pushed downwards and is eventually s~ppressed.~ Corresponding randomisation can occur in favourable cases for molecules whose approximation to figures of rotation about one or more axes is even less close.Only selected examples can be quoted here. In benzene rotation in the crystals about the hexad axis seems borne out by various lines of evidence discussed below.35 In some polymethylenic paraffins orientational randomisstion about the long- chain axis seems likely in the crystals below the melting points.36 Organic compounds of higher molecular weight such as hexamethylbenzene also Other types of randomisation of orientation. 31 Thompson and Ubbelohde Trans. Pccraduy Soc. 1950 46 343. 32 Ubbelohcie and Gallnghcr Actcz Cryst. 1965 8 71. 33 Ubbelohde Trans. Fw(id(~y Boc.1936 32 526. 3 4 For the rise in T whcn deuterium is sul>stitutcd for hydrogen and the doubling of the peaks for methane uritlcr pressure see Kruis 2. phys. C'hem. 1940 48 B 321. 35 Andrew and Eades Proc. Phys. Xoc. 1953 218 A 537 ; Friihling Ann. Physique 1951 6 401. 36 Ubbelohde Trans. Faraday Xoc. 1938 34 289. UBBELOHDE THERMAL TRANSFORMATIONS I N SOLIDS 259 exhibit orientational randomisation. 37 Transformations in crystals of organic molecules with tetrahedral symmetry with the generad formula MX, have been studied by Backer and Perdok.38 I n tetramethylthiomethane C( SCH,), for example X-ray and thermo- dynamic studies show transformations as follows 46.50 65.5'' I ,252"~ I1 .-F I11 -> Melt Tetragonal Tetragons1 Cubic Even in the cubic phase the rnolecnles are found not to be rotating freely since insufficient space is available in the crystal lattice.Randomisation of orientations in different directions does however take place at the 45.5" c transforniatjion. For these crystals specific-heat measurements and dielectric studies confirm the absence of free rotation of even the methylthio- groups in the melt. Amongst inorganic compounds a group of nitrates of the general formula MNO has been studied in some detail ; 39 for these and other inorganic examples see ref. 2. Transformations at Constant Volume.-Both classes of entropy increase discussed earlier pass through a more or less pronounced maximum rate of increase where the additional specific heat passes through a peak value This kind of behaviour is characteristic for energy increases in solids in which the magnitude of the energy jumps for individual units of structure depends on the number of units already in the higher-energy state.Normally the energy jump decreases as more units of structure assume the higher- energy state and the autocatalytic process of energy uptake accounts for the lambda shape of the curve for the excess of specific heat due to the co-operative change in question. 40 When the transformation takes place with increase in volume as often happens the progressive expansion of the crystal lattice resulting from progressive energy jumps lessens the energy barriers and in part explains the autocatalytic nature of the transformation. This explanation is confirmed by calculating the specific-heat anomaly for a change carried out a t constant volume instead of a t constant pressure.Fig. 1 shows that the sharp lambda character is almost entirely suppressed at constant volume.41 Measurements of the compressibilities are required to convert values of C into values of Cv. Quite large shifts of trans- formation temperature are involved ; e.g. for ammonium chloride the lambda transition a t - 31" shifts to 4- 30" a t 9500 atm. Structural Aspects of Other Co-operative Transformations in Solids.- Many transformations in solids are known whose structural origin is more complex than the two types described above but in which the autocatalytic decrease of the restraining crystal fields follows the same general pattern 37 Huffman Parks and Daniels J . Amer. Chem. Xoc. 1934 56 1513 ; Andrew J. Chem. Phys. 1950 18 607 ; Saki and Chiham Xci.Papers Osaka Unh. 1949 Nos. 1 and 2 . 38 Backer and Pcrdok Rec. Trav. chim. 1943 62 533. 39 Finbak and Hassel 2. phys. Chem. 1937 35 B 25 ; 40 For an elementary discussion see Ubbelohde " Modern Thermodynamical Prin- ciples " Oxford Univ. Press 1952 2nd edn. 41 Lawson Phys. Rev. 1940 57 417. 1937 37 B 468. 260 QUARTERLY REVIEWS with changes of temperature or volume. Some of these structural effects can be briefly summarised as follows. In this transformation a t high temperatures individual molecular dipoles in the crystal behave more or less independently in the paraelectric state. Below T the dipole fields co-operate to give a much higher total polarisation in the so-called ferroelectric field. Transformations of this kind are known for a range of acid phosphat'es and arsenates of the geiierd formula MH,X04 where M is an alkali-metal atom and X = P or As.Effects of isotope substitution on the transforma- t'ion temperature are interesting and may be illust'rnted by the figures in (i) Transformation from a paruelectric to a J'erroelectric solid. TABLE i Salt KNnC4H40,,4H,0* . . . . I<H,P04 . . . . . . . KH,AsO . . . . . . . RbH,AsO . . . . . . CsH,AsO . . . . . . . (NH,)H,AsO,. . . . . . 255-258" 122 215.8 05.6 109.9 143.3 2 50-2 5 1 213 298.6 162.0 177.8 212.4 * Rochelle salt. Table 1. A group of titanates of the general formula &P+[Ti0,]2- show similar effects which in some cases are of considerable technical importance. Related crystals such as NaNbO behave in a similar way.42 Examples from other types of structure seem likely to arise but have not been studied extensively .(ii) Tramformations from paramagnetic (high-temperatwe) to ferromagnetic (low-temperature) crystals. These involve co-operative 'reinforcements of the magnetic dipoles below T,. Such changes have long been known for certain metals of transitional elements including iron (T = 780") and nickel (T = 365" c). In recent years related transitions have been dis- covered in a number of crystal compounds such as the ferrites of general formula Pe,MO, where M is a bivaleht metal such as copper magnesium lead or nickel. (iii) Transformation from parama)gnetic (high-temperature) to antiferro- magnetic (low-temperature) crystals. These involve complete or partial co-operative neutralisation of magnetic dipoles below T by coupling of magnetic spins in opposition.Examples include NiCl, MnO FeO NiO and probably Cr,03. Each of these crystals exhibits a transformation with specific- heat anomaly accompanying the magnetic change. 43 4 2 Vousden Acta Cryst. 1056 7 321. 43 Street Research 1961 39 258 ; Shull and Smart Phys. Rev. 1949 76 1356 Smart and Greenwald ibid. 1951 82 113. PLATE 1 X - R a y rotation photogruphs of spontaneous reversion of a single crystal of /3 resorcinol (top) to crystallites of u resorcinol (bottom) with preferred orientation. The centrul picture shows incipient formation of the u crystwllites. [Reproduced from ltobertson and Ubbelohde Proc. Boy. Soc. 1938 A 16'7. 136.1 ( 6 ) PLATE 2 Coexisterbce phenomenu in potassium c l i l q d ~ o g e n phosphate. ( ( I ) Ilmc pliotogniphs of single ~ ~ ' y s t a l s around 123' K.(0) Surnc! crystal showing split reflections below 123" K. [ Kcproduced from Ubbc~lolitIr and Woodrvuktd A'afum 1 9 4 5 156 21.1 PLATE 3 Coexistence phenomena i n ammorLi.um chloride. B m g g X-)wj photographs exhibit coexistence in the thvee right-hand pictuaes amund T, - 31". 1 lteprodueed froin 1)iiiir Iiert lfelr. Php. ( f a 1944 17 338.1 UBBELOHDE THERMAL TRANSFOBMATIONS IN SOLIDS 26 1 Structural techniques €or studying changes accompanying transformations in solids The above summary of structural changes occurring in various trans- formations in solids is based on conclusions from a great varicty of non- thermodynamic methods of study which have been applied in the attempt to elucidate the nature of the changes taking place. These will now be briefly reviewed.Whatever othcr metlhods are applied the study of a thermal transformation can hardly be regarded as coniplete until X-ray techniques have been used. Earlier applications of X-ray inethods involved practically exclusively the taking of powder diagrams. These give useful information averaged over a large number of crystals ; modern precision powder methods are often of particular value when the temperature of transformation is remote from room temperature. For example with particular reference to a principal theme in this Review coexistence pheno- mena in powder diagrams have been claimed in a transformation in Mn0,Z and in order-disorder transformations in Pt-Co and in Cu,-Au alloys (cf. ref. 28 pp. 137 138). But powder diagrams do not make it clear how intimate the interpretation of two closely related structures can be.When single crystals are used X-ray methods give additional information of the highest importance for interpreting transformations in solids. Additional observations of special significance include (i) The detection of coexistence of regions of two alternative structures within a hybrid single crystal (the terminology follows that of ref. 9) around the transformation temperature T,. This phenomenon has been observed by means of both Bragg and Laue photographs in single crystals of substances such as Rochelle salt and potassium dihydrogen phosphate and ammonium chloride,44 also in various titanates 45 and in other cases listed in ref. 2. There are reasons to infer the presence of this phenomenon in other transformations where its existence has not yet been specifically detected.One way of describing the phenomenon of coexistence of sub-regions of two slightly different structures in a hybrid single crystal is to consider what happens when a true single crystal of one structure is examined starting well below the peak transformation temperature T,. Normal single-crystal Bragg or Laue photographs are obtained of the low-temperature structure. If the crystal is gradually warmed rushed heating being avoided since strains develop sub-regions of the second slightly different structure appear near T,. In any one single crystal the precise temperature a t which such sub-regions appear will often vary over a few degrees.46 This is partly due to the probability of growth of the new structures depending on chance factors and partly due to a real shift of the free energy of the sub-region according to its surface area within the hybrid single crystal and according to its state of strain.The size of such sub-regions varies from crystal to crystal. One estimate for potassium dihydrogen phosphate indicates an 44 Dinichert Helv. Phys. Acta 1944 17 338. 4 5 Blattner Kanaig Merz and Sutter ibid. 1948 21 207. a6 Gallagher Ubbelohde and Woodward Acta Cryst. 1955 8 561. X-Ray methods. 262 QUARTERLY REVIEWS upper limit for the sub-region edge of 5 x cm. In Rochelle salt sub-regions 9 may be about lo4 These are however only tentative estimates. It is important to use precision thermostats (such as those described in refs. 9 12 14a and 47) around the transformation temperature I' to follow what happens as it is traversed.As the temperature rises more and more regions of the high-temperature structure 2 appear until the hybrid single crystal is completely transformed into structure 2 somewhat above T,. If this crystal is cooled again the changes are traversed in the reverse sense. It is not yet clear whether the identical sub-regions appear though internal defects in the single crystal probably impose preferred growth patterns for the sub-regions. The temperatures a t which a given proportion of the hybrid crystal consists of sub-regions of one form need not be the same in the direction 1 -+ 2 as in the direction 2 + 1 for reasons of hysteresis (p. 267). (ii) Hybrid single crystals around a transformation region may be regarded as a structura'l alternative to the discontinuous transformation of structures already described.The difference arises as follows For geometrical reasons nucleation of a new structure generally occurs with preferred orientation with respect to the matrix from which it is formed. This preferred orientation can become so close to a unique choice that the whole crystal transforms with effective " persistence of axes ",12 When the difference in structure between the low-temperature and high-temperature arrangements is sufficiently small the appearance of regions of 2 within a matrix of 1 does not involve sufficient mechanical strains to lead to break-away of the new crystallites. If the orientation of regions of the new form is sufficiently close to the orientation of the matrix and if there is no break-away of crystallites the hybrid crystal survives as a unit though it passes through a state of maximum strain energy around T where regions of the two structures coexist in comparable amounts.For example Bragg and Laue photographs show " splits " in the hybrid region which are illustrated on Plates 2 and 3. This brief description should make it clear that in addition to giving information about coexistence of two structures within a hybrid (a) single- crystal X-ray photographs can establish how nearly the two structures actually correspond around T,. This can in principle also be done by precision powder photographs but single-crystal exposures are much more satisfactory. By way of example in potassium dihydrogen phosphate there is coexistence between oppositely polarised sub-regions (+ 1 and - 1) of monoclinic structure which depart from tetragonal structure by only 27' of ; l r ~ .~ Tn Rochelle salt the monoclinic sub-regions of + 1 and - 1 depart from orthorhombic by only 12' of arc. Around T they coexist with sub-regions of orthorhombic. I n ammonium chloride there is coexistence between 4 7 McKeown J . Xci. Instr. 1954 31 271. across. Coexistence can be illustrated in various ways. Around T these coexist with tetragonal sub-regions.2 UBBELOIKDE THERMAL TRANSFORMATIONS I N SOLIDS 263 regions of cubic symmetry of lattice spacing 3.8540 ,& and 3.8480A (see p. 268). ( b ) Single-crystal X-ray photographs can determine how far crystal axes actually persist in a " single crystal " in a cycle of temperature changes traversing T,. This kind of investigation has a t present been made only for some single-crystal nitrates l2 and cyanides.48 It throws into sharp relief the antithesis between thermodynamic methods of describing phase transformations which refer to statistical averages and structural methods in which the beliaviour of individual co-operative assemblies such as a hybrid single crystal are under examination.For transformations in substances other than those quoted it may be expected that many intermediate degrees of persistence of axes will be found. Transformations in which the persistence of axes of new crystallitcs is so nearly perfect that they appear as continuous (though possibly with hysteresis) present one extreme. Transformations in which any persistence is negligible so that an absolutely sharp discontinuous phase transformation may be expected form the other extreme.( c ) X-Ray photographs can give important additional information in favourable cases about the state of strain and the internal surface of a single crystal. Though such applications of X-rays are well known for metals 49 they have not been a t all extensively developed for transformations in solids. l2 After a substance has traversed a continuous transformation which involves coexistence of sub-regions the state of strain may persist above T for a period of time; in the case of barium titanate it is several hours. 50 Near a thermodynamic transformation in a crystal X-ray methods frequently show abnormal changes in the intensities of certain reflections. This has been observed for both continuous and discontinuous transforma- tions for example in caesium ~hloride,~~" sodium cyanide,51 and quartz.52 One source of such changes can arise from changes of extinction.If there is a premonitory increase of co-operative lattice defects or even if there is the appearance of sub-regions of the alternative structure as T is approached extinction would be expected to decrease. Lattice disorder would however lower the intensity of reflection in any one direction. A more subtle effect could arise if one crystal structure became thermodynamically unstable with respcct to a related structure as the temperature rises because the high-temperature structure provides a framework permitting considerably greater amplitudes of vibration with consequent enhanced vibrational entropy compared with the low-temperature structure. Such a possibility would almost cert,ainly influence the intensities of selected X-ray reflections near T, but no clear instances have yet been established.T m v . chim. 1935 54 G31. 1945. 48 Cirnino Parry and Ubbelohde unpublished work ; Bijvoet and Verweel Rec. 49 Taylor " Introduction t o X-Ray Mctallography " Chapman and Hall London 6O Kanzig and Maikoff Helv. Phys. Acta 1951 24 343. 61 Siegel J. Ghem. Phys. 1949 17 1146. 6 2 Gibbs Proc. Roy. Soc. 1925 A 107 561. 264 QUARTERLY REVIEWS Amplitudes of vibration in certain directions in a crystal which increase abnormally as the temperature rises may be accompanied by abnormal thermal expansion when the crystal structure permits it. The abnormal expansion as the transformation of certain nitrates is approached provides one example (see ref.4). Other Structural Techniques.-Other methods of investigation of struc- ture have been applied in very considerable diversity to explore certain transformations in solids. Illustrative examples are discussed below though these do not aim to be exhaustive (see refs. 4 7). As an alternat'ive to X-rays neutron diffraction has been applied. This can be particularly useful in the special case where the atoms are carriers of permanent magnetic moments. For examplc in the transformation paramagnetic to antiferro- magnetic crystal neutron diffraction shows how the spins are paired in layers in the crystals in the low-temperature form.45 Neutron diffraction is also particularly valuable for studying transformations in crystals con- taining hydrogen bonds as in potassium dihydrogen phosphate.53 Direct location of the hydrogen or deuterium atoms can be made in favourable cases. Neutron diffraction confirms that above T the orientation of protons in ammonium chloride and of deuterons in ND&l is randomised without free rotation.54 Electron diffraction does not seem to have been used in any important instances. Skilful use of the microscope can give useful supporting information about structural changes in transformations in solids though the conclusions are necessarily more superficial. Studies of boundary movement l5 have already been referred to. Changes of grain size 5 5 in a conglomerate assembly of crystals a hot stage and crossed Nicol prisms being used indicate marked differences in the extent of break-up in different solid transformations. Extensive changes are claimed in potassium nitrate ammonium nitrate and silver iodide and only small changes in silver nitrate thallium nitrate sulphur and resorcinol.The phenomena in a conglomerate are however dependent on a complex sequence of micromechanisms and observations on single crystals are much to be preferred. Various methods of measurement which introduce the time variable have given very valuable information in certain cases though the results are not always easy to interpret uniquely. The most extensively developed involve the application of electric fields with direct current to measure D.C. conductance or alternating current using a wide range of frequencies to measure con- ductance and dielectric behaviour in cyclic fields. For example in ionic crystals D.C. conductance can be of special interest in revealing enhanced lattice defects in the neighbourhood of a transformation in solids; thus enhanced conductance is found around T in the transformations in nitrates.12 This enhanced conductance falls away again above the region of pronounced coexistence of sub-regions of two related structures around T as the co- 63 Bacon and Pease Proc.Roy. SOC. 1953 A 220 397. 5 4 Zimm Driani and Hoffmann Ann. Rev. Phya. Chem. 1953 4 207. 56Ta,mmann and Boehme 2. anorg. Chem. 1935 223 365. Conductance and dielectric studies on solids of high resistance. UBBELOHDE THERMAL TRANSFORMATIONS IN SOLIDS 265 operative defects introduced by coexistence " heal ". When the conductance is predominantly electronic as in the transformation in czesium chloride,14& plots of conductance against temperature point t o premonitory effects iii thc crystals before T is reached? and to hysteresis extending over about 15" in the transformation itsclf.Other examples studied in this way include mercuric iodide and silver iodide. 56 Cyclic electric fields are particularly important in the case of solids containing polar molecules since they give information both about dielectric constants and about the dielectric relaxation which becomes pronounced a t critical frequencies in the solids. For example dielectric constants measured not too near a critical frequency show pronounced increase of freedom of orientation above T of polar diatomic molecules such as the hydrogen halides. I n principle a study of the critical relaxation frequencies as a function of temperature for such solids should give important information about the crystal potential barriers opposing randomisation of orientation.However these can be quite complex and will not in general be isotropic. Measure- ments on single crystals seem desirable in certain cases before the somewhat complex observations on relaxations can be interpreted. 57 At the com- paratively high frequencies of visible light changes of refractive index and changes from an isotropic to an anisotropic crystal structure in a trans- formation have been used in favourable cases to give supporting infor- mation about transformations in solids. I n certain cases the methods are quite sensitive. For example before the X-ray studies of Ubbelohde and Woodward9 definite evidence of a change in crystal structure in the transformation in Rochelle salt largely depended on optical measure- ments.For other applications of classical crystallographic methods see ref. 4. Infrared studies can give useful information about transformations in favourable cases. For example the absence of rotational fine structure above T in ammonium chloride lends support to the interpretation of a random distribution of molecular axes between two equilibrium orientations rather than free rotation. Raman spectre for this salt are in general agree- ment with this view.4 In this group of transforma- tioiis of crystals containing polar molecules the low-temperature form in a transformation shows a comparatively enormous enhancement of the dielectric constant. Various electrical studies which will not be detailed here (see ref.2) show that the crystals pass from ordinary '' paraelectric " behaviour to a behaviour which has been termed " ferroelectric " because of analogies with " ferromagnetism ". Perroelectric crystals contain regions of co-operative dipoles which can be identified with the sub-regions + 1 and - 1 in a hybrid crystal. A strong electric field brings all these regions to the same orientation because the co-operative action of the dipoles inbroduces only small changes of crystal structure. Many examples of Jaffray Conzpt. rend. 1950 230 525. Paraelectric-ferroelectric transformations. 6 7 Powles J . Phys. Radium 1952 13 121. 266 QUARTERLY REVIEWS coexistence of two related structures arise from transformations in solids of the type ferroelectric + paraelectric Structuro with oppositely Structuro 2 polarised domains + 1 and - 1 Magnetic measurements on transformations in solids.Many paramagnetic substances show co-operative interaction of magnetic dipoles helow T,. Such transformations exhibit many special features because of the long range of magnetic forces in co-operative systems and will not be discussed in detail here. Typical parat'nagnetic-ferroma~netic transformations m d paramagnetic-antiferroniagnetic transformations have already been re- ferred to. Application of cyclic magnetic fields permits the study of relaxation times and can give important information about the coupling between electron spins or nuclear spins in solids. 58 Paramagnetic relaxation studies have not as yet thrown much additional light on transformations in solids. Studies of nuclear magnetic resonance have proved to be of considerable importance when the interaction between neighbouring atomic nuclei of deuterium and hydrogen acting as spin carriers depends on whether the molecules containing these atoms are free to rotate in the solid or are constrained in specific orientations.As the solids traverse TC studies of nuclear magnetic resonance 59 confirm marked increase of randomisation. The transformation from conducting to superconducting _solids involves some kind of co-operative interaction between the conduction electrons. Thermodynamic studies of the influence of diverse variables on the transition temperature 2 l show some important analogies with other transformations in solids but the subject as a whole falls outside the scope of this Review.For alloys undergoing order-disorder trans- formations * * $ Go and for other electronic conductors 14b changes of electrical resistance throw important light on the change of order since the conduction electrons are scattered by disorder in the crystal lattice. No complete correlation has been made between the scattering of conduction electrons and the scattering of for example X-rays as the degree of order changes though certain analogies can be found.G Other electronic properties such as the thermoelectric power or the thermal conductance should also exhibit anomalies around T, bat have been 1eEt comparatively uninvestigated (cf. also ref. 28). In principle any cjther property of a solid could be observed on traversing a transformation and could throw light on what is taking place.For Miscellaneous techniques. 6* Cf. " Das Relaxationsverhdtcn dcr Materie " ed. Muller Steinkopff Datrmstadt 59 Richards Quart. Rev. 1966 1Q 480. 6o Nix and Shockley Rev. Mod. Phys. 1935 10 1 ; Lipson Progr. M e t . Pliys. 61 Oldliam and Ubbeloldo Proc. Roy. SOC. 1940 A 176 50. 1953. 1950 2 1. UBBELOIIDE THERMAL TRANSFORMATIONS I N SOLIDS 267 example for alloys Young’s modulus changes significantly on passing from an ordered to a disordered state. As is the case for many other properties this change exhibits hysteresis in the transformation.62 If‘ the mechanism of a transformation involves coexistence of two closely related structures in hybrid single crystals a large internal surface will develop around T,. Some of the experimental evidence for this has been previously reviewed.It seems possible that the reported influence of various absorbed gases on the transformation temperature of solids 63 may arise from the influence of gases absorbed a t large internal surfaces around T, on hysteresis. Direct solid solution leading to a depression of a true equilibrium temperature does not seem thermodynamically an adequate explanation. Further experimental work seems desirable to investigate the phenomena reported in the light of this suggestion. Release of radioactive gases trapped in a solid a t the transformation temperature forins the basis of Hahn’s emanation method of searching for transformations. This release is almost certainly associated with increased lattice defects in the coexistence region. Hysteresis.-One significant consequence of the coexistence mechanism of a smeared transformation is that it leads to a ready interpretation of hysteresis.When a system shows thermodynamic hysteresis this means that it exhibits true equilibrium in certain respects but not in others. The test of thermodynamic equilibrium always is to consider what happens when the system undergoes small fluctuations with respect to diverse variables. Solids exhibiting hysteresis always show temperature equilibrium SO that the vibrational partition functions for the structures present are always minimised. They may even show equilibrium with respect to vapour pressures for the structures present as appears to be the case for example in the palladium-hydrogen system and in transformations of solids carried out in the presence of solvents. However the minimum of free energy is not unique with regard to all possible transformations of these structzcres themselves.At any stage of the transformation the structure depends on previous history. It is easy to see for example that if the change 1 to 2 occurs with increase in volume sub-regions of 2 formed in ;t matrix of 1 will be in compression whereas sub-regions of 1 formed in a tuatrix of 2 are formed in tension. Starting well above or well below T, the transformation curve will never follow exactly the same path. This is best illustrated from observations on single crystals as in the transforma- tion (Fig. 7) of Rochelle salt or the measurements of lattice spacing (Fig. 8) of ammonium chloride.44 Many more studies of hysteresis have been made 011 polycrystalline samples than on single crystals.These do not permit the same detailed interpretation from the standpoint of the phase rule but the averaging which takes place with polycrystalline samples provides useful statistical smoothing. Staveley and his co-workers l9 have pointed out that in a group of related ammonium salts the width of the hysteresis loop increases as the 6 2 Siegel ref. 7a p. 379. 63 Forestier and Kiehl Cornpt. rend. 1950 230 2288 ; Kiehl ibid. 1952 234 943. 268 38550 d 9 38500 QUARTERLY REVIEWS - - - 0 1 2 3 Scole of thermal exponsion 10-7 O K FIU. 7 Hysteresis limits in thermal expansion of Rochelle salt in the direction of tile u axis around [Reproduced from Ubbelohde and Woodward Proc. Koy. Soc. 1946 A 185,448.1 - 4" ; projection on (001). I I I I I t -37. -35" - 3 3 O -3" -29O -27" Temp ("K) FIG.8 Lattice spacing of nmrnonium chloride showing hysteresis around Tc. [Keproclurrd froill Dinirhrrt, Ud?!. Phfls. A c h 1944 17 336.1 UBBELOHDE THERMAL TRANSFORMATIONS IN SOLIDS 269 volume change increases as might be expected from the considerations outlined earlier (see Table 2). I n all these studies co-operative fluctuations of much greater magnitude than appears kinetically possible64 would have to take place in order to dissipate hysteresis completely. Experimental tests on the hysteresis in the volume transformation in solid hydrogen bromide 2O are illustrated in Fig. 5 . The various attempts to catalyse fluctuations by ultrasonics or other means failed to shift the hysteresis curve thus verifying that this represents a path of metastable or neutral equilibrium.Reduction of the crystal size in ammonium chloride l9 or replacement of one isotope by another l9 can have a marked effect on hysteresis but precise theories 234.4 . . . . 247.95 . . . . 214.9 . . . . 244.6 . . . . 242.6 . . . . 223.4 . . . . 168.1 . . . . TABLE 3. Salt NH,Br NHD,Cl NI),Ur NH,DCl NH,Cl ND,Hr (NH,),SO AV transf. ( C l l l . ' n1ole-1) 0.03 0.07 0.08 0.11 0.15 0.35 0.6 Width of hysteresis loop (" C) 0.06 0.07 0.11 0.12 0.35 1.2 9.0 about how these changes affect the barriers between coexistent regions of slightly different structures have not yet been put forward. Other proper- ties may also throw a valuable light on hy~teresis.6~ These considerations suggest that attempts to make direct observations on shifts of the barriers between coexistent regions in hybrid single crystals should prove particularly valuable when the rather difficult experimental techniques can be mastered.Up to the present such studies appear to have been limited chiefly to single crystals in ferroelectric-paraelectric transformations. For example direct movements of + and - sub-regions in hybrid single crystals under the influence of a polarising field have been observed between crossed Nicol prisms 22 in the case of potassium dihydrogen phosphate. At the Curie point the transformation propagates with a velocity of about 2 cm. mim-l. Many mathematical theories of hysteresis introduce theoretical difficulties which lie outside the scope of this Review but a brief list of references may be given.65 Conclusions The Structural-Thermodynamic Interpretation of Transformations in Solids.-From what has been said certain structural aspects of transforma- 6 4 Ubbelohde Trans.Paraday SOC. 1937 33 1203. 6 6 Everett et al. ibid. 1952 48 749 ; 1954 50 187 1077 ; 1955 51 1551 ; Hart- mann 2. phys. Chem. 1942 52 B 338 ; Enderby Trans. Il'aruday SOC. 1955 51 835; 1956 52 106. 9 270 QUARTERLY REVIEWS tions in solids indicate significant modifications which must be made to the mathematical theory. In the first place " phases " can only behave as really " independent " when they (a) differ substantially in specific volume and molecular arrange- ment and ( b ) are generated in portions of phase space that do not require any other phase for their complete description. In this sense a vapour phase is independent of the solid phase in equilibrium with it except possibly a t very high gas densities.On the other hand when one solid structure is unavoidably generated in a matrix of another as in hybrid single crystals the two phases are not independent. This remark suggests that if it were possible to effect ,z solid transforma- tion which is usually continuous or smeared by way o€ the vapour phase as intermediary a discont'inuous transformation would be observed. At first sight this seems likely. However consideration of the theory of thermodynamic fluctuations suggests that whenever the difference between the structures and free energies of two arrangements is small both will arise spontaneously in coexistence around T,. In this sense coexistence is a necessary phenomenon not an accident of the kinetic mechanism of structural transformations.In the above discussion of some of the structural problems that arise in connection with thermodynamic transformations as actually observed in solids the quest)ion has been left open whether any ideal experimental pro- cedure might! be devised in which transformations could take place without the introduction of any " arbitrary " terms in the neighbourhood of the peak transformation temperature. Another way of stating this question is to inquire whether the factors in t)he complete partition function for the solid around T can all be given unique equilibrium values as is generally assumed in the theory of statistical thermodynamics. This ultimately depends on relaxation times for finite departures from these equilibrium values. Finite departures in sub-regions of a crystal can arise from the kinetic mechanisms followed in a transformat,ion.Finite departures in sub-regions may also be required by the theory of tjhermodynanlic fluctuation for an ideally con- tinuous transformation irrespective of the kinetic mechanism followed. When relaxation times are large as must be the case for certain types of co-operative fluctuation^,^^ some degree of thermodynamic arbitrariness seems unavoidable in the transformation whether discontinuous or even ideally continuous merely because the time scale of ordinary experiments happens to be much finer than the time scale for structural fluctuations. When there is coexistence of t,wo structures 1 and 2 modification to the phase rule becomes necessary. As already stated extra terms for the strain energy E12 and the internal energy q12 must be added to the usual independent variables that determine the free energy.For two structures that show coexistence around T the free-energy equations can be written Gl = f l h T 6123 q12) G 2 = fi(P7 T7 t 2 1 7722) The extent to which the addit,ional variables can modify the standard UBBELOHDE THERMAL TRANSFORMATIONS IN SOLIDS 27 1 free energy G = f(p 2’) is limited. by physical factors. The strain energy El2 niust not exceed the breaking strength of the hybrid crystal since other- wise an “ independent ” if strained new structure will result. The internal surface energy q12 of atoms or molecules situated a t surfaces of separation between sub-regions of 1 and 2 must not exceed the activation energy for self-annealing since otherwise one region will grow a t the expense of its neighbours by migration of the atoms or molecules and so lower G.Within these limits the operation of these additional “ variables ” leads to a modified phase rule for solids as already ~ t a t e d . ~ Since these additional variables can change from place to place within a single crystal they are not to be regarded as “ independent ” but ‘‘ arbitrary ” within limits. It is easy to see that when structures 1 and 2 coexist over a narrow range of temperature instead of the Q and G surfaces giving a clean h 1 I I I I I I I temp eroture FIG. 9 Smeared transitions due to indeterminate intersection of two free-energy curves. [Reproduced from Tibbelohdr Natuw 1950 189 832.1 intersection a t a curve as is required by the classical phase rule they will give a ‘L smeared intersection ” which simulates the geometrical contact postulated on mathematical grounds for phase transitions “ of higher order ” (Pig.9).6G In cases where this structural interpretation of con- tinuous transitions must be applied purely iiiathematjical theories of con- tinuous transitions are misleading. There are reasons for believing t]hat this interpretation of continuous phase transitions in terms of the coexistence of two closely similar structures within hybrid single crystals around T is in fact very general though direct X-ray verification has so far proved possible in a few cases only. A somewhat crude treatment of a phase transformation with coexistence Ubbelohde Nature 1952 169 832. 272 QUARTERLY REVIEWS has been developed for the case of ammonium chloride by D i n i ~ h e r t ~ ~ based on a mechanical hypothesis about the uniform distribution of stresses in a single crystal in the transformation region.Dinichert’s treatment accounts in general terms for the hysteresis loop but allowance for therniodynamic as well as niechaiiicaJ contributions to the pseudo-equilibrium seems essential in a more general theory. Unless the sub-regions are large (comparable in size with the single crystal itself) internal “ surface energy ” a t boundaries between sub-regions of structures 1 and 2 may make contributions a t least as important as tension and compression energy. Precision X-ray studies of the various kinds of lattice change and distortion during transition should throw further light on this point. Future Work on Phase Transformations in Solids.-It should be clear that provided a sufficient precision of observation can be achieved in work on transformations in solids great clarification a t least of the problems involved can ensue when structural considerations are combined with the requirements of thermodynamics.Work on single crystals practically always throws new light on these problems complementary to that obtained from work on polycrystalline samples. This is illustrated for example by the introduction of the concepts of coexistence of structures in a hybrid single crystal of the degree of persistence of axes of a single crystal in a cyclic tra.nsformation and of the strain and internal-energy contributions to the free energy of alternative structures especially when they coexist in a hylJrid single crystal around the transformation temperature. Further work will show how far these and relnted concepts are applicable quite generally to the very wide diversity of t,ransformations in solids.

ISSN:0009-2681    

DOI:10.1039/QR9571100246

出版商:RSC    

年代:1957

数据来源: RSC

摘要:

THE MQLECULAR-ORBITAL AND EQUIVALENT-ORBITAL APPROACH TO NIQLECULAR STRUCTURE By J. A. POPLE PH.I>. (DEPARTMENT OF THEORETICAL CHEMISTRY UNIVERSITY OF CAMBRIDGE) Introduction THE electronic theory of chemical valency has to explain a set of facts and empirical rules some of which suggest an interpretation in terms of localised electrons and others require a picture of electrons spread throughout the whole molecule. In the pre-electronic era a chemical bond was regarded as a genuinely local link joining neighborxring atoms in a molecule and this was associated with a pa'ir of bonding electrons in the early electronic theory developed by Lewis and Langmuir. In accounting for all the electrons some were assigned to atomic inner shells and others were supposed to form inert pairs (or " lone pairs ") on a single atom.The rules of stereo- chemistry implied certain restrictions about the geometrical arrangement of neighbouring bonds but apart from this there seemed to be considerable evidence that the pairs of electrons in different bonds behaved independently to a large extent. For a great many molecules it was found possible to interpret heats of formation on the assumption that there was a definite energy associated with each type of bond (the bond energy). The refractiv- ity of a large molecule can usually be predicted by assuming that the total is a sum of standard contributions from the various atoms and bonds. Similar additive laws also hold for magnetic susceptibilities. All these facts which imply the existence of a standard type of bond between two given atoms are best interpreted in terms of a theory in which a pair of electrons is moving in localised orbits in each bond and is mainly independent of elect,ron pairs in neighbouring bonds.On the other hand there are properties of molecules which do not seem to fit this picture. Consider the ionisation of (removal of an electron from) a simple molecule. According to the localised picture we might expect this process to consist of the removal of an electron from one of the bonds or possibly from one of the lone pairs. However in the case of a molecule such as methane where there are several bonds exactly equivalent to one another there are various possibilities. There is no a priori reason why the electron should be removed from one bond rather than another and in such circumstances what actually happens is that the electron is removed partly from them all or an equivalent statement the electron which is removed was moving in an orbit or path extending over the whole molecule.Similar situations arise when we consider the electronic excitation of a molecule. Methane being taken as an example again instead of exciting the electrons in a single bond an electron is taken out of one orbit spread over the whole molecule and placed in another excited orbit. It seems therefore that in order to interpret spectroscopic properties of molecules such as methane 373 274 QUARTERLY REVIEWS we ought to treat the electrons as moving in orbits extending over the whole molecule processes such as ionisation and excitation corresponding to the removal or reallocation of electrons among these paths.Such a procedure is in fact a logical extension of the ideas originally used by spectroscopists to interpret atomic spectral lines and it has since proved its value in the theory of the electronic spectra of molecules. It appears then that there are two apparently divergent modes of description of molecular structure localised electrons in bonds and lone-pair orbits on the one hand and electrons moving in orbits covering the whole molecular framework on the other. But the success of both descriptions in their respective fields of application is so considerable that the two must be more closely related than appears a t first sight. When we consider the general quantum-mechanical problem of finding the distribution of electrons in a molecule we find that this is so and that the localised and delocalised pictures are just two different ways of breaking down the same total wave function describing the combined motion of all electrons.The purpose of this Review is to elaborate this transformation and show how it links together alternative descriptions of certain simple molecules. To do this we begin by considering the general properties that the wave function for the electrons in a molecule must possess. If we consider only one electron moving in the electrostatic field of the nuclei then it is quite clear that its path or orbital must extend over the whole nuclear framework. Thus the electron in the hydrogen molecule-ion HZ+ is equally distributed around both nuclei. When we come to systems of several electrons how- ever we also have to take into account the indistinguishability of electrons and further the all-important antisymmetry property of the wave-function.The way in which this is incorporated into the molecular-orbital theory is discussed in the next section and its consequences are then illustrated in terms of a simple one-dimensional model. In the remaining sectioiis the transformation between the localised and delocalised descriptions is carried out for certain simple molecules. I n this way we can see the relation between the bonding- and antibonding-orbital picture of a diatomic molecule such as F and the alternative description in terms of lone pairs. The relation between the a-n and the two-bent-bond descriptions of the standard carbon double bond in ethylene also becomes apparent. Similarly a triple bond as in nitrogen or acetylene can be regarded as three equivalent bent bonds or as a 0 bond and two n bonds.Quantum-mechanical basis of orbital theories The basic quantum-mechanical problem is to formulate the wave-like description of an electron moving in the electrostatic field of the nuclei and other electrons. If the potential energy of an electron a t a point (x y x ) is V ( x y x ) this is accomplished by solving the well-known Schrodinger equation for a wave function y(x y x ) POI'LE MOLECULAR AND EQUIVALENT ORBITALS 275 where E is the energy of the electron and h and m are Planck's constant and the electronic mass respectively. (For many-electron systems some care has tlo be taken in obtaining the potential energy V for which a know- ledge of other electron distributions is required.The calculations have to be made self-consistent. The details are not relevant to the present topic however and we shall not go into them.) The function y which depends on the co-ordinates (x y x ) of the electron in space will be referred to as a space orbitaE or often just as an orbital. Its physical interpretation is that y 2 dxdydx represents the probability that the electron will be found in a small rectangular element of volume dx dy dz near the point (x y x ) . Thus y 2 is a probability density and the electron is most likely to be found where this density has its largest value. The other important property of an electron that must be specified besides its spatial distribution is its spin. According to quantum-mechanical arguments into which we need not go in detail each electron has a spin which can take one of two values.It is convenient to include this description in the wave function by defining a and /? so that a = 1 if the spin is in one direction and a = 0 if it is in the other. is defined in a complementary manner. Thus the electron moving in an orbital y(x y x ) may be associated with two functions y(x y x)a and y ( x y x)/3 according to the direction of its spin. A function such as y(x y x)a which gives the probability distribu- tion of the spin co-ordinate as well as that of its spatial co-ordinates is sometimes referred to as a spin orbital. All this is very straightforward if we are dealing with a system which contains only one electron such as the hydrogen atom or the hydrogen molecule-ion H,+. But when we consider a many-electron molecule we are faced with the problem of combining the orbitals for the individual electrons into a total wave function for the whole system.Suppose we are dealing with two electrons which occupy space orbitals yl and y2. The simplest compound wave function for both electrons is the product ypl'OdUCt = %(xl x1)w2(x29 y2 '2) ' (2) where (xl yl x l ) and (xz y2 x2) are the Cartesian co-ordinates of electrons 1 and 2 respectively. To be complete this should be multiplied by one of the four possible spin functions a( 1)a(2) a( 1)/3(2) a(2)/3(1) or /?(l)P(Z). The physical interpretation of this compound wave function is again in terms of probability. Y2 is now proportional to the joint probability of electron 1 being at position (xl yl xl) and electron 2 a t position (x2 y2 x 2 ) sinzultaneously.If the product form is used this is just the product of the two separate probabilities. Thus the product wave function implies that the two electrons move independently of one another. Product wave functions can clearly be constructed for any number of electrons. Early wave functions were constructed on this basis together with the empirical rule that not more than two electrons could be assigned to a single orbital one of each spin. Further electrons tend to occupy the orbitals with lowest possible energy in the absence of other factors. The major disadvantage of the product function is that it fails to satisfy 276 QUARTERLY REVIEWS another important quantum-mechanical principle namely that of anti- symmetry. This is really a consequence of the indistinguishability of electrons.If we consider the operation of interchanging the positions of two electrons the probability of the new configuration must be just the same as previously. Thus the square of the total wave function must be unaltered and consequently the wave function itself can only be multiplied by 4- 1 or by - 1. It is found that the second choice is demanded for electrons so that we formulate the antisymmetry principle by requiring that the wave function changes sign if we interchange the co-ordinates of any two electrons. Clearly the product function (2) does not satisfy this condition for if we interchange thc co-ordinates of electrons 1 and 2 we obtain yI(xz7 y2 x2)y2(xl yl xl) which is not a direct inultiple of its previous form. The next step is to construct a wave function from products of the type (2) which satisfies this further condition.This can be done in terins of what is called an antisymmetrised poduct. Let us consider first of all the case of two electrons in the same space orbital y1 with two different spins. The nntisymmetrised product is obtained by subtracting from this the corrcsponding product with the suffixes 1 and 2 interchanged. This gives The factor ( l / d Z ) is inserted so that the total probability added over all configurations is unity. This function may be said to be symmetric in the space co-ordinates but antisymmetric in the spins. Por an overall inter- change it is antisymmetric. Next suppose we have two electrons in different space orbitals y1 and y2 but with the same spin a. and the antisymmetrised product constructed in the same way is Both the antisymmetric functions (4) and (6) can be written as 2 x 2 deter- minants.Thus (4) is The simple product function is y1(x17 y1 z1)'~1(x27 y27 '2)a(1)P(2) * - (3) (1/d2)y1(x17 y17 "1)y1(x27 yZ7 '2) ('(')p(') - a(2)p(1)) ' * (4) Then the simple product function is y1(x17 Y1 x1)y2(x27 y2 x2)'(')a(2) * * ( 5 ) (1/d2){v1(x1y y19 '1)w2(x27 Y27 '2) - y1(x27 y27 x2)y2(x17 !/I7 '1)}a(1)a(2) (6) and (6) is Here we have written yl(l) as a short form of y1(xl y17 xl). These simple determinantal functions for two electrons suggest that we can construct antisymmetric wave functions for any number of electrons in a similar manner. Thus if we have a set of orbitals yI y2 . . . yn eacH containing two electrons one of each spin (this applies to most molecules), POPLE MOLECULAR AND EQUIVALENT ORBITALS 277 an antisymmetric wave function can be constructed as a determinant with a different spin orbital in each row.* I I . . . . . . . . . . . . . . I 1 Yn(l)rB(U Yn(2,P(2) * - - y,(24B(W 1 The interchange of the co-ordinates and spins of two electrons corresponds to interchanging two columns of this determinant. This leads to a change of sign so that the antisymmetry property is satisfied. This type of total wave function is that used in molecular-orbital theory. Another well-known property of determinants is that they vanish if they have two identical rows. This means that it is not possible to construct a non-vanishing antisymmetrised product in which two electrons in the same orbital have the same spin. Thus the rule that not more than two electrons must be assigned to any one space orbital follows as a direct consequence of the antisymmetry principle ; for product wave functions it had to be introduced as an extra postulate.Another important physical interpretation of the molecular-orbital deter- minant follows from an application of a similar argument to the columns. The elements of two columns become identical if two electrons have the same spin (a or p) and are a t the same point (x y x ) . The determinant then vanishes and consequently the probability of such a configuration is zero. Such an argument does not apply to electrons of different spin however. The antisymmetry principle operates therefore in such a way that electrons of the same spin are kept apart. We shall see in later sections that this is an important factor in determining stereochemical valence properties.The antisymmetry principle is also of great importance in understanding the dualism between localised and delocalised descriptions of electronic structure. We shall see that these are just different ways of building up the same total determinantal wave functi0ns.l This can be developed mathematically from general properties of determinants but a clearer picture can be formed if we make a detailed study of the antisymmetric wave function for some highly simplified model systems. Simple models illustrating the effects of antisymmetry The simplest system that can be used for illustrative purposes is one in which electrons are free to move in one dimension along a wire of length 1. The potential energy will be constant and can be taken as zero.If the position of a point on the wire is measured by the distance x from one end the Schrodinger equation is h2 d2y 8n2m dx2 -Ey . - - __ _. 1 Lennard-Jones Proc. Roy. SOC. 1949 A 198 1 14. S* 278 QUARTERLY REVIEWS where E is the energy. has the general solution This is just the simple harmonic equation which y = A sin (J(E)") 8n2mE -i- B cos {Jo.>. 8n2mE . (11) where A and B are constants of integration. The wave function must also satisfy the boundary conditions of being zero a t both ends (that is a t x = 0 and x = I ) . The first condition requires that B = 0 and the second that .\/(8n2mE/h2)E is an integral multiple of n. The lowest orbitals thatv electrons ca.n occupy (those with least nodes) are therefore yl = 2/(2/Z) sin (nz/Z) y = 2/(2/Z) sin (2nx/I) .' (12) y1 is positive over the whole length of the segment while y2 is zero a t the centre of the wire (Fig. 1). FIG. 1 Lowest occupied molecular orbituls in model syqtem. Now suppose two electrons are placed one in each of these orbitals. The distribution of these electrons in their individual orbitals will simply be given by y12 and y22. If we wish to examine the probability of various simultaneous positions of the two electrons we have to consider the total wave function Y which will be an antisymmetric product with a form depending on the spins of the electrons. If we wish to investigate the effect of the antisymmetry principle on the spatial arrangement of the electrons it is convenient to examine the case in which they both have the same spin a. Then the wave function will be of the form given in equations (6) and (8).If the factor cc(l)cc(2) is omitted = (4/Z) sin (nx,/Z) sin (nx2/Z) (cos (nxl/Z) - cos (nx2/Z)} . - (13) Y2 is then proportional to the probability of electron 1 being found a t position x1 and electron 2 a t x2. The significant points to be noted are (1) that if x1 = x2 the wave function vanishes so that the configuration has zero probability and (2) that there are two equivalent most probable con- figurations in which the electrons are in different halves of the wire. These two configurations differ only in the numbering of the electrons and are otherwise indistinguishable. POYLE MOLECULAR AND EQUIVALENT ORBITALS 279 antisyinmetrised wave function instead of an ordinary product therefore is to cause the electrons to move in two different regions in the two halves of the segment the probability of configurations in which both are in the same segment a t the same instant being relatively small.This suggests that the system could be alternatively described in terms of two localised orbitals one in either segment with one electron in each. This alternative description in terms of localised orbitals can indeed be set up by taking linear combinations of the orbitals y1 and yz and using these in the determinant instead. If the linear combinations are suitably chosen the value of the determinant is unaltered although t'he individual rows change. Let us consider therefore how we can construct localised orbitals froa our two starting orbitals y1 nnd y2. As we have already noted yl is positive everywhere while y2 is positive in the left-hand part of the segment and negative in the right.If we consider yl + y2 the two components will add on the left but partly cancel on the right. This therefore can be used as a localised orbital mainly concentrated in the left-hand part. Similarly y1 - y2 is mainly concentrated on thc right. We therefore define two new localised orbitals xa and xb by ' (14) The effect of using xa = (yl + y2)/2/2 = 2/(4/1) cos (nx/22) sin (3nx/21) X b = (yl - y 2 ) / 2 / 2 = d(4/Z) sin (nx/2Z) cos (3nx/21) * The factor ( l / d 2 ) is included to keep the total probability equal to unity. These funcbions are illustrated in Fig. 2. They are mirror images in the FIG. 2 Equiualent orbitals in ,model system. mid-point of the line-segment. They are sometimes called equivalent orbitals.l The total wave function can now be written in terms of the equivalent orbitals (15) If we substitute for xa and xb and expand the expression it is easily confirmed that the value of this determinant is identical with the original t,otal wave function (13).This is a particular example of what is known as an ortho- gonal transformation of the rows of the determinant. It appears therefore that we have two possible descriptions of this system. We can describe it as two electrons each of which occupies one of the delocalised (or molecular) orbitals which are solutions of the 2Lenanrd-Jones and Pople Proc. Roy. SOC. 1950 A 202 166. 280 QUARTERLY REVIEWS Schrodinger equation. Or alternatively we may say equally accurately that the two electrons occupy two localised orbitals xa and X b one a t each end of the segment.These are just two different ways of interpreting the same total wave function. If we are interested in the relative positions of the two electrons then the interpreta- tion in terms of localised orbitals gives a clearer description of the qualitative features of the overall probability distribution. On the other hand if we are interested in the removal of an electron the first description is more appropriate for the remaining electron must occupy an orbital which is a solution of the original Schrodinger equation. Thus the electron must be removed from yl or y,. This sort of model can easily be generalised to deal with more than two electrons and other assignments of the spins. The case of most interest in molecular studies is that in which a set of molecular orbitals are all occupied by two electrons.Thus if there were two electrons one of either spin in both orbitals yl and y2 the total wave function would be a 4 x 4 determinant. But most of the features of the two-electron model are retained. The system could be alternatively described as consisting of two electrons in each of the equivalent orbitals. The effect of the antisymmetry principle is then to keep electrons of the same spin apart the motion of the two opposite spin-types being uncorrelated. Although the one-dimensional model bears little resemblance to any real molecular system many of its features carry over to cases of practical interest. Suppose we consider three-dimensional motion in a central field as in atoms. The orbitals or single-electron functions now become atomic orbitals and can be classified in the usual manner as Is 28 .. . 2p 3p . . . 3d . . . Suppose we are dealing with an atom in which there are two electrons of the same spin (a say) occupying the 2s and 2p orbitals (inner shells being ignored for the present). Then the antisymmetric product function is The two descriptions are useful in rather different contexts. This wave function has many €eatures in common with t,hat of the previous model. While yZs is spherically symmetric yZP has a nodal plane through the centre of symmetry. A similar transformation can be applied and we can use two equivalent orbitals Atomic orbitals of this mixed type are usually referred to as hybrids (or more specifically digonal s-p hydrids). As with the one-dimensional model they reinforce on one side of the nucleus and partly cancel on the other.Hence the transformation is from the delocalised s and p description to a description in terms of two equivalent orbitals localised on opposite sides of the nucleus. Again a similar transformation may be applied to a 4 x 4 determinant describing a system with two electrons in each of these orbitals. POPLE MOLECULAR AND EQUIVALENT ORBITALS 28 1 For the next example consider a system of three electrons of the same Here the antisymmetric spin occupying atomic orbitals 28 2px and 2py. wave function is 1 ~ 2 ~ ( 1 ) ly2,(2) ly2,(3) I !P= ~ ~ t ) $ & ) y2,,(2) y2,,(3) ~ wZPx(2> y2Dx,(3) 4 1 ) 4 2 ) 4 3 ) - (18) In this case we can transform these into three equivalent orbitals which are 8-p hybrids (called trigonal hybrids) pointing towards the vertices of an equilateral triangle so that the angle between neighbouring directions is 120".The actual transformation is x1 = d ( 1 / 3 ) ~ 2 ~ + d ( 2 / 3 ) ~ ~ ~ ~ x2 = d(1/3)wZs - . \ / ( 1 / 6 ) ~ ~ ~ ~ + 2/(Wv)2py a * (19) x3 = 2/(1/3)wZs - d ( 1 / 6 ) ~ ~ ~ ~ - d(1/2)wZPv It is not immediately clear from the form in which these are written that they are equivalent functions that is differ only in their orientation but it is easily confirmed that they do transform into each other if the axes are rotated through 120". Again it can be shown that the determinant of X-functions has the same value as (18). One other point about this set of equivalent orbita'ls is that there appears to be no preferential direction in which any one of the vertices of this triangle may be chosen.The choice is in fact arbitrary and any set of three equivalent directions perpendicular to the x direction would suffice. This only applies for an atomic wave function of course. In molecules (such as planar XY,) there may be a preferred choice of axes on account of symmetry. This will be clear from some examples considered in the next section. The case of four electrons in the atomic orbitals 28 2px 2py and 2px can be handled in a similar manner. Here we can transform the expression into four equivalent orbitals given by x1 = %W2s + y2m -t- x 2 = %Wzs + W2DX - 3 - d w 2 s - WZPX + x -1 4 - d W 2 S - WZPX - - 1. W2PY + W 2 P t ) Y2DY - Y 2 P Z ) Y2PY - YZPJ Y2PY + Y 2 P Z ) which are directed towards the vertices of a regular tetrahedron.These equivalent orbitals are usually called tetrahedral s-p hybrids. If we have eight electrons (two of each spin in each orbital) this description can be applied directly to the outermost shell of electrons in the neon atom. The neon atom is not usually described in terms of localised tetrahedral orbitals but such a description is just as valid as the more conventional s2p6. We shall see in the next section that the localised picture is useful in discussing the structure of molecules isoelectronic with neon. The orbital description of molecules We now turn to the description of actual molecules in terms of molecular The usual procedure is to find orbital functions yl ly2 . . . which orbitals. 282 QUARTERLY REVIEWS are solutions of a suitable Schrodinger equation assign the electrons in pairs to those orbitals of lowest energy and then construct an antisymmetric determinantal wave function [as in eqn.(9)]. We can then consider possible alternative descriptions obtained by transformations of the rows of the determinant as with the models of the previous section. In the complex electrostatic field of a molecule it is usually inipractjicable to obtain accurate molecular orbitals so it is customary to express them approximately as linear combinations of atomic orbitals belonging to the constituent atoms. This is called the “linear combination of atomic orbital ” or LCAO form. Although they are only approximate the LCAO functions do show most of the properties of the precise orbitals Both molecular and localised equivalent orbitals can be expressed in this manner.Diatomic Molecules.-We shall begin by discussing diatomic molecules which bear some relation to the models discussed in tthe previous section. To begin with the hydrogen molecule has two electrons which both occupy the lowest molecular orbital whose LCAO form is y1 = A(1sA + Is,) * (21) IsA and lsB are the two hydrogen 1s atomic orbitals. The factor A is introduced so that the total probability adds up to unity. If the overlap between the atomic orbitals is small A is approximately 1 / 4 2 . Since there is only one space orbital in the determinantal wave function [eqn. (7)] no transformation of the orbitals is possible. If we now go to a pair of interacting helium atoms there will be four electrons of which the first pair will go into the corresponding orbital yl and the second pair into the next lowest orbital for the system whose LCAO form will be This function is zero for all points equidistant from the two nuclei (that is it has a nodal plane).The orbital y1 is large in the region between the nuclei (where lsA and lsB overlap and the electrostatic potential is low) and is generally referred to as a bonding orbital. Similarly y2 which keeps its electron away from the internuclear region is antibonding. The two functions y1 and y are malogous to the symmetric and antisymmetric orbitals for the one-dimensional model. A similar transformation can be applied and two equivalent orbitals constructed. y2 = pu(ls* - 1ss) * (22) These are If the overlap of the functions is not large 3 and ,u are both nearly 1 / 4 2 and so the equivalent orbitals approximate to the atomic orbitals for the isolated atoms.The complete equivalence of the two configurations y2bondingy2Santibonding and xA2xB is the simplest example of the dual descrip- tion of a molecular system. Proceeding further along the series of homonuclear diatomic molecules the 1s inner shells can still be described in either manner. Since the 1s P(7PLIr 3lnLECTJLAR AND EQIJIVALEWT ORBITALS 283 electrons do not play any appreciable part in bonding it is usually most convenient to treat them as localised. The lithium molecule Liz can be described in terms of a pair of inner shells and a bonding orbital which is similar to that in H,. There is a difference however in that there is now a possibility of appreciable hybridisation between the 2s and Zp atomic orbitals which have comparable energies.The best LCAO representation of the bonding orlital will be a sum of two hybrid orbitals of the form 4 2 4 + B(2po) where 2po represents an atomic 2p orbital with its axis along the internuclear line. Again since this is the only occupied orbital formed from valence shell atomic orbitals no transformation to localised orbitals is possible. Proceeding further along the Periodic Table let us next consider the nitrogen molecule N,. Here we have to consider molecular orbitals con- structed from all the 2p functions for each atom. (The 2p orbitals with axes perpendicular to the molecular axis are usually called 2pn functions.) To begin with four electrons are assigned to the inner shells represented by equivalent orbitals Is and Is,. Secondly there will be two molecular orbitals bonding and antibonding fornied from the next s orbitals 28 and 28,.These can be transformed into two equivalent orbitals in a similar manner and correspond t o lone-pair or inert electrons. Then there will be a bonding orbital formed from 2po functions yo-bonding = (1/'d2)(2poA + 2PoB) - (24) and two bonding orbitals whose LCAO forms are sums of' the 2pn atomic orbitals If two electrons are assigned to each of these orbitals all fourteen in the molecule are accounted for. This set of orbitals would be slightly modified if hybridisation between the 2s and 2po electrons is allowed. This description of the triple bond represents it as an axially symmetric CT bond together with two perpendicular n bonds. This is appropriate for spectroscopy and must be used if we are discussing excited N or N,+.But for N in its ground state another description in terms of three equivalent bonding orbitals can be obtained by applying the trigonal transformation to (24) and (25). Thus if we write 1 1 1 X3-bonding rL -- ,3Yo-bonding + -pjYn2-boiiciing - - d 2 n y - b o n d i n g 2 the three new orbitals will be turned into one another by a rotation through 120" about the axis of the molecule. They represent three bent bonds 284 QUARTERLY REVIEWS concentrated in three different azimuthal planes and add to get the total electron density this is found to be axially symmetric. Nevertheless the existence of the three equivalent orbitals implies that the pairs of electrons dibpose them- selves relative to each other in such a way that their distributions are similar and interrelated by a 120" rotation.Although the nitrogen molecule represents the standard type of triple bond the bond in 0 is in no way typical of a double bond. There are two extra electrons and the next orbitals t o be filled are the antibonding n orbitals If we square the orbitals p = (Xl-bonding)' + (3d2-bondiiig)2 + (XS-bonding)2 (27) Yn.x-antibonding = (1/'d2)(2PnxA - 2pnx.15) Yny-antibonding = (1/'d2)(2PnYA - 2pnYB) These both have the same energy so that in the absence of other determining factors the electrons go one into each with the same spin (or an equivalent state). This means that they are kept apart by the antisymmetry principle and so the energy is lowered by the reduction of Coulomb repulsion. In this rather exceptional case therefore the orbitals are not all doubly occupied and we cannot carry out any simple transformation into localised orbitals.If we now proceed further to the fluorine molecule both the n-antibonding orbitals will be doubly occupied. As with the s functions the configuration (vnr-borlding) '(Ynr-nntibOnding) can be transformed illto two n-lone-pair orbitals one on each atom. The localised description of F, therefore has four localised n-lone-pairs there being only one single bonding orbital. Molecules Isoelectronic with Neon.-Another set of molecules whose structure is typical of many standard cheniical environments is the set of ten-electron first row hydrides Ne HP H20 NH, and CH,. On p. 281 we saw how the outer electrons of the neon atom could be described either as being in the configuration ( 2 s ) 2 ( 2 p ) 6 or alternatively as occupying four tetrahedral orbitals xl x, x3 and x4 orientated relative to one another in a tetrahedral manner the orientation of the tetrahedron in space being arbitrary.The electronic structures of the other molecules of the series can now be discussed in terms of this basic system if we imagine unit positive charges to be removed successively from the nucleus. If a single positive charge is removed to give HF a preferred direction is established and the orbitals have to be referred to the internuclear line. Suppose we take this as the x axis. The orbitals will be somewhat distorted but their general arrangement will not be radically altered. One of the four localised neon orbitals will be pulled out into a localised bonding orbital ; it can probably be expressed fairly accurately in the LCAO form as Similarly with the ny orbitals.where A p and Y are numerical coefficients. This is a linear combination of an s-p hybrid on the fluorine atom directed along the x axis and the POYLE MOLECULAR AND EQUIVALENT ORBITALS 285 1s hydrogen orbital (Fig. 3). The ot,her three neon-like localised orbitals will not be distorted as much so they will remain as three equivalent tetrahedral hybrids pointing in directions making an approximately tetra- hedral angle with the bond. It is interesting that the most important lone-pair direction (where the negative charge is most likely to be found) may not be directly at the back of the fluorine atom. As the lone-pair electrons play an important role as the negative end of hydrogen bonds this is probably closely connected with the non-linear structure of hydrogen fluoride polymers.The molecular-orbital description of HF can be obtained if we note that the three equivalent lone pairs can be obtained from a cr orbital and two n orbitals by a transformation similar to that used for obtaining the bent-bond description of N,. In the LCAO form the u lone pair will be another s-p hybrid and the two lone pairs will be (Z(P,C)~ and (Zpy),. It is generally found that x lone pairs are less firmly bound than o lone pairs so that the lowest ionisation potential would correspond to the removal of an electron from one of the last two orbitals. We can now consider the structure of the water molecule by supposing They are three equivalent lone pairs. v x60ndh9 FIG. 3 Locnlised orbilals for hydrogen Jlzcoride.a further positive charge removed from the nucleus. The locslised descrip- tion gives some insight into the reason for the iion-linear structure. Giveq that one positive charge has been removed as in HF the second charge will prefer to be pulled out in the directions where the remaining electrons are most likely to be found. As we have seen above this is in a direction a t an approximately tetra?hedral angle to the first bond. In the localised- orbital picture therefore the outer electrons of the water molecule occupy two sets of two equivalent orbitals. The first two are bonding orbitals concentrated mainly along the O-H bonds and the other two are localised lone pairs which point in two equivalent directions towards the back of the molecule above and below the plane of the nucIei.3 Once again this is.a very useful description for understanding molecular interaction. The normal form of the ice crystal for example is held together by hydrogen bonds in such a way that each molecule is surrounded tetrahedrally by four other^.^ This is completely consistent with the electrostatic theory of the hydrogen bond according to which a proton is Pople PTOC. Boy. SOC. 1950 A 202 323. Barnes ibid. 1929 A 125 670. 286 QUARTERLY REVIEWS attracted by a localised lone pair of electrons on another molec~le.~ There is also considerable evidence that this structure persists to a large extent in the liquid.6 7 To deal with the molecular orbitals for water it is useful to examine the effect of certain symmetry operations on the molecule.We choose a set of rectangular Cartesian axes (Fig. 4) so that the x axis bisects the angle between the bonds and the x axis is perpendicular to the nuclear plane. 4 I X FIG. 4 Cartesian axes for the water molecule. Then we can classify the molecular orbitals according to whether they are antisymnietric or not in the planes of symmetry. These are Oxy and Oxx. The molecular orbitals are summarised in the Table together with LCAO forms. TABLE. Molecular orbitals for the water molecule. Symme try y1 Totally symmetric . y 2 Totally symmetric . y 3 Antisymmetric in plane y4 Totally symmetric . y5 Antisymmetric in plane 0 x 2 OXY Description LCAO form Oxygen inner shell Symmetric bonding orbita Antisymmetric bonding Symmetric lone pair Antisymmetric lone pair orbital (Wo Mixture of oxygen hybrid of (2s)o and (2pz)o with Mixture of oxygen ( 2 p ~ ) ~ Hybrid of ( 2 ~ ) ~ and ( 2 9 1 ~ ) ~ (21740 (1S)H f (1s)H' with ( 1 ~ ) ~ - (Is) The localised equivalent orbitals are connected with these by the transformations It is interesting that the molecular-orbital functions give an alternative Lennard-Jones and Pople Proc.Roy. SOC. 1951 A 205 155. Bernal and Fowler J . Chem. Phys. 1933 1 515. Pople Proc. Roy. SOC. 1951 A 205 163. POPLE MOLECULAE AND EQUIVALENT ORBITALS 257 description of the lone-pair electrons which still distinguishes them from bonding electrons. There are two distinct lone-pair molecular orbitals one of which y4 is an s-p hybrid on the oxygen atom directed along the negative x-axis that is backwards along the line bisecting the two O-H bonds. The other (y5) is antisymmetric in the €€OH plane and approximates to an atomic 2p-function.This is the orbital of lowest energy for the water molecule and corresponds to the lone-pair electron removed in the first ionisation process. The structure of ammonia the next molecule in the series can be con- sidered in a similar manner. If a further unit positive charge is removed from the nucleus in H,O the most favourable direction energetically will be towards one of the localised lone pairs. The ammonia molecule there- fore will have a tetrahedral-like structure with three equivalent localised bonding orbitals and a hybrid lone-pair orbital in the fourth direction. The three bonding orbitals can be transformed into three delocalised orbitals but here the lone pair is already symmetrical and approximates to a molecular orbital.It is interesting to consider the behaviour of the lone pair during the inversion of the molecule (this is known to occur with relatively high frequency). In the equilibrium configuration the orbital is close to a tetra- hedral s-p hybrid. As the molecule flattens the amount of s character decreases until in the intermediate planar configuration the lone-pair orbital is a pure p function. After passing through this position s character reappears causing the lone pair to project in the opposite direction. The final molecule of this series is methane the tetrahedral structure of which follows if a fourth unit positive charge is removed from the nucleus in the ammonia lone-pair direction. There are now four equivalent bonding orbitals which may be represented approximately as linear combinations of carbon s-p hybrid and hydrogen 1s functions.The transformation from molecular orbitals into equivalent orbitals or vice versa is exactly the same as for the neon atom. Molecules with Multiple Bonds.-The double bond in a molecule such as ethylene provides a striking example of the transformation between equivalent and molecular orbitals.8 The nuclear configuration of ethylene is known to be planar so the molecular or symmetry orbitals can be divided into two classes according to whether they are symmetrical or antisym- metrical in this plane. By analogy with the classification for diatomic molecules these are referred to as cr and n orbitals respectively. If we ta'ke the z direction to be normal to the plane the LCAO forins of the cr molecular orbitals (apart from the carbon inner shells) will be constructed from the hydrogen 1s and carbon 28 2px and 2py atomic orbitals.The only low-lying n atomic orbitals are 2px. Two types of transformation are possible. In the first place the CT orbitals may be transformed among themselves so that all orbitals will retain the property of symmetry or antisymmetry in the nuclear plane. The occupied CJ molecular orbitals could be transformed in this way into a set of localised CT orbitals which correspond to bonds of single axially-symmetric type. There will be five Lennard-Jones and Hall Proc. Roy. SOC. 1951 A 205 357. 288 QUARTERLY REVIEWS in all four local C-H bonds and one C-C bond whose LCAO form will be approximately where tr and tr are trigonal s-p hybrids.will occupy the n-bonding orbital which will be antisyminetric in the nuclear plane. wC-C a-bond = (1/2/2)(trA + trB) - - (30) VC-C n-bond = ( 1 / d 2 ) ( z p z A $- 2pzB) * - (31) The remaining two electrons These two orbitals o- bond n -bond FIG. 5 a and rr Bonding orbitals in ethylene. constitute the 6-n representation of the double bond (Pig. 5). carry out a further transformation by writing If we nou- we get two equivalent orbitals concentrated one above and one below the plane. This description corresponds to two bent bonds (Fig. 6). Each carbon atom takes part in four bonds in directions which are approximately tetrahedral two being bent round towards the other carbon atom. FIG. 6 Equivalent or bent bonding orbitals in ethylene. Actually the HCH bond angle in ethylene is rather larger than the tetrahedral value.According to the equivalent-orbital picture this can he attributed to the closing up of one pair of bonds leading to the opening of the other pair. The carbon-oxygen double bond in aldehydes and ketones is similar and can be described in either of these two ways. If we adopt the localised- orbital description formaldehyde will have two directed lone pairs in place of two of the C-H bonds in ethylene. In this case the axes of these hybrid orbitals will be in the molecular plane (unlike the oxygen lone pairs in water). Either $he components of the double bond or the lone pairs can bz trans- formed hack into symmetry forms. The alternative description of the lone pairs would be one a-type dong the C-0 direction and one n-type with axis perpendicular to the C-0 bond but in the molecular plane.It is the latter orbital which has the highest energy so that an electron is removed from it in ionisation or excitation to the lowest excited state. POPLE MOLECULAR AND EQUIVALENT ORBITALS 289 The carbon-carbon triple bond in acetylene can be treated in a similar way to that in the nitrogen molecule.8 The details of hybridisation may H' FIG. 7 Equivalent lone pairs in formaldehyde. differ somewhat but there will be a C-C 0 bond and two perpendicular C-C n bonds. The alternative description is in terms of three equivalent bent bonds. The triple bond in hydrogen cyanide HCGN is similar. Resonance and Conjugation.-All the molecules described so far have been simple ones which can be described in terms of a single classical valence structure.For such systems we have seen how the molecular- orbital wave function can be expressed in terms of a set of localised equivalent bonding orbitals each such orbital corresponding to a chemical bond or to a lone pair of electrons. I n many more complex molecules it is generally recognised that a single valence structure is insufficient and that the ground state should be represented as a mixture of several structures. This raises the question of what happens to the localised bonding orbitals when such mixing occurs. This can be illustrated by the & electrons of buta-1 3-diene as an example (inset). This molecule is planar and its principal structure has two ethylenic-type double bonds. The correct /y[4 equivalent-orbital description of this structure would be in terms of two localised bonding orbitals where $1 +2 $, and +4 are the Zpn atomic orbitals.The corresponding symmetrical orbitals are obtained by taking the sum and difference of these two Now actual calculations based on a simple model of a hydrocarbon such as this suggest that these molecular orbitals are better approximated by The equivalent orbitals corresponding to these are obtained by applying the reverse transformation and are 290 QUARTERLY REVIEWS Thus it appears that the best equivalent orbitals in this molecule are not completely localised in the two double bonds but are to some extent distri- buted over the whole system. This failure to obtain localisation is the molecular-orbital analogue of resonance between valence structures. Discussion The main result that emerges from the discussions of particular cases is that it has proved possible to give a description of a molecule in terms of equivalent orbitals which are approximately localised but which can be transformed into delocalised molecular orbitals without any change in the value of the total wave function.The equivalent orbitals are closely associated with the interpretation of a chemical bond in the theory for in a saturated molecule the equivalent orbitals are mainly localised about two atoms or correspond to lone-pair electrons. Double and triple bonds in molecules such as ethylene and acetylene are represented as bent single bonds although the rather less localised 0-TC description is equally valid. Another property of these equivalent orbitals is that they include in themselves effects of delocalisation. Such effects are most important in conjugated molecules although they are present in all molecules to a greater or lesser extent. In a highly conjugated system such as benzene only a limited amount of localisation can be achieved by transforming the orbitals. For large molecules the equivalent-orbital analysis is the most con- venient starting point for a molecular-orbital treatment. In a molecule such as a long-chain paraffin it is possible to write approximate equivalent orbitals corresponding to each bond and then to apply a transformation to obtain the delocalised molecular orbitals. Simple assumption about the interaction of neighbouring bonds will then lead to estimates of the relative stability of the various energy levels.g Hall Proc. Roy. Soc. 1951 A 205 541.

ISSN:0009-2681    

DOI:10.1039/QR9571100273

出版商:RSC    

年代:1957

数据来源: RSC