摘要:

CHEMICAL SOCIETY REVIEWS VOLUME 7,1978 0 Copyright 1978 LONDON THE CHEMICAL SOCIETY CONTENTS PAGE THE CONVERSION CYANATEOF AMMONIUM INTO UREA-PA SAGA IN REACTION MECHANISMS.By J. Shorter 1 SILICONIN ORGANIC SYNTHESIS. By E. W. Colvin 15 AND MOLECULAR PHENOMENA.CLATHRATES INCLUSION By D. D. MacNichol, J. J. McKendrick, and D. R. Wilson 65 TIME-CORRELATION AND MOLECULARFUNCTIONS MOTION. By G. Williams 89 INTERACTIONS CRYSTALSNON-BONDED OF ATOMSIN ORGANIC AND MOLECULES. By A. I. Kitaigorodsky 133 CHEMISTRY AND FLAVOUR STRUCTURE QUALITY. By H. Boelens,I MOLECULAR AND ORGANOLEPTIC L. M. van der Linde, D. de Rijke, P. J. de Valois, J. M. van Dort, and H. J. Takken 167 I1 APPLICATIONOF RESEARCH FINDINGS TO THE DEVELOPMENTOF COMMERCIAL By W.Schlegel 177FLAVOURINGS. 111 SAFETY EVALUATIONOF NATURALAND SYNTHETIC FLAVOURINGS. By K. R. BUTTERWORTH 185 ON RESEARCH IN FLAVOURIv THE INFLUENCE OF LEGISLATION CHEMISTRY. By W. H. Nightingale 195 V THEDEVELOPMENT IN POTABLEOF FLAVOUR SPIRITS. By J. S. Swan and S. M. Burtles 201 VI THE INFLUENCE FLAVOURCHEMISTRY ACCEPTANCE.OF ON CONSUMER By R. Swindells 212 TRANSFER ENERGY LINESHAPES.ByC~LLISIONAL OF ROTATIONAL AND SPECTRAL Krishnaji and V. Prakash 219 CONTRIBUTIONS TO CHEMISTRY.OF PULSE RADIOLYSIS By J. H. Baxendale and M. A. J. Rodgers 235 OF DENTALTHE CHEMISTRY CEMENTS.By A. D. Wilson 265 AUTOCATALYSIS.By G. A. M. King 297 REVIEWOF CHEMICAL RESEARCH INEDUCATION AND DEVELOPMENT THE U.K., 1972-1976.By A. H. Johnstone 317 LIVERSIDGE LECTURE. THESURFACEOF A LIQUID. By J. S. Rowlinson 329 MELDRUM’SACID. By Hamish McNab 345 WNDVALENCES-A SIMPLE STRU~~~RAL CHEMISTRY.MODELFOR INORGANIC By I. D. Brown 359 MONOALKYLTRIAZENES.By K. Vaughan and M. F. G. Stevens 377 CH BONDSTRENGTH^ INSIMPLE ORGANIC COMPOUNDS:INDIVIDUAL EFFECTSOF CONFORMATIONSUBSTITUTION. By D. C. McKean 399AND HAWORTH LECTURE. HUMAN BLOOD GROWS AND CARBOHYDRATE CHEMISTRY.By R. U. Lemieux 423 ~0”OPH’YSICsOF MOLECULEIN MICE-FORMING SURFACTANT SOLUTIONS. By K. Kalyanasundaram 453 SYNTHETIC PYRETHROIDS. By M. Elliott and A NEW GROUP OF INSECTICIDES. N. F. Jane 473 MELDOLA MEDAL LECTURES I MOLECULARSHAPES. By J. K.Burdett 507 II Fe(CO),.By M. Poliakoff 527 Chemical Society Reviews Vol 7 No 1 1978 Page The Conversion of Ammonium Cyanate into Urea-a Saga in Reaction Mechanisms By J. Shorter 1 Silicon in Organic Synthesis By E. W. Colvin 15 Clathrates and Molecular Inclusion Phenomena By D. D. MacNicol, J. J. McKendrick, and D. R. Wilson 65 Time-correlation Functions and Molecular Motion By G. Williams 89 Non-bonded Interactions of Atoms in Organic Crystals and Molecules By A. I. Kitaigorodsky 133 Corrigenda 164 The Chemical Society London Chemical Society Reviews Chemical Society Reviews appears quarterly and comprises approximately 25 articles (ca. 500 pp) per annum. It is intended that each review article shall be of interest to chemists in general, and not merely to those with a specialist interest in the subject under review.The articles range over the whole of chemistry and its interfaces with other disciplines. Although the majority of articles are intended to be specially commissioned, the Society is always prepared to consider offers of articles for publication. In such cases a short synopsis, rather than the completed article, should be sub- mitted to The Managing Editor, Books and Reviews Section, The Chemical Society, Burlington House, Piccadilly, London, W 1V OBN. Members of the Chemical Society may subscribe to Chemical Society Reviews at E6.00 per annum; they should place their orders on their Annual Subscrip- tion renewal forms in the usual way. Non-members may order Chemical Society Reviews for E16.00 ($33) per annum (remittance with order) from: The Publications Sales Officer, The Chemical Society, Distribution Centre, Blackhorse Road, Letchworth, Herts., SG6 lHN, England. 0Copyright reserved by The Chemical Society 1978 Published by The Chemical Society, Burlington House, London, W1V OBN Printed in England by Eyre & Spottiswoode Ltd, Thanet Press, Margate

ISSN:0306-0012    

DOI:10.1039/CS97807FP001

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Silicon in Organic Synthesis By E. W. Colvin CHEMISTRY DEPARTMENT, UNIVERSITY OF GLASGOW, GLASGOW, GI2 SQQ 1 Introduction The explosive growth of organosilicon chemistry over the past decade has created a growing awareness of its considerable synthetic utility to the organic chemist. It is the purpose of this review to demonstrate that such utility is, if anything, under-estimated ; in scope, it discusses the use of silyl-substituted reagents and substrates to activate the substrate to reaction, to direct the course of reaction, or to protect the substrate from unwanted reaction, emphasis being placed on those sequences where silicon is absent in the final product. Other sources recommended for consultation are an on-going annual survey,l a new series,2 and a short review;3 other reviews4 and monographs,5 while less timely, are of considerable value.Applications of silylation as derivatization to confer g.1.c. volatility or characterizable mass spectral fragmentation have been adequately reviewed elsewhere.6 2 Atomic Properties Silicon has the outer electronic configuration 3s23p23d0, differing from carbon in its possession of vacant d-orbitals, which can be used to expand the valency, as in SiFe2-, or to allow back-bonding. The 3p orbitals are of too high an energy to give adequate .rr-overlap with 2p orbitals, so sila-ethanes such as (1)7 are very unstable,8 and stable compounds with silicon-oxygen n-bonds are vnknown. S. S. Washburne, J. Organometallic Chem., 1974, 83, 155; 1976, 123, I.‘New Applications of Organometallic Reagents in Organic Synthesis., ed. D. Seyferth, J.Organometallic Chem. Library, Vol. 1 and 2, Elsevier, Amsterdam, 1976; see, in particular, P. F. Hudrlik, Vol. 1, p. 127; see also Vol. 4, 1977. I. Fleming, Chem. and Ind., 1975, 449. J. F. Klebe, Adv. Org. Chem., 1972,8,97; Account., Chem. Res., 1970,3,299;(b)L. Birkofer and A. Ritter in ‘Newer Methods in Preparative Organic Chemistry’, ed. W. Foerst, Academic Press, New York, 1968, Vol. 5, p. 21 I. C. Eaborn, ‘Orgsnosilicon Compounds’, Butterworths, London, 1960. A. E. Pierce, ‘Silylation of Organic Compounds’, Pierce Chemical Ca., Rockford, Illinois, 1968; G. D. Brittain and J. E. Sullivan in ‘Recent Advances in Gas Chromatography’, ed.I. I. Domsky and J. A. Perry, Marcel Dckker, New York, 1971. 0. L. Chapman, C.-C. Chang, J. Kolc, M. E. Jung, J. A. Lowe, T. J. Barton, and M. L. Tumey, J. Amer. Chem. SOC., 1976,98,7844; M. R. Chedekel, M. Skoglund, R. L. Kreeger, and H. Schechter, ibid., p. 7486. * R. E. Ballard and P. J. Wheatley, ref. 2, Vol. 2, p. 1; L. E. Gusel’nikov, N. S. Nametkin, and V. M. Vdovin, Accounts Chem. Rcs., 1975, 8, 18; N. Wiberg and G. Preiner, Angew. Chem. Internat. Edn., 1977, 16, 328; T. J. Barton and D. Banasiak, J. Amer. Chem. SOC., 1977, 99, 5199, describe the generation and trapping of a silabenzene. Silicon in Organic Synthesis Table 1 Some values of bond energieslkJ mol-1 Si-F Si-0 540-570 370-450 C-F c-0 440-465 350-360 Si-C 230-320 c-c 347 Si-H 290-320 C-H 414 Organic compounds of silicon are normally quadricovalent, the stereochemistry and mechanism of reactions at the silicon atom having been clearly expounded.9~ Silicon’s utility in organic synthesis derives from three main factors, as listed below.A. Relative Bond Strengths.-From Table 1,loit can be seen that, whereas silicon’s bonds to oxygen and fluorine are stronger than the bonds between carbon and these elements, its bonds to carbon and hydrogen are weaker. Such character- istics give rise to a wide range of thermodynamically favourable processes. B. Vacant d-Orbitals.-These orbitalsgb are of suitable energy for back-bonding with a filled 29 orbital on an adjacent atom of a first-row element, enabling silicon to stabilize, for example, an adjacent carbanion.They can also be involved in substitution reactions at silicon9 or at an adjacent atom.5 C. Relative E1ectronegativity.-Silicon has a Pauling electronegativity of I .8, and carbon a value of 2.5, making silicon-carbon bonds polarized (2), and therefore susceptible to nucleophilic attack at silicon. This leads to bond hetero- lysis, especially when the carbon fragment being expelled is a good leaving group, as exemplified in Scheme 1 ;silyl ethers behave similarly. (a)L. H. Sommer, ‘Stereochemistry, Mechanism and Silicon’, McGraw-Hill, New York, 1965; (6) H. Kwart and K. King, ‘&Orbital Involvement in the Organo-chemistry of Silicon, Phosphorus, and Sulphur’, ‘Reactivity and Structure’, ‘Concepts in Organic Chem- istry’, Springer Verlag, Berlin, 1977; see also M.E. Childs and W. P. Weber, J. Org. Chem., 1976, 41, 1799. lo L. Pauling, ‘The Nature of the Chemical Bond’, Cornell University Press, ithaca, New York, 1960, pp. 85-86; T. Cottrell, ‘The Strengths of Chemical Bonds’, Butterworths, London, 1958, pp. 270-280; see also E. A. V. Ebsworth, in ‘Organometallic Compounds of the Group iV Elements’, ed. A. G. MacDiarmid, Marcel Dekker, New York, 1968, Vol. 1, Part 1. 16 Colvin 6r 6-Si-C 0% 0-fNu : f4 H-Nu:-Si-O-R -HO-R Scheme 1 A further, profound, property is the ability of a silicon-carbon bond to stabilize an adjacent carbonium ion (3); this phenomenon can perhaps be compared with the hyperconjugative situation in (4).Si H\‘C C I IC+ C Manifestations of all the above properties will be illustrated in the succeeding reactions, which have been classified either by reaction type or by reagent type, an unavoidable but comprehensible ambiguity. 3 Directing/Stabilizing Effects of Silicon Substituents A. Carbonium Ions.-The electropositive nature of silicon results in the observ- able capacity of a carbon-silicon bond to stabilize a carbonium ion p to it,11 either by bridgingl29l3 or by hyperconjugation.l4 An elegant demonstration of bridging was reported by Eabornl2 and Jarvie;13 re-isolation of starting material from the partial solvolysis of 2-bromo-2,2-dideuterio-l-trimethyl-silylethane (5) yielded material in which the deuterium had been extensively scrambled between C-1 and C-2, consistent with a mechanism involving an l1 A. W.P. Jarvie, Organometallic Chem. Rev. (A), 1970, 6, 153. M. A. Cooke, C. Eaborn, and D. R. M. Walton, J. Organometallic Chem., 1970, 24, 301. l3 A. J. Bourne and A. W. P. Jarvie, J. Organometallic Chem., 1970, 24, 335. l4 T. G.Traylor, W. Hanstein, H. J. Berwin, N. A. Clinton, and R. S. Braun, J. Amer. Chem. SOC.,1971, 93, 5715. Silicon in Organic Synthesis anchimerically assisted ionization of the C-Br bond to give a silacyclopropen- ium ion (6) (Scheme 2). There also exists evidence that cations ct to silicon are destabilized.'j Ab initio SCF MO calculations on silyl-substituted alkanes, alkyl radicals, and carbonium ions show that the carbonium ion is destabilized by an ct-silyl group and stabilized by a 13-silyl group by comparison with the carbon analogues.These results are consistent with observations on the rates of SN~solvolysis of silylmethyl halides (Scheme 2). R,SiCH,CH,X s\ 1 +faster than analogous C compound R,SiC H ,X s\ 1---+- slower than analogous C compound Scheme 2 (i) Silyl-arenes. Such stabilization has been studied extensively in the aromatic Theserie~.l~,~~Hammett electrophilic para-substitution constant for the Me3SiCH2 group is -0.66.16 This closely approximates to the value for the Me0 grol.jp, viz. -0.74, implying that in general terms a Me3Si group p to a carbonium ion stabilizes that ion to about the same extent as does a Me0 group u to it.This has been put to practical use: under normal conditions of electrophilic aromatic substitution, such substitution on silyl-arenes will take place at the site of the silyl gro~p,~~,~~ even when the other ring substituents do not favour such regiospecificity20*21 (Scheme 3); one is of course, faced with the not inconsiderable initial problem of preparing the silyl-arenes. (ii) Vinyl-silanes. Similarly, the orientation of electrophilic attack on alkenes can be controlled by the introduction of a silyl substituent, as can (in appropriate cases) the stereochemistry. An example can be seen in the ability of vinyl- l5 C. Eaborn, F. Feichtmayr, M. Horn, and J. R. Murrell, J. Organometalfic Chem., 1974, 77, 39.l6 W. Hanstein, H. J. Berwin, and T. G. Traylor, J. Amer. Chem. SOC.,1970, 92, 829, 7476. l7 C. Eaborn and K. C. Pande, J. Chem. SOC.,1960, 1566. C. Eaborn, A. A. Najam, and D. R. M. Walton, J.C.S. Perkin I, 1972, 2481. la J. B. F. Lloyd and P. A. Ongley, Tetrahedron, 1964, 20, 2185. *O V. Chvalovski and V. Baiant, Coll. Czech. Chem. Comm., 1951, 16,580. a1 T. Hashimodo, J. Pharm. SOC.Japan, 1967, 87, 528; G. Felix, J. Dunogues, F. Pisciotti, and R. Calas, Angew. Chem. Internat. Edn., 1977, 16, 488. Colvin CO,H CO,H Scheme 3 silanes to transfer the vinyl group to acid chlorides (Scheme 4)in an attractive synthesis22 of $-unsaturated ketones. 0 Scheme 4 The stereospecific synthesis of both isomers of vinyl-silanes has stimulated much activity, most existing method~logies~~ starting with alkynes; a recent route from ketones involves electrophilic trapping of vinyl anions (Scheme 5).24 r 1 L J Reagents: i, BunLi; ii, Me,SiCl Scheme 5 23 J.-P.Pillot, J. Dunogues, and R. Calas, Compt. rend., 1974, 278, C, 787, 789; Bull. SOC. cliirn. France, 1975, 2143; I. Fleming and A. Pearce, I.C.S. Chem. Comm., 1975, 633; for a related use of cyclopropylsilanes, see M. Grignon-Dubois, J. Dunogues, and R. Calas, Synthesis, 1976, 737. 23 C. Eaborn and R. W. Bott in ‘Organometallic Compounds of the Group IV Elements’, ed. A. G. MacDiarmid, Marcel Dekker, New York, 1968, Vol. 1, Part 1; J. J. Eisch and G. A. Damasevitz, J. Org. Chem., 1976, 41, 2214; K. Uchida, K. Utimoto, and H.Nozaki, ibid., pp. 2215, 2941; R. Koster and L. A. Hagelee, Synthesis, 1976, 118. For different approaches, see K. Sachdev, Tetrahedron Letters, 1976, 4041 ;H. Westmijze, J. Meijer, and P. Vermeer, ibid., 1977, 1823; M. Obayashi, K. Utimoto, and H. Nozaki, ibid., p. 1805. 2p T. H. Chan, A. Baldassarre, and D. Massuda, Synthesis, 1976, 801; R. T. Taylor, C. R. Degenhardt, W. P. Melega, and L. A. Paquette, Tetrahedron Letters, 1977, 159; see also R. H. Shapiro, Org. Reactions, 1976, 23, 405. Silicon in Organic Synthesis The powerful directing effect of silicon in such systems can be seen in the stereospecific reactions shown in Scheme 6. The mechanism proposed25 is that, simultaneously with attack of the electrophile on the double bond, rotation occurs about the developing C-C single bond in such a direction as to permit the C-Si bond to stabilize the benzylic carbonium-ion centre continuously; rotation in the opposite direction would bring the C-Si bond into the nodal plane of the developing ion, and so preclude such continuity.1'H H E Ph SiMe, H H + PhXE L J H E+ and Ph &IMe3 H H --PhPhHXE Scheme 6 This concept has been shown to be generally applicable,26 mono-and di-substituted vinyl-silanes undergoing electrophile-induced desilylation with strict retention of configuration, and its utility has been extended by Chan,27 by developing simple stereospecific routes to disubstituted vinyl-silanes (Scheme 7). Interestingly, the treatment of vinyl-silanes with molar equivalents of chlorine or bromine results in apparent tram-addition.The resulting dihalides, on anti-periplanar elimination of the elements of trimethylsilyl halide, yield vinyl halides of opposite sterochemistry28 (Scheme 8); iodination results in either 25 K. E. Koenig and W. P. Weber, Tetrahedron Letters, 1973, 2533. 26 K. Utimoto, M. Kitai, and H. Nozaki, Tetrahedron Letters, 1975, 2825. 37 T. H. Chan, W. Mychajlowskij, R. S. Ong, and D. N. Harpp, J. Organometallic Chern., 1976, 107, C1; W. Mychajlowskij and T.H. Chan, Tetrahedron Letters, 1976, 4439; for n.m.r. and g.c. differentiation of geometric isomers of vinylsilanes see T. H. Chan, W. Mychajlowskij, and R. Amoroux, Tetrahedron Letters, 1977, 1605.28 R. B. Miller and T. Reichenbach, Tetrahedron Letters, 1974, 543. 20 Colvin H CH,CI H CH,R2 Me,Si Lih1 SiMe:, OH SiMe, ~ R X W H H SiMe, OAc Reagents: i, R’CHO; ii, SOCl,; iii, LiCuRa, or R2,CuMgBr Scheme 7 retention or inversion, as shown. Finally, HBr in pentane, which adds sluggishly to terminal alkynes, giving meagre yields of 2-bromoalk-1 -enes, reacts smoothly29 with trimethylsilyl-alkynes to give the desired bromides in high yield (Scheme 8). I. II iii-vRC-CH RC-CSiMe, -Rw”i””H H SiMe, RHR 1RHL xxxR\ HXHHHI Reagents: i, EtMgBr; ii, Me,SiCl; iii, (C,H,,),BH; iv, Ac,O-heat; v, NaOH-H,O,; vi, C1, or Br,; vii, NaOMe; viii, I,; ix, I,-CF,CO,Ag; x, KF-DMSO-H20; xi, HBr Scheme 8 (iii) Allyl-silanes.Allyl-silanes, as homologues of vinyl-silanes, undergo similarly controlled regiospecific electrophilic attack, the electrophile bonding to the y-carbon atom, which results in a net shift of position of the double bond3O (Scheme 9). R. K. Boeckman and D. M. Blum, J. Org. Chem., 1974, 39, 3307. 30 R. Calas and E. Frainnet, Compt. rend., 1955, 240, 203; 1956, 243, 595. 21 Silicon in Organic Synthesis Vinyl-silanes E+4ASiMe, +ASiMe, Allyl-silanes r 1 Scheme 9 The allyl-silane (7) has been converted into the aglucone ethanoate (8)3l of loganin, and, by a separate series of transformations, into the prostaglandin intermediate (9)32 (Scheme 10).A related study33 of the synthetic utility of l-trimethylsilylbuta-1,3-diene(10) as a Diels-Alder dienophile has been reported.An example of the powerful directing effect of silicon in such systems can be seen in a preparation of synthetically versatile allyl sulphides by acid-catalysed rearrangement of the more accessible /Lhydroxyalkyl phenyl sulphides, when, with silicon's assistance, migration from a secondary to a tertiary cationic site is observeds4 (Scheme 1 1). Similarly, the allyl-silane (1 1) gives solely35 the alkene (13),in contrast to (12), which gives a gross mixture of alkene isomers (Scheme 11); predictably, the rearrangement is faster with the silylated substrate. As with vinyl-silanes, allyl-silanes can be induced to transfer the allyl group to suitable electrophiles,36937 leading, in one case,38 to a ready synthesis of artemesia ketone (14)(Scheme 12).Allyl-silanes react regiospecifically with chlorosulphonyl isocyanate to give intermediate p-lactams, which rearrange thermally to lactim ethers (1 5) ; such species can be hydrolysed to acids,31 or, by treatment with ~yridine,~~ converted into nitriles (Scheme 13). To summarize, the two modes of interaction of a carbon-silicon bond with a 31 B.-W. Au-Yeung and I. Fleming, J.C.S. Chern. Cornm., 1977, 81. 31 B.-W. Au-Yeung and I. Fleming, J.C.S. Chern. Cornrn., 1977, 79. 33 M. J. Carter and I. Fleming, J.C.S. Chern. Cornrn., 1976, 679; I. Fleming and A. Percival, ibid., p. 681. 34 P. Brownbridge, 1. Fleming, A. Pearce, and S. Warren,J.C.S. Chern. Conrrn., 1976, 751 and references therein; P.Brownbridge and S. Warren, J.C.S. Perkin I, 1977, I 13 I. 36 I. Fleming, A. Pearce, and R. L. Snowden, J.C.S. Chern. Cornrn., 1976, 182. 36 A. Hosomi and H. Sakurai, Tetrahedron Letters, 1976, 1295; for conjugate addition to enones, see J. Arner. Chern. SOC.,1977, 99, 1673. 37 I. Ojima, Y. Miyazawa, and M. Kumagai,J.C.S. Chern. Cornni., 1976, 927; for more highly functionalized allylsilanes, see I. Ojima, M. Kumagai, and Y. Miyazawa, Tetralietlrotz Letters, 1977, 1385; K. Itoh, M. Fukui, and Y. Kurachi, J.C.S. Chenz. Cumin., 1977, 500. 38 J.-P. Pillot, J. Dunogues, and R. Calas, Tetrahedron Letters, 1976, 1871 ;see also G. Deleris, J. Dunogues, and R. Calas, ibid., p. 2449. 3@ G. Deleris, J. Dunogues, and R. Calas, J.Organornetallic Chern., 1976, 116, C45. Colvin Me H&-OH*# /MeOK SiMe, (7) MeO 0 0 -0Eg + Q -% '03+ (J:>o I0 0SiMe, 0 SiMe, (10) Scheme 10 5 products OMe (1 1) R = SiMe, (12) R = H OMe Scheme 11 (13) Silicon in Organic Synthesis R p.,ocl (14) Reagents: i, TiCl,; ii, Mg-Et,O; iii, Me3SiC1; iv, and AlCI3 Scheme 12 SiMe, 0 S0,CI (15) Reagents: i, CISOzNCO; ii, pyridine Scheme 13 cationic centre can be represented as shown in Scheme 9. In subsequent sections, more examples of such behaviour will be illustrated. B. Carbaniom-(p-d)n-Back-bonding between silicon and carbon, and con- sequent electron withdrawal from carbon, is sufficiently strong in many cases to stabilize an a-silyl carbanion.Using strong base, a proton can be removed from even tetramethyl~i.lane.4~ In most cases, however, the carbanion is also flanked by another electron-withdrawing group; in addition, the reaction partner is normally a carbonyl compound, and the final product is an alkene: these reactions are discussed in Section 4. Two reactions do not fall into this general class. The regiospecific addition of vinyl ketones to enolate anions (kinetically generated under aprotic con- ditions) is not normally practicable, owing to extensive polymerization of vinyl ketones under such conditions and relatively rapid proton transfer, resulting in 40 D. J. Peterson, J. Organonietallic Chem., 1967, 9, 373. Colvin loss of enolate regiospecificity.The silylated methyl vinyl ketone (16) successfully traps41 even readily equilibrated enolate anions (Scheme 14), with the inter- mediacy of the relatively stable, and hence non-basic, anion (17); the silyl group in the product, being now a-ketonic, is readily displaced by nucleophiles. SiEt, 0 SiEt, Reagents: i, Li-NH,-ButOH (1 equiv.); ii, Me,SiCl, then isolation; iii. LiMe; iv, NH,CI- H,O; v, NaOMe-MeOH. Scheme 14 Phenylselenomethyltrimethylsilane (1 8) furnishes a carbanion which reacts42 smoothly with primary alkyl bromides and iodides. The alkylated products, after treatment with hydrogen peroxide, did not produce vinyl-silanes by selen- oxide elimination, but did afford the homologous aldehydes directly (Scheme 15) (see Section 5).Extension to provide a general acyl carbanion equivalent should be possible. Reagents: i, LiNPr,'-THF, at -78°C; ii, RCH,X; iii, 30% H,O, Scheme 15 41 (a) G. Stork and B. Ganem, J. Amer. Chem. Soc., 1973, 95, 6152; (b) R. K. Boeckman, ibid., p. 6867; J. Org. Chem., 1973, 38, 4450; J. Arner. Chem. SOC.,1974, 96, 6179; (c) G. Stork and J. Singh, ibid., p. 6181; for a related process with a-silyl propenoate esters, see S. L. Hartzell and M. W. Rathke, Tetrahedron Letters, 1976, 2737. 4a K. Sachdev and H. S. Sachdev, Tetrahedron Letters, 1976, 4223; see also H. J. Reich and S. K. Shah, J. Org. Chem., 1977, 42, 1773. Silicon in Organic Synthesis 4 P-Hydroxy-silanes as Alkene Precursors In most examples of processes involving or-silyl carbanionoids, the reaction partner is a carbonyl compound, and the p-hydroxy-silane thus formed can be converted into an alkene by thermodynamically favourable p-elimination of trimethylsilanol or its equivalent. The classic example of this process, which is analogous to the Wittig reaction and often superior to it, especially for the introduction of exomethylene units,43 is known as Peterson olefination44 (Scheme 16).+ Me,SiO M Scheme 16 The factors influencing the ease and stereochemical requirements of this elimination have been delineated by several groups. It has been observed that lithium and magfiesium salts of P-hydroxy-silanes undergo elimination more readily44 when the resulting alkene is non-terminal than when it is terminal.Treatment of P-hydroxy-silanes with ethanoyl chloride or thionyl chloride45 is effective in promoting elimination. In a of the stereochemistry of silanol elimination, the silane (19) (of unknown relative configuration, but diastereoisomerically almost pure) gave almost exclusively E-alkene, the expected product of syn-elimination from the threo-form, when treated with potassium hydride (Scheme 17). Boron trifluoride etherate, on the other hand, gave 2-alkene, the expected product of anti-elim-ination. These different elimination pathways reflect the requirement, in the former case, for syn-elimination to occur in order that an Si-0 bond might Pr L >I e,,Si OH / -\ H->-<-pr Pr ------A Pr Pr Pr H \=c/ (19) Reagents: i, KH; ii, BF,, Et,O Scheme 17 43 R.K. Boeckman and S. M. Silver, Tetrahedron Letters, 1973, 3497. 44 D. J. Peterson, J. Org. Chem., 1968,33,780; see also F. A. Carey and J. R. Toler, ibid., 1976, 41, 1966. 45 T. H. Chan and E. Chang J. Org. Chem., 1974, 39, 3264. 46 P. F. Hudrlik and D. Peterson, J. Amer. Chem. SOC.,1975, 97, 1464. 26 Colvin be formed; in the latter case, an Si-F bond is formed, and the usual stereoeiectronic factors determine the geometry of elimination. This same general process can be used for the stereoselective production of trisubstituted alkenes,47 or, by reaction with an aldehyde, 1,2-disubstituted alkenes. The requisite reagents are generated as Grignard by direct lithiation of a suitably substituted silane or addition of an alkyl-lithium to a vinyl-~ilane,~~or by cleavage of an a-silylmethyl selenide ;49 if the epoxy-silane (20) is readily available (see Section 5), it undergoes a regiospecific ring opening on treatment50 with lithium dialkylcuprates, once again producing alkenes (Scheme 18).R',SiCH,Cl -!-+ R',SiCH,MgCl R1,SiCH,Ar -!& R1,SiCHAr I Li R',Si iii ~ Li II R',SiCHSeR4 R',SiCHR3 I I R3 Li 0-M-Reagents: i, Mg; ii, BunLi; iii, R2Li; iv, R6COR7; v, LiCuRS, Scheme 18 47 K. Utimoto, M. Obayashi, and H. Nozaki, J. Org. Chem., 1976, 41, 2940. T. H. Chan, E. Chang, and E. Vinokur, Tetrahedron Letters, 1970, 1137; T. H. Chan and E. Chang, J. Org. Chein., 1974, 39, 3264; for the original observation, see L.F. Cason and H. G. Brooks, rhicl., 1954, 19, 1278; see also P. R. Jones and T. F. 0. Lim, J. Amer. Chem. SOC.,1977, 99, 2013. J9 W. Dumont and A. Krief, Angew. Chein. Internat. Edn., 1976, 15, 161. 5u P. F. Hudrlik, D. Peterson, and R. J. Rona, J. Org. Chem., 1975, 40, 2263. 27 Silicon in Organic Synthesis The analogous direct conversion of aldehydes or ketones into homologated @-unsaturated esters (Scheme 19) has been de~cribed.~la~~ Reagent: i, R2COR3 Scheme 19 Trimethylsilylpotassium smoothly converts oxirans into alkenes, nucleo-philic ring opening being followed by spontaneous /?-elimination; this provides an excellent alternative53 to the earlier Wittig-based methodsS4 of geometric isomerization of alkenes (Scheme 20).r 0-1 Reagents: i, Me,SiSiMe,-KOMe-HMPA Scheme 20 The silicon- and phosphorus-substituted diazomethanes (21) and (22), as their metal salts, convert55 some ketones and aldehydes into homologous alkynes (Scheme 21); evidence has been presented in the phosphorus case, and (by implication) in the silicon analogue also; this implies that there is initial elimination to give a diazovinyl species, which then undergoes skeletal rearrange- ment. 51 K. Shimoji, H. Taguchi, K. Oshima, H. Yamamoto, and H. Nozaki, J. Amer. Chem. SOC., 1974, 96, 1620; H. Taguchi, K. Shimoji, H. Yamamoto, and H. Nozaki, Bull. Chem. SOC. Japan, 1974, 47, 2529. 52 S. L. Hartzell, D. F. Sullivan, and M. W. Rathke, Tetrahedron Letters, 1974, 1403; for a/?-unsaturated thiol esters, see D. H.Lucast and J. Wemple, ibid., 1977, 1103; for $3-un-saturated acids see P. A. Grieco, C.-L. J. Wang, and J. S. Burke, J.C.S. Chem. Comm., 1975, 537. 53 P. B. Dervan and M. A. Shippey, J. Amer. Chem. SOC.,1976, 98, 1265; for the analogous use of PhMe,SiLi, see M. T. Reetz and M. Plachky, Sj'nthesis, 1976, 199; for other func- tional silyl anions, see W. C. Still, J. Org. Chem., 1976,41, 3063; H. Watanabe, K. Higuchi, M. Kobayashi, M. Hara, Y. Koike, T. Kitahara, and Y. Nagai, J.C.S. Chem. Comm., 1977, 534. 54 E. Vedejs and P. L. Fuchs, J. Amer. Chem. SOC.,1973, 95, 822; A. J. Bridges and G. H. Whitham, J.C.S. Chem. Comm., 1974, 142; see also P. E. Sonnet and J. E. Oliver, J. Org. Chem., 1976, 41, 3279.56 E. W. Colvin and B. J. Hamill, J.C.S. Perkin I, 1977, 869; see also ref. 64c 28 Colvin Me,SiCN '1 I M R1CECR2i-.-.i-//+ N2 Scheme 21 A final example of the mechanistic parallel between silicon and phosphorus involves the silylated dithian anion (23), which, like the phosphorus analogue (24), converts56 carbonyl compounds into synthetically useful keten thioacetals (Scheme 22); whereas the use of the ylide (24) is restricted to aldehydes, the lithio-salt (23) can be applied generally. Vinyl sulphoxides are obtainable57 using the metallated species (25); the value of this method is reduced somewhat by the difficulty experienced in preparing (25). The reaction of 1-triphenylsilylvinyl-lithium with aldehydes leads to allenes5* (Scheme 23); in such cases, silanoxide elimination does not occur readily, and fluoride ion is used to displace the silyl moiety.It seems, however, that this reaction cannot be extended to ketones to produce 1,1-disubstituted allenes; in such cases, elimination does not occur, although the silyl group is lost.59 Symmetrical allenes6O are formed by the reaction of the phosphorane (26) with aryl ketones; alkenes are formed simultaneously, by displacement of a silyl group from the phosphorane followed by a normal Wittig reaction (Scheme 24); variation of the ylide and/or the ketone leads to a range of products. 56 F. A. Carey and A. S. Court, J. Org. Chem., 1972,37, 1926; P. F. Jones and M. F. Lappert, J.C.S. Chem. Comm., 1972, 526; D.Seebach, B.-Th. Grobel, A. K. Beck, M. Braun, and K.-H. Geiss, Angew. Chem. Internat. Edn., 1972, 11, 443; D. Seebach, M. Kolb, and B.-Th. Grobel, Tetrahedron Letters, 1974, 3171 ; B.-Th. Grobel, R. Burstinghaus, and D. Seebach, Synthesis, 1976, 121. 57 F. A. Carey and 0. Hernandez, J. Org. Chem., 1973, 38, 2670; see also F. A. Carey and A. S. Court, ibid., 1972, 37, 939, and ref. 44. 58 T. H. Chan and W. Mychajlowskij, Tetrahedron Letters, 1974, 171. 59 T. H. Chan and W. Mychajlowskij, Tetrahedron Letters, 1974, 3479. 8o H. Schmidbaur and H. Stuhler, Angew. Chem. Internat. Edn., 1973,12, 321 ; H. Schmidbaur, Accounts Chem. Res., 1975, 8, 62. 29 Silicon in Organic Synthesis 0 ?n nsysMe3Si Li LiPhsYSiMe3 (MeO),P+ (25) R' R' R' )--CHO )-co,H R+HO R? R? R3 Reagents: i, R1COR2;ii, Et,SiH-CF3C0,H; iii, HgII; iv, R3Li Scheme 22 Ph,Si Li>-+ SiMe, Me,Si Lib=+ Reagents: i, KF-DMSO Scheme 23 The treatment of a variety of ketones with trimethylsilyl chloride and zinc produces alkenes (Scheme 25);this deoxygenation may be related to the Peterson reaction, but the available evidence61 favours a carbenoid pathway.5 Vinyl-silanes and ap-Epoxy-silanes Vinyl-silanes are readily converted into ap-epoxy-silanes, which, by acid-catalysed nucleophilic displacement of the silyl group, efficiently give carbonyl 61 W. B. Motherwell, J.C.S. Chem. Comm., 1973, 935. Colvin Ph,: -c H Si M e3 \ OHI-Ph,C-C-Si Me,I +PPh, Ph,C =CH, Ph Ph Ph \ / I \C=C-;Ph, -Ph/ Reagent: i, PhCOPh Scheme 24 Reagents: i, Zn-Me,SiCI Scheme 25 compounds.62 This synthetic equivalence has found use in several general routes to carbonyl compounds, utilizing cc-lithio-vinyl-silanes,63 cc-lithio-disilylmethanes,wa or-chloro-cc-trimethylsilyl ~arbanions,6*~and cc-lithio-ap-epoxy-silanes65 (Scheme 26).Route@ to p-lithio-vinyl silanes have been devel- oped, adding further scope to this process. It has also been applied in a regio- specific alternative to the Robinson annelation sequence, using ally1 halides67 such as (27); interestingly, displacement of the silyl group in such cases is easier than in simple ccp-epoxy-silanes, possibly owing to participation by the neighbouring carbonyl group (Scheme 27).Similarly, the silyl vinylcuprate (28) effects conjugate addition68 of an ethanoyl anion equivalent. 62 G. Stork and E. Colvin, J. Amer. Chem. Soc., 1971, 93, 2080. 63 B.-Th. Grobel and D. Seebach, Angew. Chem. Internat. Edn., 1974, 13, 83; Chem. Ber., 1977, 110, 852, 867; see also K. Sachdev, Tetrahedron Letters, 1976, 4041. 64 (a)H. Sakurai, K. Nishiwaka, and M. Kira, Tetrahedron Letters, 1973,4193; (b)C. Burford, F. Cooke, E. Ehlinger, and P. Magnus, J. Amer. Chem. SOC.,1977,99,4536; F. Cooke and P. Magnus, J.C.S. Chem. Comm., 1977, 513; (c) see also U. Schollkopf and H.-U. Scholz, Synthesis, 1976, 271. 65 J. J. Eisch and J. E. Galle, J. Amer. Chem. SOC.,1976, 98, 4646. 66 R. F. Cunico and F. J. Clayton, J. Org. Chem., 1976, 41, 1480. 67 G.Stork and M. E. Jung, J. Amer. Chem. SOC.,1974, 96, 3682; G. Stork, M. E. Jung, E. Colvin, and Y. Noel, ibid., p. 3684. 68 R. K. Boeckman and K. J. Bruza, Tetrahedron Letters, 1974, 3365. 7 31 Silicon in Organic Synthesis H0NiMe3 Me3Si SiMe, (Me,Si),CLi R3 Ph,Si PLi I* I ii-iv R' Me3SiCHCI Li Me3Si vi vii ix1 1 1 Li R3 Me3Si Me,SiCCII Ph3Siyo\I MePHR2 Rl ii Me,Si R Vlll R' Reagents: i, H+ Nu-; ii, CH,O; iii, Br,; iv, ButLi; v, RX; vi, RTHO; vii, BusLi; viii, R4COR5;ix, Me1 Scheme 26 Me3sy ---;a-Me& fJJ-0 + I (27) Scheme 27 (Me3Si CuLi Colvin ap-Epoxy-silanes undergo electrophile-catalysed ring opening to give products of predominant cc-~leavage.699~0 This result is, at first sight, rather unexpected, as, although a fully developed carbonium ion may not be involved in such an opening, one would still expect P-cleavage to predominate, in view of the well- documented stability of cations ,8 to silicon (see Section 3).However, the relative orientations of the C-Si and the P C-0 bonds deviate markedly from the coplanar alignment favourable for stabilization of a developing positive charge by the C-Si bond. Indeed, the preference for cc-opening in these reactions suggests that the silyl group may actually facilitate71 bimolecular nucleophilic displace- ments a to silicon. In contrast, /!$+epoxy-silanes have no such geometric con- straint, and are not only more labile, but open by exclusive P-clea~age,~~ via a developing p carbonium ion.It would therefore appear that the conversion of ccP-epoxy-silanes into carbonyl compounds proceeds by initial solvolysis to ap-dihydroxy-silanes, followed by acid-catalysed elimination; isolation73 of the glycol (29) lends credence to this postulate, as here the trimethylsilyl groups and hydroxy-groups cannot fulfil the preferred arrti-periplanar geometry for acid-catalysed elimination (Scheme 28). Such stability to acid suggestsi4 that the standard hydrolysis conditions can be used only for those cases leading to acyclic carbonyl compounds; in principle, base-induced elimination, with its different stereochemical requirement, could be used for cyclic cases. ccp-Epoxy-silanes undergo thermolysis75.76 to the iso- meric silyl enol ethers; this route is unlikely to compete with the more standard methods for such compounds (see Section 7).Simple ap-epoxy-silanes undergo77 desilylation on treatment with fluoride ion (Scheme 29) with retent ion of stereochemistry. Chloromethyl ap-epoxy- silanes such as (30), on the other hand, give allene oxides as products of elimina-tion;i8 this provides a reliable and easy entry into the allene oxide-oxyallyl zwitterion-cyclopropanone set of valence-bond tautomers, and has recently resulted in the isolation79 of t-butylallene oxide (Scheme 29). 68 P. F. Hudrlik, R. N. Misra, G. P. Withers, A. M. Hudrlik, R. J. Rona, and J. P. Arcoleo, Tetrahedron Letters, 1976, 1453; see also ref. 50; for an application see M.Obayashi, K. Utimoto, and H. Nozaki, ibid., 1977, 1807. 70 5. J. Eisch and J. T. Trainor, J. Org. Chem., 1963, 28, 2870; J. J. Eisch and J. E. Galle, ibid., 1976, 41, 2615. 71 C. Eaborn and J. C. Jeffrey, J. Chem. Soc., 1954, 4266. 72 P. F. Hudrlik and G. P. Withers, Tetrahedron Letters, 1976, 29. 73 C. M. Robbins and G. H. Whitham, J.C.S. Chem. Comm., 1976,697. 74 P. F. Hudrlik, J. P. Arcoleo, R. H. Schwartz, R. N. Misra, and R. J. Rona, Tetrahedron Letters, 1977, 591 ; for an application to produce heteroatom-substituted alkenes, see P. F. Hudrlik, A. M. Hudrlik, R. J. Rona, R. N. Misra, and G. P. Withers, J. Amer. Chem. Soc., 1977, 99, 1993. 76 P. F. Hudrlik, C.-N. Wan, and G. P. Withers, Tetrahedron Letters, 1976, 1449.76 A. R. Bassingdale, A. G. Brook, P. Chen, and J. Lennon, J. Organometallic Chem., 1975, 94, c21. 77 T. H. Chan, P. W. K. Lau, and M. P. Li, Tetrahedron Letters, 1976, 2667. 78 T. H. Chan, M. P. Li, W. Mychajlowskij, and D. N. Harpp, Tetrahedron Letters, 1974, 351 1. 79 T. H. Chan, B. S. Ong, and W. Mychajlowskij, Tetrahedron Letters, 1976, 3253; B. S. Ong and T. H. Chan, ibid., p. 3257. Silicon in Organic Synthesis H /O$iM', I + f J x-SiMe, H,O+ Si Me, OH (29)Scheme 28 (30)Reagent: i, F-Scheme 29 Dihalogenocarbene addition to vinyl-silanes, followed by fluoride-ion-induced desilylation, similarly gives entry into strained halogenocyclopropenes80 and the transient preparation of a bicyclo[2,2,2]oct-l -ene.81 6 Protection of Functional Groups This section will concentrate on the protection afforded to various functional groups by their conversion into silyl derivatives, considerable emphasis being T.H. Chan and D. Massuda, Tetrahedron Letters, 1975, 3383. T. H. Chan and D. Massuda, J. Amer. Chem. SOC.,1977, 99,936. Colvin placed on cases where the silyl group modifies, in a positive sense, the reactivity of the parent functional group. Specifically excluded are references to silylation as a derivatization procedure for chromatography or mass spectrometry, both fields being adequately covered else~here.~96 A. Protection of Alcohols.-The protection of hydroxy-groups as their trimethyl- silyl ethers has found use in several syntheses of natural produ~ts,*~-~~ but the solvolytic lability of such ethers limits their utility.t-Butyldimethylsilyl ethers, on the other hand, are ca. lo* times less readily hydrolysed,85 and can survive several sequential synthetic operation^.^^-*^ This group is stable to aqueous or alcoholic base under the conditions of ethanoate hydrolysis, and also to pal- ladium-catalysed hydrogenolysis, and it resists mild reducing and oxidizing agents.90 It is unaffected by hydrazine hydrate under conditions used to remove P-benzoylpropanoyl or N-acyl groups, but can be removed efficiently with fluoride ion or SO% ethanoic acid; iron(rr1) chloride in ethanoic anhydride trans- forms such ethers directly into the corresponding ethan~ates,~~ with chiral retention.A final important advantage is that the formation of t-butyldimethyl- silyl ethers does not introduce further chirality, in contrast to the use of tetra- hydropyrany 1 ethers. (i) Formation. The conversion of alcohols into their silyl ethers is normally achieved under very mild conditions, using the appropriate silyl chloride in the presence of a tertiary amine base, including the efficient combinationg2 of bistrimethylsilylamine, trimethylsilyl chloride, and pyridine; silyl-transfer reagents such as (31)93 and (32)94are of value. Imidazole is a most effective OSi Me, MeANSiMe, Me,SiN HS03SiMe, 82 E. J. Corey and B. B. Snider, J. Amer. Chem. SOC.,1972, 94, 2549. 83 R. Wies and P. Pfaender, Annalen, 1973, 1269. 84 E. Negishi, G.Lew, and T. Yoshida, J.C.S. Chem. Cornm., 1973, 874. 85 Ref. 9, pp. 132, 138. 86 E. J. Corey and A. Venkateswarlu, J. Amer. Chem. Soc., 1972,94,6190;see also D. A. Evans, T. C. Crawford, R. C. Thomas, and J. A. Walker, J. Org. Chem., 1976, 41, 3947. *7 G. D. Prestwich and J. N. Labowitz, J. Amm. Chem. Sor., 1974, 96, 7103. 88 E. J. Corey and H. S. Sachdev, J. Amer. Chem. SOC.,1973, 95, 8483. K. K. Ogilvie and D. J. Iwacha, Tetrahedron Letfers, 1973, 317. 9oE.W. Yankee, U. Axen, and G. L. Bundy, J. Amer. Chem. SOC.,1974, 96, 5865; see also ref, 86. 91 8. Ganem and V. R. Small, J. Org. Chem., 1974, 39, 3728. 92 C. C. Sweeley, R. Bentley, M. Makita, and W. W. Wells, J. Amer. Chem. SOC.,1963, 85, 2497; H. E. Carter and R. C. Gaver, J.LipidRes., 1967, 8, 391. 93 J. F. Klebe, H. Finkbeiner, and D. M. White, J. Amer. Chem. Soc., 1966, 88, 3390; M. N. Galbraith, D. H. S. Horn, E. Middleton, and R. J. Hackney, Chem. Comm., 1968, 466; see also L. Birkofer, A. Ritter, and F. Bentz, Chem. Ber., 1964, 97,2196. 91 B. E. Cooper and S. Westall, J. Organometallic Chem., 1976, 118, 135. Silicon in Organic Synthesis catalyst, finding particular utility86 in the preparation of t-butyldimethylsilyl ethers. Considerable regio- and stereo-selectivity is readily attained. The rates of silylation of secondary alcohols by bistrimethylsilylamine in pyridine at 25 "C vary95 over a factor of 103 from endu-fenchol to exo-norborneol. t-Butyldimethyl- silyl chloride reactsg6 selectively with the 3P-hydroxy-group of androst-5-ene- 3/3,17P-diol.Trimethylsilyldiethylamine silylates equatorial hydroxy-groups,g7 axial alcohols being unreactive under the conditions used ;it selectively silylates the prostaglandin F series at the 1 1-, and, if secondary, the 15-position, allowing clean conversiong8 into the E series (Scheme 30). The demands made by the prostaglandins, in synthesis and interconversion, have done much to stimulate activity in studies of methods of protection that involve silyl ethers. OH '-CO,MePGFZamethyl ester -Me,SiO t)SiMe, .. ... 11, Illi PGE, methyl ester Reagents: i, Et,NSiMe,; ii, Cr0,,2py; iii, MeOH-Hf Scheme 30 Silyl ethers have been used extensively in oligonucleotide synthesis,gg affording selective protection to ribonucleoside hydroxy-functions.(ii) Cleavage. Cleavage of silyl ethers to the parent alcohols can be achieved readily in the cases of labile ethers by treatment with nucleophiles such as methanol, often with methoxide ion as catalyst. The more stable, more useful, ethers such as t-butyldimethylsilyl are cleaved by protolysis with ethanoic acid or by fluoride ion, normally as tetra-n-butylammonium fluoride, in THF;86 under such conditions fluoride ion is a strong base, so the appropriate care must be taken with base-labile substrates. (iii) Applications. Dimethyldichlorosilane and related species convert diols 95 H. 5. Schneider and R. Hornung, Annalen, 1974, 1864. 96 H. Hosoda, D. K. Fukushima, and 5. Fishman, J. Org.Chem., 1973, 38, 4209. $' I. Weisz, K. Felfoldi, and K. Kovrics, Chew. Abs., 1969, 70, 47 668. 98 E. W. Yankee, C. H. Lin, and J. Fried, J.C.S. Chem. Comrn., 1972, 1120; E. W. Yankee and G. L. Bundy, J. Amer. Chem. SOC.,1972, 94, 3651. O9 K. K. Ogilvie, E. A. Thompson, M. A. Quilliam, and J. B. Westmore, Tetrahedron Letters, 1974, 2865 and references therein; see also E. Lukevics, A. E. Zabotskaya, and I. I. Solomennikova, Russ. Chem. Rev., 1974, 43, 140; S. L. Beaucage and K. K. Ogilvie, Tetrahedron Letters, 1977, I 69 I . 36 Colvin into siliconides,100 which are analogous to acetonides; it acts as a kinetic traplol in the gibberellin-orientated pinacol cyclization shown (Scheme 3I), a complex mixture being formed in its absence.Reagents: i, Mg(Hg)-Me,SiCI, Scheme 31 Trimethylsilyl ethers are oxidized to carbonyl compoundslo2 by hydride abstraction with the triphenylmethyl cation; this has been extended to the selective oxidation of primary, secondary diols at the secondary position, though here the bistriphenylmethyl ethers are more ~uitable.10~Epoxidation of the prostaglandin (33) with alkaline hydrogen peroxide gives a mixture of cc-and p-10,ll-oxirans. Attachment of a bulky ‘remote controller’ group to the hydroxy-group at C-15 permits stereoselective epoxidation, the highest degree104 being attained with the tri-(p-xyly1)silyl derivative (34), which screens the @face of the molecule owing to the configuration of C-12; the hydroxy-group is re- generated, in this case, by reduction with aluminium amalgam (Scheme 32).(33) R = H 94 6(34) R = Si(CH,C,H,Me-p), Reagents: i, H,O,-HO-; ii, Al(Hg)-MeC0,H Scheme 32 Oxy-Cope and siloxy-Cope rearrangements of the diene (35) give quite different products (Scheme 33), in a rather dramatic demonstrationlo5 of the fact that silyl-substitution modifies the reaction course. looR. W. Kelly, Tetrahedron Letters, 1969, 967; J. Chromatog., 1969, 43, 229. lol E. J. Corey and R. L. Carney, J. Amer. Chem. SOC.,1971, 93, 7318; see also E. J. Corey,R. L. Danheiser, and S. Chandrasekaran, J. Org. Chem., 1976, 41, 260. loa M. E. Jung, J. Org. Chem., 1976, 41, 1479. lo3 M. E. Jung and L. M. Speltz, J. Amer. Chem. SOC.,1976, 98, 7882. lo4 E. J. Corey and H. E. Ensley, J.Org. Chem., 1973, 38, 3187. lo5 R. W. Thies, M. T. Wills, A. W. Chin, L. E. Schick, and E. S. Walton, J. Amer. Chem. SOC.,1973, 95, 5281 ; see also R. W. Thies and R. E. Bolesta, J. Org. Chem., 1976, 41, 1233. 37 Silicon in Organic Synthesis OR d? main I y (35) Scheme 33 Trimethylsilyloxycyclopropaneshave been involved106y lo7 in several valuable synthetic procedures, exemplified in Scheme 34. OSiMe, iv / Reagents: i, CH,I,-Zn-Cu; ii, bSph; iii, LiNR,-Me,SiCl; iv, H+ or Lewis acid; Li v, heat Scheme 34 B. Protection of Carboxylic and Sulphenic Acids.-The relative stability of silyl esters to basic and oxidizing conditions,lO* coupled with their ready cleavage on mild treatment with methanol or ethanol, makes them attractive protecting lo6 B.M. Trost and M. J. Bogdanowicz, J. Amer. Chem. Soc., 1973, 95,289, 2038; B M. Trost. and S. Kurozumi, Tetrahedron Letters, 1974, 1929. lo' C. Girard, P. Amice, J. P. Barnier, and J. M. Conia, Tetrahedron Letters, 1974, 3329. lo8See, for example, E. 5. Corey and C. U. Kim, J. Org. Chem., 1973, 38, 1233. CoIvin groups for carboxyl functions. Their use to protect the carboxy-group attached to C-3 in penicillins during the cleavage of side-chains represented an important achievementlog in devising a practical route to 6-aminopenicillanic acid (Scheme 35). Similar techniques have brought significant improvements to the prepara- tion of 7-aminocephalosporanic acid. HH HH CO,H Reagents: i, Me,SiCI-py ; ii, PC1,-py ; iii, R’OH ; iv, (NH4)HC0,-H,0 Scheme 35 The labile sulphenic acid partner in the reversible thermal rearrangement of penicillin sulphoxides can be trapped110 as the silyl ester (36), which functions as a masked RS+ species, as shown by its acid-catalysed cyclization to the cephem (37) (Scheme 36).HHPhthNhLLr3 I, PhthNv+ I 11 HH? !q OSiMe, -PhthNhi ?>-0 0 0 N/ I CO,R COzR COgR (36) (37) Reagents : i, Me,SiCI-heat ; ii, MeS0,H Scheme 36 The protected acid (38) survived two sets of reagents before liberation with methanol to give the oxepin (39)ll1 (Scheme 37). CO,SiMe, CO,SiMe, CO,H i, ii iii0 -0 -0 0 0 (38) (39) Reagents : i, N-Bromosuccinimide-CCI,-hv; ii, Et,N-Et,O ; iii, MeOH Scheme 37 loBF.M.Huber, R. C. Chauvette, and B. G. Jackson in ‘Cephalosporins and Penicillins’, ed. E. H. Flynn, Academic Press, New York, 1972, Ch. 2. 110 T. S. Chou, Tetrahedron Letters, 1974, 725; T. S. Chou, J. R. Burgtorf, A. L. Ellis, S. R. Lammert, and S. Kukolja, J. Amer. Chem. SOC.,1974, 96, 1609. J. D. Richardson, T. C. Bruice, S. M. Waraskiewicz, and G. A. Berchtold, J. Org. Chem., 1974, 39, 2088. 39 Silicon in Organic Synthesis Pyrolysis of the diester (40),followed by hydrolysis, yieldedllz the hitherto elusive butadiene-2,3-dicarboxylicacid (Scheme 38). C0,Si Me, 420 OC C0,Si Me,-M e,SiO,C C0,Si Me, Scheme 38 Sensitive and rather inaccessible acid chlorides such as 2-oxopropanoyl chloride can be prepared in good yieldl13 by the reaction of the corresponding silyl ester with oxalyl chloride. Bistrimethylsilyl malonate114J15 and alkyl trimethylsilyl ma10natesll~J~~ have found predictable utility.Trimethylsilyl oc-bromo-esters are recommended118 in the Reformatsky reaction when isolation of the P-hydroxy-acid is desired. Trimethylsilyl tribromoethanoate (41) is an effective source of dibromoketenllg (Scheme 39). The potential of the tri- methylsilyloxycarbonyl function as a nitrogen-protecting group in peptide synthesis has been explored.lZ0 Br Reagent: i, Ph,P Scheme 39 C. Protection of Alkynes and Ketens.-The use of the trialkylsilyl group to afford protection to terminal alkynes is a most active area, important contribu- tions having been made by WaltonlZ1 and co-workers, resulting in routes to lla P.Dowd and K. Kang, Synthetic Comm., 1974, 4, 151. 113 J. Hausler and V. Schmidt, Chem. Ber., 1974, 107, 145. 114 N. H. Nam, J.-P. Beaucourt, H. Hoellinger, and L. Pichat, Bull. SOC.chim. France, 1974, 1367; for conversion into carbon suboxide, see L. Birkofer and P. Sommer, Chem. Ber., 1976, 109, 1701. 116 U.Schmidt and M. Schwochau, Tetrahedron Letters, 1967, 4491. ll6 L. Pichat and J.-P. Beaucourt, Synthesis, 1973, 537. 117 B. M. Trost and R. A. Kunz, J. Org. Chem., 1974, 39, 2648. 'la A. Horeau, Tetrahedron Letters, 1971, 3227. 119 T. Okada and R. Okawara, Tetrahedron Letters, 1971, 2801. 120 Y. Yamamoto, D.S. Tarbell, J. R. Fehlner, and B. M. Pope, J. Org. Chem., 1973, 38, 2521.lZ1 R. Eastmond, T.R. Johnson, and D. R. M. Walton, Tetrahedron, 1972, 28,4601. Colvin polyalkynes,122a allene-diynes,122* and aryl-alkynes122C (Scheme 40) ; terminal substitution also allows selective oxidative transformation into carboxylic acids123 or methyl ketones.lz4 In general, protection is effected by the reaction of the alkyne anion or its equivalent with a trialkylsilyl chloride; after reaction, the terminal alkyne is liberated by hydroxide ion,125 by methanolysis, by silver(1) ion126 followed by cyanide ion,1z7 or by fluoride ion.128 iEt,Si(CEC),X + PhCICH -Ph(C=C),SiEt, R' R' \ \ Me,Si(CrC),H + C=C=CHBr C=C=CH(CrC),H R2/ /R2 Me,SiCECX + ArCu -ArCGCSiMe, R3C ECSi Me, R3CH2C0,H R3COCH3 Reagents: i, CuCI; ii, CuBr; iii, R4,BH; iv, NaOH-H,O,; v, H+-Hgz+ Scheme 40 Selective reductionl26 of non-terminal triple bonds in polyalkynes is possible if the terminal alkyne is first protected by silylation, as illustrated in the semi- hydrogenation of (42) to give a terminal Z-enyne unit in an approach129 to histrionicotoxin (Scheme 41). The Wittig salt (43), as its ylide, converts128 aldehydes into E-enyne units. The acidic hydrogen of propyne is masked by silylation, allowing preparation of the alkyl-lithium compound (44),a species used in routes to homologous lZ2(a)B.N. Ghose and D. R. M. Walton, Synthesis, 1974, 890; (b)P. D. Landor, S. R. Landor, and J. P. Leighton, Tetrahedron Letters, 1973, 1019; (c) R. Iliver and D. R. M. Walton, ibid., 1972, 5209.lZ3 G. Zweifel and S. 5.Backlund, J. Amer. Chem. Soc., 1977, 99, 3184; see also R. Koster and L. A. Hagelee, Synthesis, 1976, 118. lZ4D. A. McCrae and L. Dolby, J. Org. Chem., 1977, 42, 1607. la5 C. Eaborn and D. R. M. Walton, J. Organometallic Chem., 1966, 4, 217. la0 H. M. Schmidt and J. F. Arens, Rec. Trav. chint., 1967, 86, 1138. lZ7 E. J. Corey and H. A. Kirst, Tetrahedron Letters, 1968, 5041. lZ8E. J. Corey and R. A. Ruden, Tetrahedron Letters, 1973, 1495; E. J. Corey, G. W. Fleet, and M. Kato, ibid., 1974, 3963; see also E. Nakamura and I. Kuwajima, Angew. Chem. Internat. Edn., 1976, 15, 498. lzS A. B. Holmes, R. A. Raphael, and N. K. Wellard, Tetrahedron Letters, 1976, 1539. Silicon in Organic Synthesis OH i, ii CrC-CEC-Si Me, H H (42) .....c5H11y~\~H0c5H11+5k+ Me,SiCECCH,;Ph, Br --+111, II H H (47) H CrCH Reagents : i, H,-Pd/BaSO,-quinoline; ii, F-;iii, base Scheme 41 alkyl-alkynes,l27 oc-santalol,l30 some triterpenoids,131 and the classic synthesis of Cecropia juvenile hormone.132 The related organocopper species (45) adds 1,6 to penta-2,4-dienoate esters in a simple route133 to functionalized 1,5-enynes and 1,4,5-trienes. Me,SiCGCCH,Li R,SiC=CCH,Cu (44) (35) Bistrimethylsilylethyne reacts with acid chlorides to give134 ccp-unsaturated aldehydes (Scheme 42) by two-carbon homologation. It also undergoes a Me,SiC=CSiMe, RCOC=CSiMe, -% RCOCH,CH(OMe), iii, iv J R H HXCHO Reagents: i, RCOCl-AlC1,-CH,Cl,; ii, 0.1M-MeO-; iii, NaBH,; iv, H,O+ Scheme 42 cobalt-catalysed reaction with the diyne (46) to give the strained tetrasilyl- naphthalene (48), probably via135 the benzocyclobutene (47) (Scheme 43); 130 E.5. Corey, H. A. Kirst, and J. A. Katzenellenbogen, J. Amer. Chew. SOC.,1970, 92, 6314. 131 R. E. Ireland, M. I. Dawson, and C. A. Lipinski, Tetrahedron Letters, 1970, 2247. lS4 E. J. Corey, J. A. Katzenellenbogen, and G. A. Posner, J. Amer. Chem. SOC.,1967, 89, 4245. 133 B. Ganem, Tetrahedron Letters, 1974, 4467. 134 H. Newman, J. Org. Chem., 1973, 38, 2254. 136 R. L. Funk and K. P. C. Vollhardt, J.C.S. Chem. Comm., 1976, 833; see also K. P. C. Vollhardt and L. S. Yee, J. Amer. Chem. SOC.,1977, 99, 2010; R. L. Funk and K. P. C. Vollhardt, ibid., p. 5483. 42 CoIvin subsequent selective site-specific reaction with electrophiles (see Section 3) offers a potential route to a variety of substituted naphthalenes.J SiMe, Me,SiMe3simsiMe3 (48) Reagent: i, [CpCo(CO),] Scheme 43 Trimethylsilylketen is relatively stable, acting as a potent136 acylating agent for hindered amines and tertiary alcohols; unlike trimethylsilylbromoketen,137 it does not undergo cycloaddition reactions. The preparation (Scheme 44)and some reactions of bistrimethylsilylthioketen (49) have been described;l38 interestingly, the isomeric alkyne (50) rearranges thermally to (49). M e,SiC ECH Me,SiCGCSSiMe, (Me,Si),C=C=S (49) Reagents: i, BunLi; ii, is8;iii, Me,SiCI; iv, heat Scheme 44 7 Silyl Enol Ethers Until recently, silyl enol ethers139 were the compounds of major synthetic use of silicon, their utility being in providing regiostable, isolable species which can, R.A. Ruden, J. Org. Chem., 1974,39, 3607; for bis(trimethylsilyl)keten, see D. F. Sullivan, R. P. Woodbury, and M. W. Rathke, J. Org. Chew., 1977,42,2038. 137 W. T. Brady and R. A. Owens, Tetrahedron Letters, 1976, 1553; for (trimethylsilylrnethy1)-keten, see W. T. Brady and T. C. Cheng, J. Org. Chew., 1977, 42, 732. 13* S. J. Harris and D. R. M. Walton, J.C.S. Chem. Comm., 1976, 1008. 13y J. K. Rasmussen, Synthesis, 1977, 91. 43 Silicon in Organic Synthesis on demand, give regio-pure enolate anions140 after purification and spectral identification. They were introduced in an effort to avoid the production of an equivalent amount of base that results when metal enolates are formed from enol ethanoates or by reduction of enones with solvated electrons; the presence of such additional base encourages the formation of polyalkylated products.A. Preparation.-Silyl enol ethers are readily prepared140J41 under conditions of either kinetic or thermodynamic control (Scheme 45). OSiMe, OSiMe, i. ii -b i 00 78 22 iii. ivI-1 99 Reagents: i, Me,SiCl-Et,N-DMF-heat; ii, NaHC0,-H,O; iii, LiNPr,i-DME; iv, Me,SiCl Scheme 45 Regiospecific generation can also be achieved by trapping the enolate anion formed from an enone by conjugate reduction41c or alkylation,41b by retro- Diels-Alder fragmentation,142a or by sigmatropic rearrangement142b of /3-keto-acid silyl esters (Scheme 46).MeSi OSiM e3 + co,b Scheme 46 140 G. Stork and P. F. Hudrlik, J. Amer. Chem. Soc., 1968, 90, 4462, 4464; G. Stork, Pure Appf. Chem., 1975, 43, 553; H. 0. House, M. Gall, and H. D. Olmstead, J. Org. Chem., 1971, 36, 2361 ; H. 0. House, ‘Modern Synthetic Reactions’, 2nd edn., W. A. Benjamin, Menlo Park, California, 1972, pp. 568-569; see also R. E. Donaldson and P. E. Fuchs, J. Org. Chem., 1977, 42, 2032. 141 S. Torkelson and C. Ainsworth, Synthesis, 1976, 722; ibid., 1977, 431; G. Simchen and W. Kober, ibid., p. 259; H. Sakurai, K. Miyoshi, and Y. Nakadaira, Tetrahedron Letters, 1977, 2671 ; Y. Seki, A. Hidaka, S. Murai, and N. Sonada, Angew. Chem. Internat. Edn., 1977, 16, 174.142 (a) J. Haslouin and F. Rouessac, Bull. SOC.chim. France, 1976, 1122; (6) R. M. Coates, L. 0.Sandefur, and R. D. Smillie, J. Amer. Chem. SOC.,1975, 97, 1619. 44 Colvin An interesting method allows isolation under non-aqueous conditions (Scheme 47), low reaction temperatures favouring kinetic regio~e1ectivity.l~~ OSiMe, + Me,SiCH,CO,Et -&. 0+ CH,CO,Et Reagent: i, Bun4N+ F-Scheme 47 B. Applications.-A special feature of silyl enol ethers is their regiostability. The addition of a metal alkyl, usually methyl-lithi~rn,~~~ or of a stoicheio-metric144 or catalytic145 amount of fluoride ion, regenerates the original enolates, which are also regiostable under aprotic conditions, and undergo site-specific a1kylati0n.l~~Silyl enol ethers undergo regiospecific electrophilic substitution with strong electrophiles (Scheme 48),resulting in acylati~n,~~~~ carboxamida-tion,14@ ~ulphenylation,~~~~ conversion into en one^,^^^ sulphonylation,148 hal0genation,l4~ hydro~ylation,15~ oxirnation,l5l formation of a Mannich base,152 and azide-induced ring contraction.l53 Such en01 ethers1s4 and enol ethanoatesl55 react with carbonyl compounds, or their a~etals,l~~ in the presence of titanium@) chloride, to give /3-hydroxy- or /3-alkoxy-ketones, respectively.Similarly, Lewis-acid-catalysed Michael addition of silyl enol ethers to nitro-alkenes leads directly157 to synthetically valuable 1,4-diketones. Such diketones are also pro- 143 E. Nakamura, T. Murofushi, M.Shimuzu, and I. Kuwajima, J. Amer. Chem. SOC.,1976, 98, 2346. lP4 I. Kuwajima and E. Nakamura, J. Amer. Chem. Soc., 1975, 97, 3257. 145 R. Noyori, K. Yokoyama, J. Sakata, I. Kuwajima, E. Nakamura, and M. Shimuzu, J. Amer. Chem. SOC.,1977, 99, 1265. 146 (a) S. Murai, Y. Kuroki, K. Hasegawa, and S. Tsutsumi, J.C.S. Chem. Comm., 1972, 946; (6)I. Ojima, S. Inaba, and Y. Nagai, Tetrahedron Letters, 1973, 4271 ; Chem. Letters, 1974, 1069. IP7 E. Friedrich and W. Lutz, Angew. Chem. Internat. Edn., 1977, 16, 413. lP8 Y. Kuroki, S. Murai, N. Sonada, and S. Tsutsumi, Organometallic Chem. Synth., 1972, 1, 465. 148 R. H. Reuss and A. Hassner, J. Org. Chem., 1974,39, 1785 ;L. Blanco, P. Amice, and J. M. Conia, Synthesis, 1976, 194; see also M.Zembayashi, K. Tamao, and M. Kumada, ibid., 1977, 422. 150 A. G. Brook and D. A. Macrae, J. Organometallic Chem., 1974,77, (219; G. M. Rubottom, M. A. Vazquez, and D. R. Pelegrina, Tetrahedron Letters, 1974, 4319; G. M. Rubottom, J. M. Gruber, and G. M. Mong, J. Org. Chem., 1976, 41, 1673; for the related preparation of a-hydroxy-acids, see G. M. Rubottom and R. Marrero, ibid., 1975,40, 3783. lS1 J. K. Rasmussen and A. Hassner, J. Org. Chem., 1974, 39, 2558. lS2 S. Danishefsky, T. Kitahara, R. McKee, and P. F. Schuda, J. Amer. Chem. SOC.,1976, 98, 6715; see also N. L. Holy and Y. F. Wang, ibid., 1977, 99, 944; W. Oppolzer, H. Hauth, P. Pfaffli, and R. Wenger, Helv. Chim. Acta, 1977, 60, 1801. lS3 R. A. Wohl, Helv. Chirn. Acta, 1973, 56, 1826; Tetrahedron Letters, 1973, 31 11.154 T. Mukaiyama, K. Narasaka, and K. Banno, Chem. Letters, 1973, I01 1; T. Mukaiyama, K. Banno, and K. Narasaka, J. Amer. Chem. Soc., 1974, 96, 7503; E. Nakamura and I. Kuwajima, ibid., 1977, 99, 961. lS5 T. Mukaiyama, T. Izawa, and K. Sago, Chem. Letters, 1974, 323. lS6 T. Mukaiyama and M. Hayashi, Chem. Letters, 1974, 15. lS7 M. Miyashita, T. Yanami, and A. Yoshikoshi, J. Amer. Chem. SOC., 1976, 98, 4679. 45 Silicon in Organic Synthesis duced by oxidative coupling158 of enol ethers by silver@), good yields of cross-coupled products being obtainable. a-Trimethylsilyl esters react with fluoride ion,l59 giving ester enolates, which 0 CONHR t bSPh 0 OH 0 J ooHI 0 Reagents: i, RCOCl; ii, RNCO-Et,N; iii, PhSCl; iv, lo2;v, Ph,P; vi, RSOzCI; vii, X2; viii, m-chloroperbenzoic acid; ix, NOCl; x, CH,=NfMe2 I-; xi, ArSO,N,; xii, R1COR2-TiCll ; xiii, \\f and TiCI,; xiv, A&O-DMSO NO2 Scheme 48 158 Y.Ito, T.Konoika, and T. Saegusa, J. Amer. Chem. SOC.,1975,97,649; for similar dimeric coupling of esters, see S. Inaba and 1. Ojima, Tetrahedron Letters, 1977, 2009. 159 E. Nakamura. M. Shimuza, and 1. Kuwajima, Tetrahedron Letters, 1976, 1699. 46 Colvin condense with carbonyl compounds to give protected p-hydroxy-esters (Scheme 49). R2 iMe,SiCH,CO,R' + R2COR3 -\co2R' R3 OSiMe, Reagent: i, R4, N+ F-Scheme 49 Silyl enol ethers, as electron-rich alkenes, can be smoothly and selectively ozonizedl60 (Scheme 50).They also react readily with Simmons-Smith reagents,161 Reagents: i, 0,-MeOH; ii, NaBH,; iii, H,O+ Scheme 50 leading initially to cyclopropanol silyl ethers.162 Conia163 has described the selective ct-or or'-methylation of steroidal ctp-unsaturated ketones (Scheme 51) ; when cisoid or labile enones are involved, an alternative course164 of ring opening occurs, leading to cyclobutanones and cyclopentanones as shown in Scheme 34. Simmons-Smith addition to cyclic silyl enol ethers in concentrated solution results in zinc-iodide-induced isomerizationl65 of the initially formed cyclopropyl ethers to protected 2-methylenecycloalkanols (Scheme 52). Ally1 esters, as their corresponding silyl keten acetal~,l~~J~~ undergo [3,3 ]-sigmatropic rearrangement to protected @-unsaturated acids (Scheme 53).The use of t-butyldimethylsilyl chloride as the enolate trap is recommended, looR. D. Clark and C. H. Heathcock, Tetrahedron Letters, 1974, 1713, 2027; J. Org. Chem., 1976, 41, 1396. lB1 J. M. Denis and J. M. Conia, Tetrahedron Letters, 1972,4593; I. Ryu, S. Murai, S. Otani, and N. Sonoda, Chem. Letters, 1976, 93; Y. Ito, S. Fujii, and T. Saegusa, J. Org. Chcm., 1976, 41, 2073. lBaFor a full review, see J. M. Conia, Pure Appl. Chem., 1975, 43, 317. 163 C. Girard and J. M. Conia, Tetrahedron Letters, 1974, 3327; for a related route to a-halo- geno-np-unsaturated carbonyl compounds, see P. Amice, L. Blanco, and J. M. Conia, Synthesis, 1976, 196. 184 J. Salaun, B. Garnier, and J. M.Conia, Tetrahedron, 1974, 30, 1413. lB5 S. Murai, T. Aya, T. Renge, I. Ryu, and N. Sonoda, J. Org. Chem., 1974, 39, 858; I. Ryu, S. Murai, S. Otani, and N. Sonoda, Tetrahedron Letters, 1977, 1995; for conversion into p-bromo-ketones, see S. Murai, Y. Seki, and N. Sonoda, J.C.S. Chem. Comm., 1974, 1032. lB8R. E. Ireland, R. H. Mueller, and A. K. Willard, J. Amer. Chem. Soc., 1976, 98, 2868; J. Org. Chem., 1976, 41, 986. 16' J. Boyd, W. Epstein, and G. Frater, J.C.S. Chem. Comm., 1976, 380. 47 Silicon in Organic Synthesis Me,SiO a] L'%-Me3SiOa] &-OQ} ii, iii\y Me,SiO Reagents: i, Et,N-Me,SiCl-DMF; ii, LiNPr',; iii, Me,SiCI; iv, CH,I,-Zn-Ag; v, MeOH-Hf Scheme 51 r OSiMe, OSiMe, Reagents : i, CH,I,-Zn-Cu (concentrated solution) Scheme 52 permitting stereoselective formation and isolation166 of the acetals prior to rearrangement ; triethylsilyl chloride has also been advocated.l68 The syntheses and pyrolyses of keten alkyl trimethylsilyl and bistrimethylsilyl R+i+,Rl I, ,.Ra,&,Rl R2 & R', I1 R' R2oe R3R3 R3 0 OSi Me,But OSiMe,But Reagents: i, LiNPr',; ii, ButMe2SiC1,iii, heat Scheme 53 ld8W. C. Still and M. J. Schneider, J. Anter. Chem. SOC.,1977, 99, 948. Colvin acetals (51) have been described;169 the latter compounds provide a route to p-keto-acids (Scheme 54) ; 0-t-butyldimethylsilyl keten acetals such as (52) are valuable equivalents of ester en01ates.l~~ R,CHCO,H i ii iii, iv + R,CHCOCR,COIH/OSiMe3R,C=C \ OSiMe, * + RCOCl --!&RCOCH,CO,Et OEt Reagents: i, LiNPr',; ii, Me,SiCI; iii, heat; iv, H,O+; v, Et,N Scheme 54 The trimethylsilyloxybuta-1,3-dienes(53),171 (54),172 (55),173 and (56)174 have been used as 457components in Diels-Alder cycloadditions, silyl enol ether masking being preferred to the alternative alkyl enol ethers or enol ethanoates.OSiMe, Me3SiOjeph Me,SiO OMe (54) (53) Metallated allyloxy-silanes (57) behave175 as P-acyl carbanion equivalents (Scheme 55); metallated ally1 alkyl ethers176 show similar properties. The sym- 16* C. Ainsworth, F. Chen, and Y.-N. Kuo, J. Organometallic Chem., 1972, 46, 59; C. Ains-worth and Y.-N. Kuo, ibid., p. 73. 170 M. W. Rathke and D. F. Sullivan, Synthetic Conim., 1973, 3, 67; Tetrahedron Letters, 1973, 1297.S. Danishefsky, C. F. Yan, and P. M. McCurry, J. Org. Chem., 1977, 42, 1819; see also S. Danishefsky, T. Kitahara, P. F. Schuda, and S. J. Etheredge, J. Artier. Chem. SOC., 1976, 98, 3028; 5. F. W. Keana and P. E. Eckler, J. Org. Chem., 1976,41,2850. 172 M. E. Jung and C. A. McCombs, Tetrahedron Letters, 1976, 2935. 173 T. Ibuka, Y. Mori, and Y. Inubushi, Tetrahedron Letters, 1976, 3169. G. M. Rubottom and D. S. Krueger, Tetrahedron Letters, 1977, 61 1 ;G. M. Rubottom and J. M. Gruber, J. Org. Chem., 1977, 42, 1051. 175 W. C. Still and T. L. Macdonald, J. Amer. Chem. SOC.,1974, 96, 5561 ; with carbonyl compounds as electrophiles, exclusive a-attack is observed: J. Org. Chem., 1976, 41, 3620. 176 D. A. Evans, G.C. Andrews, and B. Buckwalter, J. Amer. Chem. Soc., 1974, 96, 5560. 49 Silicon in Organic Synthesis metrical anion (58) is an equivalent177 for the hypothetical homoenolate anion of ethyl vinyl ketone, undergoing electrophilic attack at mainly the y-position. Me,SiO-Li ii. iii-[ ] -R Me,SiO -cHO Li+ .. ...TL-% RwOSiEt, OSiEt, 0 (58) Reagents: i, BusLi; ii, RX; iii, H,O+ Scheme 55 Acetonides, including the hitherto unknown acetonide of trans-cyclohexane- 1,2-diol, are readily prepared178 from 2-trimethylsilyloxypropeneand 1,2-diols (Scheme 56). Scheme 56 C. Acyloin Trapping and Reductive Cleavage.-The enolate anion intermediates in the acyloin condensation179 can be trapped by silylation, preventing180 the condensation and polymerization which often complicate this route to cyclic or-hydroxy-ketones. The resulting bis-silyl enol ethers are readily hydrolysed or oxidized,lal allowing the preparation of, inter alia, cyclobutanedionels2 (Scheme 57), all attempts to oxidize the readily accessible oc-hydroxycyclo- butanone having failed.W. Oppolzer and R. L. Snowden, Tetrahedron Letters, 1976, 4187. lV8G. L. Larsen and A. Hernandez, J. Org. Chem., 1973, 38, 3935. l7# I.J. Bloomfield, D. C. Owsley, C. Ainsworth, and R. E. Robertson, J. Org. Chem., 1975, 40, 393. lSo K. Ruhlmann, Synthesis, 1971, 263. lS1 T. Kowar and E. LeGoff, Synthesis, 1973, 212; J. Strating, S. Reiffers, and H. Wynberg, ibid., 1971, 209; for the alkylation of the derived lithium 1,2-enediolates, see T.Waka-matsu, M. Fukui, and Y. Ban, ibid., 1976, 341; for their conversion into alkynes, see D. P. Bauer and R. S. Macomber, J. Org. Chem., 1976, 41, 2640. lapH.-G. Heine, Chem. Ber., 1971,104,2869; J. M. Conia and J. M. Denis, Tetrahedron Letters, 1971,2845; see also H.-G. Heine and D. Wendisch, Annalen, 1976,463. Colvin Reagents: i, Na-PhMe-Me,SiCl; ii, Br, Scheme 57 Under certain conditions, 1,2-diesters undergo reductive cleavage of the connecting o-bond. An extension to provide a method for the introduction of ethanoic acid fragments has also provided evidence183 for the mechanism of this reaction, which appears to proceed as shown in Scheme 58. The com- petitiveness and solvent dependence of these two reductive processes are seen in the acyloin condensation184 of (59) and the o-cleavage183 of (60).r 1 C0,Me OSiMe, OSiMe, C0,Me OMe I C0,Me C0,Me Reagents: i, 2e-; ii, Me,SiCI; iii, Na-PhMe-Me,SiCI; iv, H,O+; V, Na-NH, Scheme 58 183 P. G. Gassman and X. Creary, J.C.S. Chem. Comm., 1972, 1214. la4 M. E. Jung, J.C.S. Chem. Comm., 1974, 956. Silicon in Organic Synthesis 8 Activation/Protection of Nitrogen After the halogeno-silanes, amino-silanes are the next most reactive class of organosilane in which silicon is bonded to a more electronegative element; the silicon-nitrogen bond is readily ~leaved~9~ (Scheme 59). This section will explore the fate of the nitrogen moiety. \ \ /-Si---N / + E-Nu-d -Si-Nu + E-N /\ / \ Scheme 59 N-Trimethylsilyl secondary amines are recommended185 for easy formation of enamines.Acid halides react readily with amino-silanes, providing a now standard method4$6 for amide (peptide) bond formation. The silylated amines are normally more reactive than the parent compounds, and the co-produced silyl halide or equivalent plays no further part in the reaction. It is not normally possible to convert an inactive, ester-protected acid directly and non-hydrolytically into an activated acid derivative under mild conditions.186 Ma~amunel~~reasoned (Scheme 60) that, if R1O- could be removed by reaction with MY, M+ being a relatively hard acid (with a strong affinity for oxygen), and Y-being a relatively soft base, then such a desirable sequence might become feasible.Both phenyl and trichloroethyl esters have an acceptable degree of stability, yet are rapidly converted into acid imidazolides by treatment with N-trimethylsilylimidazole. Nitrile a-anions react with trimethylsilyl chloride to give, as expected, a-silyl-nitriles. If, however, t-butyldimethylsilyl chloride is employed, the anions are trapped in their ketenimine form; this results in an efficient method188 for the oxidative decyanation of secondary aralkyl- and diaryl-nitriles (Scheme 61). A wide range of Grignard reagents react with trimethylsilyl isocyanate (61) to give homologous primary amides ;lag the silylated aminocopper compound (62) converts aryl iodides into primary amineslgO in modest yield. 9 Silicon-substituted Bases Lithium,lgl sodiurn,lg2 and potassium193 bistrimethylsilylamide (Scheme 62) have all found extensive use as strong, non-nucleophilic bases.lES R. Comi, R. W. Franck, M. Reitano, and S. M. Weinreb, Tetrahedron Letters, 1973, 3107; but see L. H. Hellberg and A. Juarez, ibid., 1974, 3553. lE6See, however, A. G. Anderson and D. H. Kono, Tetrahedron Letters, 1973, 5121 ; D. J. Burton and W. F. Koppes, J.C.S. Chem. Comm., 1973,425. lE7G. S. Bates, J. Diakur, and S. Masamune, Tetrahedron Letter$, 1976, 4423. lE8 D. S. Watt, J. Org. Chern., 1974,39,2799; S. J. Selikson and D. S. Watt, Tetrahedron Letters, 1974, 3029. K. A. Parker and E. G. Gibbons, Tetrahedron Letters, 1975, 981 ; see also P. Bourgeois, G. Merault, and R. Calas, J.Organometallic Chern., 1973, 59, C4. lS0 F. D. King and D. R. M. Walton, J.C.S. Chem. Comm., 1974, 256; Synthesis, 1976, 40; see also T. Tsuda, H. Washita, and T. Saegusa, J.C.S. Chem. Comm., 1977, 468. lgl E. H. Amonoo-Neizer, R. A. Shaw, D. 0. Skovlin, and B. C. Smith, J. Chem. Soc., 1965, 2997. lg2 U. Wannagat and H. Niederpriim, Chem. Ber., 1961, 94, 1540; U. Wannagat, Pure Appl. Chem., 1969, 19, 329. lg3 C. A. Brown, Synthesis, 1974, 427. Colvin R'C + Y--=RIC + R20-\ \ OR2 k Y \ \ \ \ \ \ \ \ \ R20-+ MY RzOM + Y-95 % Reagent: i, PhO- (catalytic) Scheme 60 Ar\C/CN R' 'SiMe, Ar CN i \/+ /*R' \H Ar\ C -C =NSiMe,But R' Ar V Ar \/"f--R R / \x Reagents: i, LiNPr',; ii, Me,SiCl; iii, ButMe,SiCl; iv, I,, Br2, or PhSCl; v, HsO+ Scheme 61 Me,Si N CO (M e,Si),NCu (61) (62) i, ii, or iii (Me,Si),NH (Me,Si),NM Reagents: i, BunLi; ii, NaNH,; iii, KNH, Scheme 62 Silicon in Organic Synthesis The lithium amide is recomrnendedlg4 for the generation of kinetic enolates (Scheme 63); the sodium amide can also be used,195 but the resulting enolates are, as expected, less regiostable.Reagents: i, LiN(SiMe,),; ii, Me1 Scheme 63 With dienones, the y-rather than the €-proton is removed,l96 to give cross- conjugated enolate anions (Scheme 64). Reagents: i, LiN(SiMe,),; ii, electrophile Scheme 64 The lithium amide is also the preferredlg7 base in Darzens condensations, allowing the use even of ethanal as electrophile.The sodium amide has been advantageously employed in Dieckmann condensations198 of ccw-diesters, especially in those cases where additional nucleophilically labile groups are present. It is also recommendedlg9 for the convenient generation of monobromo- and monochloro-carbenes from the corresponding dihalogenomethanes. Intramolecular displacement of halide ions from halogeno-acetals provides a synthesis2Oo (Scheme 65) of functionalized bicyclic diketones; when the lithium amide is used as a base, the product is 95% trans-(63), whereas, remarkably, if the metal ion is potassium, the stereochemistry is completely reversed, giving 95 % cis-(63). Cyclizations involving attack by a carbanion on an electrophile usually result in the formation of a five- rather than of a six-membered ring, and rarely a four-membered ring.Stork201 has reported a process of ‘epoxynitrile cyclization’, lS4 M. Tanabe and D. F. Crowe, J.C.S. Chem. Comm., 1973, 564. lS5 D. H. R. Barton, R. H. Hesse, G. Tarzia, and M. M. Pechet, Chem. Cornm., 1969, 1497; M. Tanabe and D. F. Crowe, ibid., p. 1498. leeH. Hart, G. M. L,ove, and I. C. Wang, Tetrahedron Letters, 1973, 1377. R. F. Borch, Tetrahedron Letters, 1972, 3761 ;but see G. Kyriakakou and J. Seyden-Penne, ibid., 1974, 1737. R. N. Hurd and D. H. Shah, J. Org. Chem., 1973, 38, 390. lS9B. Martel and J. M. Hiriart, Synthesis, 1972, 201. G. Stork, J. 0. Gardner, R. K. Boeckman, and K. A. Parker, J. Amer. Chem. SOC.,1973, 95, 2014; G. Stork and R.K. Boeckman, ibid., p. 2016. G. Stork, L. D. Cama, and D. R. Coulson, J. Amer. Chem. SOC.,1974, 96, 5268. Colvin Br Br Reagent: i, LiN(SiMe,), or KN(SiMe,), Scheme 65 in which these tendencies are reversed (Scheme 66); these reversals are ascribed to the geometric constraints imposed by the oxiran ring in each case, making it difficult for the nitrile anion and the oxiran C-0 bond to come into line for formation of a five-membered ring. The second reaction shown is highly stereo- selective, and has been employed202 in a synthesis of ( & )-grandis01 (64). OH 0 Reagent: i, NaN(SiMe,), Scheme 66 Lithium 1 ,l-bistrimethylsilyl-3-methylbutoxide(65) is an exceptionally hindered strong base;203 it regiospecifically removes methyl protons from ethanoates2wU and methyl ketones,204b even in the simultaneous presence of aldehydes, which then trap the enolate anions and provide a new range of regio- specific aldol condensations (Scheme 67).202 G. Stork and I.F. Cohen, J. Amer. Chem. SOC.,1974, 96, 5270. 203 I. Kuwajirna. T. Sato, N. Minarni, and T. hbe, Terrahedron Letters, 1976, 1591 ; I. Kuwa-jirna, M. Arai, and T. Sato, J. Amer. Chem. SOC.,1977, 99, 4181. 204 (a) I. Kuwajirna, N. Minarni, and T. Sato, Tefrahedron Letters, 1976, 2253; see also N. Minarni and I. Kuwajirna, ibid., 1977, 1423; (6) I. Kuwajima, T. Sato, M. Araki and N. Minarni, ibid., 1976, 1817. 55 Silicon in Organic Synthesis SiMe, I Me,CHC H ,C-OLiI SiMe, OH (65) IRTHO + MeCOR2 4 R1CHCH,COR2 R2 = CH,R or OR Scheme 67 Trimethylsilylpotassium is recommendedzo5 for the metallation of vinylic, allylic, and benzylic substrates.10 Silanes as Reducing Agents The addition of the Si-H linkage to unsaturated substrates is important not only as a method of reduction but also as a major route to complex organo- silanes. Such additions can be brought about under catalytic or ionic conditions. A distinctly different method of reduction uses trimethylsilyl chloride-metal systems. A. Catalytic Reduction.-Silanes will reduce a wide variety of functional groups under catalysis ,by transition metals. Alkynes undergo cis-addition,206 with the terminal regiospecificity shown (Scheme 68) ;peroxide initiation yields the trans- isomer, and nickel(i1) catalyses a double addition.207 Whereas the catalysed addition of trialkylsilanes to ketones gives silyl ethers,208 xP-unsaturated ketones react by a process of 1 ,4-addition20g to give silyl enol ethers (Scheme 69); only conjugated double bonds are affected.Asymmetric hydrosilylationzlo of either class of substrate can be achieved using chiral catalysts. Carboxylic acid chlorides are reduced2I1 to aldehydes (Scheme 70) in an alternative to the Rosenmund reduction; yields are lower if there is cc-branching. 205 J. Hartmann and M. Schlosser, Helv. Chim. Acta, 1976, 59, 453; M. Schlosser and J. Hartmann, J. Amer. Chem. SOC., 1976, 98, 4674; M. Stahle, J. Hartmann, and M. Schlosser, Helv. Chim. Acta, 1977, 60, 1730. 206 R.A. Benkeser, M. L. Burrous, L. E. Nelson, and J. V. Swisher, J. Amer. Chem. SOC., 1961, 83,4385. 207 K. Tamao, N. Miyake, Y. Kiso, and M. Kumada, J. Amer. Chem. SOC.,1975, 97, 5603. 208 I. Ojima, M. Nihonyanagi, and Y. Nagai, J.C.S. Chem. Comm., 1972, 938. 209 T. Ojima, T. Kogure, and Y. Nagai, Tetrahedron Letters, 1972, 5035. 210 H. B. Kagan, Pure Appl. Chem., 1975,43,401;T. Hayashi, K. Yamamoto, and M. Kumada, Tetrahedron Letters, 1975, 3; I. Ojima, T. Kogure, and M. Kumagai, J. Org. Chem., 1977, 42, 1671. 211 5. D. Citron, J. Org. Chem., 1969,34, 1977; see also S. P. Dent, C. Eaborn, and A. Pidcock, Chem. Comm., 1970, 1703. 56 Colvin R\?RC=CR -/"="\H Six, R H \RCECH ?="\/ H Six, R R \/RCGCR -/"=c\ X,Si Six, Reagents: i, X,SiH-H,PtCI,; ii, X,SiH-NilI Scheme 68 Reagents: i, R,SiH-Rh* catalyst Scheme 69 RCOCl RCHO Reagents: i, Et,SiH-Pd Scheme 70 Imines are reduced212 to amines, again with potential chirality,213 in what is claimed to be the best method of reduction of such compounds (Scheme 71).Pyridines undergo 1,4-addition to give N-silyl species, which can be converted into the parent 1 ,4-dihydropyridines214 by controlled hydrolysis. Commercially available polymethylhydrosiloxane (66), in the presence of an organotin catalyst in a protic solvent, functions215 as a mild reagent for the 212 I. Ojima, T. Kogure, and Y. Nagai, Tetrahedron Letters, 1973, 2475. 213 N. Langlois, T.-P. Dang, and H. B. Kagan, 7'etrahedron Letters, 1973, 4865.214 N. C. Cook and J. E. Lyons, J. Amer. Chem. SOC.,1965, 87, 3283. 215 J. Lipowitz and S. A. Bowman, J. Org. Chem., 1973, 38, 162. 57 Silicon in Organic Synthesis )=” Reagents: i, R’,SiH-Rh* catalyst; ii, MeOH; iii, R2COCl Scheme 71 selective reduction of aldehydes and ketones to carbinols (Scheme 72), the catalyst providing a tin hydride as the active reducing agent. In the presence of Pd/C, alkenes and nitro-groups are smoothly reduced. Primary and secondary alcohol chloromethanoates are reduced to the corresponding alkanes by radical- induced reaction216 with tri-n-propylsilane. Reagents : i, (R,Sn),O-EtOH Scheme 72 The combination of trichlorosilane and tertiary amines217 reduces a range of aromatic carbonyl compounds, including acidP* (Scheme 73), to hydro- carbons: such a system also reduces phosphine oxides to phosphines219 with retention of configuration ;similar deoxygenation can be achieved with trichloro- silane220 or phenylsilane221 alone.C0,Et C02Et C02Et Reagents: i, C1,SiH-Et,N; ii, KOH-EtOH Scheme 73 N. C. Billingham, R. A. Jackson, and F. Malek, J.C.S. Chern. Comm., 1977, 344; see also M. G. Adlington, M. Orfanopoulos, and I. L. Fry, Tetrahedron Letters, 1976, 2955; M. P. Doyle, C. C. McOsker, and C. T. West, J. Org. Chem., 1976, 41, 1393. R. A. Benkeser, Accounts Chem. Res., 1971, 4, 94. a18 R. A. Benkeser and D. F. Ehler, J. Org. Chem., 1973, 38, 3660; see also G. S. Li, D. F. Ehler, and R. A. Benkeser, Org. Synth., 1973, 53, 159.21s C. R. Hall and D. J. H. Smith, Tetrahedron Letters, 1974, 1693. 2eo Y. Segall, I. Granoth, and A. Kalir, J.C.S. Chew. Comm., 1974, 501. K. L. Marsi, J. Org. Chem., 1974, 39, 265. Coivin B. Ionic Hydrogenation.-This system (Scheme 74) involves the stepwise addition to the substrate of H+ and H-, the most efficient reagent combination222 being trifluoroethanoic acid-triethylsilane. The procedure has been extensively explored and detailed,223 and will definitely find increasing use. H-\ -C-YH /IH \ H+ \;/ H-\-c-x ---HX/ I Scheme 74 Reduction of nitrilium ions by silane produces aldimines,224 and thence alde- hydes (Scheme 75), complementing the known method for reduction of such ions to amines by using borohydride.RCH,NHEt I + 7 RCN -RCzNEt BF,-.\ 111, 1v RCHO Reagents: i, Et,O+ BF,-; ii, NaBH,; iii, Et,SiH; iv, H,O+ Scheme 75 C.Chlorosilane-Metal Systems.-This area has been thoroughly investigated by French workers, who have reviewed225 their progress. The reagent system most commonly used, trimethylsilyl chloride-magnesium-hexamethylphosphor-amide, probably involves a silyl Grignard reagent, which, on reaction with a range of ctp-unsaturated ketones226 and ester~,22~ causes reductive dimerization, producing 1,4-dicarbonyl compounds in synthetically useful yields (Scheme 76). Benzene is converted into cyclohexa-l,4-diene in moderate yield by a reducing system consisting of lithium and trimethylsilyl chloride228 (Scheme 77). 222 M.P. Doyle, D. J. DeBruyn, S. J. Donneliy, D. A. Kooistra, A. A. Odubela, C. T. West, and S. M. Sonnebelt, J. Org. Chem., 1974, 39, 2740. 223 D. N. Kursanov, Z. N. Parnes, and N. M. Loim, Synthesis, 1974, 633. 22p J. L. Fry, J.C.S. Chem. Comm., 1974, 45. 225 R. Calas and J. Dunogues, ref. 2, Vol. 2, p. 277. 226 J. Dunogues, R. Calas, M. Bolourtchian, C. Biran, and N. Duffaut, J. Organometalfic Chem., 1973,57,55. 227 J.-P. Pichard, J. Dunogues, and R. Calas, J. Organometallic Chem., 1974, 77, 167. 228 J. Dunogues, R. Calas, and N. Ardoin, J. Organometallic Chem., 1972, 43, 127; see also L. Birkofer and N. Ramadan, Chem. Bet-., 1971, 104, 138. 59 Silicon in Organic Synthesis 65 % Reagents: i, Me,SiCl-Mg-HMPA, FeCI, or TiCl, catalyst; ii, MeOH Scheme 76 SiMe, I SiMe, 55 'I; Reagents: i, Li-Me,SiCI-THF; ii, KOH Scheme 77 11 Trimethylsilyl Cyanide Trimethylsilyl cyanide is a potent agent for effecting cyanide tran~fer,~~9-23~ aldehydes, ketones, and @-unsaturated carbonyl systems all reacting smoothly with the reagent in the catalytic presence of Lewis acids233 or crown-ether- solubilized potassium cyanide (Scheme 78).Its use permits an efficient and reliable synthesis234a of P-aminomethyl alcohols, including those from ketones which do not form stable cyanohydrins, and those from conjugated en0nes,234~ where clean 1,Zaddition is observed. Aryl and heteroaryl aldehydes can be converted232 into ketones, as shown in Scheme 78. Cyanosilylation of p-benzoquinones not only affords a degree of protection to the quinone system, but also provides a new synthesis234c of quinols (Scheme 79).229 D. A. Evans, L. K. Truesdale, and G. L. Carroll, J.C.S. Chem. Cumm., 1973, 55. 230 W. Lidy and W. Sundermeyer, Chem. Ber., 1973, 106, 587. 231 H. Neef and R. Muller, J. prakt. Chem., 1973, 315, 367. 232 K. Deuchert, U. Hertenstein, and S. Hunig, Synthesis, 1973, 777. 233 D. A. Evans and L. K. Truesdale, Tetrahedron Letters, 1973, 4929; for an alternative pre- paration of the reagent, see J. W. Zubrick, B. I. Dunbar, and H. D. Durst, ibid., 1975, 71. 234 (a)D. A. Evans, G. L. Carroll, and L. K. Truesdale, J. Org. Chem., 1974,39,914; (0)for the alkylation of the anions derived from such unsaturated cyanohydrins, see U.Hertenstein, S. Hunig, and M. Oller, Synthesis, 1976, 416; (c) D. A. Evans, J. M. Hoffman, and L. K. Truesdale, J. Amer. Chem. Suc., 1973, 95, 5822; for improved procedure and application, see D. A. Evans and R. Y. Wong, J. Org. Chem., 1977, 42, 350. 60 Colvin R‘ \ RL\C/OSiMe3C=O + Me3SiCN _.)/ RZ R2’ ‘CN Il-IV R’ Reagents: i, LiAlH,; ii, LiNPri2; iii, R3X; iv, H30+ Scheme 78 0 0 6 0 Reagents: i, Me,SiCN<atalyst; ii, AgF; iii, RMgX or RLi Scheme 79 The analogous carbonyl-insertion properties of ethyl trimethylsilyldiazo- ethan0ate,~35~ and mixed tervalent phosphorus-organosiliconthiosilane~,~~s~ reagents235c have been delineated. 12 Trimethylsilyl Azide Trimethylsilyl a~ide2~~ is preferable to the highly explosive hydrazoic acid for the synthesis of 1,2,3-triazole~~~~ (Scheme 80) and related238 heterocyclic systems, the silyl group in the products being hydrolytically labile.It complements sodium azide in such cycloadditions, working best with electron-rich alkynes ; azide ion is more effective with electron-poor substrates. It is also preferable239 to aryl sulphonyl azides for the preparation of aziridines. The reagent converts acid chlorides and anhydrides into acid azides prior to Curtius rearrangement to isocyanates;240 it also converts halogeno-ethanoates 235 (a) D. A. Evans, L. K. Truesdale, and K. G. Grimm, J. Org. Chem., 1976, 41, 3335; (b) D. A. Evans, L. K. Truesdale, K. G. Grimm, and S. L. Nesbitt, J. Amer. Chem. Soc., 1977, 99, 5009; (c) D.A. Evans, K. M. Hurst, L. K. Truesdale, and J. M. Takacs, Tetra-hedron Letters, 1977, 2495. 236 L. Birkofer and P. Wegner, Org. Synth., 1970, 50, 107; see also S. S. Washburne and W. R. Peterson, J. Organometallic Chem., 1971, 33, 153. 237 Y.Tanaka, S. R. Velen, and S. 1. Miller, Tetrahedron, 1973, 29, 3271. 238 E. Ettenhuber and K. Ruhlmann, Chem. Ber., 1968, 101, 743. 239 K. Wiesner, Chemical Society Centenary Lecture, Glasgow, 1977 (Chem. SOC.Rev., 1977, 6, 413). 240 S. S. Washburne and W. R. Peterson, Synthetic Conim., 1972, 2, 227; S. S. Washburne, W. R. Peterson, and D. A. Berman, J. Org. Chem., 1972, 37, 1738; J. H. MacMillan and S. S. Washburne, ibid., 1973, 38, 2982. Silicon in Organic Synthesis R R RC=CR Reagents: i, Me,SiN,; ii, H,O Scheme 80 into a~ilo-ethanoates,~4~which are precursors to alkoxycarbonylnitrenes (Scheme 81).(RCO),O RCOCl \ N3 Reagent: i, Me,SiN, Scheme 81 Trimethylsilyl azide, in combination with lead(1v) ethanoate or iodobenzene diethanoate, reacts with alkenes to give a variety of pr0ducts.2~2 The latter, milder, reagent combination converts243 cyclic alkenes into a-azido-ketones ; enol ethers and other electron-rich alkenes, on the other hand, undergo regio- specific cleavage (Scheme 82). I 4R)&R0R+ R I e*g* 0+ ON3 R X 1 \dRwx CN + O=c / R k CN 1 A0 10 Reagents: i, PhI(OAc),-Me,SiN, Scheme 82 241 H. R. Kricheldorf, Synrhesis, 1972, 695. 242 E. Zbiral, Synthesis, 1972, 285.243 J. Ehrenfreund and E. Zbiral, Annalen, 1973, 290. 62 Colvin 13 Miscellaneous A major area of application of trialkylsilyl groups utilizes their extreme bulk to provide ligands capable of stabilizing metals in low-co-ordinative environ- ments; this area has been extensively reviewed.244 A recent example245 can be seen in the first preparation of stable two-co-ordinate phosphorus- and arsenic- centred radicals, (67) and (68). A related use of such bulky substituents has allowed the preparation and conformational st~dy24~ of relatively long-lived carbon radicals such as (69). [(Me,Si),CH], M' [( Me,Si),N], M -(67) M = P or As (68) M = P or As (Me,Si),kH(SiMe,), (69) t, (50°C) = 120 h Tertiary propynyl alcohols rearrange247 smoothly in the presence of polymeric silyl vanadates to @-unsaturated aldehydes (Scheme 83).R' R' C=CH -&-R' CHO Reagent: i, -(Ph,SiOV=O)n, heat I Scheme 83 Trimethylsilyl iodide converts248 esters into the corresponding labile silyl esters, and thence into the acids, probably by the process shown in Scheme 84. No selectivity is seen with simple esters, although it may be possible to cleave t-butyl and benzyl esters selectively. Trimethylsilyl bromide cleanly dealkylate~~*~ phosphonic acid dialkyl esters under mild conditions. 244 D. H. Harris and M. F. Lappert, ref. 2, Vol. 2, p. 13; D. C. Bradley and M. H. Chisholm, Accounts Chem. Res., 1976, 9, 273. 245 M. J. S. Gynane, A. Hudson, M. F. Lappert, P. P. Power, and H. Goldwhite, J.C.S.Chem. Comm., 1976, 623. 246 D. Griller and K. U. Ingold, J. Amer. Chem. SOC., 1974, 96, 6203; Accounts Chem. Res., 1976, 9, 13. 2*7 H. Pauling, D. A. Andrews, and N. C. Hindley, Helv. Chim. Acta, 1976, 59, 1233; G. L. Olson, K. D. Morgan, and G. Saucy, Synthesis, 1976, 25; M. B. Erman, I. S. Aul'chenko, L. A. Kheifits, V. G. Dulova, Yu. N. Novikov, and M. E. Vol'pin, Tetrahedron Letters, 1976, 2981. 248 M. E. Jung and M. A. Lyster, J. Amer. Chem. SOC., 1977, 99, 968; T.-L. Ho and G. A. Olah, Angew. Chem. Internat. Edn.,1976, 15, 774; Synrhesis, 1977, 417; for the conversion of alcohols into iodides using this reagent, see M. E. Jung and P. L. Ornstein, Tetrahedron Letters, 1977, 2659. *IsC. E. McKenna, M. T. Higa, N. H. Cheung, and M. C. McKenna, Tetrahedron Lefters, 1977, 155.63 Silicon in Organic Synthesis Scheme 84 14 Concluding Remarks It is to be hoped that this short review has given some indication of the excep- tional utility of silicon in synthetic organic chemistry; space does not permit discussion of its applicability elsewhere, which is equally impressive, nor of the more physical aspects of its properties. For more detailed information on the silicon reagents mentioned, the reader is recommended to consult the books by Fieser and Fieser,Z5O in addition to the primary references. The author gratefully acknowledges many stimulating and helpful discussions with Dr. B. J. Hamill. Most of all, however, sincere tribute must be paid to Professor Gilbert Stork, whose inspiration and talents have contributed so much to the current explosive growth in this area.250 M. Fieser and L. F. Fieser, ‘Reagents for Organic Synthesis’, Vols. 1-5, Wiley-Interscience, New York, 1967-1975.

ISSN:0306-0012    

DOI:10.1039/CS9780700015

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Clathrates and Molecular Inclusion Phenomena By D. D. MacNicol, J. J. McKendrick, and D. R. Wilson CHEMISTRY DEPARTMENT, THE UNIVERSITY, GLASGOW G12 8QQ 1 Introduction In recent years a rapidly growing interest in inclusion phenomena has been focused in two major directions. In the first, the binding or complexation of guest species by unimolecular hosts in solution has received much attention, and excellent recent reviews have appeared for two particularly important classes of host, the naturally-occurring cyclodextrinsl-3 and compounds of the synthetic ‘crown’ type.4 The second equally fascinating aspect of ‘host and guest chemistry’ relates to the study of crystalline multimolecular inclusion c~rnpounds,~-~~ which may be sub-classified as the true clathrate type22 in which the guest molecules are imprisoned in discrete closed cavities or cages; the channel type23 in which the guest species are accommodated in continuous canals running See for example D.W. Griffiths and M. L. Bender, Adv. in Catalysis, 1973, 23, 209. a F. Cramer and H. Hettler, Nuturwiss, 1967, 54, 625. J. A. Thoma and L. Stewart in ‘Starch: Chemistry and Technology’, ed. R. L. Whistler and E. F. Paschall, Academic Press, New York, 1965, Vol. 1, p..209.See for example D. J. Cram, R. C. Helgeson, L. R. Sousa, J. M. Timko, M. Newcomb, P. Moreau, F. de Jong, G. W. Gokel, D. H. Hoffman, L. A. Domeier, S. C. Peacock, K. Madan, and L. Kaplan, Pure Appl. Chem., 1975,43,327; G. W. Gokel and H. D. Durst, Synthesis, 1976, 168; D.5. Cram and J. M. Cram, Science, 1974, 183, 803; C. 5. Pedersen and H. K. Frensdorff, Angew. Chem. Internut. Edn., 1972, 11, 16; J. J. Christensen, D. J. Eatough, and R. M. Izatt, Chem. Rev., 1974, 74, 351; see also R. J. Hayward, M. Htay, and 0. Meth-Cohn, Chem. and Znd., 1977, 373. S. G. Frank, J. Pharm. Sci., 1975, 64, 1585. “on-Stoichiometric Compounds’, ed. L. Mandelcorn, Academic Press, New York, 1964.’M. Hagan, ‘Clathrate Inclusion Compounds’, Reinhold, New York, 1962. * F. Cramer, ‘Einschlussverbindungen’,Springer-Verlag, Berlin, 1954. O V. M. Bhatnagar, ‘Clathrate Compounds’, Chemical Publishing Co., New York, 1970. lo G. Zilberstein, Bull. SOC. chim. France, 1951, 18, D33. l1 W. Schlenk, Fortschr. Chem. Forsch., 1951, 2, 92. Is F.Cramer, Angew. Chem., 1952, 64,437. H. M. Powell, J. Chem. SOC., 1954, 2658. l4 G. Montel, Bull. SOC. chim. France, 1955, 1013. l6 F. D. Cramer, Rev. Pure Appl. Chem., 1955, 5, 143. l* H. M. Powell, Rec. Trav. chim., 1956, 75, 885. l7 F. Cramer, Angew. Chem., 1956, 68, 115. L. Mandelcorn, Chem. Rev., 1959, 59, 827. J. F. Brown, Sci. Anter., 1962, 207, 82. so C. Asselineau and J. Asselineau, Ann. Chinz., 1964, 9, 461. a1 C. Solacolu and I. Solacolu, Stud. Cert. Chem., 1973, 21, 1307. 28 See for example H. M. Powell, in ‘Non-Stoichiometric Compounds’, ed. L. Mandelcorn, Academic Press, New York, 1964, p. 438. 83 See for example L. C. Fetterly, in ‘Non-Stoichiometric Compounds’, ed. L. Mandelcorn, Academic Press, New York, 1964, 491. 65 Clathrates and Molecular Inclusion Phenomena through the crystal; and the layer typez4 where the guest component is situated between bands of host structure.Familiar examples of these types are the p-hydroquinone clathrates, ,22 the channel inclusion compounds formed by urea and thiourea,23 and the layer or intercalation compounds formed by graphite.24 In the extremely important inorganic zeolites,25 one has an intermediate class possessing cavities interconnected by channels. The present review is mainly concerned with organic multimolecular inclusion compounds, particularly those of the true clathrate or cage type,22 and points for detailed consideration are (i) work directed towards the design and synthesis of new clathrate host materials; (ii) recent structural information which has become available on selected clathrates, and the nature of host-guest interact ions in such systems; (iii) studies of the properties of guest molecules when actually present within clathrare cavities. In Section 6 a brief account of very recent work on the cyclodextrins is also given.The present review intends to be illustrative rather than comprehensive, and hopes to stimulate further work in the field. Not all of the above main points are encountered for each clathrate or family of clathrates chosen. 2 Dianin’s Compound and Related Molecules These molecules are considered first since they are particularly well suited to illustrating the main themes of the present review. A. Structure and Properties of the Parent Host.-The parent, 4-p-hydroxyphenyl- 2,2,4-trimethylchroman (l), widely known as Dianin’s compound was first prepared26 by the Russian chemist A.P. Dianin in 1914. He reported the remarkable ability of (1) to retain tightly certain organic solvents. Subsequently this compound has been shown to be capable of including a wide range of guest a4 See for example F. R. Gamble and T. H. Geballe in, ‘Treatise on Solid State Chemistry’, Vol. 3, Crystalline and Noncrystalline Solids, ed. N. B. Hannay, Plenum Press, New York, 1976, p. 89; H. Selig, M. Rabinovitz, I. Agranat, and Chun-Hsu Lin, J. Amer. Chem. SOC., 1976, 98, 1601. aa See for example, R. M. Barrer, in “on-Stoichiometric Compounds’, ed. L. Mandelcorn, Academic Press, New York, 1964, 309; K.Seff, Accounts Chem. Res., 1976, 9, 121. as A. P. Dianin, J. Russe. Phys. Chem. SOC.,1914, 46, 1310; for later syntheses see G. G. Kondrateva, Metody Polsich. Khim. Reaktivov Prep., 1969, 20, 199 (Chern. Abs., 1972, 76, 113 017); D. B. G. Jaquiss, Ger. Offen. 2 335 854, 1974 (Chem. Ah., 1974, 81, 26 162). MacNicol, McKendrick, and Wilson species, e.g. argon,27 sulphur dioxide,28 ammonia,2* benzene,29 decalin,29 and di-t-butylnitroxide. 3O The structure of (1) was unambiguously established in the mid-fifties by Baker and co-workers,28~29 who also prepared28 over fifty adducts. At this time also Powell and Wetter~,~~ on the basis of space group, unit cell dimensions, and crystal packing considerations, suggested a true cage structure for the adducts, and the unsolvated form.Some decade and a half later, detailed X-ray studies confirmed the cage structure for the ethan01,3~ chl~roform,~~ n-heptan~l~~complexes, and for the unsolvated crystal.34 Figure 1 shows a view normal to the c-axis for the unsolvated form,34 which is isomorphous with the Figure 1 A view normal to the c-axis ofthe unsolvated form of Dianin’s Compound (l), the cage formed between sextet units being unoccupied in this case 27 W. Baker and J. F. W. McOmie, Chem. and Ind., 1955, 256. 28 W. Baker, A. J. Floyd, J. F. W. McOmie, G. Pope, A. S. Weaving, and J. H. Wild, J. Chem. SOC.,1956, 2010. 29 W. Baker, J. F. W. McOmie, and A. S. Weaving, J. Chem. SOC.,1956, 2018. 30 A.A. McConnell, D. D. MacNicol, and A. L. Porte, J. Chem. SOC.(A), 1971, 3516. 31 H. M. Powell and B. D. P. Wetters, Chem. and Ind., 1955, 256. 32 J. L. Flippen, J. Karle, and I. L. Karle, J. Amer. Chem. SOC.,1970, 92, 3749. 33 J. L. Flippen and J. Karle, J. Phys. Chem., 1971, 75, 3566. 34 H. H. Mills, D. D. MacNicol, and F. B. Wilson, unpublished results. 67 Clathrates and Molecular Inclusion Phenomena adducts of (1) [see Table which also gives a comparison of crystal data for compounds (2),(4)-(S), (lo), and (12)-(15)]. The basic feature of the structure is the linking of the hydroxy groups of six molecules by a network of hydrogen bonds such that the oxygen atoms form a distorted hexagon, with alternate molecules of opposite configuration lying on opposite sides of its plane.Two such groups are stacked along the c-axis such that their bulkier parts interlock forming a cage. The cage has an hour-glass shape of length equal to the c-spacing, 10.94 A (for the unsolvated crystal). All guest molecules in the above studies32~33 exhibit disorder; in the case of n-heptanol a gauche conformation has been assigned on the basis of cavity length con~iderations.~3 For smaller guest species such as ethanol or acetone, two molecules are accommodated per cage,28 corresponding to a host to guest ratio of 3:1, while for larger guests such as benzene or p-xylene each cage is singly occupied, the ratio then being 6:1. Several physical and spectroscopic studies have been directed towards eluci- dating the environment experienced by guest molecules in the well-defined cavities formed by Dianin’s compound.Detailed studies of molecular motion of guest molecules have been carried out employing dielectric relaxation measure- ment~,~~~~ and n.m.r. spectroscopy:37 barriers to internal rotation 36 and e.~.r.~O of 2.1 kcal mol-1 for acetonitrile35b and 2.3 kcal mol-1 for the di-t-butyl- nitroxide radical30 in the cage of (1) have been reported. An interesting study38 by Kispert and Pearson demonstrated that (1) could serve as a matrix for studying free radicals. These workers X-irradiated the 1,2- dibromo-1,l-difluoroethaneclathrate of (1) at 77 K and observed the Bri- radical by e.p.r. spectroscopy, the radical being located as lying parallel to the c-axis.1.r. studies of guest molecules in (1) have been reported,39 and a novel sug- gestion40 is the use of (1) as a suitable host for the observation of transitions between two rotational sublevels of the same vibrational state, in small organic (guest) molecules. Very recently Barrer and Shanson have described*l the ready sorption of gases such as Ar, Kr, Xe, and CH4, when (1) is suitably agitated. B. Structural Modification of Dianin’s Compound.-The first deliberate attempt to modify (1) was reported by Baker and co-workers2* in 1956. They successfully prepared the phenolic crystalline homologue (3) which possesses an extra methyl group adjacent to the hydroxy function. Compound (3), however, exhibited no 35 (a) M.Davies and K. Williams, Trans. Faraday Soc., 1968, 64, 529; (b) P. Dansas, and P. Sixou, Mol. Phys., 1976, 31, 1319; cf., idem., ibid., 1297. 36 J. S. Cook, R. G. Heydon, and H. K. Welsh, J.C.S.Furaday 11, 1974, 1591. 37 P. Gregoire and J. Meinnel, Compt. rend., 1971, 272. C 347. 38 L. K. Kispert and J. Pearson, J. Phys. Chem., 1972, 76, 133; for related studies employing y-irradiation see A. P. Kuleshov, V. I. Trofimov and I. I. Chkeidze, Khim. Vys. Energ., 1973, 7, 82 (Chem. Abs., 1973,79,25 604); A. P. Kuleshov and V. I. Trofimov, Khim. Vys. Energ., 1973, 7, 143 (Chem. Ah., 1973, 78, 146 926). 3s M. Davies and W. C. Child, Spectrochim. Acta, 1965, 21, 1195. 40 E. W. Aslaksen, Phys. Letters A, 1972, 40,47. 41 R. M. Barrer and V. H. Shanson, J.C.S.Chem. Comm, 1976, 333. 68 Table A comparison of crystal data for Dianin's compound (1) and related molecules Compound Space Group Lattice Parametem* Guest Mole Ratio Ref. Host:Guest R3 a = 26.97, c = 10.99 8, Ethanol 3:lt a R3 a = 27.12, c = 11.02 8, Chloroform 6:l R3 a = 27.12, c = 11.02 8, n-Heptanol 6:l R3 a = 26.94, c = 10.94 8, None R3 a = 27.81, c = 10.90 8, Ethanol 3 :1 R3 a = 27.91, c = 10.99 8, 2,2,5-Trimethylhex-3-yn-2-01 6 :1 R3 a = 28.00, c = 11.08 8, Di-t-butylacetylene 6:l R3 a = 29.22, c = 10.82 8, Cyclopen tane 6:l P212121 a = 11.78, b = 16.50, c = 8.48 8, f: R3 a = 33.63, c = 8.24 8, Cyclo-octane 4.5:l P21Ic a = 14.25, b = 6.52, c = 18.67 A, /3 = 113.0' f: P21h a = 12.91, b = 12.11, c = 9.798,, = 90.3" f: R5 a = 26.94, c = 10.80 8, Carbon tetrachloride 6:l pa21c a = b = 12.64, c = 17.25 8, 5 P212121 a = 10.60, b = 13.30, c = 10.08 8, f: P212121 a = 10.42, b = 13.69, c = 10.37 8, 5 P212121 a = 10.66, b = 13.55, c = 10.50 8, 0 R3 a = 27.06, c = 12.07 8, Carbon tetrachloride 3:l * For R3,the values of a and c given are referred to a hexagonal unit cell containing 18 host molecules (a = B = 90°, y = 120'); for other space groups unspecified angles are 90".t Ratio from ref. 28. $ No inclusion behaviour found to date. 9 for unsolvated form obtained by recrystallization from cyclohexane. a J. L. Flippen, J. Karle, and I. L. Karle, J. Amer. Chem. SOC.,1970,92, 3749. b J. L. Flippen and J. Karle, J. Phys. Chem., 1971, 75, 3566. H. H. Mills, D.D. MacNicol, and F. B. Wilson, unpublished results. d D. D. MacNicol, H. H. Mills, and F. B. Wilson, Chem. Comm., 1969, 1332. D D. MacNicol and F. B. Wilson, Chem. Comm., 1971, 786. f A. D. U. Hardy and D. D. MacNicol, unpublished results. A. D. U. Hardy,D. D. MacNicol and J. J. McKendrick, unpublished results. h A. D. U. Hardy, J. J. McKendrick, and D. D. MacNicol, J.C.S. Perkin ZI, 1977, 1145. 1 D. D. MacNicol, A. D. U. Hardy, and J. J. McKendrick, Naturp, 1975,256, 343. A. D. U. Hardy, J. J. McKendrick, and D. D. MacNicol, J.C.S. Chem. Comm., 1976, 355. Ic J. H. Gall, A. D. U. Hardy, and D. D. MacNicol, in preparation. Crystals (ref. 56) kindly provided by Professor J. \o Jacques. A. D. U. Hardy, D. D. MacNicol, J. J. McKendrick, and D. R. Wilson, Tetrahedron Lerrers, 1975,471 1. A.D. U. Hardy, D. D. MacNicol, J. J. McKendrick, and D. R. Wilson, J.C.S. Chem. Comm., 1977, 292. Clathrates and Molecular Inclusion Phenomena R3 OH OH (3) R1= R2= H; R3= Me (4) R' = R3= H; R2= Me (5) R2= R3= H; R1= Me inclusion behaviour. Subsequent systematic studies have not only led to the discovery of new clathrates, but also to those with much altered cage geometry in certain cases. These modifications are now considered under convenient sub- headings. Replacement of the Heteruatum. The synthesis42 of the thiachroman analogue of (l), compound (2), yielded a new general clathrate host. Indeed (2) appears to be the earliest example of a versatile organic clathrate host, of established43 closed- cage type, which was deliberately prepared.44 Thioether (2) shares the wide range of inclusion ability of (l), reflecting similar cavity geometry.43 A particularly interesting guest45 is the acetylenic alcohol, Me3CC =CCMe20H, for here a detailed X-ray study shows that all guest molecules adopt a staggered conforma- tion (with a statistical disorder of OH and Me groups to conform with the imposed 3 symmetry of the cavity).As shown in Figure 2, the acetylenic unit of the guest molecule is collinear with the c-axis, the triple bond fitting neatly into the waist of the cavity, leaving a tetrahedral unit in the upper and lower halves of the cavity. Similar results46 have also been obtained for the more symmetrical di-t-butylacetylene as guest in (2).The corresponding selena-ether,47a 4-p-hydroxyphenyl-2,2,4-trimethylselenachromanexhibits inclusion properties, a property not shared by the sulph~ne,~~~ 4-p-hydroxyphenyl-2,2,4-trimethyl-thiachroman 1,l-dioxide. Employing (2) as host, the intramuZecular group rotation of the formyl group of benzaldehyde has been studied by far i.r. spectroscopy: the increased rotation barrier of 6.0 kcal mol-1 for PhCHO in (2) compared with 4.9kcal mol-1 for the vapour is in keeping with a significant interaction between the guest and the cage 48 D. D. MacNicol, Chem. Comm., 1969, 836. 43 D. D. MacNicol, H. H. Mills, and F. B. Wilson, Chem. Comm., 1969, 1332. 44 Previously (see ref. 65) an analogue of Dianin's compound possessing an additional OH group mefuto the hydroxy function of (I) had been prepared and found to form adducts: the detailed nature of these complexes is, however, unknown.4s D. D. MacNicol and F. B. Wilson, Chem. Comm., 1971, 786. 46 (a)A. D. U. Hardy and D. D. MacNicol, unpublished results; (6) A. D. U. Hardy. D. D. MacNicol, and D. R. Wilson, in preparation. 47 (a)B. S. Middleditch and D. D. MacNicol, Org. Muss. Specfrometry, 1976, 11, 212; (6)D. D. MacNicol, J.C.S. Chem Comm., 1973, 621. MacNicol, McKendrick, and Wilson Figure 2 A view normal to the c-axis of the 2,5,5-trimethylhex-3-yn-2-01clathrate of (2),the guest molecule being shown in the cavity. Two molecules of (2), which lie directly above and below the cavity as viewed in this direction, have been excluded apart from their hydroxy-oxygen atoms (Reproduced from Chem.Comm., 1971, 786) Substitution of the Ring Skeleton of Compounds (1) and (2).The columns, part of which are shown in Figures 1 and 2, are infinite in extent and are surrounded by six identical columns related by three-fold screw axes which run parallel to the c-axis. Since the carbon atoms C-5, C-6, C-7, and C-8 of the aromatic ring of the chroman or thiachroman are situated on the 'outside' of columns, modification at these positions may be expected to affect intercolumn packing. Not un-expectedly, fusion of an additional bulky benzene ring to give (9) leads to severe column disruption with elimination of inclusion properties.48 On the other hand, introduction of methyl groups in the 6-, 7-,and 8-position of the thia-analogue of (l), to give (6), (7), and (8) respectively, produces an interesting spectrum of beha~iour.~~Of these only (7) exhibits no inclusion behaviour, and in this crystal one finds infinite chains of molecules linked head-to-tail by OH 9 S9 hydrogen bonds, such that no voids are left for solvent inclusi0n.4~ The most remarkable case is, however, (8) where a major change in cavity shape has been achievedS5OAs shown in Figure 3, the hour-glass shaped cavity of (2) has been converted into the 'Chinese-lantern' contour of (8). This change in cavity geometry is reflected in modification of selective clathration properties.48 48 A.D. U. Hardy, J. J. McKendrick, and D. D. MacNicol, J.C.S.Chem. Comm., 1974,972. 4s A. D. U. Hardy, J. J. McKendrick, and D. D. MacNicol, J.C.S. Perkin ZZ, 1977, 1145. D. D. MacNicol, A. D. U. Hardy, and J. J. McKendrick, Nature, 1975, 256, 343. 71 Clathrates and Molecular Inclusion Phenomena OHOH (6) R1= R2= H;R3= Me (9)(7) R1 = R3 = H;R2 = Me (8) R2= R3 = H;R1= Me w 0 I2 3A Figure 3 Section through the van der WaaZs’ surface of the cavity .4, for (2); B, for (8),representing the space available for guest accommodation (Reproduced by permission from Nature, 1975,256, 343) Interestingly, the 6-and 7-methyl homologues of Dianin’s compound itself, (4) and (5) form monoclinic crystals (see Table) without inclusion of solvent.51 Modification of the Substitution Pattern at C-2 and C-4 of Dianin’s Compound and its Optical Resolution.The hour-glass cavity contour of (1) owes its central con- striction to six inward-pointing methyl gr0ups,3~ one from each of six molecules of (1); the methyl group involved is the one syn to the p-hydroxyphenyl sub- stituent. A new clathrate host (lo), which corresponds to specific removal of this methyl group has been recently reported, and its modified cage geometry described.52 Figure 4 (a) shows the hour-glass cage shape of (l), and the curved broken lines represent the effect of formal replacement of the syn methyl by an appropriately placed hydrogen atom : the similarity between this predicted 61 A. D. U. Hardy, D. D. MacNicol, and J. J. McKendrick, unpublished results.6t A. D. U. Hardy, J. J. McKendrick, and D. D. MacNicol, J.C.S. Chem. Comni., 1976,355. MacNicol, McKendrick, and Wilson OHOH (10) R2= H; R1= R3= Me (1 3) S (-)-Dianin’s(11) R1= H; R2= R3= Me (12) R3= H; R1= R2= Me compound WA Figure 4 Section through the van der Waals’ surface of the cavity for: (a) Dianin’s Com-pound (1) as chloroform clathrate, replotted from data of ref. 32, the curved broken lines represent the effect of formal removal of‘the waist methyl groups (see text); (b)compound(10)as CC14clathrate (Reproduced from J.C.S. Chem. Comm., 1976, 355) contour and that actually found experimentally by X-ray methods, Figure 4 (b), is most striking. Removal of the methyl group on C-2 anti to theg-hydroxyphenyl substituent also yields53 a new host (1 l), though interestingly compound (12) which lacks the 4-methyl group crystallizes unsolvated in the tetragonal crystal system54 with infinite chains of molecules linked head-to-tail by (ether) 0 HO9 hydrogen bonds.In Dianin’s compound the centrosymmetric cage is made up of three molecules of one configuration and three of the opposite configuration. Inquiring into the outcome55 of having only one enantiomer present in which any cage formed would necessarily be chiral, Brienne and Jacques,56 have recently resolved (1) thereby obtaining S(-)-Dianin’s compound (13), which has the absolute 53 A. Collet and J. Jacques, J.C.S. Chem. Comm., 1976, 708. 64 J. H. Gall, A. D. U. Hardy, and D. D. MacNicol, in preparation.55 S. H. Wilen, Topics in Stereochemistry, 1971, 6, 128. 56 B. J. Brienne and J. Jacques, Tetrahedron Letters, 1975, 2349. 73 Clathrates and Molecular Inclusion Phenomena configuration shown.57 No inclusion compound formation has been found for (13) with either chiral or achiral guests.56 Changes in the Hydrogen-bonding Functionality of (1). In view of the key role of the hydrogen-bonded hexamers which form the floor and roof of each cavity in (1) it is of great interest to determine whether another hydrogen-bond-forming group might be capable of replacing the OH group without eliminating the clathrate forming ability. While the amine (14), recently prepared5R from (1) does not include solvent, it is noteworthy that this compound undergoes spon- taneous resolution on crystallization, the crystals being isomorphous with QY (14) Y = NH, (15) Y = SH resolved Dianin’s compound (1 3) (see Table).The corresponding thiol (1 5) is particularly interesting, undergoing spontaneous resolution from cyclohexane,58 but forming a clathrate58159 with carbon tetrachloride which is isomorphous with the clathrates of (1). A view of the hydrogen-bonded hexameric host unit of (15) is shown in Figure 5, the SH 9 S hydrogen bond is 3.75 8, in length. These 9 sextets are stacked on top of one another analogously to (l), cages being formed between units, in this case however, the top and bottom of a cage are formed by hexagons of sulphur atoms, 12.07 A apart. The related amine and thiol corres- ponding to (2), 4-p-aminophenyl-2,2,4-trimethylthiachroman,and 4-p-mercapto- phenyl-2,2,4-trimethylthiachroman,have also been synthesized, but these compounds crystallize without inclusion of solvent.60 2-Phenyl-3-p-(2,2,4-trimethylchroman-4-yl)phenylquinazolin-4(3H)-one (16) and its sulphur analogue (1 7). The wide-ranging inclusion behaviour of compound (16) was discovered61 when it was characterized as a synthetic intermediate in the conversion of Dianin’s compound (1) into amine (14). This host is extremely versatile, stable adducts being formed with a very wide range of solvents:61’62 67 A. Collet and J. Jacques, Israel J Chem., 1976177, 15, 82. 58 A. D. U. Hardy, D. D. MacNicol, J. J. McKendrick, and D. R. Wilson, Tetrcihedron Letters, 1975, 471 1.69 A. D. U. Hardy, D. D. MacNicol, J. J. McKendrick, and D. R. Wilson, J.C.S. Chern. Comm., 1977, 292. 8o D. D. MacNicol and D. R. Wilson, unpublished results. 81 A. D. U. Hardy, D. D. MacNicol, and D. R. Wilson, J.C.S. Chem. Comm., 1974,783. 6a C. J. Gilmore, A. D. U. Hardy, D. D. MacNicol, and D. R. Wilson, J.C.S. Perkin 11, 1977, 1427. MacNicol, McKendrick, and Wilson Figure 5 A general view of the hydrogen-bonded hexnnzeric host unit of thiol (15) in the CCI, clatlzrate (Reproduced from J.C.S. Chem. Conim., 1977, 292) (16) Z = 0 (17) Z = S important classes of guest are cycloalkanes, cyclic ethers and ketones, alcohols, and aromatic molecules. A very recent 62 X-ray analysis of the methylcyclohexane adduct, showed it to be of the true clathrate type, with two methylcyclohexane guest molecules accommodated in a large closed cage.Compound (17) a thia- analogue of (16), has also been prepared62 and found to exhibit inclusion pro- perties. In these cases, hydrogen-bonding between host molecules is not involved, the host structures being consolidated by van der Waals’ forces alone. C. Applications of Dianin’s Compound and Related Systems.-An early potential Clathrates and Molecular Inclusion Phenomena use of (1) involved its SF6 clathrate as a convenient means of storage and con- trolled release of SF6, a gas of considerable use in the electrical industry.63964 Johnson65 has employed amine complexes of (1) as polymerizing agents in the preparation of epoxy and urethane resins, and the (CF&O&CH2 clathrate acts as a latent curing catalyst in cationic polymerization,66 while the diethylamine clathrate can be used67 as a developer for the production of heat sensitive copy- ing sheets.Host (1) exhibits useful selective clathration properties allowing efficient separation of certain hydrocarbon mixtures.68 It has also been pro- posed69 that the highly toxic organo-mercurial dimethylmercury, may be handled with comparative safety in the form of its clathrate with thiachroman host (2). 3 Hydroquinone, Phenol and Substituted Phenols, and Other Hydroxy-aromatic Hosts A. Hydroquinone.-The inclusion compounds formed by quinol or hydroquinone (18), referred to as P-hydroquinone clathrates, 70 are of central importance in inclusion chemistry.Indeed the true cage structure of these, established by the OH OH pioneering X-ray studies of Powell and co-~orkers,~~ led to the introduction of the name clathrate compound. 72 Various aspects of these clathrates have been t22,reviewed including structural considerations, 73 thermodynamic proper-63 L. Mandelcorn, N. N. Goldberg, and R. E. Hoff, J. Amer. Chem. SOC.,1960, 82, 3297. 64 L. Mandelcorn, R. W. Auxier, and C. W. Lewis, U.S P. 2 949 424, 1960 (Chem. Abs., 1961, 55, 11 364). 65 C. K. Johnson, Fr.P. 1 530 51 I, 1968 (Chem. Abs., 1969, 71, 13 717). 66 J. E. Kropp, M. G. Allen, and G. W. B. Warren, Ger. Offen. 2 012 103 (Chem. Abs., 1971, 74, 43 074). 67 W.R. Lawton, Be1g.P. 632 833, 1963 (Chem. Abs., 1964, 61, 3 851). g8 A. Goldup and G. W. Smith, Separation Sci., 1971, 6, 791 ; D. H. Desty, A. Goldup, and D. G. Barnard-Smith, B.P. 973 306, 1964 (Chem. Ah., 1965, 62, 2655). 69 R. J. Cross, J. J. McKendrick, and D. D. MacNicol, Nature, 1973, 245, 146. 'O A form known as a-hydroquinone is obtained when (18) is recrystallized from solvents which are not included. 71 D. E. Palin and H. M. Powell, J. Chem. Soc., 1947,208; D. E. Palin and H. M. Powell, Nature, 1945, 156, 334; S. C. Wallwork and H. M. Powell, J. Chem. SOC.,1956, 4855; H. M. Powell,J. Chem. Soc., 1950, 298, 300,468; D. E. Palin and H. M. Powell, J. Chem. Soc., 1948, 571, 815. 72 H. M. Powell, J. Chem. SOC., 1948, 61. 73 W. C. Child, jun., Quart.Rev., 1964, 18, 321. 76 MacNicol, McKendrick, and Wilson tie~,~$73 and the motion of guest rn0lecules.7~ In ai.r. and Raman ~pectra,~4 recent X-ray study76a Mak and co-workers have accurately defined the p-hydroquinone host lattice by studying the H2S clathrate which has space group R3, and stoicheiometry 3 CsH4(OH)z,xHzS with x = 0.768 (if each cage was occupied by H2S x would be unity). Figure 6 shows a stereodrawing of the centrosymmetric cage, the guest molecule being denoted (S). The floor and roof Figure 6 Stereo drawing showing the hydrogen sulphide guest molecule (S) trapped inside a /3-hydroquinone cage. For clarity all hydrogen atoms have been omitted (Reproduced from J.C.S. Perkin ZI, 1976, 1169) of the cavity are formed by hexagons of hydrogen-bonded oxygen atoms which are nearly, but not exactly, planar; molecules point alternately up and down from each hexagon, cages being left between hexagons.The cavity is roughly spherical with a free diameter of ca. 4.8 A. As previously described by Po~ell,~~~~~ the upper and lower parts of the cavity belong to two identical but displaced three- dimensional interlocking networks. The space group R5 is not universally encountered in the clathrates of hydro- quinone, the space group R3 having been found in the recent X-ray and neutron diffraction study77 of the HC1 clathrate, in which the guest molecule resides in a cavity which is trigonal but no longer centrosymmetric. The lowering of sym- metry has been attributed77 to a large number of weak OH --Cl--H * -.OH interactions which orient the HCl guest molecule within the quinol cavity.A further lowering of symmetry to the space group P3 is found76b when the rela- tively long guest molecule acetonitrile is included in hydroquinone. There are now three types of clathrate cavity and all these have the shape of prolate spheroids. The three symmetry-independent Me C EN molecules fit snugly into the cages with one guest molecule aligned in the opposite sense to the other two. 74 D. C. McKean in ‘Vibrational Spectroscopy of Trapped Species’, ed. H. E. Hallam, Wiley, London, 1973, Ch. 8; i.r. and Raman studies are also currently being reviewed cf. J. E. D. Davies, in ‘Molecular Spectroscopy’, ed.J. Sheridan, D. A. Long, and R. F. Barrow, (Specialist Periodical Reports), The Chemical Society, London, 1978, Vol. 5, Chapter 2. 75 C. A. Fyfe in ‘Molecular Complexes’ Vol. I, ed. R. Foster, Elek Science, London, 1971, Ch. 5. ‘~3 (a) T. C. W. Mak, J. S. Tse, C.Tse, K. Lee, and Y.Chong, J.C.S. Perkin ZI, 1976, 1169; (6) T. C. W. Mak, personal communication. ’’J. C. A. Boeyens and J. A. Pretorius, Acta Cryst., 1977, B33, 2120. 77 Clathrates and Molecular Inclusion Phenomena Other recent studies on P-hydroquinone clathrates are concerned with i.r. and Raman spectra, 78 X-ray photoelectron spectroscopy, thermal decomposition, 80 e.p.r. spectra of X-irradiated adducts,sl n.m.r. spectra,82 the Mossbauer effect83 for Kr and Xe complexes, and dielectric relaxation measurements.35 B. Phenol and Simple Substituted Phenols.-Phenol itself (19) forms clath- rates7~8~~8~in which a basic feature of the host structure is the linking of the OH groups of six phenol molecules by hydrogen bonds such that the oxygen atoms form a hexagon, alternate phenyl groups pointing above and below this hexagon. These sextets are arranged in the rhombohedra1 lattice, space group R3,such that two types of centrosymmetric cage are formed,84 one large (effective length about 15 8, and 4-4.5 in free diameter) and one small with a free diameter of ca.4.5 A.Both cages are capable of including suitably sized guest molecules, and limiting compositions have been considered. 7918 Recent studies have been described for the inclusion of noble gases or other volatile species in phenol,86y87 p-fluorophenol,86.88 rn-fluorophenol,8g o-fluoro- pheno1,gO p-chlorophenol,863 91 p-cresol, 86j 92 and p-bromo-,ethyl-,t-butyl-, and phenyl-phenols.86 In the interesting paper by Barrer and Shanson,86 the separa- tion of mixtures by clathration in phenol and p-cresol is also described. C.Other More Complex Hydroxy-aromatic Hosts.-The naturally occurring compound guayacanin (20) forms an interesting inclusion compound with 78 K. D. Cleaver and J. E. D. Davies, J. MoZ. Structure, 1977, 36, 61 ; and references therein. 7B R. G. Copperthwaite, J.C.S. Chem. Comm., 1976, 707. H. G. McAdie, Canad. J. Chem., 1966, 44, 1373. H. Ohigashi and Y. Kurita, J. Magn. Resonance, 1969, 1, 464.82 E. Hunt and H. Meyer, J. Chem. Phys., 1964, 41, 353; P. Gregoire, J. Gallier, and J. Meinnel, J. Chim. Phys., 1973, 70, 1247; J. Gallier, Chem. Phys. Letters, 1975, 30, 306. 83 Y.Hazoni, P. Hillman, M. Pasternak, and S. Ruby, Physics Letters, 1962, 2, 337; G. J. Perlow, C. E. Johnson, and M. R. Perlow in ‘Noble Gas Compounds’, ed. H. H. Hyman, University of Chicago Press, 1963, p. 279. 84 M. V. Stackelberg, A. Hoverath, and Ch. Scheringer, 2. Elektrochem., 1958, 62, 123. 85 B. A. Nikitin, Cornpr. rend. U.S.S.R.,1940, 29, 571. 86 R. M. Barrer and V. H. Shanson, J.C.S. Faradny I, 1976, 2348. 87 P. H. Lahr and H. L. Williams, J. Phys. Chem., 1959, 63, 1432. J. E. Mock, J. E. Myers, and E. A. Trabant, Ind. and Eng. Chem., 1961, 53, 1007; Y.N.Kazankin, F. I. Kazankina, A. A. Palladiev, and A. M. Trofimov, Doklar!y Akad. Nairk S.S.S.R., 1972, 205, 1128 (Chem. Ah., 1972, 77, 172 102); Y. N. Kazankin, F. I. Kazankina, A. A. Palladiev, and A. M. Trofimov, J. Gen. Chem. (U.S.S.R.), 1973, 43, 2650; M. F. Pushlenkov and V. A. Ignatov, J. Gen. Chem. (U.S.S.R), 1974, 44, 2347; Y. N. Kazankin, F. I. Kazankina, A. A. Palladiev, and A. M. Trofimov, U.S.S.R. P. 411 062, 1974 (Chem. Ah., 1974, 80, 119 701). Y.N. Kazankin, A. A. Palladiev, and A. M. Trofimov, J. Gen. Chem. (U.S.S.R.), 1973,43, 2648. so Y.N. Kazankin, A. A. Palladiev, and A. M. Trofimov, J. Gen. Chem. (U.S.S.R.),1972,42, 2363. 91 B. A. Nikitin and E. M. Ioffe, Doklady Akacl. Nairk S.S.S.R., 1952, 85,809 (Chem.Abs., 1953, 47, 394). 92 A. M. Trofimov and Y.N. Kazankin, Ratliolihimija, 1965, 7, 288 (Chem. Ah., 1966, 64, 2999); A. M. Trofimov and Y. N. Kazankin, Radiokhimiya, 1966, 8, 720 (Chem. Abs., 1967, 66, 61 399); A. M. Trofimov and Y. N. Kazankin, Radiokhimiya, 1968, 10, 445 (Chem. Abs., 1968, 69, 92 527); for studies on dimethyl and trimethyl phenols see also E. Terres and K. Thewalt, Brenstoff-Chem., 1957, 38, 257 (Chem. Abs., 1958, 52, 1948). 78 MacNicol, McKendrick, and Wilson (21) a; R = H b; R = C1 acetone,93 the trigonal crystals have space group A?,with a host to guest ratio of 3 :1. Clusters of six molecules, analogous to those found in Dianin’s compound (l), for example, are linked by a network of hydrogen bonds involving the OH group, such that a hexagon of oxygen atoms is formed. Two acetone guest molecules are situated between adjacent sextets positioned along the c-axis.Although the detailed nature of the adducts is not yet known, noteworthy inclusion behaviour has been reportedg4 for compounds of the 2-(2-arylindan-l , 3-dion-2-y1)-1,4-napthohydroquinonetype (21), hosts (21a) and (21b) trapping a particularly wide range of guest species. A recent e.p.r. study concernsg5 the 2,2,6,6-tetramethyl-4-piperidinol-l-oxylradical, trapped by the flavan (22) which also traps many ethers, ketones, and amine~.~~ The exact structure of these complexes is, however, apparently unknown. 4 Inclusion Compounds of the Hexa-host Type A recently proposedg7 strategy has led to the synthesis of inclusion hosts not 93 R.Y.Wong, K. J. Palmer, G. D. Manners, and L. Jurd, Acfa Crysf.,1976, B32,2396. 94 L. P. Zalukaev, L. G. Barsukova, Vysokomol. Soedineniya, Ser A, 1973, 15, 2185 (Chem. Abs., 1974, 81, 14 490); L. P. Zalukaev and L,. G. Barsukova, Zhur. obshchei Khim., 1972, 42, 610 (Chem. Abs., 1972, 77, 101 263). 95 W. Smith and L. D. Kispert, J.C.S. Faraday II, 1977, 152. W. Baker, R. F. Curtis, and M. G.Edwards, J. Chem. SOC.,1951,83; for related hosts (and applications) see also for example W. Baker, R. F. Curtis, and J. F. W. McOmie, J. Chem. Sor., 1952, 1774; W. Baker, D. F. Downing, A. E. Hewitt-Symonds, and J. F. W. McOmie, J. Chem. SOC.,1952, 3796; M. P. V. Boarland, J. F. W. McOmie, and R. N. Timms, J.Chem. SOC.,1952,4691;W. Baker, J. F. W. McOmie and S. H. Wild, J. Chem. SOC.,1957, 3060; T. Ohta and S. Togano, Japan. Kokai, 75 131 533 (Chem. Abs., 1976, 84, 114 208);K. Yamada and N. Sugiyama, Bull. Chem. SOC.Japan, 1965, 38, 2057, 2061 ;and re6 67. 97 D. D. MacNicol and D. R. Wilson, J.C.S. Chem. Comm., 1976, 494. 79 Clathrates and Molecular Inclusion Phenomena directly related to any known host. The idea involved is based in the analogy between the hydrogen-bonded hexamer unit present in the clathrates of Dianin’s compound and other hosts (Sections 2 and 3), and a hexa-substituted benzene (see Figure 7). The temporary unit (A) which is subject to collapse as the group R R R P R I Figure 7 Comparison of (a), hydrogen-bonded hexamer unit with (b), hexa-substituted benzene analogue (Reproduced from J.C.S.Chem. Comm., 1976, 494) is varied is replaced by the permanent consolidated structure (B), it having been noted97 that unit (A) corresponds to (B) both in terms of overall geometric aspects and ‘hexamer’ dimensions (cJdistances d and d’ in Figure 7, where Z denotes a general atom or group directly attached to the central benzene ring). Following the idea that suitable hexa-substituted benzenes might have an increased chance of crystallizing to form non-close-packed structures, compounds with general formula (23) have been synthesized.97998 All of the compounds (23) a; Y = SPh e; Y = CH,SC6H4But-p b;Y = CH,OPh f; Y = CH,SeC6H4But-p yQy C; Y = CH,SPh g; Y = CH,SC6H4(1-adamanty1)-p Y Y d; Y = CH,SCH,Ph h; Y = CH2S-(2-naphthyl) Y (23a-h) exhibit inclusion ability, and (23e) for example, forms adducts with toluene, cycloheptane, cyclo-octane, phenyl acetylene, bromoforni, and iodo- benzene, with a host to guest ratio of 1 :2 in each case.In some cases remarkable guest selectivity is found, 95 % o-xylene and 5 % p-xylene being included by host (23e) when it is recrystallized from an equimolar mixture of these solvents.98 In the case of the CC14 adduct of hexaphenylthiobenzene (23a), the crystals are trigonal with space group R3 and a true clathrate structure is found:99 two cc14 guest molecules fit snugly into a cavity of effective length ca. 17 A, and these are oriented such that a C-Cl bond of each is collinear with the c-axis of the crystal.98 D. D. MacNicol and D. R. Wilson, Chem. and Ind., 1977, 84; for other recent work on selective inclusion see D. H. Brown, R. J. Cross, and D. D. MacNicol, Chem. and Ind., 1977, 766, and references therein; K. Takemoto, Kagaku Kogaku, 1977,41, 184 (a review) (Chem. Abs., 1977, 87, 7929). 9B D. D. MacNicol, A. D. U. Hardy, and D. R. Wilson, Nature, 1977, 266, 611. 80 MacNicol, Mck'etidrick, and Wilson A very recent X-ray study has shown"6 that, in contrast to the trigonal CCh clathrate of (23a) described above, the crystals of the adduct of (23d) with 1.4-dioxan are monoclinic with space group P21/c; the chair-shaped dioxan guest molecules being located on crystallographic centres of symmetry. 5 Hosts with Structures Possessing Trigonal Symmetry Trigonal symmetry is a feature apparent in the molecular structure of several important hosts (including the hexa-hosts in Section 4) forming multimolecular inclusion compounds in which the surrounding lattice is consolidated by van der Waals' attractive forces, but not by hydrogen bonding.The individual host molecule does not always attain exact crystallographic three-fold symmetry, how- ever, although trigonal (or hexagonal) lurrice symmetry is often encountered.1o0 Recent X-ray studies have elucidated the structures of channel type adducts of triphenyl rnethaneIO1 (24), perhydrotriphenylene102(29, tris(o-phenylenedioxy) cyclotriphosphazenel03 (26) and related compounds104,105and the unsol-vated,106--l08 channel-,106 and cage-typelOG,'Oi forms of tri-o-thymotide2"lo6 (27).In all the crystal modifications of (27) a propeller conformation is found for the host molecule with the three carbonyl oxygen atoms lying on the same side of the twelve-membered ring, although in no case is exact molecular C3 symmetry present. In 1954 Baker and co-workerslOg reported results of a study of com-pounds related to (27), but none of the compounds synthesized gave crystal- 1in e inc1usion compound s. I nter e st i ng1y how ever, N,N ',N "-t r i ben zy 1t rian t h r a n i-lide has recently been found110 to form a 1:l complex with ethanol. N.m.r. studies of cycloveratril(28) have established that it has a crown conformation.ll1 looSee for example S.,4. Puckett, I. C. Paul, and D. Y. Curtin, J.C.S. PerXin I/, 1976, 1873 (Table 3). lol A. Allemand and R. Gerdil, Acta Crj,st., 1975, A31, S130. lo2 G. Allegra, M. Farina, A. Immirzi, A. Colombo, U. Rossi, R. Broggi, and G. Natta, J. Chem. SOC.(B), 1967, 1020; G. Allegra, M. Farina. A. Colombo, G. Casagrande-Tettamanti, U. Rossi, and G. Natta, ibid., 1967, 1028; A. Immirzi and G. Allegra, Atti. Accad. naz. Lincei, Rend. Classe Sci. ,fis. mat. nat., 1967, 43, 181 ; see also for example, Z. Ciecierska-Tworek, G. B. Birrell, and 0.H. Griffith, J. Ph,~.s.Chem., 1972, 76, 1008; and refs. therein. lo3H. R. Allcock, R. u'.Allen, E. C. Bissell, L. A. Smeltz, and M. Teeter, J. Amer. Cf7en~. Soc., 1976, 98, 5120. lo4 H.R. Allcock and M. T. Stein, J. Anier. Chen7. Soc., 1974, 96, 49 [tris(2,3-naphthylene- dioxy)cyclotriphosphazene]. H. R. Allcock, M. T. Stein, and E. C. Bissell, J. Anfer. Chem. Soc., 1974, 96, 4795 [tris(I ,8-naphthylenedioxy)cyclotriphosphazene]. lo6 D. J. Williams and D. Lawton, Tefraherlron Letters, 1975, 1 11. lo' S. Brunie, A. Navaza, G. Tsoucaris, J. P. Declercq, and G. Germain, Acta Crj'sf., 1977. B33, 2645. S. Brunie and G. Tsoucaris, Cryst. Striict. Conznz., 1974, 3, 481. log W. Baker, J. B. Harborne, A. J. Price, and A. Rutt, J. Ckeni. Soc., 1954, 2042 however, see also W. Baker, A. S. El-Nawawy and W. D. Ollis. J. Cheni. Soc., 1952, 3163; W. Baker, W. D. Ollis, andT. S. Zealley,J. Chem. SOC.,1951, 201, W. Baker, B. Gilbert. W.D.Ollis, and T. S. Zealley, J. Cherrt. Sor., 1951, 209; and refs. therein. 110 W. D. Ollis, .I.S. Stephanatou, J. F. Stoddart, and A. G. Fenige, Angrtv. Chctn. Intrrncif. Ecin., 1976, 15, 223; cf. D. J. Williams, J.C.S. Chem. Comni., 1977, 170. 111 R. C. Cookson, B. Halton, and I. D. R. Stevens, J. Chein. Soc. (B), 1968, 767; and refs. therein. 81 Clathrates and Molecular Inclusion Phenomena Qo"0/ Q R (29) a; R = H b; R = Me MacNicol, McKendrick, and Wilson Compounds (29a) and (29b) have recently been synthesized,lI2 trigonal sym- metry having been taken into account in their design. Both these hosts tightly retain volatile guest species, for example (29b) forms inclusion compounds with cyclopentane, t-butyl acetylene, and 2,2- and 2,3-dimethylbutanes, the host to guest ratio being 2:l in each case.6 Cyclodextrins and Related Molecules These molecules, which have attracted much attention as enzyme active-site models, are considered very briefly here since several excellent reviews are a~ailable.1-3~j~1~~The cyclodextrins (cycloamyloses) are torus-shaped molecules made up of different numbers of cc-1,4-linked D-glucopyranose units, a and p-cyclodextrin (aand p-CD), (30) and (31) comprising 6 and 7 units respectively. In contrast to systems discussed earlier, host-guest chemistry is found both in the OH OH solid state and in solution. One may also note that the OH groups on C-2, C-3, and C-6 are available as points of structural modification without danger of eliminating the central void availabe for guest accommodation.Numerous X-ray studies114 of a-CD with various guests reveal that both cage-type and channel- type crystalline inclusion compounds are formed. Much work has been done on the binding of guests to the cyclodextrins in aqueous solution, though complexa- tion has also been found for /3-CD in non-aqueous solvents.115 Points arousing much current interest are the geometry of the complexes formed116 and the factors responsible for complexation116~117 in aqueous solutions. In extremely 112 D. D. MacNicol and S. Swanson, Tetrahedron Letters, 1977, 2969. 113 D. French, Adv. Carbohydrate Chem., 1957, 12, 189. 114 K. Harata, Bull. Chem. SOC.Japan, 1977, 50, 1416; and references therein.115 B. Siege1 and R. Breslow, J. Amer. Chem. SOC.,1975, 97, 6869. 116 R. J. Bergeron, M. A. Channing, G. J. Gibeily, and D. M. Pillor, J. Amer. Chem. SOC., 1977.99, 5146. 117 W. Saenger, M. Noltmeyer, P. C. Manor, B. Hingerty, and B. Klar, Bioorg. Chem., 1976,5, 187; R. J. Bergeron and M. P. Meeley, ibid., 1976, 5, 197. 83 Clathrates and Molecular Inclusion Phenomena elegant n.m.r. studies1lsU9 involving the nuclear Overhauser effect between host and guest, Bergeron and co-workers have shown that sodium p-nitrophenolate penetrates the a-CD cavity to only a limited extent, but is more deeply embedded in the larger /3-CD void. In an important study of the molecular dynamics of a-CD complexes by 2H and 13C relaxation, Behr and Lehn119 point out the importance of the dynamic rigidity of the complex, defined by the coupling between the molecular motions of its component parts.Solution complexa- tion120 has also been studied by e.p.r.I2l and U.V. spectroscopy,122 and by ~.d.12391~~a measurements havealso proved measurements. Micro~alorimetricl24~ valuable, and a recent of the interaction of a-CD with a series of small, chiral benzene derivatives has revealed a small, but distinct chiral discrimination for the binding of certain optical isomers, for example, the D and L forms of phenylalanine, the results being consistent with those from a parallel competitive spectral inhibition technique. An equilibrium and kinetic investigation of com-plexes of p-CD with several small inorganic anions has also been recently described.125 Stopped-flow spectrophotometry has been employed126 to study the kinetics of binding of CuII to a-and p-CD, and an e.p.r.in~estigationl2~ of the complexation of isotopically pure Cuxl to these hosts shows two distinct magnetic environments for the copper. A large number of mono-substituted cyclodextrins have been prepared in connection with enzyme model studies.l ,2v12* In recent work directed towards even more sophisticated enzyme rnodels,l29 a number of specifically bifunc- ll8 (a) R. Bergeron and R. Rowan, Bioorg. Chem., 1976, 5, 425; (b) R. Bergeron and M. A. Channing, Bioorg. Chem., 1976,5,437; (c) cf. D. J. Wood, F. E. Hruska, and W. Saenger, J. Amer. Chem. SOC.,1977, 99, 1735; (d)for other n.m.r.studies see also ref. 122. llP J.P.Behr and J. M. Lehn, J. Amer. Chem. SOC., 1976, 98, 1743. lZo See also references cited in refs. 119 and 118c. lZ1 N. M. Atherton and S. J. Strach, J.C.S. Faraday I, 1975, 71, 357; J. Martinie, J. Michon, and A. Rassat, J. Amer. Chem. SOC.,1975, 97, 1818; N. M. Atherton and S. J. Strach, J. Magn. Resonance, 1975, 17, 134. lZ2 K. Uekama, M. Otagiri, Y. Kanie, S. Tanaka, and K. Ikeda. Chem. Pharm. Bull., 1975, 23, 1421; M. Otagiri, T. Miyagi, K. Uekama, and K. Ikeda, ibid., 1976, 24, 1146; M. Otagiri, K. Uekama, and K. Ikeda, ihid., 1975, 23, 188; K. Ikeda, K. Uekama, and M. Otagiri, ibid., 1975, 23, 201 ;CJ also T. Miyaji, Y. Kurono, K. Uekama, and K. Ikeda, ibid., 1976, 24, 1155 (potentiometric titration study).la3 K. Harata and H. Uedaira, Bull. Chem. SOC. Japan, 1975,48,375; K. Takeo and T. Kuge, Starke, 1972,24,281; N. Matsuura, S. Takenaka, and N. Tokura, J.C.S. Perkin I[, 1977, 1419. 12* (a) K. Takeo and T. Kuge, Sturke, 1972, 24, 331 ; (b) E. A. Lewis and L. D. Hansen, J.C.S. Perkin II, 1973, 2081; (c) A. Cooper and D. D. MacNicol, J.C.S. Perkin II, in press. lZ5 R. P. Rohrbach, L. J. Rodriguez, E. M. Eyring, and J. F. Wojcik,J. Phys. Chem., 1977,81, 944. lZ6 K. Mochida and Y. Matsui, Chem. Letters, 1976, 963; and refs. therein. 12' A. A. McConnell and D. D. MacNicol, unpublished results. lz8 Y. Matsui, T. Yokoi, and K. Mochida, Chem. Letters, 1976, 1037; C. van Hooidonk, D. C. de Korte, and M. A. C. ReuIand-Meereboer, Rec.Trav. chim., 1977,96,25; and references therein; Y. Twakura, K. Uno, F. Toda, S. Onozuka, K. Hattori, and M. L. Bender, J. Amer. Chem. SOC., 1975, 97,4432; cf. also Y. Murakami, Y. Aoyama, and K. Dobashi, J.C.S. Perkin II, 1977, 24; and references therein. las I. Tabushi, K.Shimokawa, and K. Fujita, Tetrahedron Letters, 1977, 1527; and referenceo therein. MacNicol, McKendrick, and Wilson tionalized1299130 and multifunctionalized~3~ cyclodextrins have been prepared. Tabushi and co-workers7130 studying phosphorescence spectra of complexes of is-CD modified with a ‘capping’ benzophenone chromophore, have found highly effective and structurally specific triplet energy transfer between excited host and ground state guest molecules.In an extension of earlier work132 on the remark- able regio-specific chlorination of anisole by HOCl in the presence of a-CD (and P-CD) in aqueous solution, Breslow and co-~orkersl~~ report an even higher specificity employing dodecamethyl-a-CD (all OH groups on C-2 and C-6 methylated), the product being greater than 99 % p-chloroanisole. This reflects more effective guest binding by the modified cc-CD and shows that the C-3 hydroxy (as hypochlorite for C1 transfer) is capable of catalytic function, while not ruling out the possible role of other OH groups in or-CD itself. The parent cc-and P-cyclodextrins have recently found use as chiral n.m.r. shift reagents.134 For example, in the presence of P-CD in DzO, 19Fn.m.r. spectra of the A3B3 type (proton noise decoupled) have been observed for PhC(CF3)20H, the induced non-equivalence between CF3 groups arising from guest accommodation in the optically-active void of the host.Typical spectra for this substrate are shown in Figure 8, dissolved salts such as LiCl increasing the induced chemical shift. Cyclodextrins and their inclusion compounds have found amazingly diverse uses. In a recent study,135 is-CD was found to greatly enhance and stabilize the fluorescence intensity of dansyl amino acids, allowing improved detection and determination of these compounds by t.1.c. a-CD is an efficient separating agent for 0-,m-,and p-cymene: from an approximately 1 :1 :I mixture 97 % pure p-cymene was obtained by steam distillation of the crystalline add~ct.1~~ The nitroglycerine inclusion compound of p-CD can be used as an explosive,l37 and the chloropicrin adduct is effective as a bactericide and insecticide.138 The complex of methyl parathion with is-CD has useful and persistent activity against 130 I.Tabushi, K. Fujita, and L. C. Yuan, Tetrahedron Letters, 1977, 2503. 131 R. 5. Bergeron, M. P. Meeley, and Y.Machida, Bioorg. Chew., 1976,5, 121 J K. Tsujihara, H. Kurita, and M. Kawazu, Bull. Chem. Suc. Japan, 1977, 50, 1567; and references therein. 132 R. Breslow and P. Campbel1,J. Anter. Chem. Soc., 1969,91, 3085; Bioorg. Chem., 1971, 1, 140; see also R. Breslow, Chew. SOC.Revs., 1972, 1, 553. 133 R. Breslow, H. Kohn, and B. Siegel, Tetrahedron Letters, 1976, 1645.134 D. D. MacNicol and D. S. Rycroft, Tetrahedron Letters, 1977, 2173; cJ D. D. MacNicol, Tetrahedron Letters, 1975, 3325. 135 T. Kinoshita, F. Iinuma, K. Atsumi, Y. Kanada, and A. Tsuji, Chew. Pharm. Bull., 1975, 23, 1166; for other chromatographic applications see also D. M. Sand and H. Schlenk, Analyt. Chem., 1961, 33, 1624; H. Schlenk, J. L. Gellerman, J. A. Tillotson, and H. K. Mangold, J. Anier. Oil Chemists’ Soq., 1957, 34, 377. 136 Y. Suzuki, T. Maki, and K. Mineta, Japan. Kokai, 75 96 530 (Chem. Abs., 1975, 83, 205 896). 13’ E. Akito, Y. Nakajima, and M. Horioka, Japan. Kokai, 75 129 520 (Chem.Ah., 1976, 84, 58 617). 138 Y. Suzuki, H. Iwasaki, and F. Kamimoto, Japan. Kokai, 75 89 306 (Chem. Abs., 1976, 84, 16 737). Clathrates and Molecular Inclusion Phenomena A 10 Hz Figure 8 Proton noise-decoupled 19Fn.m.r.spectra oj (CF,),C(OH)Ph in the presence of /3-CD in D20showing induced chemical shift non-equivalence. Spectrum a, 0.01M-S-CD and 0.006M-substrate at 50°C; b, simulated A,B, spectrum with Y (A-B) = 13.8 Hz, J (A-B) = 8.9 Hz, and linewidth = 1.2 Hz; c, spectrum for O.OIM-fi-CD, 0.01M substrate, and 11M-LiCl at 25 "C; d, as b but with Y (A-B) = 26.0 Hz, J (AB) = 8.0 Hz, and linewidth = 6.5 Hz (Reproduced by permission from Tetrahedron Letters, 1977, 2173) cotton insects,l39 whereas clathrates of various pyrethroids prove more effective against cockroaches than the guest compounds in their free state.140 The cyclo- hexylamine complex of p-CD is useful in rust prevention,141 and the COZ clathrate of cc-CD can serve as a baking p0wder.1~2 The cavities of the cyclodextrins also afford protection to hydroperoxides,143 coenzyme A,144 and fatty acids for example, the latter being preserved against oxidation even in a pure oxygen atm0~phere.l~~ Currently much of the great interest in the cyclodextrins arises from their lRSI.Yamamoto, K. Ohsawa, F. W. Plapp, jun., Nippon Noyaku Gakkaishi, 1977, 2, 41 (Chern. Abs., 1977, 87, 113 013); see also I. Yamamoto, A. Shima, and N. Saito, Japan. Kokai, 76 95 135 (Chem. Ah., 1977, 86, 12 714). lgoA. Mifune, Y.Katsuda, and T. Yoneda, Ger. Offen. 2 357 826, 1974 (Chem. Ah., 1975,82, 39 586). lgl T. Hiroshi and K. Miwa, Japan. Kokai, 76 108 641 (Chem. Abs., 1977, 86, 31 101).H. Schlenk, D. M. Sand, and J. A. Tillotson, U.S.P. 2 827 452. 1958 (Chem. Abs.. 1958.52. 12 901). 143 Y. Matsui, H. Naruse, K. Mochida, and Y. Date, Bull Chem. SOC.Japan, 1970, 43, 1909, 1910. 144 T. Oguma, Y. Saito, and T. Kobayashi, Japan. Kokai, 75 142790 (Chem. Abs., 1976, 84, 117 800). Ig5 J Szejtli and E. Banky-Elod, Stiirke, 1975, 27, 368 (Chem. Ah., 1976, 84, 32 918). MacNicol, McKendrick, and Wilson pharmaceutical application^,^ 9 146 e.g.,stable clathrates of 1-butyl-I-nitrosourea, a useful anti-tumour agent are formed with a-and /?-CD.l47 Significantly, the inclusion compound of flufenamic acid is water soluble unlike the drug itself.14* The silver-sulphadiazine-/?-CD complex149 is effective in treating burns and infected wounds.Prostaglandin E2 is greatly stabilized by formation of the a-and /3-CD inclusion compounds,150 and a /?-CD complex of a bufadienolide derivative has been found to be more stable, less toxic, and more effective than the free reagent.151 Finally, in a recent paper Tabushi and co-workers described152 a novel one- step preparation of vitamin K1 or K2 analogues by cyclodextrin inclusion catalysis. 7 Concluding Remarks A striking highlight of the literature of the past decade on inclusion chemistry has been the careful design and synthesis of new host materials. The emergence of crown4 compounds, modified cyclodextrins, and other hosts,153 is of enormous importance with respect to solution behaviour. New crystalline multimolecular hosts have also been synthesized despite the tendency of the vast majority of organic molecular crystals to be efficiently close packed.Successful tactics here have been the judicious modification of known hosts, and the use of analogy which has led to the discovery of the hexa-hosts. At the present time chemical intuition is still very much to the fore, though with recent developments in crystal packing theory, and the availability of increasingly powerful computer programs for the calculation of potential energy minima in organic crystals, one may predict the possibility of complete void design in the foreseeable future. We would like to thank Dr. A. D. U. Hardy for reading and making helpful comments on the manuscript. 146 See for example, S.Tanaka, K. Uekama, and K. Ikeda, Chem. Pharm. Bull., 1976, 24, 2825; and refs. therein. 14’ T. Nagai and Y. Murata, Japan. Kokai, 73 75 526 (Chem. Abs., 1974, 80, 71 050). 148 T. Nagai, Japan. Kokai, 75 116 617 (Chem. Abs., 1976, 84, 111 654). 149 H. Trommsdorff, Fr. Demande 2 209 582, 1974 (Chem. Abs., 1975, 82, 144 957). 150 M. Hayashi and I. Takatsuki, Ger. Offen. 2 128 674, 1971 (Chem. Abs., 1972,76, 59 978). 151 S. Ohno, Japan. Kokai, 75 160416 (Chem. Abs., 1976, 84, 126 774). 152 I. Tabushi, K. Fujita, and H. Kawakubo, J. Amer. Chem. Suc., 1977, 99, 6456. 153 I. Tabushi, Y. Kuroda, and Y. Kimura, Tetrahedron Letters, 1976, 3327; I. Tabushi, H. Sasaki, and Y. Kuroda, J. Amer. Chem. SOC.,1976,98, 5727.

ISSN:0306-0012    

DOI:10.1039/CS9780700065

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Time-correlation Functions and Molecular Motion By G. Williams EDWARD DAVIES CHEMICAL LABORATORIES, UNIVERSITY COLLEGE OF WALES, ABERYSTWYTH, SY23 lNE, DYFED 1 Introduction The time-independent thermodynamic properties of molecular liquids and solids and their rationalization in terms of time-independent statistical mechanics receive considerable attention in undergraduate courses in chemistry and physics. The dynamical properties of such systems involve translational, vibrational, and reorientational modes of molecular motion and whereas the vibrational motions, which give rise to infrared, Raman, and neutron-scattering spectra, are well covered in undergraduate courses, considerably less attention is given to transla- tional and reorientational modes of motion.Many of the important physical properties of liquids and solids relate to the latter modes of motion, and in recent years there has been a considerable interest in their study using many experimental techniques. Table 1 lists a selection of the techniques, and will be discussed below. In parallel with experimental studies, a sound theoretical framework has emerged, based on time-correlation functions, which allows translational and reorientational motions to be described formally and in physical terms. In addition there have been simulations, by computer, of the dynamics of assemblies of molecules which yield various time-correlation functions and which may be used for comparison with experimental data and with simple models for motion. We shall see that molecular motions play an essential part in the interpretation of data from relaxation studies, absorption spectroscopy, and certain scattering experiments.Such experiments cover in total the frequency range lo-4-1012 Hz. Clearly an appreciation of the nature of molecular motions, their time-scale, and their variation with temperature and applied pressure, in liquids and solids, as revealed by different techniques, should be an essential part of courses concerned with molecular behaviour. However, there are several difficulties which must be overcome before this can be fully achieved. One major difficulty is that a description of translational and reorientational motions is best given through the medium of time-correlation functions and chemists are, on the whole, unfamiliar with such quantities.Excellent accounts of time- correlation functions are available, but most are at research level, with the attendant mathematical sophistication, or do not give sufficient information to serve as an introduction. One aim of the present review is to give an account of time-correlation functions amply illustrated with examples of their deduction for simple models which have practical importance. In addition, it is shown how time-correlation functions may be related to experimental quantities taking as examples (i) the linear response of a dielectric medium and (ii) quasi-elastic scattering from moving point-scatterers. The remainder of the review gives examples of time-correlation functions which have been obtained experimentally using several of the techniques listed in Table 1.Table 1 Experimental Tracer diffusion Dielectric relaxation Kerr-effect relaxation Mechanical relaxation Depolarization of fluorescence Nuclear magnetic resonance Time1 frequency Measured Molecular Time-correlation function Refs. range quantity probe Seconds to years Translational Tagged Dt = (A) 1: <m.wdt 1-3 diffusion molecule coefficient, Dt = lim (([u(t) -u(0)]2)/6t} 10-4-1011 HZ moment (ii) Ions, ion (Pl[u(t)])and mixed correlation pairs, vacancies functions 10-4-107 HZ Electric-field Dipole moments, (Pl[u(t)]), (P2[u(f)]) 19-24, 112 and 1O-l1-induced permanent and 4 x 10-11 s optical induced, birefringence optical anisotropy 10-4-108 HZ Mechanical Elastic dipole 6, 14-16, 25 storage and (in crystals) loss moduli and compliances 10-6-10-9 s Time-dependence Transit ion <Pz[u(t)l) 2, 26-30 of fluorescence dipole 103-10* HZ Relaxation times Nuclear Average correlation times 2, 31-34 Ti, Tip,Tg magnetic moment Quasi-elastic 10~-1011Hz Scattering Particle scattering 2, 35-41 light scattering functions cross-sections, (0 Fa(k,t) fluctuations in (i) Correlation functions for (ii) S(k,w) thermodynamic translational and rotational variables, motions of macromolecules, polarizability dynamics of fluctuations in pure ellipsoid liquids (ii) Correlation functions for reorientation Neutron 10s-1012 HZ Scattering Correlation functions for transla- 2,4246 scattering cross-section tional and rotational motions, correlation times d2Infrared 3 x 1010-(i) Far infrared, (i) Permanent (PMt)l), dT<P1[u(t)l) 2,47-56spectroscopy 1014 HZ n(o),Q(w), E(W) and induced dipole moments and multi- moments.(ii) Near infra- (ii) Vibration- d2 red CC(W), rotation transi- (Pl[u(t)I), d? (Pl[u(t)l) vibration-tion moments rotation spectra Raman d21018-1014 HZ a(w), vibration-vibration-(Pz[u(t)l), G2<Pz[u(t)l) 47, 50 spectroscopy rotation rotation spectra transition moments P. A. Egelstaff, ‘Introduction to the Liquid State’, Academic Press, London, 1967. B. J. Berne, in ‘Physical Chemistry, an Advanced Treatise’, Vol. VIIIB, ‘The Liquid State’, ed.H. Eyring, D. Henderson, and W. Jost, Academic Press, New York, 1971, p. 540-713. R. Zwanzig, Ann. Rev. Phys. Chem., 1965, 16, 67. C. P. Smyth, ‘Dielectric Behaviour and Structure’, McGraw-Hill, New York, 1965. N. E. Hill, W. Vaughan, A. H. Price, and M. Davies, ‘Dielectric Properties and Molecular Behaviour’, Van Nostrand, New York, 1969. sN. G. McCrum, B. E. Read, and G. Williams, ‘Anelastic and Dielectric Effects in Polymeric Solids’, Wiley, London, 1967. ’G. Williams, Chenz. Rev., 1972, 72, 55. (Refs. continued overleaf) Time-correlation Functions and Molecular Motion G. Wyllie, in ‘Dielectric and Related Molecular Processes’, ed. M. Davies (Specialist Periodical Reports), The Chemical Society, London, 1972, Vol. 1, p.21. C. Brot, ref. 8, 1975, Vol. 2, p. 1. loS. H. Glarum, J. Chem. Phys., 1960, 33, 1371. l1 R. H. Cole, J. Chem. Phys., 1965, 42, 637. l2 G. Williams and M. Cook, Trans. Faraday Soc., 1971, 67, 990. l3 M. Cook, D. C. Watts, and G. Williams, Trans. Faraday Soc., 1970, 66, 2503. l1 A. Nowick and B. S. Berry, ‘Anelastic Relaxation in Crystalline Solids’, Academic Press, New York, 1972. l5 A. S. Nowick and W. R. Heller, Adv. Phys., 1965, 14, 101. l6 A. S. Nowick and W. R. Heller, Ah. Ph.vs., 1967, 16, I. R. J. Meakins, in ‘Progress in Dielectrics’, Vol. 3, Heywood, London, 1961, p. 153. l8 J. C. Lestrade, J. P. Badiali, and H. Cachet, in ref. 9, p. 106. l9 H. Benoit, Ann. Phys., 1951, 6, 561. 2o C. T. O’Konski and B. H. Zimm, Science, 1950, 111, 113.21 C. T. O’Konski and A. J. Haltner, J. Amcr. Chem. Soc., 1956, 78, 3604. 22 E. Fredericq and C. Houssier, ‘Electric Dichroism and Electrical Birefringence’, Oxford U.P., London, 19’74. 23 M. S. Beevers, J. Crossley, D. C. Garrington, and G. Williams, J.C.S. Faraday II, 1976, 72, 1482. 24 B. R. Jennings and B. L. Brown, European Polymer J., 1971, 7,’805. 25 K. F. Herzfeld and T. A. Litovitz, ‘Absorption and Dispersion of Ultrasonic Waves’, Academic Press, New York, 1959. 26 F. Perrin, J. Phys. Radium, 1926, 7, 390. 27 ‘Fluorescence Techniques in Cell Biology’, ed. A. A. Thaer and M. Sernetz, Springer- Verlag, Berlin, 1972. 28 ‘Biochemical Fluorescence’, ed. R. F. Chen and H. Edelhoch, Vol. 1, MarceI Dekker, New York, 1975. 29 B.Valeur and L. Monnerie, J. Polymer Sci., Polymer Phys., 1976, 14, 11. 30 B. Valeur and L. Monnerie, J. Polymer Sci., Polymer Phys., 1976, 14, 29. 31 A. Abragam, ‘Principles of Nuclear Magnetism’, Oxford U.P., 1961. 32 W. P. Slichter in ‘NMR Basic Principles and Progress’, Vol. 4, ‘NMR of Polymers’, Springer-Verlag, Berlin, 197 1, p. 209. 33 T. M. Connor, ref. 32, p. 247. 34 R. H. Cole, ‘Mechanie Statistique des Mouvements Angulaires en Phase Liquide’, Fac. Sciences, Orsay, 1969. 35 H. Z. Cummins, F. D. Carlson. T. J. Herbert, and G. Woods, Biophys. J., 1969, 9, 518. 36 B. Chu, Ann. Rev. Phys. Chem., 1970, 21, 145. 37 W. L. Peticolas, Fortsch. Hochpolym. Forsch., 1972, 9, 285. 38 W. L. Peticolas, Ann. Rev. Phys. Chem., 1972, 23, 93. 39 H.2. Cummins and E. R. Pike, ‘Photon Correlation and Light Beating Spectroscopy’, Plenum Press, New York, 1974. ‘O B. Chu, ‘Laser Light Scattering’, Academic Press, New York, 1974. 41 B. J. Berne and R. Pecora, ‘Dynamic Light Scattering’, Wiley-lnterscience, New York, 1976. 42 B. T. M. Willis, ‘Thermal Neutron Scattering’, Oxford U.P., 1973. 43 J. W. White, in ‘Molecular Spectroscopy’, ed. P. Hepple, Institute of Petroleum, London, 1972. 44 G. Allen and J. S. Higgins, Reports Progr. Phys., 1973, 36, 1073. 45 B. K. Aldred, G. C. Stirling, and J. W. White, Faraday Symposia Chem. Soc., 1972, No. 6, p. 135. 46 A. J. Leadbetter, A. Turnbull, and P. M. Smith, J.C.S. Faraday II, 1976, 72, 2205. 47 R. G. Gordon, Auk. Magn. Resonance, 1968, 3, 1.48 G. W. Chantry, ‘Sub-Millimetre Spectroscopy’, Academic Press, London, 1971. 49 W. G. Rothschild, J. Clzem. Phjs., 1970, 53,990. 50 W. G. Rothschild, G. 5. Rosasco, and R. C. Livingston, J. Chern. Phys., 1975, 62, 1253. 51 P. Van Konynenberg and W. A. Steele, J. Chem. Phys., 1972, 56, 4776. 52 M. Evans. J.C.S. Furatfa>,11, 1975, 71, 2051. 53 G. J. Evans and M. Evans, J.C.S. Faraday 11, 1976, 72, 1169. 54 M. Evans and G. J. Davies, Ah. Mol. Relaxation Processes, 1976, 9, 129. 55 R. G. Gordon, J. Chern. Phys., 1966, 44, 1830. 56 G. J. Evans and M. Evans, J.C.S. Faraday I/, 1977, 73, 285. Williams 2 Time-correlation Functions A. General Considerations.-There are several accounts dealing with time-correlation functions as they arise for different modes of motion and for different experimental techniques (see Table 1and refs.therein). Of the available accounts, those of Zwanzig,3 G0rdon,~7 Berne,2 and Berne and ~o-workers~79~8are particularly instructive owing to their wide scope. In this section we consider the definitions of the autocorrelation function C(t) for a dynamical variable A of a system whose macroscopic thermodynamic properties are independent of time. A might be the velocity v, position Y, or dipole moment p, suitably defined, for a molecule in an assembly of molecules. may be defined as the ensemble-averaged quantity C(t>= jj”A(p,q; 7)m,4; t + .>f(P,s) dPd4 = <A(7)A(t + 7)) 5 (A(O)A(r)) (1) t T) is the value of A at time (t + T)given that the value was A (T)at time T.For a stationary system the product (A(T)A(t + T)) is dependent on the interval t bat not on the arbitrary time T.f(p,q)is the equilibrium phase-space distribution function; f(p,q)dpdq is the probability that a molecule has conjugate momenta and co-ordinates in the ranges p to (p + dp) and q to (q + dq) respectively. A depends upon p and q explicitly and, because these quantities vary with time for a given molecule, A will vary with time for that molecule. C(O) = IJA2(p,q; T)f(p,q)dpdq = (A~(T))is the mean-square value of A which is calculable, in principle, from time-independent statistical mechanics. The deduction of C(t)is made as follows: Figure 1 shows A(p,q),in phase-space, along a trajectory arising from the thermal motions of the system.We first obtain A(T). A(t + T) averaged over all trajectories which may occur for the interval t, and weight this averaged quantity by the probability f(p,q)dpdq of having the initial (p,q)condition for the molecule. The process is repeated from all allowed (p,q)starting conditions and C(t)is obtained using equation (1). C(f) may also be defined as a time-averaged quantity:2 C(t)= lim (f)JT 47)A(t + 7)d7 T+rn 0 This may be visualized as follows: the dynamical variable follows a trajectory in phase-space as time progresses (Figure 1) and we may form A(T)A(~4-T) starting at the arbitrary time T. But there is an equal probability that we should take such a product for the interval t at any time T through the complete trajectory in order to obtain an averaged quantity for an interval of time t.Equation (2) becomes in the limit T --f 03 this average quantity. For a stationary system the 57 B. J. Berne and G. D. Harp, Adv. Chem. Phys., 1970, 17, 63. 58 B. J. Berne and D. Forster, Ann. Rev. Phys. Chem., 1971, 22, 563. 93 Time-correlation Fuirctioiis and Molecular Motioir A t Figure 1 Schematic illustratiori of a phase-space trajectory for the dynaniical vnriable A ensemble-averaged quantity, equation (1) and the time-averaged quantity, equation (2), are equal, this being known as the ergodic hypothe~is.~,4’ For a comprehensive account of the properties of molecular time-correlation functions, both classical and quantum mechanical, the reader is referred to Berne.2 The present account considers only classical functions and we note that these have sevkral special mathematical properties2 amongst which are the following : (N) classical time-correlation functions are even in time, C(t) = (A(O)A(t)) = (A(O)A(-t)).Thus a series expansion of C(t)contains only terms in even powers oft. Several models for molecular motion give correlation functions whose series expansions involve terms in odd powers oft, and these are not strictly acceptable correlation functions (e.g. for an exponential function of time). (b) C(t)satisfies the inequality -I d [C(t)/C(O)]6 1. Thus C(t) may become negative with increased t, as is the case for the classical rotator in three dimensions (see Section 2D below).For many models for motion C(t)--f 0 as t --f cc,and for such cases we may define a correlation time -T~for the process as For the special case of an exponential correlation function C(t)= C(0)exp [ -(t/~’)], then T~ = 7‘. For a distribution of correlation (or ‘relaxation’) times, where C(t) = C(0)J p(.’) iexp[-(t/~’)] dT‘ then from equation (3) Williams T~ = (7') = ~(7')~'dr'f For certain models of motion, C(t)+ constant as t -+ a,such a result being obtained for site models of non-equivalent sites and for the rotational diffusion of a symmetric top (see e.g. ref. 41). C(t)described above refers to the autocorrelation function of the dynamical variable A, e.g. the molecular time-autocorrelation functions (vi(0) -vi(t)), (vi(0) ri(t)), and (pi(0) p.i(t))for a reference molecule i.Cross-correlation functions between molecules, (vi(0).vj(t)), i # jetc., may be important in certain systems, for example (i) cross-correlations between group dipole moments along a polymer chain or (ii) cross-correlations between diffusing particles in a bulk liquid. Cross-correlation functions will be disctissed as they arise, but for detailed aszcounts the reader is referred to Berne.2 Berne and Pe~ora.~~ and Williams.7~13 In order to clarify the nature of C(t),we consider simple models for molecular motion. B. Translational Diffusion.-Consider the centre-of-mass motion of spherical particles (atoms, molecules) in the liquid state to be governed by a diffusion equation where Vt2 is the radial part of the Laplacian operator, and is familiar from quantum mechanics; Dt is the translational diffusion coefficient and Cs(R,t)d3R is the probability that the particle is in the volume element d3R about R at time t, given it was at the origin at t = 0.It is readily verified by substitution in equation (4)that Gs(R,t)is given by Cs(R,O)= 8(R) (5b) where equation (5b) expresses the condition that the particle is at the origin at t = 0. Gs(R,t)is called the Van Hove self space-time correlation function.59 This correlation function is used in quasi-elastic light ~cattering.2~37~40~~~ The time-dependence of the intensity of light scattered from N independently moving spherical point-scatterers may be related to an 'intermediate' self-scattering function Fs(k,t)where2 where vj(t + T) is the position of the jth scatterer at (t + 7) given that its position was rj(7) at time T.The sum is taken over all N scatterers in the scattering 59 L. Van Hove, Phys. Rev.,1954,95, 249. 95 Time-correlation Functions and Molecular Motion volume. k is the scattering vect~r~~p~l of magnitude Ikl = (4m/Ao) sin(8/2) where n, Ao, and 8 are refractive index, free-space wavelength, and scattering angle respectively. Equation (6) expresses a time-average over the arbitrary time T. Assuming the system to be ergodic, and if all scatterers are equivalent, allowing the sum to be omitted, equation (6) may be written as the phase-space average (ensemble-average) Fs(k,t) = s Gs(R,t)[exp(ik.R)] d3R (7) from equations (5) and (7) Fs(k,t)= exp(-Dtk2t) (8) Thus for the simple case of independent spherical point-scatterers undergoing translational diffusion, the time-correlation function Fs(k,t) is exponential in time and Dt may be determined from the k-dependence of its correlation time (Dtk2)-1.Fs(k,t)may be determined experimentally in the time domain using photon-correlation spe~troscopy.~5-~l Scattering measurements may also be conducted in the frequency domain where the spectrum I(k,w)is measured as a function of frequency (w)for given values of k. For the simple case of scattering which led to equation (8), I(k,w) is related to Fs(k,t)according to the Fourier transformation6*>61 Z(k,w) = NAs2 -1 Fs(k,t)exp[i(w -w,)t]dt (9)2n -a3 where As is the scattering-amplitude factor and wo is the angular frequency of the incident radiation. From equations (8) and (9) N: + (wZ(k,w) = -2-[(Dtk”)”Dtk2 -wo)21 This spectrum is Lorentzian-shaped with half-width dWk = 2Dtk2; thus Dt may be obtained from the k-dependence of dWk.Thus simple translational diffusion gives rise to the time-correlation functions* Gs(R,t)and Fs(k,t)involving Dt and the latter quantity may be obtained experimentally either directly from Fs(k,t)or from Z(k,w). Before leaving the case of translational diffusion, we note that G(R,t)and F,(k,t)as given by equations (5) and (8) are not even in time and are thus not strictly acceptable as correlation functions. This is a consequence of the fact that equation (4) does not take into account the masses of the diffusing particles.We note that the Einstein relation (dR2(t)) = 6Dtt is inappropriate at the short- est times for the same reason. Proper inclusion of particle mass will lead to *The general definition of G,(R,t) takes the form of a time-correlation function: GAR4 = <WR -[rj(t>-rd0)1)>(see e.g. ref. 41, p. 58). 8O G. Arfken, ‘Mathematical Methods for Physicists’, Academic Press, New York, 1966. 61 R. Bracewell, ‘The Fourier Transformation and its Applications’, McGraw Hill, New York, 1965. Williams time-correlation functions whose series expansions contain only even powers of t, but the formulation and solution of the equations of motion will be complicated.Berne2 has outlined an approach, based on information theory, which leads to equation (5), and hence (8), in the long-time region, but includes the finite masses of the particles so that Gs(R,t)is better behaved at short times. Gs(R,t) is deduced subject to the constraints that Gs(R,t) be normalized, Gs(R,O)= &R), and that (dR2(t)) be known, and he obtains2 Equation (11) is the well-known Gaussian approximation2 for Gs(R,t).(dR2(t)) is given quite generally by2 (dR2(t))= 2 1'(Y(O).V(T))(t -T) d7 0 If (v(O).v(t)) is specified, (dRz(t)),Fs(k,t),and Gs(R,t)follow from equations (11)-(13). Berne2 specified (v(O).v(t)) = (v2(0))exp( -y It I), where y is a 'friction-coefficient'. Insertion into equation (13) gives for t > 0 1(dR2(f))= 2<v2(0))[(f) -7 [1 -exp(-rf)l] (14) Thus (dR2(t))= (v2(0)).t2;t <y-' (AR2Jt))= 2(v2(0))t/y 3 6Dd; t > y-l (15b) Equation (1 5b) corresponds to translational diffusion, equation (5a), while equation (15a) corresponds to the case of free-particle motion with (~~(0))= 3kT/M.Clearly equation (14) taken with equations (11) and (12) leads to an improvement over equations (5) and (6) and will be applicable to the translational motions of, say, spherical polymer molecules (e.g.high malec- ular weight polystyrene) in a continuum of small solvent molecules. However, equation (14) fails to account for the motions of small molecules-as evidenced by computer simulations2-since (v(0)* v(t)) there does not follow the simple exponential relation in time.C. Rotational Diffusion.-The rotational diffusion of a unit vector may be considered2941962 as a random motion of a point on the surface of a sphere of unit radius. If*f(G,t)dG is the probability that the unit vector points into the solid angle dJ2 around at time t,given that its direction was uniquely along the +z direction at t = 0, then the diffusion equation may be written in polar- co-ordinate form as *f(O,f) as defined here should be written in the notation of the conditional probability functionf(Q,tlO,O), but here and in the following sections we writef(C2,t) for the sake of brevity. 6a B. J. Berne, P. Pechukas, and G. D. Harp, J. Chern.Phys., 1968, 49, 3125. Time-correlation Functions and Molecular Motion where Dr is the rotational diffusion coefficient.If we assume that the motion always occurs in a manner such that f(Q,t) is symmetric with respect to the (arbitrary) z-axis, as may be the case for an iso- tropic liquid, thenf(Q,t) depends on 0 and I but not on 4.For this special case equation (16) may be rewritten in terms of the variable u = cos6: Equation (17) is conveniently solvedlg by expandingf(i2,t) in terms of Legendre polynomials.60 to f(Q,t)= m=O 2 Mu>arn(t> Substituting equation (18) into equation (17) gives But the term in square brackets on the 1.h.s. is -m(m + l)Pm(u)(see e.g. ref. 60, p. 424), so equation (19) becomes m=O m=O Equating coefficients of Pm(u) yields a set of uncoupled equations each of the form Hence am(?)= arn(0)exp[-m(m + 1) Drtl to m=b The probability of obtaining the vector in the range u to u + du is f(u,t) du = 1‘”f(G,t)du d+ = 2nf( In,?) du .0 At t = 0 the vector is uniquely along the +z-axis, so f’(u,O) = 6(u -l), but this co delta function may be expanded as 2&(2m+ l)Pm(u),and comparing this with m=O Williams 00 2.rrf(Q,O) = 27r 2Pm(u)am(0) gives am(0)= (2m+ 1)/(4~). Equation (23) may be m=O written as 00 m=O The orientational time-correlation functions (Pn[cos&t)]) = (Pn[u(t)]) are defined by the relation The orthogonality and normalization conditions for Legendre polynomials are expressed by Hence, from equations (24) and (25), (Pn[u(t>]>= exp[-n(n + 1) D,t] (27) Equations (24) and (27) are the results for rotational diffusion governed by equation (16). f(Q,t) involves products of space functions, Pm(u),and time func- tions, exp[-m(m + l)D,t] and, since both functions decrease rapidly with increasing rn,f(Q,t) is dominated by the first few terms in the series.The correla- tion functions, equation (27), are just individual decay functions in equation (24), and being exponential in time (Pn[~(t)])decays with increasing rapidity with increasing n. The pattern for the evaluation of C(r)for translational and rota- tional diffusion is (i) solve the equations of motion for the conditional space- time distribution functions G(R,t)and f(Q,t) and (ii) deduce the phase-space averages C(t)using equations (7) and (25).Averaging over a momentum distribu- tion is not involved since equations (4) and (16) involve co-ordinates but not momenta. This means that the mass or inertia of the molecule has not been explicitly considered, with the result that the translator or rotator moves at its terminal linear or angular velocity, but with constantly changing direction. Equations (24) and (27) may only be applied in the ‘long-time’ region for large molecules moving in a continuum of small (solvent) molecules-in com-mon with equations (5) and (8) for translational diffusion. There is ample evidence from e~periment5~~~~~~~~-56963 and from computer simula-tions2~57J8~64-69 that orientational correlation functions for small inole,cules 83 H.H. Dardy, V. Volterra, and T. A. Litovitz, J. Chem. Phys., 1973, 59, 4491. 84 B. J. Alder and T. E. Wainwright, J. Chem. Phys., 1959, 31,459. 65 A. Rahman, Phys. Rev,, 1964, 136A, 405. 66 J. Barojas, D. Levesque, and B. Quantrec, Phys. Rev. (A), 1973,7, 1092. 67 P. S. Y. Cheung and J. G. Powles, Mol. Phys., 1975, 30, 921. 68 A. Rahman and F. H. Stillinger, J. Chem. Phys., 1971, 55, 3336. 6sJ. S. Rowlinson and M. Evans, ,4nn. Reports, 1975, 72, 5. Time-correlation Functions and Molecular Motion in the liquid state do not conform to equations (24) and (27), but resemble the free-rotator correlation functions at short times (see Section 2D below), It is appropriate at this point to indicate difficulties which arise when a time-correlation function which is not even in time [s.g.equation (27)] is applied to experimental results.This may be illustrated by the example of the dielectric re- laxation and far-infrared absorption of a dipolar medium. For the special case of a low-permittivity medium, say a dilute solution of dipolar molecules in a non-polar medium, the permittivity E(W) = E’(w)-id’(w) is related to (PI[~(t)]) according to5J-12 = som 1‘(W) -Em [-$ (P,[u(r)]) [exp -iwt] dt €0-Em -iwt][exp<P,[u(t)l) 1; iw (28) = 1 -where EO and E, dt are the limiting low- and high-frequency permittivities respec- tively. For the case of a rotational diffusion, equation (28) becomes, with the aid ofequation (27), the well-known single relaxation time equation E(W) -Em -1-c0 -em 1 + iw(2Dr)-I The plot of E”(w)against logw gives a bell-shaped curve having its maximum at wm = 20,.Although such an equation may be used to represent dielectric relaxation data for a variety of liquids and solid^^-^ considerable difficulties arise at very high microwave frequencies and in the far-infrared range where the attenuation factor a(w) = od’(w)/(nc) is measured. It is a property of one-sided Fourier transforms61 that for a function of time g(t), for g(t) = [d(Pl[u(t)])/dt], equations (28) and (30) give for E”(w) For rotational diffusion, equation (27), equation (31) becomes where TI = (2Dr)-l. Equation (32) for WTI 9 1 gives OE”(W) = (EO -E~)/TI, i.e. the rotational diffusion model gives a(w) = constant at frequencies higher than the relaxation region, a wholly unrealistic and physically unacceptable result.The reason is clear: the correlation function is badly behaved at short times owing to the omission of inertia in its derivation. For (Pl[u(t)])even in time, which will be obtained when inertial effects are correctly included, (PI [~(t)]) has zero slope at t = 0 so equation (31) becomes Williams which on inversion gives while inversion of equation (28) gives Thus (Pi[~(t)]) is obtained from a cosine transform of ~”(o)vs. logo data while (i, a(o)] vs. o data.[u(t)]) is obtained as a cosine transform of od’(o)[~ D. Classical Free Rotation.-Correlation functions involve distributions over co-ordinates and momenta and in Sections B and C above we have seen simple examples where correlation is lost through change of molecular co-ordinates in time.In order to illustrate loss of correlation involving momentum distribu- tions, we consider the simple model2 of free rotation, in a plane, of a rod of moment of inertia I, whose rotational velocity or is governed by a Boltzmann distribution functionf(or) = [1/(2~kT)]*exp [ -10r~/(2kT)]. If x is a unit vector along the axis of the rod, then for a given angular velocity Or, x(0). x(t) = COWrt. This scalar product obviously does not decay in time. The average quantity (x(0) .x(t)), i.e. averaged over f(Wr), does decay as a result of the superposition of cosine functions : For free rotation in three dimensions, (x(0). x(t)) E (Pi [u(t)]) and is given by2,7,9,55,70 These correlation functions are both even in time and involve the molecular factor I but do not involve intermolecular factors. Collisions are involved in establishing and maintaining the Boltzmann distribution of Or but if the time- scale between collisions is far longer than that required for molecular rotation, collisions, and hence intermolecular interactions, are not involved in the decay of (x(0) .x(t)).The effect of collisions on time-correlation functions for three- dimensional rotators, leading for example to the J and M diffusion models of Gordon, have been extensively di~~~~~ed~~~~9,~~,52,~~ and this is a topic which continues to receive considerable attention since it embraces all the problems of the fast rotational motions of small molecules in the liquid and gaseous states.Note that (x(0) .x(t)), equation (36), is always positive for the plane rotator but goes negative for the three-dimensional rotator, equation (37). For the latter case such behaviour is rationalized by saying that the rotating vector tends, after a certain time, to point on average in the opposite direction to that which it had at t = 0. ’’ B. Lassier and C. Brot, Discuss. Faraday Soc., 1969, No. 48, p. 39. 101 Time-correlation Functions and Molecular Motion E. Barrier Systems.-The classical motions of molecules, ions, or vacancies between equilibrium sites in a crystalline solid may give rise to dielectric and mechanical relaxation processes.4-7~11J2J4-17~71-77Cole11 has shown how time-correlation functions for dielectric relaxation may be deduced for site- models.Williams and Cook12 have extended this work and have included Group Theory as an aid to the solution of the basic rate equations for complicated barrier systems. These orientational time-correlation functions are exponential, or weighted sums of exponential, functions of time since the inertia of the mole- cule is not taken into account in the rate equations.* Consider first the simple case of a two-site model, Figure 2, where a dipole Figure 2 Energy diagram for dipole reorientation between two equivalent sites T aparl may occupy two orientations, 7r apart, separated by a barrier E, and moves between sites with a !ransition probability k.The apriori occupational probabili- tiespl(t),pz(t) for silzs 1 and 2 are governed by the rate equations Whilst such equations may be solved by several methods,12,14-16,72-75 that12 involving rnatrice~7~ and Group Theory79980 is particularly useful for all site *Brats has considered the short-time behaviour for molecular motion in a barrier system. 71 H. Frohlich, ‘Theory of Dielectrics’, Oxford U.P., 1949. J. D. Hoffman and H. G. Pfeiffer, J. Chem. Phys., 1954, 22, 132. 73 5. D. Hoffman, J. Chem. Phys., 1952, 20,541. 74 J. D. Yoffman, J. Chem. Phys., 1955, 23, 1331. 76 J. D. Hoffman and B. J. Axilrod, J. Res. Nat. Bur. Stand., 1955, 54, 357. 7g C. Brot and I. Darmon, J. Chem. Phys., 1970, 53,2271. 77 A.Gavezzotti and M.Simonetta, Acta Cryst., 1975, A31, 645. 78 G. Stephenson, ‘An Introduction to Matrices, Sets and Groups’, Longmans Green and CO. London, 1965, pp. 73, 127. 7s D. Schonland, ‘Molecular Symmetry’, Van Nostrand, London, 1965. F. A. Cotton, ‘Chemical Applications of Group Theory’, Wiley, New York, 1963. 102 Williams models possessing a degree of symmetry. Equation (38) may be written in matrix form as d p(t) = TP(t) (39) whose general solution is7* p(t) = [expTt]p(O)= S[e~pDtlS-~p(O) (40) where p(t) = {pl(t),p2(t)) and is the column vector of the pi(t), and T = [-'1 . Sis the matrix that performs the transformation S-l TS = D,k -k where D is a diagonal matrix. If S and D can be found, p(t) follows from equation (40) with the aid of the relation78 exp {diag Xmt ] = {diag (expXmt) }.Here the Am are the elements of D. Although the solution to equation (40) is simple for the two-site model, we introduce Group Theory at this stage since its use in more complicated site-models is well illustrated by the two-site model. An orthogonal matrix Q is deduced using the symmetry of the sites12 and we per- form the transformation Q-lTQ = W. W is a matrix which is blocked out along its main diagonal. Its constituent smaller matrices may be taken individually and their eigenvalues and eigenvectors determined. This leads to a matrix U where U-1WU = D. Hence p(t) = QU[expDt]U-l Q-lp(O) (41) In suitable cases12 Q = S, and this occurs provided that no class appears more than once in the reducible representation generated using the sites as the basis set.For the two-site model the C2 character table gives r = A + By and forming Q from A and B irreducible representations and hence W we find Q-lTQ = D and U = E. Here E is the identity matrix, and Q = S. Hence where $2(t) = exp( -2kt). (~(0).p(t)), which is the non-normalized dipole vector-time-correlation function = p2(x(0).x(t)), is obtainedllJ2 as the average of the decay functions &(t) and &(t) for dipoles starting in sites 1 and 2 respectively at t = 0. L <P(O).P(t)> = P2 *I"pi 5dO; (4)= .2 Pja(t>CLf.Pj (44% b)1=1 z=1 'pi is the equilibrium occupation probability of site i; the sum is taken over all sites. pji(t) is the conditional probability that the dipole is in site j at t given it was in site i at t = 0.pjl(t) follows from equation (43) withpl(0) = 1,p~(0)= 0 with similar considerations for pj2(t).Now pl .p1 = p2 .p2 = -p1.p2, SO <I.@). W>= p2eXp(-2W (45) 103 Time-correlation Functions and Molecular Motion and the correlation function is exponential in time with a relaxation time (2k)-1. For more complicated barrier systems several relaxation times may arise and also (p(0).p(t)) will not generally decay to zero for sites that are non-equivalent in energy. As examples we consider12 (i) a six-site model having c6 symmetry, (ii) a six-site model having D4h symmetry, and (iii) a three-site model having CzVsymmetry. Table 2 indicates these models and gives the essential matrices.(i) All sites are equal in energy and the transition probabilities ki-j are all equal to k. Of the five decay functions,12 $j(t), only three are distinguishable and $2(t) = exp( -4kt),$3(t) = +I([) = exp( -kt),&(t) = $s(t) = exp( -3kt). For this case all the &(t) are equal since the loss of correlation in time starting from a given site is the same asthat from any of the six equivalent sites. Also 'pi = Q for i = 1-6; thus <P(O).P.(t>>= P251(t) = where Hence (p(O).p(t)) = p2exp(-kt). Thus of the three relaxation modes $2(t), $a($), and $5(t) only &(t) is active in the dielectric experiment. Similar considera- tions show that (3 cos2B(t) -1)/2, which corresponds to Kerr-effect relaxation, is characterized by $5(t).This emphasizes that different experimental techniques may probe different aspects of the motion where the motion is completely described by the basic rate equations. It is therefore neces:ary, in general, to compare the time-correlation functions obtained from several related experi- ments15J6 in order to establish the mechanism of relaxation. (ii) Sites 1 and 6 are equal in energy; sites 2-5 are equivalent but different in energy from sites 1 and 6. There are four distinguishable decay functions,l2 $2(t) = exp [-2(2k1 + kz)t],$3(t) = exp [-2(k2 + 2k3)t], yb(t)= exp [-4klt), and $5(t) = $6(t) = exp[-2(k2 + k3)tI. Since &(t) = (6(f), &(t) = &(t) = (~(t)= t5(t), and Opl = OP6 = [2(1 + 277)]-1, Op2 = op3 = op4 = op5 = 1;7 [2(1 + 277)]-1, where 17 = (kl/kz),it follows that In this case two of the four relaxation modes are active in a dielectric experiment.Note that all of (p2) = 2Opt pi2 is relaxed for models (i) and (ii), i.e i (~(0). decays to zero. ~(t)) (iii) Sites 2 and 3 are equivalent but are different in energy from site 1. Use of the CzVcharacter table gives Q and hence W,where W contains one 1 x 1 and one 2 x 2 matrix. The latter matrix has one eigenvalue which is zero; thus use of Group Theory easily leads to D and U where Table 2 T S D -2 1 00 0 1 -a a 2b 0 26 0 diag [(0,-4k, -k, 1 -2 1 0 0 0 a -a b y -b -y -k, -3k, -3k)l 0 1 -2 1 0 0 a a-b y-b y00 1 -2 1 0 a -a -2b 0 2b 0 0 0 01 -2 1 a a -b -y -b -y10 0 0 1 -2 -a -a b -y -b y T Q D k2 k2 k2 0 ' diag[(O, -2(k2 + 2k1), k3 0 k3 ki -2(k2 + 2k3), -4k1, -P k3 0 ki -2(k2 + k3), k3 -P k3 ki -2(k2 + k3))I 0 k3 -P ki k2 k2 k2 -4kl p = 2(k2 + k3) Alg w Blg A2u Eu + 2a2 = 1; 4b2 = 1 w w A1 Bz 2b2 = 1 Time-correlation Functions and Molecular Motion y = (ki/k2).p(t)and (p(0).p(t)) follow from equations (41) and (44).Hence1l9l2 + 2Y(l + 2r) (1 -cos2812) 1Cl3U)I (49) where 812 is the angle between the dipole direction in sites 1 and 2, $z(t) = exp [-(2kl + k~)t],and #3(t) = exp [-(k2 + 2ka)tl. The correlation function does not decay to zero but to p2(1+ 2yc0s812)~/(1+ 2y)2.This is just 3 [(p)]2 where (p) is the mean dipole moment; (p} = 2'pi pi for the three-site i= 1 model, Since site 1 has a different energy from that of the equivalent sites 2 and 3, (p) lies along the dipole direction for site 1.This is an example where correlation is not completely lost with increasing time. For a polycrystalline material the random distribution of the co-ordinates of barrier systems ensures that (p) will average to zero for a bulk material. For such a case dielectric relaxation deter- mines an effective dipole moment peff = [(p2) -(P}~)]*and a relaxation governed by #z(t) and #3(t). Such barrier models are ~sed~l~J~J~-~~3~~-$7 for relaxation in rotator-phase organic crystals and doped inorganic crystals. F. Many-body Systems.-The simple models considered above illustrate how time-correlation functions are deduced via time-dependent distribution functions.Although such models may approximately represent the long-time behaviour of various systems, they fail at short times (t < s), particularly for systems comprising small molecules. In general, the equilibrium and dynamic behaviour of an ensemble of molecules may only be correctly deduced by taking into account the attraction-repulsion interactions of all its molecules. Formally the problem involves the solution of the Liouville equation of motion for a given system2g3v41 or, alternatively, the N equations of motion,2 one for each molecule! Such problems are essentially intractable analytically, so as an alternative the dynamics of large ensembles (N -102) of interacting particles have been solved numeric- ally with the aid of a comp~ter,2,57,58,64-~8 a method which is commonly termed 'molecular dynamics'.Such simulations yield the equilibrium information (e.g. radial distribution functions) and the various time-correlation functions. These have been carried out for argon,65 diatomic mo1ecules,2~57~58~66~67 and liquid water68 and will be discussed below. In principle it should be possible to fit different experimental time-correlations obtained for a given system using a simulation based on a parameterized form of the intermolecular potential, hence deducing its parameters. There is little doubt that this is the most thorough approach available for interpreting the observed equilibrium and dynamic properties of liquids and solids. The technique of molecular dynamics is limited to t < 10-10 s for small-molecule systems, whereas motions occur in many systems on a far longer time-scale. Such slower motions cannot be simulated Williams since one includes a very large number of molecules and the time required for the computations becomes prohibitive (see ref.2, p. 621). Another representation of motions in liquids and solids involves the memory functions of time-correlation functions C(t).This has been reviewed by Berne and co-~orkers.~~5~~~8 It may be shown quite generally that C(t)obeys the equa- tion where Ko(T)is the memory function of C(t),and is a real even function of time. The r.h.s. of equation (50) is a convolution of KOwith C. With the aid of the convolution theoremfi1 and equation (30), Fourier transformation of equation (50) gives The memory function Ko(t)is one of a family" of memory functions Kn(t)which obey the set of coupled equations2 From equation (52)we have Repeated use of equation (53), for different values of n, in equation (51) yields the continued-fraction representation of time-correlation functions : C(0)S[C(t)]= iw + K,,(O) iw + K,(O) (54) iw + .. . . . . . . Kn-,(0) iw +9[Kn(r)] If the nth order memory function has a white spectrum so that 9[Kn(t)J = pn where pn is a constant, then the series in equation (54) is truncated. This may be used as a starting assumption from which C(t)and F[C(t)]may be obtained. Alternatively the series may be truncated using an assumed form for a particular Kn(t).Berne2J7y5B and more recently Evans and Daviess4 have discussed the use of empirical forms for certain memory functions.Evans and co-workers (e.g. refs. 52-54 and refs. therein) have fitted far-i.r. absorptions a(w) for a variety of liquids, liquid crystals, and rotator-phase solids by assuming Kl(t) = Kl(O)exp( --ylt), t > 0, which from equation (54) gives K,(O) -w2 -iwy, (55).F[C(t)J= nK,(O) + iw3 -w2y1-iw[K,(O) + KO(0)l *Note: For motion governed by the modified Langevin equation (see ref. 2, p. 609), K,(t) = (F(O)*F(t)),the correlation function of the random force F. Time-correlation Functions and Molecular Motion Now a(o) is related to F[C(t)]via equations (28) and (33) so a(w) may be expressed a~~alyticaIly~~-~~ in terms of three quantities, Ko(O), Kl(O), and 71, where Ko(0) is just (2kTII) for a diatomic molecule.In general these may be regarded as parameters to be determined by fitting a(o)by a least mean squares procedure. Knowing Ko(O),Kl(O),and 71 both C(t)and E"(w) may be determined since they are analytically related to these quantities.S2-S4 We note that C(t) thus obtained is even up to O(t4)and is a single exponential form at long times with relaxation time Thus the fitting of far-i.r. data with parameters (Ko(O), Kl(O), yl} gives a pre- diction of the lower-frequency dielectric relaxation behaviour of a given system. Ko(0) is a molecular property (e.g. 2/iT/I fcr a diatomic molecule) while Kl(0) = Ko(0) + (0( V)2), where the latter quantity is the intermolecular mean- square torque.The continued-fraction approach, as used by Evans and co- workers, represents a valuable method for characterizing, in a quantitative manner, far-i.r. data for liquids and solids and appears to be highly successful in practice. G. Interrelations between Time-correlation Functions and Orientational Distribu- tion Functions.-For the special case where the reorientation of a unit vector occurs with axial symmetry, on average, with respect to an arbitrarily chosen initial direction but does not necessarily follow the rotational diffusion equation, equations (24) and (27) may be generalized to read m f(Q,d = 2(2m+ 1) PdU) $4) (57) m=O Vnt4t)l) = $n(f> (58) $o(t) = 1;$&), m # 1 are normalized decay functions, 0 d \t,brn(r) 1 d 1.Equa-tion (57) expresses the dynamics of orientation but experimental measurements which determine individual (Pn[u(t)])or their mixtures give only a part of f(J2,t). Given this situation, it is essential that experiments should be made which determine at least $l(t) and #2(t) for a given system. A comparison of these in terms of assumed models for motion should rule out certain mechanisms and favour others. Alternatively if a computer simulation is possible $l(t) and $2(r) should be evaluated for assumed forms of intermolecular potential and agreement sought with the experimental data. In practice few experimental determinations of both $l(t) and $,(t) have been made, but examples are: (i) low-frequency motions in certain supercooled liquids using23981.82 dielectric M.S. Beevers, J. Crossley, D. C. Garrington, and G. Williams, J.C.S. Furaduy 11, 1977, 73,458. M. S. Beevers, J. Crossley, D. C. Garrington, and G. Williams, Faraday Symposia Chem. SOC.,1976, No. 11. Williams relaxation [$~(t)] and Kerr-effect relaxation [$2(t) ] and (ii) high-frequency motions in simple molecular liquids as obtained using5O i.r. [$i(t)] and Raman [$z(t) ] vibration-rotation spectra. At the present time most papers on molecular motion give results for a single experimental technique and interpretations are made with assumed models for motion involving adjustable parameters. It is hoped that this rather unsatisfactory situation will be remedied in future as a result of comparisons being made between the dynamics data (correlation function, correlation times) obtained using different techniques.We enquire whether there are inter-relations between the $n(t) of equations (57) and (58). Berne and co-w~rkers~~~~~~~ have deduced approximate inter-relations which may apply independently of the detailed mechanism for motion. Using information theory and given that f(Q,t) is normalized and positive and that $~(t)be known, they obtain where ,B(t)is a Lagrange undetermined multiplier and is evaluated at each value of t from equation (60) with n = 1. B,+$(P) = [7~/2/3]*In++(P),where In+$(/$ is a modified spherical Bessel function of the first kind. The functions B,++(p)are given by Berne2 for different values of n.Thus if $l(t) and hence P(t) is known experimentally, #2(t), #3(t), etc. are obtained from equation (60). Berne and co-workers2962 found that this method was successful for the test cases of ‘molecular dynamics’ simulations of $q(t) and $2(f) for diatomic molecules and this led them to write62 ‘nature seems to prefer smooth distributions’. The ap- proach is especially useful for the ‘fast’ motions in systems of small molecules since it provides a link between the results of different experimental techniques. If, however, molecules move in a discontinuous manner, e.g. jumps through large angles of arbitrary size as occur in site-model situations or for molecules moving slowly in the supercooled or highly viscous liquid ~tate,~398~-85 then the information-theory approach may not apply.Williams and co-workers23 have considered the ‘fluctuation-relaxation’ model (known in n.m.r. work as the ‘strong-collision’ model) for which the molecule moves ‘instantly’ and randomizes completely when it suffers a fluctuation in its environment. This leads to t,hn(t) being equal for all n (n > 1) at <(t),where c(t)is a characteristic time function for the fluctuations. This contrasts with the information-theory approach where I,!Jn+l(t)decays faster than I,!Jn(t). Williams and co-workersz3 found t,!~l(t)2: z/h(t)for several viscous liquids undergoing ‘slow’ (t > s) molecular motions, a result which is in accord with the ‘fluctuation-relaxation’ model but not with rotational diffusion [equation (27)] or with the predictions of information theory.83 G. Williams in ref. 9, p. 151. 84 G. Williams and P. J. Hains, Furuduy Symposia Chem. SOC.,1972, No. 6, p. 14. 85 M. F. Shears, G. Williams, A. J. Barlow, and J. Lamb, J.C.S. Furaduy 11, 1976, 70, 1783. 109 Time-correlation Functions and Molecular Motion Clarkson and Williamss6 used the information-theory method of Berne and co-workers to deduce f(Q,t) from a knowledge of $l(t). Using equations (59) and (60), i.e. for $~(t),gives p(t) from equation (60),and this value is inserted into equation (59) to yieldf(G,t) at t. In addition they extended the analysis to the case where both $l(t)and $z(t) are known, and this introduces a further Lagrange undetermined multiplier, x say.They applied the first approximation [equations (59) and (60)] and the second approximation (involving p and x) to (i) classical rotational diffusion [equation (24)3, (ii) computer simulations of motion in carbon monoxide by Berne and Harp,2157 and (iii) i.r. and Raman vibration-rotation data for $l(t)and $z(t)for methane.87 They conclude that the first approximation yields quite satisfactory estimates of f(Q,t)and there is no necessity in practice to use the extended analysis. Thus for suitable systems, and these include smal! molecules undergoing rapid reorientation (t < 10-10 s), it is possible to obtain good estimates of $2(t), $3(t), etc. and f(Q,t) from a knowledge of $~(t). In the above we have considered the simple case of the reorientation of a vector, occurring with axial symmetry so thatf(Q,t) depends on 8 and t. For the general case of the orientation of three chosen molecular axes it is necessary to express the generalized orientation function in terms of spherical harmonics Ylm(O,4)or Wigner rotation matrices DJ~,~(cll,p,y),where a,p, and y are Euler angles.The corresponding time-correlation functions are considerably more complicated than those considered in this article and the reader is referred to Berne,2 Berne and Pe~ora,~~ and Steeless for further accounts. 3 Relationships between Time-correlation Functions and Experimentally Deter- mined Quantities A. Introduction.-The time-correlations considered above refer to the natural motions of a system in the absence of an applied field, but how may such motions be studied experimentally? Two approaches are particularly useful : (a) the response of the system to a weak perturbing field is measured in the time or frequency domains; or (b)the scattering behaviour of the system for monochro- matic incident radiation is studied in the time or frequency domains.For (a)if the applied field is sufficiently weak the time factors of the response are those due to the natural motions of the system in the absence of the field. For (6)if the energy and momentum changes involved in the scattering process are negligible (quasi-elastic scattering) then the autocorrelation function for the amplitude of the scattered radiation or its power spectrum will simply correspond to a modulation of the frequency of the incident radiation caused by the natural motions of the scatterers.In order to see how relations between experimentally determined quantities and field-free time-correlation functions may arise we consider simple examples illustrating (a) and (b)above. 88 T. S. Clarkson and G. Williams, J.C.S. Furuduy ZZ, 1974, 70, 1705. R.G. Gordon, J. Chem.Phys., 1965, 43, 1307. W. A. Steele, J. Chem.Phys., 1963, 38, 241 1. Williams B. Quasi-elastic Light Scattering from Moving Point Scatterers.-Of the accounts of the dynamic scattering of monochromatic light (see e.g. refs. 2, 35-41, and 89) those of Cummins and co-workers35 and Peticolas37 are particularly valuable for the special case of a stationary system of point scatterers which undergo translational motions.Consider the situation (Figure 3) where a parallel Detector R away from 0I Figure 3 Quasi-elastic light scattering frompoint scatterers indicating the relation between k, kz, and ks beam of plane-polarized monochromatic radiation (light say) of angular frequencyoo and associated wave-vector kx = [2nn/h0]uz,where uxis the unit vector in the propagation direction, is scattered from a volume of material containing N equivalent point scatterers (atoms, molecules). The beam is taken to be polarized parallel to the y-axis and the scattered radiation for a scattering angle 8 is detected at the macroscopic distance R from the origin 0 of Figure 3. The scattering direction is denoted by the unit vector usand the wave-vector of this scattered radiation ks = [2nn/ho]us,where Ikz I 2 Iks I for quasi-elastic scattering.The incident radiation is in phase at plane I but the scattered radiation reaching the detector is composed of a superposition of waves of different phase since they have travelled different distances from plane I via the scatterers to the detector. If the scattering amplitude factor A is assumed to be independent of the orientation of the scatterers and of time then the amplitude Ej(k,T)of the light scattered from a scatterer j, say, which is located at Y~(T)from the origin at the . arbitrary time T is given by37 E&T) = Aexp {-i[w,~ -(277/Xo) D~(T)]} (61) Q(T)is the distance travelled by the light from plane I to thejth particle and then to the detector.Geometrical considerations (e.g. see ref. 37) show that Q(T) = [R+ u~(T)-(u~us)]so equation (61) may be written as -Ej(k,~)= Aexp (-i[w,T -k.rj(~)-ks.R]) (62) where k = (kz-ks)and is the scattering vector. For quasi-elastic scattering kz, P. N. Pusey and M. F. Vaughan, in ref. 9, p. 48. Time-correlation Functions and Molecular Motion k,, and k form an isosceles triangle with Ik I = 2 Iks lsin(8/2). The total scattering amplitude Es(k,7)is the sum of contributions from the N scatterers in the scattering volume : N E,(~,T) =KCexpi-i[woT -k.rj(7)-~~.RII j= 1 The average intensity of scattered light in the s-direction is (I) = (Es*(k,7)Es(k,7)) where * indicates the complex conjugate and () indicates a time-average (over all 7).If the scatterers are statistically independent, i.e.there is no correla- tion between the position or the motion between scatterers, then all cross-correlation terms in (I), i.e.(exp {-ik. [rj(7) -Y2(7)]}), I # j,are zero, giving (I) = NA2,the equilibrium result. The temporal behaviour of the scattered-light intensity is obtained from j= 1 N2(exp -i[wo(t + -!k.rz(t+.>I 1)I= 1 = NA [exp(-iw,t)]F(k,t) where F(k,t)is a correlation function N N j= 1 I= 1 F(k,t)contains auto- (j = I) and cross- (j # I) correlation functions, and the autocorrelation terms have been introduced above in equation (6). Experimentally G(l)(k,t)is not measured directly.In the time domain (photon-correlation ~pectroscopy35-~1~~9) the measured quantity is the normalized intensity correlation function for the scattered radiation, g(2)(k,t),which is defined as gc2)(k,t)= (Es*(k,7)Es(k,7)Es This is *[k,(t +7)]Es[k,(t+~)])/(1)~. related to g(l)(k,t)= C(l)(k,t)/(l)according to the Siegert relation :35-41989 g(2)(k,t)= 1 +/g(l)(k,t)j2 (66) Thus the measurement of g(2)(k,t) gives g(l)(k,t) and hence F(k,t).For the special case of statistically independent scatterers F(k,t)becomes F,(k,t)of equation (6). In general the cross-correlation functions (exp {-ik -[rj(~)-rl(t +~)]}),j# I, will make a contribution to F(k,t)and hence G(l)(k,t). In the frequency domain the spectrum I(k,o) of the scattered radiation is given by the Wiener-Khintchine relation35-41J39 Williams 1mI (k,w) = -1 I G(')(k,t)I exp(iwt)dt (67)2r --m Use of equations (64) and (67) for statistically independent scatterers gives equation (9) above.In general from equations (64) and (67) we have I(k,w) = IVA2-Irnexp[+i(w -w,)t]F(k,t)dt (68)2r -m Equations (64), (66), and (68) show how experimentally determined quantities G(')(k,t)and I(k,w)are related to a correlation function F(k,t)which expresses the natural motions of the scatterers. In equations (64) and (68) the incident field factor involving 00 and the correlation function F(k,t)appear as a product. In equation (64) this means that the motions of the scatterers lead to a modula- tion, through F(k,t),of the single frequency WO.In the power spectrum equation (68), this leads to a k-dependent broadening of the scattered-line, centred on WO.Note that F(k,t) is obtained from equation (64) in the time domain, while in the frequency domain it may be obtained from the Fourier inverse of equation (68). We considered the simple case of moving point scatterers to illustrate how experi- mentally determined quantities in scattering experiments may be related to certain time-correlation functions. There are many mechanisms for polarized and depolarized light-scattering from liquids and solids and many of these are considered in detail in the texts by Chu40 and Pecora and Berne.41 The develop- ment of the subject owes much to the work of Benedek, Cummins, Pecora, and Pike and the dynamic light-scattering techniques have been successfully applied to studies of the motions of small molec~les,3~-~~~63~90~~~of macro-molecules,35-41~~9~92-95of macromolecular gels,96 and of structured solutions97 and to very low-frequency motions in pure liq~ids.~~-~O~ C.Dielectric Permittivity and Dipole Reorientation.-As an example of how experimentally determined quantities may relate to time-correlation functions for the case where a system is perturbed by a weak applied field, we consider the permittivity of a dipolar medium. The theory of dielectric relaxation is well documented4-11.71 but is made complicated by local-field considerations. For detailed accounts the reader is referred to texts4-6 and reviews,7-9 and for D.A. Pinnow, S. J. Candau, and T. A. Litovitz, J. Chem. Phys., 1968, 49, 347. 91 G. R. Alms, D. R. Bauer, J. I. Braumann, and R. Pecora, J. Chem. Phys., (a) 1973, 58, 5570; (b)1973,59, 5310; (c) 1973,59,5321; (d) 1974,61,2255; (e) 1975,63, 53. sa R. Pecora, Discuss. Furaday Soc., 1970, No. 49, p. 222. 93 T. A. King, A. Knox, W. I. Lee, and J. D. G.McAdam, Polymer, (a) 1973,14,151; (b)1973, 14, 1. 9rT.A. King, A. Knox, and J. D. G. McAdam, Chem. Phys. Letters, 1973, 19, 351. 95 P. N. Pusey, J. M. Vaughan, and G. Williams, J.C.S. Faraday ZI, 1974, 70, 1698. 96 T. Tanaka, L. 0.Hocker, and G. B. Benedeck, J. Chem. Phys., 1973, 59, 5151. 97 5. C. Brown, P. N. Pusey, J. W. Goodwin, and R. H. Ottewill, J. Phys. (A), 1975, 8, 664. 98 C. Demoulin, C.5. Montrose, and N. Ostrowsky, Phys. Rev. (A), 1974, 9, 1740. 99 C. Demoulin, P. Lallemand, and N. Ostrowsky, Mol. Phys., 1976, 31, 581. looC. C. Lai, P. B. Macedo, and C. J. Montrose, J. Amer. Ceram. SOC., 1975, 58, 120. lol J. F. Dill, P. W. Drake, and T. A. Litovitz, Amer. SOC.Lubrication Engineers Trans., 1975, 18, 202. loaP. W. Drake and R. Meister, J. Phys. Chem., 1976, 80, 2780. Time-correlation Functions and Molecular Motion assessments of the current situation to the papers of Deutch and co-~orkers.~0~J0* Our derivations here follow closely those of GlarumlO and Cole.34 Consider a system of N equivalent dipolar molecules to which is applied a field EMZ(t’).The local field acting on the molecules is Ez(t‘) say, and will be related to EMp(t’).For the simple case of a medium of low permittivity, i.e. EO 21 E,, Ez(t’) N EMz(t’)[(E, + 2)/3]. The phase-space distribution functionf(p,q) for N equivalent dipolar molecules depends indirectly on time owing to the motions of the molecules and obeys the Liouville equation of m~tion,~J~ N H is the Hamiltonian of the system, i refers to molecule i, and9 is the Liouville operator: 9f= (LH) = -(H,f},where { } indicates the Poisson bracket. If the uniform electric field Ez(t)is applied to the specimen, H(a,q;t) = ffo(a,q)-Mc(dEc(t1 (70) where -Mz(q)E(t) = -2rni(q).EZ(t)is the energy of interaction between the and, noting that Mz(q)isdipole momentsand the field. We write 9’= 90+ 91 independent of momenta pi, N N Writing f = fo + f1, from equations (69)-(71) we have 20= -Lzofo;afi= -[.=POf1 + 21fo] (72%b)at at 91f1 is omitted in equation (72b) in order that f1 = Q(Ez).This is the ‘linear- response’ condition that the change fromfo to (fo + f1) is linear in the applied field Ez.The solution to equation (72a) is the field-free Boltzmann relation fo = AexP(-BHO) (73) where /3 = (kT)-1 and A is a constant.Writing fi = [exp(-t9’0)]yl, then differentiation and comparison with equation (72b) gives a” At) = -It (74a, b) _---[ex~(t~~>l.=P~fo; [ex~(t’~~)W~fofodt’at -03 Hence lo3U. M. Titulaer and J. M. Deutch, J. Chem. Phys., 1974,60, 1502. lo4 D. E. Sullivan and J. M. Deutch, J. Chem. Phys., 1975, 62,2130. Williams (75) The average moment in the field direction is = jj Mz(4)f(P,4;t)dP dq From equations (71) and (73) since2 (aHo/api) = qi, and where lkz= dM,(t)/dt. Equations (76) and (77) give Using the series expansion 29exp[-(t -t’) 9,,1= (t -t’)“ (79) n each term in the series expansion of equation (78) may be integrated by parts giving since integrals of the form ss90f0 dp dq vanish.Equations (78) and (80) yield /3 / ‘(Mz(r))= dr‘ E(t’)jjfoAkz[exp(t -t’) yo]Mz(q)dp dq (81)-K The operator exp(t -t’)Yois a tirne-displacement operator, or propagat0r.~7~~9*~ When it operates on A it transforms it from its value at time t‘ to the value it has at (t -t’) later, the change having resuited from the natural motions of the system. Equation (81) becomes We define a field-free correlation function !&(t) as @Z(f> = j1f,Mz(O)Mz(t)dp dq = <Mz(0)MZ(t)) (83) Now ddt)= (Mz(O)Mr(t)) = -(MZ(O)ZMZ(t)) , so equations (82) and (83) give the superposition integral 115 Time-correlation Functions and Molecular Motion -,B It<Mz(~)> -cc Ez(~’)= &Z(t -t’)dt’ (84) The total dipole moment correlationfunction@(t) = (M(O).M(t))/(M(O).M(O)), where M(t) = Mz(~)uz+ My(t)uy+ Mz(t)uzand ux,uy,and uzare the unit vectors associated with the x,y, and tdirections. Now @(t)= 3QZ(t)/(M(O).M(O)),so equation (84)’may be written as This is our general result for the linear-response condition. Three forms of Ez(t’)are of interest. (i) EOapplied as a step at t’ = 0: (ii) EOapplied at t = -GO is removed as a step at t’ = 0 (iii) Steady state: E(t‘)= Eoexp(iwt’); -cc < t < ao: --(M(o~$(o)) Eoexp(iwt) [l -iw 1 @(t’)exp( -iwt’) dt’] 0 Since the electric polarization PZ(t)= N(Mz(t))= (E -E,)E~KE~,where eV is the permittivity of free space and K is the internal field factor connecting the applied and local fields, we see that the time-dependent permittivity is propor- tional to [l -@(t)] and @(t)for equations (86a and b) respectively.In the frequency domain from equation (86c) we write where 9indicates the one-sided Fourier transform. For the simple case of a very dilute system of dipoles, EO 2 E, and hence ~(w)2: ~(0).Equation (87) becomes for this special case For the case where @(t)= exp [ -(t/T)],equation (88) gives the familiar single- relaxation time expression [cf.equation (29) ]. Equations (86) connect the transient experiments [equations (86a and b)] to the steady-state a.c. experiments [equation (86c)], one being related to the other by a Fourier transform of @(t). Equations (85) and (86) are the important results of the linear response theory. The moment (Mz(t)>is proportional to the applied field and the proportionality Williams factor, a susceptibility, is determined by the equilibrium quantity (M(0)* M(0))l (3kT) and a time-correlation function @(t),where @(I) is determined by the natural (field-free) motions of the system. Note @(t)contains auto- and cross-correlation functions : N N NN<[CP@)l * [CW(t)l> z: 2 <P@) Fk))I -ZJ (89)-@(t)= N‘ N<rcP40l * rg: P.(O)l> z” $ <Iri(O) P5(0))ZJ For the special case where cross-correlation functions (pi(O)*pj(f)),i # j, are zero, then for equivalent molecules @(t) = (pi(O).pt(t))/(pi2) = (PI[~(t)]), introduced and discussed above.4 Experimental Determinations of Time-correlation Functions A. Introduction.-Table 1 indicates the various time-correlation functions which are involved in the different experimental techniques, and the reader is referred to the key references given in the Table for detailed accounts. In this section we briefly consider certain of the techniques listed in the Table and give examples of results involving time-correlation functions. No attempt is made to give a comprehensive account since that is beyond the scope of this introductory re- view.However, comment is made, where appropriate, on the difficulties which may arise for the deduction of time-correlation functions from experimental data. B. Dielectric Relaxation.-Much of the dielectrics literat~re~-~ for liquids and solids gives E(O) = E’(w) -id’(w) at a limited number of frequencies and such data are usually fitted by a single relaxation time expression or by a function involving a suitably chosen distribution of relaxation times, implying an orienta- tional correlation function which is exponential or a weighted sum of exponentials in time. As examples where the experimental data have been transformed to give experimental orientational correlation functions we choose to refer to part of the work of Evans and ~o-workers52-5*~56~~05 the short-time, high-frequency on motions of liquids, liquid crystals and rotator-phase solids, and to the work of Williams and co-workers13~81-85 on the long-time, low-frequency motions of supercooled and other viscous molecular liquids and of solid amorphous polymers.Evans and co-workers have deduced (PI[u(t)])or (b1[u(t)]) for (i) 2-methyl-2-nitropropane, 2,2-dichloropropane, 2-chloro-2-nitropropane, and t-butyl chlor- ide in their liquid and rotator-phase solid (ii) water in non-polar organic solvents,l05 and (iii) 4-cyano-4-n-heptylbiphenylin its nematic and isotropic states.56 For these systems the far4.r. absorption a(o) is fitted using the parameters Ko(O),Kl(O), and 71of the memory-function approach outlined above (Section 2F), and hence (PI [~(t)])and/or (PI[u(t)])is determined.In all lob M Evans, J.C.S. Faraday 11, 1976, 72,2138. 117 Time-correlation Functions and Molecular Motion cases the short-time behaviour of the correlation function resembles that of a free rotator (or a librator for the liquid-crystal case) and at longer times the influence of molecular collisions is seen. As one example, Figure 4 shows a(w) 0.t P9”4q7 0.4E d \ 0 / b L. a \ Q db 4Q)C d30.2 / Q0 \ / ‘6) \P \ / / 31.-0 0/ I I I -\ ------100 200 300 400 w. I tlps Williams Nps Figure 4 (a) Infrared absorption coeficient a(W) against wavenumber (cm-l) for an 0.011% wlw solution of water in cyclohexune at 296 K, corrected for solvent absorption.(b) (;P,[u(t)]>calculated from the data of Figure 4 (a). (c) The normalized memory- function K,(t) calculated from the data of Figure 4 (a). (Reproduced from J.C.S. Faraday ZI, 1976, 72,2138) for water in cyclohexane together with the derived (Pl[u(t)])and its memory function Ko(t).Note the short time-scale for the reorientation process of H2O in this system. The dielectric relaxations of viscous molecular liquids and solid polymers may occur in the range 10-4-106 Hz, and are characterized by loss curves which are asymmetric in shape and are far broader than that for a single relaxation time process. As one example, Figure 5 shows E”(w)data, in normalized form, for anthrone in o-terphenyl in the supercooled liquid state84 together with the derived (PI[u(t)])obtained using equation (35).These data are well fitted by the &t) withempirical relation of Williams and Watt~,~069~0~ = exp [-(t/~~)fj], = 0.55. Such a relation with p = 0.55 is numerically very similar to a relaxation lo6 G. Williams and D. C. Watts, Trans. Faraduy Soc., 1970, 66, 80. lo’ G. Williams, D. C. Watts, S. B. Dev, and A. M. North, Trans. Furuduy SOC.,1971, 67, 1323. I I I I 1 I ---2 -1 3 1.o Figure 5 (a) Normalized dielectric-loss factor (C"/E~) against log(f/ fm) for anthrone in o-terphenyl in the supercooled liquid state. The dashed curve (----) is calculated using the Williams-Watts relation with is = 0.55.(b) (P,[u(t)]> calculated from the data of Figure 5 (a). experimental data: continuous curve (-) calculated with B = 0.55; arrowed curve (-+ +) single relaxation-time process (Reproduced from Faraday Symposia Chem. SOC.,1972, No. 6, p. 14) function deduced by Phillips and co-workersl08 for the model of relaxation in which a molecule moves as a result of the 'defect-diffusion' of nearest and next-nearest neighbour 'defects' in the liquid state. For solid amorphous polymers lo8M. C. Phillips, A. J. Barlow, and J. Lamb, Proc. Roy. Suc., 1972, A329, 193. Williams the form of the dielectric a relaxation process6 is found13J33J09 to be very similar to that in small-molecule glass-forming systems and this implies that the time- dependence of @(t), equation (89), for polymers is quite similar to the auto- correlation function (PI[u(t)]) for dipoles in highly viscous molecular liquids.It has been reasoned109 that this means that the dipole moment auto- and cross- correlation functions have the same time-dependence in solid amorphous polymers, owing to the co-operative nature of the a-process. C. Kerr-effect Relaxation.-Dynamic Kerr-effect experiments involve the measurement of the optical birefringence, dn, of a material subjected to a directing electric field.19-2*~81982~110 Experiments may be conducted in the frequency or time domains and although most studies have been made in the range 10-2-107 Hz, measurements have recently been made on liquids in the 540ps range111J12 using picosecond laser techniques. Beevers and co-workers23 have shown for the simple case of axially symmetrical molecules of dipole moment p and polarizability anisotropy Ag that the decay-transient for An following the step-withdrawal of a directing electric field is characterized by (Pz[u(t)]),where u = cosB and 8 is the angle of reorientation of the dipole vector.Since the Kerr effect is a non-linear optical effect (An cc E2), the rise transient for a step-applied directing electric field may be very different from the decay transient, this being so for the case where the molecule moves by rotational diffusion.19~23 As one example of (P2[~(t)])being obtained from Kerr-effect experiments, we refer to the work of Benoitlg and of O’Konski and co-workers20S2l for tobacco-mosaic virus in aqueous media, where they observed rise and decay transients which are a direct measure of (Pz[u(t)I) = exp( -6&t) for the rotational diffusion of this eIIipsoidal macromolecule (rod 3000 A x 180A diameter35).For this system the rise and decay transients are symmetrical, both giving (P~[u(t)]),since the Kerr-effect arises in this case from the induced moment of the molecule. Transient data for dipolar macromolecules, involving (PI[u(t)]) and (Pz[u(t)]), are reviewed by Fredericq and Houssier22 while recent studies include those by Beevers and co-workers110 for poly-n-alkyl isocyanates in non-polar solvents. As a further example of this technique, Figure 6 shows the normalized birefringence transients for fluorenone in o-terphenyl in the supercooled liquid state.82 The rise and decay transients are symmetrical at each temperature and correspond to (1 -(P~[u(t)]))and (P2[u(t)]),respectively, for the reorientation of the dipole vector of fluorenone.P2( [u(t)]) is far removed from a single exponential decay in time, ruling out rotational diffusion, but is adequately represented by the Williams-Watts function with fj 21 0.6. Dielectric measurements on the same systems2 yield lo@G. Williams, M. Cook, and P. J. Hains, J.C.S. Faraday 11, 1972, 68, 1045. M. S. Beevers, D. C. Garrington, and G. Williams, Polymer, 1977, 18, 540. ll1 M. Duguay and J. Hansen, Appl. Phys. Letters, 1969, 15, 192; Opt. Comm., 1969, 1, 254.n2P. P. Ho, W. Yu, and R. R. Alfano, Chem. Phys. Letters, 1976, 37, 91. Time-correlation Functions and Molecular Motion 1.0-0.5 tlms tls35 1.0-0.5 0.2 0.4 0.6 0 0.2 0.4 20 40 80 0 20 tls tls Figure 6 Normalized birefringence against time for 22.5 % fluorenone in o-terphenyl in the supercooled liquid state. Curves 1, 2, 3, and 4 refer to 259.6, 246.9, 241.2, and 239.9 K respectively (Reproduced from Faraday Symposia Chem. Soc., 1976, No. 11) (P~[u(t)]),which is found to have the same time-dependence and the same average relaxation time as the Kerr-effect relaxation at each given temperature. These results are consistent82 with the ‘fluctuation-relaxation’ modeI23 discussed above (Section 2G). Note that the interpretation of Kerr-effect relaxations may be made compli- cated by cross-correlation terms,113 as is the case for dielectric relaxation.It seems likely that in liquid-crystal forming systems, both in their liquid-crystal and isotropic phases, equilibrium and dynamic cross-correlation terms make a substantial contribution to equilibrium and dynamic Kerr-effect q~antities.ll4-I~~ Cross-correlations are also of importance for the Kerr-effect of alcohols118 (intermolecular correlations) and of dipolar polymersllg (intramolecular correlations). D. Depolarization of Fluorescence.-The steady-state and time-dependent fluorescence depolarization of fluorophores incorporated into macromolecules has been ~hown26-309~~ to be a useful method of studying the rotational motions of macromolecules.(Pz[u(t)])for the reorientation of the axis of the transition moment of a fluorophore may be obtained in favourable cases from measure- 113 s. Kielich, in ref. 8, p. 192. 114 M.S. Beevers, Mol. Crystals Liquid Crystals, 1975, 31, 333. 116H.J. Coles and B. R. Jennings, Mol. Phys., 1976, 31, 571. M. S. Beevers and G. Williams, J.C.S. Faraday ZZ, 1976, 72, 2171. 11’ T.D.Gierke and W. H. Flygare, J. Chew. Phys., 1974, 61,2231. 118 C. G. LeFevre and R. J. W. LeFevre, Rev. Pure Appl. Chem., 1955, 5, 261. llSK.Nagai and T. Ishikawa, J. Chem. Phys., 1965, 43, 4508. Williams ments of the components lll(t)and Il(t) for the intensity of fluorescence which emerges from a sample following its irradiation with a fast pulse of (vertically) polarized light.The time-dependent depolarization ratio (or emission aniso- tropy), r(t) is defined as If xu and Xe are unit vectors along the direction of the absorption and emission transition dipole moments respectively, then,41 r(t) = (2/15)<P2[xa(0).xe(t)1). If xu and Xe are parallel then r(t) = (2/15)(P2[u(r)]).Experimentally, the range of the technique is limited to f < 10-8 s by the lifetimes of the fluorophores, and to t > 10-lO s by instrumental factors. As examples we refer to the work of Monnerie and co-worker~~~~~~ for fluorophores contained in flexible polymer chains. Figure 7 shows r(t) for anthracene units contained in polystyrene for solvent mixtures of different viscosity.The data are not accurate at short times owing to the problem of deconvolution of the pulse excitation and fluorescence functions. Valeur and M~nnerie~~ have fitted these data with a model for chain motion120.121 which gives, for a bond in the chain, lao B. Valeur, L. Monnerie, and J. P. Jarry, J. Polymer Sci.,Polymer Letters, 1975, 13, 667, 675. 121 E. Duboise-Violette, F. Geny, L. Monnerie, and 0.Parodi, J. Chim.phys., 1969, 66, 1865. Time-correlation Functions and Molecular Motion vz [4t)l> = CexP(-t/a)l [exp(t/p)l erfdt/p)* (91) where p is a characteristic time for jumps on a tetrahedral lattice and u is a relaxation time for random fluctuations of the direction of the co-ordinates which define the lattice. Valeur and Monnerie30 have also examined the effects of quenching agents on the observed r(t) for fluorophore/polystyrene in 1,2-dichloroethane and chloroform as solvent.E. Nuclear Magnetic Resonance.-N.m.r. studies, involving the spin-lattice relaxation time TI,the spin-spin relaxation time 7'2, the rotating frame relaxation time TI,,, and line-broadening techniques, have been very successful in character- izing molecular motions in liquids and solids. Key references are to Abragam,31 Slichter,32 POW~~S,~~~Waugh,lZ4 and C0le.3~ Experimentally, n.m.r. studies are commonly and conveniently carried out at a fixed resonance frequency wo and over a range of temperature. Although such measurements may give information on average correlation times for molecular motion, they do not allow the form of the various spherical harmonic correlation functions which are in~olved3~9~~5 to be obtained without making assumptions regarding the mechanism for motion and/or its dependence on temperature.The difficulties arising from measurements made at a single frequency may be illustrated with the model of two equivalent nuclear dipoles, of gyromagnetic ratio YN and spin quantum number IN,separated by an internuclear vector r of fixed length. The spin-lattice relaxation time TIis given by31~3~9125 where, in general, J1 and JZare Fourier transforms of time-correlation functions of second-order spherical harmonics Yrn,(e,$) describing the reorientation of r. For the special case where the reorientation occurs with axial symmetry from any initial orientation of Y, the $-dependence goes out and JI and J2 become Fourier transforms of (Pz[u(t)]),where u = cod and 8(t) is the angle between r(0) and r(t).Assuming (Pz[u(t)]>= exp( -f/72), equation (92) From equation (92) it is clear that the form of the correlation functions cannot be obtained from TImeasurements at a fixed WO.Equation (93) is only applicable if (P2[u(f)]) is exponential in time which, for most solid polymers or viscous liquids, is not the case.32,337122 F.Quasi-elastic Light Scattering.-Owing to the wide frequency range, the lz2 T. M. Connor, Trans. Furuduy Soc., 1964, 60, 1574. lZ3 J. G. Powles, Polymer, 1960, 1, 219. J. S. Waugh, in 'Molecular Relaxation Processes', Chemical Society Special Publication No.20, The Chemical Society and Academic Press, London, 1966. lZ5 N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev., 1948, 73, 679. lZ6 R. Kubo and K. Tomita, J. Phys. SOC.(Japan), 1954, 9, 888. 124 Williams alternatives of polarized and depolarized scattering, and the wide application to systems of chemical and biochemical interest, dynamic quasi-elastic laser light-scattering has emerged as one of the most used techniques for studies of the motions of molecules and larger species. The reader is referred to reviews,35-39, texts,40941 and key papers90-97 where many examples of experi- mental time-correlation functions for molecular motion are given. For the purposes of this review we refer to only a few examples taken from photon- correlation and frequency-domain (Rayleigh line-broadening) experiments.Of the many studies of the diffusion of macromolecules in solution using photon-correlation methods35-41192-95~127 we refer to the work of Pusey and co-workers89~95~12~and of King and co-workersg3-95 on monodisperse poly- styrenes of different molecular weight in several solvents. Their data for polarized scattering are entirely consistent with translational diffusion, equations (4) and (8), and Dt values are obtained with good precision. In such studies the polymer molecules are of smaller dimension than the wavelength A0 of the incident light. For molecules whose dimension is comparable with, or greater than, XO modes of motion additional to centre-of-mass (c.0.m.) motion may contribute to G(l)(k,t) and I(k,o). For a rod-like macromolecule of length I, if the c.0.m.motion and rotation about the c.0.m. are uncoupled and obey simple transla- tional diffusion and rotational diffusion, then359128 m=O m even m=O [:I: m even where Bm = (2m + 1) -Jm(y)dy/y , h = k1/2, and Jm(y)is a spherical l2 Bessel function of y (see ref. 60, p. 407). The integral arises from the summation of scattering elements along the rod. Lm(*)denotes a Lorentzian of a given m centred on 00 [see equation (lo)]. In practice only the first two terms in each series, of relative magnitude 930 : 932, are significant. Thus equation (94) involves two weighted exponential decays and equation (95) involves two Lorentzians where the variation with k suffices to determine Dt and Dr.This was used by Cummins and co-workers35 and King and co-worke1s9~ for tobacco- mosaic virus in aqueous solution, yielding35 Dt = 2.8 x cm2 s-l and Dr = 320 s-1. King and co-workers94 and Frederick and c~-workers~~~-~~~ have interpreted deviations from simple translational diffusion behaviour for 12' P. N. Pusey, in ref. 39, p. 387-428. lZ8 R. Pecora, J. Chem. Phys., 1964, 40, 1604. lZ9T. F. Reed and J. E. Frederick, Macromolecules, 1971, 4, 72. 130 0. Kramer and J. E. Frederick, Macromolecules, 1972, 5, 69. 131 W. N. Huang and J. E. Frederick, Macromolecules, 1974, 7, 34. 125 Time-correla tion Functions and Mo Iecular Motion very high molecular weight polystyrenes in cyclohexane and butanone in terms of Rouse-Zimm-type internal relaxation modes41 for these spherical macro-molecules.The equilibrium and dynamic correlations for charged polystyrene spheres (radius -250A)in dilute aqueous dispersion have been studied by Brown and co-workersg7 using conventional and photon-correlation light-scattering methods. (I), when plotted as a function of scattering angle, exhibited maxima which could be interpreted in terms of a definite structure for the medium, and the derived radial distribution function indicated short-range ordering due to repuls- ive Coulombic interactions. G(l)(k,t)results were non-exponential in time, but the short-time behaviour gave an effective diffusion coefficient L)t(k)which was k-dependent in a manner which exactly paralleled the k-dependence of the equilibrium structure factor S(k).Brown and co-workers give theoretical support to this result.The motion is similar to that of a particle in a well. At short times it moves in free translational motion [equation (4)]. At longer times the particles move collectively and these motions are influenced by interparticle interactions. The light-scattering arising from fluctuations associated with structural relaxation in pure liquids has been studied for glycerol9* and other viscous liq~ids.~~0-~0~Phenomenologically, the form of the time-dependence of g(I)(k,t) is found to be similar to dielectric and viscoelastic relaxation functions for such media, being fitted with a Davidson-Cole function or Williams-Watts function.An interpretation of such scattering is given by Demoulin and co-workersgg and by Berne and Pecora4I in terms of generalized hydrodynamics. The fast reorientational motions of simple non-viscous molecular liquids may be studied by light-scattering methods in the frequency domain in terms of the width and shape of the depolarized Rayleigh-scattered line. Of the many recent studies we refer to the work of Pecora and co-workersg1 and of Litovitz and co-~orkers.~3~~~~~~~-~35For optically anisotropic molecules which possess cylindrical symmetry, the scattered light intensity for the depolarized spectrum is proportional to (gli -g1)2where g is the optical molecular polarizability. The spectrum is given by a Fourier transform of correlation functions for trans- lational and reorientational modes of motion41991,92 but if it is assumed (i) that the translational motions occur on a much longer time-scale than the reorienta- tional motions, so that Dk2 < 6Dr and (ii) that the reorientational motions follow the simple rotational diffusion model, equation (16), then the spectrum is a Lorentzian centred on wo with a half-width 60, (independent of k and so independent of scattering angle).This approach has been applied very success- fully by Pecora and co-workersg1 to obtain rotational relaxation times rz for benzene, toluene, p-xylene, chloroform, nitrobenzene, and certain carboxylic acids in solvents composed of optically isotropic molecules (e.g.cc14). In this 132 J. A. Bucaro and T. A. Litovitz, J. Chern. Phj..~.,(a) 1971, 54, 3846; (h) 1971, 55, 3585. 133 C.J.Montrose, 5. A. Bucaro, J. Marshall-Coakley, and T. A. Litovitz, J. Chern.Ph~.s.,1974, 60, 5025. 13' J F. Dill, T. A. Litovitz, and J. A. Bucaro, J. Chern. Plz,vs., 1975, 62, 3839. 135H. Dardy, V. Volterra, and T. A. Litovitz, Faraday Symposia Chern. Soc., 1972, No. 6, p. 71. 126 Williams work it is assumed that <P2[u(t)])= exp(-6Drt), and since the lineshape is analysed in the ‘low-frequency, long-time’ region satisfactory results are achieved. Litovitz and co-workers63~135 have extended measurements of the depolarized Rayleigh spectrum of benzene into the high-frequency ‘wings’ in order to obtain information on (Pz[u(r)])at short as well as at long times.Following corrections for the finite resolution of the spectrometer and, importantly, for an estimated collisional contribution to the spectrum, the Fourier inversion of the corrected spectrum yields63 (P2[(r)]),as shown in Figure 8. At short times the correlation function is that for a free rotator (see Section 2D above) while at long times the correlation function is an exponential decay in time with a correlation (or rel- axation) time 72. The simple interpretation regards the benzene molecule as a symmetric top.413135 tlps Figure 8 <Pz[u(t)!)for liquid benzene at 293.5 K obtained from a Fourier inversion of the corrected depolarized scattered Rayleigh line; experiinental data, ---A ---calculated for a free rotator (.Reproducedby permission from J.Chem. Phys., 1973, 59,4491) G. Quasi-elastic Neutron Scattering.-In recent years there have been several publications describing quasi-elastic scattering of mono-energetic slow neutrons from solids and liquids for which molecular niotion plays an important part in determining the lineshape of the scattered neutron energy at a given scattering angle. The reader is referred to review^^^-^^ and key papers45p46t136 for details of experiment and theory. The theory for quasi-elastic scattering from molecules capable of c.0.m. motion and rotation about the c.0.m. is quite similar to that for quasi-elastic light scattering,2~3514~~92 equation (99, and has been reviewed by White43144 and by Allen and Higgin~.~~ The co-ordinate R for each molecule is expanded in terms of the c.0.m.co-ordinate and the (8,$) co-ordinates of the 136 Ref. 45, discussion therein pp. 165-168. 5 127 Time-correlation Functions and Molecular Motion molecular axes. For a rigid molecule for which translational and reorientational modes of motion are uncoupled the incoherent scattering function S(k,t)may be written as a product of translational and rotational functions and for the case where translational diffusion occurs more rapidly than rotational diffusion, so that Dtk2 % D,the scattering cross-section is given by43945 where b is the scattering length for incoherent scattering from the assumed equivalent nuclei. For the case where rotational diffusion is the primary cause of incoherent scattering, e.g.for a rotator-phase crysta1,43945 a3 which corresponds to a sum of Lorentzians centred on wo involving spherical Bessel functions Jm(kr),where r is the radius of gyration of the molecule. In general the observed scattering cross-section will be due to a convolution of translational and rotational contributions. For the rapid motions of small molecules, inertial effects will be important, as discussed above, and the assump- tions of simple translational diffusion and/or translational diffusion which lead to equations (96) and (97) may not be acceptable. Experimentally it appears difficult to obtain, with good accuracy, the material scattering function from the observed scattering function.This is due to several factors136 prominent among which are corrections for back- ground levels, multiple scattering from the sample-cell, and the deconvolution of the sample lineshape from that of the incident beam and the instrument itself. Consequently current interpretations have relied on assumed models for motion, equations (96) and (97), giving the transport coefficients Dt and Dr. For examples we refer to the work of Aldred and co-~orkers~~ for Dt for liquid methanol and toluene and to that of Leadbetter and co-~orkers~~ for Drfor rotator-phase solids of the substituted cyclohexanes C6FgH3 and C6F12. The fact that the quasi- elastic scattering spectrum in general involves a convolution of translational and reorientational modes of motion suggests that it would be highly desirable to make use of experimental data on time-correlation functions for translational motions, from tracer diffusion or n.m.r.experiments, and for reorientational motions, from microwave, dielectric, far-i.r. and Raman absorption, and pico- second Kerr-effect and depolarized laser-light scattering experiments, in order to obtain a consistent interpretation of motion in a given system. H. Infrared and Raman Vibration-Rotation Spectra.-The rotational broaden- ing of vibrational lines, as observed for i.r. and Raman vibrational spectra, may be interpreted2.47-56-137 for simple molecules possessing a degree of sym- metry in terms of correlation functions (PI[u(t)])and (Pz[u(t)])for the reorien- 137 F.J. Bartoli and T. A. Litovitz, J. Chem. Phys., (a) 1972, 56, 404; (b) 1972, 56, 413. 128 Williams tation of particular molecular axes. It is recognized that many processes other than reorientation may contribute to the broadening of vibrational lines. Van Konynenberg and Steele51 have given a critical assessment of these and they include cross-correlation terms, vibrational relaxation, isotope effects, ‘hot-bands’, and collision-induced processes. As one example of the use of vibration-rotation spectra for the evaluation of (P~[u(t)])and (Pz[u(t)])we refer to the work of Rothschild and co-workers50 on the i.r. and Raman spectra of CHC13, CDC13, and isotopically pure CH35C13. Figure 9 shows the time-correlation functions --\ \ \ \ \ \ \ \ -\ 71 \ \ ‘1 Y 2 \ @,-for reorientational motion of the C3 symmetry axis.The correlation functions have zero slope at t = 0 (i.e.they are even functions of time), resemble a classical symmetric-top free rotator at short times, and become exponential in time at long times. Also (Pz[u(t)])decays faster than (PI[~(t)])which is expected for Time-correlat iori Functions and Molecular Motion a ‘smooth’ distribution function f(Q,t) (see Section 2G above). Such behaviour is interpreted in terms of the free reorientations of molecules interrupted by collisions and many models have been proposed.2~s~9~52-57~138 5 Computer Simulations of Dynamical Behaviour As indicated in Section 2F, computer simulations of the dynamics of assemblies of molecules yield both equilibrium and dynamic data, where the dynamic data are in the form of translational and reorientational time-correlation func- tions and their memory functions. Simulations have been made for argon,G5 for diatomic mo1ecules,2~~7~58~66~6i~13~~140for liquid water,68 and for ionic melts,141,142 and all relate to ‘fast’ motions with t < 10-lo s.The translational motions [as expressed by e.g. (~(0).v(t))]and the reorientational motions, as expressed by (PI [uct)])and (PP[u(t)]>,generally exhibit free-particle behaviour at short times, complicated behaviour at intermediate times due to collisions, and exponential behaviour at long times where the process may be regarded as stochastic. A good example of such behaviour is afforded by the calculations of (PI[~(t)])and (Pz(u(t)])for CO by Berne and co-workers.143 As one example of the results of simulations, Figure 10 shows (P~[u(t)])for a model of liquid water.68 At short times there is a sharp oscillatory drop of about 20% of the total correlation function, followed by the exponential decay having TI = 6.7 x s.The short-time behaviour corresponds to oscillatory motions of the hydrogen-bonded molecules, the long-time behaviour to the gross rearrangements of molecular orientations via co-operative processes involving a sequence of finite stochastic jumps. Rahman and Stillinger also simulated (Pz[u(t)]),which is found to be rather similar to (P~[u(t)])(Figure lo), but decays more rapidly with 71/72 = 2.7 [compared with 71/72 = 3 for rotational diffusion, equation (27)].Such simulations should provide a valuable means whereby experimental data may be reconstructed using molecular parameters and intermolecular potential functions. Up to the present a qualitative and semi-quantitative under- standing of fast molecular motions has been sought with the aid of computer simulation. The results obtained clearly demonstrate the inadequacies of simple models for motion [e.g.equations (9,(16), and (37)]and will, no doubt, lead to new generations of models for motion which are based on quantities having a physical interpretation. 6 Conclusions The material presented in this review has been selected so that it will act as an introduction to the time-correlation function approach to molecular motion, 138 R.E. D. McClung, S. Chem. Phys., 1972, 57, 5478. 139 W. Streett and D. Tildesley, Proc. Roy. Soc., 1976, A348, 485. 140 M. Evans, G. Evans, and G. Wegdam, (a) Mol. Phys., 1977, 33, 1805; (6) Adv. Mol. Relaxation Processes, 1977, 11, 295. 141 Ref. 84, p. 163. 142 J. W. E. Lewis and K. Singer, J.C.S.Faraduy 11, 1975, 71, 41, and refs. therein. 143 Ref. 2, p. 697, Figure 29. Williams 0 0.436 0.871 1.306 1.742 tll 0-l2s Figure 10 (P,[u(t)]), calculated by the method of molecular dynamics, for a model of liquid water at 307.5 K (Reproduced by permission from J. Chem. Phys., 1971, 55, 3336) will clarify through examples how time-correlation functions may relate to experimentally determined quantities, and will make chemists more aware that studies of liquids and solids using the diverse experimental techniques listed in Table 1 may have common interpretations through the underlying time-correlation functions for molecular motion.Up to the present, data from a given experimental technique have largely been interpreted without recourse to information from other experiments. In recent years some comparisons have been made, usually in terms of averaged relaxation times which, being integrals over time-correlation functions, only reflect a limited aspect of the dynamical process. In order that a more satisfactory understanding of the nature and form of motions in liquids and solids may be achieved, the writer suggests that greater effort should be made to obtain experimental time-correlation functions for a given system from as many experimental techniques as possible and that the interpretation of such data be made using all the results.This is now a practical possibility and is very necessary when a given experiment involves several time- autocorrelation functions, e.g. neutron-scattering, light-scattering (Sections 4F, 4G), or several cross-correlation functions, e.g. dielectric relaxation, Kerr-effect relaxation (Sections 4B, 4C).

ISSN:0306-0012    

DOI:10.1039/CS9780700089

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Non-bonded Interactions of Atoms in Organic Crystals and Molecules By A. I. Kitaigorodsky U.S.S.R. ACADEMY OF SCIENCES, INEOS, UL. VAVILOVA 28, MOSCOW-V-312, U.S.S.R. 1 Mechanical Model of Molecules The word ‘molecule’ may be used in two different meanings. Speaking about a ‘common salt molecule’ we have in mind the finest representative of this substance: one sodium atom and one chlorine atom make up a common salt molecule. However, a common salt particle consisting of one sodium and one chlorine atom does not exist in nature. When dissolved, this substance dissociates into ions. In solids, each positively or negatively charged ion has six neighbouring ions of the opposite sign located at equal distances. The same happens in the melted substance, the only difference being that the co-ordination number of six is realized here ‘on the average’.Speaking about a ‘naphthalene molecule’ we also mean the smallest repre- sentative of this substance, but unlike the previous example a naphthalene molecule, composed of ten carbon atoms and eight hydrogen atoms, exists as a separate particle in solids, solutions, or melts and in a gaseous state. Most inorganic substances behave as common salt. In inorganic substances we do not have, as a rule, to subdivide interactions into valence and non-valence (non-bonded) types. On the contrary, in the okerwhelming majority of organic substances this distinction is completely obvious. Experimental studies of the structure and properties of organic molecules and crystals, as well as practical work on chemical synthesis, testify that the model of an organic molecule in the form of a set of atoms linked by ‘springs’ in conformity with a valence scheme is a very good approximation to its actual structure.This model, which may quite appropriately be called a mechanical model, has great predictability in almost all the spheres of physical chemistry and can be equally well applied to many problems of synthetic organic chemistry. About 30 years ago, approximarely at the same time and independently of one another, Hill,1 Westheimer,2 and the present author3 showed that a mechanical model may acquire quantitative characteristics. However, its ‘computation value’ for predicting the geometry of molecules and crystals and for calculating their properties was demonstrated only after the emergence of computers.The mechanical model is based on the concept that each atom in a molecule T.L. Hill, J. Chem. Phys., 1948, 16, 938. F. H. Westheimer, J. Cheni. Phj..s., 1946, 14, 73. A. I. Kitaigorodsky, Izvest. Akad. Nauk S.S.S.R., 1951, 15, 157. Noti-Dotided Ititcmctiotis of’ Atoms iti Orgcitiic Crj:rtnI.s ntrcl A4olecirles is involved in two types of interaction, valence and non-valence interactions. The magnitude of the interaction energy of a valence-bonded pair of atoms is-100 kcal niol-I. In the absence of a valence bond, the interaction energy is a thousand times snialler, i.c. it is of the order of 0.1 kcal tnol 1. The present author3 has assumed that tiicrc i.s 110 c~ssclrticrldiferemc ill tile nature of’ ititernctiotr hctuwti citoms tlirit ciw /lot hoticki throlrgh vnlmcc.hods, regcrrdless of whether these citoms hcloiig to difiiwJtit molccidcs or to thc] scime molecirle. Therefore, such problems as the prediction of the structure and properties of crystals, adsorption, and the behaviour of real gases may be considered within the framework of the same concepts as are applicable to the calculation of optimal conformations of organic molecules, since in both cases the decisive factor is non-bonded interactions. The mechanical molecular model takes into account the ‘springs’ that prevent distortion of ‘ideal’ valence angles. Generally speaking, ideal valence angles could be found empirically.Howeber, for initial calculations the elementary schemes of quantum chemistry could be used, for instance, a 90 angle from 0, S, or Se atoms, tetrahedral angles for aliphatic carbon atoms, and 120 angles for trigonal and aromatic carbon atoms. There are many organic molecules which were called ‘strained’ as far back as the time of classical organic chemistry, because a requirement of the valence scheme was, as in cyclobutane, a marked deviation of angles from ‘ideal’ values. It is but natural to assume that such distortions require energy consumption. It would seem that valence bonds in strained molecules have to be stretched. However, physicists did not confirm this hypothesis. A great body of information accumulated on the measurement of the length of bonds in organic niolecules has shown that angle distortion does not affect the lengths of valence bonds.It can probably be assumed to a sufficiently good approximation that valence- bonded atoms are connected by ‘rods’ rather than ‘springs’. For a long time chemists used the term ‘strain’ only when speaking about molecules with distorted valence angles. However, in terms of the mechanical model of an organic niolecule, benzene also is a strained molecule. The point is that molecules are strained not only owing to distortion of valence angles, but also because atoms not bonded through valence bonds approach one another at distances smaller than equilibrium distances. X-Ray diffraction studies of organic crystals provide evidence that there is a great difference between the interatomic distances of atoms that have valence bonds according to classical chemistry and distances typical of pairs of atoms that are not linked through valence bonds.Thus, the following values can be given for the distance between two carbon atoms, which are considered the basic values for organic chemistry. The triple valence bond, which is the strongest, has atoms at a distance of 1.2 A. A single bond gives a distance of I .54 A, which in some rare cases may be up to I .56 A. As to carbon atoms of adjacent niolecules in a crystal, the distance between them is 3.4-3.8 8, whenever other atoms do not interfere with their approach to one another. Kitaigorodsky In a regular plane hexagon formed by the carbon atoms of a benzene molecule, the C atoms which are not linked through’valence bonds are spaced at 2.4 A.The meta atoms as well as the atoms in a paru position (2.8 A spacing) are repelled from each other. Such situations make a molecule strained despite the fact that its angles are not distorted. Now, what is the equilibrium distance for non-valence forces? The answer to this question will be provided by the calculations that follow later. However, it is already obvious that this distance must be close to a ‘contact’ intermolecular distance4 in crystals (strictly speaking, it is somewhat larger than the contact distance owing to intracrystalline pressure). In estimating intermolecular radii, the initial data must be derived from crystals built from molecules that are ‘framed’ with atoms of one species.For instance, for a hydrogen atom an expedient approach would be to study the geometry of an adamantane crystal. In this crystal all the contacts of adjacent molecules are of the H * * .H ty~e.~,~They are of length 2.34 A. The intermolecular radius of the hydrogen atom is 1.17 A. The equilibrium distance, i.e. the abscissa of the interaction curve potential well, must be somewhat larger than this value. Figure 1 illustrates interaction curves or, as we call them, atom-atom potential curves, for two carbon atoms and two hydrogen atoms. Distances to the left of the deepest point of the well correspond to repulsion of the atoms, and those to 0.1 0.0s 0.06 7 0.04-3 -0.02 -3 Y20 -0.02 -0.04 -0.06 -0.08 Figure 1 The C-C and H -H aton-atom potential curves [From Phys.Stat. Solid; (B), 1974, 62, 2911 A. I. Kitaigorodsky, ’Organicheskaya Kristallochimia’ (in Russian), Moscow. 1955; ’Chemical Organic Crystallography’, Plenum Press, New York, 1961. W. Nowacki, Helv. Chim. Acra, 1945, 28, 1233. 6 135 Non-bonded Interactions of Atoms in Organic Crystals and Molecules the right of this point to the attraction of the atoms. As can be seen from the Figure, the equilibrium distance of the non-bonded C.* -C interaction is 3.8 A. Cyclobutane atoms which have no valence bonds in common are spaced at a distance of 2.2 A, but still valence bonds are not stretched.Thus, neither type of molecular strain can compete with the valence bond force. On the contrary, we often observe competition between the elasticity of valence angles and the ten- dency of non-valence-bonded atoms to assume equilibrium-spaced positions. It is this competition that serves as the basis for calculation of the optimal con- formations of organic molecules using the atom-atom potential method. The principle of this method will be illustrated on the most elementary example, a water molecule. The angle between the 0-H bonds is 105". The angular 'spring' is stretched, because the angle is 15" larger than the ideal angle. What is the cause of this increase? The cause is the repulsion of hydrogen atoms not linked through valence bonds.If a valence angle remained equal to 90", the Ha * -H distance would be 1.37 A. In a real molecule it is 1.54 A, i.e. still less than the 2.34 8, equ iI ibriu m distance. In general, the problem of estimating the optimal conformation is formulated as that of calculating the minimum strain energy. In other words, assuming that the bonds are rigid, it is required to calculate a multidimensional energy surface for all possible configurations of atoms. The deepest minimum of this surface must correspond to the optimal conformation. All the problems discussed in this review involve processes that preserve intact valence bonds between the atoms in a molecule. Denoting by rik the dis- tance between a pair of non-valence-bonded atoms (they may belong to the same or to different molecules), we can write the portion of energy in a system of atoms which is not involved in electron transfer as follows: If this function could be calculated for any molecular conformation and for any molecular systems, this would help solve a very broad range of problems.6-8 What are these problems, physical or chemical? Several decades ago the boundary between physics and chemistry was quite obvious.If a molecule did not change its chemical composition, i.e. if the order of its valence bonds remained unaltered, the problem was passed over from the domain of chemistry to that of physics. However, physicists refused to accept this 'gift'. Physical chemistry emerged which began to deal with such phenomena as adsorption, catalysis, and the initial stage of chemical reactions.These phenomena are not connected with the disintegration of a molecule but are directly related to chemical technology. Until some time ago chemists engaged in chemical synthesis insisted nevertheless that their activity is quite different from the work of not only physicists, but also physical chemists, since chemical processes are characterized by the breakage of A. 1. Kitaigorodsky, Doklady Akad. Nauk S.S.S.R., 1959, 124, 1267. A. I. Kitaigorodsky, Tetrahedron, 1961, 14, 230. A. 1. Kitaigorodsky, 'Molecular Crystals and Molecules', Academic Press, New York, 1973. 136 Kitaigorodsky valence bonds. The wall collapsed when it became clear that in many cases a chemical reaction depends on the conformation of a molecule which, in its turn, is dependent on intramolecular non-bonded interactions.The above example is but one of the few that demonstrate that the traditional division of natural sciences has become hopelessly obsolete and we are keeping to it for no reason other than simple human conservatism. The problem of non-bonded interactions is of interest for specialists in many different fields. The calculation of the expression 2 U(rik) gives us an insight into the spectroscopy of molecular crystals, adsorption phenomena, and the thermodynamic properties and structure of organic crystals, and helps us under- stand the course of chemical reactions which involve overcoming steric obstacles, the phenomena of conformational isomerization, the properties of polymers, etc.This list could be continued. However, before discussing the possible applications of calculations of the interaction energy of non-valence-bonded atoms, it is necessary to consider the problem of how this function is calculated. 2 Selection of Atomic Interaction Energy Formula The idea of ‘forgetting’ about the existence of electrons and, so to say, turning back to Democritus, considering a molecule as a system of atoms, does not contradict quantum mechanics. The well-known Born-Oppenheimer theoremg states that the Schrodinger equation for an electronic-nuclear system can, under certain conditions, be transformed into an equation for a system of atoms. In other words, in a number of cases substances can be regarded as a system of point atoms.True, this simplification is obtained at a high price. In the Schrodinger equation for an electronic-nuclear system, the law of interaction between particles is known: this is the Coulomb law. Tn the transformed equation, the U(rik) interaction energy term appears about which nothing can be predicted in advance. Following this approach, we have to make a number of arbitrary assumptions and set the values of arbitrary parameters that permit computerized calculation of energy for a given specific arrangement of atomic centres. The validity of these hypotheses must be established by experiment. The first assumption is that non-valence interaction energy is composed of valence angle deformation energy and the energy of interaction of non-bonded atoms.The second assumption holds that both parts of the energy are additive. Consequently : i.e. summation involves all pairs of atoms and all the valence angles. Note that the problem of studying the packing of molecules is simpler than the conformation problem. Indeed, if a molecule is rigid, and there is no reason to think that the crystalline field changes the valence angles, the first sum only is to be calculated. M. Born and I.Oppenheimer, Ann. Phys., 1927, 84, 457. Non-bonded Interactions of Atoms in Organic Crystals and Molecules The past decade has seen hundreds of publications in which the atom-atom potential schemesglo has been used for various calculations.The two basic assumptions formulated above have been accepted by all workers. However, these two hypotheses are not sufficient to begin calculations. Some additional assumptions are required and it is here that the paths of many scientists have parted. The present author believes that of greatest importance is the third assumption, namely that the atom-atom potential curves of non-bonded interactions for a pair of atoms of one chemical species are the same regardless of what molecules contain these atoms. Being a physicist, the author is well aware of the fact that this assumption will be accepted by chemists with dismay, if at all. There is no doubt that atoms of one species are different in different chemical compounds : this is eloquently illustrated, for example, by chemical shifts in a nuclear magnetic resonance.The question is whether these differences are as important for non-bonded interactions. The author of an article” recently published in this journal is quite right in pointing out that physicists and chemists treat the theory of a phenomenon in quite different ways. Chemists try to explain the phenomenon post factum. The better the agreement between theory and experiment, the more valuable this theory becomes. When considering the problem from such point a view, it is desirable to select individual interaction energy curves for the same pairs of atoms in different molecules. An ideal agreement can always be obtained between experimentally derived and calculated values by increasing the number of theoretical parameters. As to a physicist, he will be quite satisfied if he can predict the value of a quantity with an accuracy of several tens of per cent.From the viewpoint of the physicist, increasing the number of parameters appreciably diminishes the value of theory. In lectures, the author has proposed the following formula for the evaluation of a theory (and this is quite serious, though the reader has a right to regard it as a joke): if we denote the number of parameters in a theory n, and the number of quantities that can be predicted with its help N, the value of the theory Vcan be expressed as : V= (N/n) -1 The author believes that the value of a theory is zero if for explaining the experiment the researcher had to introduce as many parameters as the number of values the experiment produced.The value of the theory is infinitely great if it does not contain arbitrary parameters (n = 0). The value of the theory is considerable if V is much greater than 1. Let us turn back to the configuration of atom-atom potential curves. All workers are unanimous that three parameters are sufficient for describing the atom-atom potential curve of the type illustrated in Figure 1. It is convenient to use a ‘six-exp’ potential : lo V. Dashevsky, ‘Conformations of Organic Molecules’ (in Russian), Moscow, 1974. l1 D. V. Theobald, Chem. SOC.Rev., 1976, 5, 203. Kitaigorodsky A r6-+ Bexp(-ar) Some scientists prefer to write both terms (the one responsible for attraction of atoms and the one taking into account their repulsion) in an exponential form.Other suggestions are, however, possible.1° In earlier work7 the author suggested the use of the single-parameter potential U = 3.5 (-0.04 (YO/Y)~+ 8.6 x lo3exp [-13 (ro/r)]} considering that the value of a model depends, in the first place, on a properly selected value of the equilibrium distance YO (or, we may say, on the value of an intermolecular radius). Many researchers were surprised to find that such a potential works excellently12 for prediction of a structure and gives errors of not more than tens of per cent when used for studying the properties of solids and molecules. At least twenty different curves1,10913-26 are probably to be found in the liter- ature for the organogenic atom interactions which are most important in organic chemistry.The reason for this great diversity is that each author studies a limited group of substances and tries to obtain the best agreement with experiment for the substances of particular interest for him. This situation cannot but be somewhat disappointing. It can only be hoped that sooner or later the optimal universal potentials will be proposed or, at least, several systems of potentials for large groups of substances (say, aliphatic, aromatic, etc.). The values of potential parameters derived by different authors are not given here, since the reader has already been referred to the original publications. Ne\,ertheless, it is appropriate to add a few remarks about the different ‘ideologies’ of the authors who use the model of atom-atom pair interaction.It seems to the present author quite logical to regard the atom-atom potential interaction curve as certain final truth. In this case one’s selection of the curve is justified only by the agreement of the calculations with the experimentally derived data. l2 ‘Conformation of Biopolymers’, ed. C. N. Ramachandran, Academic Press, London, 1967. l3 J. B. Hedrickson, J. Amer. Chem. Sor., 1967, 89, 7036. l4 P. De Santis, Nature, 1965, 206, 456. l5 R. A. Scott and H. A. Sheraga, J. Chem. Phys., 1966, 45, 2091. l8 P. J. Flory, J. Mol. Biol.,1967, 23, 47. l7 N. L. Allinger, J. Amer. Chem. Soc., 1965, 87, 3430. l8 N.L. Allinger. J. Amer. Chem. SOC.,1967, 89, 4345. lYD. E. Williams, J. Chem. Phj,s., 1966, 45, 3770. 2o F. A. Momany, L. M. Carruthers, R. F. McGuire, and El. A. Scheraga, J. Phys. Chem., 1974, 78, 1595. 21 A. T. Hagler, E. Huler, and S. Lifson, J. Amer. Chem. SOC.,1974, 96, 5319. 22 H. A. J. Covers, Arta Crjvst., 1975, A31, 380. 23 D. Nelson and J. Hermans, jun., Biopolj~mers,1973, 12, 1269. D. Williams, .4cta Crysf., 1972, A28, 84. 25 E. M. Engler, J. D. Andose, and P. von R. Schleyer, J. Amer. Chem. SOC.,1973, 95,8005. 26 N. L. Allinger, M. T. Tribble, M. A. Miller, and D. W. Wertz, J. Amer. Chem. SOC.,1971, 93, 1637. Non-bonded Interactions of Atoms in Organic Crystals and Molecules This attitude, however, does not suit many authors.In this case the expression A/r6 is considered as the London dispersion attraction term. Regrettably the rigorous theory works at great distances only. Besides, in this theory it is very difficult, if not altogether impossible, to make corrections for having to deal with a bound, rather than a free, atom. Despite this, frequent attempts are made to derive the theoretical value of the constant A in a term responsible for atomic attraction. Well known are the London,27 Slater-Kirkwood,2* and Kirkwood- Muller29 approximate formulae in which the constant A is related to the polariz- ability and magnetic susceptibility of atoms. To follow a rigorous approach, the attraction of atoms must not only be represented by one term inversely propor- tional to the r6 distance: it is also necessary to take into account the components inversely proportional to the eighth, tenth, etc.powers of the distance. The inevitably approximate nature of these calculations leads the present author to the belief that a purely empirical approach is more advantageous. The positive term in the atom-atom potential formula is interpreted as repul- sion which occurs owing to overlapping of the electron shells. A rigorous analysis of the effect is not possible even for two helium atoms. Therefore, all authors agree on the empirical approach being unavoidable for estimating this energy component. Having chosen the basis of the ‘physical nature’ of the atom-atom potential, many authors hold that, apart from repulsion forces due to overlapping of the electron shells and the van der Waals attraction forces, electrostatic interaction must also be included in the interaction formula.A number of molecules have a dipole moment, and all molecules have higher-order moments. However, it is extremely difficult to account for such interactions. For some particular examples, it was demonstrated that the contribution of electostatic interactions is but small.30 It may be asserted with a sufficient degree of accuracy that the geometry of a molecule and packing of molecules in a crystal depend on these interactions ,insignificantly on account of the shallowness of the potential well.* As to the numerical contribution to the interaction energy, it does not seem in all prob- ability to exceed 15-20%.In intermolecular interaction calculations one might describe a molecule as an entity with a dipole, quadrupole, or octupole moment. However, this is not feasible, because only dipole moments are known from experiment, and higher- order moments have been determined only for a very limited number of cases. But how can we take into account electrostatic interactions when using the atom-atom potential scheme for conformation calculations? There is only one way to do it, namely to assign a so-called residual charge to each atom. Residual charges may be found by approximate quantum-chemical techniques. However, the author considers that such calculations are highly conditional because of the vague meaning of the ‘atomic charge’ concept.Furthermore, there are many 21 F. London, Trans. Faraday Sor., 1937, 33, 8. J. C. Slater and J. G. Kirkwood, Phys. Rev., 1931, 37, 682. 29 A. Miiller, Proc. Roy. SOC.,1936, A154, 624. 30 R. Mason, Perspectives Structural Chem., 1970, 3, 59. Kitaigorodsky publications whose authors add a Coulomb component in the atom-atom poten-tial formula (see, for example, ref. 31). The values of the charges are either selected by trial (when the number of parameters increases significantly and the ‘value’ of the theory approaches zero) or taken from quantum-chemical calculations (see, for example, ref. 20). Unfortunately, owing to the vagueness of the term ‘atomic charge’, their values will vary appreciably (even as far as different signs) depending on the calculation technique. The author finds it extremely fortunate that corrections introduced into the energy formula by the term inversely proportional to the first power of the distance are mostly of no particular importance.The author believes that it is preferable to be content with rough agreement with experiment than to try to improve this agreement at the expense of the considerably diminished ‘value’ of the calculation. However, even if experiment continuously stresses the necessity of introducing into the energy formula a component slowly diminishing with distance, it is not worthwhile to assign it a physical meaning. The only thing which counts is that the additive pair interaction technique works well.Researchers who have used the methods of quantum chemistry for studying intermolecular forces have obtained convincing proof of its validity. In a monograph32 it is pointed out that our method is essentially the only technique for calculating non-bonded inter- actions of real practical value. As to an adequate configuration of the atom-atom potential curve, pertinent data can be obtained only through experimental work. The discussion of expressions for pair interactions cannot be concluded without saying a few words about the hydrogen bond. A number of researchers have shown that the hydrogen bond can be taken into account in the atom-atom potential scheme. I think that quite satisfactory results can be obtained if the known Morse curve is used for the hydrogen bond: “cihb = D[1 -exp -D where D is the hydrogen bond dissociation energy, dv = Y -YO, YO is the equili- brium H * --0distance, and n is an empirical parameter.Usually, great value is attached to the angular dependence of the hydrogen bond. There is no need, however, to include it in the formula, because when accounting for non-valence interactions between oxygen atoms, or between the oxygen and nitrogen atoms that form a hydrogen bond, we thereby take into consideration the angular dependence of the hydrogen bond as well. This cal- culation technique was used in references 33 and 34. Other authors used more complicated formulae.35-40 31 D. E. Williams, Acta Crj?st.,1974, A30, 71. 32 H. Margenau and N. Kestner, ‘Theory of Intermolecular Forces’, Pergamon Press, 1971.33 E. Popov, Mol. Biol., 1968, 2, 612. 34 A. Kitaigorodsky, Visoiiomol. Soeclitienij-a, 1968, A10, 2669. 35 R. F. McGuire, F. A. Momany, and H. A. Scheraga, J. Phjls. Chem., 1972, 76, 375. 36 M. Dentini, P. De Santis, S. Morosetti, and P. Piantanida, Z. Krist., 1972, 136, 305. 37 D. R. Ferro and J. Hermans, Biopolyrners, 1972, 11, 105. 38 F. A. Momany, in ‘Environmental Effects on Molecular Structure and Properties’, ed. B. Pullman, Dordrecht-Holland 1976, pp. 437-458. 39 Z. Korczzyk, Acta Cryst., 1976, A32, 447. 4o H. Lehman, Acta Cryst., 1974, A30, 713. Non-bonded Iiiteractions of Atoms iii Orgnrtic Crj'stclls aird Molecules We now have to discuss the second component of the strain energy associated with the elasticity of valence angles.If ideal valence angles are cw~and real angles a, this energy is: i.e. it is first of all assumed to be additive. For insignificant deviations (cw -ao) it is sufficient to use a quadratic term and write the formula in the form of quasi-elastic energy: where C are elastic constants. In references 41 and 42 an attempt is made to manage with a minimum number of constants. The authors of these works suggest that C and ao be considered as universal constants for a broad class of compounds, i.e. good agreement with experiment can be achieved assuming that all the carbon atoms are classified as tetrahedral (sp3 hybridization), trigonal (sp2), or linear (.sp). For tetrahedral atoms, a0 is 109"28'; for trigonal and linear atoms, it is 120" and 180", respec-tively.Attempts at differeniiating CCC, CCH, HCH, etc. angles are of course justified, even though this causes a slight increase in the number of empirical parameters and reduces somewhat the predictive value of the technique. The C constants are in the range 20-90 kcal mol- rad2. The C constants for 0 and N atoms also lie within this range; the ideal angles are assumed to be equal to 90" (besides, it can be assumed that an ideal angle is equal to 90" for a pyra- midal nitrogen atom and 120' for a planar case). The C constants are associated with the deformation force constants K, which are usually found from the frequency of molecular vibrational spectra. By definition, where N is the number of equivalent interactions and ae is a real valence angle.Substitution of the strain energy expression gives i?f(r) 2r(z)+ Z2f(r)drK, = C, + -T-da am~aa Calculations show that the spectroscopic deformation constants are approxi- mately twice as large as the 'conformation' elastic constants, because the former include non-bonded interact ions. Now we have to return again to the atom-atom potential formula. This interaction was implied to be central, i.e. pair interaction energy was implied to be dependent only on the distance between the atomic centres. Simple reasoning without any additional investigations suggests that this can be true only to a certain approximation. We are not interested in free atoms: 41 V.Dashevsky and A. Kitaigorodsky, Twr. i dJp. Khim., 1967, 3, 42. 42 V. Dashevsky, Zhur. srrukt. Khini., 1966, 7, 93. Kitaigorodsky our concern is valence-bonded atoms! It is quite obvious that, strictly speaking, they cannot be spherically symmetrical. The available calculations demonstrate that, fortunately, a correction for non-central interaction need be introduced only when the angle x between the line connecting two non-valence-bonded atoms and the valence bond is much larger than 90". Such a situation never arises in intermolecular interactions. However, in the case of intramolecular interactions the angle x may reach values of 110-120". If two carbon atoms are linked by a single bond and one of the atoms is linked with an atom A and the other with an atom B, the equilibrium distance A.* -B is greater than the distance between the same species of atoms which must be taken into account in intermolecular interaction calculations. How do we know it? The point is that non-bonded interaction potentials obtained from various physicochemical data give too low values for the barriers of internal rotation about single bonds. This was shown for the first time in references 43 and 44 and later confirmed in a very large number of examples. The overwhelming majority of investigators cope with this unpleasant situ- ation (the author has in mind deviation of the interaction from a central one) by including an additional, so-called 'torsion' component in the energy formula. For ethane-type molecules this component is as follows: 7' = 2'0 (1 + cos 34) where 2'0 is the constant for the bond. Of course, it is also necessary to select the origin of an angle of rotation about a single bond.The symmetry of the torsion function is selected so as to correspond to the symmetry of the arrangement of the atoms that rotate about the single bond. From the present author's point of view, the inclusion of the torsion component impairs the elegance of the atom-atom potential scheme. Modern computers would make it possible to take into account the dependence of the atom-atom potential not only on the distance between the atomic centres, but also on the angles between the vectors. No programs, however, have yet been developed for such calculations.This completes the discussion of the assumptions that permit estimation of the interaction energy of non-valence-bonded atoms in one molecule or in a system of molecules. As can be seen, in a general case calculations use the formula t' = t'nb -k :'el -t ?Jhb + L'angle -k utors where tinb is the interaction energy of non-bonded atoms from which is removed into the interaction energy of 'atomic charges' L'el and hydrogen-bond energy Z'hb. The latter two components are valence angle deformation energy and torsion energy. If the researcher is unwilling to make the assumption of the rigidity of valence bonds, he may add one more component to the above equation. 43 E. A. Mason and M. M. Kreevoy, J. Amer. Chem. SOC.,1955, 77, 5808.44 M. M. Kreevoy and E. A. Mason, J. Amer. Chem. SOC.,1957, 79,4851. 143 Non-bonded Interactions of Atoms in Organic Crystals and Molecules We can now proceed to consideration of various applications of the technique. First a few general remarks are appropriate. Investigations using the atom-atom potential method may be conducted with the dual purpose, first, of checking the concept of the method and searching for the optimal parameters, and, secondly, of evaluating the structure and properties of molecules, crystals, or other molecular systems. The authors of many works solve both tasks simultaneously. The studies described in this article are being carried out by hundreds of researchers in many different countries. There is naturally no plan governing these studies, which is regrettable, since a certain definite sequence of research work suggests itself, namely from the simple to the complex.Atomic interaction energy is the sum of many components. Would it not be proper to study problems by successively ‘including’ one component after another? It is but natural to start the investigation from intermolecular inter- actions of rigid molecules that do not form hydrogen bonds and do not have considerable electric momenta. In this case the energy will consist of one compo- nent only. Within the framework of this first problem, it is also worthwhile to conduct investigations in a specific order. Thus the studies could be started from inter- action of molecules built from one species of atoms.An excellent starting point is the study of crystals of different sulphur modifications that are composed of s8 molecules or consideration of non-bonded interactions in graphite. The next step would be research into intermolecular interactions in hydrocarbon and fluorocarbon crystals or in crystals built of sulphur and phosphorus atoms, in brief, the study of the serviceability of the model in rigid molecules composed of two species of atoms. After atom-atom potential curves have been selected, one may proceed to study the conformations of molecules built of the same atomic species. This means that a new component will be added into the energy formula. A series of calculations will help determine the values of constants in the valence angle deformation energy equation.The next step will have to be the study of molecules with free rotation which could be followed by inkestigation of the interaction of molecules with hydrogen bonds. Unfortunately, this is nothing but wishful thinking, no more realistic than plans to reduce the population of the globe. The plain truth is that research in the field of pure science is not planned on a world scale. Many researchers try to obtain concrete results with respect to the structure and properties of compounds in which they are interested without taking the trouble of analysing the capabilities and accuracy of the atom-atom potential technique. The solution of this important problem is a matter for the future. Now it remains to discuss briefly the basic applications of the atom-atom potential scheme by mentioning the fields of research where this method has already found its use and pointing to the possible applications in some new areas.3 Packing of Molecules In youth the author became interested in the regularities governing packing of Kitaigorodsky organic molecules in a crystal and this has led to the study of non-bonded interactions. The structure of not more than a few dozen organic crystals was known about 30 or 40 years ago. At that time the co-ordinates of hydrogen atoms could not be determined by X-ray diffraction study. True, physical chemistry had at its disposal certain data on C-H or N-H distances, but some crystallographers were not familiar with these data.Furthermore the drawings of structures at that time were as shown in the top part of Figure 2. Molecules seemed to be suspended in the air and rather frequently a statement could be encountered in books that organic crystals are built very loosely, in contrast to ionic crystals which obey the laws of close packing of spheres. One can only wonder that for about ten years the Stewart-Brigleb models of moIecules,43 from which it was obvious that each atom in a molecule must be described with two radii rather than one, namely atomic and van der Waals radii, in no way affected research into the structure of organic substances. Organic crystal chemistry appeared only when an attempt was made to consider the fitting of such models in a crystal.It was found that framing of molecules with intermolecular radii leads immediately, as can be seen from the bottom of Figure 2, to the concept of close packing of molecules in a crystal. The projections of one molecule fit into the hollows of another (dovetailing). The closest-packing principle was formulated in 1945.44 A number of ensuing consequences were described in detail in the author’s monograph.4 The closest-packing principle permitted prediction of the symmetry and the pattern of arrangement of molecules in a crystal. In its turn, the close-packing principle itself can be considered as the law urging molecules to assume a position associated with minimum energy. If rigid molecules are packed in a crystal, all the contacts will be equal to the sum of intermolecular radii.This will be the situation if we assume that the atoms of molecuIes interact according to the hard-sphere atom-atom potential law. The fact that the actual contact distances between molecules are only on the average equal to the sum of intermolecular radii (and it is not infrequently that deviations from this sum reach about 10%)suggests that better results could be obtained if we proceed from this elementary model to a soft molecule model. Thus we logically pass over from hard-sphere potentials to potentials of the type illustrated in Figure 1. Work with rigid molecular models (the respective techniques are described in the above monograph4) has shown that even in rather complicated cases the search for such mutual arrangement of molecules when all contact intermolecular distances are equalized and two adjacent molecules dovetail results in a correct structure. Of course, when using such an elementary method of search it is necessary to proceed from the known dimensions of a unit cell.The symmetry of a crystal (i.e. the space group) must also be known. Successful work with rigid models accounts for the excellent results obtained in calculations of a structure using the atom-atom potential method. Since this method is valid for hard-sphere potentials as well, it is not surprising that Non-bonded Interactions of Atoms in Organic Crystals and Molecules Figure 2 Projection of hexachlorobenzene crystal structure on the xz-plane different authors working with different potentials come to the same conclusions with respect to a structure.The most important thing in the atom-atom potential method is correct selection of an equilibrium distance, i.e. the abscissa of the potential well. It is for this reason that the above universal single-parameter potential proposed by the author has proved quite satisfactory for many appli- cations and quite good when the researcher’s task was to calculate the geometric parameters of a structure. At the present time the atom-atom potential method has been successfully employed for identifying many dozens and perhaps even several hundreds of various structures of organic compounds. The principle of the study is as follows.The value of interaction energy is calculated for each conceivable arrangement of molecules, taking into account interactions of all the atomic pairs in the inter- action radius of 10-20 A. Such calculations are not possible without a computer. Atom-atom potentials are assigned. The computer has to build an energy Kitaigorodsky surface in multidimensional space. The minimum of this surface gives the value of the geometric parameters of the structure, while the depth of the minimum yields the value of lattice energy in a crystal, or strain energy in a molecule. Evidently, the applicability of the method must be tested on the simplest cases. It is quite obvious that calculation of a structure is simple if a molecule is rigid and its position in a crystal has a limited number of degrees of freedom.However, it is only in exceptional cases that close packing of molecules is possible in high- symmetry crystals. Ordinarily it is observed in monoclinic systems. If a molecule possesses a centre of inversion, it has only three degrees of freedom in a given cell (three Eulerian angles that determine the inclination of the molecular axes to the axes of the crystal). A monoclinic cell is characterized by four parameters (three edges of the cell and a monoclinic angle). Thus, even in this relatively simple case we have to deal with a seven-parameter problem, i.e. with a seven-dimensional energy surface. If the object is to prove the validity of the method or to define more precisely some elements of the structure or the configuration of the atom-atom potential curves, the scope of computation is comparatively moderate. For such cal- culations, the researcher takes at random a set of parameters, which must not be very different from the actual set, and calculates the value of energy in the vicinity of this point.The computer gives us the nearest minimum of the energy. To be sure that this minimum is true, several calculations should be carried out from different starting points. If, as the result of all these calculations, we always ‘fall’ into the same potential well, this makes us positive that the calculations are correct. The success of such calculations is beyond all expectations. In publi- cations of different authors we often come across expressions of amazement with respect to the accuracy with which the derived energy minimum corresponds to the actually observed structure.The discrepancy between the theoretically obtained and experimental values of parameters is hundredths of an Angstrom; the angles responsible for orientation of a molecule differ by 1 or 2 degrees. Research work conducted before 1970 is described in reference 8. The development of computation technology has caused a great increase in the number of publications devoted to calculations of molecular packing in Crystals using the atom-atom potentials. Thus, for example, Simonetta and collaborators conducted a series of investigations, described in a review,45 the basic objective of which was the study of the conformation of biphenyl derivatives in a free state and in a crystal.Although, generally speaking, packing does not appreci- ably affect the confmmation of molecules, in particular interatomic distances, intermolecular forces in a crystal may significantly alter the angles of rotation about single bonds. The authors calculated the conformation of free molecules within the framework of the additive model of intermolecular interactions and then, using the same parameters, found the packing of molecules in crystals. It should be noted that, apart from the rotational degrees of freedom of a mole-cule as an entity, they also accounted for possible rotation around the bond between phenyl rings. The agreement between the theoretically calculated packing M.Simonetta, Accounts Chem. Res., 1974, 7,345. Non-bonded Interactions of Atoms in Organic Crystals and Molecules of molecules and the data of X-ray diffraction studies carried out by the authors permitted a conclusion that the parameters of the potential used for calculating the conformation of a free molecule had been selected correctly. The same authors conducted similar investigations for a number of annulene derivatives. The relationship of intra- and inter-molecular non-valence interactions and their effect on molecular packing are also considered in publications46947 which present calculations of the structures of benzene, biphenyl, P-ionilydene-y-crotonic acid, and other compounds for both rigid and non-rigid molecules.Whereas the first studies of the packing of molecules in a crystal were concerned mainly with non-polar molecules, with the growth of interest in calculation of the conformation and packing of polypeptides and proteins it has now become neces- sary to choose the parameters of potentials for interaction of polar molecules taking into account hydrogen-bond contributions. Sheraga’s group has selected parameters that enable calculation of packing4* for a large number of compounds, including aliphatic and aromatic molecules, sulphur- and nitrogen-containing heterocyclic compounds, carboxylic acids, amines, and amides. Dispersion interactions were taken into account using the Lennard-Jones potential, electro- static interactions according to the Coulomb formula, and the hydrogen-bond energy with the aid of the Lennard-Jones potential with specially selected parameters.Several authors49-51 have theoretically calculated packing patterns of a broad range of amino-acids, including several polyamino-acids, that show good agreement with the experimental X-ray data. In a series of articles under the title ‘Energy functions for peptides and protein~’,5~-~*Hagler and co-authors have selected the parameters of the Lennard-Jones-and Coulomb-type potentials (the hydrogen bond was well described within the framework of these potentials) on the basis of calculations of optimal packing for ten different molecules containing amide groups. These parameters were then used for packing calculations in ten crystals; it should be pointed out that for the first time for such compounds in three of these crystals the only initial data were the number of molecules in a cell.Calculated and experimental data showed good agreement ; the theoretical intermolecular contacts differ from the experimentally derived values by only 0.04--O.18 A, lengths of hydrogen bonds by 0.00-0.09 A, and hydrogen-bond angles by 0.5-1 1.9”.This group of works also includes that of Ramachandran et al.55who calculated the packing of molecules in a N-methylacetamide crystal. 4a E. Huler and A. Warshal, Acta Cryst., 1974, B30, 1822.*’ A. Warshal, E. Huler, D. Rabinovich, and Z. Shakked, J. Mol. Structure, 1974, 23, 175. aeF.A. Momany, L. M. Carruthers, R. F.McGuire, and H. A. Scheraga, J. Phys. Chem., 1974, 78, 1595. 4B R. F. McGuire, G. Vanderkooi, F. A. Momany, R. T. Indwall, G. M. Crippen, N. Lotan, R. W. Tuttle, K. L. Kashuba, and H. A. Scheraga, Macromolecules, 1971, 4, 112. 50 F. A. Momany, L. M. Carruthers, and H. A. Scheraga, J. Phys. Chem., 1974, 78, 1621. 51 Fu Yi-Chang, R. F. McGuire, and H. A. Scheraga, Macromolecules, 1974, 7, 468. 62 A. T. Hagler, E. Huler, and S. Lifson, J. Amer. Chem. Soc., 1974, 96, 5319. 63 A. T. Hagler and S. Lifson, J. Amer. Chem. SOC.,1974, 96, 5327. 64 A. T. Hagler and S. Lifson, Acta Cryst., 1974, B30, 1336. 55 G. N. Ramachandran, K. P. Sarathy, and A. S. Kolaskar, 2. Naturforsch., 1973, 28a, 643. 148 Kitaigorodsky In studies of a crystal structure composed of polymeric molecules, a lack of X-ray data renders computer-based calculations of packing particularly impor- tant.In many cases complete interpretation of a crystal structure is made possible only through the use of calculated data. Thus, Zugenmaier er d.56--58studied packing of molecules of polysaccharides and their derivatives in the following way. The first stage of investigation consisted of conformational analysis of isolated molecules, taking due account of intramolecular non-bonded interactions and hydrogen bonds. The next step was to calculate the optimal packing of chains in a crystal taking into consideration only repulsion energy. Structural factors were then calculated for the models and compared with experimentally derived values.In this way the authors studied the crystal structures of mannan, methyl- amylose, methylcellulose, and methylmannan. The same approach has been used59 to identify the structure of two polymorphic modifications of cellulose. In addition to the above, a still larger number of works is available on the calculation of crystal structures composed of polymericG0?61 and monomeric molecules.G2 -G4 Thus, advances in the methods of calculation of crystal packing and detailed checking of parameters on structures built of small molecules enhance to an ever increasing extent the applicability of this technique to the calculation of structures consisting of macromolecules, particularly proteins. At present it may be considered an established fact that an experimentally observed structure corresponds to a minimum on the multidimensional surface of interaction energy.Of course, it should be remembered that a real structure is associated with the minimum free energy, in whose equation potential interaction energy is but one of the components. However, at absolute zero temperature free energy differs from potential energy only by the value of the zero-point energy, which is negligibly small for organic crystals. To follow a strictly rigorous approach, the results of experiment and calculation must be compared at low temperatures. The demanding investigator may still remain dissatisfied. He may ask an advocate of the theory to prove that the obtained minimum is the deepest of all the conceivable minima.Strictly speaking, this requirement cannot be met. In principle, there may exist a crystal whose cell contains any number of molecules. Any symmetry group may also be visualized (their total number is 219). There is no need, however, to raise such problems before the theory. First of all, a large majority of organic crystals are known to assume the symmetry of a very limited number of space group~.~~G~ It is also known that the number of inde-56 P. Zugenmaier and A. Sarko, Acta Crj,st., 1972, B28, 3158. 5i P. Zugenmaier and A. Sarko, Biopolj~t~icrs,1973, 12, 435. P. Zugenrnaier, Biopolj3mrrs, 1974, 13, I 127. 59 A. Sarko and R. Muggli, Macrom)lPciilos, 1974, 7, 486. 6o G. Morosi and M. Simonetta, Chew. Phj..s.Lrttiw. 1971, 8, 358. 61 L. D. Ilario and E. Giglio, Acta CryJt., 1974, B30, 372. 62 M. Dentini, P. De Santis, S. Morosetti, and P. Piantanida, 2. Krist., 1972, 136, 305. 63 J. Caillet and P. Claverie, Acta Crj,st., 1975, A31, 448. 6' U. Shrnuli and I. Goldberg, Acra CrJ..st.,1973, B29, 2466. 65 V. K. Belsky and P. M. Zorky, Kristallogra~j~a,1970, 15, 704. Non-bonded Itrteractions of Atoms in Orgariic Crj!stols and Molecirles pendent molecules in a unit cell is, as a rule, a minimum. If a researcher has at his disposal a single crystal of the substance he is interested in, he may determine the size of the cell, its symmetry, and the number of molecules in one day and after that charge the computer with the task of determining the mutual arrangement of the molecules.Finally, one more consideration is important. Suppose we are interested in the properties of a non-synthesized compound, or the compound is unavailable, or the substance fails to give crystals suitable for experimental purposes. In this case it is worthwhile to assrrrne that the substance forms a crystal with a certain symmetry and that the cell contains the minimum number of molecules. The chances of making a correct guess are quite good. Let us say approximately one half of the molecules having a centre of symmetry crystallize in space group P21/a with two molecules in the cell, and more than half of the asymmetric molecules crystallize in space groups P21 or P21,21,21. The computer will find the dimensions of the cell and mutual arrangement of the molecules.But even if a mistake was made in the arbitrary assumption of the type of symmetry, it can still be expected with a high degree of probability that the properties of this imaginary crystal are close to those of a real crystal. For example, the density of a non-synthesized compound crystal can be estimated with sufficient accuracy. We must certainly not forget that the atom-atom potential method is based on many arbitrary assumptions. Therefore, the researcher must be prepared to come across a situation when a multidimensional energy surface will have many minima of similar depth rather than only one minimum. In this case it cannot be guaranteed that the deepest minimum is the true one. However, what is essential is that one of the deepest minima always corresponds to a real structure.Such conclusions are suggested by the calculations that have been made up to now. Future studies will undoubtedly help to define more accurately the possi- bilities of prediction of crystal structure using this method. Precalculation of a molecular packing may be of great use for scientists who are engaged in studying chemical reactions occurring in the solid state. Studies of the effect of molecular packing in a crystal on synthetic organic chemistry will now be briefly discussed. The examples cited below are taken from a reviewG6 whose author, J. M. Thomas, is one of the pioneers in this particular field. Until recently investigations of chemical reactions in a solid phase were un- deservedly neglected.Solid-phase reactions have the following advantages. First, molecules in a crystal have usually one, rarely two conformations. Secondly, since the mutual arrangement of the molecules is strictly fixed (unlike that in a liquid phase or solution), the course of a chemical reaction is largely predetermined by this arrangement. This makes it possible to carry out directional chemical synthesis. The researcher can, for instance, make use of the fixed positioning of molecules in a crystal by taking advantage of a difference in the polymorphic modifications 66 J. M. Thomas, Phil. Trans. Roy. Soc., 1974, 217, 251. Kitaigorodsky of the same substance. For example, on exposure to light, three polymorphic modifications of o-ethoxy-trans-cinnamic acid give two different products in the cases of the a-and p-forms, and the third modification, the y-form, is light- insensitive.This behaviour of three crystals built from identical molecules of different packing patterns is explained in the original work. The role of molecular packing in polymerization can be illustrated by Figure 3.6i76* Such synthesis is obtained through exposing a single crystal of the sub- stance to heat or light. The process becomes feasible owing to the fact that chemical bonding may form without shifting the centres of the molecules. R 'H,C CH,, R R 'H,C CH2, R Figure 3 An example of polymerization in crystal In a number of elegant works (see ref.69) it was demonstrated that the outcome of reactions which occur in the solid state depends in certain cases on the defects in a crystal structure. Thus, anthracene and 1,8-dichloro-9-methyl- anthracene are photodimerizable, although from the viewpoint of molecular packing this reaction is impossible, since the reaction centres are far from one another. If, however, we take into account shifts along certain crystallographic axes that take place due to dislocations, dimerization becomes easily explicable. It may happen also that on account of crystal defects the isomer formed is not what could be expected from a defect-free structure (for instance, 9-cyanoanthracene). Another interesting example of solid-phase chemical reactions in which packing of molecules may be of decisive importance is reactions of single crystals 6i G.Wegner, Mahromol. Chem., 1970, 134, 219. 68 G. Wegner, Mahromol. Chrtn., 1972, 154, 25. 69 J. M. Thomas, J. 0. Williams, J.-P. Desvergne, J.-P. Guarini, and H. Bouas-Laurent, J.C.S. Perkin 11, 1975, 84. 151 Non-bonded Interactions of Atoms in Organic Crystals and Molecules with gases. Thus, it can be easily demonstrated that in polar crystals the effect of a gas on a solid depends on which side of the crystal faces the flux of gas molecules. The anisotropy of chemical reactions between solids and gases has been observed on many substances.T0 In a similar manner to photodimerization, a decisive role is played here either by the structure of a perfect crystal or by the direction of dislocations.This was shown, for instance, for the ozonolysis of trans-st il bene.71 Mention has been made of solid-phase reactions the outcome of which depends on the mutual arrangement of molecules with a view to pointing to one more potential application of the atom-atom potential scheme which has not yet been used. Simple ideas underlying this model not only permit prediction of molecular packing in crystals when experiment involves difficulties for some reasons; it may be hoped that the method will help to calculate the activation barriers which molecules have to overcome in order to approach each other at a distance necessary for forming a chemical bond. The calculation of dislocation energy is undoubtedly feasible.An attempt can be made to study diffusion of molecules in a solid. Such calculations may become particularly valuable owing to the fact that serious difficulties are often involved in the experimental study of solid-phase reactions. 4 Conformations of Molecules The first step in conformational analysis is the selection of independent para- meters that are responsible for the geometry of a molecule. If the researcher agrees with the present author and assumes the lengths of bonds to be constant, the parameters required for conformational analysis will be valence angles and angles of rotation about single bonds. For simple objects, it is possible to obtain the entire conformation picture, i.e. to have an idea of potential energy for any parameters.In more complex cases the study is limited to consideration of the cross-sections of a multidimensional energy surface. The information of interest to the chemist is the parameters of the minimum or minima (if there are several minima) on the energy map. He is also interested in the values of potential well depths. In a number of cases it is essential to know the barriers of transition from one conformation to another. The computer can always find the best transition path, i.e. can find the sequence of conformations associated with overcoming a minimum of obstacles. If a molecule has only one energy minimum, as is usually the case with over- crowded aromatic molecules, the calculation is quite simple. It is sufficient to choose arbitrary values of the molecular parameters, and the computer will give a correct solution.However, in complex situations, particularly when a molecule contains many single bonds, we can never be sure, basing our calculations on an arbitrary point, that the computer will give us the point of the deepest (or, as it is 70 1. C. Paul and D. Y.Curtin, 1975, 187, 19. 71 J. P. Desvergne and J. M. Thomas, J.C.S. Perkin ZZ, 1975, 584. Kitaigorodsky called, global) minimum. There is only one way out, namely to examine the entire energy surface. The search for a global minimum of a composite function is a mathematical problem that far oversteps the limits of a search for the minimum strain energy of a molecule. The interested reader is referred to books on non-linear programming.The study of the entire conformation map and estimation of the co-ordinates of all the minima have been carried out for representatives of most classes of organic substances. It is impossible to list these works, so the reader is referred to monographssJ0 and here the results of only one piece of work are presented.72 Figure 4 shows the paths of interconversion in cyclohexene. The author has Figure 4 Interconversion in cyclohexene [Reproduced from V. G. Dashevsky, ‘Konformatsii organicheskikh molekul’ (‘Con-formations of Organic Molecules’), Chimia, Moscow, 19741 calculated the path of isomerization. The angles of rotation about the C-3-C-4 and C-2-C-3 bonds are plotted along the rotation axes.The displacements of 72 V. G. Dashevsky and A. A. Lugovsky, J. Mol. Structure, 1972, 12, 39. Non-bonded Interactions of Atoms in Organic Crystals and Molecules the carbon atoms from the plane are shown in a scale at such an angle of view that the C-3 atom is located above the C-2 atom. It can be seen from the Figure that interconversion does not entail serious deformations of the ethylene system. The saddle point corresponds to a boat conformation with the energy of 5.4 cal mol-l, which is in agreement with experiment. The atom-atom potential method is finding wide application in studying conformations of biological molecules. The enormous number of independent parameters in these molecules makes it imperative either to introduce simpli- fications or to restrict the calculation to a more exact definition of the rough experiment.Let us dwell briefly on the problem of globular protein conformations. The spatial structures of about 50 proteins have been studied up to now using X-ray diffraction analysis techniques. Nevertheless, the accuracy with which the co-ordinates of the atoms have been estimated (with the resolution of 2-3 8, typical of such studies) is not very high. Therefore, if we take the distances, say, between carbon atoms linked by single bonds, then, according to the data of original studies, many of these distances prove to be less than 1 or 2 A; the values of various valence angles will not likewise be realistic. For this reason, a number of a~thors~3-~~ have raised the problem of specifying the co-ordinates of protein atoms with due account of the atom-atom potential functions.In this case the minimum potential energy is looked for along all the independent co- ordinates using a zero approximation which corresponds to an experimentally observed structure. (Sometimes, in order not to depart too far from the initial structure, deviations from this structure are added with certain weights to the potential energy as a ‘penalty’ function.) There is no doubt that in the near future the atom-atom potential method will be widely used at the final stage of inter- preting the three-dimensional structure of globular proteins. Of no less interest so it seems is the problem of predicting the spatial structure of a protein from its original structure (amino-acid sequence).Of course, this problem involves great computational difficulties, since the potential energy of even comparatively small proteins depends cln more than 100 variables, and the number of local minima is extremely large. Nevertheless, Le~itt~~ has recently managed to find some simplifying approximations which have finally made it possible to calculate the structure of the chymotrypsin inhibitor, which is a protein consisting of 58 residues. The results he obtained are in satisfactory agreement with experiment and give us every reason to hope that the problem of predicting the spatial structure of proteins will eventually be solved. Hundreds of 73 M. Levitt and S. Lifson, J.Mol. Biol., 1969, 46, 269. 74 P. K. Warme and H. A. Scheraga, Biochemistry, 1974, 13, 757. 75 J. Hermans, jun. and J. E. McQueen, jun., Acra Cryst., 1974, A30, 730. B. R. Gelin and M. Karplus, Proc. Nat. Acad. Sci. U.S.A., 1975, 72, 2002. 77 M. Levitt, J. Mol. Biol., 1976, 104, 59. Kitaigorodsky studies are devoted to polypeptide conformations.78-87 The importance of these works for the protein problem is self-evident. The atom-atom potential method is also extensively used for handling other problems of molecular biology. Thus, the authors of references 88-90 studied the relationship between the activity and conformations of certain biological molecules. Several groups of researchers are engaged in studying conformat ions of nucleic a~ids.91-~~ Most conformational calculations are conducted for ‘free’ molecules, in other words without taking into consideration the effect of the medium.The present author has often emphasized that the crystal field does not affect the lengths of bonds in any way and alters but insignificantly the values of valence angles. This should be particularly stressed, because frequently the theoretical chemist who wishes the experiment to confirm his complicated reasoning as to n-~and 7r-u conjugations but cannot find a required fit with the data of X-ray diffraction analysis of crystals shifts the blame for this annoying circumstance on to the physicist who determined the molecular structure of a crystal, while his own argument pertains to a free molecule.However, both experiments and theoretical calculations positively deny such conclusions. That a crystal field does not affect the lengths of molecular bonds can be demonstrated in many different ways.8 It is possible to compare the lengths of bonds which are surely equivalent from the chemist’s point of view but are not equivalent in a crystal on account of the symmetry of a position taken by a molecule. The list of such examples is enormous. As a rule, molecules with three planes of mirror symmetry (naphthalene-type molecules) assume a position with an inversion centre in a crystal. If the crystal field affected bond length in any significant way, the distances between, for example, C-1 and C-2,would have to differ from the C-3-C-4 distance.However, K. Nishikawa, F. A. Momany, and H. A. Scheraga, Macromolecules, 1974, 7,797. 79 A. S. Kolaskar, S. Viswanathan, S. Kasturiranga, Theor. Chim. Acta, 1975, 38, 109. G. M. Crippen, F. Hajdu, and T. Radnai, J. Comput. Phys., 1975, 18, 224. C. M. Venkatachalam, 9. J. Price, and S. Krimm, Biopolymers, 1975, 14, 1121. 82 P. E. Grebow and T. M. Hooker, jun., Biopolymers, 1974, 13, 2349. 83 N. Go and H. A. Scheraga, Macromolecules, 1973, 6, 525. 84 H. A. Scheraga, Pure Appl. Chem., 1973, 36, 1. 85 A. W. Burgess and H. A. Scheraga, Biopolymers, 1973, 12, 2177. 86 G. M. Lipkind, S. F. Arkhipova, and E. M. Popov, Internat. J. Peptide Protein Res., 1973, 5, 381. 87 M. A. Kreissier, G. M. Kipkind, S. F. Arkhipova, and E. M.Popov, J. Chim. phys., 1973, 70, 1371. 88 H. J. R. Weintraub and A. J. Hopfinger, J. Theor. Biol., 1973, 41, 53. 9.S. Zhorov, E. V. Rosengart, V. A. Govyrin, N. V. Chromov-Borisov, and N. B. Brovtsyna, Doklady Akad. Nauk S.S.S.R., 1976, 231, 215. B. S. Zhorov, E. V. Rosengart, and V. A. Govyrin, Doklady Akad. Nauk, S.S.S.R.,1976, 228, 1460. 91 V. E. Khutorsky and V. I. Poltev, Biofizika, 1976, 21, 201 92 W. K. Olson, Biopolymers, 1976, 15, 859. 93 F. G. Calascibetta, M. Dentini, P. De Santis, and S. Morosetti, Biopolymers, 1975, 14, 1667. 9A V. I. Poltev and V. I. Bruskov, Mol. Biof., 1977, 11 (in Press). 95 S. D. Stellman. S. B. Broyde, and R. M. Wartell, Biopolymers, 1976, 15, 1951. 96 N. Yathindra and M. Sundarlingam, Biopolymers, 1974, 13, 2061.Non-bonded Interactions oj’Atoms in Organic Crystals and Molecules in all thorough studies chemically identical bonds appear to be equal in length despite the fact that they are located in different crystal fields. Equally convincing evidence is provided by the comparison of bond lengths and valence angles of two identical molecules which are not equivalent crystallographically (e.g. the crystals of tolane, stilbene, acenapthene, etc.). A very precise calculation of the effect of the crystal field on the geometry of sulphur molecules using the atom- atom potential method has been made.97 The author has found the distortion energy of a molecule to have the negligible value of 0.084 kcal mol-1. The geometry of an isolated molecule and that of a molecule in a crystal agree within experimental error.Does this mean that the effect of a crystal field on the conformation of a molecule is never manifested? The answer is no. If rotation about single bonds is possible, it often involves insignificant use of energy and is affected by the crys tal-field forces. In such cases of energy-minimization studies, it is necessary to take into account the parameters of molecular packing and internal rotation parameters. A number of studies have been carried out to this effect (the first work of this kind was on bibenzyl98); several works referred to ab~ve~s-~~ are also devoted to the same problem. The minimum of an energy surface yields both packing parameters and the value of an internal rotation angle, which may be signifi- cantly different (in the case of sloping rotation barriers) from the value for the optimal conformation of an isolated molecule.One of the most recent studies99 deals with the polymorphic transformation of p-terphenyl which takes place at 110 K. At this temperature the molecules cease to be planar. As in many other cases, the calculations with the aid of the atom- atom potential method provide an excellent agreement with the data of X-ray diffraction analysis. Molecules in a solution also alter their conformation only owing to a change in the internal rotation angles. However, here it is much more difficult to take into consideration the effect of the medium. Since the effect of water is of tre- mendous importance for the structure of biological molecules, a series of studies has been conducted in which an attempt was made to allow for the effect of a solvent within the framework of the atom-atom potential model. Thus, in references 100-103 the potential function includes components with the help of which we try to take into account the tendency of non-polar groups to contact one another (hydrophobic interactions).~3’ I. Kurittu and G. S. Pawley, Acta Cryst., 1973, A29, 615. s* V. Bereznitzkaya et al., Zhur. f;z. Khim., 1972, 16, 2492. S. Ramdas and J. Thomas, ‘On the Interpretation of Rotational Disorder in Crystalline para-Terphenyl’ (Preprint). looV. G. Dashevsky and G. N. Sarkisov, Mol. Phys., 1974, 27, 1270. Io1 A. J.Hopfinger, ‘Conformational Properties of Macromolecules’, Academic Press, New York, 1973. lo2 M. J. Huron and P. Claverie, J. Phys. Chem., 1974, 78, 1862. lo3C. Chothia, J. Mol. Biol., 1976, 105, 1. Kitaigorodsky 5 Properties of Organic Crystals The ability to calculate intermolecular interactions provides the researcher with a tool which can be used for handling various problems in the fields of molecular crystal physics and physical chemistry. It is but natural that the lion’s share of calculations using the atom-atom potential method relate to prediction of molecular conformations and packing of molecules in a crystal. However, the high validity of the atom-atom potential scheme has been demonstrated for a much larger number of applications in other areas.Physicists were naturally interested in the possibility of calculating the dynamics of a lattice built from molecules. Rigid molecules perform translational motion (the centre of gravity of the molecules shifts linearly) and librational motion (they swing with a small amplitude about the three axes). The frequencies of these vibrations can be found experimentally. The prediction of the values of these frequencies and their temperature dependence has become possible only after the development of the atom-atom potential method. The well-known formulae for determining vibration frequencies will not be given here; instead, the reader is referred to the monograph8 and to published data. Suffice it to mention that vibration frequencies can be calculated if we know the second derivative of potential energy for the shift of the molecule from the equilibrium position.Similar calculations have been made for a rather extensive number of aromatic crystals. One of the latest studieslo4 presents very accurate data on the vibrations of a sulphur lattice. The authors have calculated not only vibration frequencies, which are compared with Raman spectra, but also neutron scattering intensities that are known to depend on the lattice vibrations as well. Agreement with experiment was found to be quite satisfactory. It should be emphasized that the interaction potential of non-bonded sulphur atoms was taken from entirely independent calculations pertaining to a crystal structure.Calculations of this kind employ a so-called quasi-harmonic crystal model. This means that vibrations are assumed to be harmonic at any temperature, and the temperature dependence of the frequencies is due to thermal expansion which causes changes in spacings between the molecules and, hence, interaction forces. Knowing the vibrational spectrum of the lattice, one can evaluate the thermo- dynamic functions of a crystal. Such calculations have been described,* but they are either cumbersome or approximate, since thermodynamic quantities are expressed in terms of a so-called characteristic temperature of a crystal. Recent data on the calculations of characteristic temperatures are to be found in reference 105. Another approach to the evaluation of thermodynamic functions of crystals is based on a so-called cell model.This approach suggested by Lennard-Jones and DevonshirelOG employs the following three basic assumptions : lo4R. P. Rinaldi and G. S. Pawley, J. Phys. (C), 1975, 8, 599. lo6 E. Muchtarov et al., Fiz. tverd. Tela, 1975, 17, 2803. lo8J. E. Lennard-Jones and A. F. Devonshire, Proc. Roy. Soc., 1937, A163,53; 1938, A165, 1 Non-bonded Interactions of Atoms it1 Orgatiic Crystals atid Molecules (a) the volume of a system consisting of N molecules may be divided into N identical cells, each being able to contain only one molecule; (b) cells may be selected so that their centres form a regular lattice; (c) the motion of a molecule in a cell is independent of the motion of molecules in adjacent cells.The cell model was primarily intended for calculating the properties of simple liquids but it is also applicable to crystalline solids, and with much greater success at that, because assumptions (a)and (6) are considerably more appropriate for a crystal than for liquids. Comparison of the cell model with the quasi-harmonic approximation shows that the cell model does not make an assumption that interaction forces between particles are harmonic and employs instead the assumption of the independent motion of individual particles. In this respect the cell model is analogous to the Einstein model of a crystal; however, in contrast to the latter, the cell model takes account of the anharmonicity of ~ibratioils.~"~ It follows from rather general considerations that the quasi-harmonic approxi- mation must represent a more adequate crystal model at low temperatures, whereas the cell model is more adequate at high temperatures.Indeed, at low temperatures low frequencies make the basic contribution to the free energy of a crystal. The motion of molecules associated with low-frequency vibrations is the motion when molecules move almost in phase through rather long distances. Obviously, an adequate description of such motion must take into consideration all correlations of shifts of individual molecules. The harmonic oscillator model is able to take these correlations into account sufficiently rigorously. On the other hand, high frequencies make a major contribution in free energy at high temperatures.The motion of molecules described by high-frequency vibrations can be approximately taken as independent. Therefore, assumption (c) for the cell model is quite suitable here. In addition, the cell model more com- pletely allows for anharmonicity of the vibrations, which becomes significant precisely in a high-temperature region. The comparison of the quasi-harmonic approximation and the cell model with the results of computer experiment for the most elementary molecular crystals shows that the cell model is more adequate for simulating crystal thermodynamics at temperatures above & 1 / 2 . 1 ~ ~ p ~ ~ ~ The equations for calculating thermodynamic functions within the framework of the cell model can be obtained as follows.Let us denote the configuration part of the Gibbs distribution function as follows: P = P(41, ---7 qN) lo7 J. A. Barker, 'Lattice Theories of the Liquid State', Pergamon Press, 1963. lo8T. G. Gibbons and M. 1. Klein, J. Chem. Phys., 1974, 60, 112. looA.C. Holt, W. G. Hoover, S. G. Gray, and D. R. Shortle, Physica, 1970, 49, 61. Kitaigorodsky where is a configuration integral and U(q1,. . .,q,v) is the potential energy of the system. The assumption as to the independence of motion of individual molecules implies that P can be written as a product of single-particle distribution functions: N P = np(4di=l The best representation of P in this form can be obtained by minimizing the free- energy function expressed through p(q1).This procedure was used by Kirkwood.ilo As a result, self-consistency equations were obtained for p(q1) which, after certain modification, can be written as where $(qt) is a certain effective potential, in whose field the ith molecule is moving, U(qi,qj) is the interaction energy of the i and j molecules, and Ai is the volume of a cell which restricts the motion of the ith molecule.The self-consistency equation can be solved by the iteration method. Assum- ing as a zero approximation that p'0"qi) = 8(qi -4i) where Si are the average co-ordinates of the ith molecule, the first approximation for $(qi) will be +Vqd = c U(qi,&) 3 U(qd ifi In other words, in a first approximation which is essentially what we call a cell model, the potential $(qi) is the potential interaction energy of the ith molecule with the surrounding molecules which are assumed to be fixed at their average positions.The configuration integral of the system in the cell model has the form where U0/2 = U(4)/2 is the lattice energy and 110 I. G. Kirkwood, J. Chem. PhJIs., 1950, 18, 380. Non-bondedInteractions of Atoms in Organic Crystals and Molecules is the so-called ‘free volume’. Furthermore, it is easy to obtain expressions for all the thermodynamic functions (see, for example, ref. 111). Thus, the internal energy for molecules with three rotational and three translational degrees of freedom is calculated from the formula E = (U) -~UO+ $kT where the brackets ( ) designate averaging over the states of a molecule moving in the field U(q),i.e.In the cell model, calculation of the thermodynamic functions of a crystal amounts to calculation of six-dimensional integrals. It is convenient to use the ‘importance sampling’ method112 for evaluating these integrals. Let us denote the integrand as f(q). Let g(q) be some positively defined function normalized in d to unity. If q(l),. . ., q(n)are random points distributed ind with probability density g(q), it is easy to show that the quantity n i= 1 converges in probability to the unknown integral: P en+ J f(q>dq It can also be shown that a probable error of this estimate is minimum when density g(q) is proportional to lf(q)I .l13 Therefore, for the best convergence the function g(q)must be selected so as to reproduce as well as possible the behaviour of [f(q)lin the integration range.In references 111 and 114 a Gaussian distribution was used as g(q): with the variances a, selected by the least-squares method from the condition of the best fitting of the potential surface [u(q)-u(q‘)]/kTby the diagonal quadratic 6 form C (4, -i,)2/2aa2. This selection of g(q) proved to be highly effective. a= 1 ll1 A. J. Pertsin, V. V. Nauchitel, and A. I. Kitaigorodsky, Mol. Crystals, Liquid Crystals, 1975, 31, 205. Ila M. Weissmann and L. Blum, Trans. Faraday SOC.,1968, 64, 2605. 113 N. M. Sobol’, ‘Monte-Car10 Numerical Methods’ (in Russian), Nauka, Moscow, 1973. Kitaigorodsky Thus, already at II = lo3 the probable error in calculating free and internal energy did not exceed several hundredths of kcal mol-l, and that of entropy and heat capacity 0.2-0.3 cal K-1 mol-1.The above technique has been ~sed~~~Jl4 for evaluating the thermodynamic functions of benzene, naphthalene, and anthra- cene crystals, the results exhibiting very good agreement with experiment. The cell model can be successfully employed for calculating plastic phase transitions. Consider now the case when a molecule in a crystal may assume either of the two preferable states, say, 41and 42. Then the zero approximation to the solution of the self-consistency equations can be written as: where Wi is the probability that molecule i is in the state cjil. In this case the final form of expressions for thermodynamic functions remains unchanged with the exception that when estimating the average field potential #(q) = U(q)each of the surrounding molecules must be 'averaged' with discrete probabilities Wi and (1 -Wi), The evaluation of probabilities Wi is the problem of evaluation of the function of molecule distribution over the discrete states Gil and Gi2 and can be solved within the framework of the Ising m0de1.l~~ Using this approach we not only can describe the order-disorder transition, but also allow for changes in the vibrational motion of the molecules associated with this transition.The necessity to take these changes into account is obvious. Thus, for adamantane which has two preferred states, a change in entropy due to disordering is R In 2 = 1.38 cal K-' mol-1, whereas the experimentally derived value of the entropy change is 3.87 cal K-1 mol-l.In other words, almost 2/3 of the total change in the entropy is accounted for by the change in the vibrational motion of the molecules. A somewhat simplified evaluation of the phase-transition parameters in adamantane has been performed.'l6 An assumption was made that the low- temperature phase is completely ordered (Wi = 1) and the high-temperature phase completely disordered (Wi = i).The use of this model for the order- disorder transition makes redundant a direct solution of the king problem. Instead, both phases can be considered separately so that after evaluation of the thermodynamic functions in each phase the phase-transition point could be localized by intersection of the free-energy curves.The results of such a calcula- tion116 have shown quite satisfactory agreement with experiment. 11' A. J. Pertsin and A. I. Kitaigorodsky, Kristallografya, 1976, 21, 587. 116 P. A. Reynolds, Mol. Phys., 1975, 30, 1 165. 116 A. J. Pertsin and A. I. Kitaigorodsky, Mol. Phys., 1976, 32, 1781. 161 Non-bonded Interactions of Atoms in Organic Crystals and Molecules 6 Adsorption The study of non-valence interactions in adsorption presents considerable interest. On the one hand, this phenomenon is of great practical value and, on the other, the study of adsorption helps specify the configurations of the potential curves.This latter consideration seems to explain why the use of the atom-atom poten-tial scheme for estimating the temperature dependence of the Henry constants started from the investigation of hydrocarbon adsorption on graphite. In this case interaction is determined by only two interactions, C-C and C-H, rather than by three as is the case with evaluation of conformations for hydrocarbon packing patterns. For molecules that are composed of a rigid skeleton with one or more sym- metrical spinners attached to it (for example, ethane, propane, toluene, or xylene molecules and many others) the following expression for the Henry constant K1 in classical approximation is valid: jjj exp (-W/kT)[exp (-#/kT) -I] sin ydT dB dx Ki = 8n2A exp (-W/kT)da where W is the potential energy of an isolated molecule which depends only on spinner internal rotation angles a, # is the potential energy of a molecule-solid interaction which depends on the position of the molecule mass centre 7 and the Eulerian angles 8 (y is one of these angles) responsible for spatial orientation of the rigid skeleton of the molecule.A gas composed of molecules which form rotational isomers when rotating internally (for instance, n-alkane molecules, starting with n-butane) can be roughly considered as a mixture of the rotational isomers of the molecule which are in mutual equilibrium, while the rotational isomers themselves can be treated as quasi-rigid. In this approximation, the Henry constant for adsorption of such molecules will be rn Kl = 2Xi& i= 1 where Ki is the Henry constant for adsorption of the ith rotational isomer, and Xi is the mole fraction of this isomer in the equilibrium gas volume.The Henry constant for adsorption of a three-dimensional quasi-rigid molecule is given by the following expression: K1 = (1/8n2A) Jj [exp (-$/T) -11 sin y d7 do The interactions have been studied117 of a series of alkanes, cycloalkanes, and unsaturated and aromatic hydrocarbons with graphite. Let us consider only one example from the extensive work devoted to aromatic hydrocarbons (Figure 5). To obtain an ideal agreement with experiment, the author used somewhat different C-C curves for aliphatic and aromatic hydrocarbons. 11’ N. N.Avgul’, A. V. Kiselev, and D. P. Poshkus, ‘The Adsorption of Gases and Vapours on Homogeneous Surfaces’ (in Russian), Khimia, Moscow, 1975. 162 Kitaigorodsky -Anthracene / Phenan threnc P8-P Naphthalenc 9 4-0-2 3 4 lo3 T-]/K-Figure 5 Temperature dependence of Henry constants for organic compounds (Reproduced from D. P. Poshkus, Dissertation, Moscow State University, 1972) The present author would emphasize that this striving for an ‘ideal’ hardly seems justified. The dashed line in the Figure shows the straight line that would be obtained by the author if he used the curves that would be ‘ideal’ for alkanes in his experiments. Is it worthwhile to sacrifice the value of the theory and increase the number of parameters? If the author had used the universal C-C potential, theory and experiment would have differed by not more than several per cent. The present author would certainly have liked it better, but, as the saying goes, tastes differ. In conclusion the author would point out the following. First, studies carried out using quantum mechanical techniques have deliberately been omitted. They are not yet able to solve all problems that quite easily fit the scheme of pair additive interactions of atoms. Secondly, the reader should bear in mind that the present article has by no means listed all the problems which can be and are being solved using the atom-atom potential method. The author’s intention has been to outline the possibilities of a very simple and very descriptive model for handling many and various problems in the chemistry and physics of organic molecules and organic solids.

ISSN:0306-0012    

DOI:10.1039/CS9780700133

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Corrigenda Vol6 No 4 1977 “Properties and Syntheses of Sweetening Agents” by B. Crammer and R. Ikan. Page 443. Ref. 11 should read H. Mark, J. McKetta, and D. Othmer, Encyclo-pedia of Chem. Technol., 1969, 19, 594. Page 435. Ref. 18. For M. Bridal and R. Lavielles, read M. Bride1 and R. Lavielle. Page 436. Subunit A. For Asx read Asp. Page 438. Ref. 30. For U.S.P. 3,952,144/1976 read U.S.P. 3,952,114/1976. Ref. 31. For No. 34, 27. read No. 3, p. 27. Page 439. Reagent v. For BuizAcH read Bui2AlH. Page 440. Reagent i. For KAc read KOAc. Ref. 38. For Repn. read Prepn. Page 441. For /3-neohesperidin dihydrochalcone (23) read ,8-neohesperidin dihydrochalcone (22a). Page 443. Table 3. The heading “Benzaldehyde substitute” should not appear. Far Neohesperidin dihydrochalcone (22a) readp-Neohesperidin dihydrochalcone (22a). Pages 444 and 445.For R. M. Horowitz, Personal communication, 1973 read R.M. Horowitz, Personal communication to G. A. Crosby, 1973. Ref. 54. For 1974 read 1973. Page 446. Line 4. For base read acid. Page 447. Reagent vi. For Me2NS03 read Me3NS03. Ref. 68. For Goldberg read Golberg. andfor Corrigenda Page 449. Table 6. For n= 2readn = 3 n=3 n=4 n=4 n=5 n=5 n=6 Table 6. For Ref. 70 read Ref, 72. Page 450. Scheme 8. For kMn04 read KMn04. Page 454. Scheme 9. For MeCOCH2COCOCMe3 read MeCOCH2C02CMe3. For v,*~read vLS6 Scheme 10. For CH, CH, 0FOH3read NHS0,R NHS0,R Page 456. Scheme 12. For read CH,CO,CH,‘0 Page 460. Scheme 15. For CHC//” CH,-C\ read IHCHC >O CF,CON CF,CONHCH-C\\0 Corrigenda Page 462. Scheme 18. Reagent iii. For OH-read L~OH-O-C~H~(NH~)~,~HCI. Page 463. First line. For Thiazolo[3,2-61-a-Triazoles read Thiazolo[3,2-6]-s Triazoles. Page 464. Structure 34. For 2TzH 2T'HsCH read GCH HN HN CH 3 CH, Reagent iii, For read 07-C_HpO_dine-Piperidine ~~~~~~ri.ine-~i~eridine H H Page 465. For 565 read 465.

ISSN:0306-0012    

DOI:10.1039/CS9780700164

出版商:RSC    

年代:1978

数据来源: RSC