摘要:

Chemical Society Reviews Vol 2 No 3 1973 Page Chemical Aspects of Wty Chromatography By H. Guilford 249 Organo-transition-metal Complexes :Stability, Reactivity and Orbital Correlations By P.S.Braterman and R. J. Cross 271 The Energetics of Neighbowing Group Participation By M. I. Page 295 Quasielastic Laser Light Scattering By A. M. Jamieson and A. R. Maret 325 The Chemical Society London Chemical Society Reviews Chemical Society Reviews appears quarterly and comprises approximately 25 articles (ca. 600 pp) per mum. 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 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 bc submitted to The Editor, Reports and Reviews Section, The Chemical Society, Burlington House, Piccadilly, London, W1V OBN. Members of The Chemical Society may subscribe to Chemical Society Reviews at €2.00 per annum;they should place their orders on their Annual Subscription renewal forms in the usual way. Non-members may order Chemical Society Reviews (€8.00 per mum; remittance with order) from: The Publications Sales Officer, The Chemical Society, Blackhorse Road, Letchworth, Herts., SG6 lHN, England. 8 Copyright reserved by The Chemical Society 1973 Published by The Chemical Society, Burlington House, London, WIV OBN Printed in England by Eyre & Spottiswoode Ltd, Thanet Press, Margate

ISSN:0306-0012    

DOI:10.1039/CS97302FP007

出版商:RSC    

年代:1973

数据来源: RSC

ISSN:0306-0012    

DOI:10.1039/CS97302FX009

出版商:RSC    

年代:1973

数据来源: RSC

ISSN:0306-0012    

DOI:10.1039/CS97302BX011

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Chemical Aspects of Atsnity Chromatography By H. Guilford THE RADIOCHEMICAL CENTRE, AMERSHAM, BUCKS. 1 Introduction The use of biospecific adsorbents in biochemical purification has rapidly become widely accepted since the term ‘affinity chromatography’ was first coined by Anfinsen and co-workers in 1968.l This technique constitutes a conceptual departure from traditional methods, which generally depend on a particular physicochemical parameter such as size or charge, in utilizing the specific interaction between the macromolecule of interest and its substrate, cofactor, allosteric effectors, or inhibitors. In principle, a ligand is attached covalently to a water-insoluble matrix to form a tailor-made chromatographic material suited to adsorb from a mixture just those components having an affinity for the ligand.All other ‘non-complementary’ constituents pass through the adsorbent unre- strained, leaving the adsorbed molecules to be eluted after some appropriate change in conditions. The method thus closely parallels the use of insolubilized antigens as immunosorbents for the purification of antibodies.a Biospecific adsorbents have been used to purify a variety of substances, viz. enzymes; binding, transport, and repressor proteins; peptide substrates, antigens, and fragments from proteolytic degradation of affinity-labelled proteins ;glyco-proteins and carbohydrates; nucleic acids; intact cells and polysomes; and viruses. Appropriate insoluble ligands can prime the synthesis of specific nucleic acids, function as cofactors, hormones, or effectors, or be used as molecular probes for mechanistic studies.Affinity chromatography has advantages over conventional separation techniques apart from its specificity. As a consequence of the tiny proportion of total protein adsorbed from a crude mixture, a relatively small amount of adsorbent is required. The adsorbed material is rapidly separated from proteolytic enzymes and may be stabilized by ligand binding at the ‘active’ site. The adsorbent can usually be regenerated many times. Affinity chromato- graphy has been reviewed by several authors,8 with much duplication and restatement of data and opinions. All emphasize the biological aspects, chemical considerations being subsidiary and fragmented. In this review an attempt is made to highlight the chemical aspects of affinity chromatography, to note * P.Cuatrecasas, M. Wilchek, and C. B. Anfinsen, Proc. Nut. Acad. Sci. USA., 1968, 61, 636. 2 I. H. Silman and E. Katchalski, Ann. Rev. Biochem., 1966,35, 873. 3 A useful selection includes (a) P. Cuatrecasas in ‘Biochemical Aspects of Reactions on Solid Supports’, ed. G. R. Stark, Academic Press, New York and London, 1971, p. 79; (6)P. Cuatrecasas and C. B. Anfinsen in ‘Methods in Enzymology’, ed. S. P. Colowick and N.0.Kaplan, Academic Press, New York and London, 1971, vol. 22, p. 345; (c) R. H. Reioer and A. Wakh, Chromatographia, 1971,4578. Chemical Aspects of Afinity Chromatography recent important advances,' and to focus attention on a fieId of great biological and medical interest in which the talents of the chemist are much in demand.2 Designing the System A. General Considerations.-The requirements of a suitable system for affinity chromatography are dictated by the moiety to be purified, the coupling of ligand to matrix, and the working milieu. Enzyme purification imposes rigorous restraints on the choice of bioadsorbent, which must be stable both to the enzyme and to conditions under which the protein is not denatured. Limitations on extreme conditions become significant when the separated material is eluted; very strong adsorption is not always an unqualified advantage. The very 'lock- and-key' specificity that is the cornerstone of the technique requires that no great modification of the ligand occurs either during attachment to the support or under the experimental conditions.Not only must the key be correctly cut, it must be of suitable length such that the binding determinants of the ligand are accessible to the lock, e.g. the active site of an enzyme. For many research purposes details of molecular parameters may be vital: knowledge and repro- ducibility of coupling modes, matrix characteristics, and ligand-matrix-medium interactions then assume paramount importance. For large-scale production in particular, mechanical stability, rapid flow-rate, resistance to microbial attack, and re-use are important factors. B. Choice of Matrix.-For many years immunosorbents have been prepared by coupling antigens to cellulose or polystyrene derivatives.The requirements of these adsorbents are, however, not very stringent because of the large number of antigenic determinants, often readily accessible owing to the size of many of the coupled proteins, and the high avidity of antibodies for antigens (dissociation constants are commonly lower than lo-' mol I-l). The greater rigour of affinity chromatography has necessitated optimization of conditions, including finding more suitable carriers. In addition to the criteria cited above, the matrix must be capable of mild chemical modification without undergoing gross structural changes (particularly shrinkage), be free of ionic residues which would cause non-specific interactions with proteins, have a loose Iattice structure of sufficient porosity to allow macromolecules unimpeded access to bound ligands, and be hydrophilic enough to permit interaction between the two phases.Beaded agarose, polyacrylamide, and glass appr.:ach this ideal, can be used with certain non-aqueous solvents, and, having the additional virtue of commercial avail- ability, are now used almost exclusively. Cellulose has been superseded but is important historically for its use in the pioneering studies of McCormick6 and Lerman, who purified tyrosinase with the first biospecific adsorbent, diazotized For a comprehensive review of earlier studies see N. Weliky and H. H. Weetall, Imrnuno-chemistry, 1965, 2, 293.* (a)D. B. McCormick, Analyt. Biochem,, 196513,194; (6)C.Arsenis and D. B. McCormick, J. Biol. Chem., 1964, 239, 3093. Guilford aminophenol coupled through resorcinol to a cellulose carrier." Cellulose offers little advantage over agarose, and its fibrous, heterogeneous nature results in low porosity and poor flow-rate. Cellulose also often bears a significant proportion of carboxy-residues. Polystyrene and similar polymers are unsuitable not only because they are highly lipophilic, but because they strongly and non-specifically adsorb many proteins. Occasionally an unmodified matrix is useful as a biospecific adsorbent. Dextran cross-linked with epichlorohydrin (Sephadexa) has been used to purify several saccharide-binding proteins, e.g. anti-A agglutinin from Helix pomatia' and a fructosan-specific precipitating protein from nurse shark serum.* This polymer, however, is insufficiently porous to find much application in affinity chromatography. C. Choice of Ligand.-The ligand must interact specifically and reversibly with the molecule to be purified. If this be an enzyme, a substrate analogue, inhibitor, or cofactor should serve. Binding proteins have been purified on immobilized substrates, antigens and other substrates on immobilized antibodies and binding proteins, and nucleic acids on immobilized complementary oligonucleotides. Interactions involving dissociation constants of greater than mol I-' are likely to be too weak. The ligand must be suitable for coupling to a matrix with the minimum of modification to that part of its structure essential for binding. It will often be necessary to space the ligand from its support.This may be achieved either by coupling the ligand to one end of an 'arm', the other end of which is subsequently attached to the carrier, or by coupling it to an arm already modifying the matrix. This precaution will be superfluous if the ligand is bulky enough to make its binding site@) available, e.g. if it is a protein, polynucleotide, or other large molecule. Thyroxine coupled directly to agarose through its a-amino-group is effective in extracting thyroxine-binding globulin from serum9 because binding involves the di-iodophenol ring more remote from the point of attachment. Spacing of ligand from matrix is likely to be particularly important for purification of large proteins such as /l-galactosidaselo (mol.Nwt. 4 x 135000). D. Coupling of Ligand to Matrix.-(i) Nature of Coupfing.Almost all affinity chromatography systems involve a covalent bond between ligand and matrix. Ionic bonds or physical adsorption are prone to leakage or displacement of the Jigand from its carrier. (ii) Stability. It must be ensured that the ligand-carrier complex is stable to the experimental conditions, otherwise there may be elution of ligand during 1.S. Lerman, Proc. Nar. Acad. Sci. U.S.A., 1953, 39, 232. I. Ishiyama and G. Uhlenbruck, Z. Immun.-Forsch., 1972, 143, 147. V. Harisdangkul, E. A. Kabat, R. J. McDonough, and M. M. Sigel, J. fmmunol., 1972,108, 1244. J. Pensky and J.S. Marshall, Arch. Biochem. Biophys., 1969, 135, 304. lo M. R. Villarejo and 1. Zabin, Nature New Biol., 1973, 242, 50, and refs. therein. 2Sl Chemical Aspects of Afinity Chromatography chromatography. If this occurs to a sufficient degree, all the material of interest could elute complexed to free ligand. This may lead to completely erroneous conclusions, especially if fractions are assayed by substrate binding capacity.ll Proteins present in very low concentration are particularly susceptible to this hazard. Ligand-carrier complexes which have not been adequately processed after the coupling reaction are open to similar criticisms. Before use, the bioadsorbent must be extensively washed in several cycles with buffers of as wide a range of pH and as high an ionic strength as the stability of the covalent bonds will allow.Detergents are sometimes also advisable. All matrices have some non- specific binding properties, particularly after activation procedures and introduc- tion of ‘spacers’. Adequate washing of gels is therefore essential to remove non- covalently bound ligand. There are many reports of investigations where these precautions are conspicuous by their absence and therefore conclusions based on such work must be regarded with some scepticism (cf. Section 3Aiv). (iii) Amount of Ligand Coupled to Carrier. Some estimate of the success of a coupling reaction comes from measuring the amount of ligand not attached but, for a more precise determination of coupling yield, a direct assay is desirable.In favourable cases the ligand can be chemically removed intact from its support, e.g. by hydrolysis from glass or by dithionite reduction if a diazo-linkage is involved. Solubilizing a complete ligand-agarose, -dextran or -cellulose system, either by acidic or enzymic digestion, allows direct optical density measurement or amino-acid analysis (for peptide ligands). Electronic spectra of the intact complex can be measured by suspending the gel in a viscous medium such as 0.5 % polyethylene oxide. Attaching an isotopically labelled ligand allows a very accurate assay of coupling yield. The amount of ligand on the carrier represents the maximum theoretical bind- ing capability and should not be equated with the capacity as a bioadsorbent.In practice, only a fraction of the molecules coupled may be accessible for binding, since the matrix may have non-ideal porosity. Also, once a macromolecule is adsorbed, it may mask adjacent ligands. Therefore, although raising the ligand concentration on a matrix improves most bioadsorbents up to a point, there is usually a limit above which the capacity no longer increases and may begin to fall again.l2 3 Chemistry of the Matrix Much of the chemistry involved in fixing ligands to matrices has not been developed specifically for the purpose but is an adaptation of conventional methods to the biphasic nature of ligand-carrier coupling. Many procedures used for preparing immunosorbents and insoluble enzymes, however, are unsuitable for affinity chromatography because matrices such as carboxymethyl-, amino- (a) J.H. Ludens, J. R. DeVries, and D. D. Fanestil,J. Biol. Chem., 1972,247,7533; (b) G. I. Tesser, H.-U. Fisch, and R. Schwyzer, F.E.B.S. Letters, 1972, 23, 56.** N. Kalderon, I. Silrnan, S. Blumberg, and Y. Dudai, Biochim. Biophys. Acra, 1970. 207, 560. Gullford ethyl-, phospho-, or p-aminobenzyl-cellulose or p-aminostyrene carry a residue of ionizable groups even after coupling. Agarose, polyacrylamide, and glass are carriers of choice partly because of their minimal, non-specific interaction with proteins. The chemistry of assembly of a biospecific adsorbent should preserve this character insofar as is possible. Three variations on the theme of assembly must be considered: (a) direct linkage of ligand to carrier; (6) extension of a ligand by an ‘arm’ which is subsequently attached to the matrix; and (c) derivatization of the carrier with a spacer, the free end of which has a functionality suitable for attaching the ligand.Clearly, a system may be designed so that the functional group to be coupled to the matrix is the same for almost all cases covered in (b) and (c) and some of those in (a). Thus, for any given matrix, one coupling procedure could be generally applicable. A. Po1ysaccharides.-A general and by far the most widely employed method for linking ligands to agarose, dextran, or cellulose involves (a)activation of the carrier and (b)coupling of primary aliphatic or aromatic amines to the activated matrix.(i) Cyanogen Halide Activation. Activating polysaccharides with cyanogen bromide* at high pH was developed by Axh and co-workersls for coupling peptides and proteins specifically through their amino-groups, particularly to Sephadex, the polymer used in most definitive studies. However, comparisons with other polysaccharides have shown the method and its chemistry to be quite general. At pH 11, the optimum, activation is complete in a few minutes,? and the degree of activation increases with the amount of cyanogen bromide. Up to 6% nitrogen and a trace of bromine are incorporated into the active polymer. Scheme 1 (‘Activation step’) shows the probable course of events.14 The initial (and least well-defined) step is the formation of labile cyanate which can interact with an adjacent hydroxyl to form (in the case of Sephadex) either a trans-fused five-membered cyclic imidocarbonate or a cross-linked imidocarbonate involving an adjacent dextran chain.Cross-linking is apparent from the decrease in swelling capacity of the gel which accompanies activation.12 The cyanate can also be hydrolysed to an inactive carbamate ; prolonged, mild alkaline hydrolysis converts activated Sephadex into the completely inactive carbamylated polymer. It is therefore important to conduct the activation for the short time prescribed. After mild acid hydrolysis, which liberates ‘labile’ (i.e. imidocarbonate) nitrogen as ammonium ion, five-membered cyclic carbonates can be detected as well as carbamate. Liberation of ammonia parallels loss of most of the coupling capacity Cyanogen iodide behaves very similarly except that activation takes longer.t This is the pH of the bulk medium. The pH at the interface remains to be studied. laR. Axen, J. Porath, and S. Emback, Nature, 1967,214, 1302. I4 (a)R. Axtn and S. Ernback, European J. Biochem., 1971, 18, 351; (b) R. Axtn and P. Vretblad in ‘Protides of the Biological Fluids’, Proceedings of the 18th Colloquium, Bruges, 1970, ed. H. Peeters, p. 383; (c) R. Axen and P. Vretblad, Acra Chem. Scund., 1971,25,2711. Chemicul Aspecrs of Afinir y Chromatography Carbamate (inert) Activation step $-: lmidocarbonate (reactive) cyanate structure 'j--;i[~~ -Protein lsourea derivative lmidocarbonate $-; -NH-Protein N-substituted car bama te Scheme 1 Chemical activation of polysaccharides by means of cyanogen halides and chemical coupling of proteins to cyanogen halide-activated polysaccharides (Reproduced by permission from European J.Biochem., 1971, 18, 352) but there is some acid-resistant residual activity, due either to the presence of bromotriazine groups on the polymer (arising from trimerization of cyanogen bromide) or to the reactivity of the strained cyclic carbonate. Small amounts of peptides can be coupled to Sephadex-carbonate.l*: A model study of the reaction between cyanogen bromide and methyl 4,6-O-benzylidene-cu-~-gluco-pyranoside (1) bears out this scheme.Good evidence is adduced for the forma- tion of the trans-fused cyclic 2,3-imidocarbonate (2; X = NH) with smaller proportions of carbonate (2; X = 0)and 2-and 3-carbamates.lS (2) x Agarose, consisting of alternating (1 -.3)-linked p-~-galactopyranose and (1-4)-Iinked 3,6-anhydro-cu-~-galactopyranoseresidues, cannot form such a five-membered ring, so that the major active intermediate is probably the six- $ Poly(ally1 carbonate) has recently been described and used for insolubilizing enzymes [S.A. Barker, J. F. Kennedy, and A. Rosevear, J. Chem. SOC.(C), 1971, 27261. This polymer might be suitable for affinity chromatography since it is highly substituted with neutral, hydrophilic groups (it contains ethoxycarbonyl residues, eight-membered cyclic carbonate rings, and, after coupling through amide bonds, hydroxyl residues).1) L.Ahrgren, L.KAgedal, and S. Akerstrom, Actu Gem. Scand., 1972, 26, 285. Guilford membered cyclic 4,6-imidocarbonate (3).* Pre-activated agarose has recently become available as a dry powder, stabilized with lactose and dextran, and can be used directly for coup1ing.t HN NH 0 0 II-I-(3) (ii) Organic Cyanafes. Activation of polysaccharides with organic cyanates is optimal at pH 10-1 1 and is even more rapid than with cyanogen bromide. The active intermediatesare imidoesters(4)16and (again)cross-linked imidocarbonates. (iii) Coupling to Acrivared Polysaccharides. Unprotonated primary amines couple to cyanogen bromide-activated agarose and dextran, often with high efficiency.Coupling yields can be increased by using excess ligand or cyanogen halide for activation, although the relationship is complex because of steric and interligand repulsions. The reaction medium should be chosen to give a pH above the pKa of the ligand (-10 is the upper limit), e.g. 7-8 for aromatic amines (pKa -5), 9.5-10 for amino-acids (pKaa-NHs -8) and 10 for aliphatic arnine~.~~Cyanate-activated polymers behave similarly but more rapidly. The derivatives formed are of isourea and N-substituted imidocarbonate or carbamate (Scheme 1, ‘Coupling step’). The mechanism of the coupling reaction is but poorly studied and understood. When alanine ethyl ester is attached to activated dextran, ammonia is liberated (suggesting hydrolysis of an isourea or nucleophilic displacement from imidocarbonate) but not when the ligand is glycine.Similarly, diethyl imidocarbonate forms the N-ethoxycarbonylmethyl derivative with ethyl glycinate but O-ethyl-N-carboxymethylisoureawith the free acid.17 (iv) Stability of the Complex. The importance of a stable ligand-carrier complex * Aminopolymers (e.g. aminoethyl-Sephadex, Enzacryl@ AA) can similarly be activated, optimally at pH 8-9. The intermediates are cyanamides or carbodi-imides and coupling to amines probably involves guanidino bonds (which preserve overall charge).lsJ4 Althoughthis is unlikely to be useful in affinity chromatography because of the anionic nature ofthe polymer, it has been surprisingly little exploited for immobilizing enzymes.t Even after prolonged coupling, residual activated groups sometimes remain (especially with bulky ligands).It is advisable to incubate the adsorbent with excess ethanolamine or 1-aminopropane-2,3-diol after coupling, since unreacted imidocarbonates and isoureas con-fer ionic character to the matrix. lo L. KAgedal and S. Akerstrom, Acta Chem. Scand., 1970, 24, 1601. l7 P. Vretblad, Thesis, Uppsala University, 1971. Chemical Aspects of Afinity Chromatography has been emphasized and, for most affinity chromatography, systems prepared by the cyanogen bromide method are adequate in this respect. However, a study of stability of agarose complexes with [14C]alanine and with a radioactive adenosine 3’,5’-cyclic phosphate (CAMP) analogue (5)11bJ8demonstrated some leakage at pH’s greater than 5.l Products varied with conditions: in tris buffer, pH 8, a mixture of N-alanylguanidine and alanine (1:4) was liberated from f14C]alanylagarose; at pH 9 (same buffer) the ratio was 2: 1.At pH 11 in aqueous triethylamine (no NH2) only N-carbamylalanine and a trace of 4-methyl- hydantoin could be detected. A summary and rationale of these observations is presented in Scheme 2. This problem becomes significant if the protein to be purified is present in such low concentration that ligand leakage is of comparable magnitude. Coupled proteins seem more stable, perhaps because several lysyl residues may be involved, possibly in more sterically hindered bonds.B. Po1yacrylamide.-This matrix is a cross-linked copolymer of acrylamide NN’-methylenebisacrylamide,comprising a hydrocarbon framework carrying carboxamide side-chains which are resistant to hydrolysis in the pH range 1-10. It is available in spherical beads of various sizes and porosities. Inman and Dintzisl9 have developed a wide range of mild methods for modifying this structure with chemical groups suitable for ion-exchange and covalent bonding. Some of their derivatives are particularly suitable for preparing biospecific adsorbents because overall neutrality is preserved. The amido-NH, is readily displaced by other amino-derivatives in what is essentially acylation of an amine by an amide. Scheme 3 illustrates the principal activation pathway.Treatment of polyacrylamide with aqueous hydrazine produces an acyl hydrazide gel (6) $ 0.5 nmol h-l at pH 6 and 2.2 nmol h-l at pH 8, per gram of gel containing 1200-5000 nmol of ligand. l6 G. I. Tesser, H.4. Fisch, and R. Schwyzer, Abstracts of the 8th F.E.B.S.Conference, Amsterdam, 1972, Abstract 795. l9 J. K. Inman and H. M.Dintais, Biochemistry, 1969, 8, 4074. Guilford Activation + Fixation OH NH OH' Fission NH 1 1 NH2-C-NH ll0 -R NH2-C-NH--R II NH NH2-R +C02 I-Carbamyl derivative Guanidinium compound Free Amine (hydanto'ic acid) Scheme 2 Liberation of ligands from polysaccharide gels: a tentative scheme based on the coupling mechanism proposed by Ax& and Ernback (European J.Biochem., 1971,18, 351) (Reproduced by permission from a lecture by G. I. Tesser at the 8th F.E.B.S. Conference, Amsterdam, 1972) Scheme 3 Chemical Aspects of Afinity Chromatography which is converted by nitrous acid into the key acyl azide intermediate (7). This can be coupled either to amino-ligands or to spacers which can be modified by methods analogous to those used for agarose (vide infra). Unreacted acyl azide is reconverted into carboxamide with ammonium ion. The only disadvantage with this procedure is that azide formation is accompanied by gel shrinkage which reduces porosity, limiting the usefulness of polyacrylamide for affinity chromato- graphy of large proteins. Polyacrylamide can also be functionalized by treatment with glutaraldehyde, to which ligands are attached as Schiff's basesao Polyacetal- Enzacryl@ is also suitable for this type of coupling.C. Glass Beads.-Porous glass has been introduced as a matrix for insolubilizing enzymes as a result of a search for carriers suitable for large-scale production processes. Glass is very resistant to changes in acidity and solvent, mechanical damage, and microbial attack. Functionality is introduced on to the glass surface by using silyl coupling reagents, including 3-aminopropyltriethoxysilane (8) (Scheme 4). As well as the simple covalent bond depicted, there may be a coating I I I (Et0)3SiCH2CH2CH2NH2 + -Si-OH --Si-O-SiCH2CH2 CH2NH2 I I I (8) Glass (9) Scheme 4 of aminopropylsilyloxy-groupsaround the bead due to polymerization of (8).There are few published data on the use of glass in affinity chromatography. Glutaraldehyde has been allowed to react with (9), leaving a free aldehyde group to be attached to glycyl-D-phenylalanine, an inhibitor of carboxypeptidase A. This enzyme was selectively adsorbed from a mixture of proteins on to the modified beads, from which it could be eluted with M-acetic acid, pH 3.21 The N-hydroxysuccinimide ester of succinylaminoalkyl-glasshas been prepared, and behaves as the analogous agarose-active ester towards amino-ligands (vide infra). Other modified glass carriers, already used for insolubilizing enzymes and suitable for preparing biospecific adsorbents, include isothiocyanatoalkyl- and diazotized p-aminobenzamidoalkyl-glass.22Biologically active glass-bound catecholamines have been prepared.Immobilized L-epinephrine (1 0) and iso- proterenol [l-(3,4-dihydroxyphenyl)-2-isopropylaminoethanol] retain their ability to accelerate and immobilized propranalol [1-isopropylamino-3-(naphth-l-yloxy) propan-2-01] its ability to decelerate the heart-beat rate of dogs and chick embryon~.~~ *O T. Ternynck and S. Avrameas, F.E.B.S. Letters, 1972, 23, 24. P. J. Robinson, P. Dunnill, and M. D. Lilly, Biochim. Biophys. Acfa, 1971, 242, 659. ** H. H. Weetall, Research and Developmenf, 1971, 22, 18. J. C. Venter, J. E. Dixon, P. R. Maroko, and N. 0.Kaplan, Proc. Nut. Acad. Sci. W.S.A., 1972, 69, 1141. Guirford HO OH CH2*CH2*CH2*NH 4 CHOH (Reproduced by permission from Proc.Nut.Acad. Sci. U.S.A., 1972,69,1141) 4 Matrix Modifications and Spacers It will usually be necessary to separate small ligands from the gel by a 'spacer'; also, some ligands will not have an NH2 group suitable for direct coupling. Activated agarose and polyacrylamide can be modified with bifunctional reagents of the general structure NH,-R-X, where X is a functional group and R, chemically inert, determines rigidity, hydrophilicity, and maximum length. Useful in combining the function of spacer with the introduction of a new reactivity are a,o-diaminoalkanes, di-(3-aminopropyl)amine, eaminocaproic acid, benzidine, lysine, and small peptides, e.g. Gly-Gly-Tyr. Aminoalkylagaroses are versatile gels which can be further extended and modified.Succinic anhydride introduces a carboxy (cf. Scheme 5), N-acetylhomocysteine thiolactone (1 1) a thiol, 0-bromoacetyl-N-hydroxysuccinimide(1 2) a bromoacetyl, and p-nitro- c0 NOCOCH2 Br 'PNHCOMe 00 benzoyl azide a p-aminobenzoyl group (after dithionite reduction). Earlier reviews and papers by CUatrecasa~"~~~~~~ include extensive surveys of these manipulations. The disadvantage of some of the derivatives is the lack of select-ivity of the end product. Aminoalkyl and succinylaminoalkyl gels are usually coupled to ligands by using di-imides, so that polyfunctional amino-acids and nucleotides have to undergo elaborate blocking-deblocking procedures to ensure specific coupling modes and to prevent cross-linking between ligand molecules.Bromoacetamidoalkyl gels alkylate amino, histidyl, and phenolic compounds, 24 P.Cuatrecasas, J. Biol. Chem., 1970,245, 3059. Chemical Aspects of Afinity Chromatography and diazotized p-aminobenzamidoalkyl gels fail to discriminate between histidyl and tyrosyl residues. More selective (and rapid) methods are especially desirable for coupling peptides and proteins. Some elegant solutions to this problem are discussed below. (i) N-Hydroxysuccinimide Esters. N-Hydroxysuccinimide esters of, e.g., succinyl-ated diaminodipropylaminoagarose react rapidly and specifically in the pH range 6-9 with unprotonated amino-groups (Scheme 5). Esterification is carried out in anhydrous dioxan, which does not much affect agarose.Of a wide range of N-protected amino-acids, only N-acetylcysteine competed with alanine in the displacement step, so that only amino- and sulphydryl groups of unprotected peptides and proteins should participate in insolubilization. It is also possible to 0 Agarose \\ NHCH2CH2CH2NHCH2CH2CH2NH2 +t-.:"I"' j-42 0 i NHCH2CH2CH2NHCH2CH2CH2NHCOCH2CH2CO2H I DCC dioxan + #-OH-succinimidc * !I NHCH2CH2CH,NHCH2CH2CH,NHCOCH2t 0 0+ RNH2 0 t ItNHCH2CH2CH2NH,CH2CH2CH,NHCOCH2CH,C-NHR (C1 Scheme5 Reactions involved in the preparation and use of N-hydroxysuccinimide esters of agarose. Diaminodipropylaminoagarose is treated with succinic anhydride in saturated sodium borate bufler to obtain the corresponding suc-cinylated derivative (A).The latter is treated with N"-dicyclohexylcarbodi- imide (DCC) and N-hydroxysuccinimide in dioxan to yield the active agarosr ester (B). After removing dicyclohexylurea and the unreacted reagents (dioxan and methanol washes) the active ester of agarose is treated in aqueous medium with ligands or proteins to yield stable amide-linked derivatives (C) (Reproduced by permission from Biochern., 1972, 11, 2293) Guilford discriminate in favour of a-over E-NH~groups at low pH to allow coupling of lysine-containing peptides at the N-terminal residue only. This method seems advantageous, however, only for small ligands for, if no spacer were required, the adsorbent could be prepared by direct coupling to the activated gel.It cannot be applied to polyacrylamide, which is not resistant to dioxan, but may find wide application with glass supports. (ii) Egoxide Reagents. Alkaline 2,3epoxy-1-(p-nitrophenoxy)propaneintroduces the 2-hydroxy-3-(p-nitrophenoxy)propyl substituent into polysaccharides. Dithionite reduction and reaction with thiophosgene produces an isothiocyanato gel which forms thioureas with amino-ligands.26 Gels with the oxiran function- ality are formed by using either alkaline epichlorohydrinZ8 or excess a,o-di- epoxides, e.g. butane-l&diol diglycidyl ether.a7 Epoxidized carriers are excellent for specific coupling of polyfunctional amino-ligands, e.g. D-asparagine (Scheme 6).The adsorbent (1 3) wassuccessfully used in the purification of L-asparaginase.Me OH Me/”\ I I I ?OH * CH2CHCH$CHCHzCH20CH2CHCH, -OCH2CHCH20CHCH2CH20CH2CHCHz OH Me OH CHZCONH, ~OCH2CHCHzOCHCH2CH,DCHCHzNHCHC02HI I II 0-asparagina (13) Scheme 6 (iii) Other Methods. Sephadex has been functionalized by periodate oxidation, which liberates aldehyde groups for coupling through azomethine bridges, or involvement with isocyanides for attaching amino- or carboxy-ligands under neutral conditions in an Ugi-type reacti~n.~~~~~ (iv) Spacers. That many small ligands must be spaced from their carriers to be accessible to a macromolecular substrate and provide a viabIe adsorbent is well established. A dramatic example is provided by a comparison of two attempts to purify avidin, the egg-white protein which binds strongly to biotin (14; R = H) with a dissociation constant of 10-l6 In spite of the enormous avidity of the protein for its substrate, avidin is only weakly retarded by biotinyl-cellulose (14; R = cellulose).6a By contrast, when the binding determinants are accessible as in c-(N-biotiny1)-L-lysylagarose(1S), avidin is adsorbed so strongly that 6M-a6 Swedish P.1192784/1970.J. Porath and N. Fornstedt, J. Chromatog., 1970, 51, 479. s7 M. Einarsson, Thesis, Uppsala University, 1972. 8s R. Ax&, P. Vretblad, and J. Porath, Acta Chem. Scand., 1971,25, 1129. ‘-* Chemical Aspects of Afinity Chromatography guanidinium chloride, pH 1.5, is needed as eluant.2e Similarly, tyrosine amino- transferase from mouse hepatoma tissue culture cells is unretarded by pyridox- amine 5’-phosphate coupled directly to cyanogen bromide-activated agarose but is strongly and specifically adsorbed when this ligand is spaced from the matrix (Scheme 7), thus providing a rapier-like means of plucking out from a crude extract a polysome capable of synthetizing a single enzyme.0KHN NH The greater effectiveness of ligands when attached to spacer-arms is generally ascribed to their increased steric availability to the protein. Although this is doubtless the major factor, there are others to consider. The ligands themselves may be more separated when on a long, mobile chain, so that possible masking of those adjacent by an adsorbed protein molecule is minimized. Also, controls have rarely been run to ascertain whether the arm alone has any affinity for the protein, although, even if there were an additional effect, it would often be desirable, provided it were specific.In choosing a spacing system, the major consideration is often preparative simplicity but, although hydrocarbon chains are conveniently accessible, this should not be an overriding consideration. It should be recognized that a two-dimensional, linear picture of a polymethylene array is unrealistic. Such a lipo- philic assembly will have a strong tendency to coil in aqueous milieu, thus reduc- ing its effective length. The same criticism may be levelled at some peptides. Polyamino arms, though more hydrophilic, introduce ionic character on to the bioadsorbent.Something approaching the ideal may be the polyhydroxy-ethers laP. Cuatrecasas and M. Wilchek, Biochem. Biophys. Res. Comm., 1968,33, 235. Guilford arising from the bisepoxides described above (cJ Scheme 6). An alternative approach is to use a rigid spacer such as benzidine or a steroid. Useof an arm of greater than a certain limiting 'length' does not seem to give improved binding capacity. For instance, immobilized N'-(6-aminohexyl)- and N'-( 12-aminododecyl)-pyridoxamine 5'-phosphates exhibit equal affinity for apo-glutamic-oxalacetic transamina~e.~~ Agarose NHCH;! 0II HO CH2O-7-OH Me \ OH Agarose 0 0II II 0 OH Agarose 0 0 Scheme 7 Biospecific adsorbents prepared by coupling pyridoxamine phosphate to agarose through spacers of varying length (Reproduced by permission from Biochirn.Biophys. Acta, 1972,276,408) 5 General Ligands Much attention has been focused recently on immobilized ligands, such as nucleotides, of general application not only in affinity chromatography but as biologically active cofactors or effector^.^^ Glass-bound catecholamines were mentioned above. Adenine nucleotides are of particular interest. These molecules have a number of sites capable of chemical modification; synthesis of analogues suitable for immobilization so that the mode of attachment is specific and proven has been a considerable chemical challenge, not always adequately met. so R. Collier and G. Kohlhaw, Anafyr. Biochem., 1971, 42, 48. 31 K. Mosbach, H. Guilford, R.Ohlsson, and M. Scott, Biochem. J., 1972, 127, 625. Chemical Aspects of Afinity Chromatography A. Adenosine 3’,5’-Cyclic Phosphate.-This ligand (16; R = H) poses the least problems since the phosphate diester is stable, limiting the number of potential sites for either attachment of an arm or direct coupling to a matrix. Anhydride acylation of, successively, the 2’-OH and the 6-NH2, followed by selective hydrolysis of the ester, affords N6-acyI-cAMP’s. Wilchek has used bis-(N-benzyl- oxycarbony1)-eaminocaproic anhydride to make (after hydrogenolysis) N6-(e-aminocaproy1)-CAMP, suitable for coupling to cyanogen bromide-activated agaro~e.~~An alternative approach arises from the observation that the carbon atom with the highest electron density in the adenine ring is at position 8, so that cAMP can be brominated there specifically.The halogen atom is readily dis- placed by nucleophiles, including cysteamine in the first step of the synthesisl1* of (5) from 8-bromo-CAMP (16; R = Br) and l,Qdiaminohexane, which gives 8-(6-aminohexyl)amino-cAMP [16; R = NH(CH2)sNH2].Sa The latter coupled to agarose provides a useful bioadsorbent for purifying intact CAMP-dependent kinases.** B. Adenosine 5’-Monophosphate.-Adenosine 5‘-monophosphate offers more scope for chemical modification and hence more problems of selectivity. The vicinal diol group of the ribose moiety allows periodate cleavage to a dialdehyde, convenient for coupling to amino supports. This method is applicable to other ribonu~leotides.~~8-(6-Aminohexyl)amino-AMP is available from 8-bromo- AMP by a synthesis analogous to that of the similar cAMP deri~ative.~~ These methods take the ribonucleotides as the starting material : a synthesis 3p M. Wilchek, Y.Saiomon, M. Lowe, and 2.Selinger, Biochem. Biophys. Res. Comm., 1971, 45, I177. as H. Guilford, P.-0. Larsson, and K. Mosbach, Chern. Scripfa, 1972, 2, 165. 34 B. Jergil, H. Guilford, and K. Mosbach, in preparation. 36 P. T. Gilham in ‘Methods in Enzymology’ ed. S. P. Colowick and N. 0.Kaplan, Academic Press, New York and London, 1971, vol. 21, p. 191. Guilford of a tailor-made, immobilized AMP ligand from a simple nucleoside is sum-marized in Scheme 8. The unambiguous character of IV6-(6-aminohexyl)-AMP (17) lends a rigour and specificity to this approach which is lacking in some others.A practical disadvantage, however, of the method as outlined is the tedium of separation of the huge excess of 1,6-diaminohexane necessary to suppress the formation of NINs-bis(nuc1eotide)hexane.New reagents developed to overcome this drawback are l-amino-w-trifluoracetamidoalkanes(18),3s in which only one NHI group can participate in the displacement step, the other being subsequently regenerated by mild hydrolysis of the protecting group. CF,CONH(CH 2)1) NH2 The availability of the same ligand immobilized in different ways allows some insight into which functional groups are necessary for binding. For instance, immobilized N6-(6-aminohexyl)-AMP binds strongly to many nicotinamide adenine dinucleotide (NAD+)-dependent dehydrogenases, but weakly or not at all to those for which NADP+ is cofactor." Some NAD+-dependent dehydro- genases do not seem to be adsorbed on Sepharose-bound 8-(6-aminohexyl)- amino-AMP.Neither adsorbent retards a wide range of kinases. C. Nicotinadde Adenine Dinuc1eotide.-Bioadsorbents with nicotinamide adenine dinucleotide as ligand have been prepared by carbodi-imide coupling to agarose substituted with caproyl Several ester and amide linkages seem to be involved. NAD +-dependent dehydrogenases can be chromatographed on this preparation. Coupling, probably by electrophilic attack at C-8 of the purine ring, either to diazotized p-aminobenzamidoalkyl-glassor through benzidine attached to a polysaccharide via o-hydroxyaniline, offers alternative^.^^ Succinic anhydride reacts with NAD+ to form a hemisuccinamide with the purinyl 6-amino-group suitable for attachment to polyethyleneimine or, for affinity chromatography, o-aminohexylagarose.3a All these preparations retain a measure of cofactor activity.Ethylene oxide quaternizes the N-1 position of the purine ring with a 2-hydroxyethyl substituent which can be rearranged on to the N-6 position in alkali (the cofactor must first be reduced to the base-stable NADH).40 * 1.e. NAD+ with a phosphate group on the 2'-OH of the adenylribose. H. Guilford, in preparation. n7 P.-0. Larsson and K. Mosbach, Biotechnol. Bioeng., 1971, 13, 393. "(a) M.K. Weibel, H. H. Weetall, and H. J. Bright, Biochem. Biophvs. Res. Comm..1971. 44, 347; (b) C. P. Lowe and P. D. G. Dean, F.E.B.S. Leffers, 1971,14, 313. J. R. Wykes, P. Dunnill, and M. D. Lilly, Biochim. Biophys. Acta, 1972, 286, 260. 40 H. G. Windmueller and N. 0.Kaplan, J. Biol. Chem., 1961,236,2716. Chemical Aspects of Afinity Chromatography 0 I e=O /\00XI 0I 7 P,3 3 8U s a /To00XI 4 0 1 0I Guilford This N6-(2-hydroxyethyl) substituent should be capable of selective attachment to an appropriate arm, e.g. isocyanatoalkyl. D. Other General Ligands.-Blz coenzyme and other cobalamins have been coupled to substituted agarose either via the phosphate group41 or by amide formation at one of the side-chains.O2 Intrinsic factor, transcobalamins and B,,dependent enzymes bind to these adsorbents. Immobilized meth~trexate~~ (4-amino4deoxy-N~o-methylpteroylglutamicacid) and folk have been used in purification of, respectively, dihydrofolate reductase, of great interest in cancer research, and folate-binding protein from milk. Pyridoxal phosphate analogues were mentioned above. Thiamine pyrophosphate has been coupled to succinylaminoalkylagaroseby using di-imide.45 P *-(6-Amino-l -hexi)-P2-(5'- uridine) pyrophosphate has been described.46 6 Polynucleotides Immobilized polynucleotides are used in two kinds of affinity chromatography. One depends on the ability of single-stranded nucleic acids to hydrogen-bond specifically with complementary strands.Thus, immobilized poly(U) adsorbs KB-cell polysomal messenger RNA which has a poly(A) segment that can 'base- pair' with the adsorbent. The ribosomal and transfer RNA's lack this segment and are not retained.47 The other is the orthodox approach by which enzymes are chromatographed on nucleic acid substrates. Several aminoacyl-tRNA synthetases have been purified on columns of immobilized ~RNA'S.*~ A variety of methods have been described for attaching polynucleotides to carriers. A. DNA Embedded in Agar.-A rare example of a practical biospecific adsorbent not involving a covalent bond between ligand and carrier results from dispersing single-stranded DNA in liquid agar. When the homogenate cools, the DNA strands are firmly entrapped in the gel.4Q B.Di-imide Coupling.-Many oligonucleotides have been linked to paper strips by di-imide-mediated ester formation at the terminal phosphate.s0 H. Olescn, E. Hippe, and E. Haber, Biochim. Biophys. Acta, 1971, 243, 66. (a) R.-H. Yamada and H. P. C. Hogenkamp, J. Biol. Chem., 1972, 247, 6266; (b)R. H. Allen and P. W. Majerus, ibid., p. 7695. P. C. H. Newbold and N. G. L. Harding, Biochem. J., 1971, 124, 1. (*D.N. Salter, J. E. Ford, K. J. Scott, and P. Andrews, F.E.B.S. Letters, 1972, 20, 302. 4s A. Matsuura, A. Iwashima, and Y. Nose, Biochem. Biophys. Res. Comm., 1973, 51, 241. R. Barker, K. W. Olsen, J. H. Shaper, and R. L. Hill, J. Biof. Chem., 1972, 247,7135. U. Lindberg and T. Persson, European J.Biochem., 1972, 31, 246. "(a) 0. D. Nelidova and L. L. Kiselev, Mol. Biof., 1968, 2, 60; (b) S. Bartkowiak and J. Pawelkiewicz, Biochim. Biophys. Ada, 1972, 272, 137; (c) P. Remy, C. BirmelC, and J. P. Ebel, F.E.B.S. Letters, 1972, 27, 134. 4mH.Schaller, C. Niisslein, F. J. Bonhoeffer, C. Kurz, and I. Nietzschniann, European J. Biochem., 1952, 26,474. (a)P. T. Gilham, J. Amer. Chenr. SOC.,1964,86,4982; (b)I. E. Scheffler and C. C. Richardson, J. Biol. Chem., 1972, 247, 5736. 267 Chemical Aspects of Afinity Chromntography C. Photochemical Metbods.-Gels are formed when polynucleotides alone are irradiated with U.V. light. The strands become cross-linked through pyrimidine pairs, e.g. the thymine dimer (19). If, however, irradiation of poly(U) or poly(C) is carried out in the presence of cellulose, nylon, or polyvinyl beads, the strands become immobilized, even at an irradiation dose level at which the polynucleo- tides alone are unaffected.61 Coupling presumably proceeds through a free radical mechanism, initiated probably by electron abstraction from the carrier.Me Me D. Periodate Oxidation.-The vicinal 2’,3’-diol group of the riboses in rib-nucleic acids is readily oxidized by periodate. The modified ligand is then coupled to an amino carrier through azomethine bridges,36 or as a hydrazone to acyl hydrazide residues on a modified agarose.6a The latter has also been used to prepare immobilized guanosine 5’-triphosphate (GTP) for affinity chromato- graphy of the folate-synthetizing enzyme D-erythrodihydroneopterintriphosphate synthetase from Lactobacillus ~Zantarurn.~~ Periodate oxidation cannot be applied to 2’-deoxyribonucleotides which lack the diol system.E. Coupling to Cyanogen Bromide-activated Agarom.-Weissbach and co-workers studied the coupling of various DNA’s and RNA’s to activated agarose at pH 8.6p Single-stranded nucleic acids, especially poly(A), were coupled well but most double-stranded DNA’s were not covalently linked unless there were single-stranded extensions at each end. Native HeLa DNA with 2.2% single- strand was coupled to the extent of 4.3 %, whereas 24 % was coupled where there was 8.3% single-strandedness. It was assumed that the coupling involved the 6-amino-groups of the adenines, but little evidence for this was presented.The reactivity of these groups towards activated agarose varies with its environment: in adenosine and CAMP it is unreactive but NADf can be coupled in this fashion. One report describes the immobilization of ribonucleotides at one clearly defined site, the terminal Y-ph~sphate.~~ Cyanogen bromide-activated agarose 61 R. J. Britten, Science, 1963, 142, 963. D. L. Robberson and N. Davidson, Biochem., 1972,11, 533. O8 R. J. Jackson, R. M. Wolcott, and T. Shiota, Biochem. Biophys. Res. Comm., 1973,51,428. O4 M. S. Poonian, A. J. Schlabach, and A. Weissbach, Biochem., 1971, 10,424. b6 A. F. Wagner, R. L. Buganiesi, and T. Y. Shen, Biochem. Biophys. Res. Comm., 1971,45, 184. Guilford and poly(I) or poly(C) were incubated at pH 6, chosen to be low enough to preclude ‘amino-group participation’.It was suggested that the mechanism involves addition of the terminal group to cyanate to give an active adduct able to react with an adjacent hydroxyl on the carrier (Scheme 9). It is not clear, however, that lowering the pH would have much effect on the adenyl ring substituent since, having a pKa of N 3.5-5 (depending on ionic strength), the 6-amino-group will be largely unprotonated anyway. Conversely, it is plausible that many couplings of adenine nucleotides, e.g. other reports of insolubilized nucleic acids and the immobilization of ADP,K6may be via the terminal phosphate group even under conditions designed to facilitate amino-group participation. 7 Concluding Remarks Affinity chromatography has become an accepted part of biochemical method- ology and has facilitated the isolation of many interesting macromolecules hitherto inaccessible by less sophisticated techniques. Its success will doubtless continue.It should be realized, however, that even a tailor-made ligand-spacer- carrier system does not necessarily constitute a biospecific adsorbent. It has usually been tacitIy assumed that spacers play little part in the chromatographic process and that inhibitors and substrates exhibit similar affnity characteristics in the free state and when modified to render them sterically available. Recent studies show that these assumptions are not always ~alid.~**~~ Kinetic para- meters should be established for modified ligands, and non-specific effects must be evaluated in control experiments using matrix-spacer gels lacking a ligand.The next logical steps in the development of affinity chromatography are a theoretical treatment on which quantitative evaluations of biospecific adsorbents can be based and extensive investigations into the problems associated with the evolvement of a research tool into a useful production method. The multi- disciplinary nature of affinity chromatography will thus be extended even further, beyond the present need for collaboration between synthetic chemist and enzymologist. J. T. Neary and W. F. Diven, J. Biol. Chem., 1970,245,5585. 67 P. O’Carra, Abstracts of the F.E.B.S.Conference, Dublin, 1973, Abstract 7.Chemical Aspects of Afinity Chromatography Note Added in PruoJ A number of investigations within the scope of this review have come to the author’s notice since the preparation of the manuscript: (i) The results of a study of the mechanism of cyanogen bromide-activation of cellulose, using rrans-cyclohexane-l,2-diol as a model, are consistent with Scheme 1 (G. J. Bartling, H. D. Brown, L. J. Forrester, M. T. Koes, A. N. Mather, and R. 0. Stasiw, Biotechnol. Bioeng., 1972,14, 1039). (ii) A high-capacity, ultrastable ‘polyvalent handle’ has been prepared by immobilizing polylysine by multipoint attachment to activated agarose (M. Wilchek, F.E.B.S. Letters, 1973,33, 70). (iii) t-Butyloxycarbonylhydrazide derivatives of peptides have been introduced for coupling haptens to carriers (J.K. Inman, B. Merchant, and S. E.Tacey, Imrnunochernistry, 1973,10, 153). (iv) Immobilized colchicine derivatives have been used for affinity chromato- graphy of a brain microtubule, tubulin (N. D. Hinman, J. L. Morgan, N. N. Seeds, and J. R. Cann, Biuchem. Biuphys. Res. Comm., 1973,52, 752). (v) Alkylamino-glass was used as a carrier for lipoic acid in purifying lipoamide dehydrogenase (W. H. Scouten, F. Torok, and W. Gitomer, Biuchem. Biophys. Acra. 1973,309, 521). (vi) A hydroxamate assay has been developed for quantifying coupling yields (J. S. Wolpert and M. L. Ernst-Fonberg, Analyt. Biochem, 1973, 52, 11 1). (vii) Rigorous, comparative studies have been made, based on a semi-quantita- tive treatment, of non-specific adsorption and spacers (P. O’Carra, S. Barry, and T. Griffin,Biocherri. SUC.Trans., 1973,1, 289;cf. S.Barry and P. O’Carra, Biochem. J., 1973, in the press). It is a pleasure to express my thanks to my colleagues at the University of Lund, Sweden, especially Dr. Klaus Mosbach who first fostered my interest in affinity chromatography.

ISSN:0306-0012    

DOI:10.1039/CS9730200249

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Organoltransition-metal Complexes :Stability, Reactivity and Orbital Correlations By P. S. Braterman and R. J. Cross DEPARTMENT OF CHEMISTRY, THE UNIVERSITY, GLASGOW GI2 8QQ 1 Introduction Much of the interest in organo-transition-metal (OTM) chemistry derives from the relative ease with which o-bonds between a transition metal and carbon can be made or broken. Such behaviour is central both to organometallic catalysis and to the stoicheiometric uses of OTM species in organic synthesis. In addition, changing views on the nature of the bond-making and bond-breaking processes have led in recent years to dramatic extensions of the range of descriptive transition-metal chemistry, while spectroscopic studies of the new species formed, and mechanistic investigations of metal-carbon bond reactivity, continue to enrich our understanding of inorganic chemistry as a whole.For many years it was widely believed' that metal-carbon o-bonds in OTM complexes were inherently unstable unless a certain special condition was satis- fied.2 This condition was the presence of n-accepting ligands, which were thought to stabilize the bond to cleavage by increasing the energy separation between filled and empty d-orbitals on the metal. For many reasons, some of which the authors have summarized el~ewhere,~ this position can no longer be maintained. Instead, it has become apparent that metal-carbon bond cleavage must be discussed in terms of the mechanistic pathways open to the various complexes. The same is evidently true for processes in which metal-carbon a-bonds are formed.Evidence is rapidly accumulating that both the bond-making and bond- breaking reactions generally proceed by electron-pair processes, and that the conditions controlling such processes may be rationalized by reference to possible mechanisms. Consideration of these mechanisms leads us to suggest that many bond-making and bond-breaking processes have much in common with apparently rather different reactions involving, for example, rearrangement and insertion. It should then be a useful exercise to compare these apparently diverse reactions throughout the entire range of OTM complexes. Such a comparison is the purpose of this review. In Section 2 we survey current views on metal-carbon bond lability in the light of the recent rapid extension of the range of one-electron-donor OTM complexes.The relationships between the bonding of these one-electron-donor complexes and many-electron- donor complexes are well understood and are alluded to in Section 3. There, formal similarities are used to compare various addition and elimination M. L. H. Green, 'Organometallic Compounds', Methuen, London, 1968.* J. Chatt and B. L. Shaw, J. Chern. Soc., 1959,705; 1960, 1718. P. S. Braterman and R. J. Cross, J.C.S. Dalton, 1972, 657. Orguno-transition-metal Cotnplexes: Stability, Reactivity, and Orbital Correlations reactions. Electrno-correlation diagrams are employed to show that such comparisons are real, and more precise than those derived simply from electron counting.* The use of such correlation diagrams in determining whether or not a given process is symmetry-allowed is demonstrated. Section 4 is devoted to a discussion, with many examples, of the factors controlling the reaction types reviewed.Variations in behaviour across the length and breadth of the Periodic Table are pointed out and explained. Finally, in Section 5, the relationships between bond-breaking and other processes, implicit throughout this review, are examined and discussed. 2 The Lability of Transition-metal-Carbon Bonds A. Development of Organo-transition-metal Chemistry.-The early belief that transition-metal-carbon bonds were weak has had a profound and lasting (though not necessarily unhelpful) effect on the development of their chemistry.As far as one-electron carbon donors were concerned, the first complexes to be isolated contained other ligands (often with n-bonding properties) in the co-ordination sphere of the metal, and this led,not unnaturally, to the idea that these ligands were responsible for stabilizing the metal-carbon bonds. The situation was rationalized thus. Bonds from transition metals to carbon were weak owing to the availability of high-energy d-electrons. Facile thermal promotion of one of these electrons to antibonding levels led to cleavage of M-C, and the reactive fragments produced (free radicals, carbanions, or carbonium ions) ensured rapid and irreversible decomposition. The operation of this process in, for example, halide or olefin complexes would result in stable dissociation products (ion-pairs or olefin) and the reaction could later reverse.Main-group elements, of course, lacked the high-energy d-electrons for facile promotion. After the isolation of compounds such as (Et,P)2PtMeC1,2 it was proposed that n-bonding ligands stabilized the metal-carbon bonds by lowering the energies of the filled d-orbitals, thereby increasing the activation energy for decomposition. Numerous compounds have since been isolated which appeared to conform to this hypothesis. The evidence available today renders this ‘supporting n-ligand‘ theory unten- able. In the first place, many organometallic species are now known which contain other ligands with no n-bonding properties, e.g.[PhCH,Cr(OH,),]2+, [E~Ru(NH~)~]~+,~~~and the number of derivatives with no ‘supporting ligand’ of any kind is growing e.g. (PhCH2)4Ti,7Me,W,8 (Ph3C)BNi.s Secondly, such spectroscopic and bond-length data as are available suggest that transition- metal-carbon bonds are of similar strength to main-group-metal-carbon bonds, and the presence of other ligands has little effect on these parameters. Thirdly, a 4 C. A. Tolman, Chew. SOC.Rev., 1972,1,337. F. A. L. Anet and E. Leblanc, J. Amer. Chem. SOC.,1957,79,2649. 6 K. Thomas, J. A. Osborn, A. R. Powell, and G. Wilkinson, J. Chem. SOC.(A), 1968, 1801. 7 U. Giannini and U. Zucchini, Chem. Cornm., 1968,940.* A. Shortland and G. Wilkinson, J.C.S. Chem. Comm., 1972, 378.@ G. Wilke and H. Schott, Angew. Chem. Znternat. Edn., 1966,5, 583. Braterman and Cross consideration of the energies involved shows that the promotional mechanism originally proposed is unlikely to operate under thermal conditions. These arguments are expanded in a recent paper., Despite strong metal-carbon bonds, many transition-metal organometallics are thermally labile, however. The explanation of their lability lies in the character- istic transition-metal properties of variable oxidation states and co-ordination numbers. These allow several facile decomposition pathways to operate which are denied to their main-group analogues. They are usually concerted reactions: reactions involving other co-ordination sites as well as the metal-carbon bond under consideration.The reactions proceed by paired-electron processes. Evi- dence continues to accrue which suggests that the chemistry of transition-metal organometallic compounds is dominated by such processes. 8. Concerted Reactions.-We shall illustrate three such reaction types :reductive (1,l) and related (1,2 and 1,n) eliminations; P-eliminations of metal and, for example, hydrogen from a ligand ;and dinuclear elimination. The relationship of these to other concerted processes and to their reverse reactions is discussed in subsequent sections. Simple nucleophilic or electrophilic displacement of metal from carbon may also be an important process, e.g. in transmetallations,10 but is outside the scope of this review.Both the oxidation number and the co-ordination number of the metal are reduced by two in reductive elimination reactions, e.g.ll (Ph,P)AuMe, -+(Ph,P)AuMe + C,H, Bond-making accompanies bond-breaking, and no free-living high-energy intermediates such as free radicals, carbanions, or carbonium ions are involved. The concerted nature of reductive elimination has recently been confirmedla for the reaction (PhMe2P),PtMe,I -(PhMe,P),PtMeI + CzH6 Specific labelling shows that this reaction is intramolecular and it follows first- order kinetics in dioxan between 335 and 365 K. The activation energy of 129 & 5 kJ mol-l is less than that for the thermolysis of (h6-CSH6)PtMe3,l3the value for which might be taken (see below) as a plausible lower limit for the homolysis of a PtIV-CH3 bond.Reductive elimination frequently follows oxidative addition, and this combina- tion of reactions is a common route to overall exchange. The similar nature of 10 See e.g., G. Agnes, S. Bendle, H. A. 0.Hill, F. R. Williams, and R. J. P. Williams, Chem. Cumm., 1971, 850. G. E. Coates and C. Parkin, J. Chem.Suc., 1963,421. l* M. P. Brown, R. J. Puddephatt, and C. E. E. Upton. J. Organometallic Chem.,1973, 49, C61. l3K. W. Eggar, J. Organometallic Chem., 1970,24, 501. Organo-transition-metal Coniplexes: Stability, Reactivity, and Orbital Correlations metal-oxygen, metal-carbon, and metal-hydrogen bonds is illustrated by the following reactions :l4J6 Me1 (Ph,P)AuCH,SiMe, -[(Ph,P)AuIMe(CH,SiMe,)] -(Ph,P)AuI + EtSiMe, Me1 (Ph,P)AuOSiMe, -[(Ph,P)AuIMe(OSiMe,)] -(Ph,P)AuI + MeOSiMe, HI -HCI (Et,P),PtCI1 + (Et,P),PtH,Cl, + (Et,P),PtHCI -H* HC1 Reductive elimination is a well-established process of (1,l) elimination of two groups from the same metal centre.It has now recently become apparent that (1,2) and (1 ,n)eliminations are more common than had been supposed. Thus the thermolysis of tetramethyltitanium to give methane has been shown by labelling experiments not to involve hydrogen abstraction from solvent, and to lead to the production of titanium carbide rather than pure titanium meta1.16 A plausible first step in the reaction could then be Ti(Me), -[Me,Ti-CH,] + CHI Related elimination processes include17 -(hs-C5H,).LTi(CH,Ph)2 [Ti(C5H4),ln+ 2 PhMe also a (1,2) elimination, andla -+(h5-C6H5)2Ti(C6DS)2 [(C5H6)2TiCBD41+ C6DI a (1,3) elimination.P-Elimination is perhaps the best documented of the elimination reactions and its importance as a decomposition route for organometallics has been empha- ~i2ed.l~It may be represented thus H R Deuteriation studies have confirmed the steric course of the reaction20 I' A. Shiotani and H. Schmidbaur, J. Organometallic Chem., 1972, 37, C24. Is E. H. Brooks, R. J. Cross, and F. Glockling, Inorg. Chim. Acfa, 1968, 2, 17. F. S. Dyachkovsky and N. E. Khrusch, Zhur. obshchei Khim., 1971, 41, 1779; A. S. Khachaturov, L. S. Breslov, and I. Yu. Paddubnyi, J. Organometallic Chem., 1912.42, C18. l7 G. Fachinetti and C. Floriani, J.C.S.Chem. Comm., 1972, 654. I. Dvorak, R. J. O'Brien, and W. Santo, Chem. Comm., 1970,411. (a) W. Mouat, A. Shortland, G. Yagupsky, N. J. Hill, M. Yagupsky, and G. Wilkinson, J.C.S. Dalton, 1972, 533; (b) M. R. Collier, M. F. Lappert, and M. M. Truelock,J. Orguno-metallic Chem., 1970, 25, C36. *O G. M. Whitesides, E. R. Stedronsky, C. P. Casey, and J. San Fillipo,jun., J. Amer. Chem. SOC.,1970, 92, 1426. Braterman and Cross (Bu3P)CuCH2CD2Et-(Bu,P)CuD + H2C=CDEt though when a fast reverse reaction operates, effective mixing of H and D results.21 This process is featured in many reactions of great synthetic value, such as the formation of transition-metal hydrides from alkoxides. It also features prominently in such catalytic reactions as the isomerization of olefins, and is a frequently encountered terminator in polymerization reactions.Dinuclear elimination, an intermolecular reaction, involves the formation of metal-metal bonds and/or metal alkyl (aryl) bridges in order to bring into proximity leaving groups from different metal atoms. Dinuclear or indeed poly- nuclear reactions are clearly indicated in the process20 (Bu3P)CuD + (Bu,P)CuCHZCD,Et +2 Bu~P+ 2 CU + CHaDCD2Et and in1' 2(Ph3P)AuMe+2Ph,P + 2Au + C2HI Similar dinuclear interactions probably operate in the recently reported exchange of alkyl groups between gold(1) and gold(m):a2 (Ph,P)AuMe,I + (Ph,P)AuMe +(Ph3P)AuMe3+ (Ph3P)AuI Bridging groups other than alkyls are clearly possible and an example of hexa- fluorobut-2-yne acting as bridging ligand in a dinuclear type of elimination has been reported (Scheme 1).25 Interestingly, when tetrafluoroethylene replaces the (PhMe2P)AuMe i-c4F6 Me Me Au ether Me/\I PPhMe2 acetone1I CF3 [(PhMe2P)AuI2C4F6+ C2H6 Scheme 1 alkyne, removing the possibility of alkyne bridges, insertion is the only subse-quent Some dinuclear reactions appear to be preceded by processes that leave one of the component metal centres co-ordinatively unsaturated.A *I G. M. Whitesides, J. F. Gaasch, and E. R. Stedronsky, J. Amer. Chem. SOC.,1972,94,5258.** A. Tamaki and J. K. Kochi, J. Organomerallic Chem., 1972,40, C81. *a A. Johnson, R. J. Puddephatt, and J. L. Quink. J.C.S. Chem. Comm.,1972,938.I4 C. M. Mitchell and F. G. A. Stone, J.C.S. Dalton, 1972, 102. Organo-transition-metal Complexes: Stability, Reactivity, and Orbital Correlations dinuclear species can then be formed without necessarily involving bridging ligands (Scheme 2).2s92s HCo(C0)d + HCo(C0)a + CO HCo(C0,) + HCo(CO), -H,Co,(CO), --+--+ Co,(CO), + CO,(CO)~,+ H2 + CO RCo(C0)d + RCOCo(CO), RCOCo(CO), + RCo(CO), -+ RCo(CO), --* Co(CO),COR] 4 CO,(CO)~+ CO~(CO)~~+ RCOR + CO Scheme 2 Acceptance of the importance of concerted reactions is already proving useful in the design of new compounds and the interpretation of reactions. Theprepara-tion of derivatives with no transferable p-groups confers stability in cases where the p-elimination is likely to operate.Thus a variety of compounds with tri- methylsilylmethyl, neopentyl, and the like have been isolated lately.1e~27 The extra stability of methyls compared with higher alkyls is well known and lack of a P-migration pathway has been invoked to explain this.lg The influence of transition-metal ions on the coupling of Grignard reagents continues to receive study ; recently the complexity of products produced from copper(1)-catalysed reactions has been explained in terms of P-eliminations, whilst the operation of dinuclear eliminations is apparent in silver(1)-catalysed systems :2ea RlAg + R2Ag+R'-R1 + R'-R2 + Rz-R2 Reductive elimination from silver is a critical step in the AgI-modified addition of benzyne to cyclic po1yenes:28b 8 -Ag' F.Ungvary and L. Marko,J. Organometallic Chem., 1969,20,205. R. F. Heck, Adv. Organometallic Chem., 1966,4,243. s7 W. Mowat and G. Wilkinson, J. Organometallic Chem., 1971, 28, C34. (a)M. Tamura and J. Kochi, J. Amer, Chem. SOC.,1971,93, 1483, 1485; (b)L.A. Paquette,Chent. Comm., 1971, 1076. 3raterrnan and Cross C. The Role of Supporting Ligands.-The critical effect of other ligands in stabilizing organo-transition-metal compounds is not that of n-bonding, but that of firm occupation of the co-ordination site (n-bonding may, of course, help to achieve this). This denies the use of that co-ordination site for concerted decom- position routes. Thus with reference to P-eliminations the stabilitys of [RhR(NH3),12+ has been contrasted with the lability of [RhR(CO)(PPh,),],28 which easily eliminates Ph3P to make available an extra co-ordination site.A possible steric effect of other ligands is also implicit. Bulky ligands will prevent use of adjacent co-ordination sites as well as their own. This may account for the existence of certain highly co-ordinately-unsaturated molecules such as (Ph,C),Ni,O and for the ready formation of [Cr(tsm),]- and Cr(tsm), (tsm = trimethylsilylmethyl), whereas less bulky ligands (methyl or 1,4-b~tenyl)~~or bulkier metals (molybdenum even with tsm as ligand) give rise to dinuclear products. Oa D. Free-radical Processes.-The dominance of paired-electron processes in organo-transition-metal chemistry is not complete. Indeed, it should not be expected to be.The similarity of transition-metal-carbon bonds to main-group- element-carbon bonds, the rupture of which to produce free radicals being both well recognized and exploited, is evident: thus some free-radical reactions of transition-element derivatives are probable. One example may be the thermo- lysisla of (n-C,H,)PtMe,, referred to above, which decomposes according to first-order kinetics at 438 K in the vapour phase, with an activation energy of 163 kJ mol-l. The main organic product identified was methane, but smaller amounts of ethane and dihydrogen were also formed. It may be that methane production in fact involves 1,Zelimination from the system H3C-[Ptl-CH2-H or even from one methyl group and a cyclopentadienyl ring, but in any case the steric impossibility of squareplanar ‘(n-C6H,)PtCH3’ presumably precludes a simple concerted reductive elimination of two methyls. Photochemical reactions of metal-carbon single bonds are expected to give radical product^.^ A recent example is the photolysis of methylcobalamin, in which excitation of the ring n -+ IC*transition leads to homolytic cleavage of the co bal t-me t h yl bond.Although electron promotion from a non-bonding to an antibonding orbital does not appear to be an important thermal process, the promotion under thermal conditions of a bonding electron into a non-bonding orbital2 is feasible in compounds containing less than six d-electrons, and radical products would result. We have ourselvesa (it would now seem erroneously) advanced this as an explanation for the high lability of TiMe, compared with SnMe,.A consequence of such a mechanism would be that n-accepting ligands should ZabiZize the s* G. Yagupsky, C. K. Brown,and G. Wilkinson, J. Chem. Soc. (A), 1970, 1392. SO(,) J. Krausse, G. Mam, and G. Schodl, J. Orgunometullic Chem., 1970, 20, 159; (b) J. Krausse and G. Schodl, ibid., 1971, 27, 59. a1 J. M. Pratt and B. R. D. Whitear, J. Chem. Soc. (A), 1971, 253. Organo-transition-metal Complexes: Stability, Reactivity, and Orbital Correlations metal-carbon bonds, and this feature was invoked by Co~see~~to explain the apparent labilizing effect of olefins on titanium-aIkyl bonds in certain Ziegler catalysts. More recently, thermolysis of (h6-CsHs)1TiRCl (R = Me, Et, Bui, Ph, CH2Ph, or C2H4Ph)show first-order loss of R with an activation energy of bond-breaking of ca.105 kJ mol-l. The products were rationalized in terms of an initial electron promotion from a Ti-C o-bond, leaving species with an activated neutral R group within the titanium co-ordination sphere. This undergoes reaction by migration to other centres or (with donor solvents) by free radical formation. It must now be recognized, however, that even amongst elements at the beginning of the Periodic Group where this promotional mechanism could apply, concerted reaction paths are still able to operate. 3 Some Relationships among Bond-breaking Processes A. Formal Analogies-Dinuclear eliminations, although appearing to be quite different to the other (unimolecular) eliminations discussed in Section 2B,can in fact be regarded as intramolecular eliminations from the reaction intermediates, e.g.R'M' + M2Ra-+ RIM'MeRa ---+ R'R2 + M'-MZ or RZ MIMa +R1R2RIM' + M2R2 [ 1 R1M'M2R2] ---t M'Ma/ ___+ R1R2+ MIMe \ R' The former process is formally a 1,2-elimination of R1R2across the metal-metal bond, whereas the latter is oxidative addition of R1-M1 to Ma, followed by reductive elimination of R1-Ra. Reductive eliminations for our purpose are processes of the type X /M +M+X-Y \ Y No free-radical or high-energy intermediates need be involved since, as we have seen, there is evidence that bond formation between X and Y can accompany the breaking of M-X and M-Y.The extreme valence-bond representation of olefin-metal complexes depicts them as metalla-cyclopropanes, and as such the two M-C bonds are analogous to M-X and M-Y. Elimination of the olefin sa P. Cossee, J. Catalysis, 1964, 3,80. 33 J. A. Waters, V. V. Vickroy, and G. A. Mortimer, J. Organometallic Chem., 1971, 39, 41. Braterman and Cross from the metal co-ordination sphere is thus equivalent to reductive elimination of XY: c M + C=C Acetylene derivatives, formally metalla-cyclopropenes, can be treated similarly, as can dimerizations, polymerizations, and ring-closure reactions : ‘C c-cI/M M I -M+l I ‘c’C c-c C The number of electrons formally donated to the metal is reduced by two in each of the elimination steps mentioned.Other reactions that produce this result include the straightforward loss of two-electron unidentate ligands, and the insertion of co-ordinated CO into metal-carbon bonds : co + M-R MJCO //OM-‘R c\R The p-elimination and 1,3-elimination reactions are clearly related to each other, and may involve a common (internal) oxidative addition step [pathways (i) or (ii) of Scheme 31. Pathway (iii) of Scheme 3 can only lead to 1,3-elimination, unless further steps intervene, probably involving changes in oxidation number at X and Y. The various pathways of Scheme 3 are, of course, idealizations, in which two-centre interactions are used to describe a many-centre process. They may, nonetheless, have some reality, which could cause differences in primary isotope effects, solvent effects, or chemical requirements.279 2 Organo-transit ion-metal Complexes: Stability, Reactivity, and Orbital Correlations c=c _j M X X \ /--c\ Y ‘x M/ .......C M-[ ...... c:y] -X ....... X-Y Scheme 3 B. Orbital Correlations in Bonding and Bond-br&ng.-Figure 1 compares conventional bonding schemes for fragments of type M(alkene), ML, and MRIRa, M M L Ma MI M L M Figure 1 Bonding in M(alkene), ML, and MR1R2systems Bratermun and Cross where L is a unidentate, more-or-less .rc-accepting, ligand and R1,R2 are two groups similarly o-bonded to the metal. Figure 2 illustrates the fate of the Figure 2 Electron distribution in separated M and alkene, L[os R1-R2 fragments electrons involved in bonding on unimolecular loss of alkene, L, or R1-R2.In Figure 1 those orbitals formally regarded as filled3* are shaded.* The assignment is, of course, artificial and would differ if the metalla-cyclopropane, M-C-C, description were preferred for the alkene complex. The assignment of Figure 2 is, however, not formal but real. In each case four electrons are involved in bonding and these are in a configu- ration (a’)2(a”)2.In each case also, separating the fragments leaves the metal in the configuration (a”)2and the leaving group in the configuration (a’)2,so that there is a loss of two electrons from the co-ordination shell of the metal. Formally, there is no change in oxidation number on loss of L, whereas the oxidation number falls by two on loss of R1-R2.This is because in the former case the an electrons are regarded as localized mainly on the metal in both the bonded and separated states, whereas in the latter, the a” electrons are formally assigned to the ligands in the bound state, although they are left at the metal on separation. Which of these cases the alkene resembles will depend on whether the metalla- cyclopropane description is preferred or, as here, the ligand alkene description. A more rigorous test of the proposed correlation is given by Figure 3. Here, the loss of two mutually cis one-electron donors from an octahedral complex is compared with the loss of L or (in-plane) alkene from a trigonal-bipyramidal complex.The losses are regarded as taking place by way of CzVtransition states to give products of symmetry D4h.This maximizes symmetry at all stages and thus provides the most rigorous test of the proposed correlations. The path discussed is likely to be that in fact preferred, since it minimizes ligand-ligand interactions, and these are presumably generally repulsive. (This is of course not so for the interaction between R1 and R2 themselves, nor for related interactions in insertion, migration, p-elimination, or ring-expansion processes.) Energy orderings within the broad groupings bonding < non-bonding -=z antibonding are uncertain and probably variable, but such is the effectiveness of the correla- * In- and out-of-phase combinations of R’-M and RP-M orbitals are chosen; within the single configuration approximation this description is equivalent to that using localized a-bonded MOs.3* F. A. Cotton and G, Wilkinson, ‘Advanced Inorganic Chemistry’, 3rd edn., Interscience. London, 1972. 28 1 Organo-transition-metal Complexes: Stability, Reactivity, and Orbital Correlations D3h limit c2 v c2 V oh limit Figure 3 Qualitative correlation diagrams for loss of a n-accepting equatorial ligand from a trigonal b@yramid, and reductive cis elimination of R1R2from an octahedral complex. In the D3h and Oh limits, all ligands are treated as equivalent. In the C~v(D3h-D4h) correlation, the e$"ect of an in-plane n-acceptor orbital of the departing ligand is included tions of these broad groupings themselves that such variations are on the whole without chemical significance.[An obvious exception is the correlation of the b2 component of GO (es)in D4h with a bonding orbital of ML4R1R2;thus the formal selection rules for ground-state concerted oxidative addition to square-planar complexes could depend for electron-deficient species on the number and arrangement of non-bonding electrons present. ] More relevant to the present discussion is the general similarity of the correlations involved in reductive eliminations and in ligand loss, and the general preservation in Figure 3 of the correlations implicit in the simplified Figures 1 and 2. Braterman and Cross Contrary to the view of some concerted trans elimination of R1-R2 from an octahedral compound (and, relatedly, trans addition of R1-R2 to a square-planar complex) is not an allowed thermal process within this one- electron model.The ground state of the octahedral complex has the configuration (a’)2(a”)2 (primes representing behaviour under reflection in the xy plane, choosing z to lie along the R1-M-R2 axis), but the separated fragments have the configuration (d22)2,a(R1-R2)2, which is of type (a’)2(a’)2. Such processes have been claimed,36 but may well be non-concerted. 4 Controlling Influencesin Bond Cleavage A. 1,2-Eliminations.-It is as yet too early to say much about factors controlling the 1,2-elimination reaction. The transition state for this reaction must be of low symmetry, precluding simple theoretical discussion, while from an experimental point of view the generality of this recently recognized process is completely unknown. It is worth pointing out, however, that the process is a reduction: This reduction is presumably real as well as formal, with two electrons entering a vacant metal d-orbital, of suitable symmetry for back-donation to the vacant carbene carbon p-orbital.As such, the process may be expected to operate in metals of high formal oxidation state with empty d(n) orbitals. Moreoever, the process alleviates steric crowding and is likely to be favoured when such crowding exists, both on thermodynamic and kinetic grounds. It is relevant that the reaction is established as yet only for TiIV species, which are either octahedrally co-ordinated (TiMe, in ether) or sterically crowded by large (h5-C,H,) groups.It would be of interest to know whether this process applies to WMe6. The conditions for 1,Zelimination would appear to be similar to, but more restricted than, those suggested by us for promotional radical 10~s.~This latter process is available, as 1,Zelimination is not, for compounds in which the metals have half-filled d-orbitals, but no empty d-orbitals, of high electron-demand. B. 1,l-Eliminations.-The situation with regard to 1, l-eliminations is more clear. The essential point of similarity between these eliminations and the ligand loss processes with which they are compared in Section 3 is that they reduce the orbital occupation at the metal by two electrons.Thus compounds in which this orbital occupation is higher than usual for the metal concerned will be more prone to undergo elimination reactions, and any reaction or change in conditions which increases orbital occupation is likely to be followed by a counter-balancing elimination. Such effects are most noticeable towards the end of the transition series, where reducing d-orbital energies and increasing nd -(n + 1)p promotion energies make full orbital occupation leading to 18-electron molecules energetic- ally less fa~ourab1e.l~~~ Thus where 18-electron species are common for iron, 3s R. G. Pearson, Pure Appl. Chern., 1971,21, 145. R. G. Pearson and W. R. Muir, J. Amer. Chem. SOC.,1970,92,5519. P. S. Braterman, Strucrure and Bonding, 1972, 10, 57.Organo-transition-metal Complexes: Stability, Reactivity, and Orbital Correlations ruthenium, and osmium, 16-electron compounds are generally more stable for nickel, palladium, and platinum, and 18-electron molecules of these latter elements readily undergo elimination reactions (Ph8P)4Pt-(Ph3P)3Pt+ Ph,P (Me,As),PtMeCI(C,F,) -(Me,As),PtMeCI + C,F, (PhMe,P),PtCl,Me -(PhMezP),PtC1, + MeCl It is apparent that the formal oxidation number (0,2, and 4,respectively, in the above examples) is here less important than electron availability at the metal. Many similar reactions proceed without isolation of the 18-electron species. Examples of such addition-elimination reactions involving olefins, two-electron unidentate ligands, and two one-electron ligands are given below :15+-45 diphos(Et,P),PtH(GePh,) +(diphos),Pt + 2 Et3P + Ph,GeH (Ph3P),PtHCI + C,(CN), -(Ph,P),Pt{ C,(CN),) + HCl HCI (Et,P),PtMeCI -+ [(Et,P),PtMeHCl,] -+ (Et,P),PtCl, + CHI (cod)PtMe, + 2 py -(py)zPtMe, + cod (Ph3P)zPt(CzHz) + CZPh, +(Ph3P)2Pt(CzPhz) + C,H, (Ph,P),Pt(styrene) + SF5Cl-(Ph,P),Pt(SF,)Cl + styrene The decomposition of (bipy)NiEt, to give butane illustrates the effect of increasing orbital occupation at nickel.The activation energy for decomposition in the solid state is 275 kJ mol-l. In the presence of olefins, however, this para- meter is reduced to ca. 65 kJ mol-l, and 18-electron intermediates of the type Ni(bipy)Et,(olefin) can be isolated :46 Ea= 275 kJ mol-l (bipy)NiEt, --bipy + Ni + C4H10 H,C-CHX E,, = 65 kJ rnol--' (bipy)NiEt,(CH,=CHX) __I____+ (bipy)Ni(CH,=CHX) + C4Hro Labile, 18-electron intermediates are probably also involved in the selective cross-coupling of organic halides and Grignard reagents, catalysed by nickel(@ sa R.Ugo, Coordination Chem. Rev., 1968, 3, 319. sBH.C. Clark and R. Puddephatt, Inorg. Chem., 1971, 10, 18. J. D. Ruddick and B. L. Shaw, J. Chem. SOC.(A), 1969,2969. I1P. Uguagliati and W. H. Baddley, J. Amer. Chem. SOC.,1968, 90, 5446, 44 U. Belluco, M. Giustiniani, and M. Graziani, J. Amer. Chem. SOC., 1967,89,6494. IsC. R. Kistner, J. H. Hutchinson, J. R. Doyle, and J. C. Storlie, Inorg. Chem., 1963,2, 1255. 44 J. Chatt, G. A. Rowe, and A. A. Williams, Proc.Chem. SOC.,1957, 208. R. D. W. Kemmitt, R. D. Peacock, and J. Stocks, Chem. Comnr., 1969, 554. 46 T. Yamamoto, A. Yamamoto, and S. Ikeda, J. Amer. Chem. SOC.,1971,93,3350, 3360. Braterman and Cross and phosphine complexes (Scheme 4).47The key steps, which occur both in the formation of the ‘active catalyst’ and in the catalytic cycle, are the reactions of (biL)NiClzIR’M~X (biL)NiR’2 klR2X ~ (biL)NiR2X (biL)NiR’R* Scheme 4 the organic halide with the diorgano-nickel complexes, and these most likely proceed via oxidative addition of R2X to form 18-electron intermediates, followed by reductive elimination of RIR1or R1R2,respectively. An increase in orbital occupation through nucleophilic interactions might well account for the oft-encountered increase in lability when organometallic com- pounds are dissolved or melted.This effect has often been ascribed to lattice- stabilization effects. Evidence from the i.r. and electronic spectra of the Cr(C0)5 fragment in hydrocarbon (as opposed to argon) matrices indicates that even these ‘inert’ solvents produce interactions. 48 C. Effects of Varying the Metals and Ligands.-As the transition series is traversed left from the nickel group, 18-electron molecules become more stable. This is apparent even within the Group VIII triad: eliminations from Fe(CO), usually require energy (either heat or U.V. irradiation -examples are given later), whereas the process is spontaneous in solution for Ni(PPh3)4.38 In as much as oxidative addition is the reverse of concerted reductive elimination,? such reactions can be rationalized by converse arguments but show the effects of the same trends.Thus oxidative additions involving electron-saturated metals frequently require loss of a two-electron species as a first step. An example is in 7 This is generally true. Polar molecules in solvents of high dielectric constant may react by an ionic mechanism, however, and trans addition can result (see ‘Correlations’ section and ref. 49). The reverse of such reactions is more akin to loss of two-electron unidentate ligands. 47 K. Tamao, K. Sumitnni, and M.Kumadb, J. Amer. Chem. SOC.,1962,94,4374. 48 M.A. Graham, R.N. Perutz, M.Poiiakoff, and J. J. Turner, J. Organometallic Chem., 1972, 34, c34.4s J. P.Collman and W.R. Roper, Adv. Organometallic Chem., 1968, 7, 53. Organo-transition-metal Complexes: Stability, Reuctivity, and Orbital Correlations (h5-(SiPh3)H (h5-PPh3 Scheme 5 Scheme 5.60 Similar elimination reactions are commonly encountered as the first step in ligand-exchange reactions involving 1 8-electron molecules, such as Cr(CO),,S1 Mn(CO)5Br,62 and RU(CO)~(S~CI,)~.~~ A mechanistic study of the polymerization of olefins catalysed by the 1 8-electron species (bipy),FeEt, indicates a preliminary dissociation of an Fe-N bond before the olefins can co-ordinate to iron.64 The trend from 18- to 16-electron molecules is continued past Group VIII to the coinage metals, where stable 14-electron molecules are common, and even 1 6-electron species undergo facile eliminations. A consequence of the lanthanide contraction which is still noticeable in the Group VIII elements is that the change in the nd -(n + 1)p promotion energy as the group is descended is not regular.66 The trend towards lower orbital occupation as the group is descended is therefore also irregular, and the elements of the second row, Ru, Rh, and Pd, show the least tendency towards forming 18-electron molecules, followed by Os, Ir, and Pt.The first-row elements Fe, Co, and Ni are the elements of their groups most likely to be found in 18-electron molecules. The effect of this inversion can be seen in various systems and is particularly relevant to the elimination reactions under discussion.Thus the ndlo 3nds(n + l)pl promotion energies for Ni, Pd, and Pt (1.72, 4.23, and 3.28 eV, respectively) follow the same order as hmaxfor the lowest- energy absorptions in M(PPh3), (M = Ni, 393 nm; Pd, 322 nm; and Pt, 332 nm) and this reflects the trend Ni S Pd -= Pt for M(PPh,), to add a further two-electron ligand.56 Also, in the displacement of PF, by RNC in the complexes (F,P),M (M = Ni, Pd, or Pt), a reaction which follows the expected elimination- addition mechanism, the activation energies for breaking the first M-P bonds show the same irregular sequence.57 Similar comparisons of the tendencies for A. J. Hart-Davies and W. A. G. Graham, J. Amer. Chem. SOC.,1971,93,4388. For reviews see H. Werner, Angew. Chem. Internut. Edn., 1968, 7, 930; W.Strohmeier, Fortschr. Chem. Forsch., 1968, 10, 306. b* A. Berry and T. L. Brown, Znorg. Chem., 1972.11, 1165. 53 R. K. Pomeroy, R. S. Gay, G. 0.Evans, and W. A. G. Graham, J. Amer. Chem. SOC.,1972, 94, 272. 64 T. Yamamoto, A. Yamamoto, and S. Ikeda, Bull. Chem. SOC.Jupun, 1972,45,1104,1111. 6s C. E. Moore, ‘Atomic Energy Levels’, National Bureau of Standards, Circular 467, Washing- ton, U.S. Printing Office, 1952, vol. 2; 1958, vol. 3. 66 C. A. Tolman, W. C. Seidel, and D. H. Gerloch, J. Amer. Chem. SOC.,1972,94,2669. 57 R. D. Johnston, F. Basolo, and R. G. Pearson, Znorg. Chem., 1971, 10, 77. Braterman and Cross M(biL),+ (M = Co, Rh, or Ir; biL = cis-Ph,PCH=CHPPh,) to add either O,, CO, or Hz reveal the same type of discontinuity; Co % Rh < Ir.58 Although such comparisons of isostructural and isoelectronic complexes down an entire periodic group are rare, many effects of the inversion are apparent in compounds of the second- and third-row elements only.For example, several six-co-ordinate iridium(m) complexes, typified by (Ph,P),(CO)IrHCI(SiCI 3), are known, but five-co-ordinate 16-electron species such as (Ph,P),RhHCI(SiCI,) are favoured by rhodium.69 Addition of a further ligand leads to eliminations: co (Ph,P),RhHCl(SiCl,) + (Ph,P),(CO)RhHCl(SiCIJ-co I+. (Ph,P),(CO)RhCI + HSiC13 Also, the fact that (PhMe,P),(cod)RhIMe shows intermolecular phosphine exchange in solution whereas its iridium(r) analogue does notao reflects once again the more facile elimination from rhodium than iridium.The nucleophilicity of the ligands can exert an influence on addition or elimination reactions in two ways which appear at first to be directly conflicting. Strong nucleophiles raise the energy of metal d-electrons, which should favour their formal loss in bond formation and thus favour oxidative additions, but also raise that of the p-orbitals, favouring eliminations. The latter effect is more directional in application however, and is related to the o-bonding trans influence. These effects can be seen in the addition of molecular oxygen to (R,P),(CO)IrCI. The affinity for oxygen generally increasesa1 with increasing base strength of R3P (though steric effects also exert an influence), and the structure of the adducts (R,P),(CO)IrCI(O,) is such that the oxygen atoms lie trans to CO and C1.62 In keeping with the aforementioned trends, the affinity of analogous rhodium complexes for 0,appears to be much less.83 It can be noted at this point that the structure of olefin adducts of d8molecules, like the 0,adducts discussed above, can be described as octahedral (depicting the olefin as a bidentate ligand), though the angle subtended by the olefin at the metal is usually much less than 90"(several structures of this type can be found in ref.1). This is in keeping with the general orbital correlations described herein. The possibility of steric factors influencing elimination reactions cannot be ignored, but we believe their role to be secondary.For example, cis-(Ph,P),PtMe, is stable to 235 "C, whereas the less-cluttered (Ph,P)AuMe, loses ethane at 58 L. Vaska, L. S. Chen, and W. V. Miller, J. Amer. Chem. SOC.,1971,93,6671. E. H. Brooks and R. J. Cross, Organometallic Chem. Rev. (A), 1970,6,227. 6o D. P. Rice and J. A. Osborn,J. Organometallic Chem., 1971,30, C84. G. R. Clark, C. A. Reed, W. R. Roper, B. W. Skelton, and T. N. Waters, Chem. Comm., 1971, 758; L. Vaska and L. S. Chen, ibid., p. 1080. S. J. La Placa and J. A. Ibers, J. Amer. Chem. Soc., 1965,87,2581; M. S. Weininger, I. F. Taylor, jun., and E. L. Amma, Chem. Comm., 1971, 1172. es J. A. McGinnety, N. C. Payne, and J. A. Ibers, J. Amer. Chem. SOC.,1969, 91,6301. Organo-transition-metal Complexes: Stability, Reactivity, and Orbital Correlations 120 OC.ll This is compatible with the expected tendency to lower orbital occupation of gold compared with platinum.The geometrical arrangement of the ligands is important of course, as the leaving groups must be cis. 5 Related Processes These include n -+arearrangements of unsaturated ligands, oligomerizations, the p-interaction, and carbonyl insertions. The conversion of n-allylss or n-cyclopentadienylseb to a-bonded groups by entering nucleophiles resembles olefin elimination and is not remarkable. It is not generally known whether the addition of the nucleophile is the first or second step, and comparison with the previously discussed eliminations would suggest that this will depend upon the degree of orbital occupation of the metal involved. Where some reactions convert 18-electron molecules into 16-electron species, others are followed by eliminations of the groups under consideration :es-s7 co (h6-C,HJPt(PEt JPh +(h'-C,HJPt(CO)(PEtJPh co (h6-C,H,)Ni(PPh,)Ph -(Ph,P)Ni(CO), + PhC6H5 co (hS-C3H,),Ni --f Ni(CO), + biallyl Eliminations similar to the latter example are involved in the ring-closure steps in the cyclo-dimerization and -trimerization of butadiene at nickel atoms ?* -butadiene R3 P -3 (R3P) (cod)Ni (butadiene) 'z * Related elimination reactions forming C-C bonds between neighbouring co-ordinated olefins or acetylenes lead to metalla-cyclopentanes or metalla- cyclopentadienes.Further ring expansions, ring closures, or other eliminations can lead to a variety of products.Many examples of such reactions can be found in refs. 1 and 68. Some recent examples shown in Scheme 6s0-7aserve to indicate the variety of unsaturated molecules which can participate in such oligomeriza- tions. O4 M. L. H. Green and P. L. I. Nagy, Adv. Organometallic Chem., 1965,2, 325. Ob R. J. Cross and R. Wardle, J. Chem. SOC.(A), 1971,2000. H. Yamazaki, T. Nishido, Y. Matsumoto, S. Sumida, and N. Hagihara, J. OrganometallicChem., 1966, 6, 86. O7 G. Wilke, Angew. Chem. Internat. Edn., 1963, 2, 105. O8 P. Heimbach, P. W. Jolly, and G. Wilke, Adv. Organometallic Chem., 1970, 8,29. O* R. Burt, M. Cooke, and M. Green, J. Chem. SOC.(A), 1970,2975.'OR.Burt, M. Cooke, and M.Green, J. Chem. SOC.(A), 1970,2981. 'l J. Ashley-Smith, M. Green, and F. G. A. Stone, J. Chem. SOC.(A), 1970, 3161. lS A. J. Mukhedkar, V. A. Mukhedkar, M. Green, and F. G. A. Stone, J. Chem. SOC.(A), 1970, 3166. Braterman and Cross FH FH CF3 NH Scheme 6 P-Eliminations are only one type of a general class of reactions which proceed via an internal oxidative addition step. Examples are given in Scheme 7.73-76 Most examples are found in the chemistry of the square-planar d8complexes of Rh, Ir, Pd, and Pt, so it is most likely that the reactions are governed by the 7a J. Chatt, R. S. Coffey, A. Gough, and D. T. Thompson, J. Chem. SOC.(A), 1968, 190. 74 J. Schwartz and J. B. Cannon, J. Amer. Chem. SOC.,1972,94, 6226. 76 A. J.Cheney, B. E. Mann, B. L. Shaw, and R. M. Slade, Chern. Comrn., 1970, 1176. ’* G. E. Hartwell, R. V. Lawrence, and M. J. Smas, Chew. Comrn., 1970,912. Organo-transition-metal Complexes: Stability, Reactivity, and Orbital Correlations c1 PBu'2 Prn (BU~~PT"P)~P~CI~ + HCI Scheme 7 same factors as 'normal' oxidative additions and reductive eliminations. In general, however, the conditions for these reactions are poorly documented and the expected intermediates verified in only a few cases. A close approach of the transfer group to the metal is obviously required. Some structure determinations show such an interaction in molecules closely related to those which undergo these intramolecular rearrangements. An example is shown in (l).77 /R \ R (1) R=COzMe 77 D.M. Roe, P. M. Bailey, K. Moseley, and P. M. Maitlis, J.C.S. Chern. Comrn., 1972, 1273. Braterman and Cross P-Interactions and related processes are often involved in homogeneous catalytic reactions such as olefin isomerizationl and H-D exchange.78 The same mechanisms (and controlling influences) probably operate in heterogeneous catalysis reactions by metals and supported metal atoms. The more drastic reactions often observed in heterogeneous processes (such as H-D exchange and C-C bond breaking in saturated hydrocarbons) may result from the high levels of electron unsaturation possible at the surface atoms, as well as from the more rigorous available operating conditions. (Similar processes for homogeneous systems have been reported in a few cases.7g) The insertion of carbon monoxide into metal-carbon bonds is a common reaction, and one of some importance. Like many of the elimination reactions discussed above, the insertions are often initiated by an entering nucleophile, and this suggests that these reactions, also, may be controlled by the level of orbital occupation of the metal.The entering ligand can be the inserting group itself, but when CO is already in the metal co-ordination sphere, it is usually a ‘resident’ group which inserts. The examples in Scheme 880-82demonstrate the similarity in effect of a two-electron unidentate ligand, an olefin, or two one- electron groups in increasing orbital occupation and thus causing CO insertion. co (Et 3P)2Pt MeCl- [(Et ,P),Pt(CO)MeCI] 3 (Et ,P),Pt(COMe)Cl (R13P)(CO)PtC12 R2 2Hg [(R’, P)(CO)PtR2( HgR2)CI,] Rl3P/ \c( -\ HCR20 Scheme8 7sC.Masters, J.C.S.Chem. Comm., 1973, 191. 7BC.Masters, J.C.S. Chem. Comm., 1972, 1258; T. H. Whitesides and R. A. Budnik, ibid.. 1973,87; R. M. Tuggle and D. L. Weaver, Znorg. Chem., 1972,11,2237. G. Booth and J. Chatt, J. Chem. SOC.(A), 1966,634. M. Aresta and R. S. Nyholm, Chem. Comm., 1971, 1459. 8a R. J. Cross and R. Wardle, J. Chem. SOC.(A), 1970, 840. Organo-transition-metal Complexes: Stability, Reactivity, and Orbital Correlations Carbon monoxide can generally be eliminated from the acyls by heating in conditions which remove the gas from the reaction site. The equilibrium RCo(CO), +(RCO)Co(CO), exists in and might reflect the inter- mediate position of cobalt in its ability to accept full orbital occupation.Similar equilibria may exist with the 18-electron complex (Ph,As)(CO),IrMeCl, 83 and, interestingly, with the 16-electron (P~,As)(CO)P~M~C~.~~ Insertion reactions of related molecules such as isocyanide~~~ extend the synthetic value of this process, e.g. [(Ph3P)2Pt(CNR1)R2]+X' e-(Ph3P),Pt(CNR 1)R 2X J R2 I 'x In all of the processes discussed, the possibility of competing eliminations accompanying the desired reaction can lead to unpredictable products. In some cases this has led to unusual new compounds. The examples in Scheme 970~as-88 illustrate some results of competing processes operating alongside CO insertion. Reactions of particular interest are the insertions of CO into Mn-R in the compounds RMn(CO), and their substituted analogues.The insertion is initiated by an entering nucleophile such as CO, amine, phosphine, or, in polar solvtnts, a solvent mo1ecule.l It has been established by isotopic labellings9 that, at least where the entering nucleophile is CO, the key step of this reaction is migration of a methyl group to a neighbouring CO ligand. Such migration involves the move- ment of a ligand across a region of high electron density, and it is not immediately clear how this process is facilitated by the presence of the entering nucleophile. Relevant to this problem, however, is the probability that bimolecular nucleo- philic attack on carbonyl complexes occurs initially at co-ordinated carbon.The probable reaction scheme is shown in Scheme 10. The incoming carbonyl R. W. Glyde and R. J. Mawby, Inorg. Chim. Acta, 1970, 4, 33 1. aaR.W. Glyde and R. J. Mawby, Inorg. Chem., 1971,10, 854. (a) P. M. Treichel and R. W. Hess, J. Amer. Chem. SOC.,1970, 92, 4731. (b)B. Grociani, M. Nicolini, and T. Boschi, J. Organometallic Chem., 1971, 33, C81. B. L. Booth and R. G. Hargreaves,J. Chem. Soc. (A), 1970, 308. M. L. H. Green, L.Pratt, and G. Wilkinson, J. Chem. SOC., 1960,989; E. Weiss, R. Merenyi,and W. Hubel, Chem. Ber., 1962.95, 1170. R. Baker, B. N. Blackett, and R. C. Cookson, J.C.S. Chem. Comm., 1972,802. saK. Noack and F. Calderazzo, J. Organometallic Chem., 1967, 10, 101.(a) K. Caulton and R. F. Fenske, Inorg. Chem., 1968,7, 1273; (b) D. J. Darensbourg and M. Y. Darensbourg, Inorg. Chim. Actu, 1971, 5, 247. Braterman and Cross 0 Scheme 9 group of (3) is correctly placed to accept charge from the dzy orbital of the 4t metal (labelling the initial Mn-CH, and Mn-CO directions as x and y axes), thus reducing the barrier for the migration (3) --f (4) [or (3) -(5) if methyl and entering carbonyl migration are synchronous]. Extreme valence-bond formula- tions of the process, such as (6) -(7), illustrate both the formal analogy between Organo-transition-metal Conlplexes: Stability, Reactivity, and Orbital Correlations co c-0It *C-Me (OC)3 Mn-4 C 0 CO (OC)3Mnf c -co0 (5) Scheme 10 methyl (metal-to-ligand) migration and reductive elimination, and also that here proposed between the concomitant reverse process, carbonyl (ligand-to-metal) migration, and oxidative addition.Whether or not these detailed pathways are 0 0 11 ?#C-MQ II (OC)3Mn-MeI\c-’c =o C II II ultimately substantiated, it is already clear that such speculations can give a new unity to organometallic chemistry, relating and combining both synthetic and mechanistic aspects .

ISSN:0306-0012    

DOI:10.1039/CS9730200271

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

The Energetics of Neighbouring Group Participation By M. I. Page DEPARTMENT OF PURE AND APPLIED CHEMISTRY, THE POLYTECHNIC, QUEENSGATE, HUDDERSFIELD, HD1 3DH 1 Introduction Seminal in the development of current chemical thought has been the realization that the rates and the position of equilibria associated with reactions of functional groups are strongly dependent upon the nature of the remainder of the molecule. Such effects of a substituent are usually rationalized in terms of electronic effects transmitted through space or through bonds and steric effects. However, a substituent may exhibit its influence by interacting directly with the reaction centre through partial or complete bonding. In such cases the phenomenon is described as neighbouring group part icipati0n.l Further classification depends upon how and when participation occurs.If the presence of the neighbouring group increases the rate of the reaction then the term 'anchimeric assistance' is appropriate.2 In this case the product may or may not be that expected in the absence of participation [equations (1)3 and (2),4 0 0 respectively]. In equation (l), the neighbouring group is 'regenerated' in the product and so the phrase 'intramolecular catalysis' is often applied to reactions of this type. If neighbouring group participation occurs after the rate-determining step, i.e. in the product-determining step, then the structure of the product is affected but there is no anchimeric assistance. S. Winstein and R. E. Buckles, J.Amer. Chem. Soc., 1942, 64, 2780. * S. Winstein, C. R. Lindergren, H. Marshall, and L. L. Ingraham, J. Amer. Chem. SOC., 1953, 75, 147. T. C. Bruice and S. J. Benkovic, J. Amer. Chem. SOC.,1963, 85, 1. H. W. Heine, A. D. Miller, W. H. Barton, and R. W. Greiner, J. Amer. Chem. SOC.,1953, 75, 4778. The Energetics of Neighbouring Group Participation Between the two extremes of an intramolecular reaction, in which the reactants are covalently bound to the same skeleton, and an intermolecular reaction, e.g. equation (3),3 lies a vast field of chemistry the classification of which as involving 0 + II RMezNt MeCC&Ph--, RMezN-C-Me -!& RNMez+ MeCOzPh + PhO' (3) neighbouring group participation is questionable. These reactions involve the pre-association of catalyst or reactant and substrate through usually weaker forces, often leading to a reversible pre-equilibrium step.This class of reaction includes enzymatic, micellar, and metal-ion catalysis or simply a pre-association step favoured by hydrophobic interactions [equation (4)].5 > > t PhO-(4) Two approaches are commonly adopted to demonstrate the involvement of neighbouring group participation in a given reaction. Often the magnitude of the anchimeric assistance provided is determined by comparing the rate of the neighbouring group participation reaction with the rate expected in the absence of participation.s For example, the magnitude of homoallylic participation in the acetolysis of anti-norborn-2-en-7-yl tosylate, equation (3,is quoted as 10" by +TsO' , ~ __TLI& 6'AcOH comparison of the first-order rate constant for this reaction with the first-order rate constant for the acetolysis of the analogous saturated compound.This * C. A. Blyth and J. R. Knowles, J. Amer. Chem. Soc., 1971, 93, 3017; D.G. Oakenfull, J.C.S. Perkin II, 1973, 1006. B. Capon, Quart. Rev., 1964, 18, 45.' S. Winstein and M. Shatavsky, J. Amer. Chem. Soc., 1956,78, 592. Page approach is similar to that used in estimating the effect of substituents upon the reaction rate. The assumption is made that the rate-determining step of the reaction is the samein the absence and presence ofparticipationor ofthesubstituent group, and therefore it may be said that the substituent or neighbouring group stabilizes the transition state by so many kJ mol-l. It can thus be seen that a classification of some reactions in terms of either normal substituent effects or neighbouring group participation may become artificial in some circumstances.The second approach is to compare the rate constant for the intramolecular reaction with that of the analogous intermolecular one. This is obviously limited to those systems which have observable analogous intermolecular reactions (although in their absence a lower limit to the magnitude of anchimeric assistance may be obtained). For example, the intermolecular reaction (3) is analogous to the intramolecular reaction (l), the respective rate constants at 25 "C being 1.33 x dm3 mol-1 s-l and 1.67 x 10-l s-I.The ratio of these rate constants, 1260, has the units of mol dm-3 or molarity, M, and is known as the effective molarity or effective concentration. In this particular example, this ratio repre- sents the concentration of trimethylamine required to cause phenyl acetate to undergo reaction (3) with a pseudo first-order rate constant equal to that at which the intramolecular reaction (1) occurs. Such large concentrations as 1260 M are, of course, physically unattainable. It should be noted that the numerical value of this ratio depends upon the units employed to express the second-order rate constant and reactions of type (1) and (3) cannot be rigorously directly compared using thermodynamics because of this units problem.The use of mole fractions would remove this criticism8 but it would not affect the relative degree of anchi- meric assistance of various intramolecular reactions. This review will therefore adopt the literature practice of using effective concentrations as a measure of the magnitude of anchimeric assistance. The differences in these two approaches may be seen by considering reaction (1) again. The spontaneous or water-catalysed hydrolysis of phenyl acetate has a first-order rate constant of 1.8 x lo-* S-~,~JO therefore by the first method described the magnitude of anchimeric assistance is 10'. From the comparison of reactions (1) and (3) it has already been mentioned that the effective concentra- tion is 1260 M.These two measurements of neighbouring group participation indicate the effectiveness of an intramolecular amino-group compared with inter-molecular 55 M water and an intermolecular amino-group, respectively, in bring- ing about the hydrolysis of the ester group. In the first method not only is the molecularity different but also the nucleophilicity of the attacking group. The effective concentration provides a measure of just the effect of intramolecu- larity. Although so far only rates of reactions have been considered, the effect of intramolecularity is also manifested in equilibria. For example, the equilibrium W. Kauzmann, Adv. Protein Chem., 1959, 14, 1. W. P. Jencks and M. Gilchrist, J. Amv. Chem. SOC.,1968, 90, 2622. loJ. F.Kirsch and W.P. Jencks, J. Amer. Chem. SOC.,1964, 86, 837. 297 The Energetics of Neighbouring Group Participation constant for succinic anhydride formation, equation (6), is 3 x lo5M larger than that for acetic anhydride formation.11J2 Since the extensive review by Capon* on neighbouring group participation and intramolecular catalysis, there have been numerous reviews on the subject which have mainly confined themselves to citing exarn~les.~~-~~ Wide variations in the magnitude of anchimeric assistance have been observed, e.g. reactions (7)-(9), sffective concsntra t ion (E .C.) cornpared with EtOH + AcOH + H+ (7) Is 79d9 E.C. compared with EtOH + AcOH f H* (8) is 106 M19 E.C.compared with PhOH + AcOH + H’ (9) is lof6M’O W. P.Jencks, F. Barley, R. Barnett, and M. Gilchrist, J.Amer. Chem. SOC.,1966,88,4464. T. Higuchi, L. Eberson, and J. D. McRae, J. Arner. Chem. SOC.,1967, 89, 3001. l9 T. C. Bruice and S. J. Benkovic, ‘Bioorganic Mechanisms’, W. A. Benjamin, New York, 1966, Vol. 1. I4 W. P. Jencks, ‘Catalysis in Chemistry and Enzymology’, McGraw-Hill, New York, 1969. l6 T. C. Bruice, in ‘The Enzymes’, ed. P. D. Boyer, Academic Press, New York and London, 3rd edn, 1970, Vol. 2, p. 217. l6 A. J. Kirby and A. R. Fersht, Progr. Bioorg. Chem., 1971,1,1. l’ B. Capon, Essays in Chemistry 1972, 3, 127. B. Capon and C. W. Rees, ‘Organic Reaction Mechanisms’, Wiley-Interscience, London, 1965-1972. Page and have led to the suggestion of new concepts and descriptive phra~eology.~~~~~ However, the purpose of this Review will be to attempt to present an overall rationalization of neighbouring group participation reactions in terms of presently known and accepted theories.2 Energetics Sometimes there is a linear relationship between the rates of a series of related intramolecular reactions and their equilibrium constants.21 In such cases a special explanation for the rate differences which is peculiar to the activated complex is not required. Furthermore, the favourable reactions of intramolecular systems over their intermolecular counterparts are manifested in both rates and equilibria. A rationalization of this phenomenon may thus be sought by examin- ing the thermodynamic free-energy differences between reactants and products or between reactants and activated complex.The latter is possible by using the transition-state theory22 for reaction rates. This approach has the advantage of enabling one to examine the thermodynamic state of the molecules, and so with neither rates nor equilibria is it then necessary to be concerned with the prob- ability, kinds, or frequency of collisions between molecules. According to the transition-state theory22 all activated complexes decompose with the same frequency (kT/h),the rate is therefore determined entirely by the free-energy difference between reactants and activated complex, and it is irrelevant to the rate how that complex was reached. The free-energy difference between two states is given by equation where dEoois the standard temperature-independent potential energy change and comprises all electrical, quantum mechanical, and steric effects, i.e. it dGo= dEoO-dRTln Q (10) includes polar, resonance, and solvation effects, van der Waals interaction, bond angle, bond length, and torsional strain. The second term represents the difference in the partition functions (Q) of the two states and is a measure of the temper- ature-dependent kinetic energies of motion.The value of the function depends on the motion or degrees of freedom of the molecule as a whole and of the atoms in that molecule. To a useful approximation the partition function may be represented as a product of factors, one for each of the normal modes in terms of which classical mechanics analyses the motions involved.Typically these are translation, rotation, vibration, and internal rotation. As the partition function contribution to the free energy can often be estimated quantitatively in the gas- phase2* this will be considered first, followed by an extrapolation of the conclu- l9 D. R. Storm and D. E. Koshland, jun. J. Amer. Chem. SOC.,1972, 94, 5805. so S. Milstein and L. A. Cohen, Proc. Nat. Acad. Sci. U.S.A., 1970, 67, 1143. 81 See, for example, refs. 17 and 19. *I S. Glasstone, K. J. Laidler, and H. Eyring, ‘The Theory of Rate Processes’, McGraw-Hill, New York, 1941 ;H. S. Johnston, ‘Gas Phase Reaction Rate Theory’, Ronald Press Co., New York, 1966. 23 R. W. Taft, in ‘Steric Effects in Organic Chemistry’, ed.M. S. Newman, Wiley, 1956, Chap. 13. 34 K. S. Pitzer and L. Brewer, ‘Thermodynamics’, McGraw-Hill, New York, 1961. 299 The Energetics of Neighbouring Group Participation sions obtained to the liquid phase. Finally, the contribution of potential energy changes to intra- and inter-molecular reactions will be considered. 3 Entropy Differences There are different degrees of freedom lost in intramolecular and analogous intermolecular reactions giving rise to large differences in the entropy change between the two systems, Consider a bimolecular reaction (1 1) and a comparable intra- and uni-molecular reaction (12) in which the product on the right-hand A+B S A-B trans 3 3 3 rot 3 3 3 vib 3n-6 3n'-6 3n +3n'-6 A-Bu trans 3 3 rot 3 3 vib 3n-6 3n -6 side of these equations may represent a stable molecule or a transition state.For a non-linear molecule containing n atoms there are three degrees of translational freedom, three degrees of rotational freedom, and (3n-6) degrees of vibrational freedom. Reaching the transition state or monomolecular product of a bimolecular reaction thus reduces the number of independent species in the system with a consequent loss of three translational and three rotational degrees of freedom. There is a gain of six new vibrational modes in the product of equation (11). However, in the unimolecular reaction (12) there is no net change in the number of degrees of freedom of translation, rotation, and vibration.The differences in energy between these two systems, in the gas phase, may be estimated by Calculat- ing the partition functions and thence the related thermodynamic quantities24 e.g.: S = R In Q + RT-d In Q dT Some typical values of these quantities are shown in Table l.as The magnitude of the entropy associated with translational motion (Sotrans)is the only entropy term which depends on the space available to the molecule, hence it is necessary to specify some standard state for a reaction which involves O6 M.I. Page and W. P.Jencks, Proc. Nat. Acad. Sci. U.S.A., 1971, 68, 1678. Page Table1 Typical entropy and free-energy contributions from translational, rotational, and vibrational motions at 298 Ka Motion SO Ho-Hoo Go-Hoo J K-l mol-1 kJ mol-1 kJ mol-1 Three degrees of translational freedom for mol.wts. 20-200 standard state 1 M 120-148 6.2 -29.6 to -37.9 Three degrees of rotational freedom water 43.9b 3.7 -9.4 n-propane 90.0b 3.7 -23.1 endo-dicyclopentadiene 113.8b 3.7 -30.2 Internal rotationC 13-21 1 Sd -2.4 to -4.8 Vibrations w/cm-l lo00 0.4 0.13 0.0 800 0.8 0.21 -0.04 400 4.2 0.84 -0.42 200 9.2 1.46 -1.30 100 14.2 1.92 -2.33 a From ref. 25. b Symmetry corrected. C See text. d Typical value; this quantity is a function of the barrier to rotation and the partition function. a change in the number of molecules present in the system. This review will adopt a standard state of 1 mol dm-3 (1 M). The translational entropy of a molecule is proportional to its mass, the temperature, and the volume of space available to it.For a standard state of 1 M and at 298 K, physical constants make up the bulk of the contribution to Sotrans, which varies as 3/2R In Mywhere M is the mole- cular weight :* Sotrans = 82.22 + 28.72 log M (14) The translational entropy of most molecules therefore has only a small depend- ence upon mass; e.g. if the molecular weight is increased ten times the value of the translational entropy is increased by 28.7 J K-l mol-l. A molecule rotates about its centre of gravity and the rotational entropy (Sorot)is proportional to the moment of inertia, the temperature, and the symmetry of the molecule (a). Sorot varies as 8 R In (IAIBIc)where IA, IB, and Ic are the three principal moments of inertia of the molecule.At 298 K Sorotis given by equation (15) where D is the product of the three principal moments of inertia. So again for average size molecules the rotational entropy has a relat- Sorot = 70.96 + 9.573 log (D x lo1") -19.15log a (1 5) *All entropies are in J K-lmol-'; 4.184 J K-l mol-' = 1 cal deg mol-I. 301 The Energetics of Neighbouring Group Participation ively small dependence upon the structure of the molecule, e.g. a doubling of all three principal moments of inertia increases Sorotby only 8.8 J K-l mol-l. The vibrational entropy (S’vib) of a molecule depends upon the frequency of vibration and the temperature, as shown in equation (16) where u = h cw/kT and w is the frequency in cm-l.For frequencies less than 200 cm-1 and at 298 K equation (16) may be approximated by equation (17). Vibrational frequencies greater than 1000 cm-l make a negligible contribution to the entropy of the R In (1 -molecule at 298 K. Although S’vib for each vibrational mode is generally small (Table l),the total entropy contribution resulting from vibrational motion within the molecule can be significant because of several low-frequency vibrations. If groups of atoms within a molecule are connected by a single electron-pair bond then there is an internal rotational motion of these groups against each other and an associated entropy. Some typical values for the entropy of internal rotation (S’i.r.) are given in Table 1, and are dealt with in more detail below.For an association reaction such as (ll), three translational and three rota- tional degrees of freedom are converted into vibrational modes and possibly internal rotations. If these new modes are of high frequency (> lo00 cm-I), and there are no other changes in the contribution of internal motions to the entropy upon conversion of reactants into product or transition state, then association will be accompanied by a large increase in free energy. This is due to the loss of translational and rotational entropy which, for average size molecules, causes an entropy change of ca. -210 to -250 J K-l mol-l, equivalent to 63-75 kJ mol-l at 298 K. This negative entropy change makes the equilibrium or rate constant for a bimolecular reaction unfavourable by a factor of 1011-1013.There may be a small compensation of the Ioss of translational and rotational entropy due to the increased size and mass of the product of transition state, but this total loss represents the maximum change upon association. (In the rare situation of the reaction being accompanied by a stiffening of low-frequency vibrations upon conversion of reactants into product, then the reaction may be slightly more unfavourable than this ‘maximum’.) Indeed, a few bimolecular associations have entropy changes which are due almost entirely to the loss of translational and rotational entropy. Examples of this are the low-temperature hydrogenation of ethylene,26 some gas-phase radical molecule reactions with ‘tight’ transition state~~~p~~ and the dimerization of propene to cyclohexane.The entropy changes accompanying the latter reaction20 are given in Table 2 for a 26 E. A. Guggenheim, Trans. Faraday SOC.,1941, 37,97. 27 S. Bywater and R. Roberts, Canad.J. Chem., 1952, 30, 773. 28 S. W. Benson, ‘Thermochemical Kinetics’, Wiley, New York, 1968, Chap. 3. es L. S. Kassel, J. Chem. Phys., 1936, 4,435; K. S. Pitzer, ibid., 1937,5,473; C. W. Beckett, K. S.Pitzer, and R. Spitzer, J. Amer. Chem. SOC.,1947, 69,2488. Page standard state of 1 M and 298 K where SOint is the entropy due to internal motions (vibrations and internal rotations). Table 2 Sotrans 128.8 128.8 137.4 dS0tran.q = -120.2 Sorot 89.2 89.2 95.3 dSorot = -83.1 Saint 22.3 22.3 38.9 ASOint = -5.7 sototal 240.3 240.3 271.6 dSOtota1 = -209.0 However, a more common situation is that the product has several new internal rotations or low-frequency vibrations which compensate for the loss of translational and rotational entropy.For example, the gas-phase dimerization of cyclopentadiene (Table 3) gives a product containing low-frequency internal motions30 which causes the entropy change to be 44 J K-l mol-l less negative than that from just con~idering~~~~~~ 32 changes in rotational and translational entropy. Table 3 Sotrans 134.5 134.5 143.1 dSOtrans = -125.9 Sorot 99.6 99.6 113.8 ASOrot = -85.4 S’int 13.9 13.9 71.8 dSOint = +M.O Sototal 248.0 248.0 328.7 dSototal r -167.3 The overall calculated entropy change may be compared with experimental values of from -130 to -167 J K-l m01-l.~~This appears to be quite a general phenomenon since nearly all gas-phase Diels-Alder reactions have activation and equilibrium entropies of ca.-125 to -170 J K-l mol -l. 34 In the limit of a very ‘loose’ transition state or product the low-frequency motions can make the overall entropy change for a bimolecular reaction relat- ively small. For example, the association of two radicals is generally considered 3o G. B. Kistiakowsky and J. R. Lacher, J. Amer. Chem. SOC.,1936,58, 123. ,lA. Wassermann, Proc. Roy. SOC.,1941, A178, 370; H. E. O’Neal and S. W. Benson, Internat. J. Chem. Kinetics, 1970, 2, 423.aa H. E. O’Neal and S. W. Benson, J. Chem. Eng. Data, 1970, 15, 266. 33 W. C. Herndon, C. R. Grayson, and J. M. Manion, J. Org. Chem., 1967, 32, 526; G. R. Schultze, Oel Kohle, 1938,6,113; G.A. Benford and A. Wassermann, J. Chem. SOC.,1939, 362; J. B. Harkness, G. B. Kistiakowsky, and W. H. Mears, J. Chem. Phys., 1937,5,682. A. Wasserman, ‘Diels-Alder Reactions’, Elsevier, Amsterdam, 1965. The Enzrgetics of Neighbouring Group Participation to be encounter and thus the transition state is very ‘loose’. Typically, the standard entropy change for the combination of two methyl radicals is -128.9 J K-l mol-l, but the entropy of activation is only about -55 J K-l mol-1.28 The difference of about 74 J K-l mol-1 may be rationalized by postu-lating a ‘loose’ activated complex with four low-frequency rocking modes of the methyl groups, a free internal rotation and an increased rotational entropy (Table 4).28p36 Table 4 * aCH3*+ CH,.-+[H3C CH3]l sotrans 115.9 115.9 124.7 ASOtran, = -107.1 sorot SOint 44.8 2.1 44.8 2.1 82.0a 57.76 ASOrot ASOint = = -7.6 + 53.5 sototalc 162.8 162.8 264.4 dSototal = -61.2 aAssuming a C-C distance of 3.5 A. Qncluding free internal rotation and 4 rocking modes of 150 cm-’ each. CExcluding electronic contributions. Alternatively, the reaction may be viewed as the collision of two species which are freely rotating within the collision complex as if they were separated from each The formation of the transition state thus involves the conversion of translational into rotational degrees of freedom.38 This treatment, of course, gives the hard-sphere collision theory approximation of transition-state theory,3B and for average size spheres this corresponds to an entropy change of about -40 J K-l mol-l, corresponding to a collision frequency of M-l s-l. In summary, it may be stated that in the gas phase for a standard state of 1 M and 298 K, the entropy change accompanying bimolecular associations may vary from ca. -45 to -210 J K-l mol-1 depending on the ‘tightness’ or ‘looseness’ of the transition state or product. However, for reactions which are not col- lision-controlled, the entropy change will generally be ca. -125 to -170 J K-l mol-l, making biinolecular associations unfavourable by factors of 107-109. Unimolecular reactions.-For intra- and uni-molecular reactions of the type indicated in reaction (12) the translational contribution to the thermodynamic functions is the same for reactant and product or transition state, and hence changes in these functions are independent of the standard state.An examination of the entropy changes accompanying an intramolecular reaction which proceeds viaa cyclization step suggests that they may be divided into the following categor- ies: (i) dSrot:there is a decrease in the moment of inertia associated with the cyclization of an extended chain. However, this effect will generally be small and 36 See, however, R. M. Marshall and J. H. Purnell, J.C.S. Chem. Comm.,1972, 764; R.Hiatt and S. W. Benson, J. Amer. Chem. SOC., 1972,94, 6886. M S. W. Benson, Adv. Photochew., 1964,2, 1 ; J. H. Purnell and C. P. Quinn, J. Chem. Soc., 1964,4049; H. E. O’Neal and S. W. Benson, Internat. J. Chem. Kinetics, 1969,1,221. 37 T. S. Ree, T. Ree, H. Eyring, and T. Fueno, J. Chem. Phys., 1962, 36,281. M. I. Page, Biopliys. Biochem. Res. Comm., 1972, 99, 990. 39 S. W. Benson, ‘Foundations of Chemical Kinetics’, McGraw-Hill, New York,1960, p. 273. Page decrease the rotational entropy by less than 8 J K-l mol-l; (ii) A&.,. :cyclization is accompanied by the conversion of restricted internal rotations into torsional modes and this will generally represent a negative entropy change; (iii) dSvib: represents the change due to changes in bond stretching and bending vibrations upon cyclization.This will also generally be small and for most cyclizations be between -8 and +8 J K-l mo1-1;40 (iv) ASs,: allowance must be made for the different symmetry properties of the cyclic and acyclic species. Ssym= Rln (a/n)where CJ is the total symmetry number of the molecule and n is the number of optical isomers.24 This will also generally be small. The loss of internal rotation is usually the largest contribution to changes in entropy upon cyclization. The magnitude of the thermodynamic functions for internal rotations has been estimated theoretically and is good agreement with experiment. The value depends markedly upon the barrier to For example, the entropy of free internal rotation in ethane is 12.38 J K-l mol-1 at 298 K, but the barrier to rotation of 12.6 kJ mo1-1 reduces this to 6.95 J K-' rn01-l.~~For the more complex hydrocarbons the entropy of internal rotation increases owing to the increased moments of inertia but this is offset by an increased barrier to rotation.It has been calc~Iated~~ that the entropy contribu- tion per internal rotation in an aliphatic hydrocarbon is 18.4 J K-' mol-1 at 298 K. This may also be seen by examining the entropy changes accompanying ring closure of aliphatic hydrocarbons shown in Table 5.25The entropy changes are primarily a consequence of losses of internal rotation, cyclization of Cn linear hydrocarbon transforming (n -1) internal rotations into ring vibrations. If the small changes in overall rotational entropy, symmetry, stretching and bending vibrations, and the loss of two hydrogen atoms upon cyclization are ignored, the entropy differences between linear and cyclic compounds gives an entropy loss per internal rotation of 11.3-18 J K-l mol-l (column 3).The varia- tion is due to differing low-frequency motions in the cyclic product. For example, the pseudorotation of cyclopentane contributes 24.3 J K-l mo1-1 to the entropy of the and the out-of-plane vibration of cyclobutane is associated with an entropy of 15.9 J K-lm~I-l.~~After correction for such low-frequency motions in the C4,C,, C,, and C, rings the entropy loss per internal rotation (column 4) is 15.5 to 20.5 J K-l mol-l. Entropies of activation for ring-closure reactions are similar or smaller (Table 5).Benson and O'Neal have used an entropy of internal rotation of 20 J K-l mol-l to calculate the entropies of cyclic and polycyclic hydrocarbon^,^^ and similar values to rationalize the entropies of activation of unimolecular A value of 17-21 J K-l mol-1 for the 40 H. E. O'Neal and S. W. Benson, J. Phys. Chem., 1967,71, 2903. *l K. S. Pitzer,J. Chem. Phys., 1937,5,469; 1946,14,239; K. S. Pitzer and W. D. Gunn, ibid., 1943,10,428; K. S. Pitzer and J. C. M. Li, J. Phys. Chent., 1956,60,466. IsE. A. Guggenheim, Trans. Faraday SOC.,1941, 37,97. 43 K. S. Pitzer, J. Chenl. Phys., 1940, 8, 711, 718; W. B. Person and G. C. Pimentel, J. Amer. Chem. SOC.,1953,75, 532. 44 C. W. Beckett, K. S.Pitzer, and R. Spitzer, J. Amer. Chem. SOC.,1947, 69, 2488; F. A. Miller and R. G. Inskeep, J. Chem. Phys., 1950, 18, 1519. 46 G. W. Rathjens, N. K. Freeman, W. D. Gwinn, and K. S. Pitzer, J. Amer. Chem. Sac., 1953.75, 5634. The Energetics of Neighbouring Group Participation Table 5 Entropy changes accompanying cyclization at 298 K in J K-’ mol-l Systema dso -AS0 -ASOcorr no. int. rot. no. int. rot. 32.2 16.1 16.1 29.3 29.3 45.6 15.2 20.5 43.1 21.5 55.6 13.9 20.0 54.8 18.3 88.7 17.8 17.8 87.9 22.0 82.8 13.8 15.6 82.0 6.4 79.5 1.3 16.4 78.6 3.1 Transition State ASS -AS* no. int. rot. Six-membered Claisen rearrangement* -8 to -59 2.9 to 19.7 Cope rearrangementC -33 to -50 11.3 to 16.7 Ester pyrolysesd +I7 to -33 -5.4 to +11.3 Five-membered EtNOz-C2H4 + HN02e -38 18.8 Four-membered Elimination of HX from alkyl halide$ + 20 to -13 -20 to + 13 a From ref.25; data from refs. 32, 61, and 140. * H. Goering and R. R. Jacobson, J. Amer. Chem. Soc., 1958,80,3277; W. N. White and C. D. Slater, J. Org. Chem., 1962,27,2908. c E. G. Foster, A. C. Cope, and F. Daniels,J. Arner. Chem. SOC.,1947,69,1893. Ref. 40. M. C. Frkjacques, Compt. rend., 1950, 231, 1061. Page entropy per internal rotation in an aliphatic hydrocarbon may therefore be accepted with confidence, The loss of entropy upon freezing an internal rotation is partially compensated by a favourable enthalpy function change of about 2 kJ mol-l, so that the increase in free energy upon cyclization is about 4 kJ mol-1 per internal r~tation,~~~~~ which corresponds to a rate factor of about 5 at 298 K.It is worth noting that the entropy change accompanying ring closure to seven- and eight-membered rings is less than that for the six-membered ring (Table 5). This is presumably due to low-frequency torsional motions of the methylen groups compensating for the loss of entropy associated with internal rotation. The generally observed higher free energies of formation of seven- and eight- membered rings must thus be due to an enthalpy and not an entropy effect. Also shown in Table 5 are the entropy changes accompanying ring closure of the corresponding alkenes, which are not significantly different from those of the saturated system which initially has one more internal rotation.This is a conse- quence of the reduced barrier to rotation of a group adjacent to a double bond and of changes in the symmetry axis in the acyclic compound,46 and brings into question the common assumption that ring-closure reactions of unsaturated systems are favourable entropically compared with those of saturated systems. Gas-phase Examples.-Unfortunately, there are few suitable gas-phase data available to test the predictions made above. For reactions proceeding via 'loose' transition states the advantage of intramolecularity should be less marked. The association of radicals is unlikely to have an activation en erg^,^'^^^ and the frequency factors for the intramolecular ring closure of biradicals are estimated** to be only 10-100 times greater than the corresponding intermolecular reaction of about 1Olo M-l s-1.35 These reactions proceed through loosely structured activated complexes since the transition state closely resembles the initial state, the free radical or biradicaL2* The entropy change accompanying the bimolecular reaction is thus not as great as it would be for a more common tighter transition state.For example, the entropy of activation for the gas-phase thermal disrotat- ory ring closure of hexa-cis,cis-l,3,5-triene,reaction (18), which might be regarded as an intramolecular analogue of the Diels-Alder reaction, is -20 J K-l m~l-~.~~The difference between this value and that for bimolecular Diels- Alder reactions, such as cyclopentadiene dimerization (AS4 = -160 JK-l mol-1,32333see Table 3), corresponds to an entropy advantage of lo7M at 25 "C for the intramolecular reaction.46 K. S. Pitzer, J. Chem. Phys., 1937,5,473, L. S. Kassel, J. Chem. Phys., 1936,4,435. 47 J. A. Kerr and A. F. Trotman-Dickenson, Progr. Reaction Kinetics, 1961,1, 108. H. E. O'Neal and S. W. Benson, J. Phys. Chew., 1968,72,1866. 40 K. E. Lewis and H. Steiner, J. Chem. Soc., 1964, 3080. The Energetics of Neighbouring Group Participation Solution Reactions.-The previous considerations showed that, in the gas phase, intramolaular reactions may have a large entropic advantage over bimolecular associations. It has recently been suggested that this is also true for reactions carried out in Entropy is an anthropomorphic concept even at the purely phenomenological level,so and in the absence of a satisfactory theory of liquidsK1Ss2it is difficult to assign entropy changes to particular molecular motions in the condensed phase.s3 The application of statistical mechanics to liquids is difficult because translational and rotational motions may not be and a suitable model and potential field is required to evaluate the partition functions of such Furthermore, observed entropy changes in solution are seldom easy to interpret because of solvation effects.The entropy of vaporization of a liquid is primarily determined by the increase in volume accompanying the process of vaporization, the acquisition of rota- tional degrees of freedom frozen or restricted in the liquid and any other changes arising from loss of order in going from the liquid to the gas.Trouton’s rule states that the molar entropy of vaporization for all non-associated liquids is about 85 J K-l mol-1 at a vapour pressure of 1 atm.56 However, approximately half of this quantity is simply the entropy of dilution from a pure liquid to a standard state of 1 atm, 0.045 M. For example, if the pure liquid is 10 M, then only 40 J K-l mol-l of the entropy change is due to effects other than dilution.25 The interpretation of this difference between liquids and gases has been rational- ized on a molecular IeveP although the models used have been ~riticized.~~*~~ It is questionable whether the partition function in the condensed phase can be separated into various ‘contributions’, but it is a useful model to ascribe the bulk of this difference to the loss of translational entropy with little loss of entropy that is attributable to rotation in the gas pha~e.~~~~~~~~ Vibrational motions, as determined by i.r.and Raman bands, are not greatly perturbed on transfer from the vapour to the liquid.6D Empirical rules for vaporization entropies are valid for solutions to the same extent as for pure liq~iids.~~~~~ The difference in the entropy change accompanying a reaction upon transfer 6o E. T. Jaynes, Amer. J. Phys., 1965,33, 391. 61 J. A. Barker and D. Henderson, Ann. Rev. Phys. Chem., 1972, 23, 439, and references therein.sa J. H. Hildebrand and R. L. Scott, ‘The Solubility of Non-Electrolytes’, Dover, New York, 1964, and references therein. 63 J. H. Hildebrand and E. B. Smith, J. Chem. Phys., 1959, 31, 1423. 54 G.W. Ewing, Accounts Chem. Res., 1969,2,168; H. Welsh and R. Kreigler,J. Chem. Phys., 1969,50, 1043; G. W. Ewing and H. Chen, J. Chem. Phys., 1969,50,1044. Ks F. Trouton, Phil. Mag., 1884, 18, 54. 66 D. H. Everett, J. Chem. Soc., 1960,2566; H. S. Frank, J. Cheni. Phys., 1945, 13,478,493; J. G. Kirkwood, J. Chem. Phys., 1950, 19, 380; H. Eyring, D. Henderson, and W. Jost, ‘Physical Chemistry-An Advanced Treatise’, Academic, New York, 1971, Vols 8A-B Chap. 5. K7 J. S. Rowlinson, Trans. Faraday Soc., 1971, 67, 576. 68 L. A. K. Staveley and W.I. Tupman, J. Chem. SOC.,1950,3597; A. Bondi, J. Phys. Chem., 1954,58,929; L. H. Thomas, J. Cheni. SOC.(A), 1968,2609; L. A. K. Staveley, Ann. Rev. Phys. Chem., 1962, 13,351. H. S. Frank and M. W. Evans, J. Chem. Phys., 1945,13, 507. 6o 1. M. Barclay and J. A, V. Butler, Trgqs,Fgraday. Soc.. 1938, 34, 1445. Page from the gas to the liquid phase may be deduced from an empirical relationship between the entropies of vaporization at any temperature and the normal boiling point,62or from tabulated values.s1 For example, the dimerization of cyclo- pentadiene, reaction (19), has an entropy change of -167 J K-l mol-1 at 25 "C in the gas phase at a standard state of 1 M. Upon transfer to solution, also at a 598 248 248 329 AS"= -167 solution S 2 10 210 266 ASo= -154 standard state of 1 M, it is estimated that cyclopentadiene has an entropy of condensation of -38 J K-l mol-1 and the higher boiling dicyclopentadiene one of -63 J K-l m~l-~.~~Thus the entropy change in solution is predicted to be -154 J K-l mol-l, only 13 J K-l mol-1 different from the gas phase.The experimental difference is 21 J K-l mo1-1.a2 This is in accord with the well-known experimental fact that equilibrium and activation entropies for Diels-Alder reactions of -125 to -170 J K-l mol-1 are very similar in the gas and liquid phase^.^^^^^ This is presumably due to the product or transition state having a larger entropy of vaporization than the reactants because of its higher boiling point.25 An extreme example of this effect may be the negative difference in the entropy change accompanying NO2dimerization from -151 J K-l mol-1 in the gas phase to between -188 and -226 J K-' mol-1 in various When there is no change in the number of molecules in a reaction there appears also to be little difference between the entropy changes in the gas and liquid Many other bimolecular association reactions, which are apparently free of solvation effects, also have large negative entropy changes in solution.1,3-Dipolar addition reactions generally have entropies of activation of from -100 to -170 J K-l rn~l-~:~the morpholine-borane reduction of ketones has dS* -167 J K-l mol-1 and is almost solvent independent,g6 and the dimeriza- tion of dimethyl keten hasdS*= -176 J K-l m01-l.~~With smaller molecules '1 F.D.Rossini, D.D. Wagman, W. H. Evans, S. Levine, and I. Jaffe, 'Selected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds', Carnegie Press, Pittsburgh, 1953. G. A. Benford and A. Wassermann, J. Chem. Sac., 1939, 367. E. A. Moelwyn-Hughes, 'Physical Chemistry', MacMillan Co., New York 2nd edn., 1961, p. 1026. '4 C. M. Blair and D. M. Yost, J. Amer. Chem. SOC.,1933, 55, 4489. $6 R. Huisgen, Angew. Chem. Internat. Edn., 1963, 2, 633; R. Huisgen J, Org. Chem., 1968. 33, 2291. 66 S. S. White and H. C. Kelly, J. Amer. Chem. SOC.,1970,92,4203.R.Huisgen and P. Otto, J. Amer. Chem. SOC.,1968, 90, 5342. 309 The Energetics of Neighbouring Group Participation the entropy changes are expected to be smaller but the values are still highly negative and similar in the gas and liquid phases.The addition of CF,. to ethylene has dS* = -100 J K-l mol-1 in the gas phasess and -88 J K-l mol-1 in heptaness and the addition of HCN to acetone is solvent-independent and has dSOca. -112 J K-I m~l-l,~*whereas the calculated value for the gas phase is -121 J K-lm01-1.71 It is commonly stated that the entropy change in an association reaction is much less negative in solution than it is in the gas phase. 72 However, there is little evidence to support this claim, as seen above. Small entropy changes are often observed for bimolecular reactions in solution and these may result from (i) a loose transition state or (cf: p.303), this is probably the reason for ASo ca. -40 to -80 J K-’ mol-l for hydrogen-bonded and charge-transfer complexes, especially since the latter often have similar values in the gas phase;73 (ii) differences in the solvation of polar and hydrophobic groups of reactants, transition states, and products may make large and unpredictable contributions to observed equilibrium and activation entropies, especially in aqueous solution;25 (iii) there may be an intrinsic negative entropy of cavity formation in and since two cavities are required for reactants and only one for transition state or product this would have the effect of adding a positive contribution to observed entropies in water. To summarize, entropy changes of from -125 to -170 J K-l moI-l are to be expected for many bimolecular reactions in solution, at 25 “C this corresponds to a maximum entropic rate acceleration of about lo8M for a comparable intra- molecular reaction.25 Reactions showing effective molarities greater than this are probably the result of additional contributions from potential energy differences.Smaller rate enhancements may result from unfavourable entropy and/or potential energy changes in the intramolecular reaction or a loose product or transition state making the bimolecular reactions entropically less unfavourable. 4 Potential Energy Differences Differences in potential energy changes between intra- and inter-molecular reactions can either decrease or increase the effective molarity.The forces responsible for this difference may be partitioned into the following, formally independent, contributions: (i) bond stretching; (ii) bond angle bending; 08 J. M. Sangster and J. C. J. Thynne, J. Phys. Chew., 1969,73,2746. O9 A. A. Weir, P. P. Infecta, and R. H. Schuler, J. Phys. Chem., 1970, 74, 2596. 70 T. Stewart and B. Fontana, J. Amer. Chem. SOC.,1940,62, 3281 ;the ASo values quoted in L. L. Schaleger and F. A. Long, Adv. Phys. Org. Chem., 1963, 1, 1, Table 7 should read AHo and vice versa. 71 M. I. Page, unpublished data. L. P. Hammett, ‘Physical-Organic Chemistry’, McGraw-Hill, New York, 1970, 2nd Edn., p. 47. 7s J. E. Leffler and E. Grunwald, ‘Rates and Equilibria of Organic Reactions’, Wiley, New York 1963, p.52; R. Foster, ‘Organic Charge Transfer Complexes’, Academic Press, London, 1969, Chap. 7. 74 R. A. Pierotti, J. Phys. Chem., 1963, 67, 1840; ibid, 1965,69,281; G. Nemethy and H. A. Scheraga, J. Chem. Phys., 1962,36,3382,3401; 0.Sinanoglu and S. AbduInur, Fed. Proc., 1965, 24,S-12. Page (iii) torsional effects; (iv) attractive and repulsive non-bonded interactions; (v) zero-point energies; (vi) electrostatic interactions such as dipole-dipole and polar effects; (vii) delocalization or resonance energies ; (viii) hydrogen-bonding; (ix) solvation. Before discussing these contributions, it is worth emphasizing two points. Firstly, although it is conceivable that all of the above forces may be important, their large number makes it easy to produce ad hoc explanations for differences in effective molarities.Secondly, there is by no means universal agree- ment upon the values of the parameters to be used in the quantitative estimation of the various effects, and although they all have a physical reality (probably containing some areas of overlap), there is a tendency to treat them as adjustable parameters. The assignment of a potential energy difference to a particular contribution is therefore not always as clear-cut as it may seem, and its physical reality may be questionable since it may be an artifact of the computational method. Calculations involving contributions (i)-(v) form the basis of the proced- ure known as ‘molecular mechanics’, and the models used now are modest modifications of those formulated nearly thirty years ago by Hill,75 Ingold, 78 and We~theimer.’~The method has been used successfully to determine ‘strain energies’ and conformations of many molecules,78 and even the dynamics of conformational changes70 by various minimization techniques, 78~80~*land also to reproduce spectra.8a Bond Stretching.-Small deformations in bond lengths are usually assumed to have harmonic restoring forces and thus obey Hooke’s Law.The energy is proportional to the square of the deformation, equation (20), where kr is the force constant and ro is the ‘strain-free’ or normal bond length. Using the standard bond lengths found in n-alkane~~~e~* and the corresponding force typical equations, with r in A, are: Ec-c = 1369 (r -1.53)2 kJ mol-l Ec-H = 1333 (r -1.09)2kJ mol-1 Deformation of bond lengths is thus very difficult and rarely occur^,^^^^^ and is unlikely to be a factor responsible for differences between intra- and inter- molecular reactions.T.L. Hill, J. Chem. Phys., 1946, 14, 465. I. Dostrovsky, E. D. Hughes, and C. K. Ingold, J. Chem. SOC., 1946, 173. 77 F. H. Westheimer and J. E. Mayer, J. Chem. Phys., 1946, 14, 733. J. E. Williams, P. J. Stang, and P. von R. Schleyer, Ann. Rev. Phys. Chem., 1968,19, 531. 7D K. B. Wiberg and R. H. Boyd, J. Amer. Chem. SOC., 1972,94, 8426. R. Fletcher and C. M. Reeves, Computer J., 1964, 7, 149. K. D. Gibson and H. A. Scheraga, Comput. Biomed. Res., 1970, 3, 375. 8a S. Karplus and S. Lifson, Biopolymers, 1971, 10, 1973.O3 L. S. Bartell and D. A. Kohl, J. Chem. Phys., 1963, 39, 3097. 84 D. R. Lide, jun., Tetrahedron, 1962, 17, 125. J. H. Schactschneider and R. G. Snyder, Spectrochim. Acta, 1963, 19, 117. 31 1 The Energetics of Neighbouring Group Particbation Bond Angle Bending.-The deformation of bond angles from their 'normal' value is also usually assumed to be controlled by a harmonic potential, equation (21). The necessary force constants, k,, are usually obtained from spectroscopic E, = ke(8 -80)2 measurements and the values of the normal bond angle, O0, are those found experimentally in supposedly 'strain-free' molecules.86For the n-alkane~,~~~~~ typical equations, using the valence force-field analysis of saturated hydro- carbons,88 for methylene groups are EcGc = 0.104 (8 -111)2 kJ mol-', EcTH = 0.0602 (8 -109.5)a kJ mol-', and EHQH= 0.0504 (8 -108)2 kJ mol-l.It is sometimes assumed that changes in these angles are linearly re- lated to one another, and hence only one effective methylene group force constant is required to give the total angle strain at a given carbon af~m.~@~@~ The above equations could then be replaced by equation (22). which is only applicable Ee = 0.113 (8 -111)2 kJ niol-l (22) if the methylene groups are constrained to a local Czvsymmetry.78 Bond angle deformation is fairly easy: e.g., from equation (22), a 10" change costs 11.3 kJ mol-', and this is the pathway commonly used to relieve non-bonded interaction strain in a molecule.The extensive analysis of the spectra of hydrocarbons by Snyder and Schact- schneiderB6BE8has provided support for the basic assumption in 'molecular mechanics' that force constants are truly transferable, i.e. to a large extent they are independent of the intramolecular environment. However, it is questionable whether the spectroscopic force constants are the ones required to determine strain effe~ts.~~~~~ The value of the force constant depends on the force field employed,ge and they are effective or apparent force constants rather than true harmonic onesE8 They and the quadratic function also usually overestimate the bending energy, especially for large angle deformati~ns.~~ Because of these objections, purely empirical force constants are sometimes ~~ed~~-~~ (although criticizedg6), cubic terms are added,Q5*e7 and allowance is made for interaction (stretch-bend etc.) force Torsion.-A clear understanding of the origin of the barrier to internal rotation O6 I.D. Blackburne, R. P. Duke, R. A. Y.Jones, A. R. Katritzky, and K. A. F. Record, J.C.S. Perkin II, 1973, 332. D. R. Lide,jun. J. Chem. Phys., 1960.33, 1514, 1519. .gl R. G. Snyder and J. H. Schactschneider, Specrrochim.Acra, 1965, 21, 169. J. B. Hendrickson, J. Amer. Chem. SOC.,1961, 83,4537; ibid., 1967, 89, 7036. *O M. Bixon and S. Lifson, Terrahedron, 1967, 23, 769. @A K. B. Wiberg, J. Amer. Chem. SOC.,1965, 87, 1070. sa T. Shimanouchi and I. Nakagawa, Ann. Rev. Phys. Chem., 1972,23,217. s3 K. B. Wiberg and G.M. Lampman, J. Amer. Chem. Soc., 1966,88,4429. 94 N. L. Allinger, J. A. Hirsch, M. A. Miller, I. J. Tyminski,and F. A. Van-Catledge, J. Amer. Chem. SOC.,1968, 90, 1199. 96 N.L. Allinger, M. T. Tribble, M. A. Miller, and D. H. Wertz, J. Amer. Chem. SOC.,1971, 93, 1637. Page in ethane is a long-standing problem in quantum chemistry.ss Except when noii-bonded interactions are chosen simply to fit this barrier,gg it is generally agreed that van der Waals forces alone cannot account for the effect. Therefore the torsional potential is considered to be a separate contribution to the total energy and is usually assumed to be represented by a cosine function:looilO1 E4 is one half of the barrier height, n depends on the symmetry of rotation, 4 is the dihedral angle between bonds, and the plus and the minus signs are taken depending on whether E(#) has a maximum or a minimum, respectively, at 4 = 0".Although the experimental barrier to rotation in ethane is often used as a measure of E+ for rotation about C-C single bonds, this leads to an over-estimation of the torsional energy since it includes a contribution from 1,4-non- bonded interactions. The correct value to use for E4 depends on the non-bonded interaction functions used. If, for example, this interaction accounts for 10% of the barrier to rotation in ethane, it may be subtracted from the barrier height,s6~102J03and the torsional energy about C-C single bonds would be given by: E9) = 5.65 (1 + cos 34) kJ mol-1 (24) For dihedral angles up to about 20",equation (24) may be replaced by a quadratic function (25).103$104 Torsional energy is the 'softest' of all the potential energy Eq) = 11.30 -0.00769 (4)' terms, and hence distortion of dihedral angles is relatively easy.Instead of using the same E+ for all types of X--G-c--Y, for which there is some justification,lo6 a value dependent on the nature of X and Y is sometimes used.g7 Separate values are, of course, needed when rotation occurs around a bond which is adjacent to a S. Chang, D. McNally, S. S. Tehrany, M. J. Hickey, and R. H. Boyd, J. Amer. Chem. SOC. 1970,92, 3109. O7 J. L. Fry,E. M. Engler, and P. von R. Schleyer, J. Amer. Chem. SOC.,1972,94,4628. O8L. C. Allen and H. Basch, J. Amer. Chem.SOC.,1972, 94, 2699, W. England and M. S. Gordon, J. Amer. Chem. SOC.,1971,93,4649; 0.J. Sovers, G. W. Kern, R. M. Pitzer. and M. Karplus,J. Chem.Phys., 1968,49,2593; L. Radom, A. Latham, W. J. Hehre, and J. A. Pople, J. Amer. Chem. Soc., 1973, 95, 693. E. A. Mason and M. M. Kreevoy, J. Amer. Chem. SOC.,1955,77, 5808; H. E. Simmons and J. K. Williams, J. Amer. Chem. SOC.,1964, 86, 3222. looE. B. Wilson, Chem. SOC.Rev., 1972,1, 293. lol L. Radom and J. A. Pople, J. Amer. Chem. SOC.,1970,92,4786. lo8R. A. Scott and H. A. Scheraga, J. Chent. Phys., 1965,42,2209. lo*E. J. Jacob, H. B. Thompson, and L. S. Bartell, J. Chem. Phys., 1967,47,3736. lo' A. J. Kalls, A. L. H. Chung, and T. L. Allen, J. Amer. Chem. SOC.,1965, 88, 631. lo*E. B. Wilson, Adv.Chem. Phys., 1959, 2, 367; J. Dale, Tetruhehon, 1966, 22, 3373; J. P. Lowe, Progr. Phys. Org. Chem., 1968,6, 1. 313 3* The Energetics of Neighbouring Group Participation C=C106 or a C=01°7 bond and some other environments. 82~86~102~108-110 Lone pairs of electrons may not affect eclipsing energies105 and it appears that only the number of opposed bonds is important.lll Non-bondedInteraction.-Unfortunately, probably the most important but the least understood energy functionis that describingnon-bonded interaction. 78,108~112 As a consequence not only is there a variety of functional forms used to describe this interaction, but there is a range of values reported for the parameters of the same functions. Most of the functions in the literature are evaluated empirically from data on gas viscosity, molecular scattering, and other data relating to inter-molecular forces.By analogy with intermolecular concepts, the intramolecular interaction energy is assumed to be the sum of short-range repulsive forces and long-range attractive dispersion or London forces. Most treatments have made use of the Buckingham exp-6 (26) or the Lennard-Jones 12-6 (27) potential &.b. = A eXp (- &) -cr-6 (26) En.b. = Dr-12 -Er6 (27) functions. The attractive potential is taken as the inverse sixth power of the internuclear distance, r, and values of C or E may be derived from atomic p~larizabilitiesl~~using the Slater-Kirkwood equation.l14 The parameters used in equations (26) and (27) have been reviewed,78~8sJ08J12~115and other recent values may be found in references 79,82,95,97, 106, 107, and 109 and references cited therein.By the use of an empirical relationship the three parameters in equation (26) may be reduced to ~wo.~~J~~The variation in the parameters used for CC and HH non-bonded interaction is exemplified by equations (28)96and (29),B7with E in kJ mol-1 and r in A. The calculation of meaningful non-bonded interaction Ec.. .c = 4.018 x lo5exp (-4.53 r) -(28)-411.8 r-6 }EH ...H = 2.079 x 106 exp (-4.53 r) 795*8r-g Ec ...c = 6.263 x lo4exp (-3.15 r) -2690 r-6 }EH .. . H = 1.108 x lo4exp (-3.74 r) -114.4r-6 (29) lo( N. L. Allinger and J. T. Sprague, J. Amer. Chem. SOC., 1972,94,5734. lo‘ N. L. Allinger, M.T. Tribble, and M. A. Miller, Tetrahedron, 1972, 1173. lo8H. A. Scheraga, Adv. Phys. Org. Chem., 1968, 6, 103. logJ. F. Yan, G. Vanderkooi, and H. A. Scheraga, J. Chem. Phys., 1968,49,2713. noF.A.Momany, R. F. McGuire, J. F.Yan, and H. A. Scheraga, J. Phys. Chem., 1971,75, 2286; A. Warshel, M. Levitt, and S. Lifson,J. Mol. Spectroscopy, 1970,33,84; D. E. Brant and P. J. Flory, J. Amer. Chem. SOC.,1965, 87, 2791. 111 S. Wolfe, Accounts Chem. Res., 1972,5,102; L. Phillips and V. Wray, J.C.S. Chem. Comm. 1973,90; M. A. Robb and W. J. Haines, J. Amer. Chem. SOC., 1973,95,42. 11* F. H. Westheimer, in ‘Steric Effects in Organic Chemistry’, ed. M. S. Newman, Wiley, New York, 1956, Chap. 12. 11* J. Ketelaar, ‘Chemical Constitution’, Elsevier, New York, 1953, p.91. 11‘ K. S. Pitzer, Adv. Chem. Phys., 1959, 2, 59. 116 M.Cignitti and T. L. Allen, J. Chem. Phys., 1965,43,4472. ll‘T.L.Hill, J. Chem. Phys., 1948, 16, 399. Page energies is beset by a number of complications. Unlike the free atoms, those in molecules do not possess spherical symmetry. To allow for this anisotropic character of non-bonded interactions it has been suggested that, say, the centre of a hydrogen atom should be shifted along the C-H bond, but still treated as spherical.gc~117~118 Another problem is that the effective dielectric constant of the molecule may influence the transmission of the forces involved. Finally, the calculations apply to the gas phase and in solution the attractive part of the non- bonded interaction would be decreased by the Non-bonded interactions are normally only considered to operate between atoms separated by three or more bonds; 1,3 interactions are presumed to be incorporated into angle-bending,g1J20 unless they are treated explicitly as, say, in a Urey-Bradley force field.11*J21 It is difficult to make meaningful comparisons between the many different non- bonded force laws since they cannot really be isolated from the other terms in the total potential energy expression.Most of the methods give very similar ‘strain- energies’ and molecular geometries although, as mentioned earlier as a cautionary note, the origin of the ‘strain’ may be attributed to different physical terms. Zero-point Energies.-It is usually assumed that zero-point energy differences are not important, although they may affect the strain energy.lzZ Little work has been done on this contribution.Electrostatic Interactions.-Differences in dipole-dipole electrostatic interactions may affect the effective molarity. These are sometimes treated in a classical way, as originally suggested by Jeans,123s124 which does not allow for induction or mutual polarization effects. A simplified approach is to use partial charges on the individual atoms, obtained from group dipole moments,12s and to calculate the electrostatic interaction by Coulomb’s law (30) as a function of the distance, r A, between the partial charges, q expressed in terms of the electronic charge, in a Eel = (71-q2 x 1389 kJ mol-1Dr medium of dielectric constant D.10sJ2s On a qualitative basis, a system of altern- ate positive and negative partial charges imparts stability to a molecule, while destabilization is associated with adjacent like charges.The use of Coulomb’s law 11’ D. E. Williams, J. Chem. Phys., 1966, 45, 3770. 11* A. Warshel and S. Lifson, J. Chem. Phys., 1970,53,582. ll@N. R. Kestner and 0. Sinanoglu, J. Chem. Phys., 1963, 38, 1730. lf0 L. S. Bartell, J. Chem. Phys., 1960, 32, 827. l*lL. S. Bartell, J. Chem. Educ., 1968,45, 754. lSaB. Nelander and S. Suer, J. Chem. Phys., 1966, 44,2476. 123 J. H. Jeans, ‘Mathematical Theory of Electricity and Magnetism’, Cambridge University Press, 5th Edn. 1933, p. 377. la’N. L. Allinger, J. A. Hirsch, M.A. Miller, and I. Tyminski,J. Amer. Chem. SOC.,1969,91, 337. Iz6 C. J. F. Bottcher, ‘Theory of Electric Polarisation’, Elsevier, Amsterdam, 1952. lz6 R. K. Solly, D. M. Golden, and S. W. Benson, J. Amer. Chem. SOC.,1970,92,4653. The Energetics of Neighbowing Group Participation should be regarded as a purely empirical procedure since, when two partial charges are not well separated, the solvent molecules and the rest of the solute between and around the two charges do not behave like a continuous medium of constant dielectric and it is also difficult to know where the point dipoles should be 10cated.l~~ For two partial charges separated by greater than one width of water layer it has been suggested128 that the effective dielectric constant approaches that of bulk water, 80; hence electrostatic interactions would be negligible at these distances.Delocalization Energies.-The relief of steric strain may cause loss of some delocalization energy in both intermolecular and intramolecular systems and this may be an important factor contributing to the magnitude of the effective m01arity.l~ For example, the effective molarity of anhydride formation, equation (6), may in part be due to the fact that succinic anhydride is a planar molecule1as with presumably greater delocalization energy than acetic anhydride which is non-planar by about 45", as indicated by dipole moment The energy change may sometimes be calculated, to a first approximation, using the cosine potential for torsion and the barrier to rotation around the bond concerned.In studying 1,Zdisubstituted benzene derivatives one has to ensure that the reson- ance energies are the same in the intramolecular and analogous intermolecular reactions before ascribing rate differences to other Hydrogen Bonding.-Differences in entropy favour intramolecular hydrogen bonds over their intermolecular However, they will be less important in aqueous solution,14 and also the rates of reactions are normally less affected by hydrogen bonding than by the actual proton transfer it~e1f.l~~ Intra-molecular hydrogen bonding may be important in determining the rates of some reactions, especially in non-aqueous solvents, but it may sometimes be better to attribute rate differences to 'solvent It has been suggested that hydrogen bonding may be treated quantitatively by combining a non-bonded potential with an electrostatic part.135 Solvation.-Bimolecular substitution reactions between anions and neutral molecules are faster in dipolar aprotic than protic solvents because in the ground state the anion is much more solvated by the latter and this outweighs any effects due to transition state solvafion.la6 This suggests that an intramolecular substitu- lz7 M.Gii, N.G6, and H. A. Scheraga, J. Chem. Phys., 1970,52,2060.*** H. A. Scheraga, Ann. New York Acad. Sci., 1965, lU, 273. R. J. W. LeFbvre and A. Sundaram, J. Chem. SOC.,1962,4009. P. A. Hopkins and R. J. W. LeFbvre, J. Chem. SOC.(B), 1971, 338; 0.Exner and V. Jehlicka, Coll. Czech. Chem. Comm., 1970, 35, 1514; cJ A. Boogaard, H. J. Geise, and F. C. Mijlhoff, J. Mof. Structure, 1972, 13, 53. lS1 J. E:C. Hutchins and T. H. Fife, J. Amer. Chem. Soc., 1973.95, 2282. lsa H. H. Jaffe, J. Amer. Chem. SOC.,1957,79,2373. W. P. Jencks, Chem. Rev., 1972, 72, 705. B. Capon and M. I. Pagc, J. Chem. SOC.(B), 1971. 741. 32 D. Poland and H. A. Scheraga, Biochemistry, 1967.6, 379 1. A. J. Parker, Chem. Rev., 1969, 69, 1. Page tion reaction may be facilitated if solvation of the nucleophile is inhibited in any way,14e.g. by steric hindrance. However, it has been concluded that solvation is not important in determining the magnitude of the effective molarity of carboxy- late ion attack on an Furthermore, it has been suggestedlo8JS8 that the first hydration shell of ions and non-polar solutes contributes very much more to the free energy of solvation than all other solvent molecules.In view of the small size of water it thus appears that solvation differences will only rarely be important in contributing to the effective molarity of reactions in aqueous solution, providing that the reacting atoms are solvated by at least one layer of solvent molecules. 5 Strain The strain energy of molecules has to be defined relative to some standard and is often taken as the difference between that calculated from group increment schemes and the observed energy.140s141 The calculations described previously are not always possible and it is convenient to have a compilation of strain energies of various molecules for ana10gy.106J40J41 In Table 6 are shown the strain energies of a few cyclic systems relative to their ‘strain-free’ acyclic analogues.14o With the exception of sulphur derivatives, the strain is, to a crude approximation, characteristic of the ring size and not of its constituent parts.The strain in the hydrocarbons has been used as a model for the substituted derivatives and a remarkable correlation is obtained between accelerated and decelerated rates of solvolysis and the strain energy difference between the hydrocarbon and carbonium ion.e7J4a Intramolecular reactions involve cyclization and the combination of data given in Tables 5 and 6 should permit a rationalization of the relative rates of closure of various ring sizes.The ratio of rate or equilibrium constants involving three-, four-, five-, six-, seven-, and eight-membered rings is thus predicted to be ca. 10-14: 10-14: 1:10: respectively. Although this order is sometimes observed there are many exception~.~~~~~J~~~ Threemembered ring closure is subject to electronic effects peculiar to this ring size, and is therefore not directly comparable with the other ring~.~~l~~ This is especially true when there is the possibility of conjugation between the ring and a ~ubstituent.~~~The strain energy of rings containing S atoms is less than 0and N derivatives and this favours their relative rates of ring closure. The ca. 1-100-fold slower rate of closure of six-compared with five-membered rings in certain sN2 displace lo7T.C. Bruice and A.Turner, J. Amer. Chem. SOC.,1970,92, 3422. K. D. Gibson and H. A. Scheraga, Proc. Nat. Acad. Sci. U.S.A., 1967, 58, 420. E. Grunwald, R. L. Lipnick and E. K. Ralph, J. Amer. Chem. SOC.,1969,91,4333. IroS. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O’Neal, A. S. Rodgers, R. Shaw, and R. Walsh, Chem. Rev. 1969,69,279. lrlP. von R. Schleyer, J. E. Williams, and K. R. Blanchard, J. Amer. Chem. SOC. 1970,92, 2377. G. J. Gleicher and P. von R. Schleyer, J. Amer. Chem. SOC.,1967, 89, 582. 14a A. C. Knipe and C. J. M. Stirling,J. Chem. SOC.(B) 1968, 67. J. Dale and J. Krane, Acta Chem. Scand. 1972,26,4049. loo3. W. Larsen and A. V.Metzner, J. Amer. Chem. SOC.,1972, 94, 1614. me Energetics of Neighbouring Group Participation Table 6 Strain energies of various moleculesa Molecule Strain kJ mol- Molecule Strain kJ mol-I Cyclopropane 115.5 Cyclohexane 0 oxiran 115.5 Tetrahy dr op yran 9.2 Aziridine 115.9 Piperidine 4.2 Thiiran 74.1 Tetrahydrothiopyran 0 Cyclohexanone 14.2 Cyclobutane 109.6 Glutaric anhydride 5.9 Oxetan 110.5 Azetidine 109.6 Cyclohept ane 26.8 Thietan 81.O Cycl 0-oc t ane 41.4 Cyclopentane 26.4 2,6-endo-Dimethyl Tetrahydro furan 28.0 bicyclo[2,2,1 Jheptane 98.7c Tetrahydropyrrole 28.5 Te t r ah ydro thiop hen 7.2 Tricycl0[4,2,1 ,03p7]nonane 94.6c Cyclopentanone 25.1 Succinic anhydrideb 18.8 Maleic anhydride 19.2 Succinimide 35.6 a Ref.140. Revised value, S. W. Benson, personal communication. C P. von R. Schleyer, personal communication. ment~~s'~~presumably reflects the unfavourable geometry brought about by a 90" bond angle in the transition state,2K which is also largely responsible for the relative instability of most six-membered compared with five-membered chelate rings.14s Torsional strain may also favour spa centres in five- relative to six- membered rings.lo6 9 146 The strain energies in Table 6 are not directly applicable to rates, although there may be a correlation between these values and the relative rates, since the estimation of the strain of the transition state depends on the length of the forming bond. 6 Stereochemical Requirements In reactions with severe stereoelectronic demands, intramolecular reactions may be Zess favourable than the analogous intermolecular reaction if the geometry between the interacting groups does not correspond to the favoured configuration. (Indeed, in such cases an alternative reaction path may be followed.) The rate differences within a series of intramolecular reactions may sometimes be ration- alized in terms of rate deceleration in the slower reacting substrates rather than in 146 E.J. Corey and J. C. Bailar, Jr., J. Amer. Chem. Soc., 195Y, 81, 2620. 140 H. C. Brown and K. Ichikawa, Tetrahedron, 1967, 1, 221. 14' B. Capon, J. Cheni. SOC.(B), 1971, 1207. Page terms of special effects leading to rate acceleration in the faster reacting substrates.The most favourable configuration for reactions proceeding via four-electron three-centred bonds, such as sN2 displacements and proton transfers, is a hear The bonding consists of two electrons in a bonding and two in a non-bonding 0rbita1.l~~ However, as the system is constrained into an intramolecular cyclic case the interaction between the terminal orbitals increases and moves up in energy and, in the limit, becomes antibonding.lsO Non-linear transition states for these reactions are thus unfavourable. Experimentally, 1 ,Zproton shifts are very rare.151 For example, the aminolysis of acetylimidazole by several diamines is facilitated by the second amino-group acting as a general base; such is not the case when the diamine is hydrazine.ljz Intramolecular endocyck nucleophilic substitutions are unfavourable and rarely found because of the non-linear transi- tion state involved, but intramolecular exocyclic displacements occur readily where a linear configuration is readily attainable.153 The importance of the correct geometry for intramolecular reactions of carbonium ions has also been emphasized.15 7 Participation and Stability The effect of substituents upon both the equilibria and rates of ionization reac- tions is not cumulative but appears to be a functionof the demand made upon it.155 Similarly, anchimeric assistance occurs where it is needed and the degree of participation depends upon the stability of the system in the absence of participa- tion.lS6 For example, the ability of the double bond, in the solvolysis of 7-aryl-7-anti-norbornenylp-nitr~benzoates,~~~and of the cyclopropyl ring, in the solvolysis of 1-aryl-1 -cyclopropyl-1 -ethyl p-nitrobenzoate~,~~ to stabilize the incipient carbonium ion centre increases as the latter becomes more electron-deficient and less stable.The rate increase brought about by homoallylic participation is 10l1 in reaction (5)' but is totally absent in the solvolysis of the comparable tosylate of butd-en-l-01,~~~and an analogous situation holds for cyclopropane participa- 148 G. C. Pimentel and A. L. McClellan, Ann. Rev. Phys. Chem., 1971,22,347; P. A. Kollman and L. C. Allen, Chem. Rev., 1972, 72, 283; H. Fujimoto, S. Yamabe, and K.Fukui, Tetraheriron Letters, 1971,439,443; J. P. Lowe, J. Amer. Chem. SOC.,1971,93, 301 ;N. L. Allinger, J. C. Tai, and F. T. Wu, ibid., 1970,92, 579. 149 R. Gleiter and R. Hoffmann, Tetrahedron, 1968,24,5899. lK0 R. Hoffmann, personal communication. la D. S. Kemp, J. Org. Chem., 1971, 36,202. 16* M. I. Page and W. P. Jencks, J. Amer. Chem. SOC.,1972,94,88 18. lSa L. Tenud, S. Farooq, J. Seibl, and A. Eschenmoser, Helv. Chim. Acfa., 1971, 53, 2059. 164 D. M. Brouwer and H. Hogeveen, Rec. Trav. chim., 1970, 89, 212. lSK J. Hine, 'Physical Organic Chemistry', McGraw-Hill, New York, 1962, p. 101; L. D. McKeever and R. W. Taft, J. Amer. Chem. SOC., 1966,88,4544; H. G. Richey and N. C. Buckley, ibid., 1963, 85, 3057; S. V. McKinley, J.W. Rakskys, A. E. Young, and H. H. Freedman, ibid., 1971,93,4715; E. H. Cordes, Progr. Phys. Org. Chem., 1967,4, 1. lS6 S. Winstein, B. K. Morse, E. Grunwald, K. C. Schreiber, and J. Corse, J. Amer. Chem. SOC.,1952, 74, 1113. m P. G. Gassman and A. F. Fentiman, J. Amer. Chem. SOC.,1970,92,2549,2551. 168 E. N. Peters and H. C. Brown, J. Amer. Chem. SOC.,1973,95,2397. logK. L. Servis and J. D. Roberts, J. Amer. Chem. Soc., 1964, 86, 3773. 319 The Energetics of Neighbouring Group Participation tion.lso The absence of participation in the acyclic systems may be due more to the very unstable carbonium ion formed in 7-norbornyl derivativeslsl than to correct alignment of the neighbouring group.lS2 However, in such compari- sonsthe rate-determining steps may be different and, for example, the 'standard' may or may not involve solvent assisfance.lBS 8 Examples In Table 7 is shown a number of comparisons of inter- and intra-molecular reactions which, except for example 17, proceed via the formation of five- membered rings.When comparing rate or equilibrium constants at 25 "C a difference of 10%is equivalent to a free-energy difference of 5.70n kJ mol-l. Examples 1 and 2 in Table 7 involve proton transfer and, in general, other intramolecular general acid- and base-catalysed reactions show small effective molarities. This could be caused by (i) an unfavourable potential energy effect in the intramolecular reaction such as non-bonded interactions, bond angle, and torsional strain or the non-linear transition state involved (see p.319), or (ii) a very loose transition state making the intermolecular reaction entropically less unfavourable (see p. 303). The general base-catalysed aminolysis of acetyl- imidamle by several diamines, reaction (31), shows a small sensitivity to the structure of the dimline indicating that the potential energy effect is not predom- inant.162 Furthermore, the intermolecular reaction probably has a diffusion-controlled rate-determining step, k2in reaction (32).lS4 The transition state is thus very loose and the bimolecular step, kt,will be associated with a small entropy change giving rise to the low effective molarities of about 1 M.16a 0 0-II + I k,"lRNHz + C-Tm *RNHz-C-Tm -products (32)I I Molecules containing the function --CO-XY prefer the trans conformation i.e.with the XY bond eclipsing the C=O bond. For example, the difference in Leo H. Tanida, T. Tsuji, and T. Irie, J. Amer. Chem. SOC.,1967, 89, 1953; Y.E. Rhodes and T. Takino, ibid., 1968,90,4469. J. D. Roberts, F. 0. Johnson, and R. A. Carboni, J. Amer. Chem. SOC.,1954, 76, 5692; R. C. Bingham and P. von R. Schleyer, ibid., 1971,93,3189. lm M. Hanack and H. J. Schneider, Angew. Chem. Intern?:. ban., 1967,6, 666. le3Y. E. Rhodes and T. Takino, J. Amer. Chem. SOC.,1970,92,5270; P. von R. Schleyer, J. L. Fry, L. K. M. Lam, and C. J. Lancelot, ibid., 1970,92,2542; H. C. Brown and C. J. Kim, ibid., 1971, 93, 5765; D. J. Raber and J. M. Harris, J. Chem. Educ., 1972, 49, 60.lo*M. I. Page and W. P. Jencks, J. Amer, Chem. SOC.,1972,94,8828. Page free energy between this conformation, found in esters, and the cis conformation in lactones is about 15 kJ mol-1.165 Combined with the torsional and bending strain found in five-membered ringsg6 and the possibility of strain in some of the acyclic analogues due to loss of resonance in a non-planar conformation (see p. 316) this makes the average strain in five-membered rings about 21 kJ mo1-1 (Table 6). 166 The loss of 3 internal rotations accompanying cyclization costs about 12 kJ mo1-l. Therefore the effective molarities of such cyclizations as examples 3 to 11 in Table 7 are expected to be less than the maximum predicted from entropy considerations alone and to be ca.108/10(33/6.7),10e.*M: since the strain energy of the incipient cyclic system is normally less in the transition state than in the fully formed cyclic this prediction is in reason- able agreement with the experimental results (Table 7). Such generalizations are obviously very crude but show that observed effective molarities may be rationalized to within an order of magnitude. If torsional strain and non-bonded interactions are already present in the initial state of the intramolecular reaction causing it to be as strained as the cyclic product (cf. the last two entries in Table 6) then the maximum entropic advantage is expected. Examples 13 to 15 in Table 7 presumably fall into this category, and the effective molarities are about lo9 M.Examples 16 and 17 in Table 7 have effective molarities greater than los M and therefore must involve a potential energy effect in addition to the en- tropic advantage. X-Ray crystallographic studies indicate that the C-C-H angle is 118" in maleic but is 128.5" in maleic anhydride.16* If the methyl groups in dimethylmaleic acid adopt the same conformation as in cis-but-2- enelSs and the same angle change occurred upon cyclization, then the H * * * H distance would increase from 1.53 to 1.98 A. Even using a 'soft' potential (equa- tion 29)97this relief of non-bonded interaction upon cyclization corresponds to about 22 kJ mol-1 and an advantage of lo4 in the equilibrium constant. The author thanks Drs. W. P. Jencks and R. M. Southam for many stimulating discussions. R.Huisgen and H. Ott, Tetrahedron,1969,6,253. Excluding thiophen and succinimide. M. Shahat, Acta Cryst., 1952,5, 763. 1*8 R. E. Marsh, E. Ubell, and H. E. Wilcox, Acta Cryst., 1962, 15, 35. A. Almeningen, I. M. Afinsen, and A. Haaland, Acta Chem. Scand., 1970,24,43. w N Table 7 A comparison of some inter- and intramolecularly catalysed reactions in water 3N Intramolecular reaction Intermolecular reaction Temp/"C Eflective Ref. ma lar ity! E m01.dm-3 $ 1. Enolization of MeCOCH,CH,CO,-AcO-+ MeCOCH,CH,CO,Et 25 0.5 a 3 2. Aminolysis of AcIm by H2NCH2CH2NH2 RNH, + RNH, + AcIm 25 0.6 b'% 3. Hydrolysis of Ph02CCH,CH2C0,-AcO-+ MeC0,Phc 25 5.1 x lo4 d,e 3 -f4. Lactonization of Ph02CCH2CH2CH20 MeO-+ MeC0,Ph 25 5.0 x lo3 g,h 3Q-5. Hydrolysis of Ph02CCH2CH2CH2NMe2 NMe, + MeC0,Ph 20 1.3 x lo3 i 0+ + F 6. Lactonization of H,O,CCH,CH,CH,OH EtOH + MeCO,H, 25 80 j,k 8' 7.Cyclization of -O(CH2),CV EtO-+ EtClzs" 30 8.1 x 104 n,o Q 8. Hydrolysis of HO(CH,),CI H,O + C2H,Cll*P 55 2.4 x lo4 q,r 9. Hydrolysis of -O,C(CH,),Cl AcO-+ C,H,Clz*' 37.5 8.5 x 10, n,t 6 10. Cyclization of H,N(CH,),Br NEt, + C2HsBru 25 1.4 x lo4 v,t 2 --$. 11. Cyclization of (Et0,C),C(CH2),Brw HC(CO,Et), + C2H5Brm 25 4.6 x 103 X,Y s-g. 12. Lactonization of PhO-+ CH,CO,Ph 25 2.5 x 105 g,z 3 AcO-+ CH3C02PhC 30 1.8 x lo6 aa,e13. Hydrolysis of Uc0,-RCO2-+ PhCO2Ph 30 -1.0 x lo8 bb,cc AcO -+ MeC0,-g-C6H40MeC 25 1.8 x lo6 dye14. Hydrolysis of 11 RCOl-+ MeCH=CHCO,-p-C,H,OMe 25 -2.8 x log dd,cc\co*- P 0 25 9.1 x lo7 d,e 25 -1.1 x los ee 16.Equilibrium anhydride formation of MeC0,H + MeC0,H 25 30 3 x 1Ol6hh R. P. Bell and M. A. D. Fluendy. Trans.Furuduy SOC.,1963,59,1623; R. P. Bell and P. DeMar!a. ibid., 1970,66,930. b M. I. Page and W. P. Jencks. J. Amer. Chem. Soc., 1972, 94, 8818. C Based on estimated nucleophilic catalysis from Br6nsted plot. d T. C. Bruice and U. K. Pandit, J. Amer. Chern. Soc., 1960,82,5858. CV. Gold, D. G. Oakenfull, and T. Riley. J. Ch~m.SOC.(B),1968,515. f PKa of ROH taken as 15.9. 0 B. Capon, S. T. McDowell, and W. V. Raftery, Chem. Comm.,1971, 389.h W. P. Jencks and M. Gilchrist, J. Amer. Chem. SOC.,1968,90,2622. f T. C. Bruice and S. J. Benkovic, J.Amer. Chem. SOC.,1963.85,l.f Ref. 19.20%v/v ethanol. k J. Gerstein and W. P. Jencks, J. Amer. Chem. SOC.,1964, 86,4655.1 ~RC~/~RRTtaken as 0.02. Solvent ethanol. n Ref. 6. 0 M. L. Dhat, E. D. Hughes, C. K. Ingold, and S. Masterman, J. Chem. Soc., 1948,2055. P Solvent 4: 1 EtOH:H20 molarity of water taken as 11 M. Q H. H. Heine, A. D. Miller, W. H. Barton and R.W. Greiner, J. Amer. Chem. Soc., 1953,75,4778 L. C.Bateman, K. A. Cooper, E. D. Hughes, and C. K. Ingold, J. Chern. SOC.,1940,925. 8 k~l/k~~~taken as 2. t S. Eagle and J. C. Warner, J. Amer. Chem. SOC.,1939, 61, 488, Extrapolated data to 100% water by plotting logk vs. (6 -1)/(2~+ 1). U H. Freundlich and H. Kroeplin, 2.Phys. Chem., 1926, 122, 39. Solvent t-butyl alcohol. z A. C. Knipe and C. J. M Stirling. J. Chem. SOC.(B), 1968, 67. Y R G. Pearson, J. Amer. Chem. Soc., 1949, 71, 2212. M. L. Bender and W. A. Glasson, J. Amer. Chem. SOC.,1959, 81, 1590. J. W. Thanassi and T. C. Bruice, J. Amer. Chem. SOC.,1966, 88, 747. bb For RCO,H of pKa 2.9, estimated assuming /3 = 1 .O and kPhCOtph/kMeCOzph = 8.7 x ]Ova. cc R. W. Taft, jun., in ref. 23, p. 556. dd For RC02H Of PKa 2.7, estimated assuming /3 = 1.0 and kMeCHECHC02R/kMeCOnPh = 6.3 x lo-*. ee For RC02H of p& 3.5, estimated assuming fi = 1.0. ff L. Eberson and H. Welinder, J. Amer. Chem. Soc., 1971.93, 5821. 178W. P. Jencks, F. Barley, R. Barnett, and M. Gilchrist, J. Amer. Chem. Soc., 1966, 88,4464, A* S. Milstein and L. A. Cohen, J. Amer. Chem. SOC.,1972,94,9158 in 20%dioxan-water.

ISSN:0306-0012    

DOI:10.1039/CS9730200295

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

Quasielastic Laser Light Scattering By A. M. Jamieson DIVISION OF MACROMOLECULAR SCIENCE, CASE WESTERN RESERVE UNIVERSITY, CLEVELAND, OHIO 44106, U.S.A. A. R. Maret CORPORATE RESEARCH AND DEVELOPMENT CENTER, ADDRESSOGRAPH-MULTIGRAPH CORPORATION, CLEVELAND, OHIO 44128, U.S.A. 1 Introduction A perfectly homogeneous material would allow light to pass through it without deflection. All known materials, however, possess microscopic inhomogeneities giving rise to local fluctuations in dielectric constant (refractive index). Light passing through such systems is scattered in all directions to an extent which is typically 10-4-10-s of the incident beam intensity. Most investigators in the physical and biological sciences are familiar with the classical use of total- intensity light scattering to determine molecular weights of macromolecules in solution.In addition, information on the size and shape of the macromolecules can be obtained by studying the angular distribution of the scattered intensity.l The dielectric fluctuations of the material which cause light scattering are constantly changing with time owing to thermal (Brownian) motions and consequently the scattered light will have a frequency distribution different from that of the incident radiation. The characteristics of this light-scattering spectrum are determined by the relaxation time decay of the fluctuations. A study of the spectrum can therefore provide information on the dynamics of the fluctuations in addition to the same information derived by total-intensity measurements.The shifts from the frequency of the incident radiation represented by this light-scattering spectrum are extremely small, ranging from as little as one part in 1014 (1 O-ll crn-l) to perhaps one part in lo6(0.01 cm-l) of the incident frequency radiation. Such shifts are not to be confused at all with the large shifts observed in Raman spectroscopy.2 Because of the small frequency changes, the scattering can be assumed elastic within the accuracy of our experimental measurements. For this reason, the studies discussed in this article are often grouped under the heading of quasielastic light scattering. The theoretical basis of quasielastic light scattering has developed continuously since the early work of Brillouin in 1922.3In the simplest case it turns out that M.Kerker, ’The Scattering of Light and other Electromagnetic Radiation’, Academic Press, New \ ork, 1969. A. Anderson, ‘The Raman Effect’, Marcel Dekker, New York, 1971 (two volumes).* L. Brillouin, Ann. Physik., 1922, 17, 88. I I I W0-B wO wO+wB Angular frequency / rad 5-1 Figure 1 Hypothetical quasielastic light scattering spectrum for a pure non-relaxing fluid. w,, is the incident laser frequency, AWRis the halfwidth (full width at hay height) of the Rayleigh line, AWB is the halfwidth of either Brillouin line, and COBis the shift in frequency of the Brillouin lines from wo Jamieson and Maret the spectrum consists of an extremely narrow central component, the Rayleigh line, with two symmetrically shifted broader lines on either side, the Brillouin doublet.A schematic diagram of the quasielastic spectrum in a simple non- relaxing liquid is shown in Figure 1. Early experimental studies of the Rayleigh- Brillouin spectrum were severely hindered, principally because of the relatively low power and high bandwidths of conventional light sources and filters, coupled with the poor resolving power of classical spectrometers using diffraction gratings or interferometer^.^ For example, classical filters, with bandwidths typically around 0.01 cm-l, made it impossible to study the Rayleigh line. The widespread availability of laser light sources which can have bandwidths as narrow as cm-l, together with advances in optical and electronic detection devices, have virtually eliminated all of the experimental difficulties.The past seven years have therefore seen a profound resurgence in experimental studies of quasi-elastic light scattering. This in tun has provided theoreticians with the impetus to develop more detailed theories of light scattering from systems of practical interest. The review which follows seeks to inform the chemist of the wide variety of information which can be obtained in a rapid, efficient way by a study of the quasielastic spectrum of scattered laser light. This includes molecular weights, particle sizes and shapes, diffusion and activity coefficients, hypersonic velocities, and molecular relaxation times. Before discussing these applications in detail, it will be advantageous to provide the reader with a briefsummary of theformalism of quasielastic light scattering.In this way we hope to emphasize the close relation of the light-scattering technique to alternative methods of investigating molecular dynamics such as spin relaxation,6 dielectric relaxation,6 and ultra- sonics.’ 2 Dielectric Fluctuations and Quasielastic Light Scattering The origin of the quasielastic frequency broadening of light scattered by a fluid is conceptually most easily envisaged as a simple Doppler frequency shift due to the motions of the molecular scatterers. The collective thermal motions of statistical ensembles of molecules give rise to microscopic fluctuations in the density of the fluid or the relative concentrations of its components, which in turn represent microscopic fluctuations in dielectric constant.Incident light is scattered by these local dielectric fluctuations and the spectral frequency distribu- tion of the scattered light is therefore determined by the time dependence of the spontaneous microscopic density and concentration fluctuations of the fluid. The time dependence or relaxation of fluctuation phenomena is described by the appropriate correlation functions,8 which are obtained in turn from the I. L. Fabelinskii, ‘The Molecular Scattering of Light’, English translation, Plenumess Pr, New York, 1968. A. Abragam, ‘The Principles of Nuclear Magnetism’, Oxford University Press, Oxford, 1967.J. Crossley, R.I.C. Rev., 1971, 4, 69. E. Wyn-Jones, R.I.C. Rev., 1969, 2, 59.’R. G. Gordon, Adv. Magn. Resonance, 1968,3, 1. Quasielustic Laser Light Scattering equation of motion of the molecular dynamics causing the fluctuation. Most experimental measurements are performed in the frequency domain, however, and in general it transpires that the frequency distribution of the spectral probe is the time-to-frequency Fourier transform of the correlation function. For the simplest case, a fluctuation decay described by a linear equation of motion, the correlation function is an exponential decay with characteristic time constant T. The shape of the measured spectrum is then given by equation (l), which is the Fourier transform of this exponential.This equation represents a Lorentzian curve with halfwidth r = T-~.The Figure 2 Schematic diagram of geometry of Iight scattering from a single dieIectric fluctuation. The absolute magnitudes of k, and ks are 2n/& and 2nlhs,where A. and As are the wavelengths oj’the incident anti scattered light L. Van Hove, Phys. Rev., 1954,95249. Jamieson and Maret hypothetical spectrum shown in Figure 1 is a triplet of three such Lorentzian lines. A. Light-scattering Formalism.-The intensity of light scattered from a fluid of N molecules of polarizability a can be writtenlo Nko4a2Is(x,w)= I, 7(sinz+)S(x,w)2R where S(X,~)is a function representing the shape of the spectrum, x is the scattering vector (Figure 2), and w is the displacement in angular frequency of the scattered light from the frequency of the incident radiation.loand k, = 27r/h0 are the intensity and wave vector of the incident radiation; h, is the wavelength of incident light. R is the distance from the scattering volume to the point of observation and4 is the angle between the electric vector of the incident radiation and R. The magnitude of the scattering vector IK 1 is given by the difference in magnitude of the wave vectors of the incident radiation ko and the scattered radiation ks IxJ=Ik,-ksI (3) Since the absolute frequency shifts of the scattered light are very small compared with the incident frequency we can assume to a very high degree of approximation that no change in wavelength occurs (elastic scattering).We can thus write the so-called quasielastic relation, cf. the Bragg condition for X-ray scattering: 47~nIx I= 2nk0sin(8/2)=-sin(8/2) (4)A0 Equation (4) enables one to fix accurately the scattering geometry in terms of the known parameters refractive index n, wavelength of incident light ho7 and scattering angle 8. The shape function of S(X,W)is the space-time Fourier transform of the function G(r,t): +~+~ S(W,W)= G(r,t)exp[-i(wt -~r)]dtdr -m-m where WJ)= Wr0,to)E*(r,t)) (6) is the autocorrelation function of the electric field of the scattered light E(r.t) and the angular brackets refer to an average over the ensemble of scattered pho- tons. In simple terms G(r,t)is a function which is a statistically averaged measure of the magnitude of the scattered field at position r and time t relative to its loI.L. Komarov and I. Z. Fisher, Soviet Phys. JETP, 1963, 16, 1358. Quasielmtic Laser Light Scattering value at some arbitrary space-time origin and thus characterizes the relaxation or decay dynamics of the scattered field. Since the fluctuating field E(r,t)is proportional to the fluctuations in dielectric constant 8E(r,t)which cause scattering of the incident light, equation (5) can be written S(W,W)= A (SE(K,O) 8E(K,t))exp( -iwt) (7)s0 where &(x,t) represents the Fourier transform in space of 8~(r,t)and A is a constant. This relation now expresses the shape of the quasielastically scattered spectrum as a Fourier transform of the correlation function which describes the relaxation dynamics of the dielectric fluctuations of the material.To complete the analysis we must therefore compute this correlation function using an appropriate model of molecular dynamics. The above analysis assumes for simplification that the dielectric constant is a scalar quantity. This holds only for a liquid composed of isotropic scattering units. In a liquid with anisotropic scatterers, E will be a tensor and orientational molecular motions will cause depolarized light scattering. Details of the theoret- ical treatment of scattering from orientational fluctuations can be found in the literaturell and we will content ourselves in a later section of this review with merely discussing applications of the method.B. Fluctuation Dynamics in Fluids.-For a multicomponent fluid system, the dielectric fluctuations can be related in a very simple way to fluctuations in the independent thermodynamic variables entropy, pressure, and concentration of the component species where ct is the concentration of species i, p is pressure, and S is entropy. For small fluctuations, which is usually a good approximation for a system at thermal equilibrium far from a phase transition, the relaxation dynamics can be described by the linearized laws of hydrodynamics.lP Relaxation of the concentration fluctuations is found from Fick's Law of Diffusiod2 to be the exponential relation 8c&,t) = Sc(x,O) exp(-Doc2t) (9) l1 D. A. Pinnow, S.J. Candau, and T. A. Litovitz, J. Chem.Phys., 1968,49, 347; R. Pecora and W. A. Steele, ibid., 1965, 42, 1872; R. Pecora, ibid., 1968, 49, 1036. L. D. Landau and E. M. Lifshitz, 'Fluid Mechanics', Addison Wesley, Reading, Mass., 1959. Jamieson and Maret DZbeing the translational diffusion coefficient of species i. The decay of isobaric entropy fluctuations is also found, from the law of heat conduction,la to be exponential: 8S(K,t) = 8S(K,O) eXp[-(K2&//lcp)] (10) where At is the thermal conductivity, p is density, and Cp is the specific heat at constant pressure. Finally, from the hydrodynamic equations, it is found that the isentropic pressure fluctuations correspond to two oppositely propa- gating sound waves: 8p(K,t) = & &I(%,())COS(V.Kt) eXp[- (BK'~)] (1 1) In equation (11) z, is the velocity of sound in the fluid and the quantity B is related to the sound absorption coefficient a by the equation B = -1 [(4,3,,.+ TV + At(& -$1 2P The RHS of equation (12) contains the parameters shear viscosity rls, volume viscosity rlv, and specific heats Cpand CVwhich contribute to the sound absorp- tion a according to the relation a = BK2/V (13) To obtain the shape of the scattered-light spectrum we simply insert the relations (9), (lo), and (11) into (5), using (7) and (8), and carry out the Fourier transform in time. We find that the spectrum is indeed composed of the three lines centred on the frequency of the incident radiation as observed by early workers: I(K,Wo) = const.[lR(%,w)+ IB(') (%,a-OB) + (x,O + WB)] (14) The central Rayleigh line, ~R(K,o), is a superposition of a number of Lorentzian frequency distributions: a broad component as a result of scattering from entropy fluctuations and having a halfwidth K2At/pCp, and a number of narrow lines which arise from the concentration fluctuations, one corresponding to each species, with a halfwidth D~K~.The oppositely propagating sound-wave modes are the source of the satellite Brillouin lines IB(K,W5 OB) on either side of the Rayleigh line. The frequency shift of these Brillouin peaks is WB = +ivK and each is a Lorentzian distribution with halfwidth BK~.The ratio of the intensity in the Rayleigh line to the intensity in the two Brillouin lines is commonly called the Landau-Placzek ratio IR/21B.For a pure liquid the Rayleigh line is the result of scattering only from entropy fluctuations and in these systems the Rayleigh and Brillouin lines will usually have comparable intensities. In multicomponent systems scattering from con- centration fluctuations is very intense, perhaps 200 times greater than that from entropy fluctuations, and it may be that the Brillouin lines are much smaller in comparison. In macromecular solutions and suspensions, of course, the Ray- 33 1 Quasielastic Laser Light Scattering leigh line is so intense relative to the Brillouin peaks that it is usually difficult to observe the latter. C. Coupling of Fluctuations with Internal Relaxations.-The preceding discussion is oversimplified, applicable only to an idealized system, and designed merely to outline the general formalism used to predict theoretically the quasielastic spectrum of light scattered from fluids.The description specifically assumed that the concentration fluctuations do not couple with each other (i.e. no chemical reaction occurs between the components) and ignored internal relaxations of the scatterers, such as vibrational and rotational excitations or exchange between two structural states of the fluid, which can also cause local changes in the dielectric constant. To a good approximation, the net result of these internal relaxation processes may be regarded as twofold. First, they will introduce additional non-propagating fluctuation modes representing coupling between the internal relaxation and the concentration and entropy fluctuations. These will also scatter light in a characteristic manner, giving rise to additional unshifted Lorentzian components with halfwidths proportional to the relaxation time T characterizing decay of the fluctuation.Coupling to orientational fluctuations is characterized by a T which is inversely proportional to the rotational diffusion coefficient Dr of the moleculesll and usually will only cause a depolarized spectral line to appear when the molecules are optically anisotropic (one excep- tion discussed later is rotational diffusion of an anisometric macromolecule) ; coupling to structural states of a fluid is described by the structural relaxation time T~ representing, for example, the time constant characterizing exchange between molecules of the fluid clustered in transient solid-like configurations and those in disordered ensembles;13 coupling to intramolecular vibrational excita- tions is characterized by Tvib, a measure of the rate of decay of the vibrational state1* (in Kneser liquids T;: could be the rate of exchange of isomerizable states of a molecule); finally, coupling of diffusion fluctuations to chemical reactions decays with a relaxation time proportional to Tr which reflects the rate of the reaction.16 As an example, for the simplest reaction: kf A-+B c 'b Tr-l = (kf + kb) (1 6) These relaxation times are the same parameters measured by perturbation- relaxation techniques such as ultrasonic dispersion, dielectric relaxation, or temperature-jump methods.In general, it may be a difficult task to observe scattering from the coupled modes, for two reasons. First, the integrated intensity of the scattering is much smaller than that from the first-order fluctuations and, l3 K. F. Herzfeld and T. A. Litovitz, 'Absorption and Dispersion of Ultrasonic Waves', Academic Press, New York, 1959. R. D. Mountain, J. Res. Nat. Bur. Stand. Sect. A, 1966, 70, 207. l6 D. L. Knirk and 2. W. Salsburg, J. Chern. Phys., 1971, 54, 1251, and references therein. Jamieson and Maret secondly, it is spread over a much wider spectral range since the internal relaxa- tion processes are much faster than the hydrodynamic modes.An exception to this case is that of solutions of macromolecules which can have relatively slow intramolecular relaxations.16 The presence of internal relaxation processes has a second tangible effect on the quasielastic spectrum which is often more easily observed. At high K-vectors, when the frequency of the Brillouin peak approaches that of the internal relaxa- tions, the thermodynamic constants of the hydrodynamic equations which determine the phonon frequency and damping constant are no longer constant with frequency. Two effects can be distinguished. Structural relaxation or chemical transformation involves a volume change and causes a time-dependent viscosity, for example: CD v(f) = [dt’v(t -f’) = q,exp(-t/7s) (17) w-a3 where T~ is the structural relaxation time.Kneser relaxation on the other hand represents a time-or frequency-dependent specific heat due to vibrational coupling to translational modes. These effects cause a dispersion or shift of hypersonic velocity and absorption analogous to the dispersion at ultrasonic frequencies in relaxing media. Since the hypersonic velocity once again depends on the relaxation times of the internal fluctuations it can also be used to probe the dynamics of these processes. D. Relaxation Time-scales.-Figure 3 shows the relaxation time domains of the various fluctuation phenomena which we have discussed above, and the time-scales accessible by the various techniques currently available.It is immedi- ately evident that laser light scattering in principle provides a probe for molecular dynamics over a very wide range of frequencies. In particular, one can simul- taneously extract information on the equilibrium and kinetic properties of a system. Another feature evident from Figure 3 is that quasielastic light scattering bridges the frequency gap between ultrasonic absorption and neutron scattering, where many important relaxation phenomena occur. In general any internal relaxation process will usually be characterized by some distribution of relaxation times and the measured value T will be a mean of this distribution. Often the form of the distribution of relaxation times can be deduced by careful analysis of spectral pr0fi1es.l~ We note that one can distinguish between fluctuations involving internal and external degrees of freedom simply by studying the quasielastic spectrum at different scattering vectors K, i.e.by changing the scattering angle or changing the laser wavelength. Scattering from external fluctuations such as diffusion or sound-wave propagation exhibits a &dependence whereas the spectral contribu- l6 A. M. North, Chem. SOC.Rev., 1972, 1,49. C. J. Montrose and T. A. Litovitz, J. Acousr. SOC.Amer., 1968,43, 117. Quasielastic Laser Light Scattering Effective frequency I Hz 10” 0 lo3 1o7 10” 1015 llllllllllllll I I 1-1 1 1 1 1 1 1 1 1 Ti2’, T,, 1 1 1 1 1 1 1 1 i‘ 1 1r’] 1 1 i’ I I I I I 1 I I 1 1 I 1 I I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 lo3 0 10- lo+ 10-l6 Relaxation time-scale Is Ray diffraction 1-1-4.N.m.r. Spin relaxation ’‘chemical shift Thermodynamic Dielectric relaxation I 4’properties ...Quasielastic light 1scattering Total- intensi t y Inelastic neutron scattering -‘light scattering’ Lr.+ Raman spectroscopy H U1t r asonic absorption Figure 3 Time-scales of molecular dynamics accessible by some of the more commonly used relaxation techniques: 7e is the time required fGr an electron to complete one circuit in the innermost Bohr orbit, r,,(l)and ro(2)are representative orientational relaxation times for small molecules and macromolecules respectively, rsis a typical structural relaxation time, 7r is a typical relaxation time for chemical reaction in aqueous solution, and rcis a representative time for conformational transition of macromolecules.Depending on the type of system many of these relaxation times may vary by as much as one decade of frequency on either side tion from internal relaxations is angle-independent. Under favourable conditions the two types of scattering can be distinguished in this way. 3 Experimental Techniques The high-resolution analysis of the quasielastic spectrum requires, as we mentioned in the introduction, the use of a laser light source. Details of the characteristics of laser radiation and types of laser available can be found in previous reviews.18 The Brillouin doublet can be adequately resolved by inter- See, for example, W.J. Jones, Quart. Rev., 1969, 23, 73. 334 Jarnieson and Maret ferometry but one cannot usually achieve with interferometric methods the extremely high resolving power necessary to examine in detail the narrow spectral distribution of the central Rayleigh line. This is accomplished by a different technique which utilizes the optical mixing property of photomultiplier tubes (PMT), and we will find it advantageous to describe the two detection methods separately. Descriptions of experimental schemes used by various investigators can be found in the references quoted in the section on applications. The equipment assembled by the authors at Case Western Reserve University and successfully applied to a wide range of fluid systems is a combined optical mixing-interfero- metric spectrometer incorporating the same argon ion laser.A schematic diagram of the equipment is shown in Figure 4. A. Optical Mixing Spectroscopy.-The optical mixing methods take advantage of the fact that photomultiplier tubes act as square-law detectors. The photo- current generated is proportional to the square of the field and the oscillating components of the field therefore effectively mix or beat with each other at the surface of the phototube. The difference ‘beats’ which correspond to the molecular Doppler frequency shifts in the scattered light can be measured in the photo- current with a conventional audiofrequency spectrum analyser.Details of the basic theory and instrumentation of the technique have been reviewed e1se~here.l~ There are two ways of observing the spectrum of scattered radiation by beat-frequency detection. These are commonly labelled the homo- dyne and heterodyne methods. In the former, only the radiation scattered by the fluid medium is allowed to mix on the photocathode surface; in the latter the quasielastically scattered radiation is purposely mixed with some unbroadened laser light, either by beam-splitting some reference light to the phototubele or by elastic scattering from a stationary surface near the scattering volume in the fluid.le The advantages of the heterodyne method are that, by regulating the amount of unbroadened light, one can analyse very low light-scattering levels and also that it is easier, for the same reason, to obtain pure spectra than in the homodyne system, which will have a heterodyne component if any stray elastic scattering reaches the phototube (e.g.from the scattering cell walls, lens surface, etc.).One disadvantage is that any uncorrelated motions of the fluid and elastic scatterers will produce a false spectrum (e.g. convection in the fluid or micro- phonic vibrations of the elastic scattering source). Also, if the beam-splitting method is used, it may be difficult to phase-match the scattered and reference beams at the phototube surface, which is necessary to optimize the efficiency of the light-beating process. Fortunately these effects can all be minimized by appropriate instrument a1 design.The optical mixing spectrometer shown in Figure 4 incorporates a swept-filter audiofrequency spectrum analyser and a digital averager which smooths out the random noise of the photocurrent. The characteristics of our spectrometer, H. Z. Cudns and H. L. Swinney, in ‘Progress in Optics’, ed. E. Wolf, North Holland, Amsterdam, 1970, vol. 8. w w o\ SCATTERING 3. SPECTRUMPMT AMPLIFIER ANALYSER I I I -b AUTO PDP8/ L Q DIGITAL 'RECORDER 3' -CORRELATOR COMPUTER 400mW POWER IN I SINGLE MODE AT 4880i I INTERFEROMETER I PHOTONPMT. . AMPLIFIER COUNTER CELL Figure 4 Schematic diagram of combined optical mixing spectrometer and Brillouin spectrometer assembled by the authors Jamieson and Maret which is flat to 1 MHz, have been described previously.20 Recently a new genera- tion of multichannel, real-time spectrum analysers and correlators have become commercially available.21 These instruments have enormously decreased the time required to generate the spectral density function of equation (5) or the equivalent autocorrelation function of equation (6).Finally, it is also possible to measure the autocorrelation characteristics of the scattered light by a photon-counting method which determines the photon statistics of the light incident on the photo- tube.22 The advantages of this detection scheme are the ability to work with extremely low light levels and to study very fast relaxation processes (nano- second relaxation times) at high resolution. For experimental purposes, it is mandatory that the laser output be free of amplitude fluctuations since these will produce afalse low-frequency ~pectrum.~~,~~ Phase fluctuations, however, do not cause false spectra to appear.19 Also, because the Rayleigh linewidth is usually much narrower than the spacings of the longitudinal laser modes, beats between these modes will not usually interfere with spectral observations and experiments can be performed with multimode lasers.In addition, since the signal to noise ratio is inversely proportional to the number of coherence areas within the solid angle subtended by the collection optics, and since the number of coherence areas in a given solid angle decreases as the scattering volume decreases, it is important to make the scattering volume as small as possible.For this reason, the laser beam should have a small angular divergence and is usually focused into the scattering medium with a short focal length lens. To ensure a well-defined scattering angle, the collecting aperture should be small. As a cautionary note, however, we note that at small scattering angles a significant spread in angular definition of the focused beam can lead to distortion of the observed spectra, an effect which is equivalent to a spread in scattering angles due to a collecting aperture that is too large.23 The aperture has to be wide enough, however, so that at least one coherence area is irradiated on the photocathode surface.19 The frequency limit to which spectra can be accurately measured is also determined by the limit of flat frequency response of the PMT and operational amplifier electronics.B. Interferometric Spectroscopy.-The modern Fabry-Perot interferometer consists essentially of two very flat pieces of glass, the inner surfaces of which are coated with a dielectric coating to give reflectivities of 90-99%. The spectral content of light passing through the interferometer is analysed by changing the optical path length between the two mirrors. This is achieved by changing the air pressure between the mirrors or by moving one of the mirrors. The quality of the information obtained from a Brillouin scattering experiment is largely dependent on the stability characteristics of the interfer~meter.~~ For example, 2o A.M. Jamieson and A. G. Walton, J. Chem. Phys., 1973, 58, 1054. 21 Y. Yeh, J. Chem. Phys., 1970, 52, 6218. 22 C. J. Oliver and E. R. Pike, Brit.J. Appl. Phys. [J. Phys. (D)],1968, 1, 690. 23 R. V. Edwards, J. C. Angus, M. J. French, and J. W. Dunning, jun., J. Appl. Phys., 1971, 42, 837. 24 A. R. Maret, Ph.D. Thesis, Case Western Reserve University, Cleveland, Ohio, 1971. 337 Quasielmtic Laser Light Scattering high-resolution work demands that the two mirrors be kept parallel to angular resolutions of 0.05 arc sec. Commercial instruments are available with piezo- electric adjustment devices which permit an angular resolution of 0.01 arc sec.In the spe~trometer~~ diagrammed in Figure 4, light from an argon ion laser passes through a thermostatted octagonal scattering cell located at the centre of a rotary table. The frequency content of the scattered light collected at an angle 8 to the incident beam is analysed with a piezoelectrically driven Fabry-Perot interferometer. The light then passes to a photomultiplier detector. Three methods are used for processing the signal from the PMT. These are (i) d.c. detection: the output voltage across the PMT load resistor is fed directly in a strip chart or x-y recorder with a time constant of -0.5 s; (ii) photon counting: the PMT output passes to a photon-counting system consisting of a variable-shaping pre- amplifier, pulse-height discriminator, and linear counter ;the resulting signal is then displayed on a strip chart or x-y recorder; and (iii) signal averaging: the output of the PMT is signal-averaged by the PDP8/L computer, whose memory is swept in synchronization with the interferometer scan; at the end of a pre- determined number of sweeps the signal-averaged spectrum is displayed on an x-y recorder.Interferometric spectroscopy places more stringent demands on the laser source than optical mixing spectroscopy. To reduce the linewidth of the incident radiation as far as possible the laser is operated in a single longitudinal mode using an intracavity etalon. The frequency drift and linewidth jitter of the single mode must be minimal if the Brillouin shifts and linewidths are to be obtained to better than 5%.Good single-mode stability is therefore a very necessary criterion for the laser source which should, in addition, ideally have as short a wavelength exciting line as possible to allow study of maximum Brillouin frequency shifts. For both the optical mixing and interferometric methods, the laser should have high power to allow a good signal from fluids of low scattering power and also a short-wavelength exciting line since PMT's are usually more efficient at shorter wavelengths. Early studies were conducted with He-Ne lasers, which have high stability but relatively low power. More recently stable commercial argon ion lasers have become available and are being widely used because of their higher power and shorter-wavelength lines.Finally, it is worth pointing out that interferometric spectroscopy, like classical light scattering, is very sensitive to stray dust particles, which are highly efficient scatterers and cause an erroneously intense Rayleigh line. To obtain accurate Landau-Placzek ratios, it is therefore necessary to achieve a high degree of optical purity for the solutions, either by repeated filtration procedures or by multiple distillation. In the instrument at Case, this was achieved by incorporating the cell in a closed recycling filtration loop consisting of a centrifugal pump and a 0.45 pm Millipore filter. Since the scattering cell is permanently connected in the filtration loop it was possible to verify Landau-Placzek ratios by refiltering the sample in situ.Optical mixing spectroscopy is not nearly so sensitive to parasitic scattering from dust, which merely causes an abnormally intense signal Jamieson and Maret around zero frequency. The main part of the spectral distribution is, however, not at all affected by the dust and can be accurately studied by computer curve fits. This feature is indeed one of the attractive advantages of the technique for measuring molecular weights over alternative methods such as angular dis- symmetry of light-scattering intensity. 4 Applications A. Pure Liquids, Solutions, and Suspensions.-By far the largest area of applica-tions of quasielastic light scattering has been to the study of molecular properties in the liquid state.We feel it is convenient to separate our review of these investigations into the categories of equilibrium (steady state) and non-equi- librium (relaxation) states. (i) Equilibrium Properties. Molecular weights and particle sizes and shapes. The technique of optical mixing spectroscopy provides a powerful new method for determining particle sizes and molecular weights of macromolecular species in dilute solution which has certain striking advantages over traditional methods, i.e. the rapidity of data acquisition, the ability to work with extremely small amounts of macromolecular material, and the decreased importance of soIution contamination by large particles (e.g. dust, biological debris, etc.). The first consideration allows one to follow by repeated measurements quite rapid molecular-weight changes, as in aggregation processes,26 or rapid size changes, as in denaturation of a protein (i.e.one can monitor the kinetics of an irreversible change from the equilibrium state); the last two considerations are very important for many biological applications when only small amounts of pure material may be available or when substantial contamination by cellular debris or other macro- molecular contaminants arises.The parameter measured from the Rayleigh spectrum of concentrat ion fluctuations in a solution of macromolecules is the translational diffusion coefficient Dt of the macromolecules as described in the discussion following equation (14). To obtain a measure of the size of the macromolecules, the Stokes-Einstein relationship can be used in the limit of very dilute solutions: where k is the Boltzmann constant, T the absolute temperature, r] the solvent viscosity and rh the hydrodynamic radius of the particle.Note that quasielastic light scattering measures the hydrodynamic size, which is the same as that measured by a sedimentation equilibrium experiment but may be slightly different from the size measured by small-angle X-ray scattering or electron microscopy. The molecular weight M can be derived by rewriting expression (18) as Dt = fM-7 (19) A. M. Jamieson, C. E. Downs, and A. G. Walton, Biochim. Biophys. Ada, 1972, 271, 34. Quasielastic Laser Light Scattering where 5 and y are positive constants.2s The constant y depends on the conforma- tion of the polymer in solution and has a value which varies from ca.0.5 for a free-draining random-coil molecule to a value of ca. 1.O for a rigid rod conforma- tion. A measurement of molecular weight can be made in one of three ways: it is necessary to know the constants 8 and y either from standards or from having established the conformation of the macromolecule or to combine the diffusion- coefficient data with knowledge of the sedimentation coefficient s,for example using the equation26 -soma =M(1 -Gpo)/RT (20) where Soand Do are the sedimentation and diffusion coefficients extrapolated to infinite dilution, R is the gas constant, v2is the partial specific volume of the solute, and po is the density of the solvent.Jamieson et al.27obtained the empirical relation Dt = 1.33 x M-0.59 from the plot of log Dt versus log A4 for three sulphated mucopolysaccharides shown in Figure 5. This relation was then used to determine molecular weights Chondroitin 6-sulphate 6.50 I I 16.20 I 4.0 4.2 4.4 4.6 log M Figure 5 Plot showing relationship between weight-average molecular weight and difusion coeficient for three mucopolysaccharides at 25 "C a6 C. Tanford, 'Physical Chemistry of Macromolecules', John Wiley & Sons, New York, 1965. A. M. Jamieson, T.-Y. Lee, and 1. A. Schafer, Biophys. J. 1973, 13, A154;submitted for publication in Biochemistry. Jamieson and Maret of small quantities of the mucopolysaccharide dermatan sulphate extracted from the human placenta at two stages of foetal development.27 The susceptibility of the two species of dermatan to molecular-weight degradation by the enzyme hyaluronidase was then studied to investigate the effect of development on the hybrid structure of the material.Frederick et at. have studied the relation between Dt and M for the synthetic polymer polystyrene.2s Various workers havereported studies in which, using equation (18), hydrodynamic sizes have been deduced for a wide range of macromolecular species including viruses,29 bacteriophages,3O efl~ymes,~~,~~ as well as synthetic polymerss3 and latexes.34 and pr~teins,~~~~~ It is important to note that the diffusion coefficient must be measured in the limit of very dilute solutions where intermolecular interactions are not effective, since otherwise it will not reflect molecular size or weight in a simple way.Also, in many macromolecular systems, especially synthetic polymers, there will often be a distribution of molecular weights and the measured molecular weight will be a statistical average. The nature of the average has been discussed by several authors, notably Pe~ora~~ and Ford.36 It turns out that the average measured by quasielastic light scattering is closely related to the weight-average quantity just as in classical light ~cattering.~~ Information about the shape of the molecular-weight distribution can be obtained, but this requires careful analysis of the spectral pr~files.~~,~~ The latest instrumentation allows measurements of diffusion coefficients in as little as 30 seconds. This means that molecular weight (size) changes as in aggregation or flocculation processes or the conformational change of a macro- molecule can be monitored by the technique.Biologically significant examples of such phenomena which have been studied are the thermally driven coacerva- tion of the structural protein and the aggregation of the fibrous protein It is also possible, in principle, to deduce molecular weights by interferometric spectroscopy from the Landau-Placzek ratio of light scattered from macro- molecular ~olutions.~~ We do not feel this approach is as generally useful as the optical mixing method, however, since contamination of the solutions by macro- scopic debris can have a potentially disastrous affect on Landau-Placzek ratios so that a high degree of optical purity is required of the solutions. In addition.data acquisition is much slower. The interested reader is referred to the litera- t~re.~?Two features of Brillouin measurements of molecular weights are that an empirical relation between molecular size and weight does not have to be ** J. E. Frederick, T. F. Reed, and 0. Kramer, Macromolecules, 1971, 4, 242. aB S. B. Dubin, J. H. Lunacek, and G. B. Benedek, Proc. Nat. Acad. Sci. U.S.A.,1967,57,1164. 30 M. J. French, J. C. Angus, and A. G. Walton, Science, 1969, 163, 345. 31 L. Rimai, J. T. Hickmott, T. Cole, and E. B. Carew, Biophys. J., 1969,9, 518.32 M. J. French, J. C. Angus, and A. G. Walton, Biochim. Biophys. Acta, 1971, 251, 320. 3s N. C. Ford, W. Lee, and F. E. Karasz, J. Chem. Phys., 1969,50, 3098. 34 J. W. Dunning and J. C. Angus, J. Appl. Phys., 1968, 39, 2479. 35 R. Pecora and Y. Tagami, J. Chem. Phys., 1969,51, 3298. s6 N. C. Ford, R. Gabler, and F. E. Karasz, Ah. Chem., in the press. 37 G. A. Miller, J. Phys. Chem., 1967, 71, 2305; G. A. Miller and C. S. Lee, ibid., 1968, 72, 4644. Quasielastic Laser Light Scattering established beforehand and that it is possible to measure the molecular weights of even very small molecules such as oligomers. An anisometric molecule will have an orientational degree of freedom and a rotational diffusion mode characterized by the whole-molecule rotational diffusion coefficient. If the molecule is optically anisotropic, the quasielastic light- scattering spectrum will have a broad, unshifted depofarized component whose halfwidth is proportional to the rotational diffusion coefficient.ll A large (polymer) molecule, even if it is optically isotropic, will also have an additional, unshifted polarized component which will begin to contribute substantially to the spectrum at large scattering angles when the concentration fluctuation wavelength (1 = 277/~is of comparable size to the length of the Since the spectral component arising from rotational diffusion does not vary with scattering angle, it is possible to measure the rotational diffusion coefficient of both optically isotropic and anisotropic macromolecules by studying either the polarized Rayleigh spectrum at large scattering angles3* or the depolarized spectrum at small angles, respective1y.l' Optical mixing studies of rotational diffusion by both experimental approaches have been rep~rted.~~,~~ Comparison of translational and rotational diffusion coefficients of macromolecular species can provide accurate informat ion on the molecular ge~metry.~' Interferometric analysis of the depolarized spectrum of optically anisotropic small molecules can be used to study the mechanism of rotational diffusion of these speciesll and also to deduce the molecular geometry of macromolecules of intermediate size whose rotational diffusion is too fast to observe by optical mixing Activity coeficients.Interferometric and also optical mixing studies of solutions can provide thermodynamic data in the form of the derivative (~JL/~C)~,Tdescrib-ing the concentration dependence of the chemical potential p. This can then be used to evaluate activity coefficients or 'excess' thermodynamic functions which describe departures from ideal-solution behaviour. This information can be obtained by interferometric measurement of the Rayleigh-Brillouin intensity ratio J.42-44The complete equation determining J for a binary solution contains many term^.^^^^^ Some of the terms are small compared with the concentration- fluctuation term (an/ac)2/(ap/ac)and thus may be neglected within the experi- mental accuracy of most measurements, leading to the simple equation where Jo is the intensity ratio of the pure solvent (Landau-Placzek ratio) and K is a composite constant which can usually be evaluated from literature data.24 Maret and Yeager4* have determined values of J in aqueous electrolyte solutions R.Pecora, J. Chem. Phys., 1964, 40, 1604; ibid., 1968, 48, 4126. sg A. Wada, N. Suda, T. Tsuda, and K. Soda, J. Chem. Phys., 1969,50,3098. 40 H. Z. Cumins, F. D. Carlson, T. J. Herbert, and G. Woods, Biophys, J., 1969, 9, 518; D. W. Schaefer, G. B. Benedek, P. Schofield, and E. Bradford, J. Chem. Phys., 1971, 55, 3884. 41 S. B. Dubin, N. A. Clark, and G. B. Benedek, J. Chem. Phys., 1971,54, 5158. 4e R. D. Mountain and J. M. Deutch, J. Chem. Phys., 1969, 50, 1103. 4s R.D. Mountain and L. Fishman, J. Phys. Chem., 1970, 74, 10. O4 A. R. Maret and E. Yeager, J. Chem. Phys., 1972,57,2225; ibid., 1973, 59,206. 342 Jamieson and Maret of chlorides, nitrates, and sulphates at concentrations up to 3M. A typical Brillouin spectrum is shown in Figure 6. They obtained agreement to within *2 I\ Figure 6 Brillouin spectrum of 0.31M-NiS04 at 25 "C.The diagram represents one complete interferometer scan from Rayleigh peak R1 to Rayleigh peak R,. The strong scattering from concentration fluctuations makes it necessary to attenuate the Rayleigh peak by a factor of ten 5 % between the experimentally determined activity coefficients using equation (21) and literature data with the exception of the sulphate solutions. This discrepancy can be plausibly accounted for by the ion-association reactions of the 2:2 sulphates (discussed in a later section) which produce additional terms in equation (21).Berge et al. have examined the Rayleigh line from binary mixtures or organic solvents using the heterodyne technique.4s By computer-fitting Lorentzians, they were able to separate the two principle components of the Rayleigh line, i.e. one due to concentration fluctuations and a broader component due to entropy fluctuations, and thus obtain values of (ap/ac).This method, however, requires a complete and accurate knowledge of the Rayleigh spectral distribution whereas the interferometric method employs a simple measurement of intensities. Activation energies.By monitoring the temperature dependence of the relaxation time for a fluctuation process, it is possible to compute the activation energy for the process from the Arrhenius equation. Figure 7, for example, displays the 4D P. Berge, P. Calmettes, M. Dubois, and C. Laj, Phys. Rev. Letters, 1970, 24,89; M. Dubois and P. Berge, ibid., 1971,26, 121. >sT =300K cr.-mA$q'rt' = 7.8kHz 0,U 25.0 0 25.0 Frequency/kHz Jamieson and Maret optical mixing spectra of a 0.5 mole fraction mixture of n-hexane in carbon disulphide at temperatures of 300 K and 255 K respectively. Knowing the refractive index of the solution at the two temperatures the mutual diffusion coefficients can be calculated and the activation energy for mutual diffusion in this system derived.The value for this system turns to be 1.4 k 0.2 kcal mol-l, which is somewhat lower than typical values measured in mixtures of liquid hydrocarbons using diffusion-cell technique^.^' One reason for this is certainly the fact that the molar volume of carbon disulphide is much smaller than that of any of the hydrocarbons studied. Within the experimental error, a similar value, 1.2kcal rnol-l, was obtained for a 0.5 molar mixture of n-pentanol in carbon di~ulphide.~~ This value is much lower than typical self-diffusion coefficients in alcohols measured by n.m.r. technique^,^^ which is understandable since self-diffusion reflects the relative transport of the alcohol and requires breaking of hydrogen bonds.In order to compare these two measurements it would be necessary to study the concentration dependence of the two values and extrapolate to infinite dilution, where they should coincide. Recently these questions have been discussed in an elegant paper by Ahn et aZ.49The similarity of the values of the mutual diffusion coefficient in the n-hexane and n-pentanol systems reflects the fact that there is no substantial difference between the inter- actions of the two species with the carbon disulphide. (ii) Non-equilibrium Properties. Diffusion coeficients and electrophoretic mobilities. The diffusion coefficient of a macromolecule in a solution characterizes its rate of transport through the solvent and of course is an important parameter in its own right.For example, many important chemical and physiological reactions, such as certain free-radical reactions of polymers or the antigen-antibody re- action of the bodyare diffusion controlled. The diffusion coefficient is of course determined by other factors besides its molecular size or geometry, such as degree of ionization, ion atmosphere, and interactions with other molecules. Thus Stephenso has proposed using optical mixing spectroscopy to measure the partial charge of macromolecular species and in an interacting system of polymers, one of us has demonstrated the feasibility of studying collision-induced anisotropic translational diffusion phen~mena.~' At some smaller limiting size, the Stokes-Einstein relation (18) is no longer accurate and the diffusion coefficient does not reflect hydrodynamic diameter in a simple way but is a mutual property of solvent and solute.Berge et al. have made some small-angle measurements of mutual diffusion in binary liquid mixtures.45 Jamieson and WaltonZ0 (taking advantage of the higher power of their argon laser source) have studied the effect of concentration, chain length, and hydrogen-bonding on mutual diffusion of mixtures of primary alcohols in carbon disulphide and nitrobenzene at somewhat larger scattering angles where A. M. Jamieson and A. G. Walton, unpublished results. 47 A. L. Van Geet and A. W. Adamson, J. Phys. Chem., 1964, 68,238. 48 D. E. O'Reilly and E. M. Peterson, J. Chem. Phys., 1971, 55, 2155. 49 M.-K. Ahn, S.J. K. Jensen, and D. Kivelson, J. Chem. Phys., 1972, 57, 2940. M. J. Stephen, J. Chem. Phys., 1971, 55, 3878. 51 A. M. Jamieson and C. T. Presley, Macromolecules, 1973, 6, 358. QuasielasticLaser Light Scattering instrumental errors are easier to control. By extrapolating the concentration dependence to infinite dilution it is possible to determine the self-diffusion coefficient of one species for comparison with measurements by other techniques. An interesting recent development has involved a study of the Rayleigh spectrum of charged particles in solution or suspension when perturbed by an electric field. This combination of electrophoresis with laser light scattering permits the simultaneous measurements of electrophoretic mobilities and diffusion coefficientssa in a rapid fashion without the complications of concentration gradients and boundary effects. Electrophoretic resolutions are greater than those obtained by moving-boundary experiment^.^^ This method appears to have great potential in industrial work involving charged suspensions, e.g.electrocoat paint suspensions and liquid developer suspensions for copying machines. In addition, electrophoretic light scattering may provide an important probe for studying the kinetics of interacting of macromolecules. Vibrational and structural relaxation. Studies of the relaxation dynamics of molecular processes in pure fluids offer a powerful method of gaining insight into the mechanisms of such processes, which serves as a critical test of theories of the liquid state.As explained in Section 2C,relaxation phenomena manifest them- selves as a dispersion or change in magnitude of both the sound velocity ZI and the absorption coefficient a at frequencies near the relaxation frequency, w = 1/r. For many systems, the change in velocity due to relaxation is of the same magnitude as the experimental precision and usually absorption measurements are more applicable. Relaxation times are obtained from a relation of the form13 where A and B are constants. By studying the frequency dependence of a,we can deduce the relaxation time r. Brillouin scattering techniques have been employed in the determination of acoustical parameters at gigahertz (loD)frequencies, more or less as an extension of existing ultrasonic methods at megahertz (lo6)frequencies. The majority of liquids exhibit their important vibrational and structural relaxation phenomena within this frequency domain, which is not in general accessible by other tech- niques as pointed out earlier in Figure 3.Brillouin scattering techniques permit sound velocities to be determined to within rt 0.2 % and sound absorption coefficients to k3 %, i.e. with precisions approaching those obtainable with ultrasonic technique^.^^ Some examples of the use of Brillouin scattering as a probe for molecular dynamics will now be described. Several groups have investigated the relaxation of the vibrational specific heat of benzene using ultrasonics and Brillouin scattering. There is disagreement on whether the system exhibits a single or multiple relaxation.O'Connor et aLSs lip B. R. Ware and W. H. Flygare, Chem. Phys. Letters, 1971,12, 81 ;B. R. Ware and W. H. Flygare,J. Colloid Interface Sci., 1972, 39, 670. liS C. L. O'Connor and J. P. Schlupf, J. Acoust. SOC.Amer., 1966,40,663. Jamieson and Maret have proposed a single relaxation time of 5.2 x lo-" s. In more recent work, .~~Nichols et ~1contend that no single total relaxation of all the vibration modes can make the Brillouin scattering data (> 2 GHz) consistent with ultrasonic data (100 MHz). They proposed two relaxation times 71 = 3.0 x 10-lo s and T~ = 3.6 x s. A number of hypersonic investigations of vibrational relaxation in CCI have been reported in the literature, the most extensive being the work of Stoicheff et aZ.65(experimental) and Nichols and (theoretical).These studies used computer techniques to obtain the relaxation time by fitting theoretical expressions to the observed spectra. The results have shown that CC14 undergoes a thermal relaxation with T = 6.5 x 10-l1 s, and that the total vibrational contribution to the specific heat is 11.6 cal mol-1 OC-l, in good agreement with the value of 11.9 cal mol-1 OC-l calculated from the known vibrational frequen- cies of the CCI4 molecule. Structural relaxation is a general phenomena applicable to all liquids. The time-scales, however, vary considerably from, for example, values of s in highly associated liquids like glycerol at room temperature to 10-l2 s for water at room temperature or the liquefied noble gases at cryogenic temperatures.The noble-gas liquids have received considerable atfenti~n~~,~* because of the possibility of correlating experimental data with machine calculations as well as theories of the liquid state which can be expected to be more rigorous in these simple systems. Toluene exhibits a structural relaxation spectrum which can be entirely covered by the Brillouin scattering method. The most extensive evaluation of the relaxa- tion curve for toluene has been carried out by Chiao and Fle~ry,~~ who measured the hypersonic velocity at 14 different frequencies (1.e. scattering angles) and found a velocity dispersion of 70 m s-l between the ultrasonic value and their highest frequency.These data correspond to a relaxation time of 2 x lo-" s. Brillouin scattering in the ultraviolet offers the possibility of measuring even shorter structural relaxations. For example, one could observe in water and aqueous solutions the departure from a constant value of a/w associated with the structural relaxation curve of structured forms of water (T~= 10-12 s at 25 "C). Ma~et~~ has used an argon laser-harmonic generator system operating at 257.3 nm in an attempt to observe such deviations, but difficulties connected with poor resolving power of the U.V. interferometer prevented the acquisition of accurate data. As we mentioned earlier, an alternative way of investigating vibrational and structural relaxation is through observation of the additional non-propagating spectral line often called the Mountain line.This fourth component has been *' W. H. Nichols, C. R. Kunsitis-Swyt, and S. P. Singal, J. Chem. Phys., 1969, 51, 5659. l6 B. P. Stoicheff, G. I. A. Stegemann, W. Gornall, and V. Volterra, J. Acoust. SOC.Amer., 1971, 49, 979. W. H. Nichols and E. F. Carome, J. Chem. Phys., 1968,49, 1000. 67 L. Y.Wong and A. Anderson, J. Opt. SOC.Amer., 1972, 62, 1112. P. A. Fleury and J. P. Boon, Phys. Rev., 1969, 186,244. 59 R. Y. Chiao and P. A. Flew, 'Physics of Quantum Electronics', McGraw Hill, New York, 1966. Quasielastic Laser Light Scattering observed in carbon tetrachloride66 where there is strong coupling between vibrational and translational modes and also in glycerol,s0 where structural relaxation dominates.The relaxation time can be obtained from the relationship where represents the width of the corresponding spectral component. The advantage of this procedure is that it is possible, in principle, to obtain T from a single measurement, in contrast to the use of equation (22), which requires data at many different frequencies. Macromolecules have relatively slow vibrational relaxation times which can be observed by optical mixing spectroscopy. Fujime and co-workerssl have studied the relaxation times of these backbone flexing motions in the muscle protein actin and observed the effect of Ca2+ ion concentrations on the dynamics of the motions. Chemical kinetics.Kinetic constants of solution reactions can be obtained from a study of the width of the Rayleigh component. Relaxation times as high as s can be measured using the optical mixing technique; faster time regimes require the use of a high-resolution Fabry-Perot interferometer. However, even 'fast' chemical reactions usually have time-scales which cause dispersion at ultra- sonic frequencies rather than hypersonic frequencies. The preferred met hod is therefore the study af the additional non-propagating reactive component of the spectrum. The halfwidth of this fourth component is proportional to the re- laxation time 7~and, for a simple reaction process with only two distinct spe- cies, the kinetic rate constants are related to TR by equation (16).Yeh has used interferometry to study the relaxation time T for the following fast step in 2:2 sulphate associationsa [M2+(HzO)SO~-]aq", [MSOJaq +HBO (24) where M = Zn or Mn. The relaxation times were in good agreement with those measured by ultrasonic relaxation methods. Hypersonic absorption measure- ments of 2:2 sulphate solutions have been obtained in an attempt to complete the ultrasonic characterization of ionic association in such systems.*S It has been shown that the high-frequency absorption coefficient must be determined with an accuracy of a few tenths of a percent to distinguish adequately between various proposed mechanisms for the ion as~ociation.~~ Unfortunately, measure- ment of sound-absorption coefficients at hypersonic frequencies have not yet been of sufficient accuracy to be a useful tool for distinguishing various proposed mechanisms of ion association in the 2:2 sulphates.Optical mixing studies have been reported of the relatively low reaction rates involved in conformational transitions of macromolecules. In one study Yeh measured the rate constant for the helix-coil transition of the copolymer deoxy- 6o B. P. Stoicheff, H. F. D. Knaap, and W. S. Gornall, Phys. Rev. (A), 1968, 166, 13. S. Ishiwata and S. Fujime, J. Mof. Bid., 1972, 68, 51 1, and references therein. 6a Y. Yeh and R. N. Keeler, J. Chem. Phys., 1969,51, 1120. 63 A. R. Maret and E. Yeager, J. Acoust. SOC.Amer., 1973,54, 666. 64 L. Jacobin and E. Yeager, J. Phys. Chem., 1970,74, 3766.Jarnieson and Maret adenylate-deoxythymidylate.21Once again, the value of 2.33 x s-l was in good agreement with temperature-jump relaxation measurements. Simul-taneously Yeh found the linear diffusion coefficient within the transition region to have a value of 2.9 x cm2 s-l. Jamieson et de6have studied the helix to charged coil transition of poly-L-lysine hydrobromide and identified a broad spectral component in the transition region as due to relaxation via the conforma- tion change. Since the relaxation time derived is an order of magnitude smaller than that measured by ultrasonics, they have proposed that it represents an intra-molecular diffusion contribution to the conformational kinetics based on the earlier theoretical work of Simon.ss B.Gases, Solids, and Liquid Crystals.-In this section we will give a brief description of recent developments in applying quasielastic light scattering to the study of gases, solids, and liquid crystals. Brillouin scattering studies have given insight into the nature of molecular dynamics in gaseous ~ysterns.~~~~~ The hydrodynamic equations are valid in gases only for small scattering As K increases, the ‘size’ of the fluctuation becomes small relative to the mean free collision diameter. Under such circumstances a kinetic theory must be invoked to take into account the effects of a distribution of molecular velocitie~.~~ Thus Brillouin scattering studies of gases can effectively be used as a test of the Boltzmann equation.s7 Brillouin scattering is also a very useful tool for the measurement of the elastic and photoelastic constants of crystal^.^^-^^ For example, Gewurtz et aL70 have calculated the adiabatic elastic constants of single crystals of the noble gases from the experimentally determined sound velocity. Studies in these systems provide sensitive tests of recent theories of lattice dynamics.Other measurements have been successfully performed on the theoretically less well characterized crystal systems of calcite71 and lithium acetate.72 Berge et al. have recently made the first optical mixing experiment on a solid.73 They found that the spectrum of Rayleigh scattering from entropy fluctuations in single-crystal succinonitrile was exactly that predicted for Rayleigh scattering in a liquid; see equation (10).Brillouin measurements of hypersonic velocities74 and Landau-Placzek (J) ratio^^^*^^ at the glass transitions in amorphous polymeric solids have been 8b A. M. Jamieson, L. Mack, and A. G. Walton, Biopolymers, 1972, 11, 2267. E. M. Simon, J. Chem. Phys., 1971,54,4738. O7 T. J. Greytak and G. B. Benedek, Phys. Rev. Letters, 1966, 17, 179. 68 D. P. Eastman, T. A. Wiggins, and D. H. Rank, Appl. Optics, 1966,5, 879. e9 A. Sugawara and S. Yip, Phys. Fluids, 9167,10, 191 1. S. Gewurtz, H. Kiefte, D. Landheer, R. A. McLaren, and B. P. Stoicheff, Phys. Rev. Letters, 1972,29, 1768. n D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. (B), 1972, 6, 3109. R. Vacher and L. Boyer, Phys. Rev.(B), 1972,6,639; R. Vacher, L. Boyer, and M. Boissier, ibid., p. 674. 73 M. Adam, G. Searby, and P. Berge, Phys. Rev. Letters, 1472, 28, 228. 74 W. L. Peticolas, G. I. A. Stegemann, B. P. Stoicheff, Phys. Rev. Letters, 1967, 18, 1130; E. A. Friedmann, A. J. Ritger, and R. D. Andrews, J Appl. Phys., 1969, 40,4243. 76 P. G. de Gennes, Compt. rend., 1968,266, B, IS; Orsay Liquid Crystal Group, Solid State Comm., 1971,9, 653. 349 Quasielastic Laser Light Scattering reported. Friedman et discovered a sharp discontinuity in hypersonic velocity at the transition, indicating a discontinuity in the temperature coefficient of the specific volume, but no measurable change in J values, indicating no major discontinuity in the adiabatic compressibility.These results were taken to indicate that the glass transition is not a classical second-order transition, conflicting with the earlier work of Peticolas et With improved instrumentation Brillouin scattering experiments should provide insight into the relaxation effects associated with the glass transition. A rapidly developing area for applications of the laser light-scattering techique is that of liquid-crystalline materials which have a highly anisotropic molecular polarizability. Such systems are extremely important both in the biological area, e.g. in the physical chemistry of the lipids of the cell membranes, and in com- mercial applications, e.g.as potential electro-optic storage materials. Thermal fluctuations in the orientation of the ordered regions (equivalently, angular fluctuations of the molecular axis or director) cause large fluctuations in the optical anisotropy of these systems and intense depolarized Rayleigh scattering.The initial theoretical work of de Gennes et ~1.'~and subsequent experimental optical mixing studies by the Orsay Liquid Crystal have established a relationship between this depolarized quasielastic spectrum and the various elastic and viscosity coefficients which describe the anisotropic dynamic pro- perties of the ordered matrix of nematic liquid crystals. Recently Galerne et ~11.~~ have observed similar effects in certain smectic liquid-crystal systems. Much interest has focused on the order-disorder transition behaviour at the temperature where the liquid crystal changes to the normal isotropic liquid state.In the nematic-isotropic transition Stimson and Litster have s~ow~,~* by high- resolution interferometric studies of the laser light scattering from the fluctuations of ordered regions in the isotropic phase, that as the transition temperature is approached the spectrum exhibits the characteristics (discussed in the next section) of a second-order phase transition, even though the transition itself is known to be first-~rder.~~ Early Brillouin scattering studies79 near a cholesteric-isotropic transition temperature showed a dramatic discontinuity in hypersonic velocity and damping coefficient at the transition, which would indicate a well- defined, first-order phase transition.The more recent work of Rosen and Shen,** however, found no measurable discontinuity and indicates that the earlier results were due to crystal domain boundary effects. C. Second-order Phase Transitions.-Optical mixing spectroscopy has found particularly valuable application in studies of the critical opalescence which occurs at either the liquid-gas or liquid-liquid phase-separation temperatures. Orsay Liquid Crystal Group, Phys. Rev. Letters, 1969, 22, 1361 ;J. Chem. Phys., 1969, 51, 816. Y.Galerne, J. L. Martinand, G. Durand, and M. Veyssie, Phys. Rev. Letters, 1972,29, 562. 7B J. D. Litster and T. W. Stimson, tert., J. Appl. Phys., 1970,41,996; T. W.Stimson, tert. and J. D. Litster, Phys. Rev. Letters, 1970, 25, 503. 70 G.Durand and D.V. G. L. N. Rao, Phys. Letters (A), 1968,27,455. 00 H. Rosen and Y. R. Shen, Mol. Crystals Liquid Crystals, 1972, 18,285. Jamieson and Maret As a binary liquid mixture approaches the temperature at which its two com- ponents separate, long-range concentration fluctuations develop, causing a striking increase in the intensity of light scattered by the fluid (i.e.opalescence). The spectral halfwidth rc;of this scattered light has a more complicated depen- dence on scattering vector and temperature than that indicated by equation (7): where Do is the mutual diffusion coefficient far from the phase transition, Tcis the critical point temperature, 1 is a characteristic length defining the range of intermolecular forces which are driving the phase separation, and Y and y are critical ‘scaling’ parameters whose determination serves as a crucial test of the theories of the critical point.s1 As the temperature Tcis approached, equation (25) indicates that the halfwidth of the spectrum becomes increasingly narrow.Analysis of the temperature dependence and angle dependence of the spectrum enables one to deduce the parameters I, v, and y. A similar relation to (25) holds for the spectrum of light scattered by entropy fluctuations of a pure liquid near its critical points2 and for the diffusion coefficient of a polymer in solutions3 as the critical temperature of its separation from the solvent phase approaches. Studies of the Rayleigh spectrum in the critical region have been successfully carried out in all of these case~,~l-~~ and have proved to be extremely useful in developing a molecular understanding of these important phase-separation processes.Bak et aLs4have aIso carried out a spectral analysis of the laser scattering from concentration fluctuations at the critical point of a ternary liquid mixture to study the effect on the ‘scaling’ parameters of the third com- ponent. Brillouin spectroscopy has been successfully used to probe the behaviour of thermodynamic parameters, such as the isothermal compressibility of a fluid, and the relaxation times of internal degrees of freedom at the critical point. Mountains5 has successfully explained the experimental Brillouin linewidth data of Ford et a1.s6and the Rayleigh linewidth data of Swinney and Cuminss7 for scattering from CO, at temperatures just above the critical point.The model used was a modification of the linearized hydrodynamic equations to include a non-local relationship between density and pressure fluctuations, and a frequency- dependent volume viscosity of the type shown in equation (17). D. Miscellaneous.-A number of novel applications of optical mixing spectro- scopy have recently appeared in the literature. The early work of Bouchiat and co-workersgs demonstrated the usefulness of the method for studying the 81 B. Chu and F. J. Schoenes, Phys. Rev. Letters, 1968, 21, 6. 81 N. C. Ford and G. B. Benedek, Phys. Rev. Letters, 1965, 15, 649. 8a S. P. Lee, W. Tscharunter, B. Chu, and N.Kuwahara, J. Chem. Phys., 1972, 57, 4240. 84 C. S. Bak, W. I. Goldberg, and P. N. Pusey, Phys. Rev. Letters, 1970, 25, 1420. R. D. Mountain, J. Res. Nut. Bur. Stand, Sect. A, 1969, 73, 593. N. C. Ford, K. H. Langley, and V. G. Puglielli, Phys. Rev. Letters, 1968, 21, 9.*’H. L. Swinney and H. Z. Gammon, Phys. Rev., 1968, 21,9. M. A. Bouchiat, J. Meunier, and J. Brossel, Compt. rend., 1968,266, B, 255; M. A. Bouchiat, ibid., 1966,266, B, 301 ;M.A. Bouchiat and J. Meunier, Phys. Rev. Letters, 1969,23, 752. 351 Quasielastic Laser Light Scattering viscoelastic properties of liquid surfaces by analysing the light scattered from surface tension waves ('ripplons'). This work has been extended recently by Mann et aLB9and FanBn to studies of the mechanical deformation behaviour of model biomembrane systems. Maeda and Fujimeso have successfully con- structed a mixing spectrometer incorporating an optical microscope which will allow one to monitor the dynamics of localized cellular events in situ.Some workers, notably Berge et al., e~perimentally,~~and Nossal, in a later theoreti- cal treatment,n2 have demonstrated the feasibility of using optical mixing spectroscopy to measure the mean lateral swimming rates of motile micro-organ- isms, such as ~permatozoa.~~ The method seem to offer a useful probe for observing the effects of chemotactic agents on the mobility of these species.ns Finally, Carlson et aLg3in an important paper have recently shown that, in an associating system of macromolecules (specifically the dimerization of the muscle protein myosin), information on the association constants and geometry mole- cular complex can be deduced by quasielastic light scattering.E. Stimulated Brillouin Scattering.-We conclude the applications section with a brief discussion of stimulated Brillouin ~cattering.~~~~~ In this technique, the continuous-wave laser light source is replaced with a high-power Q-switched solid-state laser. The back-scattered Brillouin light mixes with the incident-light pulse producing extremely strong pressure waves owing to electrostrictive effects. The frequency of this pressure wave is equal to that of the thermal fluctuations which are the source of the back-scattering. Further scattering of the inci- dent pulse from these induced sound waves occurs, and the scattered light waves increase in amplitude until the energy of the incident wave is depleted. Clearly the magnitude of the stimulated Brillouin-scattered light depends on the amplitudes of the incident and scattered light waves, i.e.the maximum interaction will occur at 180" scattering angle. The principal advantage of this technique over conventional Brillouin scattering is that the sound velocity is obtained in a more direct way because the relatively high intensity of the scattered radiation permits the concentric ring output of the Fabry-Perot inter-ferometer to be photographed. For further details the reader is referred to the literature. n49 n6 5 Prognosis The past five years have seen a remarkable proliferation of literature in the field of quasielastic laser light scattering analogous to the surge of applications of laser Raman spectroscopy following the pioneering measurements of that J.A. Mann, J. F. Baret, F. J. Dechow, and R. S. Hansen, J. Colloid Interface Sci., 1971, 37, 14; C. Fan, ibid., 1973, 44, 369. *OT.Maeda and S. Fujime, Rev.Sci. Insr., 1972, 43, 566. P. Berge, B. Volochine, R. Billard, and A. Hamelin, Compr. rend., 1967, 265, D, 889. R. Nossal, Biophys. J., 1971, 11, 341. T. J. Herbert and F. D. Carlson, Biopolymers, 1971, 10, 2231. *IN.R. Goldblatt and T. A. Litovitz, J. Acoust. SOC.Amer., 1967, 41, 1301. *IT. T. Saito, L. M. Peterson, P, H. Rank, and T, A. Wiggins, J. Opt.SOC.Amer., 1970, 60, 749. Jamieson and Maret technique: there is every reason to expect this expansion to continue in the years ahead.Optical Mixing Spectroscopy.-The optical mixing technique has obvious dramatic advantages over the traditional methods for size, shape, and molecular weight determinations of macromolecules because of the ease, rapidity, accuracy, and relative freedom of the measurements from errors due to particulate con- tamination. Similarly, optical mixing spectroscopy now offers the best method for measuring diffusion coefficients, particularly since the laser beam is a light probe which does not perturb the medium. The dynamics of relatively slow solution processes (relaxation times down to s) can also be usefully studied by this technique.Again, most macromolecular systems fall into this category and consequently a single mixing spectrometer enables essentially a complete physical characterization of such systems. The major experimental difficulties have now been resolved and we expect commercial instruments to become available in the near future. Brillouin Spectroscopy.-Brillouin scattering using interferometric techniques is capable of providing acoustical information in the form of sound velocities and absorption coefficients with precision and convenience equal to that obtainable with ultrasonic techniques. In addition, the technique has won acceptance as an important tool to the investigator in chemical physics for the study of the dy- namics of processes with relaxation times in the range 10-6-10-11 s.The measurement of Rayleigh-Brillouin intensity ratios can provide accurate values for thermodynamic parameters such as activity coefficients, specific heats, and compressibili ties. The stability characteristics of commercial interferometers and lasers are less than optimum for many Brillouin measurements. However, there is every reason to expect that these difficulties will be surmounted. We have reviewed many diverse chemical problems to which quasielastic light scattering has been successfully applied in an increasing number of labora-tories. In this context we point out, in conclusion, that a single laser source in its optimum experimental configuration, allowing both the Rayleigh and Brillouin spectrum to be accurately studied, enables the investigation of a complete range of molecular dynamics from the steady-state (thermodynamic) parameters to relaxation times as small as s.

ISSN:0306-0012    

DOI:10.1039/CS9730200325

出版商:RSC    

年代:1973

数据来源: RSC