摘要:

GENERAL DISCUSSIONProf. C . A. Coulson (Oxford) (communicated): Prof. Buckingham has suggestedthat his new terms in the interaction energy, which are of order R-7 for two molecules,will probably not contribute much to the total interaction, since their mean valuesover all mutual orientations are zero. This is true. But we can easily carry thecalculation a little further.Thus, consider the dispersion interaction between a spherical and a tetrahedralmolecule. According to Buckingham’s equation (32) this is given byu = - c,/R~ - c2 cos 0, cos e,, cos 0 ~ ~ 7 + . . . , (1)where C1 and C2 are known constants for the two molecules.The classical thermal average of this expression isii = J u exp (-u/kT)dQ/Jexp (-u/kT)dQ.Straightforward calculation shows that this isU = -Cl/R6-C$/105kTR’4+ .. . (2)Thus, as might have been expected, the R-7 term in (7) leads to a mean energy oforder R-14. It is therefore entirely negligible.The same situation is found in all the examples discussed in Buckingham’s paper.These new forces obtained by averaging the angularly-dependent part of the energy,are always attractive, and of an order of magnitude in R-1 equal to twice that of thecorresponding term in the energy before averaging. This means that, if the moleculesare free to rotate, the new term will be unimportant. When they are not free to rotate,however, or when their freedom is effectively limited to a finite range, then, asBuckingham says, this term may be important. Molecular crystals, such as thosediscussed by Prof.Craig et al. in this Discussion, may well be cases where this applies.Prof. R. B. Bernstein (University of Wisconsin) said: Can Prof. Buckinghamestimate (for a few systems of practical interest) the relative importance of his newR-7 C O S ~ 6 dispersion term (in eqn. (35))’ compared to the well-known (Andersondipole-quadrupole) R-7 C O S ~ 8 induction term (eqn. (34)) ? The results should haveimplications with respect to rotational excitation via collision of polar diatomicmolecules.Prof. A. D. Buckingham (University of Bristol) said: In reply to Prof. Bernstein,the relative importance of the new R-7 C O S ~ 6 dispersion energy and the Andersondipole-quadrupole induction energy 1 is given by the ratioSimilarly, the ratio of the R-6 dispersion and induction energies isThese two ratios should be similar and may be large, for they are approximatelyequal to the sum over all excited states of a product of transition moments with theground state divided by the corresponding permanent moments of the ground state.1 Anderson, Physic.Rev., 1950, 80, 51 1.27GENERAL DISCUSSION 279Since U - 10-11 ergs, cx- 10-24 cm3 and p- 10-1s e.s.u., the ratio of the R-6 energiesis approximately 4. This figure should also be applicable to the ratio of the R-7 C O S ~ 8energies. However, if p is abnormally large, as in the alkali halide molecules, theR-6 energy ratio may be considerably less than unity, although the R-7 C O S ~ 8 ratiocould be larger since the opposite ionic charges make a large contribution to p buthave a cancelling effect on 0.Prof.J. S. Rowlinson (Imperial College, London) said: The question has beenraised of the quantitative importance of terms of higher order than r-6 in the attractivepart of the pair potential. A simple answer can be given for argon since the resultsof the first part of our discussion lead clearly to the conclusion that there is now nodoubt about two features of this potential. If E is the maximum depth, at a separationrm, and if A is the coefficient of the ratio - ( ~ m / ~ ) 6 then, by chance, the two factorsE and I. are equalHence the r-6 term alone can be extrapolated to pass through the point (rm, - E ) .There is therefore, a substantial contribution from higher negative terms to offsetthe repulsive part of the potential.This contribution must be of the same order ofmagnitude as the r-6 term at a separation r,.Prof. N. R. Kestner (Stanford University) said: In regard to the importance of theR--8 terms iii the intermolecular potential, Margenau showed in 1939 that the R-*terms could change the potential depth by 50 % for typical rare gas atom interactions.However, we should not think in terms of the multipole expansion (R-6, R-8, etc.)but rather as atomic p orbital mixing and atomic p and cl orbital mixing. At largeseparations these do indeed behave as R-6 and R-*. The statement made earliercan be rephrased to say that atomic d orbital mixings contribute substantially to thetotal intermolecular potential. In any case, adding an R-6 interaction to the repulsiongreatly underestimates the depth of the potential well.Our recent calculations onthe helium system also agree with these statements.Dr. Mansel Davies (Aberystwyyth) said : Do the Maryott-Birnbaum studies ofresonance line broadening in microwave molecular spectra provide evidence of thepresence of an r-7 term?Prof. A. D. Buckingham (University of Bristol) said: The angular dependentintermolecular potential varying as r-7 does contribute to the line-width of a micro-wave spectral line and may be dominant in such cases as the pressure-broadeningof rotational lines by inert-gas atoms. It was for these interactions that Anderson 1showed that the similar r-7 dipole-quadrupole induction energy was important.Mr.K. Schram (Inst. Theor. Physics University, Muliesingel, Utrecht) said: Is itpossible to obtain formula (7) or (8) in McLachlan's paper starting fromDzyaloshinskii's general formula (e.g., (4.13) of ref. (1)) by taking the limit of tworarified media, as can be done for bodies separated by an empty gap ?Dr. Manse) Davies (Aberystwyth) said: It is unfortunate and unnecessary tofind the factor E referred to as the '' dielectric constant " when in no adequate physicalsense is it a constant : the term " permittivity " is to be preferred.Dr. C. M. Hargreaves ( N . V. Philips' Gloeilanzpenfabrieken, Eindhoven) said : Thefollowing remarks are concerned with the retarded dispersion force between metals.Casimir 2 showed a simple method of calculating the retarded force between perfectly-conducting planes by considering the change in the total zero-point energy of all themodes in a cavity with perfectly-reflecting walls when a perfectly-reflecting partition1 Anderson, Physic.Rev., 1950, 80, 511.2 Casimir, Proc. Kon. Akari. Weteiisch., 1948, 51, 793.Elk = 145+5"K, Alk = 143+5"K280 GENERAL DISCUSSIONis moved from afar into close proximity with one of the walls. This calculationrefers to perfect conductors at the absolute zero of temperature. Real metals nolonger approximate to perfect conductors for wavelengths less than a few micronsbut it is possible to make a correction for this in a simple manner.1 The wavesmainly contributing to the interaction are those of wavelengths about equal to theseparation of the conducting planes.For a separation of, say, 1 p, we are thusconcerned with waves of Ax 1 p.One manifestation of imperfect conduction is the skin effect, characterized by afinite penetration depth 6. At the frequencies in which we are interested, “ well-behaved ” metals such as Cu, Ag, Au, are in the so-called relaxation regime, theirelectrons behaving as quasi-free particles. The penetration depth S is then nearlyindependent of A and given by 6 = (rnc2/4nNe2)*. (rn is the effective mass and Nthe density of the electrons.) The correction to Casimir’s expression, Fo = hcn2/24OZ4,now consists simply of replacing the true separation Z by an effective separationZ+6 or, better, Z+26. The Casimir force between parallel plates is thus diminishedin the ratio F,/Fox 1 -46/1 or 1 - 86/1.These corrections, calculated for silver plates,are shown as curves 4 and 4n in the figure.Lifshitz et al.2~ 3 have calculated in a diferent way what is in effect the samecorrection, but an integration error leads to a correction term (eqn. (4.27) in ref. (4))that is about five times too large (curve 2). When this error is eliminated we obtaincurve 3. The figure also shows temperature corrections to the retarded dispersionforce as calculated by Lifshitz et aZ.2, 3 and by Sauer.4 All are based on the assump-tion of perfect conductors. Curves 5 (Lifshitz) and 6 (Sauer) give the ratio FIFOof the room temperature force to the force at absolute zero for plate separations smallcompared with hc/liT.Curves 7 (Lifshitz) and 8 (Sauer) are for plate separationslarger than - fic/kT.Lifshitz 5 curves are derived from his general formula (4.13 in ref. (4)) but inmaking the approximations errors have crept in. Sauer derived his corrections by1 Hargreaves, Proc. Kon. Akad., Wetensch., 1965, 68B, 23 1.2 Lifshitz, J. expt. theor. Physics, 1955, 29, 94 and Soviet Physics JETP, 1956, 2, 73.3 Dyzyaloschinskii, Lifshitz and Pitaevskii, Adv. Physics 1961, 10, 165.4 Sauer, F., Din. (Gottingen, 1962).5 Casimir, Proc. Kon. Akad. Wetensch., 1948, 51, 793GENERAL DISCUSSION 28 1an extension of Casimir's quasi-classical method: for a cavity with walls not atabsolute zero, the temperature radiation in equilibrium with the walls also contributesto the interaction energy.The temperature correction is necessarily positive, i.e.,the force at finite temperature is always greater than the force at absolute zero(correction 5 is therefore wrong in sign). Schram,l using an essentially similar method,has independently arrived at the same results as Sauer. Some years earlier, Fierz 2also attacked the problem by the cavity method, but his intention was only tocalculate the temperature and distance at which the temperature radiation effect isstill negligible. He arrives at the conclusion that, for room temperature, thetemperature radiation pressure becomes a perceptible fraction of the zero-pointpressure only at distances > lp; this too agrees with Sauer.Of the corrections discussed, only the curves 3 (or 4) and 8 can lay real claim tovalidity.Addition of these gives a curve 3 that represents the retarded dispersionforce between silver plates at room temperature (293"K), and there is reason to expectthat this is accurate to about 1 0 %, or perhaps better. The retarded dispersion forcebetween real metals is therefore much better defined theoretically than is the case withdielectrics. For this reason and because the force between metals is larger than thatbetween dielectrics, it would seem that metals form the most profitable field forexperimental studies of the retarded dispersion force.Dr. J. A. Kitchener (Imperial College, London) said: The experimental valueobtained by Derjaguin et al. for the coefficient p, viz., - 10-34 erg cm3, can be comparedwith a rough estimate based on dispersion force theory (which, for this problem, shouldbe fairly reliable).The Hamaker-London constants ( A = n2q2p, q being the numberof molecules per unit volume and p the intermolecular dispersion force constant)for water, ethanol and silica are roughly (1/2) x 10-12, 1 x 10-12 and 1 x 10-12 ergrespectively. Therefore, the attraction constant for ethanol + silica (in vacuum)cannot exceed 1 x 10-12, and the effect of the medium will be to reduce the net energyto about 0.8 x 10-12. Now the London adsorption energy for a molecule at distanceh from a plane solid is given by U = -nqp/6d3 = p/&. As 4 ~ 2 x 1022, p can beexpected to be about equal to A/6nq, i.e., about 2 x 10-36 erg cm3. It therefore appearsthat the experimental result reported in the paper by Derjaguin et al.is too large bya factor of 50.Prof. Dr. J. Lyklema (Lab. Physic. Colloid Chern., Wageningen) said: There are inprinciple two methods to determine the van der Waals compression, a dynamicmethod, used by Scheludko et al. and a static method, used amongst others byScheludko and Ekserova in 1 9 6 0 4 and recently amplified by Lyklema and Mysels.5The principle of the static method is that in a thin layer of equilibrium thickness hthe SUM of all repulsive and attractive forces must be zero. Hence, the other forces(especially capillary pressure, double-layer repulsion) being known, the van derWaals compression can be calculated by the force balance.The static approach has four definite advantages over the dynamic method,viz., (i) the geometry of the film is a well-defined, e.g. the dimpling problem does notexist; (ii) large-area films can be used, the optical homogeneity of which can beverified; (iii) the thickness range over which van der Waals forces can be evaluatedis cn.650 A, i.e., four times as large as in the paper of Scheludko et d. ; (iv) thereproducibility is of the order of a few o/o, i.e., about ten times better than in that1 Schram, K., private communication.2 Fierz, Helv. Phys. Acta, 1960, 33, 855.3 Hargreaves, Proc. Kon. Akad., Wetensch., in press.4 Scheludko and Exerova, Kolioid-Z., 1960, 168, 24.5 Lyklema and Mysels, J. Amer. Chem. Soc., 1965, 87, 2539282 GENERAL DISCUSSIONpaper. The static method has admittedly also some minor disadvantages, notablythat model assumptions must be made in order to calculate the non-van-der-WaaIscontributions to the force.Within the limits of our knowledge, however, the slope of the n(h) curve appearsto be very close to 3, i.e., the van der Waals force is apparently non-retarded in con-tradiction to the results found by Scheludko et al.In view of the fact that hitherto the dynamic method reportedly has been appliedto films of benzene and chlorobenzene, and the static method to aqueous films, itseems therefore desirable to apply both methods to the same system.Prof.A. Scheludko and Prof. D. Platikanov (University of SoJia, Bulgaria) (corn-inunicated) : To the advantages, mentioned by Prof. Lyklema, of the measurementof equilibrium films, should be added the following essential disadvantage of thesemeasurements. The equilibrium in this case is realized on the account of the doublelayer repulsion. This eliminates the possibility of establishing equilibrium atnon-aqueous films and of using the static method for them.Also, the interpreta-tion of the results for equilibrium aqueous films is difficult, because their equi-librium thicknesses are determined by the competition of the electrostatic (Ilel)and van der Waals (IIvw) components of the disjoining pressure, but the theoriesof both are not reliable, especially at high electrolyte concentrations and smallthicknesses used by Lyklema and Mysels.1 Because of this, for example, it is notclear, whether the deviations from the theory observed in ref.(1) are due to an in-accuracy of the theory for IT,, or for IIvw or of both theories. That is why, in spiteof all difficulties, the dynamic method is unavoidable for a simple investigationonly of ITvw.Furthermore, Prof. Lyklema’s comparison of the results for aqueous films 1, 2with those for non-aqueous films, presented by us, is not reasonable. It is possiblethat the effect of the electromagnetic retardation for aqueous films is small (IIvw-l/h3), and for benzene and chlorbenzene to be larger ( I I v ~ - l / h 4 ) for the samerange of thickness. Moreover, the data for ITVW in ref. (1) and most of these datain ref. (2) are not for pure water, but for relatively concentrated electrolyte solutions.Mr.A. D. Read and Dr. J. A. Kitchener (Imperial College, London) said: Theexistence of instability in free liquid lamellae (and also either positive or negative“ disjoining pressures ” in wetting films on solids) as a consequence of long-rangevan der Waals forces was already treated by Russian workers during the period 1934-38 (cf. Frenkel).3 The classical expression for the contribution of the London-vander Waals forces to disjoining pressure in a liquid lamella of thickness h isbut de Vries 4 pointed out that allowance ought to be made for the retardation effect.We have used a method of calculation similar to that outlined in the paper ofScheludko, Platikanov and Manev (eqn. (14)) in order to estimate van der WaaIsdisjoining pressures in aqueous foams and wetting films on quartz.The followingvalues were adopted for the constants :nvdW = A/671h3,for water, A = 3.9 x 10-13 erg; 3, = 910 1$;for quartz, A = 7-9 x 10-13 erg; il = 780 A.These values-deduced from optical constants by Gregory 5-are consistent with1 Lyklema and Mysels, J. Amer. Chern. SOC., 1965, 87, 2539.2 Scheludko and Exerova, KoIIoid-Z., 1960, 168, 24.3 Frenkel, Kinetic Theory of Liquids, (Oxford U.P., 1946), chap. 6.4 de Vries, Proc. 3rd Int. Congr. Surface Act., (Cologne), 1960, 2, 566.5 Gregory, J., PI1.D. thesis, (Univ. of London, 1964), chap. 5GENERAL DISCUSSION 283estimates based on quite independent properties.1 The results are shown in fig. 1.In free films, n v d W is a negative pressure, whereas for water on quartz it is positive.The main feature of these results is to show that the transition from HvdWK l/h3 ton v d W K l/h4 occurs in the range of film thickness 100 < h < lo00 A corresponding to0*1A<h<A, a conclusion in agreement with Lyklema and Mysels.2 As this is the0.1 I aI Iloglo (film thickness in A)FIG.1 .-London-van der Waals contribution to the disjoining pressure in free water films and wet-ting films on quartz. (Awaters3.9 x 10-13 ; Asuartz=7*9 x 10-13 erg ; Awater=910 A ; Asuartz=780 A.)range over which reasonably accurate measurements of the disjoining pressure in thinfilms are feasible, one might expect an average exponent of about 3.5 to representthe data for water. For liquids such as benzene and chlorobenzene, 3, should besomewhat larger than that for water and therefore the transition should occur atgreater thicknesses.Dr.W. D. Davison (Queen’s University, Belfast) said: In an accurate two-centrecalculation of the dispersion energy for several pairs of simple atoms and ions,3 thecoefficients C(6) of the R-6 term in the H+He and HefHe interactions have beenfound to be 2.83 and 1-47 atomic units respectively. These values (which may beregarded as exact to the number of places given) have also been obtained in a one-centre calculation,4 using the formula in terms of the dynamic polarizabilities at imagin-ary frequencies which was referred to by Prof. Longuet-Higgins. Similar one-centreformulae can be given for all terms in the series expansion of the dispersion energy.59 6The one-centre approach has many advantages, e.g., once the polarizabilitiescc(ico) have been calculated or derived from experiment for a number of atomic1 Fowkes, Ind.Eng. Chem., 1964, 56, (12), 40.2 Lyklema and Mysels, J. Amer. Chem. Soc., 1965, 87, 2539.3 Davison, Proc. Physic. Soc., 1965, 87, 133.4 Chan and Dalgarno, Proc. Physic, SOC., 1965, 86,777.5 Chan and Dalgarno, Mol. Physics, 1965, 9, 349.Dalgarno and Davison, Ado. Atomic and MoZecular Physics, 1966, 2, in press284 GENERAL DISCUSSIONspecies, the calculation of the various possible two- and three-body interactionsis a trivial matter ; in a two-centre approach, on the other hand, a separate lengthycalculation must be performed for each grouping. The semi-empirical applica-tion of the one-centre formula for 0 6 ) is hampered at present by the limitedrange and accuracy of the available refractive index data, but the method is muchsimpler and potentially more accurate than previous semi-empirical procedures.1Prof. H. A. Scheraga (Cornell University) said: 1 should like to raise a questionabout the interaction of solute species in a solvent, specifically about the interactionof neighbouring nucleic acid bases in water (the so-called “ stacking ” interaction).As I understand it, Sinanoglu and Abdulnur have treated this problem from a pointof view which would imply that, if the solvent is water, the stacking interaction is dueprimarily to hydrophobic bonds.If this were so, we should expect AH>O for the formation of the interaction.However, we have recently determined the enthalpy of formation from a study of themelting of oligomers of the type PA)^, and from a statistical mechanical treatmentof these data, and find that AH< 0 (specifically, it is - 6.5 kcal/mole).a Therefore,it appears that the stacking interaction is primarily an electrostatic one.Hydro-phobic bonding may make a positive contribution to AH, but the overwhelminglylarge negative contribution suggests that hydrophobic bonding is not the major originof this interaction. Is this observation compatible with the theory of Sinanoglu andAbdulnur ?Prof. N . R. Kestner (Stanford University) said: The experimental data youmention seem to confirm the theory of SinanofjIu and Abdulnur.Their theory showsthat the contribution of water to the free energy of association of bases comes, by andlarge, from the decrease in the surface area of cavities surrounding the bases. Thiswater cavity surface enthalpy effect leads to a strong AH<O. This is in additionto the Van der Waals forces which would exist between bases even in a vacuum withno solvent around. The “vacuum ” forces do not seem sufficient, however, to holdtogether a DNA double helix, for example, as evidenced by the denaturation of the helixby solvents other than water. [The helix too has a AH<O, about -8 kcal/molebase pair, as measured, e.g., by Sturtevant and Rawitscher and others.]I may also add that there are several free energy terms that tend to associate basestogether in a solvent. These effects are calculated and compared in the papers ofSinanoglu and Abdulnur. The term “ hydrophobic bonding ” seems to have beenused by other authors to mean not all the water contributions, but only the structuralentropy effect, which may not be the dominant one.Mr. F. B. van Duijneveldt (Rijksuniversiteit, Utrecht) said : The calculations ofsteric interactions presented by Scheraga et al. have been based on the assumptionthat such interactions can be discussed in terms of the relative “ sizes ” of the inter-acting groups. While this may be a reasonable approach in calculations on saturatedhydrocarbons, difficulties will arise with moleculess containing lone pair electrons.Thus, while for certain orientations a N : . . . N : interaction may be as repulsive as aCH . . . CH interaction, a corresponding N : . . . CH interaction is far less repulsive.3Clearly, it is not possible to say that an atom carrying a lone pair is “ large ” or“small”, and the assignment of a fixed radius to such an atom may not alwaysyield the correct conformations.1 Dalgarno and Davison, Adv. Atomic and Molecular Physics, 1966, 2, in press.2 Vournakis, Scheraga, Rushizky and Sober, Biopolymers, in press ; Poland, Vournakis and3 Murrell, Gil and van Duijneveldt, Rec. trau. chim., in press.Scheraga, Biopolymers, in press

ISSN:0366-9033    

DOI:10.1039/DF9654000278

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

SUMMARIZlNG REMARKSIntermolecular Forces-the known and the unknownBY C. A. COULSONMathematical Institute, OxfordIn summing up this Discussion there is no need to stress the importance of inter-molecular forces in chemistry. They are involved in almost every part of the subject,from the gas laws to a study of liquid surfaces, compressibilities of solids, crystalstructures, all chemical reactions, and particularly catalysis : indirectly, in terms ofsteric behaviour, they influence a large part of biology. In greater or less degree,almost all of these matters have been touched on at the present meeting-from theIntroductory Spiers Memorial Lecture of Longuet-Higgins to the concluding paperby Scheraga on protein conformation. Yet there has been a little unease about thedifferent sessions of this Discussion Meeting.For we have been asking questionsat different levels ; and thus the answers given in one type of discussion have appearedhopelessly inadequate (or, alternatively, far too detailed) in another. To appreciatethe scope of this meeting and to judge the success of the papers presented to us, it isimportant to recognize this range of our enquiry.An example will serve to illustrate this difference in levels: on the one hand,to discuss the third virial coefficient of helium or argon requires a very deep and intimatestudy of the forces (both two- and three-body) existing between atoms of these gases ;and on the other hand, if we are interested in the heat of adsorption of benzene on agraphite surface, we shall have to be content with a very primitive kind of force-law,which would be of no value at all for studying the behaviour of gases.It is a result of this “ spread ” of our subject that we have been introduced to suchgreat differences in experimental technique and mathematical method that we havewondered whether we were really discussing similar subjects.For example it cannothave escaped anyone’s attention that :(a) in fundamental studies on interatomic forces, we have been compelled to followin the pioneer work of Lifshitz and McLachlan where we relate these forces to thepolarizability at imaginary frequencies. This is beautiful work, possessing greataesthetic charm. But it must be admitted that at first it appears rather bizarre tomost physical chemists.Perhaps we shall learn to live with concepts of this kind,so that they become as much part of our thinking as dispersion forces have becomein the last 25 years. It is certainly to be hoped that we shall find better ways thanare available at present for calculating their numerical values.(b) In less “ exact ” work, such as the studies by Everett on the forces between twoatoms adsorbed on some kind of surface, we have been content to add a term pro-portional to R-3, but of unknown magnitude, in order that we gain some sort ofinitial insight into a complex situation.If we were disposed to put this contrast in epigrammatic form, we could say thatin this Discussion Meeting of a Society whose official concern is with PhysicalChemistry, it has sometimes seemed as if that actually meant theoretical physics andexperimental chemistry !Contrasting attitudes of this kind suggest that we should pause, and take stockof what we may really claim to know about Intermolecular Forces, as it has been28286 SUMMARIZING REMARKSset out in the various papers in this Discussion.It will be convenient to group thisin four paragraphs, dealing with (i) the simplest cases of interatomic forces in thegas phase, (ii) interatomic forces in liquids and solids, (iii) forces between polyatomicsystems, particularly in molecular crystals, and (iv) biological phenomena.GAS-PHASE INTERATOMIC FORCESIn one sense the main problem here is very simple. If we knew the force betweeneach pair of atoms, then it would not be hard to predict the physical effects, such asvirial coefficients and compressibility, to which these forces lead.Our problem, asshown by Rowlinson, is precisely the inverse of this : given the physical effects, we areto deduce the law of force. In essence this amounts to the evaluation of a certainLaplace Transform. But-unhappily-since there is not a 1 : 1 relation between theenergy and the interatomic distance (the energy E is a single-valued function of thedistance R for all values of R, but R is a double-valued function of E in the bondingregion of the potential energy curve), there is no unique solution of our desired in-version problem. However, there are certain matters in this field where-morehappily-we can claim to know the absolute truth. Thus :(i) we know without doubt that for two closed-shell atoms the dispersion energyvaries as R-6 at large distances, tending to R-7 at such large distances that retardationeffects are important.Further, we know the coefficients in these two cases, at any ratefor such small systems that the summation methods of Dalgarno and Kingston canbe applied. It is a pity that this method does not seem capable of simple applicationto larger systems.(ii) We know without doubt the energy of interaction of two helium atoms overthe greater part of the total significant range of R. The gigantic calculations ofPhillipson, using no less than 64 electronic configurations mixed together, may besaid to provide an effectively definitive value of E(R).The agreement with Amdur’sscattering experiments is by no means perfect: but this is a case where it is almostcertain that the theory is better than the experiments. There is therefore absolutelynothing to be said for a continuance of the habit of using trial Lennard-Jones-typepotential functions for this problem, and then attempting to find the ‘‘ best ” valuesof the parameters to fit with experiment. It would be very desirable that, if possible,these admittedly difficult experiments could be repeated. It is a pity that suchcalculations are not yet available for Ne . . . Ne and Ar . . . Ar interactions. How-ever, we may hope for an almost definitive calculation for two neon atoms beforevery long.(iii) We know without doubt that in certain situations three-body forces areimportant, and we know from the work of Jansen and Lombardi that in crystals ofthe rare gases these forces are responsible for their failure to develop the expectedhexagonal close-packed structure except for solid helium (and a metastable form ofargon).It now seems probable that these three-body forces may contribute up to20 % of the total binding energy. In this connection it is interesting to recall thatit was at a previous Faraday Society Discussion, in 1937, that London described hisR-6 dispersion formula, and laid the foundation for almost all our later discussionof interatomic forces and their classification into dispersion, orientation and inductioncomponents. It seems probable that all of us will remember this 1965 Discussionas being the moment when three-body forces came to acquire their true place withinour system of concepts.Here, as in all new scientific study, it is of primary importanceto get a proper language established. We now see that three-body forces are animportant part of this. This is not to say that we have not known of these forceSUMMARIZING REMARKS 287before. For we have. Indeed, every time we speak of a valence-angle molecularforce constant we are discussing a force that depends on the mutual orientation ofthree atoms. And Murrell's charge-transfer forces in crystals such as solid argonmay equally be regarded as many-body forces. But for most purposes the discussionof these forces began with the work of Axilrod and Teller, who showed that thedipole-dipole-dipole dispersion energy of three particles should vary as (312323331)-3.These forces are significant only if all three intermolecular distances are small, i.e., ifthe three particles lie at the vertices of an approximately equilateral triangle. It maybe that a simple counting of the number of such triple-body triangles may itselfbecome a guide to the crystal structure of non-polar closed-shell systems.CONDENSED-PHASE INTERATOMIC FORCESThis discussion has led us to the next stage of complication.We have alreadyseen that except for small atoms such as He the coefficient C in the long-range dis-persion formula C/R6 is not known. Even less, however, is known about the short-range repulsive interactions, usually represented by an expression B exp (- AR).It is true that the exponential form is favoured by such tentative theoretical calculationsas exist : and it has often been assumed that the coefficient A was a sort of universalconstant.The work of Guggenheim and McGlashan shows that for the ionic crystalsKCl and NaCl the values of A which allow a fit with measured thermal expansiondiffer by only 3 7;. We need much more work of this kind before a complete patterncan emerge.There is a sense, however, in which we must be careful not to be trapped by ourown language. What we are really seeking, for solids and liquids, is an effectivetwo-body potential, which will take account implicitly of the three-body forces describedearlier. This effective two-body potential will not be the same as a genuine diatomicpotential, and there is some danger, not entirely avoided at this meeting, of lookingfor too physical an interpretation of such properties of this effective potential as itsanharmonicity, or the coefficients of higher powers of (R-Re). And again, asLonguet-Higgins has pointed out, expansions of the potential energy as a powerseries in l/(R-Re) are only physically significant for large R - R e : this is not thecase for solids and liquids.Despite these very proper reminders of the difficulties associated with the calcula-tion of effective two-body forces, some real progress has been made.For example,McLachlan has shown how to calculate the effective force between two neutral non-polar molecules dissolved in a fluid.This dispersion force is shown to depend on thedielectric constant of the fluid and the imaginary-frequency polarizability (previouslyreferred to) of the molecules. Dzyaloshinsky, Pitayevsky and their colleagues haveshown how to deal with surface forces, in the same sort of way. We can also dealwith the force between two rare-gas atoms some distance away from a semi-infinitecontinuous dielectric medium, provided that the medium is genuinely continuous andthe surface is accurately planar. More conventional methods, using third-orderperturbation theory, have been adopted by Kestner and Sinanoglu to show that theeffective London dispersion interactions between two molecules in a medium (eithera continuum or a lattice model being used) may be reduced by from 2 to 30 % by thepresence of the medium.MOLECULAR CRYSTALSThe third area in which distinct progress has been made concerns the intermolecularEarlier work of forces which are responsible for the structure of molecular crystals288 SUMMARIZING REMARKSKitaigorodskii had shown the importance of the way in which the molecules couldbest be packed together.But now much more knowledge has been obtained. Thearomatic hydrocarbons have been most studied, partly because their essentially planarframework draws attention to the role of space-filling, and partly because of theirnon-polar character, which emphasizes the short-range nature of the interactionssignificant in determining crystal-structure. Thanks to the work of Craig et al.wecan give a very good account of the roles played by the different forces in these crystals.The forces that hold the molecules together, and provide about 90 % of the sublima-tion energy, are the traditional London dispersion forces, with perhaps a further 10 %coming from quadrupole-quadrupole interactions. But, curiously enough, theseforces depend relatively little on the mutual orientations of the individual molecules.Thus the crystal structure is almost wholly determined by very short-range repulsions.For the aromatic hydrocarbons these are largely the H . . . H repulsions, for whichan approximate formula CS2/1 may be adopted ( S is the overlap integral of the atomicorbitals on the two atoms, and I is their ionization potential, and C is an appropriateconstant).Since S has an exponential type of variation at fairly large atomic separa-tions, of the order of the sum of the conventional van der Waals radii of the atoms,this shows that the effective repulsions are very short-range, and helps us to see thatC . . . H repulsions are less significant in these systems than H . . . H repulsions.It is worthwhile drawing attention to the values calculated by Salem and Banerjeefor benzene. Dispersion contributes - 10.3 kcal/mole to the total sublimationenergy (- 10-67 kcal/mole), and repulsion a mere + 1.5 kcal/mole. Yet the mutualarrangement of the benzene molecules in the crystal is almost entirely determined bythe repulsions.This may be the moment to refer to an ingenious point made by Prof. Buckingham.He has shown that in addition to the dipole-dipole dispersion energy calculated byLondon, which varies as R-6, there will also be a dipole-quadrupole energy whichvaries as R-7.Further, if the polarizability tensors of the molecules are isotropic,and if the molecules are not allowed to rotate as, e.g., in a molecular crystal, thenthese R-7-forces are the first non-vanishing angularly-dependent forces ; and theymay conceivably sometimes be important in determining crystal structure. Somenumerical applications of this very general theory would be very worthwhile.It is only fair to add, at this stage, that in choosing aromatic hydrocarbons forthe discussion of crystal stucture we are choosing some of the simplest systems forthis kind of work. If a molecule possesses a permanent dipole moment, it will giverise to longer-range Coulomb interactions, which may easily dominate some of ourprevious terms.Even in chlorine substitution, we may introduce additional termsof this kind, which will almost certainly spoil the CS2/1 formula previously men-tioned. Much more experimental work is needed.BIOLOGICAL ASPECTSThis reference to repulsive forces leads us into their application to biologicalsystems. It had already been decided that at this Discussion we should not considerthe hydrogen-bond. Despite the fact that the force which we describe in this wayis the most significant force in the whole biological world, it is rather specialized,and would require a full meeting for its proper discussion. But a real breakthroughseems to have been achieved by Scheraga and his colleagues in their discussion ofpolypeptide conformation.It is now about 15 years since Pauling and Coreydescribed, largely on theoretical grounds, the shape of the backbone of the now-familiar a-helix. However, even if the main geometrical structure is accepted, therSUMMARIZING REMARKS 289still remains an immense conceivable variety of conformations in the detailed orienta-tion of the various amino-acid residues. Scheraga etal. have used quite crude estimatesof the various repulsive forces, of which the hard-sphere model is the simplest, toconsider all possible sets of rotations around the important C-C and C-N singlebonds. They are led to the striking conclusion that there is scarcely any latitudeavailable to these polypeptides, once the sequence of residues is given.It is almostas if the steric behaviour of these helices was very largely dependent upon pure geo-metry. Plato, with his insistence on the significance of shape and form, would havebeen thrilled with this account. It is true that the types of force considered are atbest approximate, though this does not appear to matter as much as we might haveexpected. It is also true that so far only small cyclic polypeptides have been con-sidered. The complications are vast ; but, as was said in very different circumstances ;“ ce n’est que le premier pas qui coihe ” ; and no better indication could be giventhan this of the immense importance of repulsive interatomic forces in biology.Much more needs to be done along these lines, but the future is full of excitement.THE FUTUREIt is tempting, at the end of a concentrated Discussion Meeting of this kind, toask questions about possible future developments. Prediction is always dangerousand uncertain, but perhaps one or two forecasts may be attempted with Some con-fidence.On the purely theoretical level :(i) ejectronic computers grow continually bigger. We may therefore confidentlyexpect the calculation of interatomic forces to be extended from He.. . He toNe . . . Ne, and possibly to Ar . . . Ar also ;(ii) a better understanding will be found of the new important polarizabilities atimaginary frequencies so that they may be estimated without the need to convertthem into old-style sums and integrals ;(iii) this will lead to a better understanding of the influence of the surface onadsorbed molecules-it is true in this field that we need some new simple models ;(iv) our knowledge of the role of repulsive forces in crystal structure will surelybe extended, to include molecules with polar bonds.(v) far deeper study will be made of time-dependent phenomena.Here we mayneed to change our techniques, and make more use of the Green’s function method,now in much vogue among theoretical physicists. Without some such technique itdoes not seem very easy to deal with the most important, but relatively unexplained,field of chemical reactions. This study will certainly include the influence of orienta-tional effects in collisions.It is foolhardy for a theoretician such as the writer to make predictions at theexperimental level.But :(i) in discussing equations of state for gases, it does seem appropriate now to escapefrom the rare gases, and extend measurements to other systems, especially, at first,those where quadrupole effects come in.(ii) More study seems probable of the properties of adsorbed systems. Surfacechemistry is of first-rate importance, but it still has a very large empirical element.(iii) In this connection it seems that the time has come to give rather less attentionto the details of some assumed law of force (e.g., whether it is of Lennard-Jones orKihara type), and more to the provision of some simple concepts that will help us toco-ordinate as wide a variety of experimental situations as possible. Thus, are certai290 SUMMARIZING REMARKSfrequencies of vibration increased, or decreased, when a molecule is adsorbed? Andwhat does this tell us about its environment on the surface?(iv) Finally, biological applications will abound. It is going to be a characteristicfeature of the twentieth century that in its first half there were tremendous strides inphysics and chemistry : but in its second half much of the interest will shift to biology.However, this shift will be much less effective than it might be unless, as we go, wecarry with us the knowledge and the insights of the earlier years.I may be quite wrong about many (or, indeed, all) of these forecasts. But of onething there can be little doubt. The Faraday Society will continue, for many yearsto come, to discuss the nature, the size and the significance of intermolecular forces,for the simple reason that these represent one of the few great threads-the waveequation and the chemical bond are others-which serve to bind us together, andunite us in the exploration of a common subject-Chemistry

ISSN:0366-9033    

DOI:10.1039/DF9654000285

出版商:RSC    

年代:1965

数据来源: RSC

摘要:

Affsprung, H. E., 224.Barker, J. A., 117, 125.Barrer, R. M., 225, 230, 231.Barron, T. H. K., 69, 119, 120.Baughan, E. C., 127.Beenakker, J. J. M., 135, 171.Bernstein, R. B., 35, 55, 58, 278.Brzostowki, W., 126.Buckingham, A. D., 171, 219, 232, 278, 279.Byers Brown, W., 140, 173.Casanova, G., 54, 188.Claverie, P., 174.Coulson, C. A., 278, 285.Craig, D. P., 110.Van Dael, W., 225.Danon, F., 97.Davies, M., 279.Davison, W. D., 174, 283.Derjaguin, B. V., 246.Derkosch, J., 224.Dobosh, P. A., 110.Domb, C., 54.Dondi, M. G., 188.van Duijneveldt, F. B., 284.Duren, R., 56.Dzyaloshinsky, I. E., 246.Everett, D. H., 177, 219, 221, 223, 226.Groszek, A. J., 230.Guggenheim, E. A,, 53, 76, 120, 121.Hargreaves, C. M., 279.Hermans, L. J.F., 135, 171.Jansen, L., 78, 128, 129, 130, 132.Jonah, D. A., 55.Jonkman, R. M., 135, 171.Kestner, N. R., 173, 174, 266, 279, 284.Kiselev, A. V., 205, 221, 223, 228, 230.Kitchener, J. A., 281, 282.Klein, M. L., 117, 188.Knaap, H. F. P., 135, 171.Kohler, F., 224.Koptelova, M. M., 246.Leach, S. J., 268.Linder, B., 164.Lombardi, E., 78.Longuet-Higgins, H. C., 7, 127.Luoma, J., 45.Luck, W. A. P., 128.Lyklema, J., 281.Manev, E., 253.Mason, E. A., 27.Mason, R., 110.McGlashan, M. L., 59, 76.McLachlan, A. D., 239.Mueller, C. R., 45.Munn, R. J., 27, 130.Murrell, J. N., 129.O’Brien, T. J. P., 35.De Paz, M., 188.Pitayevsky, L. P., 246.Platikanov, D., 253, 282.Poshkus, D. P., 195, 221, 223, 227.Read, A. D., 282.Reissland, J. A., 123.Rice, 0. K., 118.Rigby, M., 133.Rossi, J. C., 97.Rowlinson, J. S., 19, 53, 55, 132, 279.Salem, L., 126, 133, 150, 176.Santry, D. P., 110.Saville, G., 132.Scheludko, A,, 253, 282.Scheraga, H. A., 218, 284.Schlier, Ch., 56.Schram, K., 279.Scoles, G., 188.Scott, R. A., 268.Sinanoglu, O., 266.Smith, E. B., 133.Smith, F. J., 27.Sparnaay, M. J., 219.de Vries, A. E., 56.Weir, R. D., 132.Zucker, I. J., 117.AUTHOR lNDEX ** The references in heavy type indicate papers submitted for discussion.29

ISSN:0366-9033    

DOI:10.1039/DF9654000291

出版商:RSC    

年代:1965

数据来源: RSC