THE STRUCTURE OF SIMPLE MOLECULESI. METHODS.THE last few years have seen the development of a variety of quitedistinct methods of physical investigation, throwing light on thedetails of molecular structure ; so that it is now possible to elucidatethe structure of covalent molecules by the converging results of aseries of independent physical arguments. These methods areapplicable in principle to complex as well as simple molecules, buttheir results are naturally more easily interpreted in the simpler cases.The application of wave-mechanics to the sharing of electrons hasbeen greatly extended in the last two years ; of special interest forthe subjects here discussed are the work of E. Hiickel,2 giving atheoretical basis for the absence of free rotation of doubly linkedatoms, and two recent papers by L.Pauling ; in the first of these hecalculates the valency angles, and finds that while in a 4-covalentatom they should normally have the tetrahedral value of 109-5",with atoms of covalencies of 2 or 3 the angles are approximately 90".Another important conclusion is that bivalent nickel, palladium, andplatinum and other transitional elements should form 4-covalentcompounds in which attached groups occupy the corners of a squarewith the metallic atom at its centre.4 W. Heisenberg has, however,pointed out that the basis of these calculations, which is also thatof the work of Heitler and London, is not quite certain. Pauling'ssecond paper deals with the conditions under which links of one andof three electrons are possible.The number of properties of a molecule which can be investigated,and which are of greater or less value for the determination ofstructure, is very large.In this Report only a fe,w of the moreimportant will be discussed; these are the distances between thelinked atoms, the force constants of the links (the forces required tomove the atoms further apart or nearer together), the mean restoringforces during vibration, the energy involved when the atoms formthe link, the angles between the valencies, and the dipole momentsof the links, which express the ratio in which the linking electronsare shared between the atoms.1 See Ann. Reports, 1930, 27, 10.3 J . Amel.. Chem. SOC., 1931, 53, 1367, 3225.4 Seep. 399.5 '' Chemistry at the Centenary (1931) Meeting of the British Association."2 2.Elektrochem., 1930, 36, 641.See also J. C. Slater, PhysicalRev., 1931, 37, 481368 SIDGWICE AND BOWEN :The experimental methods concerned involve the use of radiationsfrom the far infra-red down to X-rays, and, recently, electron waves ;the measurement of the heat properties; and the determination ofdielectric constants. Since the same information is often given byvery different methods, it is convenient to discuss the methods firstand the results later.Spectroscopic Methods.Molecules can absorb or emit energy in three ways : (1) by thechange of an electron from one orbit to another, (2) by a change ofthe oscillational or vibrational energy of the atoms, and (3) by achange in the rotational energy.The energies concerned can beexpressed in caIories per gram-molecule, in “volts,” or more correctlyelectron volts (the unit being the energy gained by an electron infalling through a potential drop of one volt), or in terms of thewave-length, wave-number, or frequency of the radiation emittedor absorbed. The following table gives an idea of the magnitude ofthe three kinds of quanta concerned.Energy. Separation7- in band ofKilocals./ Wave-length, Wave-number, 6000 A.,Transition. Volts. g.-mol. A. cm.-’. A.Rotational +aTB 0.023 1235 x lo4 8.1 3Electronic 1-10 23-230 12,350-1,235 8,100-81,000 (6000)Oscillational or & 2.3 123,500 810 300vibrationalor 1235por 0-1235 cm.The methods may be classified according to the region of thespectrum examined.Far Infra-red Absorption Spectru of Gases. 6-Molecules possessingan electric moment can absorb far infra-red radiation by an increaseof rotational energy (m+ m + 1).Hence a diatomic molecule(with one degree of freedom) gives an absorption spectrum in thisregion of almost equally spaced lines, the frequencies of which wereshown by Heisenberg to be :v = mh/4x2Jwhere m is an integer, and J is the moment of inertia of the molecule.Since we know the masses of the atoms, this enables us to measure r,the distance between the nuclei, from the relation :J = M1M2 x 1.65 x r2 g.-cm.2MI + M2where M , and M , are the gram-atomic weights of the atoms.Berlin, 1930),ThisSee “Das Ultrarote Spektrum,” C.Schaefer und F. Matossi (SpringerTHE STRUCTURE OP SIMPLE MOLECULES. 369method has been applied, for example, to determine the interatomicdistances in the hydrogen halides.'In principle, this method can be applied to more complex mole-cules which give several different moments of inertia. The experi-mental technique of this region (23-200 p) is, however, particularlydifficult, from the feebleness of the radiation obtainable, the lackof transparent materials for the construction of cells and prisms, andthe overlapping of different spectral orders consequent on thenecessity of using gratings for a range of frequencies of manyoctaves. Hence most investigators of infra-red spectra have con-tented themselves with the somewhat easier technique of the nearinfra-red region.Near Infra-red Absorption Spectra.-When the electric moment ofa molecule is changed by the absorption of a quantum of vibrationalenergy, that molecule is capable of absorbing near infra-red radiation,and passing from one vibrational state (almost always n .= 0) toanother (n = 1,2,3, etc.).Such a transition is coupled with changesin the rotational state of the molecule, leading to an absorption bandcomposed of lines given by the relation :The usual rotational changes are rn+ m + 1 (P branch) andm --+ m - 1 (R branch) ; in special cases the Q branch (Am = 0)is observed. These rotation-vibration spectra are investigated, bythe use of a source such as a Nernst glower, an absorption cell withsuitable transparent ends, mirrors to focus the radiation, a prism ofrock-salt or sylvine, generally combined with a grating, to disperseit, and a thermopile to record the transmission.Diatomic molecules such as the hydrogen halides show a simpleseries of absorption bands corresponding to the vibrational tran-sitions 0- 1, 2, etc., each with a rotational fine structure fromwhich values of J , and so of r, can be obtained for the molecule in itsnon-vibrating state and for the molecule with one or more vibrationalquanta. As would be expected, the values of r increase with thevibrational energy of the molecule.The spectra obtained from polyatomic molecules are naturallyvery complex, owing to the interpenetration of bands correspondingto different transitions, and the greatest interest centres at presentround triatomic molecules such as H,O.The results so far obtainedmust be regarded as provisional until the identscation of thefrequencies observed with particular transitions is more definitely7 M. Caemy, 2. Phy~ilc, 1923,16,321; 1925,34,227; 1927, 235; 45,476370 SIDGWICK AND BOWEN :established. When correct identifications are made, the structureof a simple molecule can be deduced from considerations of twokinds.(a) From the number of moments of inertia of the molecule, givenby the fine structure of the infra-red bands. A linear triatomicmolecule is easily differentiated in this way from a triangular one,and from the values of the moments the dimensions of the mole-cule can be obtained.( b ) Prom the number and values of the vibrational frequencies ofthe molecule.For a triangular triatomic molecule the angle a tthe apex between two similar bonds can be found from the threecharacteristic frequencies. 89 9Raman Spe~tra.~9 lO-Wlien monochromatic light is scatt’ered bythe molecules of a transparent substance, the greater part has itsfrequency unchanged, but a small fraction is scattered a t discreteother frequencies, the frequency differences between exciting andscattered lines corresponding to changes in one of the characteristicvibrational or rotational levels of the molecule. Rotational tran-sitions are indicated by lines very near the spectral line scatteredwithout frequency change ; vibrational transitions by lines muchfurther away.The latter are not coupled with simultaneousrotational changes, i.e., they correspond to Q branches (Am = 0 ) ,and therefore afford much clearer data on vibrational levels than dothe near infra-red absorption bands, which are restricted to vibrationchanges involving a change of electric moment, and are complicatedby P and R rotational branches. Raman lines are excited for alltypes of vibration in which there is a change of polarisibility withphase.ll The two methods of investigation are thus supplementaryto one another, and, besides directly affording material on which tobase views of molecular structure, are, taken together, of very greatimportance in interpreting the complexities of electronic bandspectra (p. 371).The study of this new scattering phenomenon, predicted by A.Smekal 12 and first discovered by (Sir) C.V. Raman,13 has now beentaken up by a great number of investigators. The scattered lines8 N. Bjerrum, Ber. deut. physikal. G‘es., 1914,16, 737; R. C. Yates, Physical9 K. W. F. Kohlrausch, “ Der Smekal-Raman Effekt,” Springer, Berlin,10 C. Schaefer and F. Matossi, ‘‘ Der Ramaneffekt,” Borntraeger, Berlin,11 A. S. Ganesan and S. Venkateswaran, I n d . J . Phys., 1929, 4, 195.l2 Natumuiss., 1923, 11, 873.13 C. V. Raman and K. S. Krishnan, Nature, 1928, 121, 501, 619; I n d . J .Rev., 1930, 36, 555.1931.1930.Physics, 1928, 2, 399THE STRUCTURE OF SIMPLE MOLECULES. 37 1are faint, and most experimenters have used modifications of tttechnique due to R.W. W00d.l~A. Dadieu and K. W. F. Kohlrausch l5 were the first clearly toshow that particular atomic groupings give characteristic Ramanlines. They identified the single Raman line observed for diatomicmolecules with the natural frequency of the system as given by theordinary mechanical expression :-1 frequency = 2x ,J&orwhere w = frequency (sec.-l), M = the reduced mass of the system(1/M = l/Ml + l / M 2 ) , and4 = the force constant of the link whichis vibrating, t h a t is, the force which arises when the nuclei are dis-placed unit distance from their equilibrium position. The forceconstant f is approximately proportional to the energy of dissociationof the link to which it refers, as is shown by the constancy of theempirical expression :f = 5.86 x 10-2Mw2 dynes/cm.v(cm.-l) 2/M(gms.)/A(where A is the dissociation energy of the link in kilocalories permole), which varies over a wide range of examples from 290 to 390.The amplitude of Vibration a can be obtained from the relation :a (cm.) = 8-187 x lo4 d l / M o ,from which can be fount1 the mean restoring force during thevibration :Values of the quantities f and K are given in Table I (p.401).I n the case of more complex molecules, lines of particular fre-quencies varying only slightly in different compounds have beenidentified with particular linkages, and in some cases with particulartypes of vibration of those linkages, i.e., the bending or stretching ofthe link.l6 As with the near infra-red measurements, the numberand value of the vibrational frequencies, and of the rotationalfrequencies of the Raman lines, enable us to deduce the size, shape,and force constants of molecules that are not too complex.Aninteresting development has been the construction of molecularmodels with masses and springs which closely imitate the Ramanspectra of carbon tetrachloride, benzene, etc.17N. N. Pal and P. N. Sen Gupta, l n d . J . Phy8., 1930,5,609.K (dynes) = fa/2 = 24.0 x 10-lO 2/03Ml4 Physical Rev., 1930, 36, 1421; Trans. Paraday SOC., 1929, 25, 792;l6 Ber., 1930, 63, [B], 251.l6 D. H. Andrews, P h y s w ~ l Rev., 1930, 36, 544.l7 C. F. Kettering, L. W. Shutts, and D. H. Andrews, ibid., p. 531372 SIDGWICK AND BOWEN :Raman data, when fully interpreted, promise to provide moreaccurate knowledge of the structure of molecules than any otherspectral method.Much work is now being done in following theshift of particular lines associated with the vibration of particularlinkages (and so related to their force constants) in series of similarcompounds, and from work of this kind a great deal of light is likelyto be thrown on constitutive problems of quite complex organiccornpounds.15s 18, 155absorbradiation at frequencies which produce an electronic transition,simultaneous changes also occur in the vibrational and rotationalstates of the molecule, leading to the production of a complex bandsystem associated with each electronic transition. l9 The case ofdiatomic molecules has been very fully investigat'ed, and greatadvances have been made in such problems as the coupling of largeor small vibration changes with the electronic transition, and theeffect of nuclear spin on the rotational states of the molecule.Suchcompleteness of detail is unlikely to be attained for more complexmolecules for some time; nevertheless it is possible in certain casesto arrive a t a structure for a polyatomic molecule from a consider-ation of its electronic absorption spectrum in the gaseous state.The analysis of the spectrum is facilitated by introducing the fre-quencies of the normal molecule as obtained from Raman or nearinfra-red data. I n favourable cases the moments of inertia of themolecule both in the normal and in the excited state can be calculatedfrom the fine structure of the vibration bands, while from the re-lationships of the frequencies of the vibration bands themselves theforce constants of the two states can be obtained.The method isthus very similar to that used with Raman or near infra-red spectra,with the addition that structures can be deduced both for the normaland for the electronically excited molecule. It has, however,serious limitations ; the complexity of the spectrum is liable to leadto incorrect assignment of lines; the spectrum may be structure-less, as with HI or C1,O; and where large moments of inertia areinvolved it is difficult to obtain satisfactory resolving power for theexamination of the rotation lines.I n Table I are given data on the structure of molecules obtainedby spectral methods.Entirely satisfactory results by any of thesemethods are a t present limited to diatomic and rectilinear triatomicmolecules. Of more complex molecules, H,O 1 4 0 9 14*, 149, H,S 1499 143,C10, 15*, and SO2 152 are undoubtedlytriangular, NH, 141 is pyramidal,l 8 Dadieu and Kohlrausch, Zoc. cit., (ref. 15); M. E. High, Physical Rev.,l 9 Ann. Reports, 1926, 23, 296.Electronic Band Absorption Spectra.-When molecules1931,38, 1837; W. D. Harkins and H. E. Bowers, .ibid.,ip. 1845TBE STRUCTURE OF SIM.PLE MOLECULES. 373and COCI, 151, S,Cl,, SOC1, 152, and CH,O 144 are Y-shaped, but thevalues of the angles and distances a t present obtained by spectralmethods must be regarded as subject to revision.X-.Ray Methods.These may be discussed under two heads, according as the materialexamined is a solid or a gas.Determination of Crystal Rructure by X-Rays.-This applicationof X-rays is too familiar to need detailed discussion here.20 Itdepends on the power of the atoms, or rather of their electrons, toscatter the X-rays, so that the crystal can be used as a grating, theinteratomic distances being of the same order as the wave-length ofthe radiation.Hence, if the wave-length is known (this can now bechecked by the use of ruled gratings at a very small glancing angle),the spacing of the atomic grating can be determined. If the arrange-ment of the atoms in the crystal can be ascertained (alternativearrangements are sometimes possible), we can calculate from themeasurements the distances between pairs of atoms.For the simplerstructures these distances can be determined with an accuracy of0.05--0.1%.21 The method was extended by P. Debye and P.Schemer 22 to crystal powders, so that it can be used where it is notpossible to obtain single crystals of any size.X-Ray Interference in Vapours.-This is a new development ofgreat importance, which we owe to Debye and his 24, 25, 26, 27In the solid state the molecules are under some restraint, and thedistances between the atoms, and more especially the valency angles,may be thereby modsed. Debye and Scherrer’s application oftheir powder method to liquids leads to great difliculties of inter-pretation, as we are not sure whether the distances we are measuringare between atoms of the same or of neighbouring molecules.28With a gas these difficulties do not arise ; the regular distances mustbe between atoms of the same molecule in an unconstrained state.On the other hand the scattering power of the quantity of materialzo See W.H. and W. L. Bragg, “ X-Rays and Crystal Structure,” 1926;R. W. G. Wyckoff, “ The Structure of Crystals,” 1924.z1 V. M. Goldschmidt, Geochem. Vert., 1927, 8, 21.22 Nach. Ges. Wiss. Bdttingen, 1916, 16; Physikal. Z., 1916, 17, 277. Seealso A. W. Hull, Physical Rev., 1917, 10, 661.23 P. Debye, L. Bewilogua, and F. Ehrhardt,’PhysikaZ. Z . , 1929, 30, 84;P. Debye, &id., p. 524; H. Mark, 2. angew. Chern., 1931,44, 125.z4 P. Debye, Physikal. Z., 1930, 31, 142, 419.z 5 P.Debye, Z . Elektrochern., 1930, 36, 612.z6 L. Bewilogua, Physikal. Z . , 1931, 32, 265.z7 H. Gazewski, a i d . , p. 219.’* see, however, Debye, aid., 1930, 31, 348; Debye and H. Menke, ibid.,2nd Edn., 1931.p. 797374 SIDGWICK AND BOWEN:contained in a small volume of the gas is minute in comparison withthat in a solid or liquid, and prolonged exposures are necessary.Originally some 24 hours were required, but this has now beenreduced to 4 or 5. The method is essentially the same as that usedfor powders or liquids, a narrow beam of X-rays being passed througha small chamber through which the vapour of the substance is flow-ing, and the scattered rays being received on a photographic plate.The calculation of the interatomic distances from the trace on theplate involves considerable mathematical difficulties ; allowancemust be made for the distortion of the electronic orbits, and also forthe Compton effect.These difficulties have now, however, beenovercome,29 and it has been possible to measure the distances with anaccuracy greater than 1 yo.Method of Electron-Ray Interference.We now know that electrons in motion are accompanied by, orconsist of, systems of waves whose length is given by the de Broglierelation :A = h/mvwhere m is the mass and ‘u the velocity of the electron.30When a narrow pencil of electrons passes through a vapour, theelectrons are scattered, and their waves produce interferencepatterns which can be received on a photographic plate.Thus thegeneral nature of the method is the same as in Debye’s experimentswith X-rays. The necessary corrections for determining thedistances have now been worked and the results agree wellwith those obtained by the X-ray method : thus for the distancesbetween the chlorine atoms in carbon tetrachloride R.Wierl 319 329 33, 34, 35 found 2.98 A. and Debye 2.99 9 0.03 A. Therelative accuracy of the two methods has been in dispute, but wemay conclude 36 that the errors of the electron ray method are slightlythe larger. It has, however, certain great practical advantages overthe X-ray method. The interaction between the electrons and the29 For a general account, see Debye, in ‘* Chemistry a t the Centenary (1931)Meeting of the British Association.”30 For its experimental verification, see G.P. Thornson, Nature, 1928, 122,279 ; “ Wave Mechanics of Free Electrons,” New York, McGrew Hill BookCo., 1930.See also Mark andWierl, “ Die experimentellen und theoretischen Grundlagen der Elektronen-beugung,” Berlin, Borntraeger, 1931 ; “ Elektroneninterferenzen,” LeipzigerVortriige, 1930, p. 13 ; Ann. Reports, 1930, 27, 31.32 2. Elektrochem., 1930, 36, 675.34 Wierl, Physikal. Z., 1930, 31, 366, 1028.35 Ann. Physik, 1931, 8, [v], 521.36 L. Bewilogua, Physikal. Z . , 1931, 32, 114.31 H. Mark and R. Wierl, 2. Physik, 1930, 60, 741.33 Nuturwiss., 1930, 18, 205THE STRUCTlJRE OF SIMPLE MOLECULES. 375molecules of a gas is much more intense than that of X-rays, and theelectrons have a much stronger photographic effect; these twocauses cut down the time of exposure to not more than 1/10,000 ofthat required for X-rays.I n Wierl’s experiments electrons ofabout 40 kilowatts energy (wave-length 0.06 pi.) were used, and thetime of exposure was not more than a few tenths of a second. Thisis more than a mere practical convenience. Many organic com-pounds decompose far below the temperatures at which they boilunder atmospheric pressure, and it is thus impossible to obtaintheir vapours except at great tenuity; such substances couldscarcely be examined by the X-ray method, as the feeble scatteringwould necessitate enormously long exposures, whereas with electronrays quite short exposures would suffice.The electron ray method is equally applicable to solids, and hereit has another advantage over the use of X-rays.Owing to the moreintense interaction of the electrons with the molecules, they penetratea very much shorter distance into the material than X-rays, and sogive us more information about the state of the surface layers.Heats of Formation of Links.The energy evolved when two atoms form it covalent link bysharing a pair of electrons (or absorbed when this link is broken)is a magnitude of obvious importance for characterising the link,and determining the thermodynamic stability of the moleculeproduced. For diatomic molecules this can be measured directlyby various methods; for others it can be calculated if we know theheat of formation of the molecule from its elements in their ordinarystates (e.g., solid carbon, gaseous hydrogen, oxygen, nitrogen, etc.),and also the heat required to convert these elements from theirordinary states into atoms-the heats of atomisation.When a, diatomic molecule composed of two similar atoms can bedissociated thermally to a measurable extent, the heat of atomisationor linking can be determined from the change of the dissociationconstant with temperature, by means of the van ’t Hoff isochore.In this way the molecules Cl,, Br,, I, and H, can be examined.Heats of Atomisation of Diatomic Molecules.37, 389 399 4Q, 419 42- (a)37 R.T. Birge, Molecular Spectra in Gases, Bull. Nat. Res. Council, 1926,ll.38 H. Sponer, “ Optische Bestimmung der Dissociationwarme von Gasen,”39 R.Mecke, “ Bandspektra,” Handb. Phys., 1929, 21.40 G. Herzberg, “ Die Priidissoziation und verwandte Erscheinungen,” Erg.41 M. Rabinovitsch, 2. Elektrochem., 1931, 37, 91.42 For complete literature, see Landolt-Bornstein, 6te Adage, ZweiterErg. exakt. Naturwiss., 1927, 8.exakt. Naturwiss., 1931, 10.Erganzungsband, 1931, p. 1614, etc376 SIDGWICK A.ND BOWEN:(b) The absorption bands of certain molecules (halogens, ICl, 0,)corresponding to an electronic excit.ation show a vibration bandstructure which converges to a sharp limit (accurately obtainable bya very short extrapolation of the band series), beyond which is acontinuous band stretching towards the short wave part of thespectrum. Franck has shown that the energy corresponding tothis limit is to be identified with the heat of dissociation of themolecule-not, however, into normal atoms, but into one normal andone excited atom.If the excitation state of the second atom can beidentified, and its energy subtracted from that corresponding to thespectroscopic dissociation, the normal dissociation energy is obtained.This method is capable of an accuracy of 0.2 kilocalorie if no error ismade in arriving a t the state of the excited atom produced. Theexcitation state is found from an exact knowledge of the spectro-scopic terms for the atom, together with the values of the normal(thermal) dissociation heat derived from methods less refined incharacter but not subject to this uncertainty as to the states of theproducts of dissociation.(c) The type of spectrum in (b) i s shown only by molecules inwhich the internuclear distance is greatly altered by electronicexcitation. In other cases, direct observation of the convergencelimits is not possible, because states of high vibrational quantumnumber are improbable. Molecules possessing electric momentsshow in the infra-red region bands corresponding to increases in thevibrational energy of the non-electronically excited molecule, theconvergence limit of which gives the dissociation energy of the linkto which the vibration belongs.This method involves a long anduncertain extrapolation, and is not available for non-polar moleculessuch as N2 or H,, which cannot change their vibrational states in thenon-electronically excited state by absorption.A more genera1method consists in an extensive and detailed analysis of the bandsystems shown by a molecule both in absorption and in emission.It is then possible in some cases to arrive at the values of the differentelectronic energy levels of the molecule, and a t those of the lowervibrational sub-levels associated with them. A long extrapolationof these vibrational sub-levels, varying in accuracy in different cases,and a determination of the distances of the limits from the groundlevel provide values for the heat of dissociation of the molecule,either into normal atoms if the sub-levels belong to the ground state,or into one normal and one excited atom if they belong to an excitedstate. In the latter event means must be found for specifying theexcited state of the atom produced.By this method a very largenumber of dissociation energies have been estimated, such as thoseof the molecules H,, Se,, Te,, CO, NO, AgCl, HgCl, LiH, as well as oTHE STRUCTURE OF SIMPLE MOLECULES. 377molecules not easily accessible to the chemist, as N2+, 02+, C,, CN,SiN, BO, TiO, CO+, SO, CS, HgH, Li,, Na,, K,.(d) The heat of dissociation DN, of the molecule N2 has beenobtained from that of the molecule N2+, DNz+ (method c), by makinguse of the relation :where I , and I2 are respectively the energies of ionisation of theneutral atom and the neutral molecule, which are obtainable fromspectroscopic data and critical potential measurements. Anaccurate solution of a problem of this kind requires precise identific-ation of measured data with particular energy states, which at lastseems to have been achieved in this case.Application to Polyatomic Molecules.-The sum of the energies ofthe links in a polyatomic molecule is directly obtainable by acombination of the ordinary thermochemical heat of formation ofthe substance with the heats of atomisation of the elements com-posing it.Where the ordinary heats of formation of the gaseousmolecules refer to the elements in a solid or liquid state, correctionmust be made for the latent heat of fusion and of volatilisation ofthat element. Many heats of linkage of this kind, as, for example,that of PH,, cannot yet be estimated for lack of the appropriatedata ; in this case, for phosphorus. Of the greatest importance is thequestion of the heats of linking in carbon compounds.The linkenergies in molecules of the type CH,, CCI,, CO, can be found if thelatent heat of volatilisation of solid carbon to carbon atoms is known.The most probable value of this quantity at the ordinary temper-ature is 150 kilocalories, as the values of the C-H link deduced fromit are fairly close to those obtained from the extrapolated convergenceof infra-red bands of organic substances (see above) and frompredissociation spectra, as described below.When the molecule contains more than one kind of link we canmake progress only if we assume that the energies of particularlinks remain sensibly constant in different compounds. Thisassumption cannot be true, but it appears to be nearly so for relatedcompounds.E’or example, by assuming that the link energy ofC-H remains constant, the values obta4ed for the link C*C from theheats of formation of the saturated paraffins up to C,, do not varybeyond the experimental error. For this calculation any heats offormation which refer to the liquid parafhs must be corrected forthe latent heats of volatilisation, which can conveniently be obtainedfrom H. von Wartenberg’s formula 43 with a further correction toreduce the value to the ordinary temperature. Similarly, fromdata for aromatic hydrocarbons, consistent values for the energies ofIs 2. Elektmchent., 1914, 20, 444.DN, == DN,+ + Iz - I 378 SIDGWICK AND EOWEN:the C-H and C-C links, but different from those for the paraffins, areobtainable.By extending the assumption into regions where itcannot be so accurate, and making use of the heats of formation ofethers, aldehydes, esters, amines, unsaturated hydrocarbons, etc.,fairly consistent values can be obtained for the energies of such linksas C-0, C=O, N-H, C=C, CEC, C-N, etc.Predissociation Spectra.-Certain molecules show, a t points in theirvibration-rotation absorption spectra associated with an electronicexcitation, a fusion of the rotation lines within the vibration bands,which can most simply be interpreted as the formation of unstablemolecules which dissociate into two atoms or residues.44 Theenergies corresponding to these limits are close to (though greaterthan) those of the links which are broken.I n this way the linkenergy in the S, molecule can be obtained, as well as approximatevalues for the link energy of C-H and C-C in aldehydes and ketones.Other Methods.-There are a few other methods of estimatinglink energies which are less accurate or less important.(a) Photosensitisation. An atom is excited to a known state byabsorption, and allowed to pass on this energy by collision to amolecule which is dissociated if the energy available is greater thanand close to its dissociation energy. The heat of dissociationH,O + H + OH can be roughly estimated in this way,45 which isof limited application.The energy of combination of two atoms,e.g., of Na and C1, to give a molecule can be passed by collision toanother atom, which is thereby raised to excited states recognisableby their fluorescent emission spectra. The highest emission stateobservable gives a lower limit for the heat of linkage of the moleculeformed.(c) Photometric methods.Where the molecule formed is inequilibrium with its dissociation products, as in 2BrC1 Br, +C12,46 its energy of linkage can be calculated by applying the van't Hoff isochore to its equilibrium constant, found by estimatingoptically the concentrations of the reactants. This can be done byphotometric means either on their absorption bands or on theirfluorescent emission spectra, according to the case examined.(d) Molecular beam method.47 There are two methods based on theuse of a " unidimensional " molecular beam of the substance.(1) When the atom possesses a magnetic moment and the mole-(b) Chemiluminescence.44 K.F. Bonhoeffer and A. Farkas, 2. pkysikal. Chem., 1928, 134, 337.45 E. Gaviole and R. W. Wood, Phil. Mag., 1928, 6, 1191; H. Senftleben4 6 W. Jost, 2. physikal. Chem., 1931, [ A ] , 153, 143,4 7 See further, p. 381.and (Frl.) I. Rehren, 2. Physik, 1926, 37, 529THE STRUCTURE OF SIMPLE MOLECULES. 379cule does not (Liz, Na,, K,, Bi,), the former only is deflected in aninhomogeneous magnetic field, so that the atoms and molecules canbe collected separately on a plate and their relative amountsestimated. Prom the temperature variation of the proportions theheat of dissociation can be calculated.4*(2) The relative proportion of atoms and molecules in a molecularbeam can be found by the spreading of a rapidly rotating beam.The heat of dissociation can t’hen be found as before from the temper-ature coefficient of the mass-action constant .492Measuremen.t of Dipole Moment.50If the centres of action of the positive and negative parts of amolecule do not coincide, the molecule is polar : it is electricallyequivalent to a rod with a positive charge a t one end and a negativecharge a t the other, and in an electric field it tends to arrange itselfwith its negative end towards the positive pole. Its dipole momentis given by the product of one of the charges into the distancebetween them. Every isolated atom is non-polar. When twoatoms share electrons, if they share them equally, the moleculeproduced will also be non-polar, but if unequally, it will be polar,51the atom which has the greater share being at the negative end of thedipole.Experiment shows that covalent links between unlike atomsare in general polar.The methods of measuring dipole moments depend almost whollyon the determination of dielectric constants. If E is the dielectricconstant of a medium of density d, containing the molar fractionsf,, f, of two substances of molecular weight M,, M,, the “meanmolecular polarisation ” PI, is related to the separate molecularpolarisations P,, P, by :f l M l + f2%d P,, = P,fi + P2f2 =“A & + 2 xThis relation depends on the Clausius-Mosotti equation, whichtakes no account of the mutual influence of the dipoles a t closeranges; it can thus only be applied when the polar molecules are so48 A.Leu, 2. Physilc, 1928, 49, 498; Lewis, ibid., 1931, 69, 786.49 I. F. Zartman, Physical Rev., 1931, 37, 383.50 P. Debye, “ Polar Molecules,” 1929; C. P. Smyth, “ Dielectric Constantand Molecular Structure,” 1931. See also H. Sack, “ DipoImomente undmolekulare Strukture,” Erg. exakt. Wiss., 1929,8,307, and Leipziger Vortrage,1929.51 The words polar and non-polar are used throughout in their strictphysical sense, and mean possessing or not possessing a dipole moment. Tothis meaning they should always be confhed : their use in other senses, forexample, to distinguish ionised from non-ionised links, or associated fromnon-associated liquids, has led to much confusion380 SIDGWICK AND BOWEN :far apart that this influence can be neglected, i.e., to a gas, or adilute solution of a polar substance in a non-polar solvent.A molecule can be polarised by the electric field in three ways :(1) The electrons are displaced with respect to the nuclei.Thisgives the electron polarisation PB. This change is very rapid, ofthe order of 10-15 sec. : it thus follows the oscillations of the electricfield up to the far ultra-violet.(2) The nuclei themselves may be displaced owing to the shift ofthe electrons. This atomic polarisation, PA, is less rapid, about10-12 - 10-13 see. : it follows the field up to frequencies in theinfra-red.(3) If the molecule has a permanent dipole moment, it will tendto orient itself in the field.This orientation polarisation, Po, isrelatively slow, requiring about 10-lO see.The dielectric constants themselves are commonly measured withwireless waves of the order of 100 m. wave-length, that is, with aperiod of about 3 x 10-7, so that the results include all three formsof polarisation. The relation of the molecular polarisation to thedipole moment was shown by Debye to be given by :P=++%+m) 4x v2where N is the Avogadro number, a,, the electronic and atomicpolarisations, p the dipole moment, k the gas constant per molecule,and T the absolute temperature. Hence in order to measure p werequire to eliminate PE and Pa. This can be done in two ways.P E and PA are independent of temper-ature, whereas Po, as the equation shows, is inversely proportionalto it, since the thermal agitation opposes the orientation of thedipoles.Hence if P is determined at several temperatures, andthe values are plotted against the reciprocal of the temperature, theresult will be a straight line, which will be horizontal if the substanceis non-polar, and if it is polar will be inclined to the horizontal at anangle from which p can be calculated.This is the most accurate method, since it eliminates both theelectronic and the atomic polarisation.(B) Optical method. A simpler but rather less accurate methoddevised by Debye and Lange is that in which the electron polar-isateion is determined by using oscillations which are too rapid tocause orientation, i.e., the waves of visible light, of which there areabout 1014 per second.The molecular refractivity, calculated bythe Lorenz-Lorentz formula, is the electronic polarisation. Henceif we subtract the molecular refractivity from the total polarisationas measured by wireless waves, we get the value of PA + Po. PA(A) Temperature methodTHE STRUCTURE OF SIMPLE MOLECULES. 381cannot be determined by this method. Its amount is usually small:for a substance of fairly large moment the orders of magnitude arePE 20, Pa about 5, Po 200. Debye has pointed out that somecorrection is automatically made for FA if we calculate the refrac-tivity not, as should strictly be done, for f i n i t e wave-length, butfrom the refractive index for sodium light. This uncertainty aboutPa is the weakness of the otherwise most convenient optical method.Where the moment is large t'he error introduced is not serious, butwhere it is small or zero, this term may become of greater importance ;any value of p less than about 0.4 x 10-l8 obtained by this methodmay mean that the substance is non-polar.Another method sometimes employed to obtain PE and FA is tomeasure the dielectric constant of the solid substance.We cannot,however, always be sure that orientation is impossible in thesolid.Most of the values of the dipole moment have been obtained bythe optical method, and in solution. Many substances have beenshown to give the same values of the moment in the gaseous state,and in solution in a variety of non-polar solvents such as benzene,carbon disulphide, carbon tetrachloride, and the liquid paraffins.Benzene is the most commonly used; but recent work has shownthat this particular solvent can sometimes combine with a solutein such a way as to affect its moment ; thus iodine has a moment of1-0 52 in benzene, but zero in hexane and cyclohexane : 53 aluminiumbromide a moment of 4.89 in benzene and zero in carbon disulphide.64Molecular Beam Method.--This is an entirely different method,which, although its results are so far less accurate than those of thedielectric methods, can sometimes be used where they fail, and in anyevent is of value as giving an independent codrmation of the truthof the general theory.It is founded on the famous atomic beamexperiments by which Stern and Gerlach determined the magneticmoments of atoms.Its first electrical application was due to E.Wrede,66 who showed in this way that the molecules of the alkalinehalides, which cannot be investigated by the dielectric methods, havemoments of the order of 10 x 10-18. It has since been greatlyextended by J. E~termann.~' The substance to be investigated isheated in a minute oven to a temperature at which it has a perceptible52 The moments of polar molecules have values up to about 8 x 10-l8E.S.U.6s H. Miiller and H. Sack, Pbysihml. Z., 1930, 31, 815.54 E. Bergmann and L. Engel, ibid., 1931, 32, 507.55 For a full account of this method and its various applications, see R. G. S.66 2. Physik, 1927, 44, 261.6 7 2. pbpiFUtl. Chm., 1928, B, 1, 164; 2, 287; Leipz.Vortr., 1929, 17.To save specs they are all multiplied by 10ls.Fraser, " Molecular Rays," Cambridge, 1931382 SIDQWICK AND BOWEN:but very small vapour pressure. A stream of molecules, too farremoved from one another to collide, and with a velocity given bytheir temperature, in accordance with the gas laws, issues througha narrow (0.01 mm.) slit into a high vacuum, and by means of asecond slit is cut down to a narrow and very thin ribbon of rays.This is passed through a highly inhomogeneous electric field, andthen received on a brass plate cooled with liquid air, and thetrace which the molecules form is observed with a microscope.I n the absence of the field the molecules go straight through theapparatus, and condense on the plate in a narrow vertical line, lessthan 0.15 mm.wide. When the field is put on (Estermann used21,000 volts) it affects even non-polar molecules, since the electronpolarisation causes an induced dipole, and so they move towardsthe stronger part of the field; but the trace shifts as a whole. If,however, the molecules are polar, the effect of the field on any onedepends on the inclination of its dipole to the field, and so the traceis broadened to an extent depending on the moment of the molecule.So far it has not been found possible to deduce more than a roughestimate of the moments.This method can be used with substances which are not volatileenough for the dielectric constant of their vapours to be measured,and which are not soluble enough in non-polar solvents for thesolution method to be practicable.Its most remarkable successwas with pentaerythritol, C(CH,*OH),, m. p. 250-255", which wasshown to have a moment of about 2.0 x 10-ls.11. RESULTS.Dimensions.The methods already described for measuring the lengths of thelinks between atoms give us the distances between the atomicnuclei. To make them intelligible we have to try to determine the" radii " of the atoms concerned. In the light of modern theoriesof atomic structure it is difficult to say exactly what the " outside "of an atom means, or what its true radius is. For our presentpurpose this difficulty can be avoided by using the word radius in thesense of effective radius, as meaning the contribution which eachatom makes to the length of the link with another atom.As we have seen, the dimensions of links can be determined bothin the solid and in the gaseous state.It does not seem that the stateof aggregation makes much difference to the length of a covalentlink; and this is to be expected, since the forces between the mole-cules of a covalent solid are small in comparison with those betweenthe component atoms of the molecule : in carbon tetrachloride, foTHE STRUCTURE OF SIMPLE MOLECULES. 383example, the latent heats of fusion and evaporation are both about7 kg.-cals. per g.-mol., while the separation of the CCl, moleculesinto their component atoms needs about 270 kg.-cals. On the otherhand, in discussing the data derived from the study of solids, whichare by far the most numerous, we have to deal with the distinctionbetween the two kinds of link, electrovalent and covalent; thisambiguity does not arise with gases, since the only molecules whichcan be obtained in the gaseous state, except at very high temper-atures, are covalent. But with solids both kinds of link occur, andit is clear, largely through the work of V.M. Gold~chmidt,~8 that thenature of the link has an effect on its length. This conclusion,however, only emerges after a rather detailed examination of thefacts. The values given by Goldschmidt and others for the radiusof an atom in the neutral and ionised states differ widely (e.g., K2.27, K+ 1-33 ; C1 0.97, C1- 1-81 A.U.) ; but the effects of a positiveand a negative charge are in opposite directions; they thereforeneutralise one another to a considerable extent in a salt, and whilethe radius of each atom is very different according as the link isionised or covalent, the effect on the sum of the two radii, which iswhat is actually measured, is much less. In fact it is of the sameorder as that of two other influences which Goldschmidt hasemphasized.The first is the deformation of the ions by one another,to which are due the small changes observed in the differences of theinteratomic distances of, say, the sodium and potassium salts of thesame halogen as we pass from one halogen to another : this mayamount to as much as 5%. The second, which probably applies tocovalent as well as to ionised links, is the effect of the type of lattice,of what Goldschmidt calls the “ co-ordination number,” which hasnothing to do with the Werner theory, but is merely the number ofnearest neighbours which the atom has in the crystal.As thisnumber gets smaller the distances between the atoms decrease, andin extreme cases (going from 12 to 4) as much as 15% : the decreaseis, however, sufficiently regular to be allowed for. When regard ishad to these modifying influences, it can be shown that there is adefinite change in the distance when the link passes from the electro-valent to the covalent form. In the compounds of silver andcadmium given in Table I1 (p. 402), those which are ionised in thecrystal are distinguished by square brackets, and it will be seenthat in all of these the observed distance is greater than that cal-culated for the covalent state.Often the distinction between thetwo kinds of link appears more clearly from the type of crystal6 8 “ Geochemische Verteilungsgesetze,” VII, Oslo, 1926 ; VIII, Oslo,1927; Ber., 1927, 60, 1263. See also L. Pauling, J. Arner. Chern. SOC., 1927,49, 765384 SIDGWICK AND BOWEN:lattice, the covalent compounds favouring, as we should expect, themore open types, while true salts assume the most close packedform.In considering molecular structure we are essentially concernedwith the covalent link, and with the effective radii of neutral at0rns.5~A list of these radii for some of the more important elements is givenin Table 11. The constancy of these magnitudes, even under verydiverse conditions of observation, is surprising.The distancebetween two singly linked carbon atoms is found from the crystalstructure to be 1.54 A.U. in diamond,60 1.6 in solid ethane,61 1.55in the side chains of hexamethylbenzene,62 and 1.55 in long-chainparaffins 63 ; while by electron scattering we get 1.5 from the vapourof paraffins and naphthene~.~4 The “ aromatic ” link is 1-42 ingraphite,64 1.45 in solid hexamethylbenzene,62 1.45 in solid naph-thalene,65 and 1.4 in benzene vapour as measured both by X-ray andby electron scattering.34~ 35 The double link C:C is 1.35 in solidstilbene,66 and 1-31 according to the spectrum of the Swan bands.67The agreement between the interatomic distances observed incompounds, and those calculated from the values for the elements,whether the data are got from the solid or the gas, and whether bymeans of the crystal structure, or the band spectra in any of theirforms, or the scattering of X-rays or electrons, is remarkably close,not only among organic compounds, but generally, even among thecompounds of the metals where these are not ionised; and it holdsalso with the hydrogen halides, in spite of the exceptional characterof the hydrogen atom.A series of examples is given in Table 11,the calculated values being obtained from the atomic radii in thesame table. The values marked “ corr.” are corrected on thehypothesis that a double link is 14% and a triple 23% shorter than asingle link. These are the observed differences with carbon (0.22and 0-36 b.U.); and while we do not know the effect on otherelements, we may assume that it is of the same order, especiallysince the interatomic distances for carbon and the succeeding elements5a A remarkable series of simple relationships between the atomic radii(especially those of the metals) and the atomic numbers has been pointed outby W.Hume-Rothery (Phil. Mag., 1930, 10, 217).6o W. Ehrenberg, 2. Krist., 1926, 63, 320.61 H. Mark and E. Pohland, ibid., 1925, 82, 103.62 (Mrs.) K. Lonsdale, Proc. Roy. SOC., 1929, 123, 494.63 A. Mdler, ibid., 1927, 114, 542 ; 1928, 120, 437.64 E. Ott, Ann. Phy8ik, 1928, 85, 81.65 K. Banerjee and J. M. Robertson, Nature, 1930, 125, 456.6 G J. Hengstenberg and H. Mark, 2. Krist., 1929, 70, 283.67 Quoted by I(.H. Meyer and a. Mark, “Aufbau d. hochpolymerenorg. Naturstoffe,” Leipzig, Akad. Verlagsges., 1930, p. 17THE STRUCTURE OF SIMPLE MOLECULES. 386present a much more regular series if they are corrected on thisbasis : c-c. E N . o=o. F-F .Observed ............... 1-54 1.11 1.20 1-36Correction - 0.34 0.20Corrected ............... 1.54 1-45 1.40 1.35In polyatomic molecules the measurement of interatomic distancescan also give us information about the angles between the valencies.The general question of stereochemical configuration will be dis-cussed later,68 but we may consider here the very remarkableinvestigations of Debye and of Wierl with their collaborators, bythe X-ray and the electron method respectively, on the chlorinatedmethanes.They measured, with concordant results,25* 26 theC1,Cl distances in carbon tetrachloride, chloroform, and methylenechloride, and the C-C1 distance in methyl chloride. In the sym-metrical CCl,, the valency angles are all obviously 109.5". From theobserved CI,Cl distance of 2-99 A.U. this gives C*C1 as 1-82. InH,C*Cl, C*C1 has the same value. We can therefore assume that ithas this length in the intermediate compounds as well, and thisenables us to calculate the angles between the C*C1 valencies as follows :............... -c-c. N-N. 0-0. F-F .Compound. C1,CI. Val. angle.CC1, ................................. 2.99 109.5'CHC1, .............................. 3.1 1 116.4CH,Cl, ...........................3-23 123.8It is clear that with the successive replacements of chlorine byhydrogen the distance between the carbon and the chlorine remainsconstant, but the angle between the C*C1 valencies increases (as theThorpe-Ingold theory assumes), and by about 6 or 7% on eachreplacement. The results are of great interest as giving us a,definite idea of the extent to which the valency angles can bemodified by the other groups present in the molecule.The general conclusion to which the study of molecular dimensionsleads is that in covalent links the effective radii are remarkablyconstant, and are but little affected either by the conditions of themolecule, whether solid, liquid, or gaseous, or by the other atomswhich it contains. The angles between the valencies are much moresubject to change.In the older stereochemistry great stress waslaid on the valency angles, but relatively little attention was paidto the interatomic distances. It is now clear that the constancy ofthese two factors is in the reverse order.Heats of .Formation of Links.As we have seen,69 these values can be determined for diatomicmolecules directly; for polyatomic molecules the sum of the values68 p. 308. 6s p. 376.REP .-VOL. XXVIII. 386 SIDGWICK AND BOWEN:for all the links in the molecule can be calculated if we know theheat of formation of the molecule from its elements, and the heats ofatomisation of those elements. If we are to obtain values for theindividual links, we must assume that these are independent of theother links in the molecule, or that we know how the latter affectthem.The heats of atomisation of the elements, a knowledge of which isessential to the problem, have only become known with any accuracyin the last few years-even now only a limited number are known-and hence the subject is of comparatively recent development,One of the first to draw attention to it was K.Fajans,‘O who showedthat the heat of rupture of the C-C link was almost the same inethane and in diamond. Further investigations were made byA. von Weir~berg,~~ A. E ~ c k e n , ~ ~ H. G. Grimm,73 and H. Wolff, andothers; the results are summarised by Grimm 74 and by Eucken ‘5 ;their data, however, need some revision in the light of later deter-minations of the heats of atomisation.The last column of Table I contains a series of values of the heatsof rupture of covalent links.For a diatomic molecule the heat ofrupture of the link is twice the heat of atomisation. Two othervalues of the heat of atomisation should be added; for solid sulphur65-6 and for solid carbon 150 kg.-cals. per gram-atom. The heat ofrupture of the C-C link in solid carbon is of course half this, or75 kg.-cals.The values given in the table for compounds are mostly derivedfrom their heats of combustion through the heats of formation.Where the links are all the same (H,O, NH,, CH,), the value givenis the total heat divided by the number of links. Where they aredifferent, rather uncertain assumptions must be made as to theconstancy of the heat of a particular link.With the organic com-pounds the value 93-6 for C-H (derived from methane) is usedthroughout. This is probably accurate for alkyl radicals. .A com-parison of benzene and naphthalene derivatives indicates that theheats of the links C-C and C-H are about 9 units higher when thecarbon forms part of an aromatic ring, but as the basis of thesecalculations is somewhat doubtful, the aromatic compounds areomitted from the table. This uncertainty as to the effect on theC-H link of the state of combination of the carbon affects the values70 Ber., 1920, 53, 643; 1922, 56, 2826.71 Bey., 1919, 52, 1501; 1920, 53, 1347, 1519; 1923, 56, 463.7 2 Annalen, 1924, 440, 111.73 2. physikd. Chem., 1922, 102, 134; 2. Elektrochem., 1925, 31, 474.74 Geiger-Scheel, “ Handbuch der Physik,” 1926, 24, 532.7 5 “ Handbuch der chemischen Physik,” Leipzig, Akad.Verlagsges., 1930,p. 882THE STRUCTURE OF SIMPLE MOLECULES. 387given for multiple links of carbon to carbon, nitrogen, and otherelements ; these are calculated on the value found for C-€I in theparaffins, as we have no means of finding its true value in theethylene and acetylene derivatives. As they stand, the values formultiple links are interesting :Abs. Rel. Abs. Rel. Abs. Rel. Abs. Rel.C--C 71.0 1 C-N 55 1 C-0 70.5 1 C-S 58.7 1C=C 125.2 1-8 C=N 111 2.0 C=O 163 2.3 C I S 127 2.2C Z C 165 2.3 -CzN 183 3.4 CGO 235.5 3.3-N?C 184 3-4It is remarkable that while with the link of carbon to carbon theheat of formation increases much less rapidly than the number oflinks, which entirely agrees with what we should expect from thebehaviour of unsaturated compounds, with the link of carbon tonitrogen, oxygen, or sulphur the heat of formation of a double linkis at-least twice, and that of a triple link more than three times,that of a single link.As will be realised, the question of the heats of formation of linksis of great importance, but so far the subject is little developed.We need to accumulate accurate data on the heats of atomisation ofmore of the elements, and the heats of combustion of a large numberof compounds of the most varied types.Dipole Moments.76The methods of measurement described above give us the dipolemoment of the whole molecule.This may be conceived t o be madeup of a series of partial moments pertaining to each of the links;these are obviously directed magnitudes, and their vector sum isthe moment of the molecule.If we knew the values of each of thepartial moments, and the angles which they make with one another,we could calculate the molecular moment. We cannot yet do thiswith any great accuracy, but it can often be done sufficiently nearlyto enable us to decide between two chemically possible structures,and in this way the study of dipole moments has already proved ofgreat value.In the first place, if the molecule is non-polar, the partial momentsmust balance one another, and the molecule must be symmetrical.The diatomic elemeiitary gases H,, N,, O,, Cl,, etc., are found to benon-polar, as we should expect.Triatomic molecules of the typeAB, should be non-polar if the three atoms lie in a straight line,7 6 Complete lists of dipole moments published up to date will be found inSmyth, op. cit. (1931) : also in Debye, " Polare Molekeln," Leipzig, Hirtzel,1929, with supplementary lists for 1929 and 1930. Moments quoted withoutauthority in the text (which are expressed in terms of the unit 1 x IO-l*E.S.U.) will be found in these lists388 SIDGWICK AND BOWEN :provided the links are the same, as they usually will be; if thevalencies are inclined to one another, the molecule will be polar.It has thus been shown that CO,, CS,, and N,O are rectilinear, whileH,O, H,S, and SO, are triangular. (Many of these conclusions areconfirmed by the spectra, and also by the scattering methods ofDebye and Wierl.) A molecule AB, will be non-polar if all the atomslie in a plane and the valency angles are equal; hence NH,, since ithas a moment of 1.5, cannot be plane but must be pyramidal, asmust PH, (0.55) and ASH, (0.15).A pentatomic molecule AB, canbe non-polar on the tetrahedral model, or if the five atoms lie in aplane. CH, and CCl, are non-polar, and the plane formula is ruledout, because if it were true CH,Cl, (in the trans-form, which mustbe the more stable) would be non-polar, whereas it has a moment of1.5. Thus the tetrahedral configuration is established, and thesquare pyramid, which was a t one time suggested, is shown to beimpossible.When we come to more complicated molecules, we need to getsome idea of the moments of individual links.We have first,however, to find the direction or sense of the moments. This canbe done by an ingenious method suggested by J. J. Thomson 77 andfirst used by J. W. Williams.78 Since the benzene ring is planar,the moments of t'he links C-X, C-Y in a para-substituted moleculeC,H,XY will lie in the same straight line. Hence if the directionof these moments with respect to the ring is the same, they willoppose, and if it is the opposite they will strengthen, one another.This enables us to divide the links into two classes of oppositesense : it is found, for example, that C-Cl, C-Br, and C-NO, belongto one class, and C-CI-I, and C-NH, to the other ; and it is easy tosee, on more general grounds, that the first class must have thenegative end of the dipole remote from the ring.In finding the moments of individual links, the first difficulty isthat of the C-H link.All saturated paraffins (22 have so far beenexamined 79) are non-polar; but it can easily be shown that, if weassume the tetrahedral model, this absence of polarity can beexplained by the symmetry of the molecule, and is compatible withany value of the moment of C-H. There is good reason to thinkthat this moment is small: it is commonly assumed to be 0.4(Williams, and A. Eucken and L. Meyer 80), but all that we reallyknow is that it lies somewhere between 0.4 and zero.has calculated the values for C-H and C-Cl from the observedL.E. Sutton7 7 Phil. Mag., 1923, 46, 513.79 See R. W. Dornte and C. P. Smyth, J . Amer. Chem. SOC., 1930, 52, 3 5 4 .* l Proc. Roy. SOC., 1931, 133, 689, note.Physikal. Z . , 1925, 29, 174.Phy8ikal. z., 1929, 30, 397THE STRUCTURE OF SIMPLE MOLECULES. 389moments of chloroform and methylene chloride, using the anglesbetween the C-Cl valencies given by the measurements of Debyeand Wierl, on the assumptions (a) that the C-H valencies inmethylene chloride have an angle of 109.5", ( b ) that this angle isreduced by the expansion of the C-Cl angle to 100". He finds thatm(C-H) (this is a convenient symbol for the moment of the linkC-H) is for (a) 0-15, and for ( b ) 0.20 : the corresponding values form(C-Cl) are (a) 1.5 and ( b ) 1.41. The moment of C-H is in anycase small, compared with mo8t of those with which we have to deal,and we may provisionally assume the value 0.4.The moments ofother links can then be calculated from the observed moments ofthe simpler molecules. For example, m(CH,Cl) = 1-9 : the resultantof the moments of the three C-H links is equal (assuming angles of109.5") to that of one : hence m(H,C-Cl) = m(H-C-Cl) = 1.9. Asm(C-H) = 0-4, m(C-Cl) = 1.5. The uncertainty as to the valueof m(C-H) implies that m(C-Cl) may be as large as 1-9. Themoments of other links can he calculated by similar methods, andthe results are given in Table I11 (p. 402), the atom which is at thepositive end of the dipole being always printed first. These valuesare only provisional; they depend on three assumptions whichcannot be strictly true : (1) the value for m(C-H) ; (2) the assump-tion that the value for a given link is unaffected by the other linksin the same molecule : this seems to be approximately true exceptin the aromatic derivatives (see p.392); (3) the assumptionthat the valency angles can be taken to be 109.5". This last pointinvolves two questions. As we saw from the distances in thechlorinated methanes, the angles between the valencies of a 4-covalentatom such as carbon vary to some extent with the nature of theatoms attached to it, but amounts of variation such as were foundin these compounds would not change the values for the links bymore than a few tenths of a unit. It is, however, maintained byPauling3 that with covalencies of 2 or 3 the normal angle is not109.5" but 90".This would make a more serious difference to thevalues calculated for the individual links, when the central atom hasa covalency of less than 4. For example, water has a moment of1.87. If the angle between the 0-H valencies is 109.5", m(0-H) =1.87 + 1.155 = 1.62. If it is go", m(0-H) = 1-87 + 1.414 = 1.32.In the same way, m(NH,) -= 1-5; if the angles are tetrahedral,m(N-H) = 1.5 : if they are 90", m(N-H) = 1.06. The figures inthe table are calculated for angles of 109.5" and a C-H value of 0.4.Inspection of the table shows that (1) the element of the earlierperiodic group (counting hydrogen as belonging to Group I) is alwayspositive so far as is known ; but we do not yet know the moments ofany links of carbon to elements in the first three groups other tha390 SIDGWICK AND BOWXNhydrogen.(2) I n the link X-Y, where X and Y are in differentperiodic groups, if X, the positive member, remains the same, andY represents a series of elements from the same group, the momentalways diminishes as the atomic number of Y increases, except inC-0 and C-F, which seem to have smaller moments than C-S andC-CI; the exception does not hold with H-0 and H-S : m(H-F) isof course unknown. On the other hand,if we keep Y (the negativemember) constant, and replace X by another atom of the sameperiodic group, we get, so far as we can judge from the scanty data,the opposite result : the heavier X is, the lgrger the moment.It will also be noticed that in the series H-C, H-N, H-0, thoughthe increase is continuous, it is much greater between H-C (0.4)and H-N (1.5) than between H-N and H-0 (1.6).This may beconnected with the fact that in H-C alone the negative atom hasno unshared valency electrons.FZexibZe MoZecuZes.-A conclusion of very general interest whichemerges from the dipole measurements concerns the behaviour of" flexible " molecules and the meaning of the free rotation of singlylinked atoms. As we have seen, a para-disubstituted benzene withthe two substituents the same would be expected to have zeromoment, and many such molecules, for example,p-C6H4CI2,p-C6H4I2,P-C6H4(CH3),, are found to be non-polar. But others are definitelypolar : p-C6H4(O*CH,), 1.74, p-C6H4(CH0), 2.35, p-C6H4(CH2C1)2,2-23, etc.I n all these it will be noticed that the resultant momentof the substituent group does not lie in the central line of the molecule ;quinol dimethyl ether, for example, may, without any departure ofthe valency angles from the normal, have any configuration between(I) and (11).(11.)H,C/ '-<)-O\CH 3H3C \ O - ( l t o \(1.1 CH3Of these, (I) is symmetrical and non-polar, while (11) should havea considerable moment. The mutual repulsion of the dipoles wouldtend to make the molecules assume the non-polar form. L. Meyer 82has pointed out that such molecules are under two opposinginfiuences : (1) the work required to deflect the groups from thefavoured position, which is the intramolecular potential of thedipoles, and (2) the energy of the thermal agitation, which i s givenby kT, where k is the gas constant per molecule (= BIN), and Tthe absolute temperature. If the potential is much the larger, themolecule will remain in its position of minimum (if it is symmetrical,of zero) moment; if the thermal energy is much the larger, the2.physilcccl. Chem., 1930, [B], 8, 27THE STRUCTURE OF SIMPLE MOLECULES. 391potential will have a negligible effect, and the molecule will assumeall possible positions with equal frequency. Meyer also shows 83that the potential of the moments pl, b, at a distance d apart isapproximately p1 - p2/d3. Hence for a molecule a t the ordinarytemperature with two moments of the order of 1 x E.S.U.,the thermal energy kT(4 x 10-14 erg) will equal the potential ifd = 3 x cm., which is about twice the distance between twolinked atoms (other than hydrogen) in an organic molecule.Weshould therefore expect that in a molecule such as ethylene dichloridethe repulsion of the dipoles would have a large effect, while in quinoldimethyl ether and other p-di-substitution products of benzene,where the two dipoles are about 6 B.U. apart, its effect would bevery small. In compounds of the latter type, as we have seen, thisis borne out by experiment; and with ethylene dichloride directmeasurement with X-rays has shown 24 that the two C-Cl links aremainly in the most remote (" trans ") position, but that they aredisturbed by thermal agitation to an extent which correspondsclosely to that.required to account for the observed dipole moment.With molecules of this type, for which the electrical and thermalenergies are of comparable magnitude, it should be possible to showthat the moment increases with rise of temperature. This has beenthe subject of a number of papers 84; the facts are not yet quitecertain, but seem on the whole to support the theory.Chemists have long realised that the principle of free rotation ofsingly linked atoms with their attached groups did not necessarilyimply that these atoms were continuously rotating ; it was foundedon the absence of isomerides capable of passing into one another bysuch rotation, and hence it only implied that the molecule was freeto take up the most favoured of all the forms which this rotationpermitted. The application of the methods of scattering, and ofthe measurement of dipole moments, has shown us how far andunder what conditions the rotation can occur.It is clear that inconsidering, especially in relation to its reactivity, the forms whicha complicated molecule can assume, we must take into account theeffect of the forces between the dipoles on its configuration, and weare beginning to learn how this can be done.The Co-ordinate Link-The theory that a co-ordinate link is acovalency formed of two shared electrons, both derived from oneof the two linked atoms, has been regarded by some chemists as8s For a further discussion of this, see C. P. Smyth, R. W. Dornte, andE. B. Wilson, jun., J.Amer. Chem. SOC., 1931, 53, 4242.84 L. Meyer, loc. cit.; R. Sanger, Phyeikal. Z., 1931, 32, 21; Meyer, ibid., p.260; Smyth and co-workers, J . Arner. Chem. SOC., 1931, 53, 527, 2005, 2988,4242392 SIDGWICK AND BOWENimprobable, on account of the large electrostatic displacement whichit implies; but the measurement of the moments of molecules con-taining such links has confirmed it. With the bivalent carboncompounds, such as carbon monoxide and the isocyanides, there isevidence of the presence of a co-ordinate link in which the carbon actsas acceptor, and it has been shown 85 that the moments of thesecompounds agree closely with those to be expected if an electron istransferred from the nitrogen or oxygen to the carbon. Again, itseries of co-ordinated compounds have been shown to have excep-tionally large moments (from 4 to 9 units), such as the sulphoxidesand sulphones,s6 and the compounds of the halides of beryllium,boron, and aluminium with ethers, nitriles, and amine~.~' Theabnormal increase of molecular polarisation with concentration shownby the alcohols 88 indicates that their association is accompaniedby the formation of co-ordinate links of large moment. The relationbetween the power of a hydrogen atom to act as acceptor, and theposition in the periodic table of the atom to which it is alreadyattached, again supports the theory.89 It is well known that thispower varies greatly : the hydrogen in C-I3 cannot act as acceptor :in N-H it does so reluctantly, in 0-H and F-H very readily.I nthe same way the co-ordinating power of the hydrogen is muchgreater in N-H than in P-H, in 0-H than in S-H, and in F-H thanin C1-H; its power in X-H increases as X changes from an earlierto a later group in the first period, or within a given group fromthe second period to the first. But these are precisely the directionsin which the moment of X-H, in which H is always positive, increases ;and if the formation of a co-ordinate link consists in the hydrogentaking a share in a pair of unshared electrons of another atom, weshould expect it to do so the more readily, the larger its positivecharge.Dipole Moment and Organic Structures.The study of dipole moments has thrown light on a whole seriesof problems of structure in organic chemistry, and the results maybe briefly summarised.(1) Substitution in Benzene.-The theories of the influence ofgroups on the reactivity of organic molecules which have been put85 D.L. Hammick, R. C. A. New, N. V. Sidgwick, and L. E. Sutton, J.,1930, 1876.86 E. Bergmann, L. Engel, and S. Shndor, 2. physikal. Chem., 1930, [B], 10,397; 0. de Vries and W. H. Rodebush, J. Amer. Chem. SOC., 1931, 53, 2888.87 H. Ulich and W. Nespital, 2. angew. Chern., 1931, 44, 750.L. Lange, 2. Physik, 1925, 33, 169; J. Errera, Leipzjger Vortriige, 1929,pp. 25, 105.89 N. V. Sidgwick, Z. Elektrochem., 1028, 34, 440THE STRUCTURE OF SIMPLE MOLECULES. 393forward by Lapworth, Robinson, Ingold, and others agree in ascrib-ing the phenomena to a displacement of the electrons in the molecule,and any such displacement must be reflected in the dipole moments.The first attempt to test these theories from the physical side hasbeen made by L.E. Sutton,"o with respect to the problem of sub-stitution in benzene. The moment of a molecule R-X is differentaccording as R is an alkyl or an aryl group; and Sutton has shownthat there is a simple relation between the sign of this differenceand the directing power of the group X in benzene. If we call thosemoments of which the positive end is away from R positive, and thosein the opposite direction negative, then if m(Ar-X) - m(Alk-X)is positive, X directs ortho-para : if it is negative, X directs meta.For example :m(Ar-CH,) + 0.45 : m(Alk-CH,) 0 : Diff.+ 0.45m(A.r-NH2) + 1.55 : m(Alk-NH,) + 1-23 : Diff. + 0.32m(Ar-Cl) - 1-56 : m(Alk-Cl) - 2.15 : Diff. + 0-59m(Ar-CC1,) - 2-07 : m(CH3*CC1,) - 1.57 : Diff. - 0.50m(Ar-N02) - 3.93 : m(Alk-NO,) - 3.05 : Diff. - 0.88The first three groups of course direct ortho-para, the last two meta.Wherever this rule has been tested it has been found to hold.These results strongly support the view that the electrons of thebenzene ring are liable to suffer displacement under the influence ofa substituent, and that this determines the position which furthersubstituents take up ; moreover the direction of the displacementis that postulated for the electromeric effect by the Lapworth-Robinson theory. The observed displacement, as the aboveexamples show, is of the order of one-tenth of that which would becaused by the transference of an electron from one atom of thering to the next (about 7.4 units), and we might suppose either thata small proportion of the molecules underwent the full transference,or that all of them suffered a small displacement.As Sutton pointsout, the latter must be true, since in chlorobenzene, for example,substitution is much slower than in benzene; if only a smallproportion of the molecules were affected, the rest would react aseasily as before, and the rate of reaction of the compound as a wholewould not be seriously diminished.It is of interest to compare this conclusion of Sutton's with thesubstitution rule put forward by D. L. Hammick and W. S. Illing-worth.g1 This rule, which seems to hold in every case, states thatif in C,H,-X-Y, Y is in a later periodic group than X, then thedirection is meta, but that if not (i.e., if it is in the same or an earliergroup, or if there is no Y, as in C6H5Cl) then it is ortho-para. NowProc.Roy. Xoc., 1931, 133, 668. g1 J., 1930, 2358.N 394 SIDGWICK AND BOWEN:in a link X-Y, as we have seen, if Y belongs to a later periodic groupthan X, it is the negative end of the dipole, but if to an earlier, thepositive end. If we accept the conclusion, that the ortho-paradirecting power involves an electronic drift in the ring away fromthe substituent, we can distinguish three cases (the arrow in thering indicates the drift) :-I+ X-YIn the first and third, the drift is in the same direction as themoment of the substituent, and may be supposed to tend to relievethe strain which this causes; but in the second, where there is onlyone atom in the substituent group, we have to assume a drift in theopposite direction to the moment, which indicates that someprinciple, other than induction, is operative, which we do notunderstand.(2) Diphenyl Derivatives.-The Kaufler formula for diphenyl, inwhich one ring was supposed to be folded over on the other,92 wasdisproved by dipole rneas~rements,~~ which showed that thep,p’-di-derivatives X*C,H,-C,H,*X had almost the same momentsas the corresponding p-di-derivatives of benzene ; they were non-polar so long as the moment of X was symmetrical to the centralaxis of the molecule, and only polar when this could be explainedby the flexibility of the X group.(3) cis - trans - Isomerism. - A cis - disubstituted ethylene,CHXZCHX, should be polar, and its trans-isomeride non-polar, sothat the moments give a simple method of determining the con-figuration.This test has been applied by J. Errera 94 to the di-halogen substitution products of ethylene. He finds that thedichloride, dibromide, and chlorobromide in the trans-form are92 For a summary of the chemical arguments for and against this formula,see C. K. Ingold, Ann. Reports, 1926, 23, 119. For the explanationof theoptical activity of diphenyl derivatives, see F. Bell and J. Kenyon, Chem. andInd., 1926,4, 864; W. H. Mills, ibid., p. 884; W. H. Mills and K. A. C. Elliott,J ., 1928, 1291.93 J. W. Williams and A. Weissberger, J . Amer. Chem. SOC., 1928, 50, 2332;Z . phgsikal. Chem., 1929, [B], 3, 367; A. Weissberger and R. Sangewald,ibid., [B], 5, 237; J. W. Williams and J. M. Fogelberg, Physikal. Z., 1930,31, 363.$4 Compt. rend., 1926, 182, 1623; Physikal. Z., 1926, 27, 764; “Polarisa-tion didlectrique,” Paris, 1028THE STRUCTURE OF SIMPLE MOLECULES. 395non-polar, and in the cis-form have moments of about 1.5 : withthe chloroiodides one form has p = 0-57 and the other p = 1-27.Since the moments of C-CI and C-Br are practically identical, whilethat of C-I is smaller, we should expect a residual moment in thetram-chloroiodide but not in the tram-chlorobromide. The assign-ment of structures previously made to the isomerides on othergrounds agrees with the dipole measurements, except in thechloroiodides.This conclusion has been confirmed for the dichlorides by D e b ~ e , ~ ~who has shown by the X-ray method that the distance between thechlorine atoms in the cis-compound is 3.6 and in the trans-compound(4) Compounds of Type CA,.-The configuration of these com-pounds has been the subject of much discussion.Guillemin andV. Henri suggested, on the basis of spectroscopic measurement^,^^that a molecule CA, could have the form of a square pyramid withthe carbon at the apex. The X-ray examination of the crystalstructure of pentaerythritol, C( CH,*OH),, was believed to indicatethat the arrangement of the groups round the central carbon atomcould not be tetrahedraLg6 Later work has weakened the force ofboth of these lines of arg~ment.9~ The dipole moments appear tobe conclusive in favour of the tetrahedral structure.CH,, CCl,,C(NO,),, and C(CH2hal),, where ha1 = CI, Br, I, have all beenshown to be non-polar. On the other hand, compounds CA, inwhich A = O-CH,, O*C,H,, CH,*OH, CH,*O*CO-CH,, CH,*O*NO,,CO*O*CH,, CO*O*C,H, have moments from 0.8 to 3-9.98 These,however, are all groups with unsymmetrical moments, whoseflexibility is sufficient to account for their polarity. The absenceof polarity in pentaerythritol tetrachloride, tetrabromide, andtetraiodide, which was confirmed for the first two by the beammethod, is remarkable. A symmetrical and non-polar arrangementof the four CH,hal groups is of course possible, but it seems unlikelythat the potential of the moments would be sufficient to fix the95 V.Guillemin, Ann. Physik, 1926, 81, 173; V. Henri, Chem. Reviews,1927, 4, 189.g6 H. Mark and K. Weissenberg, 2. Physik, 1923, 17, 301 ; M. L. Hugginsand S. B. Hendricks, J . Amer. Chem. SOC., 1926, 48, 164.9 7 Fordhe spectroscopic evidence, see A. E. Ruark and H. C. Urey, “ Atoms,Molecules, and Quanta,” 1930, p. 436; for the crystal structure, I. Nitta, Bull.Chem. SOC. Japan, 1927,1, 62; A. Schleede, 2. anorg. Chem., 1928,168, 313;172, 121; also H. Miiller and A. Reis, 2. Krist., 1928, 68, 385; (Miss) I. E.Knaggs, PTOC. Roy. SOC., 1929, 122, 69.98 J. W. Williams, Phy8ikaE. 2.. 1928, 29, 683; L. Ebert, R. Eisenschitz,and H.von Hartel, 2. physikal. Chem., 1928, [B], 1, 94; I. Estermann, ibid.,1929, [B], 2, 287; Leipziger Vortrilge, 1929, p. 17; 0. Fuchs, 2. PhysiE, 1030,63, 824.4.7 A.U396 SIDQWICK AND BOWEN :molecules in this position, especially as the orthocarbonates,C( Oalk),, are polar. It is probable that steric influences co-~perate.~~(5) Bivalent Carbon Compounds.-The dipole moments indicatethat in carbon monoxide and the isocyanides the carbon is triplylinked to the oxygen or the nitrogen, the third link being co-ordinate :o z c R--MI-CThe link of carbon to oxygen or nitrogen has, as we have seen, aconsiderable moment, the carbon being positive. C=O andR-N=C should therefore be highly polar, and the moment inthe latter should have its positive end remote from the group R.Carbon monoxide is almost non-polar (0-l), and it has been shown 85that the moment of the -NC group in the aryl isocyanides (3.5) isin the opposite direction.This can only be explained by the trans-ference of an electron to the carbon in the formation of the (third)co-ordinate link, and the effect of such a transference through thedistance separating the two atoms is in good agreement with themagnitudes of the observed moments. The existence of a triplelink between the atoms is codrmed by the heats of formation andthe parachors, and further for carbon monoxide by the interatomicdistance (obs. 1.14, calc. 1.13 A.U.) and by the force constant (18.6(6) 0ximes.-A decision between the opposed theories of Hantzschand Meisenheimer as to the configuration of the syn- and anti-oximes has been promoted by the measurement of the moments ofx 105).(I.) O 2 T 4 - a 0 O+N-CH, o > N - o - f a 0 H,C-N+O (11.)the N-ethers of p-nitrobenzophenoneoxime. loo The -N+ 0group should have a moment comparable with that of the nitro-group, and hence the moment of the syn-compound (I) should belarge, and that of the anti-compound (11) small.It was found thatthe a-compound (m. p. Ego), which according to Meisenheimer hasthe syn-formula, gave p = 6-60, and the p-compound (m. p. 136"),1-09. This seems conclusive in favour of the Meisenheimer theory.The only known N-ether of p-nitrobenzaldoxime was found.to havea moment of 6.4, indicating the syn-configuration.(7) Axo-compounds.-It was pointed out long ago by Hantzschthat the remarkable stability of azobenzene (b.p. 293") shows thatit must have the more stable anti-configuration. This has beenconfirmed by the dipole moment, which is zero. The pmonochloro-99 A. Weissberger and R. Siingewald, Physilcal. Z., 1929, 30, 792.lo" L. E. Sutton and T. W. J. Taylor, J . , 1931, 2190THE STRUCTUXE OF SIMPLE MOLECULES. 397and p-monobromo-derivatives have almost the same moments lo1(1.55 and 1.42) as chloro- and brorno-benzene (1.55 and 1.52).(8) Axides and Aliphatic Diazo-compounds.-These compoundswere originally assumed to have ring structures, but this view waslater abandoned in favour of open-chain formulE, mainly throughthe work of Thiele and Staudinger, who showed that they gavederivatives containing these open chains.This argument is notconclusive, because the double link between nitrogen atoms (unlikethat between carbons) is very strong, and the rings, if present, aremore likely to break at the single link. The possible structures,assuming that the atoms have complete octets, areR-N<g nTR - N t N f N(1.) (11.) (111.)Of these, formula (I) should have a small moment, owing to thesymmetry of the ring, while the moments of (11) and (111) should belarge, because they contain a co-ordinate link. The volatility ofthe azides and diazo-compounds suggests lo2 that they have smallmoments; the parachor values lo3 are also in favour of the ringstructures, though the difference between the two calculated valuesis so small that this cannot be regarded as decisive.Recently, themoments of phenyl-, p-tolyl-, and p-chlorophenyl-azides have beenfound 104 to be 1-55, 1.96 and 0.35, indicating that the N, group hasa moment of about 1-5, with the negative end away from the aromaticring. This is the wrong direction for structure (111), and too smallfor (11), which should have a moment of 3 4 (compare diphenylsulphoxide, R,S + 0, p == 4.1). Also the practical absence ofpolarity in the p-chloro-compound indicates that the moment ofthe group is symmetrical to the axis, and this is possible only forstructure (I).Thus the moments favour the ring structure for the aromaticazides. This is remarkable, since the X-ray examination of thecrystal structure of the metallic azides has shown 105 that the azideion has a rectilinear codguration.This implies the presence oftwo double links, so that the ion must be written N-N-tN orN=N=N; it is thus quite symmetrical, and has no turning- f -lol El. Bergmann, L. Engel, and S. Sfindor, Ber., 1930, 63, 2572.lo2 N. V. Sidgwick, J., 1929, 1108.lo3 H. Lindsmann and H. Thiele, Ber., 1928, 61, 1529.lo4 L. E. Sutton, Nature, 1931, 128, 638; E. Bergmann and W. Schutz,lo6 S. B. Hendricks and L. Pitding, J . Amer. Chem. SOC., 1925, 47, 2904.ibid., p. 1077398 SIDGWICK AND BOWEN :moment; but if it passes into the covalent state by the addition ofan imaginary phenyl kation, this must attach itself to a terminalnitrogen, giving the highly polar and so presumably less stablestructure (11). This may be why the ion and the covalent form havedifferent structures.The moments of the aliphatic diazo-compounds have not yetbeen determined.Preliminary (unpublished) measurements byL. E. Sutton indicate that they are not large, as the volatility alsosuggests, and so favour the ring structures. The supposed opticalactivity found in the diazo-compounds by P. A. Levene, W. A.Noyes, and H. Lindemann, which would necessitate structure (111),has been shown to be due to an impurity.lo6General Stereochemical Conclusions.The classical methods of stereochemistry have shown that thereis a tetrahedral arrangement of the groups surrounding 4-covalentatoms of beryllium, boron, carbon, nitrogen, silicon, phosphorus,sulphur, copper, zinc, arsenic, selenium, tin, and tellurium I07 ; andan octahedral round 6-covalent atoms of aluminium, chromium,iron, cobalt, nickel,los copper, arsenic, rhodium, iridium, andplatinum.The examination of crystal structures shows that theseconfigurations, for 4- and 6-covalent atoms respectively, are almostuniversal. The only exceptions for which there is experimentalevidence are the 4-covalent compounds of bivalent palladium andplatinum, and quite recently, nickel. Werner's view that the4-covalent platinous compounds have the four groups and thecentral atom in a plane was attacked by Reihlen,lo9 but has appar-ently been vindicated by A. Hantzsch,llo who showed that the twoforms of P t ( ~ y ) ~ C l , have the same molecular weight in phenol.With palladium, F.Krauss and F. Brodkorb 111 obtained isomericforms of the analogous Pd(py),Cl, and of Pd(C2H5*NH,),CI,, andshowed that these had the same simple molecular weight in solution.T. M. Lowry 112 adduced evidence of a different kind in favour ofthese plane structures. He pointed out that R. G. Dickinson 113had found that while zinc, cadmium, and mercuric salts of the typeK,[X(CN),] formed cubic crystals, whose structure indicated atetrahedral form of the ion, the salts K,[PdCl,], (NH,),[PdCI,], and106 A. Weissberger and R. Haase, Ber., 1931, 64, 2896.107 For tellurium, see H. D. K. Drew, J., 1929, 560; T. M. Lowry and F. L.108 G. T. Morgan and F. H. Burstall, Nature, 1931,127, 854; J., 1931, 2213.109 H. Reihlen and K.T. Nestle, Annnlen, 1926, 447, 211.1 1 O Ber., 1926, 59, 2761.111 2. anorg. Chem., 1927, 165, 73.113 J . Amer. Chem. SOC., 1922, 44, 774, 2404.Gilbert, ibid., p. 2867.llZ Xature, 1929, 123, 548THE STRUCTURE OF SIMPLE MOLECULES. 399K,[PtCI,] formed tetragonal crystals, in which X-ray analysis showedthe metal to be at the centre of a square, with the chlorine atomsat the four corners.On the other hand, F. G. Angell, H. D. K. Drew, and W. Ward-law 11* have examined the two forms of the thioether compound(Et,S),PtCl,, and find that, while both have the normal molecularweight in benzene, their chemical behaviour shows greater differencesthan cis-trans isomerism will account for. In particular, with silveroxide the a-form reacts slowly with liberation of the thioether andprecipitation of platinous oxide or hydroxide, while the @form israpidly converted into the soluble and fairly strong base(Et,S),Pt(OH),.The structures which they propose for the twoforms seem for various reasons unsatisfactory, but their resultscertainly indicate that these compounds need further investigation.This question assumes peculiar interest in the light of Pauling’srecent conclusion from wave mechanics that bivalent nickel,palladium and platinum, unlike the non-transitional elements, canform 4-covalent compounds of the plane type, which can further bedistinguished by their smaller paramagnetic moments. This con-clusion has recently been supported by the discovery of s. Sugden l15that the nickel compound of benzylmethylglyoxime occurs in twoisomeric formsPh*CH,-$-G-CH, Ph*CH2-EI_;--CH3O t N N-OH O t N N-OH\g \& Ni/k oti4; R-OHPh*CH,-C-C-CH,r\HO-i t-+OH,C-C-C-CH,Phand that these are diamagnetic.With a tetrahedral configurationthe two forms would be optical antimerides, and should be para-magnetic.The general principles of structure which these physical investig-ations show to be applicable to the volatile compounds of the lighterelements, with which we are mainly concerned, may be brieflysummarised. G. N. Lewis’s conception of the two-electron link, inwhich the electrons may come either one from each of the linkedatoms (normal) or both from one (co-ordinate), holds for all but afew molecules,3 and the dipole moments indicate that the electronsare shared nearly (within 20%) equally between the two atoms.The maintenance of the valency octet is a condition of stabilitywhich is almost always fulfilled.For the configuration of themolecules the tetrahedral atomic model of van ’t Hoff has received114 J., 1930, 340. 115 J . , 1932, 246400 SIDGWICK AND BOWEN:the fullest support, not only for atoms forming four, but also forthose forming two or three links, although in the two last casesPauling's theoretical conclusions indicate a valency angle of 90"rather than 109.5", a view which it is not yet possible to test experi-mentally. The valency angles can change to some extent with thenature of the groups in the molecule, but apparently not muchmore than 15%.The effective radii of the atoms are now known, and are evidentlyremarkably constant factors in determining the configuration ofthe molecule; apart from certain ascertained changes due to themultiplicity of the link (up to 20%) and in crystals to the natureof the lattice (rarely more than 5%), the differences betweenobserved and calculated values of the distances between linkedatoms scarcely exceed the experimental error.But the form whichthe molecule assumes, through the liberty of free rotation of singlylinked atoms, without change of the valency angles or of the lengthof the links, is largely determined by the intramolecular attractionsof its dipoles, especially when these are near together.As a final example, we may repeat the conclusions reached for aseries of familiar triatomic molecules :o=c-0, s=c=s :[NtN=N]- :N t 0 - N[C=N=O]-H-CZN :\HH-0\HH-So=shORectilinear.Spectrum, dipole moment.Crys t a1 structure.Spectrum, dipole moment.Crystal structure.Spectrum.Triangular.Spectrum, dipole moment.Dipole moment.Spectrum, dipole moment.The last example may be dealt with in more detail. The altern-ative structure O=SzO gives the sulphur a valency group of 10electrons, 8 being shared.This would presumably imply a straightline molecule, but we cannot be sure what effect the decet wouldhave. It is, however, a very improbable structure, because a valencygroup of more than 8 electrons never occurs unless either (a) theyare all shared or (b) it can be reduced to the normal form by assumingthat two of the electrons become inert; but (b) is only found in theheavier elements.The chemistry of sulphur supports this con-clusion. A quadrivalent and 4-covalent sulphur atom never occurs ;the stability of the optically active compounds of the type RR,S-+THE STRUCTURE OF SIMPLE MOLECULES. 401proves that they cannot assume the tautomeric form RR,S=O(containing the decet) which would lead to racemisation ; whileSC1, has been shown by T. M. Lowry and G. Jessop 115a to occuronlyin the solid state, and then probably as the salt [SCl,]CI. Thefinal proof that in SO, one of the oxygen atoms is singly and theother doubly linked is given by the values of the force constantsfor the two links, which are 7.23 and 4.93 x lo5 respectively.TABLE I.1G’3H-Hdui128w 2 rn w 2116H103 5.0611.322.24.55 151.2051.1071-351.932.262-660.9291.2821.4211-6171241251261261271267777128 4.14 15128 7.14 15118 117208 11863.5 11957.4 120,121.45.8 12136.0 122146.5102.286.770.911089.887.483-393.671-0125.21655511118018818470.572.6181.3160165235.558.712773.272.560.042.8126.90 3N2 NF-Fc1-CI F2 c1, 3.212-471.69129 1.32 15121121Bi2 Br-BrHF H-FHC1 H - C lHBr H-BrHI H-IH-0:&:*OH H-0NHS H-NH-SH-SCH.4 H - CC,Hs C-CC2H4 C=CC2H2 CECCH,*NH2 C NCH,*NCO C=NHCN C E NCH,-CN - C SCH,*NC -NECCH,*OH C-0I 2 1-1CH3*NH2 H-N4.43-562-9130 3.47 15131 2.94 15131 2.52 156.34 132 4-59 156-04 132 4-45 153-77 133 3-094.58 134 3.624-31 135 2-059-36 135 3.8816.4 136 6.324.86 132 2-2215151515151517-9 137 6.17 154-98 132 2.25 15 c-0 c=oc-0 c=oG O c-sc-s c=sC - c lC - c l11.9 137 4.49 151.14 6 18.6 15 6.28 153-01 133 1-44 153-12 138 1.48 15CHiBr C-BrCH,I C-I so, s=o2-61 139 1.23 152.15 139 1-05 15llba J., 1930, 782402 SIDGWICK AND BOWEN :TABLE 11.A.Atomic Radii in a.77. : from the Elements.Element. Radius. State. Ref. Xlement. Radius. State. Ref.H 0.37 Gas 123 Si 1.17 Solid 21C 0-77 Diamond 60 cu 1.28 Metal 146N 0-55 Gas 125 1.44 Metal 1400 0.60 Gas 124 1.12 Metal 147F 0.68 Gas 126 Zn 1.33 Metal 147c1 0.97 Gas 126 Cd 1.49 Metal 147Br 1.13 Gas 127 Ge 1.22 Metal 21I 1.33 Gas 126 Sn 1.40 Grey tin 21B.Dimensions of Links in B . U .Com-pound. Link.HF H-FHCI H-ClHBr H-BrHI H-IH,O H-0H--NN,O N-N co, 0-0H,S H-Scs, s-sH,CO C-0KClO, Cl-0K,SO, S-0H,CCI C-CICCl, C-C1CBr, C-BrSiC1, Si-C1GeCl, Ge-CISnC1, Sn-Cl3 c-0Distance. Distance. - Com- - Calc. Corr. Obs. Ref. pound. Link. Calc. Obs. Ref.1-05 0.93 7 CuCl Cu-Cl 2.25 2-34 1451.34 1.28 7 CuBr Cu-Br 2-41 2.46 1451-50 1.42 7 CUI CU-I 2.61 2.62 1451.70 1-62 7 cu,o cu-0 1.88 1.85 580.97 1.08 1.03 140 cu,s 2.32(l:i: g7 0-92 1.10 0.97 1411.37 1.13 1.14 62.30 2.37 2.38 34, 1422.52 2-25 24,27, 341-41 1.25 1433.63 3.40 { i:;: 2,:i41.37 1.15 1.2 1441.56 1.67 1.56 1531.64 1.66 581.74 1-83 25,261.74 1.85 25,261.90 2.05 342.14 2-02 342-19 2-10 342.37 2.33 34AgFI A r FAg[Cl] Ag-ClAg[Br] Ag-BrAg[I]a Ag-IAgIp Ag-IAg2O Ag-0 2: ;gI;BeS Be-SZnF, Zn-FZnO Zn-0ZnS Zn-SCd[F] Cd-FCd[O] Cd-0CdS Cd-S2.12 '2-46 582.41 2.77 212.57 2.88 212.77 3-05 212.77 2-81 212.04 2.04 212.48 2-61 581.72 1.65 1452.16 2.10 212-01 2.04 211-93 1.97 212.37 2-35 582-17 2.34 212.09 2.35 212.53 2.53 21TABLE 111.Dipole Moments of Links, x 1018.H-C 0.4 H-N 1.5 H-0 1.6 H-F (2)H-P 0-55 H-S 0.8 H-C1 1-03H-As 0.15 ' H-Br 0.78H-I 0.38C-N 0.4 C-0 0.7 C-F 1.3 c=o 2.3CZN 3.1 c-s 1.0 c-Cl 1.6C-Se 0.9 C-Br 1.4C-Te 0.7 C-I 1.2Y-C1 0-8 As-CI 2.0 Sb-Cl 3.8 P-J3r 0.6 As--Ur 1.7-~ ~~~116 E. 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