ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.1. INTRODUCTION.Owma to the lack of recently published work in physical chemistry it isbecoming increasing difficult to adhere to a planned scheme of articles overa short period of years. Any lack of balance in the present report is entirelydue to this state of affairs.Much attention is usually devoted to spectra as a means of determiningthe structure of molecules. In such surveys, however, there has been smallmention of electronic absorption spectra in the ultra-violet. Although it isdifficult to go deeply into the origin of the absorption bands in this region ofthe spectrum, yet there is much to be learned from an exact study of spectraof this type. Magneticmeasurements provide yet another tool for investigation of molecularstructure and reactions. The subject is a wide one and therefore W.R. Angusrestricts his report exclusively to results from substances exhibiting dia-magnetism. It is hoped in the future to deal with paramagnetism.If two groups of atoms are joined together by a single bond, it is knownthat these groups may or may not rotate with respect to each other. Thecriterion for non-rotation has hitherto been the isolation of the two isomers.This condition only obtains when the energy required to rotate the group ismuch greater than kT. When that energy is only somewhat greater thankT, chemical methods are inapplicable. Here, however, specific heatmeasurements, coupled with observations on infra-red spectra, revealphenomena which can only be explained if it is supposed that there is hinderedrotation.H. W. Thompson reviews the subject in his report together withsome additional infra-red work.R. A. Morton records recent advances in this field.H. W. M.2. ABSORPTION SPECTRA.The present Report deals with absorption spectra as a part of physicalchemistry, but the topic has such wide ramifications that a unified pictureof the state of the subject is not easy to achieve in a small space. Theapplications of spectrophotometry to analytical and biochemical problemshave been discussed elsewhere (see p. 26 for references).In no field has improved experimentation given a greater reward tha8 GENERBL AND PHYSICAL CHEMISTRY.in the study of absorption spectra. This is not the place to discuss the greatadvances which have been made in technique, but it is noteworthy thatfor at least 20 years the possession of adequate equipment has acted asa stimulus to the assimilation of theoretical ideas.The foundations forfundamental advances have been well laid; the need is now for better data,and, as will be seen in many of the researches reviewed below, the capacityto make use of such data is not lacking.Notation.-If lo is the intensity of light of wave-length A incident uponan absorbing medium of thickness d, and I the intensity of the emergentlight, log &/I = E (extinction) = 7cd. Beer’s law states that absorptionis proportional to the number of molecules in the light path, i e . , I =l o .l O - & d where c is molar concentration (e.g., of an absorbing solute in a“ transparent ” solvent), d is thickness in em., and E is the molecular ex-tinction coefficient. (Alternatively, I = Ioe-4nd/a, K = 0.1832~cA, A incm.) The expression stands for log I o / I for a d-em. layer of concen-tration c, and is useful as a way of describing an actual measurement, andfor specifying the intensity of absorption of mixtures or substances of un-known molecular weight, in the form E;&.. An absorption band is usuallydescribed in terms of Amax. or vmx. i.e., the wave-length in A.or millimicrons, mp, of maximum absorption, or the corresponding wave-number 1 / ~ cm.-l = ; or frequency c / h = v*, and the molecular extinctioncoefficient a t that wave-length.It is also desirable to note the half-widthof a, band, i.e., the distance in cm.-l between wave-numbers such thatE = h a x . / 2 , and the band strength SE . dv.The theoretical aspect of the intensity and width of an absorption bandis discussed by N. G. Chako and by Th. For~ter.~ Let vi stand for thefrequency of maximum absorption c (for a band sufficiently distant fromother bands) and y j a quantity measuring the damping and responsible forthe width of the band, whilst f’ measures the strength; in classical theoryfj is the number of electrons per molecule producing the band, and in quantumtheory it is a measure of the probability of the transition compared with thatof the standard classical band. The sum of all thefj’s is equal to the numberof electrons.Moat visible and ultra-violet bands are weak, i.e., the bandsmainly responsible for the refractive index lie in the vacuum ultra-violet.From the theory of dispersion (e and m, charge and mass, respectively, ofan electron)andand with E = 4xnk/A and N’ = N p (p = molecules/c.c.)1 A. E. Gillam and R. A. Morton, Proc. Roy. Soc., 1929, A, 12Q, 609.a J . Chem. Physics, 1934,2, 644.2. Elektrochem., 1939, 45, 661. * c = 3 x 1010 cm./sec., velocity of lightMORTON : ABSORPTION SPECTRA. 9and if the band is narrowFurther,ne2CrnVj$E . dv = -2. .f", which is independent of y.and if y were independent of v throughout the band, the half-width (Le.,distance between places where E = +q,& is Av = 2y.Numerically SE .dG = 2.32 x 108 cm.-l, so with a value of ca. 2000 cm.-lfor the half-width, hx. - 105. An approximate upper limit of 100,000 for E isnot inconsistent with either quantum mechanics or general experience for asingle electronic transition in a molecule. The absorption process impliesthat a molecule in its ground state Eo (lowest energy) passes to excited statesEl, E,, etc., in accordance with h v = E, - E, by an electronic transition.Vibrations may also be excited, so that a more accurate relation is h v =El - Eo + E,, where E, is the vibrational energy.Instead of attemptinga detailed exposition, it is proposed to select a number of representativerecent studies with sufficient references to enable the reader to amplify theargument where it suffers from over-condensation.Halogens.-The continuous absorption of chlorine has been studiedover the range 18-700", and analysis of the curves reveals a dual mechanismA (A=.330 my, - 1). A leads to dissoci-ation into normal atoms (2P,t), whereas B leads to one normal (2Plt) and oneexcited ("+) atom. Similarly, bromine vapour exhibits composite ab-sorption ( hAmax, 415 and 495 mp) in the near ultra-violet and visible, but lacksan ultra-violet maximum shown near 250-300 mp in solution. Liquidbromine (Amax. 405 my, hx. 350) also shows no ultra-violet maximum of thistype,g but the main band is more than twice as intense as in the vapour.I n passing through a range of solvents from water to cyclohexane, A,,,, variesfrom 393 to 422 mp and Emax from 164 (2N-sulphuric acid) to 360 (toluene).The effects of different solvents on different electronic trhnsitions are quitemarked.Iodine molecules(vapour or violet solutions) give rise to two regions of aelective absorption,the main one near 500 my resulting in dissociation to one normal and oneexcited atom, and the other (near 732 mp) in two normal atoms.738 Theseparation of these two bands (0-8 volt) reappears in the spectrum of iodineR.G. Aickin and N. S. Bayliss, Trans. Faraduy SOC., 1937, 35, 1332.R. G. Aickin, N. S. Bayliss, and A. L. G. Rees, Proc. Roy. SOC., 1939, A , 169, 234;N. S. Bayliss, ibid., 1937, A, 158, 661; A. F. Acton, N. S. Bayliss, and R. G. Aickin,J . Chem. Physics, 1936, 4, 474.Absorptive processes are of many different types.66) and B (A,,,.- 425 mp,The data on iodine are less difficult to interpret.D. Porret, Proc. Roy. SOC., 1937, A , 162, 414.W. G. Brown, Phy&ul Reu., 1931,38, 1187.7 C. B. Allsopp, &id., 1937, A, 158, 16710 GENERAL AND PHYSICAL CHEMISTRY.adsorbed on calcium fluoride with very intense absorption characteristicof a very thin adsorbed layer (AA,,,. 345 and 284 mp). The large displace-ment (1.9 volts) is an indication of the change in binding energy on adsorption.Hydrated iodide ions I- show twin maxima (11 193.5, 226.2 mp; log E 4-13),and similarly spaced bands occur in alcoholic solutions of mercuric andcadmium iodides.10 In the simple alkyl iodides 11 the A process (lmaX.256 mp) leads to an excited iodine atom (2Pt) and an unexcited alkyl group,whereas the B process (Lax.286.5 mp) liberates both in the unexcited state.The absorption of tri-iodides generally is characterised by two maximaresembling those of iodine adsorbed by calcium fluoride.The original observation by T. M. Lowry l2 that the spectra of iodoformand potassium tri-iodide are very similar raised interesting issues beyondthe scope of simple valency theories.The results in Table I make it clear that the simultaneous productionof iodine atoms in the normal and in the excited metastable state accountsTABLE I.Substance. Solvent. A,,., mp.KI, ........................... EtOH 355 'CsI, ........................... EtOH 360352358 Cs1,Br ........................ EtOHI, .............................. (on CaF,) uz.350H2O........................ TeMe,I, C6H14A d , 7 ........................... EtOHSbI, 13 ........................ EtOH17BiI, 7 ........................... EtOH(vapour) Is(VaPOW@ & P O WSnI, 7 9 14 ..................... C6H14 Ca.CI, 7 ........................... CCl, ........................... PI, 16 C6H12 CHI,16 CCl,(vapour)357356386357343356338.6365386375351345log bar..3.94.463.34.025.03-74.2 14-074.02--3.93.23.31A,,., m p . log %ax..290 3.9290 4.6290 3.44290 4.22ca. 285 5.0(very thinlayer)284 4.05294 4.34284392 4.20277 -294 4.19281304285 3.82306.5 3.20294-ca. 285 3.6for absorptive processes. The occurrence and stability of interhalogen 1'compounds in sohtion and also the phenomena of dichroism in iodinederivatives have been studied spectroscopically, as have the properties ofhydrogen iodide and bromide.l*v l9 In these compounds absorption isJ. H.de Boer, 2. physikal. Chem., 1931, B, 14, 163; 1933, B, 21, 208.lo E. Lederle, &bid., 1930, B, 10, 121.11 D. Porret and C. F. Goodeve, Proc. Roy. SOC., 1938, A , 165, 31.1' J . , 1926, 622.l4 M. I. Grant, Trans. Faraday Soc., 1935, 31, 433.l6 K. E. Gibson and T. Iredale, aid., 1936, 32, 571.l6 R. H. Potterill and 0. J. Walker, ibid., 1937, 33, 363.l7 A. E. Gillam and R. A. Morton, Zoc. c i t . ; Proc. Roy. SOC., 1931, A, 132, 152;l8 C. F. Goodeve and A. W. C. Taylor, PTOC. Roy. SOC., 1935, A , 152, ,221; 1936,le P.Fink and C. F. Goodeve, aid., 1937, A, 163, 592.19 K. Butkow, 2. Physilc, 1934, 90, 81.A. E. Gillam, Trans. Paraday SOC., 1933, 29, 1132.A, 154, 181MORTON : ABSORPTION SPECTRA. 11localised in one part of the molecule, but the position of the band (i.e.,size of h v ) may be affected by the presence of atoms or groups which disturbthe electronic levels. This is in sharp contrast with the data for mesomericsystems, which will be referred to later.Departures from Beer's law are usually a clue to some significant change,a simple example being sulphur dioxide in water.20 An absorption band withhXa 275 mp shows log Emax. 1.82 at 0 . 0 0 4 ~ ~ 2.2 at 0.04 and 0 . 4 ~ ~ and 2.4 a t0 . 1 ~ . The system consists of S02,H20 H2S0, H+ + HS03-,but HS03- and H2S03 make negligible contributions to the absorption.The absorbing entity is S02,H20, and when the equilibria are elucidated,constant E values for this substance can be calculated.In pure hexane,sulphur dioxide exists unsolvated and Beer's law is valid (Lax, 290 mpyNitrous acid (freshly prepared) exhibits a main maximum at 366 mpwith vibrational fine structure (narrow bands with a constant frequencydifference of A cm.-l 1000).21 Similar absorption appears in P-octyl nitrite 22and in methyl and ethyl nitrite,23 and the vapour of nitrous acid 24 showsA cm.-l 1000 and 250 (vibration of 0--N-0 group in an excited state).A maximum near 230 mp in octyl nitrite corresponds with an electron-affiity spectrum.26The NO,- ion (sodium nitrite in sodium hydroxide) shows Amax.353.5 mp,and crystalline sodium and potassium nitrite at - 250" 26 show absorptionin the same region with well-resolved vibrational bands (A cm.-l 600)although barium nitrite crystals show no such bands. An inflexion near287 mp is possibly indicative of a second electronic excitation. Nitro-methane shows a different weak band (Amax, 270 mpy log 1.16) sharplyillustrating the effect of an alternative structural arrangement.The NO,- ion shows a strong band (A,,, 193.6 mp, 12,000) and a weakband (Ama,. 302 mp, t 6 ~ 4 ) , ~ ' the latter due possibly to a forbidden transitionoccurring only when coupled with vibrational frequencies. In solutions theabsorption is diffuse, probably as a result of an intermolecular Stark effect.Very dehite evidence of vibrational frequencies ( A cm.-l 800) is obtainedin the spectra of crystalline nitrates at - 250" (potassium nitrate 350 and750 cm.-l). The effects of interionic forces are shown in the displacementssuffered by the NO3- band :log Ernax.2.4) -Crystals.r A\ Dilute solutions. KNO,. NaNO,. Ba(NO& Temp.302 304 291-5 277.5 mp. Room temp.307 287 272.5 - 250'4o H. Ley and E. Konig, 2. physikal. Chem., 1938, B, 41, 366.21 G. Kortum, ibid., 1939, B, 43, 418.22 W. Kuhn and H. L. Lehmann, ibid., 1932, B, 18, 32.23 G. H. Purkis and H. W . Thompson, Trans. Furaday SOC., 1936, 32, 1466.24 E. H. Melvin and 0. R. Wulf, J . Chem. Physics, 1935,3, 753.H. W. Thompson, ibid., 1939,7, 136.26 H. Schaumann, 2.Physik, 1932, 76, 106.e7 R. A. Morton and R. W. Riding, Proc. Roy. Soc., 1927, A, 113, 71712 GENERAL AND PHYSICAL CHEMISTRY.Departures from Beer's law occur in concentrated solutions owingprobably to formation of ion-pairs.28 15~-Nitric acid shows weak selectiveabsorption near 265 mp, and a similar curve occurs with 0*15~-acid in thepresence of 9-1N-perchloric acid, which is itself transparent. Nitric acidin pure hexane, however, shows end absorption (inflexion 280 mp) similarto that of ethyl nitrate. The equilibriaH,O+ + NO,- + H,O+ NO,- + HNO, + H,Oion-pairappear to cover all a.queous solutions, the concentration of homopolarmolecules being at most ca.The Mn0,- ion gives rise to groups of equidistant narrow bands 29 shownby solutions and by crystals.The solution spectra commence near 370 mpand extend to the region near 600 mp : 1 / ~ = 17520 + 747n cm.-l (n =0 . . . 8). In ethyl acetate the separation is 785 cm.-l. Various purepermanganates have been studied at low temperatures in the solid state :First principal H (half-maximum, cm.-l. A;. width).KMnO, ........................ 17632 774 200RbMnO, ........................ 17875 768 170CsMnO, ........................ 18125 757 160NMe,MnO, .................. 17622 756 110BaMnO, ........................ 1757 1 772 220Dilute mixed crystals K(Cl,Mn)O, possess rhombic symmetry and at lowtemperatures exhibit three principal spectra in which the light vibratesparallel to the a, b, and c axes :3: = 18051 + n 763 + m 273 11 a18043 + n 768 + m 310 11 b18049 + n 767 + m 286 11 cThe bands become sharper as the temperature falls; e.g., the half-widthis 130 cm.-l at 150" K., 70 cm.-l at 83" K., and 35 cm.-l at 20" K.Sodiumperchlorate possesses a different crystal structure from the potassium,rubidium, or czesium salt, and the absorption of Na(C1,Mn)04 mixed crystalsdepends markedly on crystal orientation : A cm.-l I I a. 718,l I b 796, I I c muchless intense, ill-defined absorption. Absorption by ~,(C1,Mn)o4 is leessharp than that of NMe4(Cl,Mn)04, and hydrated crystals give poorlydefined bands in many cases. The hexagonal crystals like LiC104,3H20and Ba(C10,),,3H20 exhibit very sharp bands (H 30 cm.-l) for the ordinaryray l c , whereas resolution is feeble or lacking for the extraordinary ray.The term disturbance due to water of crystallisation is thus confined to onedirection.In K(CI,Mn)O, a second electronic transition gives rise to a veryweak sequence of bands near 14570 crn.-l (A; variable, ca. 800 ; H 40-90 cm.-l depending on direction). The MnO,- band system in sodiumperchlorate shows several electronic transitions, depending to a striking28 H. v. Halban and J. Eisenbrand, 2. physikal. Chem., 1928, A, 132, 433.29 A. M. Taylor, Trans. Faraday Soc., 1929, 25, 860.ao J. Teltow, 2. physikal. Chem., 1938, B, 40, 397; 1939, B, 43, 198MORTON : ABSORPTION SPECTRA. 13extent on direction. The crystal field shows specially great anisotropy,and suitable crystals exhibit dichroism, changing colour in polarised lightbetween red and deep violet.An ultra-violet system (with E one-tenththat of the main system) near 277 mp (A cm.-l756) occurs even in solutions.This kind of electronic band spectrum with a large number of equidistantbands is characteristic of totally symmetrical vibrations (expansion andcontraction of the Mn04- tetrahedron). Osmium tetroxide, OSO,, is anexample of a similar state of affairs in a free molecule (3 ultra-violet systems :A; 811, 835, 832 cm.-1).The MnO,-- and CrO,-- ions in I<,(S,Cr,Mn)04 exhibit similarly spacedmaxima, but no resolution can be detected with the VO,--- ion. The crystalK(Cl,Mn)O, with a moderate manganese concentration shows a single verysharp line at ‘v 14446 ( H = 8 cm.-l) in the 11 b direction, but this is lackingaltogether in the 11 a direction.The line is a pure electronic transition whichcan only occur in combination with a vibration. In some instances wholeband systems are missing. The Mn04- ion possesses an incomplete shell,well shielded by valency electrons : it is the tetrahedral ions of the transitionelements which show selective absorption, unlike the transparent ClO,- ,SO,--, and PO,--- ions.The Co(Hal),-- ions are not altogether dissimilar, but the position is notquite so clear.31-37New effects appear with neodymium salt spectra at low temperature^.^^Electronic transitions in the well-shielded incomplete neodymium shell areshown, in NdCl,,GH,O crystals at the temperature of liquid hydrogen, tocouple with internal vibrational frequencies of the molecules as well as withvarious modes of vibration of the lattice.This is shown by the recurrenceof certain intense groups, the intervals between the parent pattern and therepetitions eonforming frequently with well- known vibrational frequencies : 39Substance. AV, cm.-1. A i (Raman), obs.( a ) 716, 746 7253Zn(N0&2Nd(NO3),,24H20 ............... ( b ) 1046, 1051 1056(c) 1310 1370 .............................. 995, 1011 9901342, 1120 11251640Nd2(S0,),,8H20The chloride and bromate with ordinary water of crystallisation also showAV 1640 and 1650. With heavy water A i values of 1199 and 1431 cm.-l(bromate) and 1238 and 1481 cm.-l (chloride) are recorded. From other31 W. R. Brode, PTOC. Roy. SOC., 1928, A, 118, 286; J .Amer. Chem. SOC., 1931,53, 2457.sa W. R. Brode and R. A. Morton, Proc. Roy. SOC., 1928, A , 120, 21.31 W. Feitknecht, Helv. Chim. Acta, 1937, 20, 669.3s 0. R. Howell and A. Jackson, Proc. Roy. SOC., 1933, A, 142, 587.88 R. J. Macwdter and S. Barratt, J . , 1934, 617.I* IT. Ewald, Ann. Physik, 1939, [v], 34, 209.89 K. H. Hellwege. 2. Phyaik, 1939,113, 192.A. v..Kiss and M. Gerendhs, 2. physikal. Chem., 1937, A , 180, 117.P. Job, Ann. Ckim., 1936, 6, 9714 GENERAL AND PHYSICAL CHEMISTRY.independent work the inner vibrations to be expected are 1615 cm.-l or1220 and 1460 cm.-l respective1y.m Smaller intervals are associated withlattice vibrations.Crystals of europium salts homologous with those of neodymium possesssuch sharp absorption spectra 4 ~ 4 ~ that phenomena similar to those recordedat very low temperatures can be studied at room temperature.Changes inthe environment of Eu+++ ions bring about alterations in the structure ofthe absorption spectrum. Thus EuCl, in water to which potassium nitrateis added exhibits the structures shown in Eu(NO,), as well as EuCl,.The spectra of europium salts in alcohol differ from those shown byaqueous solutions. In a, mixed solvent both spectra are shown with relativeintensities which vary according to the proportions of the components.Repetitions of prominent patterns enable lattice vibrations to be evaluated,and in some cases a given electronic level of an ion in an electrostatic field isdecomposed in strict accordance with theory into a number of sub-levels.The interpretation of absorption spectra is rooted in classical dispersiontheory, it comes to flower in the quantum-mechanics of diatomic molecules,and is reaching fruition with larger molecules.Simple saturated hydro-carbons like methane and ethane exhibit selective absorption 473 48 in thevacuum ultra-violet only (methane, lmaX. 120-130 mp). Replacement ofhydrogen by alkyl groups brings about progressive displacements towardslonger wave-lengths (n-hexane, hX. ca. 153 mp).49 If absorption occurs a twave-length8 >200 mp, the presence of a double bond is indicated.Absorption by ethylene begins near 175 mp, and following a well-definedpattern, extends to 160 mp, with additional bands near 139 and 129 mp.The separate vo values fit into a R-ydberg formula and converge to an ionis-ation potential of 10.45 v.:C,H, vg(n) = 84,750 - R/(n + 0-91)2; n = 2, 3, 4, etc.C,D4 vg(n) = 84,850 - ~ / ( n + 0 ~ 9 2 ) ~ ; ?z = 2, 3, 4, etc.The absorption bands (and ionisation potentials) refer respectively toexcitation and removal of a " x " electron (see p. 15) from the double bond.Electrons of the [a12 single G C or C-H links need much higher frequenciesfor ionisation.The vibrational structure, C,H, A crm-1 1370, C,D, A cm.-l 1290, corre-40 L. Kellner, Proc. Roy. SOC., 1937, A, 159, 414.4a S. Freed and H. F. Jacobson, ibid., p. 654." S . Freed, S. I. Weimmann, F. E. Fortress, and H. F. Jacobson, ibid., 1939, 7, 824." S. I. Wehsmann and S. Freed, ibid., 1940, 8, 227, 878." S . Freed, S.I. Weissmrtnn, andF. E. Fortress, J . Amer. Chem. SOC., 1941,63, 1079-" F. H. Spedding, C. C. Moss, and R. C. Wdler, J . Chem. Physics, 1940, 8, 908." W. Groth, 2. Ekktrochem., 1939, 45, 262.48 E. P. CarrandM. K. Walker, J . Chem. Physics, 1936,4, 751.'* E. P. Carr and H. Stucklen, i&id., p. 760; 2. IphysikaE. Chem., 1934, B, 5, 57 ;J . Amer. Chem. Xoc., 1937,59, 2138; J . Chem. Physics, 1938,6, 65.'* w . c. Price and W. T. TuttIe, Proc. Roy. SOC., 1940, A , 174, 207.61 W. C. Price and A. D. Walah, ibi&., p. 220.51S. Freed and S. I. Weissmann, J . Chenz. Physics, 1938, 6, 297MORTON : ABSORPTION SPECTRA. 15sponds with the totally symmetrical valency frequency of the double bond,which in the ground states is either C,H, A cm.-l 1623, or C,D, A cm.-l 1515.The change in frequency resulting from isotopic substitution is in accordwith expectations : 1370/1290 = 1.062 ; [16(CD2)/14(CH,)]* = 1.069.Bands near 170 mp appear in pairs, A cm.-1470 and 300 for C2H, and C,D,respectively.The mass factor (D/H)* = 1.41 is not very different from470/300 = 1.57; probably the CH, groups twist about the double bond.The spectrum of butadiene is very important because this substanceaffords the simplest example of resonance between conjugated double bonds.The first strong absorption (217 mp) is a progression of four diffuse bands,A 1440 cm.-l (isoprene, 221 mp, A 1450 cm.-l). The symmetrical C S Cvalency vibration (1634 cm.-I in the ground state) is reduced a little by theexcitation.Other electronic states are shown at higher frequencies, andtwisting vibrations (pairs, A 350 cm.-l) are recorded. Below 152 mp vibra-tionless electronic transitions lead as before to the ionisation potential(9-02 v.) : ~ 2 ) = 73115 - R/(n + 0 ~ 9 0 ) ~ ; n = 2, 3, 4, etc.= 73006 - R/(n + 0 ~ 5 0 ) ~ ; n = 3, 4, 5, etc.With alkyl substitution, simple inductive effects diminish the ionisationpotential. The absence of vibrational bands in the Rydberg transitions is adirect result of resonance; the removal of an electron shared between twobonds having a reduced effect on each.The main absorption of the C:O group also falls in the Schumann region( <200 mp) and so also does that of the carboxyl group.62-54Mesomerism in conjugated compounds is now accepted as a fact of majorsignificance.Molecular resonance in polyene and aromatic hydrocarbonshas been treated with success as a theorem in wave-mechanics 55-59 leadingto the calculation of C-C distances and of colour. The only experimentalparameter needed (a or J ) may be evaluated from heats of hydrogenation.Those dealing with wave-mechanics distinguish between localised electronpairs responsible for directed valency (interaction of Q electrons) and xelectrons.w-s2 These “ mobile electrons ” (Lennard- Jones), “ electronsof the second kind” (HU~kel),~~ are not strictly localised and in planarmolecules are antisymmetrical to the plane of the C-C links, and cannotbe paired according to their spins in a unique way to fit an ordinary structure.st W.M. Evans and W. C. Price, Nature, 1937, 139, 630.6a A. B. F. Duncan, J. Chem. Physics, 1936, 3, 131.6 s J. E. Lennard-Jones, Proc. Roy. Soc., 1937, A , 158, 280.6 6 J. E. Lennard-Jones and J. Turkevich, ibid., p. 297.b7 W. G. Penney, ibid., p. 306.s8 A. L. Sklar, J. Chem. Physics, 1937, 5, 669.6s Th. Forster, 2. physikal. Chem., 1938, 23, 41, 304; 2. Elektrochem., 1939, 45, 548.80 J. H. van Vleck and A. Sherman, Rev. Mod. Physics, 1935,7, 237.61 L. Pauling, J . Amer. Chem. Soc., 1931, 53, 1367; J . Chem. Physics, 1933, 1, 280.6* E. Hiickel, 2. Elektrochem., 1937, 43, 752, 827; J. E. Lennard-Jones, Zoc. cit.V. R. Ells, J . A m r . Chem. Soc., 1938, 60, 1864.J. C. Slater, Physical Rev., 1931, 37, 481 ; 38, 110916 GENERAL AND PHYSICAL CHEMISTRY.R,R,nSuch electrons cause links to become intermediate in distance betweenisolated double bonds and single bonds.Benzene is treated as a six-electronsystem with spin degeneracy only, and the single exchange intepal betweenadjacent carbon atoms is a. Two electrons present on adjacent atoms lowerthe energy of a structure (by forbidding resonance) by - a (a is negative)if the electrons are paired to form a bond, and raise the energy by - +a ifthey are not paired. Thus a Kekul6 form of benzene has an energy loweringof (3a -+a) 7 1.5~~. In the result for benzene, 2.6a represents the normalstate.Total Resonanceenergy. energy.Single Kekulh structure .............................. 1-5a 0Resonance between two Kekul6 structures ......2 . 4 ~ 0.9aResonance between all 5 canonical structures ... 2.605,~ 1 . 1 0 5 ~From heats of hydrogenation,M Sklar evaluates a as 1.92 v. (44 kg.-cals./mol.). The location of selective absorption can then be calculated :Fury1 Ph CH3CHO or Ph CH3CH3CHOorC0,H C0,H1, 2, 3, 4 0, 1’ 2, 3 1,3 . . . 7,11,15 1 , 2 . . . 6Molecule.Benzene .........Naphthalene ...Anthracene.. ....Pentacene ......PhenanthrenePyrene .........Naphthacene ...Excitation energies.*2 . 4 0 ~1 . 9 7 ~ (3.34~)1 . 6 0 ~ (3.0~1, 3 . 8 ~ )1.3 l a (2.62~1, 3-56u, 4.07a)1 . 0 8 ~ (2*2a, 3*lu, 4*0u, 4 . 2 ~ )1 . 9 4 ~ ( . . . )1 . 7 0 ~ ( . . . )Wave length of firstabsorption region, in mp :cab. obs.245 255295 275365 370450 460545 580300 295345 330* Approximate higher excitation states in parentheses.6MORTON : ABSORPTION SPECTRA.17l/lc/nm (vo, the first absorption band). =4x2c2nm/L, i.e., = k'n. On plotting A;4 against n, for the diphenyl polyenes,a very good straight line is obtained cutting the n axis at - 4.7, so thaton this basis each Ph equals 2.35 double bonds. The next higher vibrationallevel CAv = 2) involves increasing anharmonicity and the levels comecloser as v increases. The carotenoids show two well-marked regions ofselective absorption (e.g., p-carotene, ca. 477 mp and 270 mp; A,, &).70The ratio k,/A, is approximately constant in this class of compound at 1.7-1-85. This type of second-order band may be fairly common, but easilyobscured by absorption due t o a part of the molecule rather than theentire resonance system.69Similar relationships with polymethin dyes (pseudoisocyanine, isocyanine,and cyanine types),59 conjugated azo-dyes,71 etc., fit in with the idea of- resonating whole molecules.The p -- -/=\ - -\ /=\- polyphenyls (I) exhibit some approach \=/(-<=/=In\=/- towards double-bond character 72* 73 forthe internuclear link, but the rn-series (I.)is quite different :Solvent : CHCI,. m-Series.Hence & = 2xc,ldk/nm orp - Series. %ax. xAmax.7 Emax. A,,., cmar. NO. of be=- 'Compound. m p . x10-3. Compound. mp. x 10-9. ene nucleiDiphenyl ...... 251.5 18.3 (Diphend) ............ 251.5 18.3 9Sexiphenyl ... 317.5 56 Quinquideciphenyl ...254 309 20.6Terphenyl ... 280 25 Terphenyl ............ 251.5 44 14.7Quaterphenyl 300 39 Noviphenyl ............ 253 184 20.5Quinquiphenyl 310 62.5 Deciphenyl ............ 253 213 21.3(Stilbene ...... 295 23.4) (Tetraphenylmethane) 262 2.0 0.5The marked difference between tetraphenylmethane and the m-seriesindicates for the latter-a " semidiphenyl " chromophore ( A 253 mp, E 20,000)functioning additively. I n the p-series A,,,. is converging to a limit as nincreases, so that the plot of h2 against n would not be a straight line.6g Thiscan only mean that k (the restoring force) increases with nm, and for thehigher members the ordinary Kekul6 resonance becomes more importantthan in the lower members, which behave more like the conjugated polyenes.The conjugation effect requires a planar structure for the " mobile "electrons to play their full part.The steric effects of substituents are verymarked, thus bi~mesityl,~~ (C,H,Me,),, shows ha=. 265 mp, 560, ie.,the mesitylene spectrum doubled 280). Steric effects are also shownon p. 18 : 75-7770 R. Kuhn, Angew. Chem., 1937, 50, 703.'l W. R. Brode and J. D. Piper, J . Arner. Chem. Soc., 1935,57, 135.7e A. E. Gillam and D. H. Hey, J., 1939, 1170.78 A. E. Gillam, D. H. Hey, and A. Lambert, J., 1941, 364 (on phenylpyridines and74 L. W. Pickett, G. F. Walter, and H. France, J . Amer. Chern. Soc., 1936, 58, 2296.76 H. Ley and H. Dirking, Ber., 1934, 67, 1331.7 6 A. Smakda and A. Wassermann, 8. physikal. Chem., 1931, A, lS5, 353.7 7 H.Ley and F. Rinke, Ber., 1923, 56, 771.p yridyldiphenyls ) 18 GENERAL AND PHYSICAL CHEMISTRY.&n€u., mp. Emax. x 1oJ. AlmX.9 mp.278 9.35 222294 23-4 225 Ph*CH:CHPhPh*CMe:CHPh trans 372 18.2Ph.CMe:CMePh trans 24 1 11-7262 9.1Ph*CH:CH*CO,H { i:Zns 274 20.8324319 Ph-N:NPh 78 {ij:nsMe299<L>-N:NPh { ;;zns 32215.119.58.5SO43844 5447446F a x x lo-*.2315.61.160.292.26.8A break in conjugation by insertion of [CH,], (n = 1, 2 . . .) producesa clear-cut insulating effect and the two separated chromophores functionindependen fly.but the superposition of chromophores isoften a more complicated affair, which is not easy to disentangle. A singleisolated absorption curve drawn on a frequency scale should be symmetrical,and the band-strength SE .dv and half-width H should be significant quantities.Variants (e.g., substituents in benzene rings) giving rise to large or smallinner field effects may be strongly or weakly uariochrornic, and it is con-venient to describe displacement on the wave-length scale as ~hromolatory.~The curve for p-methoxystilbene is practically that of stilbene plus that ofanisole, p-nitrostilbene is a summation of the stilbene curve slightly displacedand that of nitrobenzene, whilst p-nitro-p’-hydroxystilbene is a summationof phenol, nitrobenzene, and stilbene (displaced) absorptions. The absorp-tion spectra of rottlerin 81 and its derivatives afford a good example of bothCH, insulation and superposition of chromophoric effects due to parts oflarge molecules functioning independently.The spectra of a@-unsaturated ketones82983 show the additive and theR*CO*$:CR, (* de- constitutive effect clearly.noting the site of the transition), is displaced by induction from (200 rnp(log zmax.ca. 4) to an extent depending on the degree of substitution :This effect is wellR The ethenoid absorption,Substitution. Am+, mp. No. of examples.Mono- a or fl .............................. 225f5 6Di- a/3 or pi3 ........................... 239&5 36Tri- a/3p ................................. 254*5 9(Pp = H, H ................................. 218)7 8 A. H. Cook, D. G. Jones, and J. B. Polya, J., 1939, 1315.7* (Mme.) Ramart-Lucas, BUZZ. SOC. chim., 1932, 51, 289 ; also Grignard’s “ Trait680 E.Hertel and H. Luhrmann, 2. physikal. Chem., 1939, B, 44, 261.81 R. A. Morton and Z. Sawires, J., 1940, 1052.82 R. B. Woodward, J. Amr. Chem.. Xoc., 1941,65, 1123.L. K. Evans and A. E. Gillam, J . , 1941, 815.de Chimie Organique,” Vol. 11, Paris, 1936MORTON : ABSORPTION SPECTRA. 19R * The above table is of great diagnostic value. The low-intensity R > G Oketone band at 275 mp in acetone is displaced to 305-325 mp in (11), E==.R * remaining low (20-80 as a rule).83 The acetone absorp-R>c-(?-(?=O tion a t 187-195 mp also appears in methyl chloride, andis not displaced to 225-250 mp.84,s5 The effects in(11.) aromatic ketones, keto-enols, hydroxy-aldehydes, andhydroxy-ketones 86987 are more complicated, but additive and constitutiveeffects are easily sorted out.The effects of substitution in benzene derivatives are complicated (ratherthan difficult) and cannot be dealt with in detail.88-92 It is perhaps preferableto deal fairly fully with an illustrative series and refer the reader to work onothers.Simple mixtures may form loose complexes breaking down ondilution, e.g., C,H5*N0, . . . . H2N*C,H,. In the 0-, m-, and p-nitroanilinesintramolecular forces displace absorption towards the visible, but a competingenvironment (containing, e.g., hydrochloric or perchloric acid) reverses thep r o c e ~ s . ~ ~ ~ gp The actual absorption is additive to the extent that a transitionlocalised in -NO, (cf. p. ll), and made more probable by induction, issuperimposed upon a benzenoid transition already familiar in aniline andother derivatives of benzene.In 10% hydrochloric acid the nitroanilinesexhibit merely the absorption of nitrobenzene. The concentration of per-chloric acid needed to achieve this result varies :HClO, concentration, N.Wo-Nitroaniline ........................ 6m- ........................ 0.1........................ 3 P-Compound. a ma,., mp. Emax. L a x . , mp. hax............... 287.2 1,950 236-9 11,500p - ............ 290.5 2,000 235.7 10,300............ 403.6 5,400 275.2 6,100............. 374 15,350 230 13,900NH, : NO,.c6E,<2 r; ............ 284.3 2,130 233.1 11,500C 6 H & C 2 {i- ......... 375 1,580 233 18,000Nitrotoluidines.KO. of isomers.0 - 404-4 1 7 5,000 284 5,000332 20,0004,5001,500(2) P- 374-379 15,000 233 7,000** L.K. Wolf and W. Herold, 2. physikal. Chem., 1929, B, 5, 124; 1931, B, 12,86 G. Scheibe and C. F. Lindstrom, ibid., 1931, B, 12, 387.6 7 R. A. Morton and A. L. Stubbs, J., 1940, 1347.8D K. L. Wolf and W. Herold, 2. physikal. Chem., 1931, B, 13, 201.so K. L. Wolf and 0. Strmser, ibid., 1933, B, 21, 389.Dl G. Scheibe, Ber., 1926, 59, 2618.sa H. Conrad-Billroth, 2. physileal. Chern., 1932, B, 19, 76; 1933, R, 20, 222, 227;OS L. Dede and A. Rosenberg, Ber., 1934, 67, 147.(4)(4)(;;;)m- 375 (352) I , 500165; 1932, B, 18, 265.R. A. Morton, A. Hassan, and T. C. Calloway, J . , 1934, 883.M. Pestemer, Angew. Chem., 1937, 60, 343.1933,B, 23, 139; 1935, B, 29, 170; 1936, B, 33, 133, 31120 GENERAL AND PHYSICAL CHEMISTRY.With two exceptions (CH, : NO, : NH, = 1 : 3 : 2 and 1 : 4 : 3) the curvesin hydrochloric acid for the nitrotoluidines agree almost exactly with thoseof the parent nitro toluene^.^^The curves for all pHH O e N 0 2 += GA \-/- so2 1 values between these ex-tremes intersect at two wave-lengths .The same " nitro " band reappears in 0- and p-nitrophenol : 93(in o .~ ~ - N ~ o H ) (in O-~N-HCIO,)lmm. 318 mp + A,,,. 400 mpandb x . 350 mp hnax. 410 mp* Denotes the site of the electronic process.Another example of equilibrium is afforded by p-nitrosophenol :-ON f i OH =+ O=/-\=N.OH95 71- \=/" Nitrosophenol " in ether.An,., mp. fmar.. &la,. - Emax..526.3 1-44,467 454.5 8.7436.7 13.2 423.7416.7294.1 25,120O=(=_)=N.O-CH, 21.4 14,800The parent substance appears to consist of 70% quinonemonoxime and30% nitrosophenol when at equilibrium in ether.The equilibrium (111) (IV) affords an even clearer example ofNO~>OCH,-- =N.NH<>/ \\J (111.) \Jdesm0tropy,~6 since in pyridine the azo-form predominates (A,.415 mp)whereas the hydrazone (A=. 480 mp) preponderates in glacial acetic acidor nitrobenzene. The two forms occur in approximately equal proportionin benzene. Confirmation of this interpretation comes from the spectraof the two methyl derivatives of fixed constitution. The o-hydroxyazo-analogues exist almost entirely as quinonehydra~ones.~7The spectra of at least some series of benzene substitution products showOP R.A. Morton and A. MoGookin, J., 1934, 901.96 L. C. Anderson and M. B. Geiger, J. Amer. Chem. SOC., 1932, 54, 3064.* 6 R. Kuhn and F. Blir, Annakn, 1935, 616, 143; see also H. Shingu, Sci. Papers*' A. Burawoy, J.pr. Chem., 1932,135.146; J.. 1937,1866;; 1939,1177.Inst. Phye. Chem. Ree. Tokyo, 1939, 36, 78MORTON : ABSORPTION SPEUTRA. 21that the electronic transition located in the benzene ring may be changed(as a result of inductive effects) in discrete steps differing by a well-knownvibration frequency (A; 1450 ~rn.-l).~' The effect of " partials " or simplechromophoric effects functioning additively is shown clearly in anthraquinone(in alcohol) : 98Am. mp ...... 405 326-5 272.0 262.8 252-5 243-5log em=. .........1-96 3.76 4.31 4.31 4-7 1 4.52( b ) (a) ( b ) ( b ) (a) (a)The ( a ) bands are due to 86H4<co (e.g., o-hydroxyacetophenone) and the( b ) bands to 0 : A . O (e.g., a-tocopherylquinone).R R\-/* R RHeterocyclic compounds of the type of pyridine and quinoline Qg exhibita marked resemblance to benzene and naphthalene. From the standpointof resonance this is not surprising, and a striking similarity between the curvesof acridine and anthracene has been recorded'l together with significantresults on acridinium and phenazinium ions.The absorption spectra of dyes in relation to resonance have been dis-cussed for triphenylmethyl derivatives (crystal-violet, etc.). 59* 69 A fewaspects of the wider problem will be reviewed.(a) Polymerisation in soZution.2 The two ionised dyes shown below donot follow Beer's law.Thionine .Met hylene-blue .Purple a 2-10 Blue p~ 2-12In both cases two resonating structures are postulated each with one or otherof the two benzene rings in the pquinonoid state :M-Band ........................ A,,, 597 m p (Thio+) 656.6 mp (MB+)(prominent in very dilute solutions)(more prominent in concentrated solutions)D-Band ....................... .Amw., 557 m p 600 m pThe deviations from Beer's law are not due to formation of undissociatedmolecules (e.g., thionine chloride) or to ion-pairs (Thio+ . . C1-). The Mbands are due to monomeric and the D bands to dimeric ions 2T+ a T,++ ;O8 R. A. Morton and W. T. Earlam, J., 1941, 159.R. A. Morton and A. J. A. de Gouveia, J., 1934, 927; D.Riidulescu andIdem, ibid.G. Ostrogovich, Ber., 1931, 64, 2233.a E. Rabinowitch and L. F. Epstein, J. Amer. Chem. SOC., 1941,83,6922 GENERAL AND PHYSICAL CHEMISTRY.K = [T+J2/[T$+] ; &&& = EMX + &g(l - x) where cdl and ED are the molecularextinction coefficients of the monomer and dimer respectively, and z is thefraction of monomer. K = 2Cx2/( 1 - x) = 10 x lo4 (thionine) or 2.8 x 104(methylene-blue); z varies from 0.359 to 1 (thionine) or from 0.232 to 0.986(methylene-blue). For thionine ion the temperature effect is given bylog,, K = 1.9886 - 1492/T and the following results are obtained : freeenergy of dimerisation AF = - RT In K (4-9 kg.-cals./mol. at 26.7");heat of dimerisation AH = RT2 (d In K/dT) (6.82 kg.-cals./mol.) ; entropy ofdimerisation A 8 = (AH - AP)/T (9-1 cals./mol.-degree).I n pure alcohol,thionine conforms with Beer's law and the band ( Amma 603 mp) is narrower ;addition of water causes the E value to fall rapidly, and this corresponds witha sharp drop in the free energy of dimerisation.Thionine fluoresces with a red light and the yield is constant for alcoholicsolutions, but decreases in aqueous solution with increasing concentration(self-quenching due to the dimer). Fluorescence does not occur if the dyemolecules are dimeric a t the moment of excitation or if they form a dimerduring the excitation period. This phenomenon is important because nearlyall water-soluble dyes show D bands 1-50 mp on the violet side of the Mbands.They often form trimers and polymers, but leuco-dyes are usuallymonomeric. The tendency to form polymers more readily in aqueous thanin alcoholic solution is at first sight strange (cf. carboxylic acids, which aredimeric in the vapour state and dissociated in water) but is explained byadditive forces of the van der Waals type. The E values are high, theexcitation probability being often >04.The absorption spectra in the visible region of cyanine and relateddyes 599 3-6 afford numerous examples of intense bands in " linear oscillators "conforming to the relation gmax. = k'n (p. 17) where n represents thenumber of -C€€=CH- groups, e.g.,A,,., nlCL. x 10-4.423 8.45~ / s ~ ~ I - n = O 1 557.5 14.8I (two identical resonance forms)G.Scheibe ti was the first to demonstrate that reversible polymerisation isresponsible for new bands in dyes. Using pinacyanol chloride, A,,,.600 mp belongs to the monomeric ion, but if the concentration is increasedor the temperature decreased a maximum a t 548 due to the dimeric ionappears. Both maxima almost disappear at higher concentrations and arereplaced by a third maximum a t 510 mp due to the polymeric ions.With pseudoisocyanine (V), Scheibe has obtained results of great(Miss) N. I. Fisher and (Miss) F. M. Hamer, Proc. Roy. SOC., 1936, A , 154, 703.4 W. Konig, Z . wiss. Phot., 1935, 34, 15.5 L. G . S. Brooker, R. H. Sprague, C. P. Smyth, and (2. L, Lewis, J. Amer. Citem.SOC., 1940, 62, 1116.6 KoEloid-Z., 1938, 82, 1MORTON : ABSORPTrON SPECTRA.23interest.'- In alcohol the dye ion is largely monomeric ( lmaX. 523 mp, E-.75,000) at 0 . 0 1 ~ ~ whereas in aqueoussolution the dimeric ion (hmax. 485 mp) is pQ=d'Of- already present a t 0.0001~, and at con-centrations >0.007~ a very narrow ( H140 cm.-l) intense band (Amm. 572 mp)appears and grows more intense withincreasing concentration. The concentrated solutions are powerfullyfluorescent, the fluorescence band coinciding in position and half-widthwith the absorption band. The appearance of the 572 mp maximum isaccompanied by a marked increase in viscosity, and the curves for viscosity-temperature) absorption-temperature ) and conductivity-concentration showsharp discontinuities. For instance, when c = 0.0144~ the 572 mp absorp-tion is strong a t 42" and has nearly gone at 44".\y'"E t(V.)The mechanismrearrangement A+ A,++ + -4, -- -+ crystalsMonomer Dimer Polymertemp.iucreasingf----fconcn. increasingis not it sufficient explanation. The minimal concentration for polymerformation is lower if the dye is adsorbed on a surface (e.g., 0.0003~ on freshlycleaved mica), and the polymer maximum a t 572 mp appears accompaniedby a further band at 579 mp. Adsorption depends on the structure of theP O4.47/0 =Position o f the K'ion in the mica surface.FIQ. 1.solid (calcium fluoride is here useless) and the crystal structure of micapresents K ions suitably disposed for the reception of planar pseudoiso-cyanhe ions as shown in Fig. 1 (adapted from Scheibe's figure).If a mixedcrystal of quinaldine ethiodide and pseudoisocyanine iodide is obtained(from alcohol) the dye ions will be parallel, and it is found that the character-' E. E. Jelley, Nature, 1937,139, 631. s G. Scheibe, Angew. Chern., 1939, 62, 03124 GENERAL AND PHYSIOAL CHEMISTRY.istic absorption in polarised light occurs only when the electric vector of thelight is parallel to the plane of the molecules (Ama. 545, 490 mp), whereasvertically to the plane only weak and modified absorption (Amx. 530 mp)occurs. The monomeric ion gives rise to two electronic transitions, cu.530 mp in the direction of the long x axis of the planar molecule, and ca.490 mp in that of the y axis. In the dirneric ion this second band is intensified,and in the polymer the 573 mp absorption arises in the x axis because a giantmolecule is formed (rather like a stack of coins) to form a cylinder or filament(Fig. 2 ; after Scheibe).FIG.2.Polymerisation in aqueous solzrtion.The directional effect has also been shown for chrysene single crystal^.^The crystal structure is known.10 The unit cell [see (VI)] contains 4 mole-cules, two oriented so that their OA directionsmake with the a and b axes angles of 102" andA of 118.4" and 29". The orientations of the othertwo molecules are obtained by reflection fromthe (010) plane. The crystal is used in the form90.5" respectively, and the OB directions angles(VI.)' K. A. Krishnan and P. I(. Seshan, PTOC. Indian Acad. Sci., 1938, 487.lo J. Iball, Pmc.Roy. Soa., 1934, A, 146, 140MORTON : ABSORPTION SPECTRA. 25of a flake parallel to the c(OO1) plane, and the molecular planes make anglesof 3 296" with the b axis. The absorptions in different directions at 397mp (first maximum) differ in intensity exactly as would be expected :ka/kb = 310/1020 = tan2 29"and the ratio of fluorescence intensities (420,438,449 mp excited by 365 mpHg) is a/b = 0.4, corresponding to 32". In addition to these neat results,it is clear that the light vibrations incident along the normal to the molecularplane are not absorbed a t all.The study of optical sensitising of silver halides in relation to the absorptionspectra and constitution of dyes has recently advanced considerably.llThe sensitising spectrum is usually closely related to the absorption spectrumof the dissolved dye, but Amas (sensitising) is > Amax.(ethyl-alcoholic solution)by at least 16 mp.l2 The absorption spectra of dyed silver halides (Le., ofadsorbed dyes) have been measured and found to coincide with the sensitisingspectra,l31 l4 so that the distribution of spectral sensitivity (in the visible)is equivalent to the adsorption spectrum.In order to give precision to the concept of adsorption energy, certainnon-ionising dyes have been studied in the vapour state. One of these, amerocyanine,ll shows at 250" Amax. 470 mp (with subsidiary bands at 505,R 0 R -0445 and 420 mp).( A cm.-l remaining -1000).The band system is displaced as a whole in solutionsThe structure recalls that of the polyenes : l5v = Vo + I 7 + mi", where if = 1590 cm.-l and 7' = 1240 cm.-1The absorption of the merocyanine in the visible arises then from an electronictransition on which are superimposed -CH=CH- vibrational quanta, etc.In aromatic hydrocarbons there is progressive relaxation of the -CH=CH-link :P h a [ CH:CH];Ph. An thracene.Naphthalene. Benzene.1600 1430 1360 900 cm.-1The greater complication of the cyanine dyes results in the superpositionof a variety of vibrational frequencies, but the predominance of -CH:CH-is often quite clear. In itself this fact affords no more than a clue, for thevalues of AA,,. and hx. are much more sensitive to structural changes thanwould be expected from aimple analogies. The location of the long-wavel1 S.E. Sheppard, R. H. Lambert, and R. D. Walker, J. Chem. Physics, 1941,9, 96.l2 E.g., (Miss) F. M. Hamer, Phot. J., 1922, 62, 8; 0. Bloch and (Miss) F. M. Hmer,ibid., 1928,68, 22; L. G. S. Brooker, G. H. Keyes, and F. L. White, J . Amer. Chem. SOC.,1935, 57, 2492.( I and m = 0, 1, 2, 3, etc.)13 S. Natanson, Nature, 1937, 140, 197 (erythrosin and phloxhe).14 J. A. Leermakera, B. H. Carroll, and C. J. Stand, J. Chem. PhysiCe, 1937, 5, 876.l5 K. W. Hausser, 2. tech. Phly&, 1934,15,1036 GENERAL AND PHYSICAL CHEMISTRY.maximum in a cyanine dye depends upon the shape of the molecule [themost extended form of the molecule (Mulliken); the greatest range in themolecule of electron transfer ( Pauling)]. The electrons make the transitby moving from atom to atom, and this " appears to be consonant with thesuperposition of a vibrational frequency possible to a given link." Thespectrum may also be decisively modified by the character of the nuclei(quinoline, thiazole, etc.) even in the visible region." Dominating everythingelse, however, is the possibility of a planar configuration for the dye mole-cule.This allows the fullest development of resonance, and of a transitionpolarised in the plane of the molecule. Even with planar structures, differentstereoisomers will differ with regard to the extent to which they undergoedge-on adsorption to silver halide. On this basis coplanar coupling ofelectronic displacements in the dye and in a congruent plane of the silverhalide lattice is a key factor in the whole problem of sensitising. I n somecyanine dyes the E values of planar isomers are twice those of non-planarisomers, and the former alone are effective sensitisers.Electrons of theBr- ions have a vector E, in the 111 plane, and this component may undergocoupling with a parallel component of the resonance energy of the adsorbeddye. This would correspond to the adsorption energy and to the displace-ment of kmSx. (adsorbed dye + vapour), and implies that the couplingproceeds prior to adsorption and hence in the ground levels. The progressof this work will be followed with interest.Attention is also drawn to the following publications :(a) Review articles.50, 193).Kortum and M. Seiler (Angew. Chem., 1939, 52,687).Potter (Ann.Rev. Biochem., 1941, 10, 509).(Institute of Chemistry, 1938).Photoelectric Spectrophotometry : G. Kortum (Angew. Chem., 1937,Colorimetric, Spectrophotometric and Spectrographic Methods : G.Spectrometric Studies in Relation to Biology : T. R. Hogness a i d V. R.Practical Aspects of Absorption Spectrophotometry : R. A. Morton(b) Books.Absorption Spectrophotometry and its Applications : Bibliography andAbstracts, 1932-1938 (866 papers) : 0. J. Walker (Adam Hilger, London,1939).Absorption Spectra of Natural Products : F. Ellinger, Tabuh Biologic=,Vol. XI1 (W. Junk, Den Haag, 1937).Losungsspektren : H. Mohler (G. Fischer, Jena).Chemical Spectroscopy : W. R. Brode (John Wiley and Sons, and Chap-man and Hall, 1939).* Cf. Morton and Stubba, Eoc.cit., ref. (87). This effect is to be distinguished fromthe superimposed ultra-violet absorption of parts of the large moleculeANGUS : DIAMAGNETISM. 27The Identification of Molecular Spectra : R. W. B. Pearse and A. G.Gaydon (Chapman and Hall, London, 1941).Absorption Spectra of Vitamins, Hormones, and Co-enzymes : R. A.Morton (Adam Hilger, London, Second edn., 1942), also Ann. Rev. Biochern.,1942, 12, article on Pat-soluble Vitamins.Proceedings of Conferences on Spectroscopy held annually a t the Massa-chusetts Institute of Technology, Vols. I-VI, Ed. G. R. Harrison (JohnWiley, New York) .Molekulspektren von Losungen and Flussigkeiten : G. Scheibe and W.Fromel (Eucken-Wolf, Hand- und Jahrbuch der chemischen Physik, Band 9,Abschnitt III-IV, 142, 1937).R. A. M.3. DIAMAGNETISM.Recent Annual Reports do not contain many references to magneto-chemistry. In the last volume the application of magnetochemistry tofree radicals was discussed,l and in 1937 H. Terrey and 0. J. Walker2reviewed its application to the rase-earth elements. No summary of workon diamagnetism has been given for a t least 10 years, and it is the aim of thisReport to summarise the present state of knowledge in this branch ofmagneto c hemist r y , to review the applications of diamagnetic - susceptibilitymeasurements to problems of molecular structure, and to indicate severalinteresting and promising new lines of application which were being studiedjust before the outbreak of war.The fundamental investigations in diamagnetism are associated with thenames of Curie, Pascal, and Langevin.On the experimental side, theextensive and systematic investigations of P. Pascal 3 on organic compoundsshowed that the diamagnetic susceptibility of a molecule, xM (xM = x .1M,where x is the mass susceptibility and M is the molecular weight), is anadditive and constitutive property. Hence, for a compound XGYbZc,X M = axx + bxp + cxz + h, where a, 6, and c are the numbers of atoms ofX, Y , and Z having, respectively, susceptibilities xx, xy, and xz, and h is aconstitutive correction constant dependent upon the nature of the chemicallinkings between the different atoms.derived mathematical expressions for the susceptibilities of atoms which showthat diamagnetism is independent of temperature.Since these investigations,a considerable amount of work has been done on both the experimentaland the theoretical side. In the main, this Report will deal with experi-mental aspects of more recent work.An excellent general review of magnetochemistry was given by (Sir)From classical theory, P. Langevin1 D. H. Hey, Ann-. Reports, 1940, 37, 263.8 Ann. Chim., 1909, 16, 531 ; 1910, 19, 5 ; Bull. Soc. chim., 1911, 9, 79, 177, 336,Ibid., 1937, 34, 126.809, 868.Ann. Chim. Phy8. 1905, 5, 7028 GENERAL AND PBYSIUAL OKEMISTRY.S. S. Bhatnagar in 1938 and general advances are discussed in severalrecent monographs.6There is still considerable confusion in the literature owing to the diverg-ence in the recorded values of x for many compounds.This may arisefrom the fact that x may be measured by a variety of methods and it isquestionable if all these are of equal accuracy. Although none of the methodsinvolves a highly-skilled technique, each possesses inherent errors and itwould help greatly in assessing recorded values if more details of experi-mental procedure were given when data are published, e.q., number ofdeterminations made, methods of calibrating apparatus, reference substances,methods of purification, criteria of purity, and temperature.(1) The XusceptibiZity of Water.-It is usual to calibrate apparatus bymeasuring the susceptibility of some compound for which the value of x iswell established, and H. R. Nettleton and S. Sugden have discussed thisproblem in detail in their investigation of the susceptibility of nickel chloride.Following P.Pascal: many investigators use water as reference substance.[Pascal records x of water as - 0.75 * but, since the value accepted today is- 0.720, all his recorded values must be corrected by multiplying themby 0.72/0*75 = 0.96.1 The employment of water as reference substancerequires that the water must be subjected to a rigorous purification process,otherwise all data will be vitiated. To obtain water of x = - 0.72 is muchmore diEcult than many investigators appear to believe.showed that xla. was - 0.72 and remained practically constant at differentfield strengths ; P. S h e 9 found - 0.72, W. J. de Haas and P. Drapier lorecorded - 0.721, and A.Piccard and A. Devaud 1°a give xZw as - 0071864,slightly less than - 0.72183, the value found by H. Auer.11 Severalinvestigators have measured x for water a t different temperatures and,generally, they found that the value increases with rising temperature.For instance, R. N. Mathur l2 found that x increased from - 0.7195 at 15”to - 0-7297 a t 75”, M. A. Azim, S. S. Bhatnagar, and R. N. Mathur l3report an increase from - 0.720 at 25” to - 0.726 a t 75”, and H. Auer,llin a very accurate determination, gives x16.30 as - 0.72145 5 0.00048 andxzon as - 0.721834 &0.00048. P. S. Varadachari,14 on the other hand,6 Proc. Twenty-fifth Indian Sci. Congress, 1938, 11, 49; summarised in Scienceatad Culture, 1938, 3, 446.6 E. C. Stoner, “ Magnetism and Matter,” Macmillan, London, 1934; L.F. Bates,“ Modern Magnetism,’’ Cambridge, 1939 ; B. Cabrera, “ Dia- et Paramagn6tisme etStructure de la MatiCxe,” Hermann, Paris, 1937; S. S. Bhatnagar and K. N. Mathur,“ Physical Principles and Applications of Magnetochemistry,” Macmillan, London,1935 ; W. Klemm, “ Magnetochemie,” Akademische Verlagsgesellschaft M.B.H.,Leipzig, 1936; J. H. van Vleck, “ Theory of Electric and Magnetic Susceptibilities,”Oxford, 1932.A.. P WillsProc. Roy. SOC., 1939, A , 173, 313.J . Physique, 1913, 3, 8.laa Arch. Sci. phya. nat., 1920, 2, 455.l2 Indian J . Physics, 1931, 6, 207.l4 Proc. Indian Acad. Sci., 1935, A, 2, 161.* All values of x in this Report have been multiplied by 10’.* Physical Rev., 1905, 20, 188.lo Ann.Physik, 1913, 42, 673.l1 Ann. Physik, 1933, 18, 693.l3 Phil. Mag., 1933, 16, 580ANGUS : DIA.MAONE!CISM. 29found a much smaller increase ( - 0.7200 a t 28"; - 0.7216 a t 55").W. Johner 15 put forward the formula xp = xzO4l + 0.00013( 8 - 20)] for thetemperature coefficient of the susceptibility of water, and later, A. P. Willsand G. F. Boeker l6 deduced a parabolic formula for the variation of x withtemperature for 14 temperatures in the range 20-66", but this is contestedby B. Cabrera and H. Fahlenbrach 17 who state that water has a positivetemperature coefficient and that x increases linearly with temperature.K. Honda and Y. Shimizu l8 have calculated theoretically the variation ofx with temperature.This variation of x with temperature appears to contravene the state-ment that diamagnetism is independent of temperature but it is probablydue to simplification of the molecular species present in water as a result ofthe breakdown of hydrogen-bonded structures a t the higher temperatures.lgSupport is lent to this view by the fact that L.Sibaiya 2o records that x forice is constant from - 120" to 0" and is - 0.708, considerably lower than thevalue for water. B. Cabrera and H. Fahlenbrach, however, have found thatthe susceptibility of ice (xoo = - 0.7019) varies linearly with temperaturebetween - 60" and OoY21 but that above 100" x of water is constant.22That the presence of isotopic analogues does not affect the value of XMhas been experimentally substantiated by P.W. Selwood and A. A. Frost,23(Miss) V. C. G. Trew and J. F. Spencer,% F. E. H ~ a r e , ~ ~ and V. Nehra andM. Qureshi26 from measurements on deuterium oxide. F. W. Gray andJ. H. Cruickshank27 measured H20-D20 mixtures containing 44, 62, and87% of D20 and concluded that H20, HOD, and D20 have identical valuesof xM, whilst, from similar measurements, H. P. Iskenderian 28 has deducedvalues of - 0.6807 and - 0.6466 for x of HOD and D20, respectively.B. Cabrera and H. Pahlenbrach have investigated the magneto-thermalbehaviour of D20 but, since they report29 that its molecular susceptibilitydiffers from that of H20, their statement 30 that, between - GO" and 150",dx/dO is faster in solid and slower in liquid D20 than in H,O must beaccepted with reserve.On the Thomas-Fermi atom model, T. Takduchi,T. Sugita, and T. Inai31 have calculated the susceptibility and dx/dOfor D,O.It would, therefore, appear that the choice of water as a standardreference substance is not a particularly happy one.(2) Effect of Temperatwe on Other Diamagnetic Substances.-Littleattention has been given to this problem, and available data are notl6 Helu. Physica Acta, 1931, 4, 238.l6 Physical Rev., 1934, 46, 907.l8 Sci. Rep. Tdhoku Imp. Univ., 1937, 25, 939.2o Current Sci., 1935, 4, 41.22 Ibid., 1934, 32, 525.24 Nature, 1936, 137, 998.26 Current Sci., 1937, 5, 533.40 Physical Rev., 1937, 51, 1092.3a Naturwiss., 1934, 22, 417.l7 2. Physik, 1933, 82, 759.W. R. Angus and W. K. Hill, Trans.Faraday SOC., 1940,36, 923.21 Anal. Pis. Quim., 1933, 31, 401.a3 J . Amer. Chm. Soc., 1933, 55, 4336.27 Nature, 1935, 135, 268.2@ Anal. Pis. Quim., 1934, 32, 538.31 Bull. Tokyo Univ. Eng., 1937, 6, 116.Ibid., p . 49730 GENERAL AND PHYSICAL CHEMISTRY.sufficiently plentiful to permit an unequivocal explanation of observedeffects. There appear to be three classes of substance : (i) a group whichshows, like water, a positive temperature coefficient, but the only data arefor n- and iso-propyl and -butyl alcohols; 13 (ii) those which have a negativetemperature coefficient and comprise, almost entirely, aromatic de-rivatives ; 12*13* 32 and (iii) those which are independent of temperature.In the h s t group are hydrogen,% the rare ga~es,~3 boron34 (from - 183" to20°), cyclohexane and carbon tetrachloride l3 (20-75"), acetic l4 (25-55")and n- and iso-butyric acids,12 butyl bromide,12 and, unexpectedly, isoamylalcohol 12 (20-80").P. S. Varadachari 14 has examined the system sodiumsulphate-water throughout the range 25-55' but finds no change at 33"the temperature of transition from decahydrate to anhydrous salt. Varioustentative explanations have been advanced. M. A. Azim, S. S. Bhatnagar,and R. N. Mathur13 have attempted to correlate their results with the,polarisability and high associating tendency of substances having a positivecoefficient. The non-polar, symmetrical characters of cyclohexane and carbontetrachloride are attributed by the same authors as reasons for the temper-ature-independence of x of these compounds ; but this is an ad hoc explanationwhich is inapplicable to butyl bromide and the fatty acids.The negativecoefficient exhibited by aromatic compounds finds no explanation, but thereis the interesting observation of S. R. Rao and S. Sriraman35 that x ofnitrobenzene, in the range 30-102", slowly diminishes to a minimum valuea t 75" and then increases, a behaviour which they attribute to changes inassociation. More work in this direction might yield some extremelyinteresting results and relationships.(3) Influence of Physical State on the Value of X.-The big increase in xMon vaporisation reported by V. I. Vaidyanathan 36 for a number of organiccompounds must be doubted because, more recently, R. Jaanus andJ. Schur 37 have reported a value for benzene vapour of - 59 &- 3 which is ofthe same order of magnitude as the accepted value of - 55.0 for liquidbenzene, the difference probably being due to the greater difficulty of measur-ing x for gases.Likewise, the influence of fusion is not clear. B. Cabreraand H. Fahlenbrach38 state that a sudden change occurs on fusion due todeformations caused by crystal forces, whereas T. Ishiwara 39 found nodiscontinuity at the melting points of silver halides. There is good reasonto believe, however, that the liquid state has a slightly higher value for xthan the solid state. This is borne out by the work of A. E. Oxley4O onorganic compounds. Also, J. Farquharson and E. Heymann41 haves2 S. S. Bhatnagar, M.B. Nevgi, and M. L. Khanna, 2. Physik, 1934, 89, 506;G . F. Boeker, Physical new., 1933, 43, 756.33 G. G. Havens, Physical Rew., 1933, 43, 992.34 L. Klemm, 2. Elektrochem., 1939, 45, 354.ae Ibid., 1927, 2, 135.3s Sci. Rep. TGhoku Imp. Univ., 3920, 9, 233.40 Phil. Trans., 1914, 214, 109; 1915, 215, 79; 1926, 220, 247.41 Trans. Faraday SOC., 1935, 31. 1004.35 Indian J . Physics, 1934, 8, 315.37 Natw-e, 1934, 134, 101.Cornpt. rend., 1933, 197, 379; 2. Physik, 1934, 89, 682ANUUS : DIAMAUNETISM. 31examined cadmium, mercurous, and lead chlorides as powders, solidifiedmelts, and in the molten state. They found that x increased in this orderand, since the value of x for an aqueous solution of cadmium chloride wasfound to decrease with increasing concentration of the salt, they suggestedthat the increase in x on melting may be due to ionisation.Y. Shimizu hasreported abrupt changes a t the melting points and transition points of anumber of metals, whilst G. E. R. Schulze 43 found a slight change a t thetransition points of ammonium bromide and nitrate, potassium and thallousnitrates, and silver iodide. Ammonium halides have also been examinedby A. Dinsdale and F. A. L ~ n g . ~ ~ a The observed effects are attributed tolattice changes. K. C. SubramaniamU attributes the increase in x ofbenzophenone on melting to breakdown of polymerides, and gives the sameexplanation for the diminution of y, on melting p-nitrotoluene. Here isanother fertile field of enquiry from which much interesting informationshould be forthcoming.(4) The Diamagnetic >CH, Increment.-The values (corrected) given byP.Pascal for the introduction of a methylene group vary from - 11436 to- 11.42. The determination of this value is fundamentally important tothe determination of values for atoms in organic molecules and for bondingand constitutive correction constants because these derived values form thebasis of the testing of the additivity of diamagnetism. Many workers haveaccepted Pascal's values, but others have pointed out discrepancies. Acritical examination of Pascal's data made by (Sir) S. S. Bhatnagar andN. G. Mitra 45 led them to suggest that the (numerically) maximum valuewas - 11.68. B. Cabrera and H. Fahlenbrach 46 give - 11.48 from measure-ments on seven alcohols ; D.B. Woodbridge 47 obtained - 11-67 from aceticacid and five alkyl acetates; F. W. Gray and J. H. Cruickshank 48 report- 11-87 from an investigation of homologous organic nitrates, nitrites,and nitro-compounds; J. Farquharson and M. V. C. Sa~tri,*~ from fivenormal aliphatic acids, deduced - 11.64; and - 11.36 was obtained by(Sir) S. S. Bhatnagar, N. G. Mitra, and G. D. Tuli 50 from an examinationof twenty compounds belonging to four different homologous series. Thiswas the unsatisfactory state of affairs in 1938 when a systematic re-investig-ation," under carefully controlled conditions, was started at the UniversityCollege of North Wales, Bangor. About 50 compounds were measuredwhen the work had to be discontinued, but analysis of the ascertained datapa Sci.Rep. T6hoku Imp. Univ., 1937, 25, 921.4a 2. physikal. Chem., 1938, B, 40, 308.49a Proc. Leeds Phil. SOC., 1937, 3, 270.44 Proc. Indian Acud. Sci., 1936, A , 3, 420.4 b J. Indian Chem. SOC., 1936, 13, 329.46 2. Physik. 1933, 85, 568.4 7 Physical Rev., 1935, 40, 672.40 Trans. Faraday SOC., 1935, 31, 1491.4D Ibid., 1937, 33, 1472. * Full details will be given in forthcoming papers by W. R. Angus, W. K. Hill, andPhil. Mag., 1934, 18, 449.E. Roberts32 GENERAL AND PaYSICAL UHEWSTRY.on aliphatic alcohols, acids, esters, aldehydes, and ketones, and aromatichydrocarbons and esters yields the value of - 11-68 0.01. This valuewas obtained by the subtraction method of P. Pascal3 and by a graphicalmethod49 in which observed values of XM are plotted against the numberof methylene groups.The straight line obtained can be represented by theequation XM = u?z - b, where b is the intercept on the XM axis and representsthe diamagnetic effect of the “ end ” group, and a is the diamagnetic incre-ment of a methylene group, of which there are n in the molecule. Bysubtracting b from the observed xu value the contribution made by n methyl-ene groups is obtained, and hence the >CH, increment. This method ispreferable to that of Pascal in that it involves each member of the seriesindependently, whereas his method yields a mean value for x CBI whichis dependent on the purity of the first and the last member of the series only-intermediate members can be neglected.E’urther work on a wide varietyof series will be continued when conditions permit, because, although thedata are self-consistent for each series, the values of x , ~ , derived for thedifferent series vary from - 11.65 to - 11.72. Other interesting resultsobtained in this investigation are (i) that when an acid is converted into itsmethyl ester the increment is - 10.66, i.e., about 1 unit less than the averagevalue of x>cIIs ; (ii) that branched methyl substitution causes the susceptibilityto increase by approximately - 12.70 irrespective of whether an iso- or asec.-compound is formed, i.e., about 1 unit greater than the average valueof x , ~ ~ * ; and (iii) a second branched methyl substitution gives the usualincrement of - 11.68.These results amply demonstrate the necessity forfundamental investigations on homologous series before applications toproblems of molecular structure can be reliably made.( 5 ) Diamagnetism of Imneride.s.-From the viewpoint of Pascal’s additiv-ity rule the susceptibilities of isomeric compounds should be identical. Manyrecorded data confirm this, but a critical examination of available dataindicates that this identity is probably fortuitous. For instance, althougha number of isomeric pairs show identical ~ a l u e s , ~ ~ ~ ~ ~ P. Pascal 51a recordsfor ethyl butyl ketones the following values : tert.-, - 82.2; iso-, - 81.9;n-, - 81.1. This sequence has been borne out by later workers, and acomprehensive discussion of the question by (Sir) S.S. Bhatnagar, R. N.Mathur, and M. B. Nevgi 52 led them to conclude that, generally, the sus-ceptibilities of isomeric compounds were : tert.- > sec.- z iso- > n- ; o > p> m ; cis > trans. They also state that the susceptibilities of the n-, iso-,and tert.-aliphatic isomerides fall into the above sequence as a result of cha’ngein the radii of the electronic orbits owing to changes in the effective electroniccharges. Various attempts to correlate these differences with other physicaldata have been made 53 but none has proved successful. This arises partlyfrom the paucity of data and partly from conflicting values, particularlyfor aromatic isomerides as is shown in the following table.Mag., 1928, 5, 636.61 (a) Pascal, Compt.r e d . , 1909, 149, 342; ( b ) Bhatnagar and C. L. Dhawan, PhiE.tia Z. Phyeik, 1931, 69, 373ANGUS : DIAMAGNETISM.Compound.Cresol ..................Nitro t oluene .........Toluidine ............Phene tidine .........Chlorophenol .........Values of - XM x 10'./-0. m.73-62 73.3273.54 72.3071-475-70 76.9471-85 72.4272.872-97 { ;::t5 74-6{ 72.4{ 74.3-- --723.72-7671-3272.170.8970.672.195.997.465.5476.7--33Ref.63b546563b645553a5553a1253b55For aliphatic isomerides the sequence given above has been found bymany workers, but widely different values for the numerical increase ingoing from the n- to the iso-isomeride have been recorded, ranging from- 0-74 to - 2.74.s6 From a recent study * of homologous series ofaliphatic alcohols, acids, and esters, carried out by Mr.W. K. HilI, the follow-ing conclusions can be drawn : (i) position isomeric esters have identicalsusceptibilities ; (ii) the susceptibility of the corresponding isomeric acid isnumerically greater by approximately 1 unit ; (iii) all n-isomeric estershave identical susceptibilities, as also have all iso-isomeric esters ; (iv) thesusceptibility of an iso-isomeride is greater than that of the n-isomeride by anapproximately constant amount ( - 1-03) ; and (v) the sequence is tert.-slightly > sec.- =: iso- > n-.(6) Atomic and Ionic Xwce~tibilities.-The derivation of values for thegram-atomic or gram-ionic susceptibilities from experimental data was firstcarried out by P.PascaL3 He obtained susceptibilities for atoms linkedtogether by homopolar bonds and, hence, his derived values contain bondingeffects. These values enabled him to demonstrate the additive nature ofdiamagnetism and are probably substantially of the correct order of magnitude.When the atom participates in forming a polar salt, the molecular susceptibilityof the salt may be considered as the sum of the susceptibilities of the ions,XM = Xcation + xanion. Values for ionic susceptibilities have been derived bytwo methods-from experimental data and, for spherically symmetricalions, from theoretical calculation. The lack of agreement in experimentaldata published by different workers renders comparison of values derivedby different methods difficult and, possibly, has led to the publication of somany methods of obtaining these values.In each method certain assump-tions are made which frequently cannot be completely justified.The divergence amongst recorded values was pointed out 57 some years63 (a) (Sir) S . S . Bhatnagar and R. N. Mathur, PhiE. Mug., 1931,11,914; (b) (Sir) S. S.64 B. Cabrera and H. Fahlenbrach, 2. Physik, 1934, 89, 682.5 5 K. Kido, Sci. Rep. Tdhoku Imp. Univ., 1936, 24, 701.66 B. Cabrera and A. Madinaveitia, Anal. Pis. Quirn., 1932, 30, 528; see also Refs.67 W. R. Angus, PTOC. Roy. SOC., 1932, A, 136, 669. * A detailed discussion will be published later by W. R. Angus and W. I(. Hill.Bhatnagar, R. N. Mathur, and R. S. Mal, ibid., 1930, 10, 101.12, 13, 510, 62, 63a, 53b.REP.-VOL.XXXVIII. 34 GENERAL AND PHYSICAL OHEMISTRY.ago in a review of the methods and is again stressed in a recent review by(Miss) V. C. G. T r e ~ , ~ ~ in which she summarises the various methods andobtains an average set of values for ionic susceptibilities derived fromexperimental results. These methods will be considered first. The widevariation in them will be self-evident, and the necessity for an early re-investigation of the whole problem will be fully apparent from an examinationof the values collected in the table below. G. Joos,~~ using the data ofJ. Koenigsberger,Go obtained values for salts having ions with an inert-gasconfiguration, e.g., potassium chloride and rubidium bromide, by assumingthat such ions contribute amounts to the molecular susceptibility which areinversely proportional to the square of the nuclear charge.K. Ikenmeyer 61applied this method to his measurements on alkali and alkaline-earth halidesbut, later, G. W. Brindley 62 modified the method by taking the suscepti-bilities as inversely proportional to the squares of the effective nuclear chargesevaluated by using the screening constants and effective quantum numbersproposed by J. C. Slater.63 G. W. Brindley and P. E. HoareG4 havemeasured the susceptibilities of crystalline alkali and alkaline-earth halidesand, taking the value of xw = - 0.7, which is the calculated value, theyderived values for the other metallic ions and for halide ions, justifying theirprocedure on the grounds that, since XLY is so small, any error in it will notgreatly influence the values for the other ions.They also showed that in-creasing co-ordination causes a slight decrease in diamagnetism, i.e., gives anumerically larger value for XN. Thus, the change from the usual 6-co-ordination of alkali halides to 8-co-ordination in cssium iodide is accom-panied by a diminution of 3.1 units.P. Weiss65 has employed two methods of obtaining values for ionicsusceptibilities. In the first, he takes Pascal's values for atoms and adds + 3 units for a univalent anion and - 3 and - 6 units for uni- and bi-valentcations, respectively. This unwarrantable procedure neglects the specificbonding effects of different ions. In the second method, he shows that dia-magnetic susceptibilities of aqueous solutions are influenced by the actionof charged ions on the water molecules in the same way as molecular re-fraction is influenced. From the relationship AR/R = 2AxIx he deducesthat the hydrogen ion has an effective paramagnetism of + 1.1 units.The value of a halogen ion will thus be more diamagnetic by 1.1 units thanthe corresponding halogen acid.By this method Weiss derived values foralkali and halide ions from the measurements of R. Hocart 6G andK. Reicheneder.67 This method has also been used by L. Abonnenq68ti* Trans. Faraday Soc., 1941, 37, 476.69 2. Physik, 1923, 19, 347; 1925, 32, 835.6o Ann. Physik, 1898, 66, 698.e2 Phil. Mag., 1931, 11, 786.64 Proc. Roy. SOC., 1935, A , 152, 342; see also F.E. Home and G. W. Brindley, ibid.,66 J . Physique, 1930, 1, 185.g7 Ann. Physik, 1929, 8, 68.61 Ibid., 1929, 1, 169.63 Physical Rev., 1930, 36, 57.1937, A , 159, 395.66 Compt. r e d . , 1929, 188, 1151.#II Compt. rend., 1934, 198, 2237ANGUS : DIAMAUNETISM. 35V. Veiel,sO and 0. E. Frivold 70 on their measurements on aqueous solutions ofmetallic halides. K. Kid0 7 1 has found, contrary to existing evidence, thatthe numerical value of XM for salts of metals in the same group of the periodic:classification with a common anion increases linearly with the number ofelectrons in the cation. When x M is plotted against the number of electronsin the cation the intercept of the x M axis will give the value correspondingwith the parent acid of the anion; and, by assuming that XH' = 0, he thusobtains a value for the anion.Miss Trew 58 has added another method,applicable only to halide ions. From Pascal's work the values of the sus-ceptibilities of halogen molecules are known. Methods are available forcalculating these molecular susceptibilities and also for calculating thesusceptibility of a halide ion. On the basis of the ratio XM(theor.)/XM~exptl.) =Most of these methods are reviewed by Miss Trew and she then averagesthe individual values and obtains the following ionic susceptibilities :F' = 9.1 1.8; Cl' = 23.4 & 1.3; Br' = 34.6 -+ 1.6; I' = 50.6 & 1.6;Li' = 1.0; Na' = 6.8; K' = 14.9; Rb' = 22.5; and Cs' = 35.0. Thejustification for including all the individual values she has used is ratherquestionable.Experimental confirmation of data is the first step towardssettling these difficulties. Then only can some rigorous treatment be applied.Empirical adjusting of values by an arbitrary choice of the susceptibilitiesof the ions from which other susceptibilities are deduced will never attainthe desired objective. After all, L. Pauling 72 by choosing values of - 5.2and - 14-5 for XNa' and XK-, respectively (in each instance numerically 4 unitsless than the values chosen by Pascal), deduced, from Pascal's data, values forions of alkali and alkaline-earth salts which were satisfactory for simple ions.for the diamagnetic susceptibilityof a spherically symmetrical atom or ion is x = - (e2/6mc2)Z?2, where p 2 isthe time average of r2, the distance of the electron from the nucleus, and thesummation is extended over all the circumnuclear electrons.In quantummechanics this formula also holds but the value of P is different. W has beencalculated, independently, by J. H. van Vleck 73 and L. Pauling ; 72 the latterhas calculated a number of ionic susceptibilities but they are, generally,higher than experimental values. D. R. Hartree's 74 space charge dis-tribution method has been utilised by E. c. Stoner 75 and G. W. Brindley 62but, again, values numerically greater than the experimental values areobtained. J. C. utilising the fact that the nodes in a wave functionare unimportant, has shown how wave functions of atoms and ions may becalculated conveniently by neglecting the nodes and taking as the radialpart of the wave function of one electron in a symmetrical atom $ =Xion(theor.)/Xion(exptl.), Trew derives values for Xion(expt1.).The classical formula of Langevin68 Ann.Physik, 1935, 24, 697.70 Avh. norsk. Vidensk.-Akad. Oslo, Mat.-mt. Kl., 1933, No. 9, 21 pp.7 1 Xci. Rep. Tdhoku Imp. Univ., 1932, 22, 149, 288, 869; and Rep. Yokohama Tech.72 Proc. Roy. SOC., 1927, A, 114, 181. 73 Proc. Nat. Acad. Sci., 1926, 12, 662.74 Proc. Camb. Phil. SOC., 1928, 24, 89, 11 1. 7 6 Proc. Leeds Phil. Soc., 1929,1,484.Coll., 1934, No. 2, 203, 223, 233Author.Experimental :Joos . .. .. . ... . .. ... . . . .. . .. . . . .Ikenmeyer . . . . . . . . . . . . . . . . . .Brindley .....................Brindley and Home .. . . . .Weiss (Pascal) ... ... ... ... ...,, (Hocart) ... ... ... ... ...,, (Reicheneder) . . . . . . . . .Abonnenc .....................Veiel .. . .. . .. . . . . . . . . . . ... . . . . . .Kido . . . . . . . . . . , . . . . . . . . . . . . . . . .Trew . . . . . . . . . . . . . . . . . . . . . . . . . . .Pauling . . . . . . . . . . . . . . . . . . . . . . .Brindley ......... ............Slater ...... ... ...... ...... ... ...AngusBrindley . . . . . . . . . . . . . . . . . . . . .Miowka ........................Hirone . . . , . . . . , . . . . . . . . . . . . . . .GombBs ......... ...............Theoretical :, . . . . + , . . . . . . . . . . . . . . . . .Li.I4.00-70.7I - -2.63.81-61-00.60.70.70.70.9 ---N&.6.510.45.26.17-68.27-59.07.66.8-4.25.24.23.75.12.91016K.14.516.913.514-616.016.516.317.413.614.9-16.713.514-413.113.58.41820Rb.-31.324.022.024.3I -25-027.222.53524.025.824.123.627.83228cs.-45.7636-835.141.0 --38-341-035-05536.839.637.236-94333-ICa.911.010.810.710.611.112.46.5---13.310.811-410.410-41117-Sr.2425-419.518.018.919.922-516.6---2819.521.520.218.718.2232r(n*-%o-~)~nf~, where n* is the effective quantum number and (2 - 8 )the effective nuclear charge.Rules are given by Slater for the evaluationof n* and 8, the screening constant, for an electron group.By integrationof the wave function t 2 = (n*)2(n* + #)(n* + l)/(Z - a)* and for eachelectron in the group x x lo6 = - 0.807F2. By means of this formulavalues for ionic susceptibilities in better agreement with experimentaldata are obtained. For many ions an improved value is obtained by amodification of Slater's method proposed by W. R. Angus.57 This consistsof treating separately s and p electrons having the same principal quantumnumber. The justifkation for this procedure has been questioned; 58 butall these methods are empirical, so criticism can be levelled at each.A. Heydweiler's refraction data at infinite wave-length 76 have been usedby G. W. Brindley 77 and B.Mrowka 78 to obtain xM by means of the relation-ghip between xN and p~larisability.~~ Values obtained on the basis of theThomas-Fermi statistics by T. Hirone 80 and P. GombAs 81 do not agreewell with experimental values. From such a diversity of methods a diversityof values is obtained which, at present, cannot be satisfactorily sorted out.The table on p. 36 illustrates these diiliculties.(7) Applications of Additivity in Simple Nolecules.-In section (6) referencehas been made only to ions which have a rare-gas configuration. If it isassumed that diamagnetism is strictly additive, the susceptibilities of otherions can be deduced from measured molecular susceptibilities by subtractingknown susceptibilities of other groups. Thus, to find x of a cation a numberof salts are examined and the anionic contributions are subtracted from themolecular susceptibilities. This procedure is of doubtful value because ofprevailing uncertainties regarding the true value of simple ions.Someworkers use one set of data, some choose another; there is, accordingly,great confusion in the derived quantities and no real basis for comparingthem. Inthe simple form outlined above the method has been employedto ascertain values for the following ions : BiIII,82#83*a BiV,84 SbIII,84 SbV,84Rb',85 Hg' and Hg",86 Sn" and SnIV,87 Ag' and Cu',88 Cd",89 T1',58* 839 9 0 ~ 9 176 Physikal. Z., 1925, 26, 526. Physical Rev., 1933, 43, 1030.7a Z . Physik, 1933, 80, 495.7 * J. G. Kirkwood, Physikal. Z., 1932,33, 5 7 ; J.P. Vinti, Physical Rev., 1932,4l, 813.ao Sci. Rep. TGhoku Imp. Univ., 1935, 24, 264.8a (Sir) S. 8. Bhatnagar and B. S. Bahl, Current Sci., 1936, 4, 153, 234.a4 V. I. Vaidyanathan, Indian J . Physics, 1930, 5, 559.-2. Physik, 1933, 87, 67.K. Kido, Sci. Rep. Tdhoku Imp. Univ., 1933, 22, 835.(Sir) S. 5. Bhatnagar, M. B. Nevgi, and M. L. Khanna, J . Indian Ohm. SOC.,80 (Sir) S. S . Bhatnagar, M. B. Nevgi, and G. L. Ohri, Proc. Indian Acud. Sci.,a 7 (Sir) S. S. Bhatnagar, M. B. Nevgi, and R. L. Shanna, J . Indian Chem. SOC.,1935, 12, 799.1939, A, 9, 86.1936, 13, 273.C. Courty, Compt. rend., 1936, 202, 1929.(Miss) W. R. A. Hollens and J. F. Spencer, J., 1934, 1062; 1935, 495. * (Miss) V. C. G. Trew, Tram. Famday SOC., 1936,82, 1658.*l M.B. Nevgi, J , Univ. Bombay, 1938,7, 1938 GENERAL AND PHYSICAL CHEMISTRY.K. Kid0 83 has combined the subtraction method with a graphicalextrapolation method and thereby deduced values for TiIV, CeIV, LaIII,0”, S”, ClO,’, SO4”, PO4”’, PO,’, and NO,’ ions and, recently, Miss Trew 58has used a graphical method to assist in deducing values for NO,‘, CN’,CNO’, CNS’, C03”, SOi’, NH,’, halogenate, and perhalogenate ions. K.Kid0 93 has derived values for oxy-acid ions and finds that the susceptibilityof an ion with a similar co-molecular structure decreases with increase of thenuclear charge on the central atom in the same group and increases withincrease of the nuclear charge on the central atom in the same series.In their work on alkali halides, G.W. Brindley and F. E. Hoare64 foundthat, with the exception of lithium and czsium chlorides, bromides, and iodides,the other crystalline salts were strictly additive within the limits of experi-mental error. They suggest reasons. I n a lithium halide there is a smallcation and a relatively large anion. The anions approach closely and thegreater electrostatic repulsions produce larger interatomic distances thanwould normally be expected. The caesium halides, on the other hand, have adifferent crystal structure from other alkali halides (sodium chloride structure)and this is responsible for their deviation from strict additivity. The sameauthorsss have also pointed out that ammonium iodide, which has thesodium chloride structure, gives the normal value of x, whereas ammoniumchloride and bromide give low values.Solid lithium hydride gives a valueabout half that calculated, and this is attributed1 to a factor which, in-operative in isolated ions, introduces in crystals a paramagnetism practicallyindependent of temperature.I n deducing values for the formate, acetate, iodate, nitrite, nitrate, andselenite ions, S. R. Rao and S. Sriramang4 found that the values obtaineddepended on whether they used crystalline salts or aqueous solutions. Thesusceptibilities in solution were greater than those for the crystalline salt.Similar observations have been reported in respect of metallic halides byK. C. Subramaniam 95 but, on the other hand-again using metallic halides-M. Flordal and 0.E. Frivold 96 found no substantial difference. The morerecent work of F. E. Hoare and G. W. Brindley 97 conclusively supports theIndian workers and leads to the following conclusions : (i) the susceptibilitiesof ions in solution are closely additive, (ii) the susceptibility of a large uni-valent ion in solution is approximately equal to its value in the crystallinestate, (iii) the susceptibilities of small and bivalent ions in solution are lessthan in the crystalline state owing to hydration effects, (iv) the differencebetween the values in solution and in the crystalline state (xcryst.), zlix.,x ~ ~ ~ ~ . - xcrsst., varies progressively with Cn/R2, where n/Ra is the field at theboundary of the ion and C is the degree of hydration.92 S . P. Ranganadham and M.Qureshi, Indian J . Physics, 1940,14, 129.B3 Xci. Rep, Tdhoku Imp. Uniz)., 1932,21, 069.s4 Current Sci., 1937, 8, 64; Phil. Mag., 1937, 24, 1025; J . Annamalai Univ., 1938,95 Proc. Indian Acad. Sci., 1936, A , 4, 404.96 Ann. Physik, 1935, 23, 425.97 Trans. Faraday SOC., 1937, 33, 268; Proc. Physical Soc., 1937, 49, 619.7, 187ANQUS : DIAMAGNETISM. 39Very few data exist for salts in non-aqueous solvents, The suscepti-bilities of mercuric halides in pyridine are less than in the crystalline state,86and 0. E. Frivold and H. Sogn 98 found that susceptibilities of salts in non-aqueous solvents were less than in aqueous solution.Measuredvalues are for combined atoms, and F. W. Gray and his collaborators postulatethat experimental values should be less than the calculated values (Pauling 72)and that the difference is due to depression of diamagnetism resulting frombond formation. Estimates of the magnitude of bond depressions weremade for a large number of compounds 2 before a new and intricate techniquewas published by F.W. Gray and J. H. Cruickshank3 which may be sum-marised as follows. Selecting Pauling’s 7, method of calculating ionicsusceptibilities, they modify it so as to calculate the susceptibility of anatom which is not exhibiting its extreme values of positive or negativevalency corresponding with inert-gas structures. For example, withcarbon they calculate values for C+4, C+3, V2, C+1, Co, C-l, C2, C3,and (3-4. To each atom in a molecule residual charges are assigned on thebasis of dipole moments of links, Ae, the residual charge being equal t o thebond moment /internuclear separation.These residual charges representthe fraction of time spent in a particular valency state by a particular atom.Thus, since the residual charges on carbon and hydrogen in a C-H bond are,respectively - 0-04 and + 0.04, the CH, group is H+O.04#*Hf0*O4.The theoretical diamagnetic susceptibility of this group is computed asfollows : the carbon atom is 0.08 of the time C-1 and 0.92 of the time Go,and analogously for each hydrogen ; therefore, XM(theor.) = 0 . 0 8 ~ ~ - 1 + 0 . 9 2 ~ ~ 0 + 2(0.04xH+1 + 0.96m) = - 14.90. The experimental value (Pascal)is - 11.86 and the difference, - 3.04, is the depression arising from oneC-C single bond and two C-H bonds.Depressions for a large number ofbonds of different types have been computed, and the values are used tointerpret the diamagnetic measurements and to discuss the molecularconfiguration and resonating species of benzene, naphthalene, the carboxylgroup, water, and hydrogen peroxide ; urea and its derivatives ; * organicsulphur compounds; and derivatives of SO4”, S203”, SOs“, and S,O,”radicals.6 The agreement between experimental values and calculated valuesis astonishingly close. The method involves a knowledge of screeningconstants, bond moments, and internuclear distances, quantities which arenot known for very many bonds and, even when known, are not known withcomplete certainty. I n the discussions of molecular structure more attentionmight have been paid to researches on molecular structure by other andCalculated values of x A are for isolated, free atoms or ions.Ann.Physik, 1935, 23, 413.( a ) F. W. Gray and J. Fsrquharson, PhiE. Mag., 1930, 10, 191; ( b ) F. W. Gray’* Nature, 1935, 100, 473.1 S. FreedandH. G. Thode, J. Chm. Physics, 1935,3,212.and J. Dakers, ibid., 1931, 11, 81, 297; (c) J. Farquharson, ibid., 1932, 14, 1003.a Trans. Faraday SOC., 1935, 51, 1491. 4 A. Clow, ibid., 1937, 33, 381.A. Clow and J. M. C. Thompson, ibid., p. 894.A. Clow, H. M. Kirton and J. M. C. Thompson, ibid., 1940, 36, 101840 GENERAL AND PHySIOaL OHEMISTRY.more firmly established methods. The existence of bond depressionsis indisputable; they are implied in Pascal’s corrections although he makes,unlike Gray and his collaborators, no adjustments for single bonds.MissTrew 58 has recently published values, deduced by a different method, forthe C1-0, Br-0, and 1-0 bonds. Likewise, the variability of the valencyof certain atoms has been recognised for a long time and other attempts toevaluate the appropriate susceptibilities have been made.M. Prasad and S. S. Dharmatti have recently published data on com-pounds of selenium,s teUuriurn,g and sulphur lo which they interpret interms of bi-, quahi-, and sexa-valent Group VI atoms and for each statededuce susceptibilities, using a modification of Angus’s method.57 Thecompounds yield experimental values in reasonable agreement with thecalculated values.K. Kid0 has also derived values for “ intermediate ”valencies of atoms from his ionic values and applies them to aliphatic com-pounds 1la and to mono- and di-substituted derivatives of benzene.llbSummation of Pascal’s values has yielded results in agreement withmeasured data in many instances and has been widely adopted. G. B.Bonino and R. Manzoni-Ansidei 12 use it with success for thiophen, furan,pyrrole, and their derivatives, and it yields values in excellent accord withexperimental data on uu’-phenylpolyenes l3 and the diamagnetic hexa-ar~lethanes.1~ Its applications to inorganic compounds have been equallysuccessful. It has aided in investigations which have shown the non-existence of single-electron links in dimethyltellurium halides l5 and in basicberyllium acetate and higher analogues ; 16 in demonstrating the non-existence of cadmous compounds; 89 and in the study of rhenium com-pounds l7-t0 cite only a few random examples.This variety of treatment betokens the present unhealthy state of thesubject. Much of the Mculty will remain until accurate and independentlyconfirmed experimental values are available through which generalisedtreatments can be accomplished.Then, and only then, will it be possible fordiamagnetism to occupy that important place among the methods of de-termining molecular structure which many feel it should.(8) Polymerisation.-In 1936 two papers appeared dealing with thechanges occurring during and after polymerisation. (Sir) S. S. Bhatnagar,M.B. Nevgi, and R. N. Mathur 18 reported a decrease in diamagnetism of aSee, e.g., M. B. Nevgi, J . Univ. Bombay, 1938, 7, 82.Proc. Indian Acad. Sci., 1940, A , 12, 185.@ Ibid., p. 212.l1 ( a ) Sci. Rep. Tdhoku Imp. Univ., 1936, Honda Anniversary Vol., p. 329; (b) ibid.,l2 Ric. sci., 1936, 7, Reprint.l3 E. Miiller and I. Dammerau, Ber., 1937, 70, 2561.l* E. Miiller and W. k c k , ibid., 1938, 71, 1778.l6 W. R. Angus and J. Farquherson, Proc. Roy. SOC., 1932, A, 136, 579. ’’ N. Perakis and L. Capatos, J . Phya. Radium, 1935, 6, 462; W. Klemm andlo Ibid., 1941, A , 13, 369.1936, 24, 701.(Sir) S . S. Bhatnagar and T. K. Lahiri, 2. Physik, 1933, 84, 671.G . Frischmuth, 2. anorg. Chem., 1937, 230, 220.l8 2. P&&, 1936, 100, 141ANGUS : DIAMAGNETISM.41number of compounds, including anthracene and furfuraldehyde, onpolymerisatim. The other paper, by J. Farquharson,lg discusses the poly-merisa tion of py -dime t h y lbu t adiene , cy clopen t adiene , c y anogen chloride , andnitrosobenzene and the molecular susceptibility of a n-polymeride of X isgiven by xM = nXx + (n - 1)A, where A is the correction factor for the newchemical bonds, these being assumed to be all of one type. The dis-appearance of a double bond in the polymerisation of &-dimethylbutadienecauses, as predicted from Pascal’s correction factors, a progressive increasein x with time. This enables Farquharson to combine his magnetic datawith existing chemical evidence and to calculate the mean molecular weightunder different conditions.A later paper 2o reports that in the uncatalysedpolymerisation of dimethylbutadiene x decreases for the first 3 hours andthen increases. This is attributed to the preliminary stage of poly-merisation being the formation of paramagnetic free radicals of the bufadienewith one electron missing, and their concentration has been calculated.Although double bonds also disappear in the polymerisation of cyclopenta-diene, the anticipated increase in diamagnetism is not found; insteadthere is a fall which, it is tentatively suggested, may be due to the bridgedring of the polymeride. The ring closure which accompanies the polymeris-ation of cyanogen chloride to cyanuric chloride may be responsible, as wellas the change from CiN to C:N bonds, for the marked diminution in dia-magnetism which is encountered.More recently 21 it has been found thatring formation in hydrogen-bonded structures-formed by either inter- orintra-molecular hydrogen bonds-of benzoic or monohydroxybenzoic acidsin solvents of different proton-attracting powers leads to a value of xnumerically less than the anticipated additive value and diminishing as theconcentration of solute increases. On the other hand, when an “open”addition compound is formed by intermolecular hydrogen bonding betweensolute and solvent %,,lute increases with solute concentration.J. Farquharson 22 has used magnetic measurements and a modificationof his earlier formula for x of the polymeride to evaluate the diamagneticsusceptibility of the recurring -CH20- group in polyoxymethylene diacetatesand to calculate the number of these groups in a- and P-polyoxymethylenes.This treatment yields an explanation of the earlier results of W.Good 23 ona-, p-, y-, and 8-polyoxymethylenes.Dianthracene is produced by photopolymerisation, in a vacuum, ofanthracene in the solid state or in benzene solution, and the net result is thatthe anthracene molecule loses two double bonds and gains a bridged four ring.This is accompanied by a fall in diamagnetism according to (Sir) S. S.Bhatnagar, P. L. Kapur, and (Miss) G. Kaur,= who have also studied thepolymerisation of styrene in oxygen and in a vacuum.2518 Tram. Paraday SOC., 1936, 32, 219.20 J. Farquharson and (Miss) P. Ady, Nature, 1939, 143, 1067.21 See ref.(19), p. 29.24 Proc. Indian A d . Sci., 1939, A, 10,468.23 Trans. Paraday SOC., 1937, 88, 824.J . Indian Chmn. SOC., 1940, 17,177.J . Roy. Tech. CoU. G b g o w , 1931, 2, 40142 GENERAL AND PHYSICAL CHEMISTRY.Diamagnetic measurements in the temperature range - 40” to + 10”have been invoked by J. Farquharson, C. F. Goodeve, and F. D. Richard-son26 to determine the concentrations of CIO, in mixtures of C10, andCl,O, and, hence, the corresponding equilibrium constants. CIO, is an odd-electron molecule and is, therefore, paramagnetic ; its susceptibility wascalculated from the van Vleck formula. Since all the mixtures were dia-magnetic it follows that Cl,O, is diamagnetic and must, therefore, be in the1Z state.Although it was impossible by magnetic measurements to differentiatebetween the odd-electron (KO,) and the even-electron (K,O,) formu1atio1-1,~~the following formuls have been adduced as preferable to KBH,, KBH,*OH,and NaSO,, respectively : &B2H6,28 &B,H,( OH),,,8 and Na,S,04.29(9) Addition Compounds and CompEexes.-Although the addition com-pounds formed between m-dinitrobenzene or picric acid and amines orhydrocarbons were found, in the solid state, to be more diamagnetic thanwas t o be expected from additivity relationships,3* the same compoundsexhibit less diamagnetism in benzene solution than in the solid state.31KHgI, (solid 86 and in solution 32), NH,Hg13,2H,0,86 K,HgI, and Na,HgI, 32have x values approximately equal to those obtained by additivity, whereasAg,HgI, 33 gives a value about 30% less than the additivity value.Many complexes of transition elements containing CO or CN groupsexhibit diamagnetism, e.g., carbonyls.Recent work has shown that thefollowing are diamagnetic : K4Mo( CN),,= KT13[Re0,(CN)4],35[Re(NH3)s]C1,.36 [Fe(NO,),]”’ and [Co(NO,),]’” are diamagnetic, but[CO(NO,)~]’”’ and [Cu(NO,) 6]’”’ are paramagneti~.~, DiamagneticAg,[Co(H,O)(CN),] changes colour from yellow to blue and becomes feeblyparamagnetic on dehydrati~n.~~ The diamagnetism of nickel complexes ofdiazoaminobenzene and 4 : 4‘-dimethyldiazoaminobenzene indicates that theycontain square co-ordinated nickel atoms and that the triazene group func-tions as a chelate(10) Binary Mixtures.-From 1918, when A.W. and A. W. Smith 39showed that the mixtures COMe2-H,O, AcOH-C,H,, and COMe,-EtOHa6 Trans. Faraday SOC., 1936, 32, 790.a7 W. Klemm and H. Sodomann, 2. anorg. Chem., 1935, 225, 273; E. W. Neumann28 L. Klemm and W. Klemm, 2. anorg. Chem., 1935, 225, 258.29 L. Klemm, ibid., 1937, 231, 136.so (Sir) S. S. Bhatnagar, M. J. Verma, and P. L. Kapur, Indian J . Physics, 1935, 0,3 1 (Sir) S. S. Bhatnagar, M. B. Nevgi, and G. Tuli, ibid., p. 311.33 F. GalIais, Compt. rend., 1937, 205, 1052.as Idem, ibid., 1932, 195, 1390.34 W. A. Rawlinson, J . Proc. Austral. Chem. Inst., 1941, 8, 42.* 6 W. Klemm and G. Frischmuth, 2. anorg. Chem., 1937, 230, 220.36 L. Cambi and A. Ferrari, Cazzetta, 1935, 65, 1162.37 P. Ray and N. K. Dutt, Current Sci., 1937, 5, 476.s* F.P. Dwyer and D. P. Mellor, J . Amer. Chem. SOC., 1941, 63, 81.( J . Chem. Physics, 1934, 2, 31) reported that the superoxide was paramagnetic.131.J . Amer. Chem. SOC., 1918, 40, 1218ANGUS : DIAMAGNETISM. 43obeyed the additivity relationship, until about 1931 little attention was paidto the variation of x with the concentration of the components of a binarymixture. Since then a number of papers have appeared40 which indicatethat the additivity relationship holds approximately ; there are slightdeviations from linearity attributed to co-ordination and de-associationeffects by some workers,40ci m and to the mutual influence of electricallypolar molecules by Rangant~dham,~Oe although Rao and Narayanaswamy,hfrom an investigation of the susceptibilities of mixtures of formic and aceticacids with methyl and ethyl alcohol, acetone, and ethyl ether, maintain thatthe slight deviations are independent of the electric moments of the com-ponents of the mixtures.On the basis of additivity, aqueous solutions of formic acid show small butdefinite diminution in diamagnetism with maximum deviation at 70% ofacid, which may be due to the formation of the monohydrate or to the di-merisation of the acid.41 Acetic acid solutions, on the other hand, obey the ad-ditivity rule.14‘~.2 8 ) s 39* 40n With aqueous solutions of inorganic acids irregu-larities in the X-concentration curves occur which are interpreted as due toformation of hydrates. For hydrogen chloride, J.Farquharson 42 found anumber of maxima corresponding with all the hydrates from 3 to 10H20,but A. F. Scott and C. M. Blair43 could find no maximum or minimum.Farquharson 42 reports irregularities corresponding with H,S0,,H20 andH,S04,3H20, to which P. S. Varadachari l 4 ( P . 28) has added H2S0,,18H20,H2S04,6H20, and 2H2S04,H20; but B. N. Rao 44 could find none of theseand reports only H2S04,2H20. The departures from linearity in the curvesfor nitric acid correspond with the four hydrates HI)U’O3,50H,O, HN03,6H20,HN03,4H20, and 2HN03,5H,0.45 Recently M. R. Nayar and N. K. Mundle 46have examined solutions of iodic acid (0.01-1.0~) and found breaks in theX-N curves at 0.04 and 0 . 0 8 ~ .(1 1) Gases.-Molecules with an even number of circumnuclear electronsare diamagnetic if they are in a 1 2 state. Oxygen, although it containsan even number of electrons, is in a 3C state and is, consequently, para-magnetic.Nitrogen mono- and di-oxide and chlorine di- and tri-oxideare paramagnetic by virtue of their unbalanced structure resulting from at40 (a) H. Buchner, Nature, 1931, 128, 301; ( b ) J. Farquharson, ibid., 1932, 129,25; (c) J. E. Garssen, Compt. rend., 1933, 196, 541; ( d ) K. Kido, Sci. Rep. T6hokuImp. Univ., 1932, 21, 385; ( e ) S . P. Ranganadham, Indian J . Physics, 1931, 6, 421;(f) S. R. Rao, ibid., 1933, 8, 483; ( 9 ) S. R. Rao and G. Sivaramakrishnan, ibid., 1931,6, 609; ( h ) S. R. Rao and P. 8. Varadachari, Proc. Indian Acad. Sci., 1934, A, 1, 7 7 ;( 6 ) C. Salceanu and D.Gheorghiu, Compt. rend., 1935, 200, 120; ( j ) S. Seely, PhysicalRev., 1936, 49, 812; (k) J. F. Spencer and (Miss) V. C. G. Trew, Nature, 1936, 138, 974;( I ) (Miss) V. C. G. Trew and J. F. Spencer, Trans. Furuday Xoc., 1936, 32, 701 ; (m) (Miss)V. C. G. Trew and (Miss) G. M. C. Watkins, ibid., 1933,29,1310; (n) S. R. Rao and A. S.Narayanaswamy, Proc. Indian Acad. Xci., 1939, A , 9, 35; see also Ref. 56.See also Ref. 40n. *l S. R. Rao and S . Sriraman, J . Anmmalai Univ., 1938, 7, 187.42 Phil. Mag., 1931, 12, 283.44 Proc. Indian Acad. Sci., 1936, A , 3, 188.O6 8. P. Ranganadham and M. Qureshi, 2. physikal. Chm., 1936, B, 33, 290.46 Current Sci., 1941, 10, 76,43 J . Physical Chem., 1933, 37, 47544 GENERAL AND PHYSIOAL UHEMISTRY.least one electron not being paired.However, if such molecules undergodimerisation the dimeride will contain an even number of circumnuclearelectrons and will be diamagnetic, e.g., C1,0,26 and N20,,47*64 or feeblyparamagnetic.Experimental difliculties are most probably the cause of the limitedamount of data in this field and particularly in respect of organic vapours.The experimental procedure of J. Schur 46 was the most promising, and byit, the constancy of x for both the liquid and the gaseous state of carbondisulphide, and bromine 49 has been established. Much more workin this direction is required to adjudge the existing conflicting evidence withregard to the probable alteration in x on vaporisation.The values of x obtained experimentally and theoretically for the raregases, hydrogen, and an isosteric pair are collected in the table below.- x x 106.Author.He. Ne. A. Kr. Xe. Ha. N,. CO.Ealperimental :Willa and Hector ...... 1-95 3.96Hector ..................... 1.88 6.66 18.1 11.83Abonnenc ............... 19-2 29.2 44.1Gerlach .................. 19.7Havens .................. 1.91 7-65 19.2 4.01 11-94Mann ..................... 6.75 19.5 28.0 42.4Jaanus and Schur ...... 11.8Pauling .................. 1.54 6.7 21.6 42 66Slater ..................... 1.68 6.7 18.9 31.7 48.0Angus ..................... 1.68 6.1 16-95 29.3 44.8Brindley .................. 1.97 6.1 16.7 29.3 45.6Vinti ........................ 1.97 6-97van Vleck and Frank 4.2Wick ..................... 3-96Witmer .................. 3-87Honda and Hirone ......3.85Theoretical :WFg ..................... 1-53 4.7 1* References denoted thus relate to the second one so numbered.Ref.60*61*52*63*54*55*66*7263677757*58*69*60+61*62*By means of the methods discussed in section (6) for the calculation ofthe susceptibility of an ion with a rare-gas configuration, values of x for raregases can be obtained. The agreement with experimental data is notparticularly good for any method; but the measured values are in tolerableagreement with each other. Comparison with the experimental data for therare gases must surely be the criterion by which a method of calculationcan be judged, and the failure of Pauling's method in this respect suggeststhat it is unsuitable for use in calculating ionic suaceptibilities.Neverthe-less, as has already been pointed out, Gray et found that values calculated47 G. G. Havens, Physical Rev., 1932, 41, 337.48 Physikal. Z . Sovietunion, 1937, 11, 194.$9 J. Schur and R. Jamus, ibid., 1935, 7, 601.6o Physical Rev., 1924, 23, 209.s3 Compt. rend., 1939, 208, 986.64 Phy8ical Rev., 1932, 41, 337.68 Physikal. 2. rSov&union, 1935, 7, 19.51 Ibid., 1924, 24, 418.53 Z . Phyaik, 1933, 85, 545.65 2. Phy8ik. 1936, 98, 648.6 7 Phyaical Rev., 1933, 4l, 813by a method basically related to Pauling's agreed very closely with theirmeasured values. To reconcile these opposing facts most satisfactorilywould involve remeasurement of the rare gases; confirmation of the exist-ing values would indicate a fundamental error in the interpretation of thedata on the plyatomic molecules and necessitate a readjustment of ideasregarding bond diamagnetism.Quantum-mechanical treatment is possible only with the simplestaystems and for helium and hydrogen yields values 68-62 which are, on thewhole, acceptably close to the experimental data.It is noteworthy that the isosteric molecules, carbon monoxide andnitrogen, have identical susceptibilities.This is in line with other physicalproperties of the pair. T. Son6 found values very close to each other forcarbon dioxide 63 and nitrous oxide,64 another isosteric pair. Unfortunately,his method appears to be a t fault because his value for carbon dioxide is- 18-61, which is considerably less than - 20.9 found by other investigators.66No reliable comparative datum for nitrous oxide exists.( 12) MisceZlaneous.-An interesting application to molecular structurehas been made recently by R.W. Asmussen.66 On X-ray evidence incompounds of the type Rb2SbC1, all antimony atoms are equivalent. Thesimplest explanation would be to assign a valency of four to antimony,which would then possess an odd-electron structure and, consequently,would confer paramagnetism on the molecule. From measurements on eightcompounds, all of which are diamagnetic, it is concluded that these com-pounds do not contain SbIV but, probably, alternate SbIII and SbV. Theseconclusions support the earlier suggestion of N. Elliott 67 that (NH,),SbBr6contained no single molecules but only dimerides.Magnetic measurements by P.W. Selwood have recently shown that i t isunlikely that hexaphenyldigermane 68 is dissociated in the solid state orto more than 20% in benzene a t 25", whilst for hexaphenyldiplumbane 69the upper limit of dissociation to triphenyl-lead in benzene is 104% and in thesolid state O*lyo a t temperatures from 30" to 80". Trimethyltin and tri-cyclohexyl-lead do not exist in the monomeric form in dilute benzene s0lution.7~These results cast doubt on the existence of long-life organometallic freeradicals. The fact that the vapour of calomel is diamagnetic between250" and 375" excludes the formula HgC1.7168 Proc. Nat. Acad. Sci., 1929, 15, 539.8o 2. Physik, 1933, 85, 25; Nuovo Cim., 1933, 10, 118.59 Ibid., 1927, 13, 798.82 2.Physik, 1933, 84, 208. Physical Rev., 1935, 48, 380.Sci. Rep. TGhoku Imp. Univ., 1919, 8, 116.E. Lehrer, Ann. Physik, 1926, 81, 229; S. R. Rao ctnd G. Sivaramakrishntm,O4 Ibid., 1922, 11, 139.Proc. Physical SOC,. 1934, 46, 318; and Ref. 54 (p. 33).86 2. Ekktrochem., 1939, 45, 698.67 J . Chem. Physics, 1934, 2, 419.J . Amr. Chem. SOC., 1939, 61, 3168.R. Preckel and P. W. Selwood, ibid., 1940, 62, 2765.70 H. Morris and P. W. Selwood, ihid., 1941, 63, 2609.71 P. W. Selwood and R. Preckel, ibid., 1940,62, 306646 GENERAL AND PHYSICAL CHEMISTRY.G. N. Tyson and S. C. Adams 72 prove that the salicylaldimine complexof nickel is planar and diamagnetic whereas, although planar, the cupriccomplex is paramagnetic.The paramagnetic salicylaldehyde complexesof nickel(I1) and cobalt(I1) are tetrahedral but the corresponding cupriccomplex is planar. Most probably cupric disalicylaldehyde is also planar.73C. M. Beeson and C. D. C ~ r y e l l , ~ ~ from measurements on gaseouv nitrosylchloride at 25", concluded that it was diamagnetic and in a 1x state; itresembles sulphur dioxide in physical properties. This, and the fact thatthe x values for additive compounds of nitrosyl chloride with inorganicchlorides indicate that it is diamagnetic, led R. W. Asmussen 75 to postulateresonance between the forms Cl-(NO)+, Cl-NXO, and CEN-+O, J. A. A.Ketelaar 76 showed, on electron-diff raction evidence, that there is resonancebetween the two structures, Cl-KO and Cl-(NO)+.An examination of solid sodium and potassium salts of acetic, propionic,and butyric acids has shown that the experimental values agree with thosecalculated.On the other hand, the corresponding salts of palmitic, stearic,oleic, and myristic acids give values less than the calculated values; this isattributed by M. B. Nevgi 77 to the formation of micelles of large particlesof colloidal dimensions.I n view of the limitations necessarily imposed on the size of a Reportof this kind it has been decided to omit certain topics in spite of their intrinsicinterest and importance ; notable omissions are anisotropy and the dia-magnetism of metals, with the influences exerted by pretreatment of thesamples, particle size, and crystal structure.W. R. A.4. MOLECULAR SPECTRA AND THERMODYNAMICS.I n recent years thermodynamics has received considerable help fromaccurate spectroscopic measurements, since the evaluation of the energylevels occupied by molecules enables specific heats to be computed. Mostof the data come from infra-red and Raman spectra, and therefore in thefollowing survey little reference is made to ultra-violet spectra, which werereviewed two years ago.1Internal Rotation in NoZecuZes.-The application of physicochemicalmethods to the study of internal rotation in molecules has been mentionedin previous Reports.2 During recent years information about this hasaccumulated rapidly. Some advance has come from the measurement ofdipole moments and the effect of temperature upon them,3 and from X-rayand electron-diff raction measurements, but the main progress has been madeby the use of optical methods, and the correlation of optical data with otherphysicochemical results.72 J , Amer.Chern. Soc., 1940, 62, 1228.78 G. N. Tyson and R. E. Vivian, ibid., 1941, 63, 1403.74 J . Chem. Physics, 1938, 8, 666. 7 b 2. arorg. Chem., 1939, 243, 127.7o J . Uniu. Bombay, 1938, 7, 74. Atti X Cong. intern. China., 1938, 11, 301.Ann. Reports, 1939, 36, 47. Ibid., 1938, 35,42.3 G. I. M. Bloom and L. E. Sutton, J., 1941, 727THOMPSON : MOLECULAR SPECTRA AND THERMODYNAMICS. 47In a molecule such as ethane, rotation of one end of the molecule withrespect to the other will lead to two sets of three identical positions.Onlyone form of ethane is known. Hence, either the potential barrier resistingthe torsion must be very small, so that effectively free rotation occurs, or itmust be high, leading to an effectively fixed relative orientation of the twoend groups. I n all such cases the state of affairs can only be understoodcompletely by a knowledge of the potential energy as a function of theazimuthal angle of internal rotation, which gives the height of the barriers ( Uo).If kT is much greater than Uo we have free rotation, and if k!Z' is less thanU , we have a torsional oscillation, and the problem is therefore essentiallya determination of the heights of the restricting barrier potentials. Acomparison of these barriers in different compounds should throw light onthe causes of such restriction potentials.Herein lies the real reason for therecent advances, since estimates of the barriers in a series of related moleculesare now available, and although in some respects the values determinedmust still be accepted with reserve, it is probable that refinement of therelevant theory will soon lead to important progress. One factor which isdirectly relevant to the understanding of the origin and size of potentialsrestricting the rotation about bonds is the mutual influence of neighbouringnon-bonded atoms upon each other. For instance, if in ethane the hydrogenatoms of different methyl groups had a mutual attraction, the stable structuremight be expected to be that in which the three pairs of hydrogen atoms areopposite each other, i.e., one end of the molecule " eclipsing " the other,with a symmetry of the class D3h.On the other hand, repulsive forcesbetween the pairs of hydrogen atoms will lead to a " staggered " structure(symmetry OM), obtained from the eclipsed form by rotation of one methylgroup through 60" with respect to the other methyl group. There hasconsequently been much discussion about the relative stability of theeclipsed and the staggered configuration, and this relative stability affectsthe structure of certain molecules in other ways discussed below.Apart from less studied phenomena such as the Kerr effect, there arethree principal optical approaches to this question, viz., (1) the use of Ramanspectral data, (2) the analysis of the rotational fine structure of infra-redvibrational absorption bands, and (3) the comparison of thermodynamicalproperties of molecules calculated statistically, using the energy levels deter-mined spectroscopically, with the values of these properties determined byother experimental methods.Of these three independent lines of work, thethird has been the most productive, and will be considered first.The thermodynamical-statistical procedure may be summarised asfollow^.^ It is first necessary to determine, by a correlation of data from theinfra-red and Raman spectra, the vibration frequencies of the moleculeconcerned, as regards both magnitude and assignment to vibrational types.Values for the moments of inertia must then be obtained, either from the' See S.Glasstone, Ann. Reports, 1936, 32, 66; L. Kassel, Chem. Reviews, 1936, 18,277; R. H. Fowler and E. A. Guggenheim " Statistical Thermodynamics," Cambridge,19-1048 GENERAL AND PHYSIUAL (XtEMISTRY.rotational structure of vibrational absorption bands, or by other methodssuch as electron diffraction. These either lead directly to the values of therotational energy levels, or in more complex cases of asymmetrical rotatorsto less specific but nevertheless adequate data about these levels, since thetotal rotational partition function for molecules at reasonable temperaturesis given by an explicit function of the moments of inertia. Similar knowledgeof the electronic energy levels above the electronic ground state may also berequired, although as a rule the comparatively high value of all such levelsabove the lowest makes this information unnecessary.The molecularpartition function, Q = Zpi e-Ej/kT, in which pi is the degeneracy of an energylevel Ei, may then be calculated. Actually, the total partition functionQ = &.&hd.&vib.Qrot., and since it appears in the expressions for all thethermodynamic functions as log &, the several contributions from the differenttypes of energy are additive. As a rule Qel. = 1, and at reasonably hightemperatures for polyatomic molecules = ( 2xM)3‘~~5’2TS’2/h3pIV312, inwhich M is the molecular weight, P the pressure, N the Avogadro number,and k and h the Boltzmann and the Planck constant respectively. AlsoQ,t.= 8x2(2xJCT)312d1m&3~ in which I*, IB, and I. are the principalmoments of inertia, and o the “ symmetry number,” i.e., the number of indis-tinguishable configurations which may be arrived a t by rotations of the moleculein space ; and Qdb. = II( 1 - e-Wkr)-l, a product which is taken over all thevibrational frequencies v. By statistical methods the total partitionfunction can now be related directly to the various thermodynamic functions.The expressions for the molar entropy, free energy, and specific heat atconstant pressure are as follows :X = R In & + RT. d In &/dTCP = RT2d2 In Q/dP + 2RT. d In Q/dTG = - R T I n QReduced expressions for S , G, and Cp as functions only of the several mole-cular magnitudes aftpvr numerical substitution of the fundamental constantshave been given by E.B. Wilson.5 It is customary in practice to calculatethe “ virtual ” entropy, which ignores any contribution of nuclear spin effectsto the partition function, since for all molecules other than hydrogen theyare negligible a t reasonable temperatures.The same thermodynamic quantities can, on the other hand, be measured,the specsc heat directly, the entropy by integration of a Cp-h T plot, thethird law of thermodynamics being assumed and due allowance made forchanges in state and any “ order-disorder ” phenomena in the solid state,and the free energy from the experimental determination of equilibriumconstants. The measured values, which must be referred to some standardstate such as one atmosphere pressure, will in general require wmection fornon-ideality of the gas laws applying to the real vapours, for which purposesome knowledge of the equation of state or virial coefficients is required.Chm.Revku(8, 1940,27, 17THOMPSON : MOLECUIJR SPEUTRA AND THERMODYNAMICS. 49Suitable approximations for the latter can be derived if the critical data areknown.It has long been known that satisfactory agreement exists between thecalculated and the measured thermodynamic properties for many simplemolecules having a rigid framework. This indicates the validity of assumingthe third law of thermodynamics as well as the general correctness of thestatistical method, which has therefore been used extensively for calculatingunknown magnitudes.Discrepancies were noticed, however, with othermolecules, such as those in which a torsional motion, or double minimumpotential energy function (e.g., invertable pyramid) may occur. Thesediscrepancies were, moreover, greater than those to be expected because ofthe anharmonic character of vibrations, and must be explained in some otherway. If a twisting vibration of an essentially rigid framework passes intoa free internal rotation, an alteration will be necessary in both the vibrationaland the rotational partition functions. The torsional vibration frequency isthen omitted from the product in calculating QVlb., and a further Q for theinternal rotation is introduced given by 2~(27cIkT)lE/nh ; I is the reducedmoment of inertia of the two mutually rotating end groups, and n the internalsymmetry number defined below.If the torsional motion is neither free norvibrational, but intermediate in character, the form of the partition function&,,t. cannot be given explicitly, but will depend on several factors such as theform of the function relating potential energy and azimuthal angle of rotation,and upon the absolute height of the restricting potential barriers. K. S. Pitzer,first gave a fundamental treatment of this problem,6 assuming a potentialbarrier function of the type U = U0/2( 1 - cos n0). He has given tables for S, G,and Cp from which for given values of U,,, I , and n the contributions towardsthe several properties can be read off. This makes it possible to reverse theprocedure and, from the disparity between observed and calculated values, toestimate the value of U, which will give agreement.This method has beenused by most workers. B. L. Crawford 7 has attempted to extend andimprove Pitzer’s theory, by considering the general system of several topsattached to a rigid framework, and has suggested that in some cases calcula-tions by Pitzer’s method may lead to serious errors in the values determinedfor U,. This argument has been questioned by K. S. Pitzer and W. D.Gwinn,* who draw attention to several defects in Crawford’s treatment.Neither theory appears yet to be entirely satisfactory, if for no other reasonthan that there is uncertainty in the form of the function relating potentialenergy and azimuthal angle of rotation, but the main principles of the methodcan be regarded as established.Of the various properties which may beused in the comparison, the specific heat seems to be the most sensitive, butif this is used rather than entropy, there must be complete certainty aboutthe values of the molecular vibration frequencies.In considering experimental results, we take the classical case of ethane’ Ibid., 1940,8,273; see also €3. L. Crawford and E. B. Wilson, ibid., 1941,9, 323.J . Chem. Physics, 1937, 5, 469.Ibid., p. 48550 GENERAL AND PHYRTCAL CHEMISTRY.first. Earlier specific-heat measurements by Eucken and the analysis ofthe vibrational spectrum by E. Bartholomb and J. Karweil suggested freeinternal rotation in this molecule, but it is now certain that a considerablerestricting potential exists.J. D. Kemp and K. S. Pitzer 10 compared themeasured and the calculated entropies and inferred a barrier of 3150 cals.per mol. The analysis of the vibrational spectra of ethane and hexadeutero-ethane led F. Stitt l1 to a more precise assignment of the vibration frequencies,and a comparison of the measured and the calculatcd specific heats by G. B.Kistiakowsky, J. R. Lacher, and F. Stitt l2 then gave a value of 2750 cals.Confirmation of a value close to 3000 cals. is obtained from the statisticalcalculation of the ethylene-hydrogen-thane equilibrium by E. A. Guggen-heim.13 Neither the spectroscopic data nor a consideration of the symmetrynumber throws much light on whether the molecule is eclipsed or staggered,although for other reasons it now seems that the stable configuration is prob-ably the staggered form.Both the entropy and the specific heat of dimethyl-acetylene show that in this molecule, by contrast, the restricting barrier isclose to zero l4 and certainly less than 500 cals. per mole. It might then beinferred that mere separation of the two methyl groups is a controlling factorin fixing the height of the barrier. Against this hypothesis, however, is theestimate by Stitt l5 of 4000-6000 cals. for the barrier in diborane by acomparison of the measured and the calculated specific heats. The separ-ation of the methyl groups in diborane is greater than in ethane. With neo-pentane, C(CH3)4, J. G. Aston, R. M. Kennedy, and G.H. Messerly l6 estimatea barrier of about 4200 cals. restricting each methyl group, whereas intetramethylsilicon17 it is about 1300 cals. These facts suggest that moresubtle factors than mere separation of the rotating groups are operative, andthere is a suggestion that a repulsive force may exist between the interactingcentres which varies with a high power of the distance. Specific-heat data,together with the vibrational assignment of R. G. Owens and E. F. Barker,18led J. G. Aston and P. M. Doty 10 to a value of 1500 cals. for the barrier inmethylamine, and J. G. Aston, M. L. Eidinoff, and W. S. Forster 20 similarlyfind a potential of 3460 cals. per methyl group in dimethylamine. Torsionof each methyl group in dimethyl sulphide 21 appears to be impeded by a* Z.physika1.Chem., 1938, B, 39, 1.l 1 J . Chem. Physics, 1939, 7, 297.lJ Trans. Faraday SOC., 1941, 37, 97.1' D. W. Osborne, C. S. Garner, and D. M. Yost, J . Amer. Chem. SOC., 1941,63,3492 ;l6 I b d . , 1940, 8, 981.1' J . Amer. Chem. Soc., 1936,58,2354; 1937,59,1743 ; see also K. S. Pitzer, J . Chem.l7 J . Amer. Chem. SOC., 1940, 62, 2567; 1941, 65, 2343.la J . Chem. Physics, 1940, 8, 229.l' Ibid., p. 637.*O J . Amer. Chem. SOC., 1939, 61, 1539.t1 D. W. Osborne, R. N. Doescher, and D. M. Yost, J . Chem. Physica, 1940, 8, 506;10 J . Amer. Chem. SOC., 1937, 59, 276.Ibid., p. 289; see also G. B. Kistiakowsky and W. W. Rice, ibid., pp. 281, 289.J . Chem. Physics, 1940,8, 131; B. L. Crawford and W. W. Rice, ibid., 1939, 7, 437.Physiw, 1937,5,469, and J.G. Aston, Chem. Reviews, 1940, 27, 59.H. W. Thompson, Trans. Faraduy SOC., 1941, 37, 3852 GENERAL AND PHYSICAL UHEMISTBY.cases. The usefulness of such a treatment, though as yet necessarily approxi-mate, is already apparent, and it is to be expected that refinements will shortlyfollow.Reference should also be made to earlier measurements of the entropy ofdinitrogen tetroxide by W. F. Giauque and J. D. Kemp; 38 the vibrationalfrequency assignment of this molecule is still somewhat uncertain, but thedata appear definitely to suggest a fairly high potential preventing the twoNO, end groups from rotating with respect to each other. In an attempt toestimate the barrier in ethyl chloride, J. W. Linnett 39 has compared themeasured equilibrium constants of the reaction ethylene-hydrogen chloride-ethyl chloride with those calculated on the assumption of different barrierheights.Unfortunately here, as in many other cases, the experimental dataon the equilibrium constants do not seem sufficiently accurate for the purposerequired.The rotational structure of the infra-red absorption bands of a few lightermolecules provides semi-quantitative data about internal rotation. For thepurpose of considering this rotational structure, molecules are usually classi-fied according to their symmetry, since, in part, this determines the arrange-ment of the rotation lines. In reality, however, most molecules are asym-metrical rotators, having all three moments of inertia unequal, and therotational structure in these cases is very complex.At the same time, somemolecules approximate sufficiently closely to a symmetrical top (IA = IB .t.Io) for the rotational structure of their vibration bands to deviate onlyslightly from that to be expected for the symmetrical rotator. The absorp-tion bands may be of two types, according as the change in electric momentis parallel or perpendicular to the symmetry axis, and these respectiverotational structures have been described in a recent Report.4* For ourpresent purpose the main point is that the structure of a perpendicular typeband may be fundamentally affected by the occurrence of internal rotation.A theoretical treatment of the energy levels of a torsional oscillator was firstgiven by A.H. Nielsen.41 Qualitatively the results may be expressed bysaying that if there is free internal rotation the spacing between the Qbranches of the perpendicular type bands is much increased above its valuefor the rigid molecule. The exact theoretical background of the phenomenonis not yet fully worked out, but the effect can conveniently be sought in theinfra-red bands of such molecules as ethane, methyl alcohol, and methylamine.J. B. Howard 42 first showed that the rotational structure of certain infra-redbands of ethane is consistent with a barrier of about 2000 cala. resistingrotation about the C-C bond. This value compares reasonably with thevalue given in the preceding paragraphs. The rotational structure of aharmonic band of the 0-H bond vibration in methyl alcohol, photographedby R.M. Badger and S. H. Bauer,43 is consistent with a fairly high restrictingpotential about this bond. The analysis of the absorption bands of this38 J . Ohem. Physics, 1938, 6, 40.do Ann. Reports, 1935, 82, 53.4a J . Chem. P h y h , 1937,5, 461.I* Trana. Famday SOC., 1940, 86, 627.4 1 Phy8ic.d Rev., 1932, 40, 446.48 Ibid., 1936, 4, 469THOMPSON : MOLECULBR SPECW AND "HERMODYNAMICS. 53molecule at longer wave-lengths led A. Borden and E. F. Barker 44 to a valueof about 1500 cals., which seems on other grounds to be too low. Their datahave also been discussed by J. S. Koehler and D. M. Denni~on.~~ Therotational analysis of a photographic infra-red band of methylamine byH.W. Thornpson4s shows that this molecule is essentially rigid. A. P.Cleaves, H. Sponer, and L. G. Bonner 47 agree with this conclusion, whichaccords with the thermodynamic-statistical considerations given above.Many papers continue t o appear dealing with the application of Ramanspectral data to this problem. If rotational isomers exist, arising from aninternal potential barrier resisting torsion, the number of Raman intervalsfor a given substance will be greater than might be expected for a singlecomponent, and by the application of selection rules and the measurementof polarisation properties it might, in theory, be possible to assign thedifferent frequency intervals to characteristic vibrations of different sym-metry types, such as eclipsed and staggered configurations.K. W. F. Kohl-rausch48 and his collaborators have examined a wide range of compoundsin which torsion is possible, and claim defmite conclusions in many cases.The majority prefer to think, however, that this method can rarely be un-ambiguous. W. F. Edgell and G. Glockler 49 have reviewed the whole posi-tion with particular reference to the alkyl halides and dihalogenoethanes.They point out that, although there seems to be clear evidence that the higheralkyl halides exist in two forms, the evidence as to their form--&-, trans-,or other-is far less conclusive. With the dihalogenoethanes the facts arethought to be in best agreement with the hypothesis that the two forms arethe tram-form and the pair of identical C, staggered structures, the latterbeing obtained from the former by an internal rotation through 120"Edgell and Glockler conclude that there is no evidence for a cis-(eclipsed) formof a molecule of the ethane type.G. Glockler and C. Sage 50 also believethat the staggered forms are predominant .in a series of multihalogenatedethanes. Ta You Wu 61 arrives at a different result, and A. Langseth,H. J. Bernstein, and B. Bak 52 claim that &man measurements on 2-bromo-1 -deuteroethane show that the rotational isomers have the eclipsed (opposed)configurations, from which an eclipsed structure of ethane is inferred. Lang-Seth and Bak 53 have extended their hypothesis of the stability of opposedstructures to a consideration of the form of cyclohexane. The Raman dataof this molecule and of deutero-substituted cyclohexanes are said to be con-sistent with a planar cyclohexane ring, with the hydrogen atoms in opposedpositions with respect to neighbouring hydrogen atoms.Langseth andBernsteina applied the hypothesis of opposed structures further in con-44 J . Chm. Physics, 1938, 6, 553.46 J . Chem. Physice, 1938,6, 7 7 5 ; 1939, 7, 448.47 Ibid., 1940, 8, 784.155; 1939, B, 45, 329, 341 ; 1940, B, 48, 1.61 Ibid., 1939, 7, 965.4 5 Physical Rev., 1940, 57, 1006.See 8 series of papers in 2. physikal. Chem., especially 1940, B, 46,165 ; B, 47, 65," J. Chem. PhYhC8, 1941, 9, 376. Ibid., p. 375.Ibid., 1940, 8, 430.Ibid., p. 403. I4 Ibid., p. 41054 GENERAL AND PHYSICAL CHEMISTRY.nexion with the Raman spectrum of tetrachloroethane and the effect oftemperature upon it. That eclipsed structures, as proposed by Langsethand his colleagues, are unsatisfactory, has been pointed out by severalauthors.Many workers appear to overlook the fact that with liquids theselection rules for the Raman effect may cease to operate rigidly, because ofdistortions leading to alteration of the molecular symmetry. In particular,V. Schomaker and D. P. Stevenson 55 and K. S. Pitzer 56 have shown thatevidence of different kinds strongly favours the staggered forms, and someform of repulsive interaction between neighbouring non-bonded atoms.Measurements on the heats of bromination of certain unsaturated cyclichydrocarbons seem also to support this idea.57General Thermodynamics.-In addition to the examples referred to in theprevious section, the thermodynamic properties of many other molecules havebeen computed from spectroscopically determined molecular magnitudes.In some cases the calculated values have been compared with direct measure-ments, and in nearly all cases a close agreement has been found.Thus,measured and calculated entropies have been compared for methyl chloride,5*hydrogen cyanide,5Q cyanogen,SO and arsenic trifluoride ; 61 and specificheats for ethylene,62 cyanogen, 63 and several lower hydrocarbons. 64 Certainequilibrium data have been used to compare calculated and measured freeenergies. This last method has been applied to check the frequency assign-ment in nitrosyl chloride,65 to derive a more probable value for the heat offormation of carbonyl chloride,66 and to show the desirability of a re-examina-tion of the thermal dissociation of sulphuryl chloride.67 D.Grafe, K. Clusius,and A. Kruis 68 obtain satisfactory agreement between the measured and thecalculated equilibrium D, + H,S =+ D,S + H,. A series of papers dealswith the thermodynamic properties of hydrocarbons which are of particularimportance in modern fuels.Other calculated values are available for phosphorus,"-) phosphine, the55 J . Chem. Physics, 1940, 8, 637.56 J . Amer. Chem. SOC., 1941, 63, 3313; see also J. G. Aston, S. G. Schumann,6 7 M. W. Lister, ibid., p. 143; G. R. Kistiakowsky, ibid., 1939, 61, 1868.58 G. H. Messerly and J.G. Aston, &id., 1940, 62, 887.5' R. A. Ruehrwein and W. F. Giauque, ibid., 1939,61,2626.60 Idem, ibid., p. 2940.61 H. Powell, R. E. Rundle, and D. M. Yost, ibid., 1941, 63, 2825.61 E. J. Burcik, E. H. Eyster, and D. M. Yost, J. Chem. Physics, 1941, 9, 118.6s E. J. Burcik and D. 31. Yost, ibid., 1939, 7, 1114; F. Stitt, ibid., p. 1115.6' J. G. Aston and G. H. Messerly, J . Amer. Chem. Soc., 1940,62,1917 ; J. G. Aston,R. M. Kennedy, and S. G. Schumann, ibid., p. 2059; J. D. Kemp and C. J. Egan, ibid.,1938, 60, 1521.H. L. Fink, and P. M. Doty, ibid., p. 2029.6 5 C. M. Beeson and D. M. Yost, J . Chem. Physics, 1939, 7 , 44.66 H. W. Thompson, Trans. Puruday SOC., 1941, 37, 251.67 Idem, ibid., p. 340.( 8 Z.physikaZ. Chem., 1939, B, 43, 1.6' See J .Amer. Chem. SOC., 1940,62, 1224, 1917, 2988; 1941, 63, 1133, 2039, 2413;70 D. P. Stevenson and D. M. Yost, J . Chem. Physics, 1941, 9, 403.J . Chem. Physics, 1940, 8, 711 ; Chem. Reviews, 1940, 27, 39THOMPSON : MOLECULAR SPECTRA AND THERMODYNAMICS. 55phosphorus halides, several halogenomethanes, 71 formaldehyde and deutero-formaldehyde, 72 diatomic hydrides and halides, 73 hydrazoic acid,7* thecyanogen halides, 75 methyl cyanide 76 and isocyanide, hydrogen fluoride,The specitic-heat measurements of G. B. Kistiakowsky and his collabor-ators in recent years have made it possible to correct previously measuredheats of hydrogenation of unsaturated hydrocarbons to absolute zero and tothe non-vibrating states of molecules.79 As a result it is found that the heatchange in a hydrogenation reaction definitely depends on the nature of thegroups adjacent to the bonds being reduced, and it must be concluded thatthese contiguous groups appreciably influence the bonding strength of theunsaturated link.In a very interesting attempt t o obtain a general formulafor the entropy of long-chain compounds, M. L. Huggins 80 has used anapproximate model to derive simple expressions for the contribution of thevarious degrees of freedom to this property, which agrees well with values sofar measured for short-chain paraffis. The problem of the energy levels,partition function, and thermodynamic properties of molecules like ammoniawith a double minimum potential energy function, has been considered byK.S. Pitzer,81 and by R. F. Haupt and E. Teller.82 Reference should alsobe made to a general symposium on thermodynamic^,^^ where other referencesare compiled.Concurrently with these developments in our knowledge of thermo-dynamic functions, further studies have been made of the best equations ofstate for vapours, and virial coefficients have been determined in some cases.The considerable progress made in developing a theory of liquids must beleft over for a future report.Infru-red and Raman Spectra.-Since about 1930 valuable and highlyaccurate data about molecular structure have been obtained from the studyof the absorption bands of the vapours of some simpler polyatomic moleculesin the photographic region of the infra-red, viz., between 0.7 and 1 .2 ~ (7000and 12,000 A.). The success of this method lies in the ease with which highresolving power can be obtained by means of an ordinary diffraction grating.It was clear from the start, however, that this region would have limitedapplicability, since in order to bring the absorption into this spectral range,several vibrational quanta must be absorbed simultaneously, and the path71 W. F. Edge11 and G. Glockler, J. Chem. Physics, 1941, 9, 484; D. W. Osborne,C. S. Garner, R. N. Doescher, and D. M. Yost, J. Amer. Chem. SOC., 1941, 63, 3496.72 H. W. Thompson, Trans. Paraday Soc., 1941, 37, 251.75 D. P. Stevenson, J. Chem. PhyBic8, 1941, 9, 898.74 E. H. Eyster and R. H. GilIette, ibid., 1940, 8, 369.7 6 D. P. Stevenson, i b d ., p. 171.76 R. H. Ewe11 and J. F. Bourland, ibid., p. 365.7 7 G. M. Murphy and J. E. Vance, ibid., 1939, 7, 806.78 H. W. Thompson, Trans. Paraday Soc., 1940, 37, 249.79 G. B. Kistiakowsky, J. B. Lacher, and R. W. Ransom, J . Chem. Physics, 1940, 8,*O Ibid., p. 181.84 Ibid., p. 925.and carbon s~boxide.~*970.81 Ibid., 1939, 7, 251.83 Chem. Reviews, 1940, 27, 1-8556 QENERAL BND PHYSIOAL CHEMISTRY.length of vapour required increases very rapidly for each successive harmonic.Thus even with compounds containing a C-H bond of relatively high vibra-tion frequency, three or four will be required, and for heavier molecules manymore. In the case of heavier molecules, too, the larger moments of inertiawill preclude the resolution of fine structure. Hence, the usefulness of thisspectral region appears now to have been exhausted, so far at least as resolu-tion of the rotational structure of bands is concerned.It is therefore oppor-tune to review some of the most recent investigations in this field.Perhaps the most striking of these is the measurement by L. Zumwaltand P. A. Gigubre of the absorption of the second overtone of the 0-H bondvibration in hydrogen peroxide vapour at 0.97p. The rotational structurefound for this band is of particular importance, since it appears to settlefinally the question as to whether the molecule has a planar or a non-planarstructure. In principle, the OH groups of hydrogen peroxide may be eitherin the cis- or the trans-position with respect to each other, or in some inter-mediate non-planar position.If the molecule is non-planar, the hinderingpotential towards internal rotation will have two minima of equal depth andtwo barriers of unequal height, and there will be two enantiomorphic forms.According to the height of the potential barrier, there will be free rotation,restricted rotation, or a, torsional oscillation. If the molecule had a cis-structure, the change in electric moment accompanying the 0-H link vibra-tion would be either entirely parallel or entirely perpendicular to the sym-metry axis. The band observed appears, in fact, to be double and to have apeculiar hybrid structure, with features characteristic of both the paralleland the perpendicular band types, thus implying that the structure is notcis-.The large dipole moment measured by E. P. Linton and 0. Maass 85shows, on the other hand, that it is not trans-. A non-planar structure istherefore the only alternative. At the same time the finer detail8 of therotational structure of the infra-red band show that the molecule is not quitea symmetrical rotator, as it would be if the azimuthal angle between thedirections of the two O-H bonds were go", since then two of the moments ofinertia would be equal. An azimuthal angle of about 106" is suggested, sothat the 0-H bonds are set obliquely to each other. These conclusions areespecially interesting in view of the earlier considerations of G. B. B. M.Sutherland and W. G. Penney.86E. H. Eyster87 has measured the third and fourth harmonics of thePIT-H stretching vibration in hydrazoic acid vapour, and the rotationalstructure of the bands shows that the molecule is not completely linear, ashas been suggested by some investigators.The bond lengths calculatedare N-H, 1-012 A. ; N,-N,, 1.241 A. ; N,-N,, 1.128 A. ; and the angle HNNis 110" 52'. Eands of methylamine vapour have been photographed byH. W. Thompson,88 one only showing resolved rotational structure charac-Aa4 J . Chem. Physics, 1941, 9, 458.g6 J . Chern. Phyeics, 1934, 8,492.88 Ibid., 1939, 7, 448.as Canadian J . Re&, 1932, 6, 81.Bid., 1940, 8, 136, 369TIfOMPSON : MOLEUULAR SPECTRA AND TECERMODYNBMICS. 57teristic of the perpendicular type vibration of a slightly asymmetrical rotator,and the rotational analysis gives results which agree with the molecularstructural constants to be expected on other grounds, vix., C-N, 1.47 A.;N-H, 1.02 A,; and CNH angle of 108" with a tetrahedral methyl group.This result has been confirmed by A?P. Cleaves, H. Sponer, and L. G. B ~ n n e r , ~ ~who also measured bands of dimethylamine.After much discussion the structure of ethylene appears now to have beenfixed by the measurement of two bands90 in the region of lp, one beingessentially parallel type, and the other perpendicular. Values for all themoments of inertia have been deduced, and the (3-H bond length beingassumed to be 1.085 A., it is found that the carbon-carbon bond length is1.331 A. and the angle HCH 118". These values have been confirmed by acompletely independent measurement of some in€ra-red bands by L.G. Smith.91The fourth harmonic of the 0-H vibration in formic acid vapour,measured by H. W. Thompson,92 has a hybrid structure in which the perpen-dicular component is very marked, similar to that of the third harmonicpreviously photographed by R. M. Badger and 8. H. B a ~ e r . ~ ~ Althoughexact figures for the molecular dimensions cannot be obtained, the structureof these bands gives a qualitative picture of the form of the molecule. Similarqualitative information is obtained from the structure of a band of formald-oxime vapour measured by L. Zumwalt and R. M. Badger.94 H. W. Thomp-son 95 has surveyed the absorption between 0.7 and 1 . 2 ~ of a residuum ofmolecules thought likely to have bands with resolvable rotational structure.W.H. J. Childs and H. A. Jahn 96 have measured the spectrum of deutero-methane in the photographic infra-red. A band a t 1-lp has a simple struc-ture, which leads to a C-€€ bond length of 1.093 A. These authors have alsodiscussed some complexities in certain bands of methane, one of which is oftheoretical significance for all molecules having a three-fold or higher axis ofsymmetry. Interesting features of the absorption by pyrrole vapour atabout 1p have been noted by Zumwalt andRecent infra-red work a t longer wave-lengths covers a wide field, and itis not possible to refer to all the subjects studied by measurement of themolecular absorption spectra in this region. The importance of the methodas a means of analysis is now being fully r e a l i ~ e d .~ ~ As a means of simplifyingvibrational analysis and the assignment of frequencies to particular normalmodes, the spectra of molecules and their deuterium analogues have beenemployed. In this way F. Stitt 99 has established the normal vibrationalAAJ . Ohem. Physics, 1940, 8, 784.J . Chem. Physk.8, 1941, 8, 798.go H. W. Thompson, Tran8. Paraday Soc., 1939, 35, 697.OS Ibid., 1936, 4, 469.90 Proc. Roy. SOL, 1939, A, 169, 428, 451 ; A , 1'71, 460.O P J . Chem. Phy~6~8, 1939, 7, 629.B2 Ibid., 1939, 7, 463.Ob Ibid., p. 441. O4 Ibid., 1939, 7, 235.See, e.g., N. Wright, Ind. Eng. Chem. (Anal.), 1941, 13, 1 ; W. K. Avery, J . Opt.SOC. Amer., 1941, 31, 633.@' J .C h n . Physia, 1939,7, 29768 GENERAL AND PHYSIUAL CHEMISTRY.frequencies of ethane and hexadeuteroethane, and of acetylene and thedeuteroacety1enes.l G. K. T. Conn and G . B. B. M. Sutherland2 havesimilarly studied tetradeuteroethylene and have cleared up some doubtfulpoints connected with the vibrations of ethylene.have analysed the rotational structure of some vibration bands of arsine,trideuteroarsine, and trideuterophosphine, and from the resulting dataSutherland, Lee, and Wu have estimated the dimensions of the molecularpyramid in each chse. In phosphine the barrier restricting the passage ofthe phosphorus atom through the plane of the hydrogen atoms is about2000 cm.-l (about 6 kg.-cals.), a value close to that previously suggested forammonia by D.M. Dennison and G. E. Uhlenbe~k.~ Calculations suggest,however, that in the case of phosphine the substitution of large massivegroups in place of the hydrogen atoms may give a molecule for which thefrequency of inversion is small enough to permit the separation of opticallyactive isomers at sufficiently low temperatures. A study of the spectra ofhydrogen selenide, deuterium selenide, and deuterium hydrogen selenide byD. M. Cameron, W. C. Sears, and H. H. Nielsen 6 has suggested a triangularstructure for these molecules with an apex angle somewhat greater than aright angle. In this work the correctness of the vibrational assignment waschecked by use of the product rules of 0. Redlich.' Structure of methylchloride infra-red bands has been used to re-determine the C-C1 bond1 eng t h .8High resolving power has also been used in measuring the infra-red bandsof other molecules. C.K. Wu and E. F. Barker9 partially resolved therotational structure of several absorption bands of propane, and R. G. Owensand E. F. Barker 10 obtained similar data for methylamine. The spectrumof the latter has been measured with lower resolution by C. R. Bailey,S. C. Carson, and E. F. Daly,ll and by A. P. Cleaves and E. K. Plyler,12but a satisfactory vibrational analysis was achieved only with the help ofthe rotational fine structure found by Owens and Barker.13 D. H. Gage andE. F. Barker l4 measured the vibrational spectrum of boron trifluoride andpartially resolved certain bands. An estimated moment of inertia gives1.29 A.for the B-P distance, but a considerable vibrational-rotational inter-action complicates the structure of some of the bands of this substance. Thegeneral problem of interaction between vibrational and rotational energy ofpolyatomic molecules has been examined by H. H. Nielsen, by S. Silver,W. H. Shaffer, and by Shaffer,15 and relevant effects in two parallel bands ofE. Lee and C. K. Wul J . C h . Physics, 1940, 8, 56.8 Trans. Faraday Soc., 1939, 35, 1366.6 Physical Rev., 1932, 41, 313.8 G. B. B. M. Sutherland, ibid., 1939,7, 1066.lL Proc. Roy. Soc., 1940, A , 173, 339.l9 LOC. cd., ref. (10).l6 H. H. Nielsen, Physical Rev., 1941,60, 794; S . Silver and W. H. Shaffer, J . Chem.Proc. Roy. SOC., 1939, A , 172, 172.Ibid., p.1373.J . Chem. Physics, 1939, 7, 994.2.physikal. Chem., 1935, B, 28, 371; J . Chem. Phy&, 1937.5, 529.Ibid., 1941, 9, 487. lo Ibid., 1940, 8, 229.la J . Chem. Physics, 1939,7, 563.I4 J . Chem. Physics, 1939, 7, 455.Physics, 1941, 9, 599; W. H. Shaffer, ibid., p. 607THOMPSON : MOLECULAR SPECTRA AND THERMODYNAMICS. 59ammonia have been described by H. Y. Sheng, E. F. Barker, and D. M. Denni-son.16 A. H. Nielsen measured rotational structure in some bands ofdeuteroacetylene,l' and H. H. Nielsen has re-examined certain absorptionbands of water vapour.l* L. G. Smith l9 used the rotational structure of aparallel type band of ethylene to deduce the moments of inertia, as referredto above. A Coriolis perturbation similar to that discussed by W.H. J. Childsand H. A. Jahn for methane bands has been observed and measured byG. M. Murphy 2o in the spectra of silane and germane.Some molecules which have been studied in order to determine the funda-mental vibration frequencies include cyanogen,21 nitromethane,22 pr~pylene,~~methylacetylene,= and dimethyla~etylene.~~ Absorption bands of hydrazoicacid vapour have been measured by M. M. DaviesJ26 and by EysterY2' whoalso examined methyl azide and methyl isocyanate. The spectrum ofhydrazine has been recorded by W. Fresenius and J. Karweil.28 The vibra-tion frequencies of ethylene sulphide have been determined by H. W.Thompson and D. J. D ~ p r t 5 , ~ ~ of dimethyl sulphide by R. Fonteyne 3O andby H. W. Thompson,3l and of methylthiol by H.W. Thompson and N. P.Skerrett.32 Other molecules investigated in this connexion include dimethylether,33 dimethylzinc J34 eth~leneimine,~~ a~etaldehyde,~~ and several hydro-carbons such as n-pentane.37J. J. Fox and A. E. Martin 38 have examined the variation in the char-acteristic vibration bands of the C-H bond in the region of 3p in a series ofparafKns and olefins. The characteristic frequencies of this bond differslightly according to the precise group of which it forms a part, but theyseem to remain reasonably constant for a given type of C-H bond in a largeseries of molecules. Similarly, in cc- and p-methylnaphthalenes, quinolineand isoquinoline, and similar molecules, small differences are traced in theregion of absorption of C-H bond vibrations which appear to provide a basisfor the analysis of these compounds.39 Infra-red studies on the proteins andrelated substances continue$O and the effect of state of aggregation uponl6 Physical Rev., 1941, 60, 786.l8 Ibid., 1940, 50, 665.2o Ibid., 1940, 8, 71.22 A.J. Wells and E . B. Wilson, ibid., 1941, 9, 314.23 E. B. Wilson and A. J. Wells, ibid., p. 319.24 B. L. Crawford, ibid., 1939, 7, 140; 1940, 8, 526.25 Idem, ibid., 1939, 7, 553.27 J . Chem. Physics, 1940, 8, 369.29 Trans. Farccday Soc., 1940, 36, 805.31 Trans. Paraday Soc., 1941, 37, 38.33 B. L. Crawford and L. Joyce, J . Chem. Physics, 1939,7,307.34 H. W. Thompson, J. W. Linnett, and F. J. Wagstaffe, Trans. Faraday Soc., 1940,35 H. W. Thompson and W.G. Leeds, ibid., in the press,36 H. W. Thompson and G. P. Harris, ibid., in the press.37 G. C. Stinchcomb, J . Chern. Physics, 1939,7, 853.38 Proc. Roy. SOC., 1939, A, 175, 208.40 J. W. Bath and J. Ellis, J . Physical Chem., 1941, 45, 204; A. M. Buswell, K. F.l7 Ibid., 1940, 57, 346.l9 J . Chem. Physics, 1941, 9, 798.21 Ibid., 1939, 7 , 859.26 Trans. Faraday SOC., 1939, 35, 1184.28 2. physikal. Chem., 1940, B, 44, 1.30 J . Chem. Physics, 1940,8, 60.32 Ibid., 1940, 36, 812.36, 797.39 J., 1939, 318.Brebs, end W. H. Rodebush, J . Chem. Physics, 1940, 8, 112660 GENERAL AND PHYSIOAL UHEMISTBY.infra-red absorption bands has been e~amined.~l Fox and Martin42 havemeasured the spectra of both liquid water and ice and discussed their resultsin relation to the structure of liquid water.On the theoretical side referencemust be made to a further article by D. M. Dennison on the infra-red spectraof polyatomic molecules.*3Of the many measurements of Raman spectra recently made, only a fewcan be mentioned here. Apparatus is described by J. S. Kirby-Smith andL. G. Bonner 44 for obtaining the Raman displacements with gases, usingreasonable exposure times, and these authors have first studied methylaminevapour. The fine structure of Raman lines of carbon tetrachloride has beenmeasured by A. C . Men~ies,4~ and found to be consistent with an explanationin terms of chlorine isotopy, and also with the abundance ratio to be expected.The carbon isotope shifts have been calculated for a series of acetyleniccompounds by F.F. Cleveland and M. T. Murray,46 and compared withexperimental data.A particularly interesting series of Raman measurements has been carriedout by G. Glockler 47 and his collaborators for the halogenated methanes.The alteration in the observed displacements as the substituents are changedone by one is valuable in assigning the magnitudes to different vibrationalmodes, and these data should prove valuable for the calculation of forceconstants and force fields for this type of molecule. Another series ofmolecules whose Raman spectra have proved interesting is a group of metallicand non-metallic a l k y l ~ . ~ ~ The displacements observed with octane, decane,and higher hydrocarbons are complex and not easily interpreted.49Potential Energy Functions, Force Constank, and General Xtructurd.Relationships.-The importance of force constants as a measure of the natureand strengths of linkages has been referred to in previous Reports, in whichthe principles underlying these calculations and the approximations necessaryhave been explained.60 Serious discrepancies were noticed, however, in someof the earlier computations by different workers for the same molecules.Itis clear that the exact significance of the magnitudes described as forceconstants depends upon the particular potential energy function used todescribe the molecular vibrations. Several types of function have from timeto time been adopted, the most common being that which assumes forcesconsistent with the idea of conventional valency bonds, and known asvalency force field.Internal molecular interactions, however, which are41 See, e.g., W. West, J . Chem. Phy8iics, 1939, 7 , 795; G. B. B. M. Sutherland et al.,Proc. Roy. SOC., 1941, A , 176, 484, 493.Ibid., 1940, A , 174, 234.p3 Rev. Mod. Physics, 1940, 12, 175; 1931, 3, 280." J. Chem. PhySii28, 1939, 7, 880.46 Proc. Roy. SOC., 1939, A , 172, 89.47 G. Glockler and G. R. Leader, ibid., 1940, 8, 125, 699; G. Glockler and C. Sage,ibd., p. 291 ; J. Kahovec and J. Wagner, 2. physikal. Chem., 1940, B, 47,48; B, 48,188. '* E. J. Rosenbaum, D. J. Rubin, and C. R. Sandberg, J . Chem. Physics, 1940,8,366.40 E . J. Rosenbaum, ibid., 1941, 0, 295.llQ Ann. Reports, 1936, 88, 69.46 J .Chem. Physics, 1941, 9, 390THOMPSON : MOLEUUIXR SPEUTRA AND !CHERXODYNAMIOS. 61to a large extent specific, make this simple type of force field seldom rigidlyapplicable, although in some cases an apparently satisfactory solution isobtained, perhaps by a fortuitous cancellation of a series of inaccuracies. Itis customary to find that a simple potential function of this type fails toaccount satisfactorily for the entire array of frequencies of a molecule.More complex functions must therefore be assumed, and tested by theirindividual performance. In some cases the number of “ constants ” whichhave to be introduced in order to obtain a complete prediction of all vibrationfrequencies for a, given molecule may exceed the actual number of these fre-quencies.In such cases the reverse procedure of estimating the “con-stants ” from the measured frequencies is usually not possible, unless addi-tional vibration frequencies of an isotopic molecule which has the samepotential function are available. It has been suggested, in fact, that thecorrectness of a given potential function may be measured by its ability toreproduce, not only the vibration frequencies of the molecule to which itapplies, but also those of an isotopic molecule of the same composition.This use of the isotope effect is particularly applicable to structures inwhich hydrogen may be replaced by deuterium, and several cases of thiskind have now been examined. Por example, F. Stitt obtained a self-consistent potential energy function for ethane and he~adeuteroethane,~~which accounts very well for all the fundamentals of these molecules.Stittalso studied acetylene and the deuteroacetylenes in the same way. Measure-ment of some of the infra-red bands of tetradeuteroethylene enabled G. K. T.Conn and G. B. B. M. Sutherland 52 to compare the rglative merits of differentpotential functions which have been proposed for ethylene.It cannot be denied that the above method is a powerful one, but thenumber of molecules to which it can be applied in practice is small, sinceisotopic frequency changes are in general too small to be easily determinable.Another approach which has seemed attractive is to add to the conventionalpotential functions of simple valency force field such interaction terms asseem likely to be significant in the particular case, and to consider whetherin a series of related molecules force constants can be carried over from onemolecule to the next and predict its vibration frequencies correctly. Thismethod was used some years ago by H.W. Thompson and J. W. Linnett 63and has since been adopted with success by several authors. In this wayLinnett6* calculated the force constants of bonds in ethane, the methyl halides,methyl cyanide and isocyanide, and concluded that in methyl cyanide thecarbon-carbon bond has some double-bond character, as suggested on othergrounds by L. Pauling, H. D. Springall, and K. J. Palmer.65 Interesting vari-ations in the bending constantswere also noted by Linnett. Z. I.Slawsky andD. M. Dennison’s treatment 66 of the same molecules does not appear to be sosatisfactory. B. L. Crawford and S. R. Brinckley 57 have also given a61 J . Chem. Physics, 1939, 7, 297; 1940, 8, 56.64 J . Chem. Physics, 1940, 8, 91.66 J. Chern. Physics, 1939, 7, 622.Proa. Roy. SOC., 1939, A , 172, 172. 63 J . , 1937, 1376.5 5 J . Amer. Chem. Soc., 1939, 61, 927.6 7 Ibid., 1941, 9, 6962 QENERAL AND PHYSICAL CHEMISTRY.normal co-ordinate treatment of hydrogen cyanide, methyl cyanide, and themethyl halides which is closely similar to that of Linnett. They are able tocalculate satisfactorily 52 vibration frequencies of this series of moleculesfrom potential functions involving only 20 constants, and the main stretchingconstants of the bonds can be carried over from one molecule for use with thenext.In a later paper, Linnett 58 has shown, however, that Crawford andBrinckley have used a carbon-carbon bond force constant which is probablyin error, and has discussed a simple potential function not only for use withthe methyl halides but also for methyl- and dimethyl-acetylene, which werepreviously treated by C r a ~ f o r d . ~ ~ Ta You Wu 60 has also considered thepotential function of acetylene, and it is perhaps relevant here to refer to animportant paper by E. C. Baughan, M. G. Evans, and M. Polanyi on thenature of carbon-carbon linkages.Other normal co-ordinate treatments have been carried out by S. Silverfor structures of the type M(CH,),, by E. J. Rosenbaum, D. J. Rubin, andC.R. Sandberg 63 for trimethyl-phosphine and -arsine (and by J. Wagner 64for the methylene halides); and S. E. Whitcomb, H. H. Nielsen, andL. H. Thomas 65 have analysed the vibrations of a normal hydrocarbon chainwith particular reference to undecane. L. Kellner 66 has carried through anextensive calculation on the force constants of links in urea and the guani-donium ion, but in a case of this kind it is doubtful whether the simple treat-ment used can be of much value, particularly in view of the uncertainexperimental data.The technique of the calculations involved in determining force constantshas been further examined by E. B. Wilson, and simpler methods of dealingwith the complex secular equations usually encountered have been suggestedby B.J. 0. Hirschfelder 68 has provided a compact formula bywhich the moments of inertia of irregular structures may be rapidly calculated.0. Redlich 69 studied the effect of vibrational anharmonicity on the potentialfunction of polyatomic molecules.All the above remarks imply the importance for chemical theory ofknowing the potential functions of polyatomic molecules. Meanwhile acompletely satisfactory general expression for the variation of potentialenergy of a diatomic molecule with internuclear separation is not yet known.The limitations of using the Morse equation for nuclear separations far re-moved from the stable position have been realised for some time, and effortsto obtain a better relationship have been made by H. M. Hulbert and J. 0.Trans. Paraday Soc., 1941, 37, 469.69 J. Chern. Physics, 1939, 7, 140, 553; 1940,8, 526.6o Ibid., 1939, 7, 178; 1940, 8, 489.e2 J. Chem. Physics, 1941, 8, 919.G4 2. physikul. Chem., 1939, €3, 45, 69.G 5 J. Chern. Physics, 1940, 8, 143.6 6 Proc. Roy. Xoc., 1941, A, 177, 447, 456.67 E. B. Wilson, J. Chem. Physics, 1941, 9, 76; 1939, 7, 1047; B. Hicks, ibid., 1940,68 Ibid., p. 431. 69 Ibid., 1941, 9, 298.Xruns. Paraday SOC., 1941, 37, 377.63 Ibid., 1940, 8, 366.8, 569THOMPSON : MOLECULAR SPECTRA AND THERMODYNAMICS. 63Hirschfelder ' 0 and by J. W. Linnett.71 The last-named has examined theusefulness of a " reciprocal-exponential " function U = a r m - be-"', whichincorporates features of both the standard Morse equation and the generaldouble reciprocal formula U = a?+ - br-9a. G. B. B. M. Sutherland 72 hasrecently used the double reciprocal function in attempting a derivation of therelation between force constant and equilibrium nuclear separation. Linnetthas drawn attention to the shortcomings in Sutherland's treatment, andprovides evidence on a wide variety of diatomic molecules to show that thereciprocal-exponential function is an improvement on other existing relation-ships. Incidentally, there is some indication that the relationship betweenforce constant and nuclear separation Eer,6 = const. ? originally proposed byC. H. D. Clark, is more satisfactory than the Badger equation (re - dij)3 =C,/lc,, which has been found so useful in much recent work. In a furtherseries of papers, Clark 73 has developed his formuke further and comparedthe relative merits of the various relationships.J. J. Fox and A. E. Martin 74 have also directed attention to some inter-esting relationships between force constant? bond length, and energy of somecarbon-carbon bonds. A typical instance of the use of these semi-empiricalrelationships is found in the use by D. P. Stevenson '5 of Badger's rule todetermine the P-H bond length in phosphine (1.40 A.) which, taken with thesingle moment of inertia obtained from the spectrum, leads to a value of theapex bond angles close to 93". Stevenson also considered the structure ofother hydrides. The connexion between bond length and bond strengthhas also been discussed by R. F. Barrow,76 D. Wrinch and D. Harker,77M. Burt0n,~8 and C. A. C o ~ l s o n . ~ ~Miscellaneous Xpectrosmpy.-Recent developments in ultra-violet spectro-scopy include diverse topics, but these must be reserved for a future Report.Attention may be directed, however, to a review by H. Sponer and E. Teller 80on the ultra-violet spectra of polyatomic molecules, and some progress hasbeen made in analysing the rotational structure of some of the bands.N. Metropolis 81 has considered the relevant theory for this rotationalstructure, which has been analysed for bands of sulphur dioxide and carbon di-sulphide.82 Spectroscopy in the far ultra-violet is described by J. C. Boyce,83and the rBle of optical measurements in the borderland of physical chemistryand biology has been outlined by J. R. Loofbourow.%The Hydrogen Bond.-Progress in this subject has been reviewed fullyin a recent discus~ion.~~ In this, W. T. Astbury has outlined the evidence70 J . Chem. Physics, 1941, 9,61. 71 Trans. Faraday SOC., 1940, 36, 1123.7a J. Chem. Physics, 1940, 8, 161.75 Trans. Paraday SOC., 1940, 36, 370; 1941, 37, 293, 299.74 J., 1939, 884.76 Trans. B'araday SOC., 1940,36, 624, 1053.78 Ibid., p. 743.82 Ibid., pp. 295, 496.a4 Ibid., 1940, 12, 272.T 5 J . Chern. Physics, 1940, 8, 285.7 7 J . Chern. Physics, 1940,8, 602.79 Ibid., 1939, 7, 1069.Physical Rev., 1941, 60, 283.83 Rev. Mod. Physics, 1941, IS, 1.Rev. Mod. Physics, 1941, 13, 75.Trans. Paraday SOC., 1940, 30, 871-92864 UENERAL AND PHYS1gA.L UHEMISTRP.for the existence of hydrogen bridges in proteins, and C. E. H. Bawn, E. L.Hirst, and E. T. Young have concluded that some properties of starch areconsistent with the union of macromolecules with each other through thistype of link to form particles. G. B. B. M. Sutherland has summarised theapplication of infra-red spectroscopy to the problem, and J. J. Fox and A. E.Martin from a similar standpoint have given data, on the specific cases ofassociation of alcohols, and carboxylic acids, and internally chelated mole-cules. In the same symposium, J. M. Robertson has discussed the X-rayevidence for hydrogen bonds, and W. R. Angus and W. K. Hill have describedpreliminary work on diamagnetic susceptibilities (see this vol., p. 29) whichappear to be capable of revealing the occurrence of this phenomenon.Models for proteins involving hydrogen bonds have also been consideredby M. L. Huggins,86 and a series of papers deal with the associating propertiesof different solvents.87 The infra-red association bands of several hydroxy-compounds in solution and in the solid state have been examined by M. M.Davies,8* and polymerisation of hydrogen fluoride has been measured byA. Wahrhaftig 89 and by A. M. Buswell, R. L. Maycock, and W. H. Rodebush.90R. Mecke and his co-workers 91 have developed a new technique for studyingthe association bands of alcohols in the photographic infra-red and havemade calculations on the equilibrium relationships of the association. Aconsideration of boiling points and other physical properties, such as solu-bility in donor solvents, of a variety of pyrazole and indazole derivativescontaining the imino-group has led to the suggestion that there is a bond ofthe type N-H-N in these molecules.92H. W. T.W. R. haws.H. W. MELVILLE.R. A. MORTON.H. W. THONPSON.8@ J . Chem. Physics, 1940, 8, 598.See, e.g., W. Gordy et at,, J. Chem. Physica, 1939, 7 , 93, 99, 163, 167; 1940,8, 170,516; 1941, 9, 204, 216; J. Amer. Chem. SOC., 1940, 62, 497, 1247; E. S. Barr andG. J. Craven, J. Chern. Physics, 1939, 7, 8.Ibid., 1940, 8, 677; Trans. Faraday Soc., 1940, 36, 333, 1114.89 J . Chem. Physics, 1940, 8, 349. So Ibid., 1939, 7, 857.O1 2. physikal. Chern., 1939, B, 44, 299; 1940, B, 46, 229; B, 40, 309; see also0. Wulf and E. J. Jones, J . Chem. Physics, 1940, 8, 745, 753; and L. Zumwalt andR. M. Badger, J . Amer. Chem. SOC., 1940, 62, 305.ga H. T. Hayes and L. Hunter, J., 1941, 3