COLOUR AND CONSTITUTION By A. MACUOLL M.Sc. (I.C.I. RESEARCH FELLOW UNIVERSITY OF LONDON) 1. Introduction THE birth of the organic dye industry with the discovery of mauve by Perkin in 1856 made possible attempts at the correlation of the colour of an organic compound with its chemibal constitution. The first observation was made by C. Graebe and C. Liebermam twelve years later. These writers pointed out that all the coloured compounds known a t that time became colourless on reduction. Their conclusion was that the colour of a compound was in some way due to a close linking between the C 0 rand N atoms contained in it. 0. N. Witt in 1876 introduced the con- ceptions that have formed the basis of all subsequent theories. According to his theory before colour can appear in a compound two conditions have to be satisfied.First the molecule must possess a potentiality for colour ; secondly there must be a salt-forming group present for developing the colour potentiality. A group of atoms possessing the potentiality for colour is known as a chromophose the molecule containing it being a chromogen. The group responsible for developing the colour is known as an auxochrome. Typical chromophores are -NO -NO, -N=N- C=C and C=O and auxochromic groups are represented by -OH -NH, -NHR and -NR,. Some chromogens are themselves coloured for example nitrosobenzene (I) fulvene (11) and diacetyl (111). But it is of NO CH2 I ti 0 A nil 0 0 II I1 CH3-C-C-CH3 (1.) (11.) (111.) interest to note that none of the chromogens possesses dyeing properties. Thus Witt’s concept of the function of an auxochrome was not only to develop the colour latent in the chromogen but also to develop its dyeing propensities.H. E. Armstrong in 1888 advanced the view that many organic dyes either contained the quinonoid grouping or could be modified in such a manner as to contain it. This view was probably arrived at from a con- sideration of the recently discovered phenomenon of tautomerism. That the quinonoid theory was not sufficient to account for all the facts is seen 1 An excellent account of the development of dolour theory up to 1918 is to be found in Watson’s ‘‘ Colour in Relation to Chemical Constitution,” Longmans Green & Co. London 1918. Ber. 1868 1 106. Ibid. 1876 9 552. Proc. 1885 4 37. 16 MSCCOLL COLOUR -4ND CONSTITUTION 17 from a consideration of iminoquinone (IV) and di-iminoquinone (V) both (IV.) of which possess the quinonoid structure but are colourless.Then again a number of coloured substances are known to which a quinonoid structure cannot possibly be assigned. However the quinonoid theory was of great importance both because of the impetus it gave to experimental work and because of its practical application in the hands of dye chemists. In attempting to correlate the data on the triphenylmethane dyes R. Nietzki in 1879 postulated that the colour of a dye may be deepened by adding groups so as to increase t'he molecular weight the deepening being roughly proportional to the increase in molecular weight. M. Schutze 6 in 1892 subjected this rule to a careful scrutiny and was able to point out many exceptions. He was able to show that the chemical nature of the added group was of importance and introduced the terms bathychromic and hypsochromic.The former refers to a group the addition of which t o a molecule gives rise to a deepening of the colour the latter referring to a group which has the opposite effect. The term deptlh of colour will be defined later. Although the colour of organic compounds is one of their most striking properties yet it was realised early in this century that it is unsatisfactory to attempt t o base a theory of colour merely upon visual observation. The human eye is only sensitive to the spectral region from about 4000 A. t o 7500 A. and this physiological fact places a severe limitation upon the range of observation. The recognition that the ultra-violet region is merely a continuation of the visible made possible an explanation as to how an apparently small change of structure might convert colourless substance into a yellow one.This view was well expressed in the Annual Reports for 1907 " It is now generally recognised that a more precise meaning must be given to the idea of colour than has often been the caee. The production of physiological colour due to the occurrence of absorption in the visible spectrum is more or less an accidental circumstance. Absorption bands may occur in the ultra-violet of equal importance with those in the visible spectrum. I n some cases a change in the frequency of the absorbed rays may cause a band to move from the ultra-violet into the visible region without any change of form. A colourless substance may therefore be converted into a coloured one without any real change in constitution having taken place.. . . The quantitative study of the absorbing power of a substance . . . makes an exact comparison of Merent derivatives possible and relationships are made evident which would escape notice if the ex- amination were confined to visual observation of colour. '' This realisation of the importance of objective measurements of colour enabled the basis of the physicochemicsl theory of colour to be laid. However this theory 6 Verhandl. Vereins Bef6rd. Gewerbefleisses 1879 58 231. 2. physikal. Chem. 1892 9 109. B 18 QUARTERLY R;ICVIEWS is dependent upon quantum concepts and did not develop until some thirty years later. The colour of an organic compound is due to its having one or more absorption bands in the visible region of the spectrum.The relationship between the wave-length of the absorbed light and the colour of a compound is shown in Table I. This table is strictly only applicable to a substance TABLE I Absorption Wave-length and C o h ~ Wave-length A. 4000-4350 4350-4800 4800-4900 4900-5000 5000-5600 5600-5800 5800-5950 5950-6050 6050-7500 Colour absorbed. violet blue green-blue blue-green green yellow-green yellow orange red yellow-green yellow orange red violet blue green-blue blue-green Purple which has a single narrow absorption band between 4000 and 7500 A. High intensity of absorption often implies a wide absorption band which may invalidate conclusions drawn from the table. Also colour is a subjective phenomenon. I n view of these complications the desirability of representing the colour of a compound by an objective method becomes obvious.The term depth of colour which has been used in a number of senses may now be defined. I n the following one substance will be said to have a deeper colour than another if the wave-length of maximum absorption is greater for the former than the latter. As the absorption moves towards the red the colour is said to deepen. He noted that the introduction of an amino-group into fuchsonimine (VI) to give Doebner’s violet (VII) led to the development of colour and he attributed An important observation was made by A. Baeyer in 1907. ’ A m d e n 1907 354 162. MAccOI& COLOUR AND CONS!lXTUTION 19 this to an oscillation of the quinonoid condition between the two benzene nuclei. However here again not all coloured compounds could be classified as of this type.R. Willstattm,e as a result of his observations on the quinhydrones came to a similar conclusion namely that colour is due to an oscillation by which two benzene nuclei alternately become quinonoid. Following investigations on the colour of azo-compounds J. T. Hewitt and H. V. Mitchell in 1907 concluded that the colour of a substance is deeper the longer the conjugated chain. This view was modified in 1916 by A. C. Sircar,l* who suggested that the important factor was the length of the conjugated chain in the part of the molecule containing the auxo- chrome. In 1913 E. R. Watson 11 propounded the view that dye molecules. which are quinonoid in all possible modifications will have a deep colour Thus indamine (VIII) is blue while 4 4’-diaminoazobenzene (IX) is yellow.Two years later E. R. Watson and D. B. Bleek l2 suggested that the col’oa is deeper the longer the conjugated chain reversed in the tautomeric change. These authors were led to distinguish two cases. The first was that in which the substance was ionised and the oscillation consisted merely “ in a rhythmic rearrangement of strain within the molecule,” which wag responsible for the deeper and more intense colour ; thus for Michler’s hydro1 (X) the oscillation was represented by. The second case was concerned with hydrogen atom tautomerism. Another phase of colour theory WM initiated in 1910 by P. Pfeiffer,ls who from a study of free aryl radicals concluded that the tervalent carbon atom was the essential chromophore. W. Dilthey lP in 1920 went further and regarded chromophoric properties as being associated with atoma rather than with groups of atoms as Witt had postulated.The roots of chromo- phoric activity in atoms lay in their “ co-ordinative unsaturation.” Thus while the carbon atoms in diamond or in a paraffin have all their valencies satisfied in ethylene benzene and graphite this is not so. Thus the carbon atoms in the latter substances can act as chromophores. Similarly in the triphenylmethyl cation (XI) the carbon atom marked with a dot (in Dilthey’a Ber. 1908 41 1458 3245. J. 1907 91 1251. lo J. 1916 109 757. l 1 Proc. 1913 29 348; J . 1914 105 759 l * J . 1915 107 1567. l 3 Annalen 1910 376 292. l4 Ber. 1920 53 261. 20 QUARTERLY REVIEWS nomenclature) possemea chromophoric activity. Dilthey also observed that in non-polar compounds chromophoric activity ie often weak but becomes strengthened on conversion into an ionic form.(XI.) R. K. Wizinger l6 in 1926-27 emphasised the fact that the action of auxochromes was most observable in kationic chromogens. This led t b the concept of anti-auxochromes which function in the opposite sense to the auxochrome in that they behave in an anion in the same way as do auxochromes in a cation. Such anti-auxochromes are -NO -NO, -N=N- and >C=O. ,The colour of electrically neutral molecules in the Dilthey-Wizinger theory is due to the presence of an intramolecular ionoid state between auxochrome and anti-auxochrome. In the case of p-nitro-p’-methoxystilbene (XI) the chromophore auxochrome and anti-auxochrome are respectively the >C=C< -OMe and -NO groups.- L M~o-~-cH=cH-C-)-NO (XII.) J. Stieglitz l6 approached the problem of colour from the viewpoint of oxidation-reduction. Reduction of a dye as noticed by Graebe and Liebermann usually destroys its colour while gentle oxidation will restore it. Strong oxidation on the other hand may completely destroy it. The concept of a dye being in an intermediate state of oxidation led Stieglitz to identify chromophores and auxochromes with groups capable of oxidation and reduction respectively. The colour of a compound is then due to a type of intramoleculaT oxidation-reduction. The importance of the intensity as well as the wave-length of maximum absorption was emphasised by N. Q . Chak0.l’ He pointed out that a number of the bands which were responsible for the colours of organic compounds were relatively weak and by applying the classical theory of the light absorption process he was able to calculate a fundamental measure of the intensity of absorption in the so-called oscillator strength.Some interesting relationships between the oscillator strength and structure of related compounds emerged although no readily interpretable dependence of band width the other constant of the classical theory and structure came out. l5 “ Organische Farbstoffe,” Ferd. Dummlers Verlag Berlin u. Bonn 1933. 16 Proc. Nut. Acad. Sci. 1923 9 303. 17 J . Chern. Physics 1934 2 644. MACCOLL COLOUR AND CONSTITUTION 21 The development of quantum mechanics in the years following 1926 made possible a more detailed theory of colour in terms of molecular energy levels.C. R. Bury l* suggested that the basis of the colour of an organic compound might lie in the quantum-mechanical resonance phenomenon and he was able to translate many of the older ideas on colour into modern terms. Thus Baeyer had postulated that the colour of Doebner’s violet was due to an oscillation between (XIII) and (XIV) whereas Bury pointed NH,CI=<=)=CC>-NH + I - Ph (X1II.I Ph (XIV.) out that the oscillation was only structural resonance theory providing a mechanism for the “rhythmic rearrangement ” suggested by Watson and Meek. The function of the auxochrome then was to realise the ~H,-/-)=C(T>-NH 1- + NH2-C)-P={=>=&H2 - Ph Ph possibility of resonance. The same type of mechanism holds for the case of acidic dyes such as benzaurin (XV). However Bury was at a lorn to Ph Ph (XV.) provide the mechanism for neutral dyes like indigo (XVI).I1 II 0 0 (XVI.) + NH NH I1 0 I 0- (XVII.) Before 1937 quantum-mechanical calculations had aimed a t determin- ing the energy of the ground state of a molecule and thus its resonance energy. However in that year A. L. Sklar l9 realised the importance of the excited states of a molecule for the light-absorption process and was able to calculate the absorption bands of a number of unsaturated hydro- 18 J . A m r . .Chem. SOC. 1935 57 2115. J . Chem. Phyeice 1937 5 669. 22 QUARTERLY REVIEWS carbons. In the next year this work was extended by Th. Forster.20 The attack on the quantum-mechanical problem of the colour of dyes was sketched out by L. Pauling 21 in 1939. As well as outlining the general solution of the acid and basic dyes problem Pauling was able to account qualitatively for the absorption bands of neutral dyes such as indigo in terms of resonance between the classical valency structures and dipolar structures of higher energy such as (XVII).This problem was also con- sidered by F. Arndt and B. Eistert.22 Since 1939 this work has been followed up by R. S. Mulliken Th. Forster A. L. Sklar K. F. Herzfeld and others. It is of interest to note that whereas the older theories were concerned with complex molecules and were inadequate to deal with simple systems quantum mechanics has reversed this position and having started with the simple systems is now developing methods of attack for the more complex. G. N. Lewis and M. Calvin 23 in 1939 set out “ t o re-examine the data of light absorption and to see whether by applying the more inductive methods of chemistry together with such general results of quantum theory as are applicable to all systems we may obtain a better understanding of the data.Starting with the idea that in the absorption of light the energy is taken up by electronic oscillations we have considered these oscillations as analogous to classical oscillations but subjected to the rules of simple quantisation.” This quasi-classical theory has correlated a great deal of data and has stimulated some extremely interesting experimental investigations. From this point this article will be primarily concerned with a more careful scrutiny of the development of the theory of colour that has taken place in the last decade or so. 2. The Clmsical Theory of Light Absorption 24 The classical theory of the interaction of light with matter due to Drude is based upon Maxwell’s electromagnetic theory and the concept of electrons.The former theory shows that a beam of light may be con- sidered as consisting of transverse waves the oscillating entities being the electric vector E and the magnetic vector H these two vectors being per- pendicular to each other and t o the direction of propagation. The plane through the electric vector and the direction of propagation is known as the plane of polarisation. Explicit solution of Maxwell’s wave equation shows that a plane monochromatic wave of frequency Y travelling in the z direction in a medium of refractive index a and polarised in the x direction is given by E = S,~~IZ~V(~-UZ/C) H = j ~ y e 2 n i r 3 ( t - ~ ~ / ~ ) .. (2.1) ao 2. physikal. Chem. 1938 B 41 287. e a Ber. 1939 72 202 860. a 4 (a) The treatment of this section closely follows that of Chako (ref. 17). a1 Proc. Nat. Acad. Sci. 1939 25 577. 23 Chenz. Reviews 1939 25 273. Com- pare also ( b ) Th. Forstor 2. Elektrochem. 1939 45 551 ; (c) R. A. Morton Ann. Reports 1941 38 7 ; ( d ) R. S . Mulliken and C. A. Rieke Rep. Prog. P h y s k 1941 8 231. MACCOLL COLOUR AND CONSTITUTION 23 where i and j are unit vectors along the x and y axes and c is the velocity of the waves in @ vacuum. In order to investigate the interaction of radiation with matter some hypothesis as to the structure of matter has to be made. It is satisfactory for the present purpose to assume that in a gaseous medium containing N molecules per C.C.each molecule containsjj electrons bound by an elastic force to an equilibrium position and having a frequency of oscillation vj. The electric force acting on a given electron in the molecule is the product of the electric vector and the charge e of the electron. It can be shown that the magnetic force is negligible. The oscillating electric field of the light wave will cause forced vibrations of the electrons the equations of motion of the latter being of the form where w = 2nv wj = 2nvi ; vj is the proper frequency of the electron and is determined by the elastic force binding the electron to its equilibrium position. A solution of (2.2) together with the solution of Maxwell's equations suffices to evaluate a the refractive index usually represented by n.The result is mh + w;mz = eE&W(t-uZ/c) . (2.2) an equation in accord with the experimental results. It can be seen that for w <aj the refractive index increases with the frequency of the light a phenomenon known as normal dispersion. If the frequency of the light coincides with one of the electronic proper frequencies the refractive index becomes infinite. The analysis may however be carried through if it is assumed that the electrons are subject to a " damping force," proportional to their velocities. The eqhation of motion then becomes mx + mgjx + dmx = eE,&w(t-44 . . (2.4) The refractive index may be determined by the same procedure as before and is given by aa = + T & a - 0 2 3 + ~ i w * . (2.5) Thus the motion of the light wave in the medium is governed by a complex refractive index.Writing a = n(1 - i ~ ) . . (2.6) and separating real and imaginary parts we have 4nezN' 3 . (2.8) The refractive index thus shows a marked change in the neighbourhood of an electronic proper frequency. If it is assumed that there is a single 24 QUrnTERLY BEVIEWS electronic freqnency then (2.7) shows as the frequency of the light approaches that of the electron the refractive index increases until a maximum is reached after which it begins to decrease reaching a minimum when it again increases. The existence of more than one electronic frequency will complicate this phenomenon which is known as anomdous dispersion. To interpret K the ratio of the energy of the wave after having traverqd a distance x in the medium to its value on entering the medium has to be determined.This treatment leads to I = Ioeb-/c . . (2.9) where I, and I are the entrant and emergent intensities. While this law has been derived for the gaseous state most of the relevant data refer to solutions. For this reason (2.9) wil’l be written in a form appropriate to solutions and the corrections which are necessitated by this procedure will be discussed later. Thus since K is proportional to N’ (2.9) mcby be expressed as I IQO-E’Cd * . (2.10) E’ being a new constant c being the concentration of the medium and d the distance through which the light has travelled. Formula (2.10) combines Beer’s and Lambert’s laws and has received experimental confirmation. By the um of (2.8) (2.9) and (2.10) the following expression is obtained for E’ ( 2 . i l ) where yj = gj/2n and N is Avogadro’s number.F’rom (2.11) it follows that if Y is markedly different from v, E’ is essentially zero. The curve of E’ against v is bell-shaped E’ reaching a maximum at Y = vj. The substance is said to have an absorption band at vj. The integrated intensity over the whole band may be obtained in the following way. If the band in question is a weak one removed from the strong bands that are responsible for dispersion then its contribution to n may be neglected and for n may be written the value due to all other bands at Y. In addition if the band is sufficiently narrow it can be shown that neaN x 10-5 cmn d.dv = (2.12) Up to the present it has been assumed that the absorbing substance is in the gaseous state. To test the effect of a solvent which does not absorb in the region in question the Lorentz-Lorenz forces acting on the absorbing molecule due to the polarisation of surrounding molecules have to be taken into account.e’.dV = . C17t . ( L ) j j 9n Q - . (2.13) This treatment leads to nelN x 10-3 (na 4- 2)’ I MACCOLL COLOUR AND CONSTITUTION 25 for a dilute solution no being the refractive index of the solvent at fre- quency Y . This constitutes a correction to the integrated intensity as measured in solution t o give the vdue for the gaseous state. Chako haa tabulated fi 5 and also f” which is obtained from (2.12) by setting n = 1. With regard to the solvent correction Chako came to the conclusion “ that it is impossible t o account for the influence of the solvent through the Lorentz-Lorenz forces.” This problem of solvent correction has also been considered by R.S. M ~ l l i k e n . ~ * ~ Some interesting data which throw light on this question have been recorded by V. Henri and L. W. Pickett 25 for cyclohexadiene and by L. W. Pickett E. Paddock and E. Sackter *6 for cyclopentadiene. For cyclohexadiene the vapour and the solution values agreed very well but for cyclopentadiene the integrated absorption was about 20% higher for the vapour than for the solution. This effect is the opposite t o that which would be predicted from a consideration of the Lorentz-Lorenz forces On such grounds as these Mulliken concluded that in the absence of empirical data as to the ratio of vapour to solution intensity the best procedure is t o neglect the correction given by (2.13) and to assume n = 1 which would be true for the substance in the gaseous state.The importance of the correction of f values derived from measurements in solution t o f values for the gaseous state lies in the fact that the latter quantities may be calculated by quantum-mechanical methods as will be shown in Section 3. - From (2.11) it follows that I 2e2N x 1 0 - 3 fj (n = 1) CmYi E max. = or by using (2.12) (2.14) If y is constant throughout the band dv = 2yj . . (2.16) where dv is the distance between the points at which E’ = 1 / 2 ~ ’ ~ ~ ~ . . The “ damping constant ” y is equal to the half-width of the band. Both (2.15) and (2.16) were used by Chako to evaluate yj. However no readily interpretable relationship was found between y j and the chemical constitution of the substance or the nature of the solvent. Equation (2.14) allows an estimate to be made of the magnitude of For if it is assumed that fj = 1 i.e.that there is one electron per molecule concerned in the absorption process and that y - 2000 cm.-l then substitution in (2.12) shows E ’ ~ ~ ~ . to be of the order of 100,000. How- ever for many molecules Experimental results are usually expressed in terms of E or E defined by 7 = 1 l O - E . . (2.17) E = ECd . . (2.18) is much smaller. a 5 J . Chew. PhysicR 1939. 7 439. 2 6 J . Anzer. Chem. SOC. 1941 63 1073. 26 QUARTERLY REVIEWS E is known as the extinction while E the extinction for unit concentration and chtance is known as the molecular extinction coefficient c being the molar concentration. The data are conveniently represented by plotting E or E or their logarithms as abcissa the ordinate being either the wave- length or the frequency.In the former case either hgstrom units (A. ; 1 A. = cm.) or millimicrons (mp ; 1 mp = lo-’ cm.) are used while in the latter the frequency (Y) in sec.-l or the wave-number.(Y” = AL1 = Y / C ) in cm.-l is employed. The frequency is conveniently expressed in fresnels one hsnel being equal to a frequency of lo1 sec.-1. To determine the f value of a band the method usually employed is to measure the area under the curve obtained by plotting e as a function of 5 ; f can then be calculated from (2.12) allowance being made for the change of base of the logarithms. Thus f - 4.31 x lo-’ &.dG . . (2.19) While Lambert’s law-that the proportion of light absorbed by a sub- stance is independent of the incident intensity but directly proportional to the logarithm of the distance travelled-always holds Beer’s law is not of such universal applicability.Beer’s law states the proportionality be- tween the light absorbed and the number of molecules of the absorbing substance through which the light passes. It does however apply where chemical reaction either between solute molecules or between solute and solvent molecules does not occur. A more detailed picture of the electronic proper frequencies and the oscillator strengths is afforded by Bohr’s adaptation of the old quantum theory to the discussion of the energy states of atoms and molecules. Bohr showed that atoms and molecules exist in radiationless stationary states of constant energy known as energy levels. When the electron jumps from a stationary state of energy El to one of energy E, light is absorbed or emitted according as El 2 E, the frequehcy being J (2.20) where h is Planck’s constant.The electronic proper frequencies are the values of Y given by (2.20) and E - El is the transition energy. In the molecular case the vibrational-rotational energy of the molecule as a whole is quantised as well as the electronic energy. As the order of magnitude of these energies is usually Erot.@Evib.&Eelec. the internal energy of the molecule (Le. excluding translational energy) may be written E = Erot. + Evib -t- Eelec. Three types of spectra can be distinguished viz. rotational spectra occurring in the far infra-red vibration-rotation spectra in the near infra-red and electronic spectra in the visible and ultra-violet. Molecular spectra are distinguished from atomic spectra in that the latter consist of a number of h e e whereas the former consist of bands except at very high resolution MACCOLL COLOUR AND CONSTITUTION 27 in the gas phase when the bands are seen to consist of closely and regularly spaced lines.The bands arise from the fact that concurrently with an electronic transition there are vibrational and rotational transitions. The spectrum of a molecule in the gas phase is thus very complex and a great deal of work has been published dealing with the interpretation of the fine structure of molecular spectra. However this lies outside the scope of the present review.27 In silution owing to inter molecular interact ions the fine structure of the electronic bands is largely lost and smoothed off regions of relatively large width appear.Vibra- tional structure may still remain as is shown for benzene in Fig 1 . 2 8 The vibrational energy levels obtained from the electronic absorption spectra will be those of the excited state since most of the absorbing molecules will be in the lowest vibrational level of the normal electronic state. Because of the compli- cations produced by vibrational struc- ture it is not surprising that Chako found no correlation between the half- widths of absorption bands and the nature of the absorbing molecule or of the solvent. The old quantum theory also pro- vides an explanation of the low values of f (- 0.0001) which are sometimes observed for molecules. On the classical theory the explanation would be naive namely that only one in 10,OOO molecules was of a kind capable of absorption.The old quantum theory I . ._ I moo 2500 d A. FIG. 1 The absorption spectrum of benzene in ethyl-alcoholic solution showing the fine structure. interprets f as the probability of transition for a given molecule. This view makes possible fractional f numbers but no further information as to their magnitude could be obtained apart from the fact that zlfj was equal to the total number of electrons in the molecule. On the basis of dispersion theory the j’ are known as oscillator strength. The procedure adopted in obtaining the f value of a band is equivalent to comparing it with a single line in an atomic spectrum. Where the band shows vibrational structure the analogous case would be an atomic line showing fine structure. The justification for this procedure has been examined by R.S. M~lliken.~~ $7 This field is reviewed by H. Sponer and E. Teller Rev. Mod. Physics 1941 13 76. 28 W. V. Mayneord and E. M. F. Roe Proc. Roy. SOC. 1935 A 152 299. 4D J . Chem. Phyeice 1939 7 14. 28 QUARTERLY REVIEWS 3. The Quasi-classical Theory of Lewis and Calvin 3Q This theory is based on the concept that the energy absorbed during the interaction of a molecule with radiation is taken up by electronic oscil- lations within the molecule. The oscillations are regarded as being analogous to classical oscillations but quantum methods are used to determine a set of energy levels. One of the simplest molecules that can be considered is ethane which shows continuous absorption below 1600 A. Indeed it is characteristic of most simple molecules that absorption commences only in the far ultra-violet.The oscillating unit is taken to be the pair of electrons constituting the C-C bond. Since electronic motion is very rapid compared with nuclear motion no difficulty arises from taking the nuclei as being fixed in space. The electronic oscillations may be interpreted in terms of the following resonance structures for ethane f - H,C :CH H,G-CH H86 6H It is not necessary to assume a complete transition from (XVIII) to (XX) an approach towards these structures from (XIX) being all that is required. If now a restoring force proportional to the displacement of the electron pair from its equilibrium position is assumed the energy levels of the system are given by En - (n + 1 / 2 ) h v n - 0 1 2 . . . . (3.1) where Y is the frequency of the electronic oscillation related to the restoring force/unit distance (k) by (XVIII.) (XIX.) (=.I . (3.2) and n is the quantum number specifying the energy level. Absorption then corresponds to a change in n from 0 to 1 the frequency of the light absorbed being Y as given by the Bohr frequency condition (2.20). Even when the oscillator is in the state n = 0 there is a certain energy associated with it the zero-point energy. The authors next consider a series of double bonds c=s \ / --N=N- \ C=N- \ / \ / \ / c=c arranged in order of decreasing force constant by the following argument. Simple compounds containing a carbon-carbon double bond absorb in the region of 2000 A. those containing a carbon-oxygen double bond a t about 2800 A. while the absorption characteristic of the azo-group lies at about 3500 A.Although the spectra of simple compounds containing carbon- nitrogen or carbon-sulphur double bonds have not been studied the positions of these groups can be asaigned from their behaviour in more complex compounds. Assuming that the double bond is the essential chromophore 30 Reference 23. MACCOIL COLOUR AND CONSTITUTION 29 k.e. neglecting the lone pairs on the nitrogen sulphur and oxygen atoms it follows that the force constant diminishes in the series from >C=C< to >C=S. The extreme structures t o which the eleotronic oscillations tend are represented by (XXI) and (XXII) (XXIII) being the clttrssical + - - + A- :B A :-B A=B (=I.) (XXII.) (XXIII.) structure. If the oscillations are simple harmonic a series of parabolae representing the potential energies of the electron pair in the various nuclear frameworks can be plotted.For this type of potential function tho selection rules lay down that An = & 1 i.e. the oscillator can only jump from a given state to an adjacent one. However if the potential function becomes non-parabolic a t large displacements the transition An = 2 becomes allowed the intensity varying with the degree of departure from the parabola.31 In the case of a conjugated molecule as well as there being a possibility of overtones there is also the possibility of the molecule possessing a band which is relatively insensitive to the structure of the molecule as a whole. These considerations led Lewis and Calvin to propose the following classifica- tion of absorption bands. ( A ) Fundamental Bands (1) First order n changes from 0 to 1.(2) Second order n changes from 0 to 2. (B) Bands of Partial Oscillation. Whereas type A are characteristic of the molecule as a whole type B are. the result of a 1oca.lised oscillation. This classification may be illustrated by the compounds (XXIV) (XXV) and (XXVI). Although the absorption (XXIV.) CH= I t Et Et (XXVI.) 31 The second-order bands aro further dodt with by G. N. Lewis a.nd J. Bigeleisen J . Amer. Chew. SOC. 1943 65 2107. 30 QUAB-Y BBVIEWS curma of (XXrV) md (XXV) are closely similar that of (XXVI) while showing a band similar to that of (XXV) also shows an entirely new band at longer wave-length. The former band can be considered aa due to partial oscillation the latter being characteristic of the molecule as a whole. A further classification comes from a consideration of %he geometry of the molecule.In the case of a diphenylpolyene such as (XXVII) the D-CH=CH-CH=(XXVII.) 0 0 I (XXVIII.) oscillation may be thought of as following an approximately linear path. However in a molecule such as crystal-violet (XXVIII) the positive charge can be placed on any of the three nitrogen atoms and so the oscillation can be resolved into two component oscillations at right angles. I n this case the oscillation frequencies in the two directions will be equal but if there is a marked dissymmetry in the molecule this degeneracy will be removed. Similarly if the absorbing molecule possesses extension in three dimensions there will be the possibility of a third component oscillation. In this way the fundamental bands of a molecule can be classified as NMe (a) x Bands.One-dimensional oscillator. ( b ) x and y Bands. ( c ) x y and x Bands. Two-dimensional oscillator. Three-dimensional oscillator. By convention the band of longest wave-lcngth characteristic of the molecule as a whole is taken to be the x band.32 The nature of the electronic oscillations may be enquired into in further detail. If as a first approximation the effect of the end groups is neglected these systems can be represented by the extreme structures being R-CH-[CH =CHI,-,-CH-R and R-CH-[CH =CH].-,-CH-R The polyenes form one extreme class. R-[CH =CHJ.-R + - - 4- .. .. 33 Additional evidence for y bands is afforded by Lewis and Bigeleisen ibid. p 2102.' MACCOLL COLOUR AND CONSTITUTION 31 The normal state of the molecule will be non-polar.However in the presence of an electric field of strength E a moment ( p ) will be induced in each > CH-CH < unit given by ,u = e x = x E . . (3.3) x being the displacement of the charge and a the polarisability of the molecule. When the electrons are displaced the eIectric force acting on them must be balanced by the restoring forces. Thus eE = k z . . (3.4) From (3.3) and (3.4) it follows that the force constant is given by k = e 2 / x . . (3.6) If the molecule now be placed in the field of a light wave whose wave- length is long compared with the dimensions of the molecule individual oscillations are set up in the units of the chain the displacements being the same for each unit. On the assumption that in the excited states of the molecule the oscillations are of the same character as the induced oscillations discussed above the dependencc of frequency on chain length can be investigated.If rn is the mass of the effective electrons in each unit then for a chain of n units the vibration frequency will be determined by the force constant k and the mass nm. It is given by v = & J n G . k . (3.6) or 1 2 = k'n . . (3.7) k' being a new constant This treatment predicts a linear relationship between lb2 and the number of units in the chain. However the effect of the end groups cannot be predicted to this approximation. In the above treatment it is assumed that while the individual units vibrate in phase there is little interaction between them. Even in the excited state of the molecule the electrons may never get far from their mean positions.However a second extreme type of oscillator is illustrated by the carbocyanines the essential structures being + + > N =CH-[CCH = ClI],,-X < > N-[CH =CH],-CH =N < I n this case even in the normal state the charge is distributed through tho whole molecule. The restoring force on each electron pair is dependent on the position of the other electrons. Lewis and Calvin liken the oscil- lations of such a system to the longitudinal oscillations of a stretched string and conclude that the wave-length of absorption should be proportional to the length of the chain or A = k"n . . (3.8) The two types of molecules just discussed represent extreme cases. in between these extremes intermediate types of behaviour may be expected. The determining factor is the mobility of the electrons within the molecule.When the normal state of a molecule can be represented by a formula without any formal charges the mobility will be small. However as the 32 QUARTBRLY REVIEWS normal state of the molecule departs from the classical formula so will the mobility increase becoming greatest when two structures can be written down differing only in the position of the charge. 4. The Quantum Theory of Light Absorption 33 Although the Bohr theory led to a general understanding of the light- absorption process it was left to quantum mechanics to elucidate the details. The quantum-mechanical treatment of organic molecules goes back t o 1927 when Heitler and London put forward their theory of the hydrogen molecule. Heisenberg had shown in 1926 that if a number of structures can be written down for an atomic or molecular system of equal or nearly equal energy then the actual state of the system is more stable than any of the hypothetical states represented by the structures.The system is said to be stabiliaed by resonance. The principle of indeterminacy expressed the fact that electrons could not be rigidly located and Heitler and London were able to account for the stability of the hydrogen molecule by casting off the concept of Iocalised electrons. The resonance phenomenon rather than being fundamental is a legacy from classical chemistry which thought in terms of particle electrons and rigid bonds and which guided the choice of structures used in the quantum-mechanical calculations. Before considering in more detail the Heitler-London approach t o the hydrogen molecule it is necessary to consider the quantum-mechanical description of the hydrogen atom.The starting point is the Schrodingur equation Hy -Ey . . (4.1) where H is a differential operator E the energy of the system and ly a function c the co-ordinates which specifies the state of the system ; H can be obtain3d from the classical mechanical expression for the total energy of the aystem by substituting certain differential operators for the co-ordinates and momenta of the particles comprising the system. If now it is stipulated that y shall be single valued and continuous and such that . (4.2) where fy* is the conjugate complex of y d t being tt generaliid volume element then these conditions can only be satisfied for certain valuea of E. These values of E are known as eigenvalues the corresponding y’s being the eigenfunctions or wave functioh.The “space )’ of which dz is an infinitesimal element is not ordinary three-dimensional space except in the The following papers review the quantum mechanical treatment of molecules (a) “ The Quantum Theory of Valence,” J. H. van Vleck and A. Sherman Rev. Mod. Physics 1935 7 167. ( b ) “ The Quantum Mechanics of MOl0~d08,” G. J. Kynch and W. G. Penney Ann. Reports 1936 23 37. (c) “ Gnrndziige der “heorie ungesiittige und aromatischer Verbindungen,” E. Hiickel 2. Ekktrochem. 1937 43 762. ( d ) “ The Theory of Molecular Structure,” W. G. Penney Rep. Frog. Phy& 1939 6 212. ( e ) ‘‘rille Quantum Theory of the Chemical Bond,” C. A. Cod~on Prm. Roy. Sm. Edin. 1941-43 A 61 114. (f) C. A. Coulson this vol.to appear. MACCOLL COLOUR AND CONSTITUTION 33 case of a ayatem comprising a single particle but has dimensions equal to the number of co-ordinates required to describe the system. The quantisa- tion of the energy of the system then arises as the result of placing certain limitations on the solution of (4.1). A justification of the foregoing con- ditions is provided by the interpretation of y namely that y*ydr . . (4.3) measures the probability of the system being in the " volume element " dz. The normalising condition (4.2) ensures that the probability of finding the system somewhere in " space " is unity. In the case of a single electron may be interpreted as the probability of finding the electron in the element of volume dz in the neighbourhood of ( r 8 4) or if multiplied by e the quantity of charge in an infinitesimal region surrounding the point.As well as being a function of the co-ordinates the wave function of an electron in a spherically symmetrical field depends upon four parameters known as -quantum numbers ; Y - Yn I m AT 8 $1 The first n is known as the principal quantum number and determines the energy of the electron. The second and third I and m are known as the azimuthal and magnetic quantum numbers and determine respectively the total orbital angular momentum and the orbital angular momentum in the direction of an external magnetic field not strong enough to affect the energy of the electron. The fourth quantum number s the spin quantum number describes the spin momentum of the electron which can be orientated parallel with or antiparallel to the magnetic field.All the quantum numbera except s are integers and are subject to l g n - 1 - l < r n < l The spin quantum number can only have the values & 1/2. The Pauli exclusion principle stipulates a condition on the quantum numbers describing the electrons in an atom. It states that no two electrons in an atom can have the same four quantum numbers. Thus the maximum number of electrons in an atom with specified n I m is 2 ; the number with specified n I is 2(2I + l) while the number with a given n is 2n2. A more general statement of the exclusion principle is that the wave function of an atom must ghange sign (be antisymmetric) when the co-ordinates of two electrons are interchanged. While the individual angular momenta of the eleotrons in a many-electron atom are not constants the total angular momentum of dl the electrons is.As the total angular momentum is related to the values for the individual electrons these latter still provide a useful means of clrtssification. A wave function specified by n I m is known as an atomic orbitul (A.O.). By the exclusion principle each orbital can contain a maximum of two electrons and these must have their spins opposed. For purposes of classification it is sufficient to specify the electrons of an atom in terms of n 1. Electrons with 1 = 0 1 2 . . . are known as 8 p d . . . electrons an electron with n = 2 1 = 1 being represented by 2p. In this Y*(T 8 qb)~(r 8 +)dr C 34 QUBRTERLY REVIEWS way the electron structure of the carbon atom may be represented by 1 ~ 2 2 ~ 2 2 ~ 2 the superscripts indicating the number of electrons of the given type* Once the Schrodinger equation has been solved all information concern- ing the state of the system can be obtained.I n general the mean value of a property of a system represented by the operator F for a system in the state yn is given by F = v*nFvndt . (4.4) However most of the systems of chemical interest are too complex to admit of a solution of the Schrodinger equation. Recourse has then to be had to approximate methods. It usually happens that the wave-equation may be solved for the system if some simplifying assumptions are made. The wave functions thus found can be taken as a starting point for an improved calculation. A theorem of very great utility states that the energy of a system calculated with an approximate wave function is always greater than the true energy the difference decreasing as the approximate wave function approaches the true one.If a system were considered as possibly existing in n structures represented by yl y . . . yi,& an approximate wave function of the form '1' = ulyjl -t a2y2 + . . + a,,yj . . (4.5) The a are then determined so as to make the energy of the This niinimising process gives rise to the quantum - I could be used. system a minimum. mechanical secit1a.r equation (4.6) where The energies of the structures are %i E7.Z being the interaction energies sii ASlij between these structures ; E is the approximation to the energy of the system. This equation is an algebraic equation of the nt,h degree the n roots El E, . . . En bcing the approximations to the energy levels.The approximations to the states of the system are found by substituting the values of ai corresponding to the required energy level into (4.5). I n the case of the hydrogen molecule two possible structures present themselves (XXIX) and (XXX) ; (XXTX) for example represents elec- MACCOLL COLOUR AND CONSTITUTION 35 This was It is essentially the theory of the tron 1 being attached to nucleus a and electron 2 to nucleus b. the method used by Heitler and London. / * l /*b a. ' 2 (XXIX.) (XXX.) homopolar molecule ionic structures like (XXXI) and (XXXII) playing no part. 1 1 i *b a*\ i (XXXI.) (XXXII.) The wave functions representing (XXIX) and (XXX) are and the approximate The wave-mechanica,l tions are Y A A A [ 1 Y ( 1 ) " b ( 2 ) - Wa(2)?#3(1)1 - . (4.8b) the corresponding energies being E and E,.These quantities are functions of I? the internuclear distancq and computation shows that whereas E,(R) possesses a minimum E,(R) does not. Hence (4.8a) corresponds to the formation of a stable molecule. The subscripts S and A refer to symmetry or asymmetry with respect t o the interchange of electrons. When electron spin is taken into account four spin wave functions present themselves. If a(1) represents electron 1 with s = $ and p(2) represents klectron 2 with s = - 4 they are a(l)a(2) a(l)p(2) a(2)/3(1) /3(1)@(2). These four wave functions can be combined to give four new functions one of which is antisymmetric and the other three of which are symmetric with respect t o interchange of electrons. I n order to satisfy the exclusion principle (4.h) must be multiplied by the antisymmetric spin' function and (4.8b) by the symmetric spin function to give the complete wave function of the molecule.As E represents the stable state and as the antisymmetric spin function is made up from a( 1)p(2) and a(2)/3( l) it follows that the electrons forming a chemical bond have opposed spins. 36 QUABTERLY RBVrEWS The second method of treating molecular structure wan developed by Hund Lennard-Jones Mulliken and Huckel. It involves the buMing up of a molecular orbital (M.O.) from the wave function of a single electron moving in the potential framework of the nuclei and the other electrons. The energy of their molecular orbitals may in principle be determined by a rigorous solution of the Schrodinger equation. Each molecular orbital can contain two electrons and so to determine the molecular energy the elec- trons are fed two at a time into the orbitals of lowest energy.Rather than rigorously solve the Schrodinger equation the L.C.A.O. method assumes that the M.O. is given by a linear combination of atomic orbitals. The molecular orbital for the hydrogen molecule to this approximation would be y = a,Yu(l) + %Yb(1) * . (4.9) The correct linear combinations are found to be Y4 - 47[Yu(l) + Wb(1)l - * (4.9a) Yu = Au[Ya(l) - Yb(1)I * . (4.93) The subscripts g and u indicate symmetry and asymmetry with respect to inversion of the orbital in the centre of symmetry. Quanta1 calculation shows (4.9a) to be the orbital of lowest energy (y is said to be a bonding orbital while yN is antibonding). Hence the molecular wave function is - Ag*[lUu(1) + Yb(l)I[Wa(2) + Yb(2)I * .(4.10) If this expression is multiplied out it is seen to contain two terms correspond- ing to (4.8a) together with two additional terms of the type Yo( 1 )Yu(2) Y b ( l ) Y b ( 2 ) * . (4.11) which are the wave-mechanical transcription of (XXXI) and (XXXII). Thua the molecular orbital treatment gives as much weight to the ionic structures as to the purely homopolar ones considered in the Heitler- London treatment. Both of these methods when generalised so as to apply to complex organic molecules suffer from limitations the Heitler-London or valence-bond (V.B.) method on account of its neglect of ionic structures the M.O. method because of its treatment in terms of a single electron with consequent neglect of interelectronic interaction.However both methods may be modified to overcome these deficiencies. The Heitler-London treatment of the hydrogen molecule shows that the pair of electrons forming a chemical bond have their spins opposed. This suggests that the valency of an atom is equal to the number of electrons with unpaired spins that it possesses. Thus carbon in the state ls22s22p2 would be bivalent the two p electrons being capable of forming bonds. It is of interest to enquire into the directional properties of valence bonds. To do this requires a qualitative discussion of the nature of the s and p electron distributions. The solutions of the Schrodinger equation for an electron in a spherically symmetrical field shorn that 'while the charge distribution of s electrons is spherically symmetrical those of p d .. electrons exhibit maxima in certain directions. In the case of the p elec- trons the maxima are mutually perpendicular and so they can be classified as pz p y or p,. If the formation of a chemical bond is regarded as the MACCOLL COLOUR AND CONSTITUTION 37 building up of a charge between bonded atoms then an atom with two p electrons would tend to form bonds directed at right angles with two other atoms. Iteturning to the case of carbon in order to obtain a quadrivalent state it seems reasonable to assume that a 29 electron is promoted to the 2p state giving the structure ls22s2p3 in which case there me four electrons with unpaired spins. If however these orbitals are used for bond formation a model comprising three mutually perpendicular bonds with the fourth symmetrically disposed with respect to the other three would be obtained.On this basis methane would not possess the symmetry of a regular tetra- hedron a structure which has been amply confirmed by physicochemical studies. However as has been seen a better approximation to the system can be obtained by taking four linear combinations of the four orbitals. This was the method used by Pauling who took as his criterion in the formation of linear combinations the principle of maximum overlapping. This assumes that a bond between two atoms will be stronger the greater the degree of overlapping of the orbitals forming the bond. Pauling defined the strength of bonds formed by s orbitals as 1 and of those formed by p orbitals as 3112. By linear combination of the 2s and the three 2p electrons he was able to form four bonds directed tetrahedrally with the maximum strength of 2.Similarly the strongest bonds that can be formed from the configuration sp2 are inclined at 120". The latter process gives rise to the trigonal bonds of great importance in the discussion of conjugated systems. This process involving the mixing of s and p electron wave functions is known as hybridisation. 34 Huckel was the first to apply these ideas to unsaturated molecules. In the case of benzene for example he assumed that the 9 p, p electrons were hybridised to give the trigonal bond system already referred to the three cr orbitals being used in forming the C-C and C-H bonds. He was then able by both methods to determine the energy of the pz or z electrons and hence the energy over and above that of the framework bonds.While the L.C.A.O. treatment of conjugated systems is relatively straight- forward the valence-bond treatment introduced several new concepts. The latter method employs the fact that for a conjugated system the electron spins of the various p electrons may be coupled in a number of different ways corresponding to different structures or bond diagrams. A useful theorem due to Rumer limits the number of bond arrangements that have to be considered. He showed that for a system of n bonds (2n electrons) any conceivable structure can be represented in terms of a fundamental set of structures. These are known as a canonical set. For benzene the now famous structures are (2n) ! (n)! (n + l)! (4.12) / \ A . B. c. D. E. For a more complete discwion of this process see Reference 33 (f).38 QUARTERLY REVIEWS Structures C D E containing a para-bond are said to be excited. The number of canonical structures increases very rapidly with the number of bonds ; for anthracene there are 429. The number of structures cont'aining formal bonds (bonds between non-adjacent atoms) also increases with the number of bonds. A structure containing no formal bonds is said to be unexcited with one formal bond first excited and so on. It is unfortunate that the same term " excited '' is used to refer both to the structures and to the actual states of a molecule. However the context usually makes clear the sense in which it is used. Largely as the result of work by Slater Pauling and Eyring simplified methods were evolved for setting up the secular equation in terms of the canonical structures.These methods were then employed to calculate the resonance energies of a large number of conjugated molecules. Before 1937 attention had been focused upon the lowest root of the secular equation i.e. on the ground states of molecules. However in that year Sklar 35 calculated the differences in energies between the ground and the first excited states of a number of molecnles and was able to show that this energy differenco or transition energy corresponded to their long wave-length absorption bands. Rather than to use explicit expressions for the atomic orbitals his method was to determine the energy difference between the states in terms of a quantum-mechanical parameter a. He obtained the value of this parameter from purely thermochemical data.His results for benzene are given in Fig. 2(a) arid these are to be compared with the experimentally determined values s1ion-n in Fig. 2(c). With a value of a equal to 1.92 v.e. the long wave-length absorption band of benzene is found to lie at 2470 A. compared with t'he experimentally determined band 2470 J MOO 2470 2700 1500 t The electronic energy levels of benzene by (a) the valence bond (b) the antisymmetrbed molecular orbital method ( c ) experimental. The allowed transitions are shown with an asterisk. 35 Reference 19. MACCOLL COLOUR AND CONSTITUTION 39 a t 2600 A. The attempt to calculate the position of the shorter wave-length bands by this method led to results in poor agreement with experiment. Sklar attributed this breakdown to the neglect of excited ionic structures such as (XXXIII) (XXXIV) and (XXXV).Because oE the large number +<3- (XXXIII.) (XXXIV.) (XXXV.) of these structures he was only able to incorporate the twelve (XXXIII). The calculations show that while the ionic structures only slightly with the lower states of the molecule they become importance when the highly excited states are considered. of type of great interact The problem may also be approached from the molecular orbital view- Calculation shows that the energies of the various molecular orbitals w = 28 cos (2,2/6)1 . . (4.13) where is the resonance integral which may be evaluated empirically. The energy of the orbitals increases with I I I. Thus two electrons are placed in the orbitals with l = 0 and four in those with \ I I = 1. The total energy is then 8/3.In the first excited state one electron is raised from I I I = 1 to 1 I / = 2. This state is fourfold degenerate since the odd electron in the 1 I I = 1 level may have l = & 1 while the electron in the I I I = 2 level may have I = 3 2. The energy of the first excited level is 6/3 the energy difference corresponding to the long wave-length band being 28. Since estimates of by different workers differ considerably all that can be said of this calculation is that it gives a value of the right order of magnitude.36 In order to refine the molecular orbital method M. Goeppert-Mayer and A. L. Sklar 37 utilised a modification suggested by Mulliken. It is known as the method of antisymmetrical molecular orbitals. One of the main sources of error in the L.C.A.O. method (molecular orbitals formed as a linear combination of atomic orbitals) is the neglect of the interelectronic repulsions.These interactions are responsible for removing the degeneracy previously discussed. But as has been seen the molecular wave function which is the product of the appropriate molecular orbitals allows many electrons to congregate around a gieen nucleus. Because of this the intro- duction of the interelectronic repulsion may lead to results ih worse agree- ment with experiment. However if the molecular wave function is multiplied by an appropriate spin function and the whole antisymmetrised in the co-ordinates of the electrons all terms which represent an accumula- tion of more than two electrons on a single nucleus vanish. By means of this refinement the limitations of the molecular orbital method are largely overcome.In addition the expression for the energy levels may be obtained *6 R. S. Mulliken and C. A. Riske Rev. Mod. Physics 1942 14 259. 17 J . Chem. Physics 1938 6 645; A. L. Sklar and R. H. Lyddane ibid. 1939 7 374; F. London discusses some of the approximations involved in the method (ibid. 1945 13 396). point. for benzene are given by (I = 0 f 1 3 2 3) 40 QUARTERLY REVIEWS in terms of certain integrals which are calculable analytically the only empirical data used being the internuclear C-C distance. In this way the results shown in Fig. 2(b) were obtained. The calculakd values are seen to be in good agreement with experiment. In 1939 R. S. M ~ l l i k e n ~ ~ in a series of papers developed methods for calculating the intensity of a band quantum mechanically.The transition (electric) moment is defined as (er)mn = jy*n(zeri)ymdr . . (4.14) where the summation is taken over all the electrons and ri is a vector defining the position of the ith electron. The theory of radiation now relates the tramition moment or the dipole strength ( T ) ~ ~ ~ with the oscillator strength of dispersion theory. The relationship is i fj=(T)*; . (4.15) where the subscript j refers to the transition m -+ n. It is often convenient to consider the components of q namely xj yj zj. If it so happens that xj yj zj = 0 then t o this degree of approximationfj = 0 and the transition is said to be forbidden. Mulliken’s method may be illustrated by his treatment of the hydrogen molecule. From the L.C.A.O. viewpoint the ground state is represented by y N = Ys(l)lyd2) - .(4.16) while the first excited state to which transition is allowed is given by . (4.17) The transition corresponding to absorption is that of an electron from a bonding M.O. to an antibonding one. If the molecular axis is taken as the z direction then xj = yj = 0. 1 Y E = -“f!‘~(l)Yu(2) + Y&2)%(l)1 - 4 2 Expression (4.14) thus reduces to ( z ) N B = Y E ( z l + z,)YAVdr . (4.18) This expression on substitution for YJE and !Pa becomes after reduction s (4.19) Now yazyaCi’r is simply the average value of z for atomic orbital a and as 5 the internuclear distance R = zA - zB R (Z)N,E = ~ * d2(1 - 8 2 ) (4.20) The factor [2(1 - s2)]-4 is related to A and A of (4.9a) and (4.9b). the V.B. point of view it can be shown that From . (4.21) SR ( 4 N E = - 1 / 1 - 8 4 SaJ.Chem. Physics 1939 7 14 20 121 339 353 364 570. MACCOLL COLOUR AND CONSTITUTION 41 the transition being that from an essentially non-polar ground state to an essentially ionic excited state. Substitution of the known values for R and S gives f = 0.68 from (4.20) and 0-49 from (4.21). The agreement between the two values is excellent in view of the approximations involved. The theory of groups can be applied to simplify the calculation of the energy states of a molecule and to decide the question as to whether a given transition is allowed or not. For benzene which has the symmetry of a plane regular hexagon it can be shown that transitions from the ground state 2 A. FIG. 3 The absorption spectrum of solid hexantethylbenzene (1) electric vector in the plane of the ring ; (2) electric vector perpendicular to the plane of the ring.to the two lowest excited states are forbidden. This is in qualitative agree- ment with the experimental data which show a weak band at 2500 A. a stronger one at 2000 A. and a very intense band at 1800 A. The appearance of the weak long wave-length band is due t o a distortion of the symmetry of the molecule by vibrations. The intensity of the forbidden band at 2000 A. is probably related to its proximity to the allowed transition at 1800 A.39 An interesting study has been the effect of the distortion of the benzene symmetry by the gentle method of replacing the hydrogen atoms H. Sponer G. Nordheim A. L. Sklar and E. Teller J . Chem. Phyeics 1939 7 207, 42 QUARTERLY REVIEWS by deuterium40 or by the more drastic method of replacing them by F,41 OH,42 NH2,43 or CH,.44 For the conjugated molecules to be discussed in the present review it is assumed that the energy levels of the 7c electrons are concerned in the long wave-length spectra.That ultra-violet absorption can arise in other ways is shown by satarated molecules such as ethane for which absorption starts a t about 1600 A. The recent work of G. Scheibe St. Hartwig and R. Miiller 45 strikingly demonstrates the part played by the n electrons in the long wave-length spectrum of hexamethylbenzene. This molecule possesses a layer structure in the solid state and so a known orientation of a crystal implies a known orientation of the molecular planes.46 The absorption spectrum can then be determined by using polarised light with the electric vector parallel and perpendicular to the plane of the molecule.If the n electrons are responsible for the absorption the extinction in the latter case should be very small. The extinction wit’h the electric vector perpendicular to the plane of the molecule is a tenth of that with the electric vecbor parallel thus confirming the r6le of the ?t electrons. Other examples of the directional properties of light absorption are discussed by R. A. RIorton.47 The results are shown in Fig. 3. 5. Some Qualitative Applications of the Resonance ThRory 48 The problem of the relationship between the colour of an organic com- pound and its chemical constitution has been approached from two directions. The first was along the lines of classical organic chemistry and consisted in the examination of a series of related molecules in order t o find the effect upon the absorption maximum of the parent substance caused by changes in constitution.Unfortunately much of the early work is marred by the neglect of “subsidiary ” changes in constitution which may have had a greater effect than the change which was t o have been investigated. The second approach is the calculation of the wave-length and intensities of ab- sorption by quantum-mechanical methods. The quantal treatment however is limited to relatively simple molecules although qualitatively the theory of resonance is capable of providing much valuable information. The present section will deal with the applications of the resonance concept and the last section with the results of the quantal calculation. The relationship between the resonance energy of a compound and its light absorption is of interest.I n Section 4 it has been shown that if more than one structure can be written for a molecule interaction between the 40 C. A. Beck and H. Sponer J . Chem. Physiccl. 1942 10 575. 41 S. H. Wollman ibid. 1946 14 123. 4 2 F. A. Matsen N. Ginsberg and W. W. Robertson ibid. 1945 13 309. 43 N. Ginsberg and F. A. Matsen ibid. p. 167. 4 4 N. Ginsberg W. W. Robertson and F. A. Matsen ibid. 1946 14 511. 4 5 2. Elektrochem. 1943 49 372. 48 K. Lonsdale Proc. Roy. SOC. 1929 A 123 494. 47 Reference 24 (c). 48 A discussion of the colour of organic compounds from the M.O. viewpoint is given by E. J. Bowen Ann. Reports 1943 40 12. MACCOLL COLOUR AND CONSTITUTION 43 structures will give rise to a set of states which will be better approximations to the actual molecular states.The energy difference between the lowest state found in this way and the structure of lowest energy is the resonance energy of the molecule whereas the energy difference between the two lowest molecular states is equal t o the energy corresponding with the long wave-length absorption band provided of course that the transition is allowed. In the diphenylpolyenes (XXVII) the resonance energy increases with addition of each successive vinylene group while the absorption maxima move towards the red. However an increase in the resonance energy does not always imply a bathychromic effect as a consideration of the isomeric molecules naphthalene and azulene (XXXVI) shows. For while naphtha- lene has a greater resonance energy than azulene the former molecule absorbs at a much shorter wave-length than the latter.Another example comes from the work of G. Schwarzenbach et U Z . ~ ~ who have studied the spectra of indicators capable of undergoing several colour changes. These authors concluded that the most highly coloured form of the indicator was the most stable. However chemical evidence would suggest that malachite- green (XXXVII) has a smaller resonance energy than crystal-violet (XXXVI.) c (XXXVII.) (XXVIII) while the wave-lengths of absorption are 6230 and 5900 A. respectively. 50 The bathychromic effect together with the increase in resonance energy observed in the case of the polyenes as the series is traversed can be understood on the following basis. The successive addi- tions of vinylene groups cause a rapid increase in the number of excited structures there being only one unexcited structure corresponding to the classical formula in each case.Thus on proceeding up the series the ground state of the molecule is lowered corresponding with an increased resonance energy but the first excited state is still further lowered corresponding with a shift of the absorption towards the red. Although the prediction of the relationship between the resonance energy and light absorption may safely be made for a related series of molecules yet great care has to be exercised when the argument is extended to molecules outside the series. For closely related molecules the greater the extent of the resonance 4D Helu. Chim. A& 1937 20 1591. Reference 23. 44 QUARTERLY REVIEWS system the longer the wave-length of absorption.This is clearly shown by the phenomenon of insulation of chromophores. The spectrum of 6 15-dihydrohexacene (XXXVIII) is almost identical with the sum of the (XXXVIII.) spectra of naphthalene and anthracene.61 The extent of the resonance system is reduced and the spectrum of the molecule reverts to the spectra of the two systems formed by the insulating effect of the two methylene groups. The insulating effect may be achieved by more subtle methods as has been shown by the work of L. W. Pickett G. F. Walter and H. France on some substituted diphenyl~.~~ The long wave-length band of diphenyl is very similar in position to that of benzene but has a greatly increased intensity 18,000 compared with 200 for benzene). Yet the spectrum of 2 2’ 4 4’ 6 6‘-hexamethyldiphenyl for example approximated to that of mesitylene.This phenomenon is understandable in terms of reson- ance theory. The structures for diphenyl are the four classical structures and excited ones such as (XXXIX) and the corresponding ones with a +<=x=>- - - -<=x>+ - - a a7 (XXXIX.) formal bond between the pp’ positions. The question of the relative import- ance of the ionic and the formal bonded structures will be discussed in Section 6. For the maximum interaction between structures of this type the two rings must be coplanar.53 This follows from the principle of maximum overlapping since the n orbitals of atomB a and a’ have their maxima perpendicular to the plane of the rings. Thus any effect which tends to force the rings far out of the coplanar condition will decrease the contributions of the above structures and the spectrum of the molecule will revert to that of the corresponding benzene derivative.So far the discussion has been mainly concerned with chromogens. According to Bury the function of an auxochrome is to provide a greater possibility of resonance. Thus in aniline as compared with benzene 51 E. Clar Ber. 1942 75 1283. 5 2 J . Amer. Chem. Soc. 1936 58 2296. 6s For a discussion of the structure of diphenyl see J. Karle and L. 0. Brockway s4 Reference 18. ibid. 1944 66 1974. MACCOLL COLOUR AND CONSTITUTION 45 utmctures such as (XL) participate as well as the two Kekul6 and the p-bonded types. Confirmation of this view comes from a comparison of the spectrum of aniline with that of the anilinium ion for which structures of the type represented by (XL) become highly improbable.The two ; H a &H2-==>- h2<=> (XL. 1 spectra are very merent that of the anilinium ion being practically identical with that of benzene. The anti-auxochromes of Wizinger can be inter- preted in a similar fashion. Thus in p-nitro- enhanced limiting structures such as (XLI) Some very interesting results have been re- - aniline the possibility of resonance becomes further &H2=r>=yB playing a part. (XLI.) corded showing the relationship between the spectra of members of a series of compounds. In particular may be mentioned the work by K. W. Hausser et aZ.55 on certain polyenes and the attack on the cyanine dyes initiated by N. I. Fisher and F. M. Hamer,56 and extended by L. G.S. Brooker and his c o - ~ o r k e r s . ~ ~ Other data have been obtained by A. E. Gillam and D. H. Hey 58 for two series of polyphenyls and by E. Clar et U Z . ~ ~ for certain polycyclic aromatic compounds. Only the first two series will be discussed here as they are illustrative of tho general method of approach. The polyenes are members of R vinologous series which can be repre- sented by the general formula (XLII). The compounds considered were of the following types R,R’ = CH, CHO ; CH, CO,H ; ( 11 CHO ; and <I> a. Of particular importance is the tabulation of the integrated intensities of the bands for as was shown in Section 2 the integrated intensity or the related f value constitutes the best measure of the intensity of absorption. The tabulation of Amax. and E ~ ~ ~ .is unsatis- O r + - R-[ CH=CH] TL-R’ R-CH-[CH=CH],- 1-CH-R (XLII. ) (XLIII. ) factory since f is a function of both E,,,. and y the half-width of the band. In Table I1 are given the results obtained for the diphenylpolyenes the data referring to benzene solution. 5 5 2. physikal. Chcin. 1935 B 29 363 371 378 384 391. b6 Proc. Roy. SOC. 1936 A 154 703 ; 1937 A 163 138. b7 Rev. Mod. Physics 1042 14 275. 58 J. 1939 1170. 6o E. Clar “ Aromutische Kohdonwasserstoffe,” Springer Vorlag Berlin 1941 ; see also R. N. Jones Chem. Reviews 1943 32 1. 46 QUARTERLY REVIEWS TABLE I1 The dip hen ylpolyenes I -I-- -I__ -~ A,,,. . . 2515 3190 3520 3770 f . . . 0.41 1 0.58 ~ 0.77 1 1.26 The other series show the same general type of behaviour. In terms of the resonance theory the structures are the classical structure (XLII) and excited ones such as (XLIII).There are of course many other contributing structures involving smaller separation of charge. If it is assumed that structures of the type (XLIII) are of main importance for the excited state then a bathychromic effect would be expected upon ascending the series and this is observed. Since all the polyene series examined show the same type of dependence of absorption maxima upon n the end groups may as a first approximation be neglected. Fig. 4 shows the resonance energy over I T -m- - I n = O n = I n=2 n=3 FIG. 4 The resotiuiLce eriergies (t - - -+) and transitioii energies (-4) of some diphenylpo1yene.u. and above that of the four phenyl groups and the transition energy as a function of n. The increase in intensity with increase in n may be accounted for qualitatively since the transiiion moment will be greater the longer the chain.This series of compounds formed the first type of linear oscillator in the sense of Lewis and Calvin. The relationship derived (3.7) indicates that a plot of A 2 against n should give a straight line. This is shown in Fig 5 the agreement being excellent. This series also affords evidence of the existence of a “ second-order band,” as the polyenes all show a second band at shorter wave-lengths. The ratio of 3L1 to A 2 approaches 2 as the length of the chain increases as is to be expected for a second-order band. The light absorption of an important series of polyenes the carotenoids has been discussed by L. Zechmeister L. Pauling et Of particular 6o J . Amer.Chem. SOC. 1943 65 1941 ; see also R. S. Mulliken J . Ghem. Physics 1939 7 364. MACCOLL COLOUR AND CONSTITUTION 47 8 % e h 0 interest is the existence of steric isomers due to the possibility of dieerent arrangements around the double bonds. Quanta1 calculations show that for a polyene in the all-trans-configuration transitions are allowed from the ground to the first and the third excited states but forbidden to the second. I I 1 I I I I I ' h e 75 - 10 - ?* 8 co 5 - 2 A. Fra. 6 - - - - equilibrium mixtiire of isomers. If however the molecule possesses a cis-arrangement about some of the double bonds transition to the second excited state becomes allowed. This accounts for the third peak characteristic of the cis-carotenes. Fig. 6 shows the development of the " cis-peak '' in y-carotene.The development of the '' cis-peak " i n carotene - a11 trans-carotene ; 48 QUARTERLY REVIEWS The cyanine aeries investigated by N. I. Fisher and F. M. Hamer can be represented by the general formula (XLIV) TI T, T, T being atoms in a heterocyclic molecule. Molecules of this type form another example TI \+ N==C/H-[ CH=CH],-N n. of a vinologous series. The cyanines may be divided into two classes the symmetrical cyanines for which the two end groups are the same and the unsymmetrical ones in which the end groups differ. Three general relation- ships emerge from this work. In the fist place there is a bathychromic shift as n increases and secondly the intensity of the long wave-length band increases with n. The third conclusion that may be drawn is that in many cases the wave-length of absorption of an unsymmetrical cyanine can be calculated as the mean of the wave-lengths of absorption of the two related symmetrical compounds.The colour of dyes has been extensively investigated by L. G . S. Brooker and his collaborators. The first point of interest lies in a comparison of the spectra of a series of cyanines (XLV) with those of the related anhydro- I I I I I I Et Et (XLV.) 0 . . . . 1 . . . . 2 . . . . 3 . . . . I I Et (XLVI.) bsscs (XLVI). alcohol. The data are given in Table 111 the solvent being methyl TABLE 111 Comparison of the Spectra of a Series of Cyanines with those of tJx Corresponding Anhydro-bases 4 P d x . . emax x 1 0 - 4 . 4 m x em,,. x lo-'. 4230 8.43 3060 5.85 5575 14.8 4580 5.65 6500 22-9 4900 6.4 7.380 2 i . 6 5100 6.8 I - I Cynniney.1 Anhgdro-bases. M-4CC'OLL COLOUR AND CONSTITUTION 49 For the cyanines Amax is approximately linearly related to n the behaviour to be expected from " linear oscillators of the second type '' in the Lewis and Calvin sense. The increase in intensity on ascending the series is also to be expected on this view. However an entirely different state of affairs exists for the anhydro-bases. In the first place E,,,. is approximatlely constant for all members of the series and secondly whereas a change in n from 0 to 1 causes a bathychromic shift of 680 A . yet the change in n from 2 to 3 only causes a shift of 200 A. The marked difference between the behaviour in these two cases enables Brooker to classify the spectra of series of compounds on the grounds of convergence or non-convergence.The former series is non-convergent while the latter is convergent. This author attributes the difference in behaviour in the two cases to the degeneracy or non-degeneracy of t,he extreme structures. This term will be used to signify structures with the charge placed at the end of the chain. Whereas in the cj-anines there exist two extreme structures of equal energy for the anhydro-hases there is it single low-encrgy classical structure together with two extreme structures such as (XLVII). In both there are additional intermediate strnctures (XLT'TI.) but it is not necessary to considcyr thew for the present argument. For the cyanine series a degeneracy csists among t hc extreme structures whereas in the anhydro-bascs the classicd struct uro differs widely i n energy from the ionic structures.This tlegcncracy nccorcling t o Brooker is ;t prerequisite for the non-convergencc of a series. of a sjmimetrical cj-aninr of' give11 chaiu leiigth with alterations in the end groups can be explaiiied by the consideration of intermediate structures such as (SLVITT). Pauling 1133 pointtxl out the The variation in i Et I Et (XLVIII.) necessity for taking into account structures of this type since the extreme structure representcd by (XLV) and the corresponding one with the charge on the left-hand nitrogen atom will not by themselves interact. Brooker concludes that the greater the energy difference between (XLV) and (XLVIII) the Icw t Iir resonance splitting of the degenerate levels and tlhe P 4 s P. 9 found that it decreased with n. If it is assumed that the process involves the addition of a proton to the chain and thus the loss of resonance stabilisa- tion the decrease in this quantity with increasing n is verified.Non-degeneracy may also be observed in the unsymmetrical cyanines if the basicity of the two heterocyclic nuclei are different. In this case there would be a stabilisation of the extreme structure with the positive charge on the more basic nitrogen atom. For the compound (XLIX) there is a marked convergence the absorption maxima for n = 0 1 and 2 being 5045 6170 and 6800 A. respectively. I--$--I I I I I I I I n-0 n = I n=2 n=3 I Et (XLIX.) The non-convergence makes itself apparent in another fashion. It had been noted by Fisher and Hanier that the wave-length of absorption of an unsymmetrical cyanine could be calculated from the mean of the values for the two related symmetrical compounds.This relationship must obviously break down if the series of the symmetrical cyanines are non-convergent while that of the unsymmetrical compound is convergent. Brooker has used the deviation 3Lcalc. - lobs. as a measure of the relative basicity of heterocyclic nuclei. For a given value of n one of the end groups is kept constant while the othor is varied. The greater the deviations in 61 L. G. S. Brooker “ Resonance and Orga,nic Chemistry,” “ Frontiers in Chemistry,” Vol. 3 Interscience Publishers Inc. New York 1945. MACCOLL COLOUR AND CONSTITUTION 51 such a series of compounds the greater is the difference in basicity between the two end groups. Consistent results for the order of basicities have been obtained by Brooker from measurements both in the cyanine and in the styryl dye series.G . N. Lewis 6 2 has recently published a classification of dyes based upon the concepts of the Lewis and Calvin theory together with rules for estimst- ing their long wave-length absorption bands. The parent molecule con- sidered is (L) and the various families of dyes are obtained by specifying X” X”’ and the X” = N X”’ zz= 0 auxochromic groups X and X’. the oxazine dyes are obtained. For example with X”’ may be absent as in the triphenylmethyl dyes. The positive charge formally represented as. residing at X” is distributed through the molecule owing to resonance. The “ electronic oscillation ” responsible for the colour is supposed to take place between X and X‘ the auxochromic groups.The simplifying assump- tion is made that the effects due to alterations in X X’ X” and X”’ act independently and the direction of these effects is calculated by the use of the following rule. “ I f the colour of a compound is associated with an oscillation of positive charge along a given path the frequency of absorption will be increased by anything that diminishes the amount of positive charge and decreased by anything that increases it.” Thus the bathychromic effect of X,X‘ = NR2 as conipared with X,X‘ = OH and the hypsochromic effect of X”’ = 0 as compared with a molecule in which X‘” is absent can be accounted for on this basis. Malachite-green being taken as the standard molecule the effect of constitutional changes upon the colour can be deter- mined empirically as additke effects.Lewis has considered a large number of dyes and the’agreement between lobs. and ILcalc. is very good the mean error being 30 A. In the acridine family X” = CR X”’ = N the agree- ment is very poor and this is interpreted as indicating that the long wave-length band of such compounds corresponds to a “ vertical oscillation.” The foregoing are typical of the arguments used in the application of resonance theory to a correlation of the absorption spectra of organic molecules. The value of such treatment will be discussed at the end of the next section. 6. The Application of Quantul Methods The calculation of the colour of an organic compound besides having an intrinsic importance also has a utilitarian importance outlined by Sklar 63 “ The determination of the structure of a natural product perhaps J .Amer. Chem. SOC. 1945 67 770. 6 8 Reference 19. 52 QUARTERLY REVIEWS a hormone is a matter of many years' work in which many guesses are made and later rejected. One could calculate the spectrum of a proposed structure check it against the experimental one and so keep on the right track." Although at the present time this desirable vista is still distant considerable progress has been made towards it. Sklar considered the four molecules butadiene benzene fulvene and azulene and was able to calculate the transition energy for each molecule by the valence-bond method in terms of 8 quantum-mechanical parameter x . Rather than evaluate a analytically recourse was had to thermochemical data which led to an empirical value for the constant.The results of the calculations together with some results obtained by other authors are shown in Table IV. TABLE I V Application of the Valence-boftd Method Molecule. ButadieneO . . . . Hexatriene . . . . Octatetraeneb . . . Fulvene". . . . . Benzene . . . . Styrened . . . . . cycZoOctatetraene . . Azulene" . . . . Naphthalene c . . Diphenyld . . . . hthracone C . . . . Phenanthrene . . . Naphthacenec . . . PyroneC . . . . . Pentaceno . . . . Calc. (Sklar). 1900 2570 3120 3650 2470 2570 3320 6910 2680 2570 - - - - - Calc. (Farster). - 2450 3860 7800 2950 3650 3000 4500 3450 5450 - - Obs. 2100 2600 3020 3650 2600 2850 - 4000 7000 2750 2515 3700 4600 3300 5800 3-100 d a A. L. Sklar Reference 19. &I. Kovner Actn Physicochiw. U.R.S.$. 1914 19 385; cf. Conipt. rend. Acad. Sci. U.R.S.S.1942 35 54. C Th. Forster Reference 20. d G . W. Whelrtncl "The Theory of Resonance," Wiley New York 1944. A. BIuccoll Nature 1946 157 695. The difference botwoen the values quoted in the table and those in the reference is duo to the choosing in the present case ofvalues of the parameter a to conform with the values med by Sklar and Forster. Unless explicit references are given tho soux~cos of tho oxperimental data are taken from the papers which rocord the resuits of the calculations. I n setting up the secular equations for butadiene benzene and fulvene Sklar included all the canonical structures. Since the number of these rapidly increases as the number of electrons increases the met hod becomes unmanageable for a inolecule such as azulene I n this case onlj- thc two unexcited structures and the first excited ones were coiisidercd.This can be justified on the grounds t'hrtt t'he highly excited structures will riiake onljr MSCCOLL COLOUR -4ND CONSTITUTION 53 a small contribution to the ground and the first excited state. Even with this approximation the work involved in the calculations for complex mole- cules becomes very great and so Forster 64 in 1938 went a step further and neglected all but the unexcited structures in setting up the secular equation. This method is obviously only applicable to molecules for which more than one unexcit,eci structure exists. Forster was able to treat molecules such as pent,acene (LI) and pyrene in this way. &I.) As well as the nssuinption discussed above a number of others of a more fundamental nature are made in the treatment of the states of molecules by the V.B.method. A justification of these assumptions is indicated a posfiori by the success of the method in calculating the resonance energies of molecules. However a much more serious criticism of the results obtained comes from a consideration of tho intensities of the calculated absorption hands. Kovner 6 5 has shown in the case of butadiene that the valence-bond method lends to the conclusion that the long wave-length transition is for- bidden for the model with a trans-a,rrangement abont the single bond (LII). (LII.) (LII I. ) As this transition becomes allowed for thc model with a &-arrangement (LIII) Kovner concluded that butadiene must possess the s-cis-arrangement. (This term has been introduced by Mulliken 66 to denote cis- and trans- isomerism about a single bond.) Kovner’s conclusion is in direct conflict with the work of i l l ~ l l i k e n ~ ~ using the molecular orbital method.Even if butadiene possessed the s-cis-configuration it is doubtful whether a sufficiently large transition moment could be obtained by considering as Kovner did only homopolar structures. The same type of argument applies to many of the molecules listed in Table IV. That this argument is correct is borne out by the calculations of Sklar 6 8 for benzcnc where in order to obtain a reasonable value for the position of the first allowed transition ionic structures had to be taken into account. There exists the anomaly that while the positions of the absorption bands of molecules listed in Table IV show good agreement with the experimental values there is little reason to assume that the treatment would lead to agreement in the inten- sities.The case of cyclooctatetraene is hardly a fair test insofar as a planar configuration was assumed and the effects of strain neglected. A great deal of theoretical work in recent years has been concerned with the bond lengths in conjugated systems. Thus Pauling et aZ.89 and 6 4 Reference 20. 66 Rev. Mod. Physics 1942 14 266. 67 Reference 24 (d). 69 L. Pauling L. 0. Brockway and J. Y. Beach J . Am?. C h m . Soc. 1935 57 2705. 6 5 Reference b Table IV. 68 Referenoe 19. 54 QUARTERLY REVIEWS W. G. Penney 70 have adapted the valence-bond method and J. E. Lennard- Jones71 the molecular orbital method to deal with such problems. The simple valence-bond treatment assumes in the first plam that all the bond lengths are the same in a conjugated system and secondly that the bond lengths in the excited state of such a system are the same as those in the ground state.Both these limitations have been removed by G. J. Kynch and W. G. P e n n e ~ ~ ~ who have taken explicit account of the variation of the quantum-mechanical parameter in calculating the light absorption of buta- diene hexatriene and benzene. Results calculated on this basis show good agreement with experiment and in particular the high value of the reson- ance energy of benzene which is implied by Sklar’s treatment is brought into line with the observed value. Mulliken however has criticised this treatment in particular the identification of the calculated absorption band with the observed.F. S. Shifrin 73 has examined the valence-bond treatment of the colour of organic compounds and has pointed out that one of its limitations is the restriction of the calculations to hydrocarbons. He extended the calcula- tions to certain heterocyclic molecules by assuming that a nitrogen atom in a heterocyclic molecule contributes one n-electron and that the nitrogen atom can be considered as a CH group. On this basis he arrives a t the results shown in Table V. The calculated values have been altered from those in TABLE V I Benzene. 1 Pyridine. I Naphthalene. I - _.____________- I Amx.(calc.) ’ 2450 1 2450 2950 2950 1 3650 3650 3650 I Amax.(obs.) I 2600 1 2650 1 2750 1 3150 I 3700 1 3600 1 3750 ~ I the paper referred to in order to take account of the fact that the values for benzene and pyridine are obtained by Sklar’s method whereas the remainder were obtained by Forster’s method.The case of naphthalene is not straight- forward as it seems likely that the band observed at about 3100 A. should be used for the comparison. Evidence against the treatment of nitrogen atoms simply as CH groups comes from a study of the gaseous absorption spectra of benzene pyridinc and pyrimidine. The observed 0-0 transitions are respectively 2600 2900 and - 3100 A. indicating a bathychromic effect upon the replacement of a CH group by it nitrogen atom.74 Shifrin has also considered the case of pyrrole indole and carbazole pointing out that the NH groups in these compounds possess a lone pair of electrons which may interact with the ring electrons. On this basis the spectra of the above-mentioned compounds would be expected to resemble benzene naphthalene and anthracene respectively.70 Proc. Roy. SOC. 1937 A 158 306. 7 2 Ibid. 1941 A 179 214. 73 Compt. rend. Acnd. Sci. U.R.S.S. 19.10 29 27. la A. Maccoll J. 1946 670. 7 1 Ibid. p. 280. MACCOLL COLOUR AND CONSTITUTION 55 The calculation of the intensities of transitions for conjugated systems by the M.O. method has been investigated by R. S. M~lliken.'~ The transi- tions arise from the transfer of a n-electron from a bonding molecular orbital to a non-bonding one corresponding in valence-bond nomenclature to the transition from a mainly homopolar ground state to a largely ionic upper state. The calculations are made by the method outlined in Section 4. As the L.C.A.O. method leads t o values for 5 in disagreement with experi- ment Mulliken calculated a " semi-theoretical " f.This was done by using the experimental value for ? in equation (4.15). Some of the results obtained are shown in Table VI. The agreement is seen to be reasonably satisfactory TABLE VI f Values Calculated by the M.O. Treatment ~ Model. Ethylene . . . . . Butadiene . . . . . #l-Carotene . . . . . Benzene. . . . . . Diphenyl . . . . . Stilbene . . . . . 1 4-Diphenylbutadiene . 1 8-Diphenyloctatetraene ~ - I . I . trans Cis . ' tram I intermediate - . I - . ' trans . trans . I traits I cis 61,000 47,700 - 22,000 56,000 4 1,000 32,000 37,000 30,000 26,000 - f (calc.). 0.30 0-52 0.43 7.0 4.8 0.71 0.4 1 0.55 0.33 0.85 1.57 f (obe.). - 0.53 2.69 - - - 0.41 0.62 0-39 0.84 1.42 although it must be borne in mind that the values listed under f (calc.) were obtained from the theoretical values by multiplication by an empirical correction factor.In general the method leads to results which are greater than the experimental values; this being probably connected with the overemphasis that the L.C.A.O. treatment places on ionic structures. The antisymmetric molecular orbital method has been employed by Sklar 76 to investigate the intensities of the long wave-length transitions in substituted benzenes. The study of the directing power of substituents in a benzene ring as regards further substitution has led to two mechanisms whereby the sym- metrical charge distribution of benzene may be altered in an.isolated mole- cule. The first is known as the inductive effect and arises from the electro- static influence of the substituent upon the n-electrons of the benzene ring ; the second is the mesomeric effect which is brought into play by a migration of charge from the substituent into the ring or vice Groups such as C1 OH NH, which possess a lone pair of electrons are capable of trans- ferring an electron to the ring ; whereas groups such as NO, CHO CO,H which are electron deficient can accept an electron from the ring.It is found experimentally that a substituent which has a strong directing power also exerts a marked intensifying effect on the forbidden transition of benzene 7 5 Reference 24 (d). i 6 J . Client. Physics 1939 7. 984; 1942 10 135. 'I7 C. K. Ingold Chem. Reviewa 1934 15 225. 56 QUARTERLY REVIEWS at 2600 A. Whereas the NH group in aniline possesses a lone pair of elec- trons capable of migration into the ring this possibility no longer exists for the anilinium ion.This means that the only effect left to the ion is the inductive effect. Experimentally the absorption curves of H+ H the anilinium ion and benzene are almost superimposable c ' /H whereas in aniline the shape of the curve is markedly altered II and the intensity of the long wave-length band greatly increased. On these grounds Sklar assumes that migration effects will be mainly responsible for intensity changes. 0 - The case of toluene is of interest insofar as the migrating (LIV.1 electrons must be conceived as coming from a C-H bond. This effect is known as hyperc~njugation.~~ On the valence- bond view the effect can be represented in terms of structures such as (LIV).That this effect is negligible for the anilinium ion is explained on the basis of the increa.sed ionisation potential of NH3. The transition moment was calculated in terms of a parameter which determined the extent of migration of a radical electron into the benzene ring. The parameter was then determined by minimising the energy. The results obtaincd are shown in Table VII in which the f values are uncor- rected for the solvent effect. The value for fluorobenzene is estimated from the work of S. H. W0lleman.7~ On the whole the agreement is good con- sidering the uncertainty in the solvent correction. It follows from the treat- ment that a radical will produce a large intensification effect if it has a low ionisation potential a lone pair of electrons and not too great a ring-radical distance.Sklar has also dealt with polysubstituted benzene derivatives. + TABLE VII Migration Moments of Mofzosu bstit uted Ben- &enes f (theor.). f (oh.). 0.00 13 0.0246 0.0197 Fluorobenzeno . N 0.001 The colour of organic dyes has been investigated by Th. Forster,Bo along the lines suggested by Pauling. 81 Using the V.B. method he considered two idealised systems (LV) and (LVI) representing the cyanine and triphenyl- ineth yl type dyes respectively. In both calculations show that an increase in chain length or an increase in the strength of the auxochrome groups will cause a bathychromic shift, such as is found experimentally. System (LVI) is related to (L) which G. N. Lewis took as the basis of his classification of dyes. The empirical relationships The A groups represent ausochromes.MACCOLL .COLOUR AND CONSTITUTION 57 observed by this author receive a quantum-mechanical foundation on the basis of Forster's work. A I CH CH I I I C+ TI T4 ./ \ \+ -I- + + +/ C'H CH \ N-CH- -[CH-C'H),-N \C'H \ A T3 / \ rJ-z (L\-II*) A (LYI.) K. F. Herzfeld and A. L. Sklar,82 independently of Forster have exam- ined the cpnine dyes in greater detail by both the V.B. and the L.C.A.O. method. The structures used in the IT.B. treatiiient have already been discussed in Section 5 . There will be (2n -i 3) of them for the system repre- sented by (SLIV) corresponding t o the (212 + 3) atoms on which the positive charge may be placed. The secular equation is of degree (212 + 3) and the difference betwecn the two lowest roots is the energy corresponding with the long wave-length transition of the molecule.On the L.C.A.O. view the probloin is that of finding the energy of an electron in the field of t'ho framework (LVII) and of the ( 2 n f 2) othcr electrons. The secular equation gives the energies of ( 2 r ~ f- 3) molecular orbitals and the (2n + 2) electrons are fed into the (11 + 1 ) molecular orbitals of lowest energy. The long wave-length transition then corresponds with the removal of an elect'ron from the highest filled to the lowest unfilled molecular orbital. The secular equations obtaiiied by these two methods are formally similar although the various terms occurring in them have a different interpretation in the two eases. On carrying out the calculations which involve a number of approximations it is found that both treatments predict that the absorp- tion wave-lengths of the members of the series will go to infinity as ?t increases.However only the L.C.A.O. method giws a liiicar relationship between Amax. and n as is observed experimentally. For the unsymmetrical ions the V.B. method is superior predicting the convergence of the lb,n:,x. values as n increases. The present state of affairs in the field of colour and constitution may now be examined. Dealing first with the Lewis and Calvin theory it is found that the simple concept of the two types of linear oscillators is not sufficicnt to explain the behaviour of certain series of compounds. Thus with the p-polyphenyls 83 the convergence is too rapid to give it linear plot of 1.2 against n. This behaviour may be accounted for a p o ~ t i o r i but such a state of affairs is not very satisfactory.It niust be pointed out, however e2 Rev. Mod. Phys?ks 1942 14 294 ; J . Chew. Physicrr 1942 10 508 521. R 3 Reference 58. 58 QUARTERLY REVIEWS that the authors regarded the two types of oscillators as limiting cases but much of the attractiveness of the quantitative treatment is lost when subsidiary assumptions have to be made. Perhaps the greatest achievement of the theory is the broad correlation it has made possible yielding a panoramic view of the field rather than LL “close-up.” The same conclusions can be drawn from an examination of the results of the qualitative application of the theory of resonance. Here again a broad correlation has been achieved,-not only in the field of colour but in the many other aspects of chemistry that can be accounted for on the resonance concept.The theory has aEorded a correlation on the grand scale of the apparently divergent hypotheses introduced by the early works. More specifically a chromogen may be thought of as a resonating system the absorption of which does not extend into the visible. Auxochromes and anti-auxochromes are groups capable of extending the resonance system of the chromogen in such a way that the absorption moves into the visible. The importance of the quinonoid structure in producing colour and in particular the oscillation of the quinonoid condition become intelligible with the aid of resonance concepts. The limitations of the early theories were largely due to their derivation in terms of specific systems ; the power of the resonance treatment lies in its general applicability.Finally there remain the quantal calculat’ions. Here again the position leaves much to bc desired. On the one hand the V.B. treatment has been very successful in predicting the position of the absorption bands for a number of compounds but a t present there exists no guarantee that the calculated absorption bands refer to those actually observed. Only by an investigation of the intensities of the transitions can this point be settled and such an investigation would have to take account of ionic structures which greatly complicate the calculations. Very little evidence can be adduced from the literaturc as to the importance of ionic structures. On the other hand the L.C.,4.0. method has had reasonable success in computing the intensities of absorption bands but only with the aid of the observed wave-length of absorption.It is still to be shown that the bands for which the intensities are calculated are the observed bands. In both these methods the approximations made are rather disconcerting although some justifica- tion may be obtained from the success of similar approximations in the treatmcnt of the ground states of molecules. The most satisfying treatment is with the us0 of antisymmetrical molecular orbitals but here the labour involved restricts a t present the treatment to relatively simple molecules. Many loose ends are apparent in the quantal treatment and only the passage of time will show how successfully they may be tied. The author wishes to acknowledge the award by the University of London of an Impcrial Chcmical Industries Fellowship during the tenure of which this rovinw was written. He also wishes to thank Professor C. K. Ingold F.R.S. for the interest he has shown in this review and Dr. C. A. Coulson and Mr. D. P. Craig for discussions on the subjects under consideration.