DISCUSSION ON MOLECULAR SPECTRA AND MOLECULAR STRUCTURE

In September 1929 the Faraday Society organized a conference on the subject of molecular spectra and molecular structure. The conference took place on September 24 and 25 at the Physical Institute of the University of Bristol, under the chairmanship of Prof. T. Lowry. More than 30 specialists from various countries took part in it.

They included: O. Richardson, St. Allen, MacLennan, Lennard-Jones, Garner and others (England), F. Hund, R. Mecke, Clemens Schaefer and others (Germany), C. Raman (India), R. Birge, R. Millikan, R. Wood (U.S.A.), V. Kondrat’ev (USSR), V. A. Henri (Switzerland), J. Errera (Belgium), J. Lecomte, J. Cabannes, Doré (France), and others. The proceedings of this conference (papers and discussion) have recently been issued as a separate offprint from the Transactions of the Faraday Society.1 Appended to this report is a summarizing survey by the organizers and principal leaders of the discussion, Professors Garner and Lennard-Jones. We give a translation of this survey below.

The 38 papers submitted for discussion cover the whole field of research on molecular spectra and concentrate attention on certain still unresolved problems. The discussion was especially valuable, since it brought together all those working in the infrared, visible, and ultraviolet regions of the spectrum and gave them the opportunity to bring the results they had obtained into agreement with data recently obtained in the study of the Raman effect.

Notation in Molecular Spectra

One of the most important questions subject to discussion was that of notation, since the present lack of agreement in this respect has caused many unnecessary difficulties in reading

of the abundant literature published up to the present time.¹ R. S. Mulliken, F. Hund, and others recently agreed to adopt the approximate scheme proposed by O. W. Richardson. The principal aim of this scheme was to work out a notation in the closest possible harmony with what has already been adopted for atomic spectra. The quantum numbers \(n\) and \(l\) retain a meaning analogous to that used for atoms, and in addition the quantum number \(\lambda\) is introduced to denote the projection of \(l\) on the molecular axis. Lower-case letters are used to denote individual electrons, and capital letters to denote the system of electrons as a whole. Thus, the resultant of the values of \(l\) of the individual electrons is denoted by \(L\), while the resultant orbital moment with respect to the molecular axis is denoted by \(\Lambda\). The quantum numbers of the rotation of individual electrons about their own axis (spin) are denoted by \(s\), and their resultant by \(S\), while the projection of \(S\) on the molecular axis is denoted by \(\varkappa\). The quantum number of the sum of the total resultant angular momentum is denoted by \(J\), as in the case of atoms. It is composed of the electronic vector \(s\) and the resultant angular momenta of orbit and rotation (together denoted by \(K\)). When it is known that individual electrons have a definite angular momentum with respect to the molecular axis, they are denoted as \(\sigma, \pi, \delta, \varphi,\ldots\) electrons, corresponding to \(\lambda = 0, 1, 2, 3,\ldots\), analogous to the notation for atoms \(s, p, d, f\ldots\). For the molecule as a whole, the state is denoted by \(\Sigma, \Pi, \Delta, \Phi\), corresponding to \(\Lambda = 0, 1, 2, 3\ldots\), likewise analogous to the atomic notation \(S, P, D, F\ldots\). Multiplets are denoted as in atomic spectra, for example \({}^{2}\Sigma, {}^{4}\Pi_{3/2}\).

Apparently, among the investigators present at the discussion there was general agreement concerning these main points, and the criticism was directed chiefly against more minor details. The changes which, in Mulliken’s opinion, should be made as a result of the discussion are: the use of \(v\) instead of \(n\) to denote the vibrational quantum number; the use of superscript numbers after the designation of an electronic term to indicate the vibrational quantum number, as in \({}^{2}\Pi^{3}_{3/2}\), and, where necessary, the addition in parentheses of the rotational quantum number (\(K\) or \(J\)).

During the discussion it was emphasized that in experimental work a simpler notation was often desirable, and to meet this need it was proposed to regard such symbols as \(A^{1}\Sigma\) or \(N^{3}\Pi\), or even only \(A\) or \(N\), as sufficient. It was further proposed to denote transitions between molecular electronic states in the form \({}^{2}\Pi \to {}^{2}\Sigma\), in order to indicate clearly the direction of the transition. Those interested in polyatomic molecules insisted that the notation

¹ Cf. the articles by V. N. Kondrat'ev, Uspekhi fizich. nauk, 9, 1929, and R. Mecke, ibid., 9, 1929; cf. also the article by S. E. Frisch in the present issue, p. 110. Ed.

accepted for diatomic molecules could be extended to more general cases.

A significant feature of the discussion was that it led to a general reconsideration of the present situation and prompted researchers to examine the successes achieved in the last several years. O. W. Richardson gave a survey of the results obtained for the hydrogen molecule, for which about forty different electronic levels are now known, all of them accounted for by modern theories. W. I. Curtis presented a report on the current state of the band spectrum of helium, the analysis of which is almost completely finished in the visible and ultraviolet regions. This spectrum is especially interesting, since it shows that the vectors \(l\) of the individual atoms, as the rotation increases, become less and less connected with the nuclear axis of the molecule and tend to merge with the axis of rotation. The transition from one case to the other leads to sharp anomalies in the structure and intensity of the spectra. The theoretical significance of these anomalies was shown in convenient form in the energy diagrams presented for discussion by G. H. Dieke.

Besides the spectra of hydrogen and helium, much attention was attracted by the band spectrum of carbon monoxide; at present 16 systems of bands of this compound are known. A detailed report on them was given by R. Johnson, who drew attention to Asundi’s recent discovery of a quintet level \({}^{5}\Pi\) in this spectrum (the first quintet known for band spectra); the speaker assigns the third positive system of carbon bands to the transition \({}^{5}\Sigma \to {}^{5}\Pi\). This conclusion is important, since, if it is correct, it requires changing the electronic levels of the CO molecule that had been assumed up to now. Johnson proposes a detailed scheme for the arrangement of the electrons of carbon monoxide in various levels. He also indicates the states of the carbon and oxygen atoms after dissociation from each state.

Formation and Dissociation of Molecules

For physicists and chemists it is extremely important to know the true state of excitation of the constituent parts of a molecule upon dissociation, since this knowledge can be used to test the reverse effect of combination. J. Lennard-Jones proposes an “Aufbauprinzip” for a series of diatomic molecules, which is reported here.

His investigation shows theoretically that it is to be expected that some molecules dissociate into normal components, while others dissociate into one or several excited components. For example, one may expect that the molecular ion \(N_2^+\) dissociates from its normal state into one normal atom \(N\) and one excited ion \(N\); Heitler and Herzberg have recently arrived at the same conclusion experimentally.

Other cases of the decomposition of a normal molecule into excited atoms are given in the work of E. Bengtsson and E. Hulthén.

(Hulthen) (Stockholm), who described some new results obtained in the study of the spectra of certain metal hydrides (CuH, AgH, AuH, etc.). A typical result is that CuH decomposes from its normal state \({}^{1}\Sigma\) into an excited Cu atom (in the state \({}^{2}D\)) and an H atom with the \(3d\) level.

F. Hund (Leipzig) reported on general criteria for the chemical bond. It is at present theoretically possible, with the aid of the new quantum mechanics, to determine the interaction of two atoms in a molecule; however, in practice the calculations are so intricate and difficult that they have been carried out only in one or two simple cases. It is therefore desirable to have other, simpler methods indicating whether two atoms can combine to form a stable molecule or not.

The method, in many cases successfully applied by Hund, can be illustrated by considering two pairs of atoms, \(\mathrm{H} + \mathrm{H}\) and \(\mathrm{He} + \mathrm{H}\), in their ground states. One pair can form a molecule (\(\mathrm{H}_2\)), the other probably cannot (\(\mathrm{HeH}\)). The characteristic difference can be explained by the change in the bond between the electrons in two hypothetical processes: \(\mathrm{H} + \mathrm{H} \to \mathrm{H}_2 \to \mathrm{He}\) and \(\mathrm{He} + \mathrm{H} \to \mathrm{HeH} \to \mathrm{Li}\). In the first case the bond between the electrons increases in passing from separated atoms to the united atom, whereas in the second case the bond of one of the three electrons proves to be considerably weakened.

One of the interesting results of work with band spectra is the determination of heats of dissociation. It was noticed that series of vibrational levels often approach a point of convergence, i.e. that the distance between successive levels approaches zero, and at present it is generally accepted that at the point of convergence one part of the molecule (usually an atom) separates from the remaining part. If it were possible to trace the vibrational-energy levels up to, or almost up to, the point of convergence, the amount of energy required for dissociation from a known electronic level would become known. The usual heat of dissociation, as chemists define it, can then be found when the energy reserve (i.e. the state of excitation) of the dissociated atoms is known. Unfortunately, it is not always possible to obtain a complete series of vibrational-energy levels all the way to the limit of dissociation, and when only an incomplete series can be obtained, special methods must be applied in order to carry out a correct interpolation up to dissociation. The most successful of such methods was given three years ago by Birge and Sponer and was applied to molecules of nitrogen, oxygen, carbon monoxide, and others. At present R. T. Birge has proposed an improved method, described in the report presented at the discussion. The essential point of the paper concerns a new way of calculating the vibrational frequency, which, as the speaker states, leads to a more reliable estimate of the heat of dissociation. The most probable values of the heats of dissociation of nitrogen and oxygen are at present determined as 9.1 volts for the former and 6 volts for the latter,

From this investigation follows the circumstance that in many cases the graph of the difference of frequencies, as a function of the quantum number, possesses an inflection point which, it is supposed, is due to a discontinuity of the dissociation process; it is considered that the rupture corresponds to a molecular redistribution. P. Johnson, during the discussion, expressed the suggestion that the critical point marks a change from the quasi-molecular to the truly atomic state within the constituent atoms.

The band spectra of polyatomic molecules reveal a more gradual transition from banded to continuous spectra. V. Henri and his collaborators found that, in complex molecules, the bands before the transition into a continuous spectrum become diffuse. These diffuse bands are attributed to the disappearance of the quantization of rotation. V. Henri uses the term “predissociation” to designate the state of a molecule after it has absorbed energy corresponding to the wavelength in these diffuse bands, and advances evidence in favor of the view that the molecule in this state is chemically active. He comes to the conclusion that vibrational bands become diffuse as a consequence of molecular redistribution, which takes place in a time interval smaller than the period of rotation but greater than the period of vibration of the molecule. This redistribution may consist in dissociation into atoms, or may be due to some change in the molecular level. In discussing the above-mentioned phenomenon, V. Henri indicated that an increase in temperature promotes the formation of diffuse spectra. A report by S. Barrat states the appearance of similar diffuse bands in the spectrum of molecules formed by zinc, cadmium, and mercury with alkali metals, while Gerderberg found similar bands also in the ultraviolet part of the absorption spectra of metal halides. Gerderberg assumes that the state of predissociation sets in only in the case when the energy content of the molecule is higher than the dissociation energy of the normal state.

Ellis applies the methods of Birge and Sponer to the calculation of the heat of dissociation of the C—H and N—H bonds in organic compounds. The results proved to be in agreement with thermal data and indicate that the heat of dissociation of these groups depends on the chemical structure.

In the work of Goodeve and Stein on the absorption spectrum of chlorine dioxide, an interesting example is given of a change in the curvature of the curve of frequency differences as a function of the quantum number. The curve is of a different type from that described by Birge. The rotational structure of the vibrational bands disappears at the point where the curvature changes; thus these experiments are connected with V. Henri’s experiments on predissociation.

Band spectra and atomic nuclei

The study of band spectra promises to be a valuable source of information about the mass and structure of nuclei and, in particular, may lead to the discovery of many new isotopes. The rapid successes achieved in this field during the past year have been summarized by R. T. Birge. It has been established that isotopes of oxygen exist whose masses are 17 and 18, and that carbon has an isotope with mass 13. It is possible that all elements have isotopes, although the agreement of Aston’s mass determinations with the usual chemical atomic weights proves that each of the as yet unknown isotopes can occur only in very small quantity. For the discovery of such weak isotopes, analysis of band spectra seems more effective than the mass-spectrograph method; but since band spectra indicate only the relative masses of two isotopes, both methods should be used to supplement one another.

In Mulliken’s work it is reported that band spectra are connected with the intrinsic rotation (spin) of nuclei. In the spectra of molecules that contain two nuclei of equal charge and mass, in all series of band lines every other line is comparatively weak or even absent. Heisenberg and Hund suggested that this phenomenon can be explained by assuming that a necessary condition for the existence of any state of a molecule is the antisymmetry of that state with respect to all protons as well as all electrons. The validity of this antisymmetry rule for extranuclear electrons in atoms has been well established by data on line spectra. Its applicability to protons is confirmed by data on the specific heat and band spectrum of hydrogen, but it is still doubtful whether this rule applies to protons and electrons in complex nuclei. In the case of N₂ difficulties arise. In most cases the alternating intensity observed in the Raman effect is in complete agreement with the changes in the intensity of band spectra and agrees with theoretical calculations; but for nitrogen Rasetti found that transitions between even levels of the ground state are more intense than those between odd levels. Since nitrogen in the ground state corresponds to the term \(^{1}\Sigma\), like H₂, and from the structure of the nuclei one might have expected that rotation of the nucleus about its own axis would be the same as in hydrogen, this result apparently proves to be in contradiction with the rule stated above.

It appears that the fundamental functions of the nitrogen molecule are symmetric with respect to the nuclei. This means that nitrogen nuclei obey Bose statistics, whereas, as Mulliken emphasizes, they had been expected to obey Fermi statistics, since they contain an odd number of particles that obey Fermi statistics. G. Herz-

berg cites the recently published views of Heitler and his own, according to which the electron in the nucleus not only loses its rotation about the axis [as Kronig showed], but also its influence on the statistics. If this is true, it is a new and remarkable result.

The isotope effect in chlorine compounds was discussed by Patkowski and Kurtis for the absorption spectrum of JCl, by V. Henri for COCl₂, and by Gudiv and Stein for ClO₂. Patkowski and Kurtis showed that, for a molecule in which relatively large quantum numbers occur, the isotope separation of the band heads reaches a maximum for a particular value of the vibrational quantum number. From the position of the maximum it is possible to calculate the true values of \(n'\). This circumstance was used to obtain the true vibrational quantum number for the bands in the spectrum of JCl.

Raman Effect

The discussion of the Raman effect was opened by Sir C. V. Raman; communications were made by R. W. Wood, J. Cabannes, P. Daure, T. S. Allen, A. M. Taylor, and A. C. Menzies. Raman gave a historical survey and emphasized the need to connect the effect with diamagnetic susceptibility and the optical anisotropy of crystalline substances. The new method has opened up many possibilities of development for chemists, in particular in the direction of extending our knowledge of the frequency of vibrations and the structure of organic molecules. Light scattered when a monochromatic ray passes through a gaseous, liquid, or solid medium is split into a series of bands of frequency \(N \pm n\), where \(n\) is identified with the characteristic frequency of rotation and vibration of the medium. The closeness between the values of \(n\) and the frequency of infrared bands is proof of the correctness of such an interpretation. However, one of the important features of the Raman effect is the fact that the frequency of the scattered radiation indicates the existence of vibrations in molecules which are optically inactive in the absorption spectrum. This has already been reported, but it could not be proved from infrared spectra. For example, Cl. Schaefer showed in his article that the levels of the infrared vibrations of the CO₃ ion can be explained only by allowing that some absorption bands are due to inactive vibrations occurring together with active vibrations. The frequency of the optically inactive vibrations required for a proper interpretation of the infrared spectra is exactly the same as that strictly found in the Raman effect. A parallel case is presented by the carbon dioxide molecule; optically inactive vibrations of this molecule are sharply revealed in the Raman spectrum (Rasetti).

V. Henri reported on the significance of the Raman spectrum for the analysis of the ultraviolet spectrum of organic compounds. In such an analysis it is important

know what the fundamental frequencies of unexcited molecules are, and they are given by the Raman spectrum.

MacLennan finds in the Raman spectrum of ordinary liquid hydrogen two possible transitions between rotational states \(0 \to 2\) and \(1 \to 3\), the latter being the stronger. The relative intensities of the lines corresponding to these transitions become intelligible if in the state of the first rotational quantum there are two or three times as many molecules as in the state of zero rotation. This result is in agreement with the result obtained on the basis of the study of the specific heat of gaseous hydrogen, with allowance for the relative weights of the odd and even rotational levels.

Owing to the high degree of dispersion that can be obtained by Raman’s method, a splitting of the C—H band into several components is observed. Raman showed spectra in which this band decomposed into four clearly distinguishable component parts; such a decomposition was also obtained by Petrikaln and R. W. Wood. The latter reported improvements in experimental technique necessary for obtaining such a result.

It was emphasized that the frequencies of the lines due to the C—H bond in compounds of the aromatic and aliphatic series are different, and that the degree of polarization is also different. The lines from cyclohexane occupy an intermediate position between the lines of compounds of the aromatic and aliphatic series. Attention was drawn to the theory of the intensity and degree of polarization of Raman lines in Kabann’s paper, which stresses the importance of these spectra for extending information on the structure of crystals—information obtained by means of X-rays. Doré draws attention to differences between the spectra of liquids and gases and points to the great importance of the effect for the study of liquid compounds. R. Mecke supplemented the results obtained by Doré concerning the difference between the spectra of gases and liquids with a table of data for ammonia, water, methane, ethylene, and for the ion \(\mathrm{SO}_4\). A. M. Taylor’s work on the Raman lines of the ions \(\mathrm{AX}_4\) shows that the frequency of oscillations decreases upon destruction of the crystal lattice and upon hydration of the group, while Menzies describes experiments in which measurements of the Raman effect were made on crystals ground into powder (see also Nature, Oct. 5, 1929, p. 511).

Structure of Unexcited Molecules

In the last few years there has been a rapid increase in our knowledge of the rotational and vibrational levels of molecules in the unexcited state. The study of infrared absorption spectra has revealed not only the magnitude of intranuclear distances, but has also given precise indications concerning the rotational and precessional motions of the molecule. Detailed study at present

STRUCTURE OF UNEXCITED MOLECULES

...time has been limited to simple molecules in the gaseous state. In complex organic molecules studied in the solid or liquid state, only the vibrational levels of such groups as C—H, C=O, C—OH, N—H, C≡N, as well as the character of the changes in these levels with changes in chemical composition, have been systematically investigated. In the introductory address on the infrared spectra of gases, P. Robertson outlined the advances achieved, drawing particular attention to their relation to the problems of chemistry. I. K. Reidel also gave a survey of the latest advances in this field that are of interest to chemists.

I. F. Barker and K. F. Meyer, in a review of experimental investigations of the vibrational bands of simple molecules in the gaseous state, propose a method for classifying molecules by groups, depending on the complexity of the rotational levels. Diatomic and linear molecules, such as the molecules of carbon dioxide and acetylene, rotate only in one plane and exhibit no precession. Methane, owing to its symmetry, can rotate about any axis without precession, but in general polyatomic molecules rotate with precession, the complexity of which depends on the symmetry of the molecule. Ammonia, ethane, methyl fluoride, and other molecules symmetrical about one axis of rotation give a less complex rotational structure than water, hydrogen sulfide, and ethylene, which possess three unequal moments of inertia.

It is curious that the molecules of carbon dioxide are linear, whereas the molecules of water are triangular.

Noteworthy are the successes in interpreting molecular spectra obtained by applying the concept of the rotation of nuclei about their own axis. The bands of acetylene present a striking example of alternately varying intensity, analogous to that observed in the hydrogen molecule and explainable in the same way. The two hydrogen protons of acetylene, both rotating parallel to the axis of rotation of the molecule, may have either identical or oppositely directed rotations. Thus, apparently, there exist two kinds of acetylene molecules, just as there exist two kinds of hydrogen molecules. In the bands of such molecules as methyl fluoride and ammonia, which have a threefold symmetry of the protons with respect to the axis of rotation, every third rotational level proves to be enhanced.

Robertson and Barker considered the double \(Q\)-branch of ammonia, situated at 10.3 μ and 10.7 μ. Barker suggested that the ammonia molecule has the form of a low triangular pyramid. Two of the four fundamental types of vibration are vibrations of the N atom along the axis of symmetry, i.e., normal to the plane of the three H atoms. The 10.5 μ band is connected with the symmetrical motion of the H atoms: the distance between the latter increases when the N atom approaches the plane in which they are situated. The N atom may be in a position of equili-

weights on both sides of this plane; therefore the potential-energy function displays two minima separated by a comparatively low maximum. Thus, with each vibrational state there may be associated two fundamental functions, one of them symmetric and the other antisymmetric. Since in this case transitions occur between states of opposite character with respect to symmetry, i.e. \(1a \to 2_s\) or \(1_s \to 2_a\), two absorption bands appear, differing only slightly in frequency.

F. I. G. Rawlins gave a survey of the data at present known concerning the infrared absorption spectrum, the molecular heat, and the electric moment of carbon dioxide, and came to the conclusion that this molecule is linear. C. P. Snow, in a report on the vibrational-rotational spectra of diatomic molecules, draws attention to the appearance of a \(Q\) branch in the rotational-vibrational spectrum of nitric oxide; this is attributed to the fact that the molecule under consideration contains an odd number of electrons.

Mekke and Badger successfully photographed the higher harmonics of the spectral bands of ammonia in the near part of the infrared spectrum. The fine structure of these bands is analogous to the structure of the bands in the more distant infrared region. This is a notable achievement in the technique of studying vibrational bands.

Liquid State

It has already been reported that progress has been made in our knowledge of the structure of liquid molecules by means of Raman-spectrum investigations. The Raman spectra of liquids in their main features agree with infrared spectra, and from both of these sources one can obtain data concerning vibrational levels. Jean Lecomte, in an introductory article on the infrared spectra of liquids, summarizes the experimental results obtained in this field up to the present time.

The vibrational levels of the groups C—H, N—H, C=O, and others are now known, thanks to the work of Bonino, Lecomte, Ellis, Sallant, and others; by the Raman method it has been found that the C—H levels are multiple. Apparently, in the molecule there is a special level for each C—H group, and the greatest difference in frequency occurs between the C—H levels of compounds of the aliphatic and aromatic series. G. B. Bonino discusses the influence of chemical structure on the fundamental frequency of this group and considers the influence of lengthening the carbon chain, the presence of a double bond between carbon atoms, and the influence of hydroxyl and halogen substitution. Bonino found that the damping coefficients of absorption bands are not proportional to the number of groups in the molecule; investigation of the individual C—H levels from this point of view still remains to be undertaken.

Solid State

In a report on the infrared spectra of solids, K. Schäfer summarizes the information obtained up to the present concerning the vibration frequencies of crystal lattices and the vibrations of atoms forming physically distinct groups in the crystal. Schäfer’s detailed investigations of crystalline carbonate and nitrate salts have clarified the optically inactive vibrations of the ions \(CO_3\) and \(NO_3\), and have also shown how the vibrations of atoms in these groups depend on the symmetry of the crystals. The cations have only a small influence on the principal features of the vibrations of these groups—for example, on their frequency. This is in agreement with the structure of these ions as derived by means of X-ray analysis. In uniaxial crystals, however, the frequency of the bands is higher, and this may mean that the equilateral character of the \(CO_3\) ion is disturbed, although this has not yet been detected by X-ray analyses. The infrared spectrograph can therefore be used to supplement investigations carried out with the aid of X-rays.

Water of crystallization gives almost the same vibration frequency as liquid water, but the bands are doubled in uniaxial crystals and tripled in biaxial crystals, which indicates that the symmetry of the water molecule has the character of the symmetry of the crystal as a whole.

A. M. Taylor describes experiments carried out on crystals containing the group \(AX_4\). The groups \(SO_4\), \(CrO_4\), and \(ClO_4\) give very similar absorption spectra. For these groups there are two fundamental vibrations that are optically active, and one that is optically inactive.

1. Molecular Spectra and Molecular Structure. A general Discussion held by the Faraday Society. September, 1929, pp. 343, price Sh. 15/6. ↩