APPLICATION OF RAMAN SCATTERING OF LIGHT TO THE STUDY OF THE COMPOSITION AND STRUCTURE OF MATTER

M. M. Sushchinskii and P. A. Bazhulin

1. INTRODUCTION

At the present time Raman scattering of light is widely used for studying the composition and structure of matter. On the basis of the Raman-scattering method, qualitative and quantitative analysis of complex organic mixtures is possible; determination of their composition by other methods is very difficult, and in a number of cases even impossible. Molecular analysis from Raman spectra has become a widespread method of investigation and has already found application in solving a number of practically important problems.

No less important are the applications of Raman scattering of light to the study of molecular structure and to the determination of the parameters characterizing molecules. The data provided by Raman spectra (and by infrared spectra) make it possible to determine the frequencies of intramolecular vibrations and the forces acting between atoms in molecules, as well as important electro-optical parameters of the latter. Finally, Raman spectra are successfully applied to the investigation of the condensed state, making it possible to elucidate subtle features of the structure of liquids and crystals.

The purpose of the present article is to give a summary of the principal results obtained in the works of G. S. Landsberg, his students, and collaborators in the field of studying the composition and structure of matter by the method of Raman scattering of light. The review in no way claims to provide a complete treatment of the questions touched upon or a systematization of the entire extensive literature. We also touch only briefly upon those questions that have received sufficient reflection in a recently published monograph[^1].

Owing to the specific character of the proposed review, we have not been able to cover properly the work of a number of authors on the application of Raman spectra of light to the study of molecular structure and to molecular analysis. Therefore a number of important results obtained in the works of M. V. Vol’kenshtein, P. P. Shorygin, V. M. Tatevskii, V. M. Chulanovskii, and other authors are not reflected in the present work. We hope that this gap is partly compensated by the existence of the very thorough reviews by P. P. Shorygin[^18] on the questions mentioned.

2. APPLICATION OF RAMAN SCATTERING OF LIGHT TO THE STUDY OF MOLECULAR STRUCTURE

In characterizing the significance of Raman scattering of light for the study of molecular structure, G. S. Landsberg usually compared it with the methods of X-ray diffraction and electron diffraction. He pointed out that, just as those methods became fundamental for solving questions of the statics

molecules—for determining the mutual arrangement and distances of the atoms and ions constituting a molecule or crystal, combination scattering of light is the principal method for studying molecular dynamics.

In the spectra of combination scattering, the complex intramolecular processes that arise when a light wave interacts with a molecule are reflected. The lines in combination-scattering spectra are directly connected with intramolecular vibrations; therefore the data obtained with the aid of these spectra can be used to determine important parameters characterizing the dynamical and electro-optical properties of molecules, above all to determine the force constants of a molecule. However, because the structural features of a molecule manifest themselves in combination-scattering spectra through intramolecular vibrations, the regularities connecting these spectra with molecular structure are complex and highly distinctive.

The simplest conclusions of a structural nature from combination-scattering spectra are connected with establishing the symmetry properties of molecules, which determine the selection rules in vibrational spectra. Data on the number of lines, their intensities and polarizations—even if only roughly qualitative—make it possible in many cases to decide whether the molecule under study possesses certain elements of symmetry. For simple molecules these data are often sufficient for choosing between one or another possible model and for establishing the real geometrical configuration of the molecule. A number of examples of determining molecular structure in this way are given in works \(^{2-5}\). However, as molecules become more complicated, this path becomes less and less effective, since with a large number of expected lines in the vibrational spectra the interpretation of the observed lines becomes ambiguous.

In the search for a solution to the problem of establishing the connection between combination-scattering spectra and the structure of complex polyatomic molecules, two main directions have by now taken shape. The first direction, which may be characterized as theoretical, is based on the application of methods for calculating molecular vibration frequencies. The second direction rests on the establishment of regularities that appear when comparing the combination-scattering spectra of a number of closely related compounds. This direction is to a considerable degree empirical. Both directions arose and developed over a long period of time independently of one another, although it is quite clear that the solution of so complex a problem as establishing molecular structure and interpreting their vibrations requires the use of all possible means, both theoretical and experimental.

The first attempts to apply computational methods to the determination of molecular vibrations were rather primitive and were usually based on replacing the real molecule by a crude model. It is therefore natural that, despite some successes, no substantial results were obtained along this path, and in some cases the conclusions to which such calculations led proved erroneous. A substantial step in the direction of a theoretical calculation of molecular vibrations was made by the Soviet scientists M. A. Elyashevich and B. I. Stepanov \(^{6,7,8}\), who laid the foundations for a rigorous calculation of vibrations. Thanks to their work, the calculation of the vibration frequencies of complex molecules became quite realistic, and the interpretation of observed spectra considerably more reliable. A substantial contribution to the theory of molecular vibrational spectra was made by L. S. Mayants \(^{10}\). Despite the great successes, it is necessary to note certain features of the existing computational methods that limit the prospects for their application. By their very nature these me—

methods are semiempirical and approximate, since the values of force constants are borrowed from experiment; moreover, constants found from the spectra of simple molecules are, as a rule, considered unchanged in passing to more complex molecules[^8]. In determining force constants from observed spectra, molecular vibrations are assumed to be harmonic, as a result of which the real anharmonicity of the vibrations enters implicitly into the values of the force constants. The latter is especially significant in those cases where hydrogen atoms take a noticeable part in the vibrations. Thus, the very fundamental basis of the existing computational methods contains possible sources of error which, for all the fruitfulness of these methods, must not be forgotten in order to avoid overestimating the accuracy they provide. To this one may add that, in most cases, in order to facilitate the calculations, the simplest and most symmetrical of the various possible models of the molecule is chosen, often without serious grounds for doing so.

In view of the above circumstances, a cautious approach is required toward the data supplied by calculations of vibrational frequencies. In interpreting spectra, it is necessary to make use of as extensive experimental material as possible—measurement, alongside the frequencies, of other parameters of the lines in Raman spectra; use of data from infrared spectra; and, in a number of cases, investigation of deutero derivatives. Such comprehensive studies have so far been carried out only for a small number of the simplest molecules. As for the calculation of electro-optical parameters—the intensity and degree of depolarization—then, despite the important results obtained by M. V. Vol'kenshtein[^8][^9], progress here is still insufficient for their application to molecules of any complexity.

The second direction, which we characterized above as empirical, uses the comparison of spectra of a series of closely related compounds in order to draw conclusions about the connection between Raman spectra and molecular structure. The principal result obtained along this path was the establishment of the existence of characteristic frequencies. It was found that the spectra of molecules possessing the same characteristic groups of atoms, bonds, etc., often have certain common frequencies, or frequencies differing little from one another. These frequencies, accompanying definite chemical groups included in different molecules, received the name characteristic frequencies.

The initial, highly simplified conception of characteristic frequencies as vibrational frequencies in which some one bond or a small group of atoms participates proved to be, to a considerable extent, incorrect. On the basis of such simplified notions, numerous errors and misunderstandings occurred1. Nevertheless, the comparative method itself, which led to the discovery of characteristic frequencies, raises no objections; and the fact that characteristic frequencies exist undoubtedly reflects important properties of polyatomic molecules. With a reasonable approach, the use of characteristic frequencies for conclusions about the structure of molecules has in a number of cases yielded very positive results[^11].

Of particular importance is the systematic study of whole classes of compounds with gradually increasing complexity of molecular structure. Such studies are very few in number; as a rule, the selection of the objects of study is, to a greater or lesser degree, random

character. Systematic studies of the spectra of combination scattering of hydrocarbons, which were carried out over a number of years by the Optical Laboratory of the Lebedev Physical Institute jointly with the laboratory of catalytic synthesis of the Institute of Organic Chemistry, headed by Academician B. A. Kazanskii, made it possible to apply fully the comparative method of investigation for establishing the correspondence between spectra and the structure of molecules.

It should be noted that, because of the insufficient development of methods for investigating combination-scattering spectra, when only one parameter—the frequencies—was measured in these spectra, the possibilities afforded by the comparative method of studying spectra were far from fully utilized. After rigorous methods had been developed for measuring the intensity, the degree of depolarization and, somewhat later, the widths of the lines of combination scattering, and it became possible to compare the values of these parameters in spectra quantitatively, the comparative method of studying spectra received further development.

A comprehensive investigation of combination-scattering spectra presents great difficulties. From the point of view of experimental technique, these difficulties are connected mainly with the need to measure the intensity of weak and diffuse lines situated on a considerable continuous background. More substantial, however, are the difficulties of principle and methodology associated with the necessity of taking into account the influence, on the measured values of the parameters of the combination-scattering lines, of the conditions of excitation of the spectra, the spectral apparatus, etc. These difficulties were for the most part overcome as a result of a cycle of works carried out over a number of years by G. S. Landsberg and his collaborators. The methods developed for measuring the parameters of combination-scattering lines are described in detail in the monograph¹; therefore we shall not dwell on them here. It is important to note that these methods give values of the parameters of combination-scattering lines that unambiguously characterize the substance under investigation under given experimental conditions—temperature, pressure, and state of aggregation. Therefore the values obtained for the parameters give a physical characteristic of the substance under investigation.

Table I

Valence vibrations of the CH₂ and CH₃ groups in normal paraffins
\((m\)—number of the corresponding groups)

In comparing the spectra of compounds possessing common structural features, it became clear that in a number of cases, along with the frequencies, other parameters of the lines also retain their significance in the transition from one molecule to another—intensity, degree of depolarization, and width. As an example, in Table I we give data for the valence vibrations of CH in the spectra of normal paraffins ^12 and in Table II data—

Table II

Characteristic line of the double bond \(C=C\)

for the vibrations of the double bond \(C=C\) in the spectra of \(\alpha\)-olefins ^13. It is essential that the characteristic nature of some parameters is closely connected with the characteristic nature of other parameters; i.e., there is an internal connection between the various parameters of lines in combination-scattering spectra. Thanks to this, it proved possible to broaden the concept of characteristicity, established in the study of frequencies, and to formulate the concept of characteristic lines, by which are meant lines in combination-scattering spectra that possess a set of characteristic parameters ^14. The concept of characteristic lines is a natural generalization of the concept of characteristic frequencies.

The study of combination-scattering spectra showed that not every branching, combination of branchings, or other peculiarity of molecular structure that recurs in a series of related compounds leads to the appearance of characteristic lines in their spectra. Only certain specific groups of atoms or bonds (in a number of cases, individual atoms and bonds) possess characteristic lines in combination-scattering spectra. Such structural units, whose presence in molecules is accompanied by the appearance in combination-scattering spectra of a stable set of characteristic lines, may be called characteristic structural elements of the molecule ^14.

The special role of characteristic structural elements is due to the fact that they represent those structural units of molecules which actually manifest themselves in vibrations and, through vibrations, in combination-scattering spectra. We emphasize this circumstance because in complex molecules possessing a large number of branchings of different types, one can speculatively single out the most diverse combinations of branchings, complexes of atoms, etc., to which, however, no characteristic features in combination-scattering spectra correspond.

Establishing the characteristic structural elements of a certain group of compounds is an important stage in the work of revealing the connection between combination-scattering spectra and the structure of molecules, for the fundamental properties of the spectra are determined by the presence in complex molecules of one or another characteristic structural element.

The identification of characteristic structural elements with their inherent aggregate of characteristic lines requires, along with experimental study and comparison of the spectra of a series of related compounds, also carrying out calculations of the vibration frequencies of the simplest molecules possessing the given characteristic structural element. Therefore, in the method of characteristic structural elements and characteristic lines, the two principal directions mentioned above, which arose in the study of vibration frequencies, are naturally combined and generalized.

A good example of a characteristic structural element is a complex of the form

\[ \begin{array}{c} \mathrm{C}\\ |\\ -\mathrm{C}-\mathrm{C}-\mathrm{C}-\\ |\\ \mathrm{C} \end{array} \]

which is often encountered in molecules of paraffins and other hydrocarbons (a quaternary carbon atom). The spectra of hydrocarbons possessing such a complex have certain characteristic features. Thus, for example, in the case of paraffins possessing a quaternary carbon atom, the following features of the combination-scattering spectra may be noted in comparison with other paraffins:

1) The lines belonging to the fully symmetric valence vibrations of the skeleton are shifted into the region of lower frequencies and are situated in a narrow interval, \(700—750\ \mathrm{cm}^{-1}\), for paraffins with one isolated quaternary atom, or \(650—700\ \mathrm{cm}^{-1}\) for paraffins possessing quaternary atoms with adjacent branchings. These lines are distinguished by great intensity and comparatively small width.

2) In the spectra there are characteristic lines of the quaternary carbon atom in the regions \(925\ \mathrm{cm}^{-1}\) and \(1200—1250\ \mathrm{cm}^{-1}\).

3) A certain characteristic shift of the frequencies of the lines is observed in the region of CH valence vibrations.

To illustrate features 1) and 2), we give in Table III data for several paraffins possessing a quaternary carbon atom.

Another characteristic structural element in the case of paraffins is the tertiary carbon atom, i.e. a complex of the form

\[ \begin{array}{c} \mathrm{H}\\ |\\ -\mathrm{C}-\mathrm{C}-\mathrm{C}-\\ |\\ \mathrm{C} \end{array} \]

The features of this characteristic structural element are expressed more weakly than those of the quaternary carbon atom. The most reliable indication is the presence of characteristic lines in the region \(950\), \(1140\), and \(1170\ \mathrm{cm}^{-1}\). The fully symmetric lines of the valence vibrations of the skeleton in the spectra of paraffins having tertiary atoms are shifted somewhat into the region of lower frequencies, in comparison with normal paraffins, but this shift is small and is expressed less distinctly than in the spectra of paraffins having quaternary atoms.

The combination-scattering spectra of complex polyatomic molecules possessing several characteristic structural elements are in many cases formed by additive superposition

spectra of individual structural elements. For example, in the spectrum of 4-methyl-4-ethylhexene-1

\[ \begin{array}{cccccc} & & & \mathrm{C} & & \\ & & & | & & \\ \mathrm{C}{=}\mathrm{C}{-}\mathrm{C}{-}\mathrm{C}{-}\mathrm{C}{-}\mathrm{C} \\ & & & | & & \\ & & & \mathrm{C} & & \\ & & & | & & \\ & & & \mathrm{C} & & \end{array} \]

which possesses two characteristic structural elements—a quaternary carbon atom and a double bond—lines of both elements appear.

Table III

Characteristic lines of the quaternary carbon atom

  C

  C

    C

  C

  C

  C

In the spectrum there is a line at \(1641\ \mathrm{cm}^{-1}\) (80), characteristic of the structural element \(\mathrm{C}{=}\mathrm{C}\), and the lines 913 (7), 1211 (14), and 1244 (10), characteristic of the quaternary atom (the intensities at the maxima of the lines are given in parentheses). In the region of valence polysymmetric skeletal vibrations there is a strongly polarized line at \(724\ \mathrm{cm}^{-1}\) (31), analogous to the lines of paraffins possessing a quaternary carbon atom (see Table III).

If the molecule under investigation contains several identical characteristic structural elements, then the frequencies of the characteristic lines belonging to them coincide in many cases. As a result of this

the intensities of the corresponding lines are proportional to the number of similar structural elements. This phenomenon is well illustrated by the example of lines belonging to the valence vibrations of the CH₂ and CH₃ groups of normal paraffins¹². Another example of the additivity of intensities may be provided by the spectrum of diallyl, which has two C=C bonds:

\[ \mathrm{C{=}C{-}C{-}C{-}C{=}C} \]

In the spectrum of this compound the integral intensity of the line 1641 cm⁻¹ is equal to 780 (calculated per 1 gram-molecule), whereas in the spectra of α-olefins, which have one C=C bond at the end of the molecule, the intensity of the corresponding line is equal to 400 (cm⁻¹)¹⁵.

It is very important to note that the indicated additivity is far from always manifested. In a number of cases there is a complex and peculiar “interaction” of characteristic structural elements, accompanied by violations of additivity. The most characteristic violation of additivity consists in the fact that in the spectrum of a molecule possessing several characteristic structural elements, first of all the characteristic lines of one, the most “strong” of these elements appear, while the lines of the other elements prove to be weakened or do not appear at all. As an example let us consider the spectrum of 2,2,4-trimethylpentane

\[ \begin{array}{ccccc} & & \mathrm{C} & & \\ & & | & & \\ \mathrm{C} & - & \mathrm{C} & - & \mathrm{C} - \mathrm{C} - \mathrm{C} \\ & & | & & | \\ & & \mathrm{C} & & \mathrm{C} \end{array} \]

In the spectrum of this hydrocarbon there are all the indications of a quaternary carbon atom (see Table III). If one proceeds from the idea of additivity, one might expect that the lines of the tertiary atom should also be present in the spectrum of this compound. However, this assumption is not justified. Not all of the lines of the tertiary carbon atom are present, and moreover they are very weakened in comparison with analogous lines in the spectra of compounds close in structure but not possessing quaternary atoms (see Table IV). The parameters of the line belonging to the valence

Table IV

Characteristic lines of tertiary carbon atoms

fully symmetric skeletal vibrations, correspond fully to the tetrahedral carbon atom; the presence in the molecule of a tertiary atom likewise did not manifest itself in any way in this respect.

If, when the structure of the molecule changes, the vibrations of the main characteristic structural element are disturbed, then the lines of other characteristic elements appear more distinctly in the spectrum. Such changes are often observed in the spectra of naphthenes, where the ring vibrations, for certain types of substitution, are disturbed, and then lines of other structural elements appear in the spectra.^14

The identification of characteristic structural elements with the set of characteristic lines inherent to them is the first step toward establishing a correlation between combination-scattering spectra and the structure of molecules. The second step is the study of the regularities in the change of the parameters of characteristic lines, i.e., deviations from characteristicity. Since every characteristic structural element is a component part of the molecule, its vibrations are, strictly speaking, always vibrations of the whole molecule. Therefore a change in the structure of the molecule, even one that does not affect the given structural element, is reflected to one degree or another in the values of the parameters of the characteristic lines belonging to it. Such “deviations from characteristicity” are of great interest for determining the structure of molecules. As an example, Table V gives

Table V

Frequency of vibrations of the double bond C=C for various unsaturated hydrocarbons

data for the frequencies of lines corresponding to vibrations of the double bond C=C in the spectra of unsaturated hydrocarbons with different types of substitution.^15,16 Such comparatively small frequency shifts make it possible to determine the type of substitution from combination-scattering spectra.

The use, alongside frequencies, of other line parameters considerably broadens the possibilities of applying combination-scattering spectra for conclusions about the structure of molecules. For example, when only the frequencies of lines in the region of deformation vibrations of the skeleton (frequencies below $500\ \mathrm{cm}^{-1}$) were used in the combination-scattering spectra of hydrocarbons, it was not possible to establish any regularities. This region always contains many lines of different origin, which greatly complicates the interpretation of spectra. The use of the whole set of

parameters makes it possible to identify in this region a line belonging to the deformation vibrations of the longest free chain (outside a branching) present in the molecule. The line belonging to these vibrations has the greatest intensity, the greatest polarization, and the smallest width of all the lines in this region of the spectrum. The frequency of the indicated line is related to the length of the free chain by a simple empirical formula (see^17)

\[ \Delta \nu = \frac{a}{m + 6}, \tag{1} \]

where \(m\) is the number of carbon atoms in the longest free chain (including the carbon atom of the branching from which the chain begins), and \(a\) is a quantity varying somewhat depending on the type of characteristic structural elements present in the molecule. Having established, from the totality of features, a line in the region below \(500\ \mathrm{cm}^{-1}\) belonging to vibrations of the free chain, one can, from its frequency by means of formula (1), find the number \(m\) and, consequently, the length of the chain. In the simplest cases, when the molecule contains, for example, only one quaternary or tertiary carbon atom, it is possible by the method described to establish its position in the molecule and thereby to solve completely the problem of determining the structure of the molecule.

Combination-scattering spectra, despite the complexity and the peculiarity of their regularities, provide rich material for conclusions of a structural character. The presence in the spectra of particular characteristic lines testifies to the presence in the molecules under investigation of definite structural groups. The intensity of characteristic lines is in a number of cases proportional to the number of the corresponding structural groups. Small changes in the parameters of characteristic lines often make it possible to establish the position of a given characteristic structural element in the molecule, the type of substitution, etc. The totality of such features makes it possible to form a rather complete picture of the structure of the molecules under investigation and, in many cases, to solve the problem of establishing the structure to the end. As an example, we present a scheme for the structural analysis of paraffins. The scheme is drawn up on the assumption that the molecular weight and density of the paraffin under investigation are known and that the problem consists in establishing its structural formula (a detailed substantiation of the scheme is given in work^17).

The proposed scheme is based on the division of hydrocarbons into groups in accordance with the presence in them of one or another characteristic structural element. Such elements in the case of paraffins are quaternary and tertiary carbon atoms, two adjacent tertiary atoms, and a free chain of carbon atoms. Thus four groups of paraffins are established, for each of which additional features are given, making it possible to judge the details of the structure of the corresponding molecules. As has been emphasized more than once before, in order to avoid errors it is necessary, in analyzing the structure of molecules, to take into account the entire totality of features.

Group I. Paraffins possessing quaternary carbon atoms. These paraffins are characterized by the presence of lines of high intensity, strongly polarized and comparatively narrow (\(4—6\ \mathrm{cm}^{-1}\)) in the region \(650—750\ \mathrm{cm}^{-1}\), and of fairly intense depolarized lines in the region \(925\ \mathrm{cm}^{-1}\) and \(1200—1250\ \mathrm{cm}^{-1}\). The number of quaternary atoms is established from the intensity of the fully symmetric lines (the integral intensity per one quaternary atom is approximately 300). In very symmetric molecules the fully symmetric line lies

in the region of \(670\text{–}700\ \mathrm{cm}^{-1}\) and is distinguished by a very small width, while in molecules with adjacent quaternary atoms it lies in the region of \(650\text{–}670\ \mathrm{cm}^{-1}\).

The total number of \(\mathrm{CH}_3\) groups in the molecule and, consequently, the number of branches is determined from the intensity of the line \(2965\ \mathrm{cm}^{-1}\) (for one \(\mathrm{CH}_3\) group \(I=80\)). If the paraffin under study contains only one quaternary atom and no other branches, then the position of the quaternary atom is established from the frequency of the most intense and polarized line in the region of deformation vibrations (\(200\text{–}400\ \mathrm{cm}^{-1}\)) according to empirical formula (1).

Additional indications: a) totally symmetric lines in the region \(870\text{–}890\ \mathrm{cm}^{-1}\) indicate the presence of a free chain of two (line \(890\ \mathrm{cm}^{-1}\)) and three or more (line \(870\ \mathrm{cm}^{-1}\)) carbon atoms; b) a quaternary atom at the end of a chain is characterized by the frequency \(1250\ \mathrm{cm}^{-1}\).

If tertiary carbon atoms are also present in the molecule, their number, as mentioned above, is determined from the intensity of the line \(2965\ \mathrm{cm}^{-1}\), proportional to the number of \(\mathrm{CH}_3\) groups. The presence of adjacent quaternary and tertiary atoms is characterized by the appearance of the line \(530\ \mathrm{cm}^{-1}\) and the disappearance of the frequency \(1250\ \mathrm{cm}^{-1}\). If this complex branch is located at the end of the molecule, then three lines (instead of two) appear in the region \(1200\text{–}1250\ \mathrm{cm}^{-1}\). The presence of ethyl groups in a branch is characterized by the appearance of an intense (depolarized) line \((I_0 \sim 7\text{–}20)\) in the region \(1020\text{–}1080\ \mathrm{cm}^{-1}\).

Additional indications of tertiary atoms are weak lines in the regions \(950\) and \(1140\text{–}1170\ \mathrm{cm}^{-1}\). Additional indications a) and b) of a free chain and an isolated quaternary atom at the end of a chain (see above) are retained.

Group II. Paraffins possessing adjacent tertiary carbon atoms (in the absence of quaternary atoms). This group of paraffins is characterized by the presence of totally symmetric lines in the region \(720\text{–}750\ \mathrm{cm}^{-1}\) and by the presence of the lines \(950\), \(1160\), and \(1190\ \mathrm{cm}^{-1}\). The presence of ethyl groups in a branch is marked by the appearance of a strong line in the region \(1020\text{–}1080\ \mathrm{cm}^{-1}\). The signs of a free chain (lines in the region \(800\text{–}890\ \mathrm{cm}^{-1}\)) are retained. The total number of branches is determined, as above, from the intensity of the line \(2965\ \mathrm{cm}^{-1}\). The presence of three adjacent tertiary atoms is characterized by the appearance of three lines in the region \(1160\text{–}1190\ \mathrm{cm}^{-1}\) (instead of two).

Group III. Paraffins possessing only isolated tertiary carbon atoms. This group of paraffins is characterized by the set of frequencies in the region \(950\ \mathrm{cm}^{-1}\), \(1145\text{–}1170\ \mathrm{cm}^{-1}\). The totally symmetric lines lie in the region \(800\text{–}900\ \mathrm{cm}^{-1}\) (exception: molecules with high symmetry are characterized by a lowering of the frequency of the totally symmetric lines to \(730\text{–}800\ \mathrm{cm}^{-1}\) and by a decrease in their width). The intensity of the line \(2965\ \mathrm{cm}^{-1}\) gives the number of \(\mathrm{CH}_3\) groups. Additional data are provided by the intensity of the line \(1300\ \mathrm{cm}^{-1}\), proportional to the number of \(\mathrm{CH}_2\) groups, and of the line \(1340\ \mathrm{cm}^{-1}\), proportional to the number of \(\mathrm{CH}\) groups. Features of these lines: the line \(1340\) is more intense when the branch is located at the end of a chain; the intensity of the line \(1300\ \mathrm{cm}^{-1}\) drops sharply when the \(\mathrm{CH}_2\) group is located between two branches.

In the case of paraffins with one branch, on the basis of the frequency of the most intense and strongly polarized line in the region of deformation vibrations one can determine the position and type of branching, using empirical formula (1).

Additional indications of a free chain are lines in the region 870–890 cm\(^{-1}\) (see above). Ethyl groups in a branching are characterized by an intensification of the line in the region 1020–1080 cm\(^{-1}\). The disappearance of the line in the region 950 cm\(^{-1}\) characterizes the absence of branches at the end of the chain, while three lines in the region 900–950 cm\(^{-1}\) indicate the presence of branches in positions 2,4 (the indications are unreliable).

Group IV. Normal paraffins. This group is characterized by the presence of a series of totally symmetric lines in the region 800–900 cm\(^{-1}\), an intense line at 1300 cm\(^{-1}\), and an intense, strongly polarized line in the region of deformation vibrations (200–400 cm\(^{-1}\)), whose frequency decreases as the chain length increases. Additional indications: lines 1070 and 1140 cm\(^{-1}\).

General character of the spectrum. A decrease in the number of lines in the spectrum and a decrease in the width of the totally symmetric lines characterize the high symmetry of the hydrocarbons under investigation.

In the above scheme of structural analysis of paraffins, most of the indications established by B. I. Stepanov on the basis of an analysis of frequencies have been used. At the same time, owing to the broad use of all the parameters of the Raman lines, it has been possible to establish a number of new structural indications, and some of them have acquired greater definiteness and unambiguity. Of course, it is assumed that, in carrying out structural analysis, the investigator will have the possibility of measuring in the Raman spectra all those parameters of the lines that he requires.

The present scheme is based on the identification of characteristic structural elements as structural units of molecules, to which there corresponds a stable set of characteristic lines in the Raman spectra. Thus, structural analysis consists in seeking those features of molecular structure that are actually reflected in the Raman spectra. This circumstance must be emphasized, since the experimental data show that far from all types and combinations of branchings in spectra correspond to definite, stably recurring indications.

On the other hand, the proposed scheme takes into account that some characteristic elements “suppress” others, as a result of which the general character of the spectrum and the presence in it of particular characteristic lines are determined primarily by the “strongest” characteristic structural element. Strictly speaking, only by taking into account the indicated interaction of characteristic structural elements can a general scheme of structural analysis be constructed. Without this, we have only a set of structural indications, the application of which, although it may sometimes lead to favorable results, does not on the whole solve the problem of structural analysis.

The scheme proposed by us has been constructed as applied to the structural analysis of individual paraffins of unknown structure. The problem of analyzing mixtures is, of course, considerably more complicated, and a complete solution of it is by no means always possible. In a number of cases, however, it is sufficient to establish the group composition of a mixture. In this case the scheme proposed by us basically retains its significance, since the indications on which it is based are, as a rule, group indications.

Similar schemes of structural analysis have also been developed by us for five-membered and six-membered naphthenes and for unsaturated hydrocarbons\(^{17}\).

We have considered in detail the problem of determining from Raman spectra the chemical structure of complex molecules, i.e., the problem

of establishing their structural formula. Combination-scattering spectra can also be successfully applied to the solution of more subtle questions of establishing the geometrical configuration of molecules. Here one should first of all mention the study, by means of combination-scattering spectra, of rotational isomerism. An extensive literature is devoted to these questions, which have independent significance (see, for example, the review by M. V. Vol’kenshtein \(^{19}\) and the monograph by Mizushima \(^{20}\)). We shall confine ourselves to a review of the work in this direction carried out under the guidance of G. S. Landsberg.

In the work of M. L. Sosinskii \(^{21}\), investigations were made of the rotational isomerism of 1,2-dichloroethane in mixtures. He developed a simple (purely spectroscopic) method for determining the concentrations of isomers, based on measuring the intensities of combination-scattering lines belonging to different rotational isomers in mixtures of the substance under investigation with solvents. Using this method, M. L. Sosinskii measured the concentrations of the rotational isomers of 1,2-dichloroethane at various concentrations of this compound in a variety of solvents. He also measured the temperature dependence of the relative intensity of combination-scattering lines belonging to different rotational isomers. On the basis of these measurements M. L. Sosinskii determined the difference in the energies of the rotational isomers of 1,2-dichloroethane in mixtures of this substance with dipolar and nonpolar solvents, which made it possible to trace the influence of the surrounding medium on the properties of molecules.

M. L. Sosinskii also investigated three-component mixtures. By varying the concentration of the components, he was able to obtain a medium with a prescribed dielectric constant. In this way it was possible to trace the action of this parameter on the molecules present in solution. On the basis of the results obtained, M. L. Sosinskii came to the conclusion that, for a number of mixtures (solvents of the normal-paraffin type), the transition energy of the rotational isomers does not depend on the concentration and nature of the components of the mixture, but is determined mainly by the macroscopic dielectric constant of the medium. In some solvents (dioxane, methyl alcohol) an anomalous change in the transition energy of the isomers was found, caused, apparently, by peculiarities in the arrangement of electric charges in the molecules.

The investigations carried out by M. L. Sosinskii show that molecules with single C—C bonds can serve as sensitive indicators of certain features of the structure of solvent molecules and of the medium itself.

Of considerable interest is the study of the rotational isomerism of paraffins. The combination-scattering spectra of normal paraffins, upon cooling and freezing of these substances, become considerably simpler, since only the lines of a single, most stable isomer remain in them. In the spectra of branched paraffins no such simplification was observed; therefore the question of the presence of rotational isomers in branched paraffins remained unresolved for a long time. Only comparatively recently did a brief communication appear \(^{22}\) indicating a simplification of the infrared spectrum of 2,3-dimethylbutane upon its crystallization. In this connection, the observation made by G. V. Mikhailov \(^{23}\) is of great interest: in the spectrum of isopentane, recorded with large dispersion, he found a line with frequency \(757\ \mathrm{cm}^{-1}\) that disappears on cooling. Thus, the existence of rotational isomers in the case of branched paraffins, despite the limited experimental material, is beyond doubt.

For solving the question of the geometric configuration of the isomers present in the substance under study, the calculation of the vibration frequencies of various possible rotational isomers is of great importance. Comparison of the calculated frequency data with experimentally observed spectra makes it possible to establish which of the possible isomers are actually present in the substance studied under the experimental conditions. Such calculations, carried out by B. I. Stepanov for n-butane[^8], showed that the most stable isomer of this hydrocarbon has the configuration of a planar zigzag chain, which agrees well with the data of other authors obtained by other methods.

In B. I. Stepanov’s work two rotational isomers of n-butane were considered: trans-planar and trans-rotated (Fig. 1, a and b). In the calculations carried out by us[^24], in addition to these isomers, two possible cis-isomers were also considered (Fig. 1, c and d).

Fig. 1.

The indicated calculation was carried out by the method developed by M. A. Elyashevich and B. I. Stepanov, with the special feature that an electronic calculating machine was used for the computations. The calculation carried out confirmed the conclusion about the greatest stability of trans-isomers in the case of n-paraffins. An analogous calculation, carried out by us jointly with L. M. Sverdlov for 2,3-dimethylbutane[^25], showed that in the case of branched paraffins cis-configurations may also possess considerable stability.

Experimental study of vibrational spectra makes it possible to determine the set of vibrational frequencies from which the force constants of a given molecule may be calculated. For solving this problem, the study of deuterium-substituted compounds is of essential importance, since the number of frequencies is smaller than the number of force constants to be determined (see[^8]). In the works of G. S. Landsberg and his coworkers[^26],[^27], the combination-scattering spectra and infrared spectra of a number of deuterium-substituted aromatic compounds (derivatives of benzene, toluene, diphenyl, naphthalene) were carefully studied. The data obtained made it possible to calculate the force constants for these molecules[^28].

3. MOLECULAR ANALYSIS

BY SPECTRA OF COMBINATION SCATTERING OF LIGHT

The application of combination scattering of light for analytical purposes is based on the fact that the spectrum of combination scattering is an individual optical characteristic of a molecule. Owing to this, the spectrum of combination scattering can serve for the identification of scattering molecules.

A necessary prerequisite for qualitative and quantitative analysis is the careful study of the spectra of individual compounds. For qualitative analysis, the determination of the frequencies of the lines of combination scattering is most essential. The set of these frequencies is an important analytical feature that makes it possible to identify the molecules of the scattering substance. The relative intensities of the lines prove to be an important auxiliary feature. The identification of a certain substance in a mixture may be considered reliable when the coincidence of several lines characteristic of it has been established, with the proper ratio of intensities.

Quantitative molecular analysis, based on measurements of the intensities of the lines of combination scattering, is considerably more complicated. Knowing the intensity of some line in the spectrum of a pure substance and the intensity of the same line in a mixture, one can find the content in the mixture of the component to which the given line belongs; therefore, in principle, the course of the analysis is not difficult. However, in order to be able actually to carry out analysis from spectra of combination scattering, it is necessary, first, to possess a reliable method for measuring intensities; second, to have complete data on the intensities of the lines of individual substances; and third, to know the law governing the dependence of line intensity in mixtures on concentration.

The development of molecular analysis by spectra of combination scattering of light is of special importance for organic chemistry, since it makes it possible to distinguish numerous isomeric compounds, for the analysis of which chemistry often does not have the necessary means. At the same time, the enormous variety of organic compounds and the difficulties of their synthesis and isolation in pure form make entirely unpromising those methods of analysis in which the intensity of the lines of some component of a mixture is directly compared with the intensity of the lines of the same substance in pure form, as well as methods of analysis in which standard mixtures are used. Thus, what is needed is a method of quantitative molecular analysis that would be based on tabulated values of the intensities of the lines of combination scattering of light, suitable for use in any laboratory. This circumstance imposes stringent requirements on the method of measuring line intensities, in which, along with impeccable measuring technique, complete reproducibility of the results obtained in different laboratories must be ensured. The task of developing such a method of analysis was posed in the work of N. D. Zelinskii and G. S. Landsberg29. An extensive series of works by G. S. Landsberg, his pupils, and collaborators was devoted to the development of methods for measuring the intensities of lines of combination scattering30–36. At the same time, in close cooperation with a large group of organic chemists under the direction of Academician N. D. Zelinskii and Academician B. A. Kazanskii, extensive investigations were carried out of the spectra of combination scattering of individual substances. Hydrocarbons forming part of light motor fuel were chosen as the object of study, since what was primarily envisaged was the application of optical methods

of analysis in the study of gasolines. In a series of papers[^37-48] the spectra of about 150 individual hydrocarbons were investigated. The data obtained made the problem of molecular analysis of complex mixtures of hydrocarbons quite realistic.

In the course of methodological studies connected with the measurement of the intensities of combination-scattering lines, the actual need became clear for data on the width of these lines[^33]. The point is that the quantity most accessible for measurement, both in photographic and in photoelectric recording of spectra, is the intensity at the maximum of the line. The results of measurements of this quantity depend on the width and shape of the combination-scattering lines, since these parameters determine the influence exerted by the spectral apparatus and by the shape of the exciting line on the measured value of the intensity.

Thus, for a rational choice of the conditions for measuring line intensities, a comprehensive investigation of combination-scattering spectra proved necessary. In the works of G. S. Landsberg and his collaborators, methods were developed for measuring the principal parameters of combination-scattering lines. These methods are described in detail in the monograph[^1], and therefore we shall not dwell on them here. With the aid of the indicated methods, standardized in a proper manner, line parameters were measured in the spectra of 140 individual hydrocarbons. The data obtained are presented in the monograph[^1]. On the basis of these data it also proved possible to process the literature data[^49] on the spectra of individual hydrocarbons and to express the intensity values reported in these works on a common scale. The processed data are, of course, less reliable than the data of direct measurements; nevertheless, they may still be used in molecular analysis.

The standardized methods developed for measuring line intensities, and the factual material collected in the monograph[^1] on the spectra of about 300 hydrocarbons, create a real possibility of carrying out the analysis of complex mixtures of hydrocarbons from tabular data.

To carry out quantitative analysis from combination-scattering spectra it is necessary, as indicated above, to know the law relating the intensity of a line of some component to the content of this component in the mixture. General considerations argue in favor of the fact that, in the absence of strong intermolecular interaction, the intensities of lines in a mixture should be proportional to the number of scattering molecules. Under ordinary experimental conditions the scattering volume remains constant. Consequently, if measurements are made of the intensity \(I_{100}\) of a line of some individual substance and of the intensity \(I_c\) of the same line in a mixture, then the equality

\[ \frac{I_c}{I_{100}}=\frac{n_i}{N_i}, \tag{2} \]

will hold, where \(N_i\) and \(n_i\) are the numbers of the given molecules in the scattering volume, respectively in the individual substance and in the mixture. Knowing the densities of the individual substances \(d_i\) and of the mixture under study \(d\), one can find the weight concentrations \(C_i\) of each of the components of the mixture from the formula

\[ C_i=\frac{n_i M_i}{\sum n_i M_i}=\frac{I_c d_i}{I_{100} d}, \tag{3} \]

where \(M_i\) is the molecular weight of the \(i\)-th component.

Practically for most mixtures, the intensities of the lines are proportional to the volume concentration of the corresponding component in the mixture, i.e.,

\[ (C_v)_i=\frac{I_c}{I_{100}}. \tag{4} \]

Measurements carried out by us \(^{32}\) and data of other authors \(^{50,51}\) confirm the linear dependence of line intensity on concentration for a wide class of compounds, including hydrocarbon mixtures*).

The simple dependence between line intensities and concentrations is a major advantage of the method of combination scattering of light in comparison with other methods of molecular spectral analysis.

The success of optical analysis is to a great extent determined by the appropriate physicochemical preparation of the sample for analysis. The lines of combination scattering are comparatively weak and therefore can easily be lost against a continuous background caused by scattering of light on mechanical impurities, as well as by luminescence of minute impurities of certain substances. Thus, for successful analysis the mixture must be “optically pure,” which requires the use of special purification methods.

An important feature of combination-scattering spectra for analytical applications is that all the lines in these spectra are located in a comparatively narrow spectral interval, which for the most interesting region of the spectrum is no more than 300 Å. In this spectral interval there are several tens of lines possessing considerable width (from 2 to 20 \(cm^{-1}\)). Therefore, in the analysis of mixtures, lines belonging to different components often overlap. Because of this, the possibility is lost of using the analytically most interesting lines for quantitative analysis. In the case of analysis of hydrocarbon mixtures, it is also significant that the lines of some classes of hydrocarbons are considerably more intense than the lines of other classes. For example, the lines of aromatic hydrocarbons and six-membered naphthenes are tens and hundreds of times stronger than the lines of paraffins and five-membered naphthenes.

From what has been said it is clear that, for successful molecular spectral analysis, preliminary simplification of mixtures is necessary, first of all the removal from them of components having strong combination-scattering lines. Thus, optical analysis must be preceded by a carefully performed separation of the mixture into narrow fractions containing a comparatively small number of components.

The combination of physicochemical methods of separation into fractions with the optical method of analysis of narrow fractions forms the basis of the combined method of gasoline analysis. This method was developed as the result of many years of research by a large group of physicists under the direction of G. S. Landsberg and chemists under the direction of B. A. Kazanskii. The method makes it possible to determine the qualitative and quantitative content of individual hydrocarbons in gasolines. The determination of the individual composition of gasolines by the combined method is based on the following four processes:

1) precise rectification,
2) chromatographic adsorption,
3) dehydrogenation catalysis,

*) In the presence of intermolecular interactions, deviations from the linear dependence of line intensity on concentration occur (see, for example, \(^{52}\)).

Table VI

Individual hydrocarbons found in gasoline from Emba crude oil55

4) optical analysis of fractions by means of combination scattering of light.

A detailed description of all the processes indicated, as well as practical directions for their application, are contained in a special monograph[^53]. It should be noted that the combined method has already found broad application in the analysis of petroleum products. With the aid of this method several dozen gasolines from various deposits of the USSR have been analyzed1.

As an example showing the possibilities of the combined method, Table VI gives the results of the analysis of one of the gasolines. As can be seen, the combined method makes it possible to establish the composition of a gasoline in considerable detail, which is of great importance for the rational choice of methods of petroleum refining. Knowledge of the composition of petroleum products is also of great importance for solving the question of the origin of petroleum, geochemistry, etc.

With an increase in the boiling temperature of petroleum products, the number of possible individual hydrocarbons in the fractions rapidly increases. Therefore, for establishing the composition of ligroin fractions, the use of methods for the analysis of gasolines proves to be irrational. In the analysis of such mixtures the very problem of analysis changes substantially: the establishment not of the individual, but of the group composition of the mixtures becomes of principal interest.

The accumulated material on the spectra of combination scattering of individual hydrocarbons makes it possible to approach in a new way the solution of the problem of analyzing high-boiling (ligroin) fractions of hydrocarbons. If, in the analysis of gasolines, the necessary prerequisite for analysis was the investigation of all the individual hydrocarbons boiling in a given temperature interval, then in the analysis of ligroin fractions, relying on the general regularities connecting the spectra of combination scattering with the structure of molecules (see the preceding section), one can solve questions of the group (and sometimes also individual) composition of fractions, relying on these general regularities, without a preliminary investigation of all individual hydrocarbons. An example of the analysis of ligroin fractions is given in work[^56].

In the present review we do not touch upon a whole series of questions connected with the use of the method of combination scattering of light for the study of the aggregate state, nor applications of infrared spectroscopy for solving structural and analytical problems, since this lies outside the scope of the present work.

CITED LITERATURE

1. G. S. Landsberg, P. A. Bazhulin, M. M. Sushchinskii, Basic Parameters of the Spectra of Combination Scattering of Hydrocarbons, Publishing House of the Academy of Sciences of the USSR, 1956.
2. G. Placzek, Rayleigh Scattering and the Raman Effect, ONTIU, 1935.
3. G. Herzberg, Vibrational and Rotational Spectra of Polyatomic Molecules, IL, 1949.
4. K. Kohlrausch, Spectra of Combination Scattering, IL, Moscow, 1952.
5. I. E. Rosenthal, G. M. Murphy, Rev. Mod. Phys. 8, 317 (1936).
6. M. A. El’yashevich, Dissertation, FIAN, 1944.
7. M. A. El’yashevich, DAN SSSR 28, 605 (1940), ZhOKh 14, 1381 (1940); 15, 1847 (1941); M. A. El’yashevich, B. I. Stepanov, DAN SSSR 32, 48 (1941); B. I. Stepanov, Izv. AN SSSR, Ser. Fiz. 11, 357 (1947).
8. M. V. Vol’kenshtein, M. A. El’yashevich, B. I. Stepanov, Molecular Vibrations, Gostekhizdat, 1949.

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5. P. A. Bazhulin, Kh. E. Sterin, Izv. AN SSSR, series phys. 11, 456 (1947).

6. M. M. Sushchinskii, Izv. AN SSSR, series phys. 17, 608 (1953).

7. S. V. Markova, P. A. Bazhulin, M. M. Sushchinskii, Optics and Spectroscopy 1, 41 (1956).
8. J. Goubeau, Die Raman-Spectren von Olefinen, Beihefte No. 56 zu der Zeits. “Angew Chemie,” 1948.
9. M. M. Sushchinskii, Doctoral dissertation, Moscow, FIAN, 1957.
10. P. P. Shorygin, Advances in Chemistry 13, 90 (1944); 19, 419 (1950).
11. M. V. Vol’kenshtein, Advances in Chemistry 13, 234 (1944).
12. S. Mizuschima, Structure of molecules and internal rotation, New York, 1954.
13. M. L. Sosinskii, Dissertation, FIAN, 1956.
14. J. K. Brown, N. Sheppard, J. Chem. Phys. 19, 976 (1951).
15. G. V. Mikhailov, Proceedings of the 10th Conference on Spectroscopy, Scientific Notes of L’vov State University 4 (1957).
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19. G. S. Landsberg, A. I. Shatenshtein, G. V. Peregudov, E. A. Izrailevich, L. A. Novikova, Optics and Spectroscopy 1, issue 1 (1956); A. I. Shatenshtein, G. V. Peregudov, E. I. Izrailevich, V. R. Kolindatsche-Néoc, ZhFKh, in press.
20. M. A. Kovner, DAN SSSR 91, 499 (1953); ZhETF 26, 598, 704 (1954); Optics and Spectroscopy 1, 742 (1956).
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22. G. S. Landsberg, P. A. Bazhulin, G. V. Rozenberg, A. S. Eliner, Izv. AN SSSR, series phys. 4, 158 (1940).

23. P. A. Bazhulin, Izv. AN SSSR, series phys. 5, 468 (1941).

24. M. M. Sushchinskii, DAN SSSR 33, 21 (1941).
25. M. M. Sushchinskii, Dissertation, FIAN (1947); Trudy FIAN 5, 185 (1950).
26. M. M. Sushchinskii, DAN SSSR 70, 221 (1950); ZhETF 20, 304 (1950).
27. P. A. Bazhulin, G. V. Peregudov, Izv. AN SSSR, series phys. 17, 647 (1953).
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31. P. A. Bazhulin, Kh. E. Sterin, T. F. Bulanova, O. P. Solovova, M. B. Turova-Pollak and B. A. Kazanskii, Izv. AN SSSR, OKhN 1, 7 (1946).
32. P. A. Bazhulin, S. A. Ukholin, T. F. Bulanova, A. V. Koperina, A. F. Plate and B. A. Kazanskii, Izv. AN SSSR, OKhN 5, 480 (1949).
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35. P. A. Bazhulin, A. I. Sokolovskaya, N. A. Belikova, A. L. Liberman and A. F. Plate, Izv. AN SSSR, OKhN, 1130 (1956).
36. P. A. Bazhulin, S. V. Markova, G. V. Peregudov, M. Yu. Lukina, A. F. Plate and B. A. Kazanskii, Izv. AN SSSR, OKhN.
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3. A. Michel, Spectr. Acta, 5, 218 (1952).

4. Ya. S. Bobovich, T. P. Tulub, ZhETF 30, 489 (1956).

5. G. S. Landsberg, B. A. Kazanskii, P. A. Bazhulin, T. F. Bulanova, A. L. Liberman, E. A. Mikhailova, A. F. Plate, Kh. E. Sterin, M. M. Sushchinskii, G. A. Tarasova, S. A. Ukholin, Determination of the individual hydrocarbon composition of straight-run gasolines by a combined method, in press.

6. G. S. Landsberg, B. A. Kazanskii, P. A. Bazhulin, M. M. Batuev, A. L. Liberman, A. F. Plate, G. A. Tarasova, A Comprehensive Method for the Detailed Investigation of the Individual Composition of Gasolines, Moscow, Gostoptekhizdat, 1949.

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1. Already in its original form the indicated method gave positive results in the analysis of a number of gasolines. For example, during the years of the Patriotic War analyses of a number of captured gasolines were carried out[^54]. ↩↩