BAND SPECTRA AND THE STRUCTURE OF MOLECULES.

V. Kondrat’ev.

In the question of the structure of molecules, spectroscopy is evidently destined to play the same chief, decisive role as in the question of the structure of the atom. The problem of molecular structure is developing in two directions, complementary to one another: in the direction of theoretical investigation of molecules1, of constructing models of molecules, sometimes of a purely formal kind, and in the direction of spectroscopic investigation. The task of the present report is to bring together those already significant results that have been achieved by the latter, spectroscopic, direction.

§ 1. Structure of band spectra.

In accordance with the complexity which a molecule presents in comparison with an atom, the band molecular spectrum is incomparably more complex than the line atomic spectrum. This complexity of the band spectrum finds its explanation in the new degrees of freedom of the molecule, which the separate atom does not know—in the vibrations of the atoms forming the molecule, and in the rotation of these atoms about their common center of gravity. The energy associated with these motions naturally takes part in the processes of emission and absorption of light by molecules. The jump of an electron from one orbit in the molecule to another is accompanied, generally speaking, by a change in the quantum states of vibration and rotation of the molecule, and the frequency of the light emitted (or absorbed) in this process is determined by Bohr’s formula:

\[ h\nu = W_1 - W_2, \tag{1} \]

where \(W_2\) and \(W_1\) are already the values of the total energy of the molecule (including the vibration and rotation of the atoms), respectively in the initial and final states. Leaving aside for the time being the rotation of the molecule, the share

for which only an insignificant amount of energy is required, the result of the superposition of the vibrations of the atoms on the electronic transition may be represented by the formula of Deslandres, which describes, with sufficient accuracy, the majority of the band spectra studied:

\[ \nu=\nu_e+n(a-bn)-n'(a'-b'n')^{1}). \tag{2} \]

In this formula \(\nu_e\) is the frequency corresponding to a purely electronic transition, \(n\) and \(n'\) are the quantum numbers (integers) of the initial and final states, respectively, of the molecule’s vibration, and \(a\), \(b\), \(a'\), and \(b'\) are numbers characterizing the dynamical conditions of the two vibrational states. As is evident from formula (2), each electronic transition in a molecule \((\nu_e)\) appears optically in the form of a group of lines corresponding to different values of the numbers \(n\) and \(n'\) (beginning with \(n=0\) and \(n'=0\)), i.e., to different changes of the vibrational regime of the molecule accompanying the electronic transition. Each band spectrum is therefore a double manifold of bands\({}^{2}\).

Bands are obtained as the result of a new superposition of the rotation of the molecule on the motions that determine the emission of the frequencies specified by formula (2), and they are groups of lines arising from the splitting of each of these frequencies. Each line of a band thus corresponds to a definite state of rotation of the molecule. Since, according to the selection principle, the quantum number \(m\), characterizing a definite state of rotation, may change only by \(\pm 1\) or \(0\), for each \(m\) we must expect three lines corresponding to the transitions \(m\to m-1\), \(m\to m+1\), and \(m\to m\). These three possibilities give three branches, called: \(R\)—the positive branch, \(P\)—the negative branch, and \(Q\)—the zero branch, into which each band splits (very often the \(Q\)-branch is absent). These branches diverge from one place in the band (see Fig. 1), which is distinguished by the minimum of intensity produced as a result of the absence of the line corresponding to \(m=0\) and bearing the name of the zero line. This zero line corresponds to nonrotating molecules, the probability of whose appearance, according to the Maxwell–Boltzmann law, is very small.

Fig. 1.

The distribution of intensity in a band is usually such that, beginning from the edge of the band, called in this case the head, the intensity falls toward the other edge, gradually becoming diffuse. The heads of bands

\({}^{1}\) See Heurlinger. ZS. für Phys. 1, 82, 1920.
\({}^{2}\) Mecke. Phys. ZS. 26, 227, 1925.

are a purely random accumulation of lines depending on the distribution of lines in the branches (cf. Fig. 1). An accumulation of lines on the \(R\)-branch, which extends from the zero line toward shorter wavelengths, is the cause of the edge at the violet end of the band (the blurring of the red end of the band). If, however, an accumulation of lines occurs on the \(P\)-branch, the red ends of the bands are edged and the bands are blurred in the direction of the violet part of the spectrum.

In addition to the bands just described, bands with a more complicated structure are very often observed. The latter have either complex branches (for example, in the CN bands each of the three branches is double), or several zero lines (three in the \(N_2\) bands). The latter circumstance is due, as is easy to see, to the complexity of the energy levels of the emitting electron.

Here we shall note one further very important circumstance. Besides the zero line \((m=0)\), one also distinguishes the zero band: this is the band for which \(n=n'=0\). As follows from all that has been said above concerning the structure of bands, the zero line of the zero band must correspond to the line emitted by the molecule under the condition that the initial and final states of rotation and vibration of the atoms in the molecule are identical and correspond to rest of the molecule, i.e. to a line having a purely “electronic” origin.

§ 2. Study of band spectra.

In contrast to the line spectra of atoms, band spectra in most cases make it possible to establish easily the nature of the carriers of these spectra and the relationship between individual bands. The key to this is precisely the complexity of the spectrum. Bands which, by their origin, are due to one and the same electronic transition and differ only by different vibrational quanta \((n)\) are usually located in a narrow spectral region, always have the same structure, the same arrangement of edges, and appear under identical excitation conditions. The aggregate of such bands is called a system of bands. To a considerable extent, everything said about the bands of one system also applies to the various systems of bands belonging to one and the same molecule. Having established that bands belong to one system, it is already easy to find the zero band \((n=n'=0)\). Almost always (the exception is represented by the so-called multi-edge spectra), the zero band is the most intense band of the system1. By means of the usual methods of approximate calculation, one attempts,

then to fit the band quanta (or zero lines) of the system under investigation into a formula of the form (2). There exist various criteria for checking the correctness of such a classification. The most frequently used criterion consists in forming differences of the frequencies of band quanta arranged in a definite order. Namely, arranging the bands so that in each horizontal row there are bands (quanta) corresponding to one and the same initial vibrational quantum number \(n\) (a longitudinal series), and in each vertical row—bands with identical \(n'\) (a transverse series)—as the tables on p. 390 are arranged, we must expect that the frequency differences of two neighboring bands of each series will be the same. This follows from formula (2), from which, in forming the differences, in the case of a longitudinal series the final term \((n'a' - n'^2 b')\) drops out, and in the case of a transverse series the initial term drops out (usually the order of magnitude of \(a\) and \(b\) is as follows: 1000 and 10). In view of the accidental character of the quanta (see above), this criterion proves more rigorous when applied to the zero lines of bands. In a large number of bands the zero lines lie very close to the quanta—then the criterion is sufficiently rigorous also in its application to the quantum scheme (2). However, cases are not rare when the zero line is difficult to find. Here one may point to a criterion based on the investigation of the so-called perturbations. Perturbations are those violations of the regularity of the arrangement of lines in a band, which are often observed in various spectra and which consist in an unexpected crowding or rarefaction of lines, in the disappearance of lines or in the appearance of new ones, or else in an anomalous intensity of individual lines. These perturbations may be imagined as phenomena of a resonant character: at some frequency of rotation of the molecule, one or another frequency of electronic or vibrational motion falls into step with the rotation, as a result of which this or that “perturbation” appears1. In view of the presence of common terms in the case of bands belonging to one and the same series (transverse or longitudinal), the bands of each series must have the very same perturbations. This makes it possible to establish the quantum scheme unambiguously.

When the quantum scheme of the various systems of bands has been firmly established, the problem of investigating the spectrum is already almost solved. Now there remains, perhaps, the most difficult problem—the problem of establishing the energy levels of the molecule and the connection between the individual levels, which already marks a major step in the study of the molecule. Here great assistance to spectroscopy is provided by ionization methods, which make it possible to measure the resonance potentials (i.e., the energy levels) of such molecules whose resonance spectra2 lie in a region inaccessible to

research of the far ultraviolet region. An important role is also played here by the analogy that exists between the spectra of a whole series of molecules, on the one hand, and the well-studied spectra of various atoms, on the other.

§ 3. Energy Levels of Molecules

A direct method for establishing the energy levels of a molecule is the method of bombarding a gas with slow electrons (“the ionization method”), which is successfully applied in the case of monatomic gases1. This method consists in measuring those minimum potential differences through which the bombarding electron must pass in order to be able to excite certain lines (or bands in the case of complex molecules). However, this method encounters difficulties in the low intensity of the discharge (and consequently also of the radiation accompanying the discharge) at small voltages, requiring enormously long exposures, especially since in the case of many gases the first energy levels lie below 1.5–2 volts, when the space charge excludes any possibility of obtaining a discharge of appreciable intensity. Indeed, in the literature we find only two cases (see below) of the application of this ideal method (in the case of molecules). In many cases, however, even the investigation of the spectrum alone makes it possible to establish the energy levels of a molecule—in cases where these latter are not so high that it is impossible optically to observe at least the first resonance band (the transition of an electron from the nearest orbit to the normal one). In other cases, optical investigation, together with a modification of the “ionization” method described—the observation of the first inelastic collision of the electron in the corresponding gas, or the observation of the photoelectric effect caused by the radiation of the resonance band excited by electron bombardment—make it possible to determine unambiguously the energy levels of the molecule2.

As early as 1915, Fowler succeeded in establishing a serial formula for the frequencies of various bands in the many-lined (band) spectrum

helium (\(\mathrm{He}_2\)). Namely, in the spectrum of molecular helium there are bands with double edges and a series of single bands. These two kinds of bands Fowler represented by a simple series formula with Rydberg’s constant. He established a principal series (double-edged bands) and a subordinate series (single-edged bands), which correspond to the principal and first subordinate (diffuse) series of the atomic spectrum of helium. However, the completeness of the analogy between the band and line spectra of helium is violated by the absence of bands that would correspond to the second subordinate (Sharp Series) series of the atomic spectrum.

Apparently, the energy levels of the hydrogen ion \(\mathrm{H}_2^+\) also fit into the series formula; its resonance potentials, measured by Olsen and Glocker\(^1\), were interpreted by Urey\(^2\); this simple formula,

\[ \nu = 16.68\left(1 - \frac{1}{n^2}\right), \quad n = 3,4,\ldots \infty \tag{3} \]

was also derived theoretically (Urey, loc. cit.) from a calculation of the model of the ion under consideration (with an accuracy of up to \(0.2\%\)).

The energy levels of the nitrogen molecule have been established with the greatest completeness. The energy scheme of \(\mathrm{N}_2\), established initially by Birge\(^3\) on the basis of purely optical data, was confirmed in an ionization apparatus independently by two authors—Duncan\(^4\) and Gertrude Sponer\(^5\), who observed the gradual appearance of various bands as the velocities of the bombarding electrons were increased. The latter work is distinguished by particular precision; its author was even able to observe the successive appearance of bands in each system corresponding to increasing vibrational quantum number \(n\). The scheme of the energy levels of the nitrogen molecule given here (Fig. 2) is taken from the cited work of Sponer; the wavelengths indicated in the scheme correspond to the zero lines of various groups of the nitrogen spectrum (the energy levels are calculated in volts):

Fig. 2.

\[ 9108\ \text{\AA} \;—\; \text{of the I positive group,} \]

\[ 3371\ \text{\AA} \;—\; \text{of the II positive group,} \]

\[ 2262\ \text{\AA} \;—\; \text{of the IV positive group.} \]

\(^1\) Olsen and Glocker, Proc. Nat. Acad. Sc. 9, 122, 1923.
\(^2\) Urey, Proc. Nat. Acad. Sc. 11, 618, 1925.
\(^3\) Birge, Nature, 104, 642, 1924.
\(^4\) Duncan, Astrophys. Journ. 62, 145, 1925.
\(^5\) Sponer, ZS. für Phys. 34, 622, 1925.

The line \(3914\ \overset{\circ}{\mathrm A}\) is the zero line of the first negative spectrum of nitrogen, belonging to the ion \(\mathrm N_2^+\). The final term of this spectrum corresponds to the normal state of the ion \(\mathrm N_2^+\) and is numerically equal to the ionization potential \((J)\) of the molecule \(\mathrm N_2\). Sponer succeeded in expressing the totality of zero lines (terms) of all three groups of the spectrum emitted by the neutral nitrogen molecule by Rydberg’s serial formula

\[ \frac{R}{\left(m-0.073+\dfrac{0.346}{m^2}\right)^2} \tag{4}, \]

where \(R\) is the Rydberg constant. The possibility of preserving the dependence between energy levels in the form characteristic of the atom, also in the case of the molecule, can be explained by a small change in the moment of inertia (i.e. in the configuration of the atoms) of the nitrogen molecule at different stages of excitation, as follows from an analysis of the fine structure of the nitrogen band spectrum. From formula (4) one can calculate the fourth member of the series, which brings one into the region of \(2000\ \overset{\circ}{\mathrm A}\).

Fig. 3.

The structure of the spectrum of carbon monoxide (CO) is to a considerable degree analogous to the structure of the nitrogen spectrum. An analysis of this spectrum on the basis of purely optical data led Birge\(^{1}\) to the establishment of the energy levels of the CO molecule, represented by the diagram in Fig. 3. Here, as in the case of the nitrogen diagram, the indicated wavelength values correspond to the zero bands of the carbon monoxide spectrum:

\[ 1545\ \overset{\circ}{\mathrm A} \]
— of the IV group,

\[ 4511\ \overset{\circ}{\mathrm A} \]
— of the Ångström bands,

\[ 4880\ \overset{\circ}{\mathrm A} \]
— of the comet-tail bands,

\[ 2190\ \overset{\circ}{\mathrm A} \]
— of the first negative group,

\[ 3974\ \overset{\circ}{\mathrm A} \]
— of the combination bands;

as in the case of nitrogen, the ionization potential of CO, equal to \(14.2\) volts, is numerically equal to the final term of the group of bands bearing the name of the comet-tail bands and belonging to the ion \(\mathrm{CO}^+\).

\(^{1}\) Birge. Nature 117, 229, 1926.

Significantly less complete is the energy scheme of the oxygen molecule, established by Locurov1. In the scheme presented (Fig. 4), the numerals I and II denote the first and second groups of the band spectrum of oxygen: the first of these groups extends from 4870 to 2400 Å, the second—from 6583 to 4955 Å. The absence of an exact analysis of the oxygen spectrum, incomparably more complex than the two spectra considered, does not permit a more detailed establishment of the scheme of the energy levels of the molecule \(O_2\).

Fig. 4.

Interesting in its simplicity is the energy scheme of the cuprous iodide molecule (\(\mathrm{CuJ}\)), whose spectrum has been studied in detail by Mulliken2. This spectrum consists of five homogeneous groups of bands, shaded toward the red part of the spectrum. Analysis of these bands shows that all five groups of bands have a common final term. This circumstance, as well as the absence of other spectral groups (apart from the five indicated groups of bands), led Mulliken to the conclusion that the common final term of all five groups is at the same time the ground term of the normal (unexcited) state of the \(\mathrm{CuJ}\) molecule (Fig. 5).

Fig. 5.

We shall also consider the spectrum of \(\mathrm{HgH}\). This compound belongs to an interesting class of hydrides, in which, besides the spectrum of \(\mathrm{HgH}\), the spectra of \(\mathrm{CdH}\) and \(\mathrm{ZnH}\) have also been studied. In the case of these compounds we encounter one application of spectral analysis which, in the field of atomic spectra, has played and continues to play an enormous role—namely, the use of the analysis of the fine structure of bands as spectral analysis in the sense of the word that leads to the very sources of our knowledge in this extensive and important domain of physics. The band spectrum observed in the luminous vapors of \(\mathrm{Hg}\), \(\mathrm{Cd}\), and \(\mathrm{Zn}\) was at first ascribed to molecules of these metals, i.e. \(\mathrm{Hg}_2\), \(\mathrm{Cd}_2\), and \(\mathrm{Zn}_2\). Only on the basis of an analysis of the fine structure of these spectra did Kratzer3 finally succeed in determining the true nature of their carriers. The principal resul—

V. KONDRAT'EV

the results of this investigation are as follows. The carrier of the spectrum cannot be the molecule \(\mathrm{Hg}_2\) (we take the case of the \(\mathrm{HgH}\) spectrum), since its enormous moment of inertia gives an entirely different distance between the lines entering into the band than is actually observed\(^1\). Consequently, our molecule must be considerably lighter than the \(\mathrm{Hg}_2\) molecule. A calculation concerning the possible influence of mercury isotopy further shows that this cannot be any molecule except the \(\mathrm{HgH}\) molecule. The influence of isotopy is manifested in the appearance of different systems of spectra belonging to different isotopes. If one of the atoms (of masses \(m_1\) and \(m_2\)) of a diatomic molecule, say the atom with mass \(m_1\), has an isotope with a mass differing from \(m_1\) by \(\Delta m_1\), then as a consequence there must be two systems of spectra, displaced with respect to one another by the amount (on the frequency scale):

\[ \Delta \nu = \frac{|\Delta m_1|}{m_1 + m_2}\, \frac{m_2}{m_1} \left(\nu_k + \frac{1}{2}\nu_b\right) \tag{5}. \]

where \(\nu_k\) and \(\nu_b\) are, respectively, the frequency of vibration of the nuclei and the frequency of rotation of the molecule. In view of the smallness of the ratio \(\frac{m_2}{m_1}\) in the case of \(\mathrm{HgH}\)

\[ \left(\frac{m_2}{m_1}=\frac{1}{200}\right) \]

the effect of mercury isotopy cannot be detected optically. Any other molecule, for example the molecule \(\mathrm{HgN}\), would give a corresponding measurable effect\(^2\).

The \(\mathrm{HgH}\) spectrum, studied by Hulthén\(^3\), consists of two groups of bands, the band heads of which are arranged according to the following scheme:

\(^1\) According to the theory of the fine structure of band spectra, the distance between lines, taken in units of frequency, is in the first approximation inversely proportional to the moment of inertia of the molecule (see Sommerfeld, Atombau und Spektrallinien. 4 Aufl. IX, § 2).

\(^2\) We shall point out still another case in which the investigation of the structure of a spectrum in the presence of isotopy made it possible to clarify the nature of the carrier of the spectrum. This concerns the compound \(\mathrm{BO}\), the spectrum of which was studied by Mulliken (Phys. Rev. 25, 259, March 1925). The experimental conditions were such that there remained a doubt whether the observed spectrum was the spectrum of \(\mathrm{BO}\): there were grounds for ascribing this spectrum to \(\mathrm{BN}\). The presence in boron of two isotopes with masses 10 and 11 is the cause of two systems of \(\mathrm{BO}\) spectra; from the displacement of these systems with respect to one another it was possible to calculate the ratio of the masses of molecules containing different isotopes \(\left(\frac{m_1}{m_2}\right)\): for \(\sqrt{\frac{m_1}{m_2}}\) the value \(1.0291 \pm 0.0003\) was obtained, in complete agreement with the expected theoretical value \(1.0292\) for \(\mathrm{BO}\), whereas for \(\mathrm{BN}\) the theoretical value is \(1.0276\).

\(^3\) Hulthén, ZS. für Phys. 32, 32, 1925.

The first of the tables presented represents a group of bands distinguished by double edges; the second, a group of simple bands. The poverty of this spectrum in bands leads to the conclusion that the compound HgH is a compound of a low degree of stability. The band corresponding to the final quantum number (the quantum number of the ground term), \(n' = 4\), is extraordinarily poor in lines. From the assumption that five vibrational quanta \((5h\nu_k)\) represent the upper limit for the vibrational energy of the unexcited HgH molecule1, a value of 0.37 volts is obtained for the dissociation energy of the latter. The scheme in Fig. 6 represents the scheme of the energy levels of the HgH molecule known up to now (the double term is denoted by a double line). The spectra of CdH and ZnH have a structure analogous to the structure of the HgH spectrum.

Fig. 6.

§ 4. Structure of Molecules.

After, along with various physical and chemical properties, the spectrum of the molecule has been studied at least in general outline, and its energy levels have been established with greater or lesser completeness, the physicist is faced with the task of constructing that mechanism which possesses these properties—the model of the molecule. The path by which modern physics proceeds toward the solution of this problem is the path of analogy, the path of comparison of molecules and atoms similar in their properties. Our knowledge of the structure of the atom, perhaps still too crude and general, plays the leading role here. To the exposition of the present section, however, we must premise the reservation that everything that can now be said in a section entitled “Structure of Molecules” is of necessity only a conjecture, a half-hint, a weak attempt to bind together scattered facts.

With respect to the bond between the atoms composing the molecule, all molecules may in rough outline be divided into two classes2. One class consists of molecules with a comparatively weak interatomic bond. Together with Franck (loc. cit.) we shall assume that the interatomic bond in molecules of this class is, in first approximation, effected by van der Waals forces. In the formation of molecules of this class the electronic orbits of the corresponding atoms, of course, undergo some deformation; however, the quantum numbers of the atoms are preserved. Such molecules can be adiabatically decomposed into the atoms composing them, and their heat of dissociation has an order of magnitude

heats of evaporation. In view of the small deformation of the electronic orbits, the spectrum of such molecules in general outline repeats the spectrum of the atoms composing them. The metastable states of the atoms are at the same time also metastable states of the molecules.

The properties described for molecules of this kind, which may be called van der Waals molecules1, are especially clearly expressed in the case of the molecule $\mathrm{Hg}_2$. Already the negligible heat of dissociation of the molecule $\mathrm{Hg}_2$2 is an indication of the negligible deformation of the atoms forming this molecule. A consequence of this is the almost complete identity of the energy levels of the molecule $\mathrm{Hg}_2$ and of the atom $\mathrm{Hg}$. Indeed, the spectrum of diatomic mercury, observed3 in the form of absorption bands, consists of bands coinciding with the lines $2536.7\ \text{\AA}$ $(1S — 2p_2)$ and $1849\ \text{\AA}$ $(1S — 2P)$ of the atomic spectrum. This circumstance indicates the practical identity of the electronic transitions in $\mathrm{Hg}_2$ and $\mathrm{Hg}$. Similar bands, observed both in the emission and in the absorption spectra of sodium, potassium, zinc, cadmium, and calcium4 and coinciding with the resonance lines of the corresponding atomic spectrum, indicate the existence of the molecules $\mathrm{Na}_2$, $\mathrm{K}_2$, $\mathrm{Zn}_2$, $\mathrm{Cd}_2$, and $\mathrm{Ca}_2$, which are typical van der Waals molecules.

The relations between the atomic and molecular spectra of molecules of this class are not always as simple as in the cases just described. In most cases the presence of the second atom quantitatively distorts the initial energy levels, but the structure of the spectrum always qualitatively repeats the structure of the atomic spectrum. The molecule $\mathrm{He}_2$ must be assigned to the class of van der Waals molecules; the analogy of its spectrum with the line spectrum of helium has already been indicated above (see p. 382). To this same class belong the molecules of the metal hydrides $\mathrm{ZnH}$, $\mathrm{CdH}$, $\mathrm{HgH}$, $\mathrm{MgH}$, and $\mathrm{CaH}$, whose spectra reveal in broad outline the structure of the spectra of the corresponding metals. The quantitative difference between the energy levels of the atoms and of the molecules in this case is explained by the strong deforming action of the hydrogen atom5. In any case, the preservation of the individuality of the atom in the molecule is always accompanied by a small heat of dissociation, which is thus

thus, a measure of the mutual deformation of the atoms forming the molecule. A considerable difference between the molecular and atomic spectra is always observed in the case of molecules with a greater heat of dissociation. The molecules of the halides \(F_2\), \(Cl_2\), \(Br_2\), and \(J_2\), apparently, also belong to the class of molecules under consideration. Van der Waals molecules are capable of dissociating under the influence of absorption of light\(^1\), provided that the change in vibrational and rotational energy associated with the absorption exceeds, in sum, the energy of dissociation of the molecule. Molecules of the second class, normal molecules, are distinguished by a comparatively high heat of dissociation. In the formation of such molecules from atoms there apparently occurs a far-reaching rearrangement of the electronic orbits of the latter, which excludes the possibility of an adiabatic return of the molecule to the initial state of two free atoms. A typical representative of normal molecules is the nitrogen molecule\(^2\).

The whole set of chemical and physical facts\(^3\) leads to the view that the bond between atoms in a normal molecule is effected predominantly by pairs of electrons. The most regular molecules are those with an even number of electrons. “Odd molecules” (“odd molecules”) are always chemically unsaturated, optically active, and paramagnetic\(^4\). The completeness of even molecules points to the special stability of the orbits of two valence electrons (an electron pair), belonging to both atoms and above all responsible for the intramolecular bond. According to the ideas of Lewis, the orbits of the valence electrons of both atoms (in the molecule) form a certain closed stable system\(^5\), while—

the difference of the terms of the doublet band spectrum \((\nu_2-\nu_1)\) is practically equal to the difference of the \(p\)-terms of the atoms, as is seen from the following table:

\(^1\) Dynond. ZS. für. Phys. 35, 1925, also Franck, loc. cit.

\(^2\) The heat of dissociation of the nitrogen molecule into two atoms is estimated (Sponer, loc. cit.) at 11.5 volts.

\(^3\) See the book by Lewis, Valence and the structure of atoms and molecules.

\(^4\) Taylor and Lewis. Proc. Nat. Acad. Sc. XI, 456, 1925.

\(^5\) The distinctness of the electrons participating in the intramolecular bond, with respect to the other electrons of the outer shell of the molecule, is seen by Hogness and Lunn (Phys. Rev. XXVI, 786, 1925) in the existence of two ionization potentials of the nitrogen molecule, revealed in their investigation of the products of ionization of nitrogen by slow electrons. From their experiments it follows that at 16.95 volts—the ionization potential of the nitrogen molecule \((N_2 = N_2^{+} + e - 16.95)\), also obtained from optical data—only \(N_2^{+}\) ions appear, the number of which does not depend on their stoi-

belonging, generally speaking, simultaneously to both atoms. The number of such systems (pairs) determines the character of the intramolecular bond: one pair of electrons gives a single bond, two—a double bond, and so on. In the case of a molecule with atoms identical or close in their properties, the pair of electrons is situated neutrally with respect to both atoms. Typically homopolar molecules are constructed in this way. In molecules with unlike atoms, however, the pair of bonding electrons is arranged asymmetrically with respect to the two nuclei. In molecules built from atoms standing at opposite ends of the rows of Mendeleev’s table, for example NaCl, the pair of electrons is completely captured by the strongly electronegative chlorine atom, filling its electron shell to the eight-electron shell of a noble gas. The NaCl molecule is a typical representative of heteropolar molecules, characteristic in their ionic structure \((\mathrm{Na}^{+}\mathrm{Cl}^{-})\).

These general, rough notions give only a qualitative picture of the structure of molecules. The problem of the molecule could be considered solved if it were possible to find the orbit of each electron in the molecule, to clarify the participation of each electron in those processes that make the molecule accessible to experiment. The present stage at which the question of the structure of molecules stands may be characterized as a stage of accumulation of factual material, a stage of comparative study of molecules and of drawing analogies.

The investigation of the spectra of the compounds \(\mathrm{BeK}\), \(\mathrm{BO}\), \(\mathrm{CO}^{+}\), \(\mathrm{CN}\), and \(\mathrm{N}_{2}^{+}\) indicates a far-reaching analogy of the band spectra of these compounds with the spectra of the alkali elements \(^{1}\). The bands of these spectra can be represented by a combination of three terms. These are the simple term \(\mathrm{N}\) \(^{2}\), corresponding to the normal state of the compounds under consideration, the doublet term \(\mathrm{A}\), corresponding to the first excited state, and the simple term \(\mathrm{B}\)—to the second state of excitation. These terms are completely analogous to the two \(s\)-terms (\(1s\) and \(2s\)) and the doublet \(p\)-term of the serial spectrum of the alkali metals. This analogy holds not only for the first members of the series. Thus, in the case of \(\mathrm{BO}\) and \(\mathrm{CN}\) the so-called

encounters with \(\mathrm{N}_{2}\) molecules. The ions \((\mathrm{N}_{2}^{+})\), obtained at 24.6 volts, diminish in number in the presence of collisions, while, in parallel with the disappearance of these ions, \(\mathrm{N}^{+}\) ions appear. The authors interpret these results in the following way: the 17-volt ions differ from the 25-volt ions in that the former have lost one electron from the shell, while retaining intact the pair (or pairs) of bonding electrons, whereas the latter have lost one electron from the pair, thereby becoming unstable formations that disintegrate upon collisions.

\(^{1}\) Birge. Nature 117, 300, February 1926. Mullikan. Phys. Rev. 26, 561, 1925.

\(^{2}\) The terminology of terms is according to Mulliken; for ions Mulliken denotes the corresponding terms by the same letters, but with bars.

the $\alpha$- and $\beta$-systems of the spectrum of the first compound and the red and violet bands of cyanogen are analogous, respectively, to the first two members of the principal series of the sodium spectrum ($1s—2p$ and $1s—3p$). The corresponding energy levels differ in absolute magnitude in the case of the different molecules of the series under consideration; however, their ratio is even quantitatively the same as in the case of the sodium atom. Here we shall point only to the fact, noted by Mulliken,¹ that the ratio of the first two resonance potentials for the molecules BO and CN (corresponding to the spectral groups of these molecules just mentioned) is very close to the ratio of the two resonance potentials of sodium, namely:

\[ \left(\frac{5.3}{2.9}\right)_{\mathrm{BO}} = \left(\frac{3.2}{1.8}\right)_{\mathrm{CN}} = \left(\frac{3.74}{2.10}\right)_{\mathrm{Na}} =1.8 . \]

The analogy between the terms of these molecules, on the one hand, and the terms of the atom Na, on the other, further makes it possible to calculate the ionization potential ($1s$ term) of the molecules BO and CN: $I_{\mathrm{BO}}=7.0$ volts, $I_{\mathrm{CN}}=4.4$ volts.

The molecules of the series under consideration all have, in addition to the K-electrons, nine outer electrons. The close analogy of the spectra of these molecules with the sodium spectrum leads Mulliken to the conclusion that eight of the nine valence electrons are situated around both nuclei, forming the inner shell of the molecule, constructed according to the type of the L-shell of atoms of the light elements, whereas the ninth—optical—electron occupies a position analogous to that of the valence electron in the Na atom. Thus, according to Mulliken, eight electrons (out of nine) in the molecule CN, BO, etc., rotate around both nuclei in orbits $2_1$ and $2_2$, while the ninth electron is in the orbit $3_1$ (as in the case of the sodium atom).

The analogy of spectra further unites the following series of molecules: CO, $\mathrm{NO}^{+}$, $\mathrm{N}_2$, SiO. The similarity of the spectra of the latter to the magnesium spectrum indicates the similarity of their structure to that of the Mg atom. The ten electrons of the molecules CO, $\mathrm{N}_2$, etc., must be arranged in two groups: an eight-electron inner group and an outer two-electron group. It is quite clear, however, that not all properties can be repeated by molecules analogous to the Mg atom. For example, nitrogen is not known in the state of the ion $\mathrm{N}_2^{++}$ (analogous to $\mathrm{Mg}^{++}$), which is apparently connected with the absolute instability of the binuclear system $\mathrm{NN}^{++}$.

One may also point to the analogy of the following series of compounds: HF, LiF, BN, NaCl, etc., for which only rotational and rotational-vibrational spectra are known (i.e., spectra not connected with an electron jump), with atoms of the noble gases, which are difficult to excite—

¹ Mullikan, Phys. Rev. 25, 259, March, 1925.

gases. The presence of a band spectrum in the case of CuJ (p. 389), or in general, CuX (where X is a halogen atom), which also belongs to this series of compounds, is only an apparent contradiction. The compound CuX is a typical heteropolar compound. This means that the copper atom in the CuX molecule has completely lost its outer electron, which has passed to the halogen atom. It is unlikely that in the molecule \(\overset{+}{\mathrm{Cu}}\overset{-}{\mathrm{X}}\) the optically active electron should be the eighth electron of the halogen ion—this would be connected with the presence of a series of quantum orbits in the ion X, which one can scarcely expect. On the contrary, there is much reason to expect that the optically active part of the molecule \(\overset{+}{\mathrm{Cu}}\overset{-}{\mathrm{X}}\) will be the ion \(\overset{+}{\mathrm{Cu}}\), one of whose electrons is distinguished by easy excitability. This follows directly from the presence of valence 2 (alongside 1) in the copper atom, in which two Cu electrons must be involved, and which permits the existence of cupric salts \(\overset{++}{\mathrm{Cu}}\overset{--}{\mathrm{X}}_{2}\) alongside salts \(\overset{+}{\mathrm{Cu}}\overset{-}{\mathrm{X}}\). Our assumption1 is also confirmed by the presence of a band spectrum associated with electronic transitions in the case of the halide salts of gold, AuX: the gold atom, as is known, has two valences—1 and 3.

Extrapolating these considerations to the case of salts of divalent metals of the type MeX\(_2\), we arrive at the conclusion that these salts, on the same grounds as the compounds of the series considered, cannot have band spectra. The spectra known for them (for example, the spectrum observed when HgJ\(_2\) is present in a discharge tube) must evidently be attributed to unsaturated molecules MeX (in the example taken—to the compound HgJ).

1. Mullikan, Phys. Rev. 26, 1 July, 1925. ↩↩↩↩↩↩↩↩

2. According to the measurement of Koernicke (ZS. für Phys. 33, 219, 1925), the heat of dissociation of the molecule $\mathrm{Hg}_2$ is equal to 0.06 volt. ↩↩↩↩↩

3. Franck und Grotrian, ZS. für Phys. 4, 89, 1921. ↩↩

4. Gerlach, Phys. ZS. 24, 467, 1923. ↩

5. Investigation of the fine structure of the spectra $\mathrm{HgH}$, $\mathrm{CdH}$, and $\mathrm{ZnH}$ (Hulthén, Nature 116, 642, 1925) showed that these spectra consist of two systems of bands close to one another (the spectrum of the first of the tables given on p. 390), corresponding to two different electronic transitions. This doublet structure of the spectra under consideration brings them all the closer to the spectra of the corresponding metallic atoms, which ↩