ENERGY LEVELS AND STRUCTURE OF MOLECULES

V. N. Kondrat’ev, Leningrad.

§ 1. Atomic terms

The model representation of atoms, based chiefly on Bohr’s theory and on the rotating electron of Uhlenbeck and Goudsmit, has led to a convenient and very clear classification of atomic terms. It turned out that, for the unambiguous determination of any term in the absence of a force field, three quantum numbers are sufficient: \(n\)—the principal quantum number, \(l\)—the subsidiary quantum number, and \(j\)—the inner quantum number; moreover, these numbers have a simple mechanical interpretation, at least in the case of atoms with a small number of valence electrons. The principal quantum number determines, in the first approximation, the energy of the given term and is usually placed as a coefficient before the symbol designating the term, for example, \(1S\), \(2S\), \(2P\), etc. With the subsidiary quantum number is associated the existence of an angular momentum of the orbits of the valence electrons (precession). By means of the subsidiary quantum number a general classification (without taking fine structure into account) of atomic terms is established, in which all terms are divided into groups: the group of \(S\)-terms, for which \(l=0\), the group of \(P\)-terms with \(l=1\), the groups of \(D\)-, \(F\)-, etc. terms with \(l=2,3\), etc. Finally, the inner quantum number \(j\), which determines the fine structure of terms, can in some cases be interpreted as the quantum number corresponding to the angular momentum of the atom as a whole.

This angular momentum, equal to \(j \dfrac{h}{2\pi}\), is composed—

is composed of the angular momentum of the orbits of the valence electrons, determined by the quantum number \(l\) and equal to \(l\frac{h}{2\pi}\), and of the intrinsic angular momenta of the electrons \(\sum \frac{1}{2}\frac{h}{2\pi}\). Thus, in the case of atoms of the alkali metals, which possess a single valence electron, \(j=l\pm\frac{1}{2}\),¹ and for the various terms of this group of atoms the subsidiary and inner quantum numbers therefore have the following values:

TABLE 1.

(Since the additional energy corresponding to \(j\) is determined by the square of \(j\), the negative values of \(j\) play no role in establishing the number of components of each term.) From Table 1 we see that, whereas the \(s\)-terms of the alkali metals are simple, all the other terms (\(p,d,f\)) are double (doublet terms).

Further, in the case of atoms of the alkaline-earth elements, two valence electrons may give a resultant angular momentum equal either to

\[ \frac{1}{2}\frac{h}{2\pi}+\frac{1}{2}\frac{h}{2\pi}=1\frac{h}{2\pi}\quad (s=1), \]

or

\[ \frac{1}{2}\frac{h}{2\pi}-\frac{1}{2}\frac{h}{2\pi}=0\quad (s=0). \]

Here we obtain two systems of terms: a system of singlets \((s=0,\ j=l)\) and a system

¹ The electron magnet is oriented either parallel or antiparallel with respect to the axis of the angular momentum of the orbit, just as the atomic magnets in the Stern and Gerlach experiment are oriented along the field or against the field.

triplets \((s=1,\ j=l-1,\ j=l,\ j=l+1)\). The quantum numbers corresponding to the terms of both systems are given in Tables 2 and 3.

TABLE 2.

TABLE 3.

Let us note that the \(S\)-terms in both systems are again singlets.

In Tables 2 and 3 we have used a notation for the terms (capital letters) different from the notation adopted by us in Table 1 (lowercase letters). Let us clarify the meaning of both notations. The letters \(s, p, d, f\) denote the orbit of an individual electron and correspond to the value of \(l\) characteristic for the given orbit. Henceforth we shall denote this number by the symbol \(l_i\), taking into account the belonging of \(l_i\) to the orbit of the \(i\)-th electron. By the symbol \(l\), however, we shall denote the numerical value of the resultant vector obtained from \(\sum \vec l_i\) for all valence electrons. The new meaning of the symbol \(l\) corresponds also to the capital letters by which we have denoted the terms of the alkaline-earth elements. Thus the capital letters describe the state of the outer electron shell of the atom as a whole. Thus, for example, the \(F\)-term of an atom of an alkaline-earth element \((l=3)\) may be constructed from one \(d\)- \((l_1=2)\) and one \(p\)-electron \((l_2=1)\). (This term belongs to the group of so-called mixed terms and is denoted by the letter \(F\) with two primes—\(F''\)—in distinction from the normal terms of the alkaline-earth elements, for which \(l_1=0\), i.e. for which one of the valence electrons is always in an \(s\)-orbit.) It goes without saying that in the case of normal terms of the alkaline earths \((l=l_2)\), as also in the case of ter-

terms belonging to elements with one outer electron, the letters \(s, p, d \ldots\) and \(S, P, D \ldots\) denote one and the same thing.

To finish with the notation, let us also point out that it is sometimes useful to use both designations of terms, combining them into one, as is done in the examples below. For example, the term corresponding to the normal state of the calcium atom, both of whose electrons are in the state \(4s\) (\(4\) is the principal quantum number), is customarily denoted as follows: \(4s\,4s\,S\) or \((4s)^2\,S\). Here the lowercase letters denote the character of the orbits of the corresponding electrons \((l_i)\), while the capital letter indicates the character of the term sought (\(l\), in the present case \(l = 0\), as do the \(l_i\)). In addition, we must also note the belonging of our term to one or another system (multiplicity): \((4s)^2\,{}^1S\). Finally, the corresponding \(j\) is indicated by a subscript at lower right: \((4s)^2\,{}^1S_0\). In the same way, we may denote the normal term of the sodium atom by the symbol \(3s\,{}^2S_{\frac12}\), and so on. These designations are the most complete designations of atomic terms. Some authors sometimes use designations obtained from those given above by means of certain conventional abbreviations; however, we shall not go into further details on this question here.1

§ 2. Determination of molecular terms.

Before we proceed to present the method that led Hund to the determination of molecular terms, we must dwell somewhat on the Stark phenomenon, without, however, entering into great detail. The Stark phenomenon consists in the displacement and splitting of spectral terms in an electric field. This phenomenon was studied in especially great detail for the hydrogen lines. The most complete theory also applies to hydrogen. According to it, a state (term) characterized, in the absence of an external field, by the quantum number \(n\), splits in an electric field into \(2n - 1\) states with different energies 2. This theory may be extended

also for the simplest atoms with a small number of valence electrons. The model representation of the atom here too makes it possible to establish a definite connection between the number of components of the Stark splitting and the corresponding quantum number (inner or subsidiary).

Let us now turn to the consideration of the classical model of the simplest molecule, consisting of two positively charged nuclei and one electron. The motion of the electron takes place in a field whose potential has the form:

\[ U = U_1(r_1) + U_2(r_2), \]

where \(r_1\) and \(r_2\) are the distances of the electron from the two nuclei, respectively. We shall regard the vibration and rotation of the molecule as small perturbations that do not affect the character of the motion of the electron in the molecule. The entire set of stationary states of our system is easily established for two limiting cases. Let us first imagine that both nuclei are removed from one another to a very great distance. In this case we may think of the electron as bound to one of the nuclei; however, its motion around this nucleus is perturbed by the field of the second nucleus. Consequently, in this case we obtain the entire set of terms of our model of the molecule as the set of terms into which the terms of one of the atoms are split in an electric field (the Stark effect). The other limiting case we shall have if we replace the nucleus of an atom by two nearby nuclei. The perturbation caused by such an operation, as is shown in quantum theory, leads qualitatively to the same terms as in the Stark effect. Between these extreme cases there obviously lies the case that corresponds most closely to reality.

However, in classical mechanics an adiabatic1 transition from the case of separated nuclei to the other limiting case—nearby (in the limit coalescing) nuclei—is impossible

[classical calculation of such a model \((\mathrm{H}_2^+)\) belongs to Pauli and Niessen]. As a consequence, it proves impossible to establish unambiguously the terms of the molecular model on the basis of the known terms of the separate (first limiting case) or original (second limiting case) atom. However, as Hund showed, these difficulties disappear in wave mechanics, and with the aid of the latter Hund arrives at results which are of such essential importance for the establishment and systematics of molecular terms.

Let us consider, using a one-dimensional system as an example, the foundations of Hund’s method. The stationary states of such a system correspond to solutions \(\psi(x)\) of the Schrödinger equation:

\[ \psi''=\psi\,[U(x)-W] \]

under certain boundary conditions. Suppose the potential energy \(U(x)\) has two minima corresponding to two positions of equilibrium. In this case there is obtained a series of discrete energy levels \((W_0, W_1, W_2,\) etc.), each corresponding to a definite solution \(\psi_i\) of the Schrödinger equation (let us note in parentheses that \((\psi)^2\) gives the probability of finding the system in the given state). In Fig. 1 the function \(U(x)\) is shown at the top; the numbers 0, 1, 2, etc. denote the energy levels \((W_i)\), while the lower curves represent the functions \(\psi\) for the stationary states 0, 1, 2, 3, 4.

Fig. 1.

Let us return for a moment to the classical interpretation of this problem. Classical mechanics establishes three types of motion belonging here. If the energy of the system is less than the threshold \(U(x)\)

between the two equilibrium positions, then the motion takes place exclusively either near one (type I) or near the other (type II) equilibrium position. Type III is obtained when the energy is greater than the threshold \(U(x)\) and when, consequently, the motion is performed about both minima. (Analogous three types of motion were found by Pauli and Niessen in considering the model \(\mathrm{H}_2^+\).) In the old quantum mechanics an adiabatic transition between these types of motion is impossible. In wave mechanics, however, every distinction between all three types of motion disappears, and we can no longer assert that even in the case when the energy of the system is less than the threshold \(U(x)\), the oscillating particle cannot pass through the threshold; on the contrary, the existence of even a small but finite probability of finding the particle on the other side of the threshold (Fig. 1, \(\psi_0\) and \(\psi_1\)) indicates that, being in any of the discrete states, the particle can always, with one probability or another, pass through the threshold. Thus here any state is uniquely determined by the corresponding quantum numbers.

Let us now trace what will happen to the system if we gradually raise the threshold separating the two equilibrium positions and, finally, raise it to \(\infty\), so that the region of motion breaks up into two completely separate parts. This process is represented by the two figures given below (2 and 3). From these figures we see that, in passing from a high to an infinitely high threshold, the functions \(\psi\) retain a finite value (not zero) only in one of the two parts. Thus, from the discrete states of the composite system we obtain the stationary states of its parts, and, as we see, not a single state of the system is lost upon its division. Renumbering the levels in both parts of the separated system, denoting the lower level of each part by the symbol 0, the next by 1, etc., we may represent in the following manner (Fig. 4) the distribution of terms that occurs when the system is divided into two parts. The analogous situation also occurs when a molecule is divided in our model representa-

Fig. 2. Almost separated system.

Fig. 3. Separated system.

...tion into the constituent atoms, or when constructing a molecule from atoms or ions. When the nuclei are moved apart, each term of the molecule passes either into the term of one atom (ion), or into the term of another. In exactly the same way, when the nuclei are brought closer together, a term of the molecule passes into the term of the atom thus obtained. This circumstance makes it possible to establish molecular terms by means of qualitative interpolation between the terms of atoms or ions known from spectroscopic data.

Fig. 4.

Here it is necessary to draw attention to one very important circumstance. It is known that when external conditions change, for example in the transition from weak to strong magnetic fields, some terms, mixing, intersect. In establishing molecular terms by means of adiabatic approach or

in the displacement of the nuclei, it is necessary to take into account the possibility of crossing of terms; otherwise we may obtain an incorrect order of the terms in the system (molecule) under consideration. It follows from theory that terms may cross when the system contains identical particles (electrons, nuclei), or when some coordinate of the system is separable.

The problem of finding the terms of a system consisting of one electron and two nuclei is solved as follows. This problem reduces to Schrödinger’s equation, separable in elliptic coordinates \(\xi, \eta, \varphi\). The stationary states are enumerated

Fig. 5.

by means of the quantum numbers \(n_{\xi}, n_{\eta}\), and \(n_{\varphi}\). The exact position of the terms can be found by numerical or graphical solution of the Schrödinger equation. An approximate solution of the question of the arrangement of molecular terms may be obtained by investigating, together with Hund, the transition from two separated nuclei to two nearly coincident nuclei. Such a transition is depicted in Fig. 5. Here, on the left, are indicated the terms associated with the motion of the electron around one of the nuclei in a “separated” system (infinitely distant nuclei). As the nuclei approach one another, the terms split (distant nuclei). In our case this splitting, even at a large distance between the nuclei, corresponds

to the linear Stark effect. On the right are shown the terms corresponding to the system of electrons—two merged nuclei (hydrogen terms). By slightly separating the nuclei, we obtain a splitting of the terms, each term corresponding to a given quantum number \(n\) (marked by a symbol) splitting into so many components that all possible combinations \(n_{\xi}\), \(n_{\eta}\), and \(n_{\varphi}\) are obtained, with \(n_{\xi}+n_{\eta}+n_{\varphi}=n\). The triple numbers by which the dotted lines connecting the terms of “near nuclei” with the terms of “distant nuclei” are marked correspond to \(n_{\xi} n_{\eta} n_{\varphi}\). Fig. 5 refers to a model of a molecule with different nuclei. In the case of identical nuclei the picture is essentially the same. We shall note only that in this latter case there are more crossing terms (see above).

Of greatest interest to us is the case of systems with several electrons. This problem is, of course, considerably more complicated than the preceding one (already in the case of a molecule with two electrons—\(\mathrm{H}_2\)—this problem is, approximately, as much more difficult than the preceding one as the problem of the helium atom is more difficult than the problem of the hydrogen atom). First of all, here there is a larger number of parts into which the system can be decomposed. Further, the transition from the terms corresponding to a system of separated nuclei to the terms of a system with a single nucleus is not unambiguous here. However, by solving the problem in one approximation or another (for example, by admitting separability of the variables), we can establish in each individual case a more or less probable picture of the molecular terms. Here various rules come to our aid, such as the following, established by Heisenberg: a singlet molecular term can pass only into such atomic terms as correspond to a state of identical multiplicity of both atoms; a doublet molecular term can pass only into such atomic terms whose multiplicities differ by at most one, etc. (3).

§ 3. Systematics of molecular terms and certain properties of molecules. In the case of molecules, as in the case of atoms, one may speak of a “coarse” and a “fine” structure of spectral terms. The fine structure of molecular terms, apparently, as in the case of atoms, is primarily-

... is determined entirely by the angular momentum of the electron. However, owing to the interaction of this latter quantity with the rotation of the molecule,¹ molecular terms have a more complicated structure than atomic ones. The character of the structure of a molecular term is determined by two quantum numbers. One of them, $i_l$, corresponds to the total angular momentum of all the electrons about the line joining the nuclei, and may be equal to $0, 1, 2$, etc. The number $i_l$ plays, in the classification of molecular terms, the same role as the subsidiary quantum number $l$ in the classification of atomic terms. The other quantum number, $s$, corresponds to the resultant angular momentum of the electrons (made up of the intrinsic electronic moments) and takes the values $0, 1, 2 \ldots$ for an even number of electrons and $1/2, 3/2 \ldots$ for an odd number. From this, theoretically, the following types of molecular terms are obtained (Hund):

Fig. 6.

Fig. 7.

Fig. 8.

1. $i_l = 0$.

a) $s = 0$ (Fig. 6). To each rotational quantum number $(p)$ there corresponds only one term.

b) $s > 0$ (Figs. 7 and 8). With increasing rotational quantum number the term splits into $2s + 1$ components (this splitting is caused by the interaction of $s$ with the rotation of the molecule).

1. $i_l > 0$.

a) $s = 0$ (Fig. 9). The terms split into two with increasing $p$, owing to the interaction of $i_l$ with the rotation of the molecule.

¹ The electron receives additional energy in the magnetic field that arises upon rotation of the nuclei. In the first approximation this energy is proportional to the rotational quantum number $p$.

c) \(s > 0\) (Figs. 10 and 11). The terms are split into two as a consequence of rotation. In addition, all terms are split into \(2s+1\) components independently of rotation1 (5).

This classification of molecular terms is fully accommodated by the empirical classification created mainly through the investigations of Mecke, Mulliken, and Birge (6). A detailed study of the structure and properties of various types of molecular terms led these authors to establish a systematics of molecular terms entirely analogous to the systematics of atomic terms. This empirical systematics of terms, in Hund’s investigations (see the classification given above), received a solid theoretical basis. In this systematics the following molecular terms are established: \(S\)-terms are terms corresponding to \(i_l=0\), \(P\)-terms to \(i_l=1\), and so on. The belonging of a given term to one or another system of multiplets, as in the case of atomic terms, is denoted by an index at the upper left, this index being equal to \(2s+1\).

Fig. 9.

Fig. 10.

Fig. 11.

We have seen that the symbols denoting molecular terms (\(S, P, D\ldots\)) have a somewhat different meaning than the symbols of atomic terms (the former correspond to the quantum numbers \(i_l\), the latter to \(l\)). Therefore it will be more rational in what follows—

henceforth, together with Wigner and Witmer, use the following notation for molecular terms: to denote terms with \(i_l=0\) by the symbol \(\Sigma\), with \(i_l=1\) by \(\Pi\), with \(i_l=2\) by \(\Delta\), etc.

In the case of molecules, as in the case of atoms, there are definite selection rules to which optical transitions between different terms are subject. In order for two terms to combine, it is necessary that the integral

\[ \int \mu \psi_1 \psi_2\, d\omega \]

be different from zero. Here \(\psi_1\) and \(\psi_2\) are the Schrödinger functions characterizing the two terms, \(\mu\) is the electric moment determining the radiative process associated with the transition of the molecule from one state to another, and \(d\omega\) is the differential of the coordinate space. The selection rules obtained from this state that, when two terms combine, the quantum number \(i_l\) may change only by \(+1\) or \(0\); moreover, \(\Delta S=0\) (the latter applies chiefly to light molecules).

The existence of selection rules in the case of molecules1 is a direct indication of the existence of metastable states of molecules. Let us note that this question, still by no means fully studied, is of very substantial importance for chemical kinetics (heat of activation, energy chains in explosive reactions).

In the preceding paragraph we saw how, by means of Hund’s method, the terms of a molecule are obtained from the terms of the corresponding atoms. In Fig. 12 the lower terms of the CH molecule are presented as they are obtained from the terms of C and H, on the one hand, and from the terms of the N atom, which has the same number of electrons as the CH molecule, on the other. We see that the normal term of the CH molecule is the term

ENERGY LEVELS AND THE STRUCTURE OF MOLECULES

\({}^{2}\Pi\), the terms next in order are \({}^{4}\Sigma\), \({}^{2}\Delta\), \({}^{2}\Sigma\), etc. If we turn to the data of spectroscopic investigation, still far from complete, we shall see that both the multiplicity of the terms found experimentally and the combinations between terms correspond exactly to the theoretical ones. We are convinced of this by the data given in the following table. Here the Roman numeral denotes the number of valence electrons in the atoms (e.g., \(A^{\mathrm{II}}\), \(A^{\mathrm{III}}\), etc.); H denotes the hydrogen atom. In parentheses are placed combinations forbidden by the selection rule. In the last column are also indicated molecules in whose case the corresponding transitions (combinations) have been found.

Fig. 12.

TABLE 1.

We see that in almost all cases the theoretically expected transitions take place, and the selection rules are never violated. It is necessary, however, to note that the theoretically established order of molecular terms (the scheme of energy levels) is not always in complete agreement with experiment. The ambiguity already noted above in establishing the order of terms is especially felt in the case of molecules with a large number of electrons. In the latter case one may speak of one or another degree of probability of the given theoretical scheme of energy levels—

of the molecule. This explains why, in the works of some authors, we sometimes find a different order of molecular terms than that established by Hund (see below).

The theory of the origin of molecular terms from the terms of the atoms composing a given molecule sheds light on those experimentally established elementary processes that take place in the optical dissociation of molecules. We shall consider some of these processes, which are of great interest for photochemistry, using the example of ionic (heteropolar) molecules. As the investigations of Franck and his collaborators have shown, a distinctive property of ionic molecules is their capacity for optical dissociation into normal atoms (7). This property of ionic molecules follows directly from Hund’s theory.

Fig. 13.

From Fig. 13 we see that the normal term of the NaCl molecule is obtained adiabatically from the ionic term \(3p\). The higher-lying term, the third, is obtained from the terms of the normal atoms Na and Cl. Thus the first stage of excitation of the NaCl molecule corresponds to the transition \((\mathrm{Na})(\mathrm{Cl}) \to (\mathrm{Na})(\mathrm{Cl})\). From the absorption spectrum corresponding to this transition [Sommermeyer, 8], it is evident that the excited NaCl molecule is only weakly stable (negligible heat of dissociation) and, consequently, readily breaks up into atoms. In accordance with the origin of the term of the excited NaCl molecule (see figure), the products of its dissociation must be normal atoms, as is confirmed by experiment. One of the subsequent excitation levels of the NaCl molecule, according to Hund, is obtained from an excited Na atom and normal Cl. Hence follows the possibility of optical dissociation of NaCl according to the following scheme: \(\mathrm{NaCl} + h\nu = \mathrm{Na}' + \mathrm{Cl}\). This kind of dis-

dissociation was experimentally discovered by Terenin (9). Everything said about the NaCl molecule must naturally apply to any ionic diatomic molecule.

Using as an example the terms of certain atomic (homeopolar) molecules, we shall consider another very important question connected with the doctrine of valency. Wave mechanics, in complete agreement with experiment, establishes the following terms of the CN molecule1.

Table 5.

According to this table, the normal term of the CN molecule is obtained from an excited carbon atom \(({}^{5}S)\) and a normal nitrogen atom \(({}^{4}S)\), whereas the terms of the excited states of the CN molecule are obtained from the terms of normal C and N atoms; the same also occurs in the case of the molecules \(\mathrm{N}_{2}^{+}\), \(\mathrm{SiN}\), \(\mathrm{CO}^{+}\), \(\mathrm{BO}\), \(\mathrm{AlO}\), and, apparently, in the case of the molecule \(\mathrm{N}_{2}\)2. In the last column of Table 5 are given the heats of dissociation of the normal (9.7) and excited CN molecule (6.8 and 4.8). From these data we see that the CN molecule is most stable in the normal state. This fact is in complete agreement with our ideas about valency. Indeed, from the multiplicity 5 of the term of the excited carbon atom \(({}^{5}S)\), we must conclude—

...that in the normal state of the CN molecule the C atom is tetravalent (12), whereas the normal carbon atom \(({}^{3}P)\), which together with the nitrogen atom \(({}^{4}S)\) forms the excited CN molecule, is divalent.^1

As was to be expected, tetravalent carbon is more firmly bound than divalent carbon (the strength of the bond increases with the number of binding pairs of electrons). The excited CN molecule, arising from normal C and N atoms, passes, with the emission of light, into the normal state, corresponding to a stronger bond. In this process the valence of carbon changes from 2 to 4. Fig. 14 illustrates the intramolecular bond in the case of the excited and the normal CN molecule.

[Figure: electron-pair diagrams for the excited and normal CN molecule, labeled \(C\), \(N\), \(C'\), and \(CN\).]

Fig. 14.

In conclusion, a few words about the general structure of the electron shell of the molecule. The possibility, following from the model representation of molecules, of assigning definite quantum numbers \(i, l\), and \(s\) to the electron shell of a molecule indicates that the electron shell in the case of molecules is built according to the same principle as the shell of atoms. As in the case of atoms, here too we may speak of one or another degree of closedness of electron shells, of valence electrons, and so forth. Thus, from Fig. 14 one obtains directly the following representation of the CN molecule. We see that eight of the nine outer electrons (the firmly bound \(K\)-electrons are not counted) in the CN molecule are paired. These electrons form a closed eight-electron shell, analogous to the \(L\)-shell of the sodium atom. The ninth electron remains free and can play the role of the valence electron of the Na atom. This representation is confirmed, on the one hand,

^1 To these two states of the carbon atom there corresponds the following orientation of the electronic moments:
\(C:\) [[unclear: arrow diagram of electronic moments with shells \(K\) and \(L\)]];
\(C':\) [[unclear: arrow diagram of electronic moments with shells \(K\) and \(L\)]].

tendency of the CN molecule toward the formation of more complex molecules analogous to the molecules corresponding to sodium compounds (e.g. \(C_2N_2\) and \(Na_2\), HCN and HNa, CNCl and NaCl, etc.), and, on the other hand, by a structure and ordering of terms analogous to the terms of the Na atom. This kind of analogy between atomic and molecular terms occurs in a whole series of molecules. Thus, the terms of the molecules BO, BeF, \(CO^+\), \(N_2^+\), which have 9 outer electrons, like the CN molecule, are also analogous to the terms of Na (13). The molecules CO, \(NO^+\), \(N_2\), SiO, with respect to their structure and ordering of terms, are analogous to the Mg atom (14), etc. This analogy between atomic and molecular terms, first noted by Mulliken, gave the first impetus to the establishment of the systematics of molecular terms, which later, thanks to Hund’s investigations, received a firm theoretical foundation.

Literature

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1. This order of terms was established by Heitler and Herzberg (10) and differs from Hund’s. The order of terms established by Hund in the case of the CN and \(\mathrm{N}_{2}^{+}\) molecules contradicts certain experimental facts, as a result of which it must be recognized as erroneous. ↩↩↩↩↩

2. In the case of these molecules, optical dissociation into normal atoms proves to be possible in principle, as occurs in the case of ionic molecules—contrary to Franck’s views (11). ↩↩