THE RELATIONSHIP BETWEEN SPECTROSCOPY AND CHEMISTRY*

James Franck, Göttingen

The field I have chosen as the subject of this lecture is so extensive that, in the short interval of time at my disposal, I have no possibility of exhausting it in any way. I shall therefore permit myself to confine my remarks to those parts which are closely connected with work carried out in my institute in recent years.

First of all, we shall dwell on the determination of the work of dissociation from molecular spectra and on the criteria for classifying molecules according to their chemical bond.

The simplest case of determining a thermochemical quantity from band spectra is the determination of the work of dissociation of a diatomic molecule from the position of the convergence point of the bands. Four years ago I already reported here, in England, at a meeting of the Faraday Society in Oxford, on the first examples investigated in this way. The spectroscopic picture was as follows: in the absorption spectrum of diatomic iodine, obtained at room temperature, a series of bands was found whose quanta, on shifting toward shorter wavelengths, came closer and closer together until a convergence point was reached, adjoining which—toward the short-wave side—there was a continuous absorption spectrum. It was quite natural to suppose that the interpretation

* Lecture delivered in Bristol (Wills Memorial Lecture) on October 25, 1930. The German translation was printed in Naturwissenschaften of March 6, 1931.

the place of convergence of the bands must be analogous to the interpretation of the place of convergence of series in atomic spectra. In exactly the same way as, in the latter case, upon illumination with light of the frequency of the place of convergence, dissociation of the atom into an ion and an electron occurs, so also upon convergence of a sequence of band quanta there must occur dissociation of the molecule into those particles whose vibrations determine the very series of quanta, i.e., in our example, dissociation of the ion molecule into two atoms. The continuum adjacent to the place of convergence indicates that the products of dissociation can separate with a continuous sequence of values of kinetic energy. The state of the electron shell of the dissociation products and the circumstances of the transition upon absorption of light can best be clarified on energy diagrams. In the left-hand part of Fig. 1 are plotted the values of the vibrational terms that belong to the ground state of the electronic system of the halide molecule, and, in addition, the vibrational terms of the first excited state of the electron shell. In absorption experiments at low temperatures the initial state is the nonvibrating state of the molecule with an unexcited electron shell. If convergence of bands is observed, this means that, with the transition of the electron shell into the excited state, the transformation of such an amount of energy into vibrational energy is associated that we arrive at the place where the excited molecule dissociates. It is clear that, by means of an absorption experiment, one can find the sequence of quanta of the excited molecule and, at the same time, from the magnitude corresponding to the convergence of the bands, determine the sum of the energies of excitation of the molecule and of dissociation of the excited molecule. If now, by illumination with monochromatic light or by collision with an excited atom, one excites one definite vibrational term of the excited molecule, then in an analogous manner, from the spectrum of fluorescence light, one can establish the transitions into the system of vibrational terms of the ground state and, at the same time—by following the latter to the place of convergence—the work of dissociation of the ground state. It turns out that, for the overwhelming majority of simple

nuclearly bound molecules of elements, such as halides, oxygen, hydrogen, etc. When the vibrational energy is increased to the point of convergence of the ground state, the molecule dissociates into two normal atoms, which agrees with the modern theory of the homopolar bond; an excited diatomic molecule, however, when its vibrational energy is increased to the limit, dissociates into a normal and an excited atom.

If the amounts of energy required for the excitation of atoms are known from atomic spectra, then for the convergence point observed in absorption the relation is obtained:

\[ h\nu = A - D, \]

where \(A\) denotes the excitation energy of the atom, and \(D\) the work of dissociation. Observation of the convergence point of the ground state from the emission spectrum gives the work of dissociation of the ground state from the equation:

\[ h\nu_a - h\nu_c = D, \]

where \(\nu_a\) denotes the frequency of the exciting absorption line, and \(h\nu_c\) the observed frequency of convergence.

In recent years, by a similar method, the work of dissociation has been determined with very great accuracy for a number of molecules. The premise of this method is that the convergence point in absorption or emission is accessible to observation. This, however, is far from the case for all molecules. Often electronic transitions are observed with which only a very small change in the vibrational energies of the molecule is associated, for example only the transitions \(0—0\), \(0—1\), \(0—2\). In other cases transitions are observed with which so considerable an increase in vibrational energies is associated that in absorption only transitions into the continuum appear, so that in the elementary act of absorption of light dissociation always occurs. In these cases the discrete band spectrum is completely absent. This different behavior of molecules can most conveniently be made clear by depicting the curves of the mutual potential energy of the nuclei as a function of their distance, as is done in the right half of Fig. 1. I suppose it is known that the distances of the nuclei in the position of equi-

the equilibrium position can be calculated from the rotational structure of each individual band, since the rotational quanta are connected in a simple way with the moment of inertia of the molecule.* For iodine, two potential curves are obtained, whose position relative to one another is seen from Fig. 1. From these two curves one can easily see what region of the system of vibrational quanta of the excited state may be expected in absorption transitions from the ground state. It is enough merely to recall that the behavior of a molecule can, to a known approximation, be established by replacing the molecule with a mechanical system constructed from the heavy masses of the nuclei and very light electrons. Light falls on the electronic system, and the transition to the excited state of the light electrons takes place so rapidly that the nuclei, during the time of the transition, practically do not change their relative positions and velocities. If, as in our case, the initial state is the non-vibrating ground state of the iodine molecule, then the electronic transition, which must not change the relative positions and velocities of the nuclei, leads to such a point of the potential curve of the excited state which lies on the perpendicular passing through the minimum of the ground state.

Fig. 1. Vibrational terms and course of the potential of a halide molecule.

At the same time the nuclei acquire potential energy, which after the act of absorption is periodically transformed into kinetic energy. In iodine the point reached in this way lies somewhat above the horizontal asymptote, and consequently belongs to the continuum. Thus the maximum of absorption in this case will lie on the other side of the place of coalescence. Analogous curves for bromine show—

* Cf., for example, the article by Mecke, “Band spectra and their significance for chemistry,” Advances in the Physical Sciences, vol. IX, p. 631, 1929.

take into account transitions that lie considerably farther in the continuum, as a result of which only an insignificant part of the discrete band spectrum appears. Finally, in chlorine the upper curve, relative to the lower one, is so displaced by its minimum toward large radii that an almost exclusively continuous spectrum is obtained. This fact makes it possible to understand why molecular fluorescence is obtained very easily in iodine, with difficulty in bromine, and not at all in chlorine.

The displacement of the minimum toward large radii upon excitation by light generally corresponds to a weakening of the bond as a result of an electronic transition, whereas a displacement of the minimum toward small radii, which is also often observed, in most cases corresponds to a strengthening of the bond as a result of excitation (Fig. 2). The following figure shows the position of the potential curves for the various typical cases listed.

Fig. 2. Course of the potential for the normal and excited states: I) with weakening of the bond, II) with preservation of the magnitude of the bond, III) with strengthening of the bond as a result of electronic excitation

In all cases the position of the transition region, in agreement with experiment, is obtained as the intersection of the perpendicular drawn through the equilibrium position with the curve of the final state. We may briefly formulate the result as follows: whenever, upon excitation, the bond changes strongly, the electronic transition is accompanied by the transfer of a large amount of vibrational energy; if, however, the bond strength changes little or not at all, as is shown in the middle part of the curve, then only the \((0,0)\) bands and those adjacent to them appear. The conclusions drawn on the basis of the model are, of course, correct only qualitatively. In order to obtain a quantitative formulation, one should—

one must turn to Condon’s quantum-mechanical treatment of this picture, introduced for the first time. According to quantum mechanics it follows, for example, that the state of a molecule with vibrational quantum number zero corresponds not to a state with no vibrations, i.e. not to a point fixation of the distance between the nuclei, but that there exists a so-called zero-point vibration. The distance between the nuclei is characterized by a probability curve. The greatest probability in the state of zero energy corresponds to the position of the minimum. To the right and to the left of this state, the probability that the nuclei are at a given distance falls along an exponential curve.

Therefore we obtain transitions not between two definite points of the potential curves, but between broad regions with a maximum at the place where, according to the laws of ordinary mechanics, the transition alone should occur.

If we start from a vibrating molecule, i.e. if we carry out absorption experiments at high temperature, then the mechanical model makes us expect that the transitions should occur chiefly at sharply defined turning points of the vibration. Quantum mechanics again presents not sharply defined turning points, but entire broad regions of transition probabilities. It turns out that in this way, in all cases observed so far, the position of the transition regions in band spectra can be interpreted exactly.

If we now return to the previously mentioned example of the haloids, we shall see that, owing to the different position of the transition regions, the observation of places where bands converge is not always possible with equal convenience. In iodine it appears sharply in absorption; in bromine and in chlorine—provided only that a sufficiently high pressure or else a high temperature is chosen—the establishment of the place of convergence, and thereby the determination of the work of dissociation, is also possible. In other cases, as for example in nitrogen, the places of convergence of the bands can be observed neither in absorption nor in emission, since here the bond strength, i.e. the mutual disposition of the po-

tential curves under excitation changes only insignificantly. Berndt and Sponer have indicated how one can help in such cases so as to determine, at least approximately, the convergence of the bands, and from it the work of dissociation. For this purpose, from the observed vibrational quanta of the excited or ground state, one must find the decrease of the vibrational quanta with increasing quantum number, and from this extrapolate the position of the point of convergence. This procedure is facilitated by the fact that in most homopolar compounds the vibrational quanta, as it turns out, in first approximation decrease linearly with the quantum number. For ionic compounds this regularity does not hold, as may also readily be verified theoretically. The position of continua that are observed without discrete bands, owing to the fact that excitation changes the strength of the bond very greatly, likewise makes it possible, with known approximation, to estimate the work of dissociation, at least in those cases when the gas is not heated too strongly. In these cases it is known that the long-wavelength boundary of the continuum lies on the far side of the point of convergence, so that in this way one can establish an upper limit for the work of dissociation. Instead of establishing the long-wavelength boundary of the absorption spectrum in those cases when the molecule decomposes into an excited and a normal atom, it is possible to observe, upon the return of the excited atom to the normal state, the resulting atomic fluorescence. The longest wavelength of the incident light that excites atomic fluorescence upon illuminating the molecule is, in such a case, identical with the long-wavelength boundary corresponding to the absorption region, and together with this it also gives the upper limit of the work of dissociation. This method was found and developed by Terenin.

Let us now say a few words concerning the possibility of learning something about the nature of the chemical bond—the possibility opened up by the methods described. The homopolar molecules considered up to now behave in such a way that, when the vibrational quanta of the ground state are traced to the point of convergence, dissociation into normal atoms is obtained, in that

time the tracing of the vibrational quanta of some excited state of a molecule up to coalescence indicates dissociation into a normal and an excited atom. In contrast to this, for an ionic molecule the ground state of the electronic system is such that, when the vibrational terms are traced up to coalescence, dissociation into ions is obtained.

Thus here the electronic state whose system of vibrations in the limit leads to normal atoms will no longer be the most stable one, but at the same time will be an excited state of the molecule. These relations can again be shown most clearly by considering the potential curves of typical ionic compounds, namely the vapors of alkali-halide salts (Fig. 3). I must emphasize here that the course of the potential curves of the excited state in the present case is known only approximately. The first thing that is striking is that the potential curve of the first excited state intersects the potential curve of the ground state. This means that the work of dissociation into ions is greater for all alkali-halide compounds than the work of dissociation into atoms. It is possible to determine exactly the distance from one another of the rectilinear asymptotes of the potential curves. These distances are, both experimentally and theoretically, equal to the energies required for exciting the products of dissociation (i.e., the atoms of the alkali metal or of the halide). Further, it can be shown that all the potential curves of the excited states run parallel to one another and possess only very weakly expressed potential minima. This follows from the structure and position of the absorption spectrum of the alkali-halide compounds. If we study them at not too high temperatures, at which the majority of molecules

Fig. 3. Course of the potential of alkali-halide molecules

If it is in a non-oscillating state, continua are observed; of these, the longest-wavelength one leads to a transition into the first excited state, in the limit passing over into dissociation into normal atoms, whereas the continua of shorter wavelength indicate dissociation into excited states. Since the maxima of the continua, within small errors, are separated from one another by distances corresponding to the excitation stages of the dissociation products, it is possible to assign to each of the observed continua a definite act of dissociation. It turns out thereby that, in addition to dissociation into normal atoms, there is dissociation in which the alkali-metal atom is in the ground state, and the halogen is in the state corresponding to the higher of the two terms of its doublet splitting. Further, dissociations are also found in which the halogen atoms are in the ground state, and the alkali atoms—in one of the excited states. All stages of excitation of the alkali metals can be found from the corresponding absorption maxima. The higher stages of excitation naturally give an unresolved broad region of absorption. The correctness of this interpretation follows from the fact that, upon illumination with the light of various continua, in some cases the corresponding atomic fluorescence can be observed. From the fact that the maxima of the continua, to a good approximation, are located at distances that correspond to the excitation stages of the atoms, it follows that the potential curves run almost parallel throughout. It follows further that the excited states are very diffuse, since the absorption regions lie mainly in the continuum. Since molecular fluorescence cannot for this reason be observed, the possibility of constructing the potential curve of the ground state from observations of molecular fluorescence is lost.

Thus, although no discrete band spectrum is observed for the molecules of alkali-halide compounds, it is nevertheless possible, from their spectra, to draw conclusions about the ground state of the molecule. In this case one obtains dif-

diffuse bands, which constitute a special type of spectra. Their occurrence, according to the ideas of Zommermeier, modified by Kuhn, reduces to the following. Let the potential curves of the excited state of the molecules run at a smaller angle to the horizon, for example as shown in Fig. 3. For a definite vibrational state of the fundamental term, the magnitude of the most probable transition is given by the perpendicular distance of the turning point, corresponding to the greatest separation of the nuclei, from the potential curve of the excited state. This distance is marked in Fig. 3 by an arrow on the right-hand side. What is essential is that, owing to the small inclination of the upper curve, to a definite indistinctness of the coordinate of position \(r\) there corresponds only an insignificant indistinctness of the frequency (i.e., the length of the arrow). In contrast to this, at the turning point corresponding to the approach of the nuclei, there arises a very narrow absorption maximum, and the maxima due to different vibrational states are perceived separately, as a fluctuation of intensity. If the inclination of the upper potential curve may be neglected, then the distances of the fluctuations give the vibrational quanta of the fundamental state. As far as can be expected with this simplifying neglect, the vibrational quanta of the fundamental state, measured by Zommermeier by this method for certain alkali-halide molecules, agree with the values calculated by Born and Heisenberg.* In the case of bands of this type it is immaterial whether the transitions occur into the discrete region of the terms of the excited state (as is shown in the figure) or into the region of dissociation. In the first case we obtain fluctuations of intensities possessing a fine structure, in the latter—fluctuations in a true continuum. It is probably precisely in the case of alkali-halide molecules that we are dealing with the latter case.

* Already after this lecture had been delivered, Van Leeuwen (H. I. Van Leeuwen, Z. Physik 66, 241, 1930) calculated these vibrational quanta of the fundamental state by means of quantum mechanics; and these calculations agree satisfactorily with the experimental values.

The course of the vibrational quanta is not known with sufficient accuracy for the energy of dissociation into ions to be estimated by extrapolating the point of convergence. It is, however, possible to estimate the work of dissociation into atoms fairly well if one measures the frequency corresponding to the transition from the non-vibrating ground state to the first level of excitation. According to Kuhn’s new results, the value obtained in this way by Sommermeyer is incorrect, since the observed transitions already originated from a vibrating molecule. A further error arises from the fact that the upper curve does not run parallel to the abscissa axis. I shall return to this point somewhat later. In turn, the work of dissociation into ions can be calculated from the work of dissociation into atoms, from the ionization potential of the alkali-metal atom (which is known exactly), and from the electron affinity of the halogen atom. As regards the last quantity, at present one can already rely not only on Born’s excellent results from the theory of the crystal lattice, but very recently in my institute Meyer has determined the degree of thermal dissociation of alkali-halide compounds for decomposition into ions as a function of temperature, and at the same time has directly measured the electron affinity by thermochemical methods. The values found for iodine agree well with those obtained from Born’s theory.

Thus, in ionic molecules the first stage of dissociation under the action of light corresponds to decomposition into normal atoms. If, however, the first stage of dissociation represents decomposition into a normal and an excited atom, then this is a strong argument in favor of the fact that what we have before us is not an ionic molecule. According to these criteria, silver halide salts in the vapor phase, as well as the hydrogen halide acids, are not ionic but atomic molecules. The fact that a molecule possesses a dipole moment is not sufficient to assign it to the class of ionic molecules. Of course, besides these negative criteria, in each case one must also look for positive criteria before finally

to carry out a classification of molecules. As a positive criterion one may use the study of the vibrational system of the ground state. For silver-halide compounds, in which molecular fluorescence is observed, in agreement with other criteria it follows that the extrapolated point of coalescence corresponds to dissociation into atoms, so that here we are dealing with atomic molecules.

For some time, from the theoretical point of view, the objection was raised that, when potential curves cross, as occurs in alkali-halide compounds, an ambiguity may arise; for example, if in sodium iodide the nuclei are separated adiabatically with respect to the electronic system, then near the point of intersection of the curves the very concept of this adiabaticity loses its meaning, and precisely after the point of intersection the particles may follow the ionic curve or else pass adiabatically onto the atomic curve. Recently this assertion of the theory has again been subjected to criticism. However, quite apart from theoretical considerations, it is possible to establish the character of the bond of a molecule. For this it is sufficient to determine unambiguously the course of the curve at a known distance from the point of intersection. Once this has been done, it can always be established that the ionic or atomic curve is the continuation of the potential curve of the ground state at some distance from the point of intersection.

As was mentioned above, ionic molecules, upon absorption of light, in contrast to the ordinary behavior of atomic molecules, can be decomposed into two normal atoms. However, the converse proposition—namely, the assertion that a molecule is ionic if, by absorption of light, it can be decomposed into two atoms in the normal state—is incorrect. There are cases in which, as Herzberg and Geitler have shown, atomic molecules, upon absorbing light, can dissociate into normal atoms. This occurs when the most stable state of the molecule is formed by the combination of a normal and an excited atom. An example is carbon monoxide.

The state which, in the limit upon dissociation, leads to normal atoms is in this case characterized by a weaker bond; at the same time carbon in the normal state exhibits divalency. In order to make it tetravalent, excitation energy is required, as is also evident from the distribution of electrons in the periodic system. However, the work which must be performed for this is considerably less than the potential energy acquired as a result of the increase in bond strength; hence the crossing of the curves. In Fig. 4 entirely analogous conditions are presented for the SiN molecule.

On the basis of what has been said so far, one might form the impression that by the method described one cannot obtain grossly erroneous values for the heats of dissociation. This, however, is not so. Even when a point of coalescence is observed, it is sometimes not easy to decide in which state of excitation the atoms obtained upon dissociation are found. It often happens that the serial scheme of the atomic spectra is unknown or insufficiently known. This explains why the value of the dissociation energy of oxygen determined in this way often changed until, as a result of the study of the atomic spectrum, the exact value was found. Other sources of error arise when what are observed are not true discrete bands, but fluctuations of intensity, i.e. diffuse bands of the type which we saw in iodine-halogen compounds. Fig. 5 gives the corresponding case. Here too the transition regions corresponding to the turning points of vibration \(B, C, D\), etc., owing to the flatness of the upper curve, are separated from one another, and for large internuclear distances the distance between the transition regions is again specified by the magnitude of the vibrational quanta of the ground state. Since, however, at small internuclear distances (for example at \(A'\)) the upper curve reveals

Fig. 4. Course of the potential of SiN.

exhibits an even more noticeable decrease and does not run parallel to the abscissa axis, it is clear that the distance between the maxima is initially considerably greater than the vibrational quanta, and decreases considerably faster than corresponds to the diminution of the vibrational quanta of the ground state.

Recently Kuhn has discovered such peculiarities in a number of molecules both in the case where the lower state is flat and combines with a steep excited state, and in the opposite case. Since the transition regions in this case are narrow, the maxima give the impression of blurred bands, from which one might conclude that the vibrational quanta rapidly decrease in magnitude; moreover, by such a procedure an entirely incorrect position of the convergence point would be extrapolated. As an example I may point to the incorrect values of the dissociation work obtained by Morozovsky and his collaborators for Hg₂, Cd₂, and Zn₂, who took fluctuations of intensity for vibrational quanta and extrapolated to a false convergence point. Precisely these substances have a very small dissociation work in the ground state and may serve as prototypes of that class of compounds which, owing to the smallness of the dissociation work, are chemically unknown and are revealed in the spectrum as molecules bound by polarization forces.

Fig. 5. Origin of fluctuations.

In the excited state these substances, like the noble gases, form true homopolar compounds with dissociation works such as we know in normal chemical substances. As an example I shall mention mercury vapor, about whose absorption spectrum a considerable number of works have appeared. Mercury vapor serves for chemists as the prototype

monatomic metallic vapor. And indeed, at low pressures it reveals in the absorption spectrum only atomic lines. But if the pressure is increased, broad absorption bands arise, which adjoin the atomic lines. Under certain conditions one can observe a banded structure in emission or absorption. Here one should mention chiefly the work of Lord Rayleigh. The whole behavior of mercury vapor indicates that in the ground state there is a loose molecular bond with a dissociation work of the order of 1 kg-calorie. In the excited state, however, a strong bond arises.

I cannot go into detail and shall confine myself to a qualitative description of the features of band absorption in the region of the absorption line 2537 Å. With increasing pressure, the region of absorption expands manifestly asymmetrically with respect to the position of the line: toward the shorter wavelengths a rather sharp boundary is obtained, which, with a further increase in pressure, changes no more, whereas toward the longer waves the region of absorption, with increasing pressure, can be traced ever farther, right up to the visible part. If we consider the potential curve of the two states of the molecule that interest us, it turns out that these features, as Winans has shown, can be fully discerned from the course of the potential.

Fig. 6. Absorption of the mercury line 2537 Å at various pressures.

In Fig. 7 these relations according to Winans are given for the completely analogous case of the cadmium line 2288 Å. The distances of the horizontal segments of the curves are proportional to \(h\nu\) of the atomic line. Large distances of the curves from one another, and consequently large energy differences, correspond to a slight broadening of the line in the direction

to short waves, we obtain it on passing from the flat minimum of loose bonding, i.e., from point \(c\), to the potential curve of the excited state. The increase in the separation of the potential curves corresponds approximately to the work of dissociation of the ground state. The inaccuracy lies in the fact that the upper curve, too, does not run strictly parallel to the abscissa axis but, owing to the appearance of polarization forces, slowly falls in the direction of small radii.

Thus one can approximately estimate the work of dissociation of the ground state from the short-wave boundary of the absorption region, if from the values \(h\nu\) corresponding to the short-wave boundary of the absorption region one subtracts \(h\nu_a\)—the value for an atomic line. The result obtained is of the order of several kg-calories, in agreement with the results of other optical methods. If we follow the curve further into the region of small values of the internuclear distance, then the perpendicular distance of the two curves from each other will become ever smaller; it falls especially rapidly at those values of the radii at which the sharp descent of the upper curve toward the minimum begins. Therefore we obtain a broadening in the direction toward long waves, which, with increasing pressure and especially with increasing temperature, is rapidly displaced, since the distance of the atoms in collision, owing to the increase with temperature, decreases relative to the energy. I have considered this example in somewhat greater detail, since it is typical not only for monatomic pairs of metals, but also for the noble gases.

Fig. 7. Asymmetric broadening of the Cd resonance line according to Winans.

An excellent example of this is provided by the recently described

MacLennan and Terbell’s work on the absorption features of light by gaseous, liquid, and solid xenon. With increasing pressure, the xenon resonance line at \(1469\ \text{Å}\) exhibits exactly the same properties as the resonance line of mercury. In the transition to the liquid state of mercury, the long-wavelength boundary shifts relative to the line by several hundred Å. When we pass to the solid state of xenon, then, as the temperature is lowered, the absorption region again becomes considerably narrower. The extension toward short waves is insignificant and tends, as the pressure increases, toward a definite limit. MacLennan gives no interpretation of this phenomenon; however, it is entirely analogous to the behavior of mercury and of other gases regarded as monatomic. It is especially remarkable that at low temperatures in the solid state the spectrum again becomes narrower. Evidently, at low temperatures the atoms (owing to the decrease in the amplitudes of vibration) approach one another less closely, despite the fact that the density increases. The order of magnitude of the work of dissociation of xenon in the ground state is, in turn, close to the van der Waals attraction. It is pointless to give more exact results, since one cannot assert that only diatomic molecules are formed in the ground state; it is possible that at high densities there also exist larger aggregates of molecules. Further examples of loose van der Waals compounds of noble gases were studied by Oldenberg.

I shall also briefly mention Kuhn’s proof of the existence of polarizational molecules in potassium. Here the spectra show that identical kinds of atoms, besides true homopolar molecules, form polarizational molecules. The relations present here are evident from the potential curves in Fig. 8. Alongside the attraction curves in the ground state for the homopolar bond according to the generally accepted Heitler–London theory, there is also a repulsion curve. As a result of polarization forces, the asymptote of the attraction curve is somewhat lowered. On the repulsion curve, however, at large distances between nuclei

a new minimum arises. Analogous features are exhibited by the excited states. In transitions between the potential curves, truly bound molecules give transitions whose position has nothing in common with the position of the atomic lines, i.e., they form a genuine band spectrum, whereas transitions between shallow minima on repulsion curves give narrow regions of bands which are observed as diffuse satellites of atomic lines.

Fig. 8. Potential curves \(K_2^*\) of exchange molecules and \(K_2\) of polarization molecules.

A fundamentally different possibility of finding the dissociation work from band spectra is opened by Angerer’s observations. In studying band absorption spectra he found that sometimes in a series of bands, beginning from a definite limit, there occurs a more or less sudden disappearance of the fine structure of the individual bands, which become blurred into continuous regions; moreover, on further transition to shorter waves the structure gradually appears again. The explanation that was given by a number of investigators, especially Bonhoeffer and de Kronig, can also be obtained by considering the potential curves.

Let us assume (Fig. 9) that between the curve of the normal state \(n\) and the potential curve \(a\) there are transitions, whereas transitions to the curves \(a'\) and \(a''\) are forbidden. In that case, at low temperatures we observe transitions to the upper curve, which lead to the region between \(A'\) and \(G'\). The bands leading to vibrational quanta between \(A\) and \(D\) have the normal appearance. The same bands that lead to levels above \(D\) exhibit the phenomenon of blurring, i.e., predissociation according to Angerer. This phenomenon arises because the molecule on the curve \(a\) vibrates, thereby reaching the point of intersection \(c'\) or above it. Beginning with \(D\)

possible transitions to the curve \(a'\) without radiation, and since the latter here already runs parallel to the abscissa axis, this means a transition to a dissociated state. According to quantum mechanics, in principle there is always a probability of transition of a system with a given energy to another system with equal energy. If one disregards certain selection principles, then a transition without radiation occurs with appreciable probability only when the distance between the nuclei and the velocity of the particles do not change substantially, and it is assumed that the transition takes place in a short interval of time. If the transition from the curve \(a\) to the curve \(a'\) occurs without radiation very rapidly, then the lifetime of the excited molecule will be so insignificant that molecular fluorescence will no longer be detectable. Further, the shortening of the lifetime leads to such strong damping that a strong broadening of the lines occurs. Since at the same time the sudden onset of diffuseness indicates a transition to a state of dissociation, from the onset of predissociation one can find the work of dissociation, provided that the state of the dissociation products corresponding to the asymptote of the curve \(a'\) is known. The situation is somewhat different when the curve \(a\) intersects a potential curve running in the manner of the curve \(a''\), which intersects \(a\) at the point \(c''\). Here it is evident that the dissociation products separate with a definite kinetic energy, since at the point of intersection the energy absorbed is somewhat greater than that corresponding to the height of the asymptote. Consequently, observations of predissociation often lead to excessively high values of the heat of dissociation. This was pointed out by Herzberg. Further, in this case the onset of band diffuseness is not sudden, but gradual, since according to quantum-mechanical laws the transition from the curve \(a\) to the curve \(a''\) can already pro—

Fig. 9. Explanation of predissociation.

go below the point of intersection. The latter consideration is due to Turner. Recently Turner considered a case in which the transition from curve \(a\) to curve \(a''\) is forbidden by the selection rules, but may be forced by the action of a magnetic field. It then turns out that, when the magnetic field is switched on, owing to the ensuing dissociation, molecular fluorescence also exists when the excited levels lie above the point \(c''\). The latter is observed in iodine vapor when excited by visible light. This gives an explanation of the quenching of iodine fluorescence by a magnetic field, long ago observed by Steubing.

To summarize, it may be said that from band spectra, by various methods, one can obtain, in part, exact values of the work of dissociation of molecules, and in part an estimate of its order of magnitude. The most important results are given in the following table, taken from G. Spone[r]’s survey. As is evident, by this method even substances have been investigated for which measurement of the work of dissociation by thermochemical methods is impossible.

In conclusion I shall dwell briefly on the fact that from the study of potential curves one can also find another thermochemically important molecular constant—the heat of activation of chemical reactions. London, on the basis of wave mechanics, showed that an atom or molecule capable of reaction, on approaching another closed molecule, must overcome a potential barrier in order to approach close enough for reaction to occur. Calculation of the heat of activation would in principle be possible if the potential curves of the colliding molecules in the collision state were exactly known. Since, however, we cannot compare the potential curve of an unperturbed molecule with the curve for a molecule in the collision state, even approximate results cannot be obtained from theory. Qualitative results, however, can be found from the data of the kinetic theory of gases in conjunction with spectroscopic data. The kinetic theory of gases gives the distance to which they can ap-

Table of spectroscopically found dissociation works

the molecules are to be brought close together, i.e. the boundary of the potential barrier, while spectroscopy gives the distance between the nuclei of the initial compounds and reaction products, calculated from band spectra. One may expect small heats of activation when the distance,

to which the nuclei can approach in collisions is less than, or at any rate only slightly greater than, the distance between the nuclei in the compounds formed. If, however, the distance at impact is substantially greater than the distance in the unexcited state of the reaction products, then the heat of activation will be small only when a large positive heat effect permits the formation of strongly vibrating molecules of the reaction products. I shall also mention that, in agreement with experiment, it follows that the reaction of halides with one another requires a small heat of activation, whereas in the case of the reaction of nitrogen with oxygen or hydrogen the heat of activation must be large.

This principle can also be applied to reactions between free atoms and molecules. In this way one obtains, in agreement with experiment, that chlorine atoms, in order to form hydrogen chloride with hydrogen molecules, must possess a greater heat of activation.

Likewise, proceeding from the point of view set forth, one can obtain an interpretation for cases of homogeneous catalysis. Indeed, homogeneous catalysis should be expected in those cases when an intermediate reaction opens a path for which a smaller heat of activation is required.

An example may be the reaction between chlorine atoms and hydrogen molecules, which is catalytically accelerated very strongly by minute amounts of water vapor. In the spirit of the views set forth, this can be interpreted as follows: a loose adsorption compound between Cl and H₂O collides with an H₂ molecule, with one of the H atoms of the water entering into combination with the chlorine and one of the H atoms of the hydrogen molecule taking its place in the water molecule. Consequently the reaction

\[ \mathrm{Cl}+\mathrm{H}_2=\mathrm{HCl}+\mathrm{H} \]

requires a greater heat of activation than the reaction

\[ \mathrm{ClHOH}+\mathrm{H}_2=\mathrm{ClH}+\mathrm{HOH}+\mathrm{H}. \]

The reason for this may be the following: in the water molecule

The H-atoms are considerably farther apart from one another than in a hydrogen molecule; upon collision the chlorine atom can approach the H-nucleus of water considerably more closely than the H-nucleus of the hydrogen molecule. Furthermore, the nuclear distances for the reaction \(H_2 + OH = H_2O + H\) prove to be favorable. Thus one can understand that the heat of activation of the reaction between Cl-atoms and hydrogen molecules must be reduced owing to the presence of water. Of course, this attempt at explanation cannot claim to be a flawless explanation of the reaction between chlorine and hydrogen.

Consideration of the course of the potential curves makes it possible to draw conclusions that are also of interest for the explanation of heterogeneous adsorption catalysis. If, following London, one may imagine that on the surface of the adsorbing substance there are free valences, owing to the proximity of which the strength of the catalyzed molecules is diminished, then thereby the height of the potential ridge—and consequently also the heat of activation—must be decreased. However, according to the theory proposed by Born and me, one can see the essential influence of adsorption in the fact that, in a certain sense, it increases the time of collisions of molecules with one another by an enormous factor in comparison with gas-kinetic collision times. As was already mentioned above, according to quantum mechanics, passage through a potential barrier is possible even when the vibrating particle has none of the energy required to overcome this potential ridge according to the laws of classical mechanics. These probabilities of transition for small times increase in proportion to the square of the time. It is so small that for the short time intervals of gas-kinetic impacts it may be neglected, and it becomes noticeable only when the same individual molecules remain unhindered near one another for sufficient intervals of time, as happens in adsorption. The absolute magnitude of the mean transition time in this case depends extraordinarily strongly on the height of the ridge and on the distance that is not-

must be overcome. To what extent these quantum-mechanical effects play a role in the cases of good adsorption catalysts cannot yet be judged. In principle, however, they must play a role.