MECHANISM OF ELEMENTARY PHOTOCHEMICAL PROCESSES

E. V. Shpolskii, Moscow.

I.

The first step of any photochemical process is the absorption of radiant energy: only those rays act which are absorbed. Therefore the analysis of the mechanism of photochemical action must begin with an analysis of the process of light absorption.

From the standpoint of classical physics, all the molecules of the illuminated body uniformly borrow energy from the radiation passing through it. Modern physics, on the contrary, shows with complete certainty that the act of absorption has a discontinuous, quantum character, and therefore not all, but only selected molecules receive an excess of energy. Since each molecule absorbs only one quantum of radiation, the number of these selected molecules must be equal to the number of absorbed quanta. And if each elementary act of absorption ends in a chemical reaction not complicated by any side processes, then the number of molecules that have reacted will also be equal to the number of absorbed quanta. This is the essence of the so-called “photochemical law of equivalence” of Einstein, which for the first time provided the key to interpreting the mechanism of photochemical reactions.

Experience shows, however, that if we compare the number of molecules that have actually reacted with the number of absorbed quanta, then the law of equivalence is justified in such a simple form only very rarely1. In fact, the ratio of these numbers (the quantum yield) is often expressed by a small number close to unity, for example 2; but cases are also not rare in which it is expressed either by a very small fraction or by an enormous number. In this result, at first sight quite discouraging, there is, however, nothing surprising. The law of equivalence is applicable only to elementary processes. The excess energy which a molecule receives in the elementary act of absorption is extremely large; un-

it is easy, for example, to calculate that the absorption of a quantum corresponding to the extreme violet rays, \(\lambda = 4000\ \text{Å}\), is equivalent to heating by approximately \(25\,000^\circ\). It is quite natural that the products obtained as a result of the primary process prove to be unstable to the highest degree and, at the same time, very active chemically. Therefore the primary reaction is almost always followed by secondary reactions caused by the products of the primary reaction. These secondary reactions are sometimes quickly interrupted, and then the yield has small values; in other cases an entire chain of reactions is obtained, as a result of which the yield assumes enormous values (up to \(10^6\) in the case of the reaction of the combination of chlorine with hydrogen). Some examples of such secondary reactions are given below; a detailed discussion of questions connected with the application of the law of equivalence is not part of the purpose of the present article \(^{1}\).

If, therefore, in application to the final products of a reaction the law of equivalence is often not justified, then for the elementary process it is always valid, for, as we have seen above, the law of equivalence is an inevitable consequence of the quantum mechanism of the absorption of light. But once the number of elementary processes has been fixed, a further question naturally arises: what is the nature of these processes? On this point, down to the very recent past, there were three different theories, each of which claimed universal applicability in all cases.

A. Even before the rise of quantum photochemistry, P. P. Lazarev \(^{2}\) put forward a hypothesis according to which the elementary photochemical process is always reduced to the ionization of the molecule. Lazarev, in doing so, quite naturally proceeded from classical conceptions and assumed that the bound electrons in molecules gradually accumulate energy, borrowing it from the radiation passing through. However, by no means in all molecules does this process end with the ejection of an electron. In order for this to occur, the molecule must be under especially favorable conditions, namely, the accumulation of energy sufficient for the ejection of an electron must be completed in the interval between collisions of the molecule with the surrounding ones. This naturally explains why the reaction proceeds with a finite velocity and does not occur instantaneously in all molecules of the substance. On the other hand, in some cases, when the bonds holding the electrons are such that light cannot directly cause ionization, the latter may occur as a result of collisions “excited—

\(^{1}\) Cf. the review by Olmando cited above, or the chapter “Photochemie” in vol. XXIII of Handbuch d. Physik, v. H. Geiger und K. Scheel. Cf. also V. Kondrat’ev, N. Semenov and Yu. Khariton, Electron Chemistry. GIZ, 1927.

\(^{2}\) Cf., for example: P. P. Lazarev, Fading of Dyes and Pigments in the Visible Spectrum (doctoral dissertation). Moscow, 1911.

prepared” molecule of the photosensitive body with a molecule of another substance participating in the reaction (for example, with an oxygen molecule in the fading of dyes). In these cases the lacking energy is supplied at the expense of the energy of thermal motions.

Despite the fact that for a number of photochemical reactions it was possible to detect the appearance of free charges1, in other cases this could not be done. Thus, J. J. Thomson, and subsequently Le Blanc and Vollmer2, showed quite convincingly that in the formation of HCl from a mixture of chlorine and hydrogen no preliminary ionization occurs.

W. Warburg3, in his work on the experimental verification of the law of equivalence, was guided by different conceptions. Let \(D\) denote the heat of dissociation, calculated per gram-molecule of the substance decomposing under the action of light, and let \(\nu\) be the frequency of the absorbed light; the reaction is possible in general on the condition that the magnitude of the corresponding quantum \(h\nu\) is greater than the work of dissociation, i.e.

\[ Ah\nu > D, \]

where \(A\) is Avogadro’s constant. If this condition is fulfilled, then the molecule that has absorbed a quantum of light, according to Warburg, immediately dissociates, for—it would seem quite natural—a molecule cannot retain, without disintegration, an energy exceeding the work of its destruction. Thus the mechanism of the decomposition reaction of hydrogen iodide should be represented not only formally, but also in essence, by the equation:

\[ \text{1. }\quad \mathrm{HJ} + h\nu = \mathrm{H} + \mathrm{J}, \]

and this primary process is followed by two secondary reactions:

\[ \text{2. }\quad \mathrm{H} + \mathrm{HJ} = \mathrm{H}_2 + \mathrm{J}, \]

\[ \text{3. }\quad \mathrm{J} + \mathrm{J} = \mathrm{J}_2. \]

Adding equations 1, 2, and 3, we have:

\[ 2\,\mathrm{HJ} + h\nu = \mathrm{H}_2 + \mathrm{J}_2, \]

whence it follows, in agreement with experiment, that for each absorbed quantum two molecules of \(\mathrm{HJ}\) decompose.

However, this theory too encountered a whole series of difficulties, and above all its basic premise, according to which a molecule cannot absorb, without disintegration, an energy greater than its work of dissociation,—

this premise has proved to be incorrect. Facts contradicting it are reported below.

C. On the basis of the theory of Bohr, Stern and Volmer1 drew attention to the fact that the immediate result of the absorption of light must be the excitation of the molecule, i.e. its transfer to some higher energy level. Such an excited molecule cannot dissociate by itself, even in the case when the excess energy acquired by it exceeds the work of dissociation. For chemical decomposition to occur, it is necessary that the excited molecule, in that short interval of time during which it remains in the excited state \((10^{-7}—10^{-8}\ \mathrm{sec},\) see p. 455), should have time to collide with another molecule.

That a molecule can indeed absorb, without decomposition, energy exceeding its work of dissociation is shown with complete certainty by numerous facts. Let us give several examples. When iodine vapor is illuminated by the green mercury line \(\lambda = 5460.7\ \text{\AA}\), this vapor fluoresces intensely. The fluorescence spectrum has a peculiar character, testifying, however, that its carrier is the molecule \(\mathrm{J}_2\).2 The heat of dissociation of iodine vapor is equal to \(1.5\ \mathrm{V}\); meanwhile, on absorption of the line \(\lambda = 5460.7\), the energy store of the molecule increases by approximately \(2.2\ \mathrm{V}\), i.e. by an amount \(1^{1}/_{2}\) times greater than the work of dissociation. Molecular fluorescence is also excited in an entirely different region of the spectrum, namely on illumination with the line \(\lambda = 1849\), although in this case the magnitude of the absorbed quantum exceeds the work of dissociation already by 5 times!

Another example may be the hydrogen molecule. The heat of dissociation of the hydrogen molecule, calculated by thermodynamic means, is equal to \(97\) b. cal.,3 which corresponds to \(4.2\ \mathrm{V}\). From this one may compute conversely (from the equation \(eV = h\nu\)) that a quantum of light corresponding to \(\lambda = 2800\ \text{\AA}\) ought to decompose the molecule \(\mathrm{H}_2\). But hydrogen not only does not dissociate under the action of this wavelength, it does not absorb it at all. In exactly the same way, electrons flying with a velocity of \(4.2\ \mathrm{V}\) rebound from \(\mathrm{H}_2\) molecules, undergoing an elastic impact. Absorption in pure hydrogen begins only at \(\lambda = 1115\ \text{\AA}\), and the absorption spectrum down to \(800\ \text{\AA}\) is a typical band spectrum, i.e. mole-

cular spectrum¹). The increase in energy upon absorption of the corresponding quanta already exceeds the work of dissociation by approximately a factor of 3. Likewise, the investigation of emission spectra under excitation by electron impacts shows²) that a molecule—at sufficiently low pressure—can, without being destroyed, absorb energies many times greater than its work of decomposition.

The use of excitation energy for a chemical process, as was said, is possible upon a subsequent collision of the excited molecule. Thus, the fluorescence of iodine vapor is strongly weakened when the pressure is increased, i.e., when the probability of collisions between molecules increases. Likewise, an increase in the pressure of hydrogen, or the admixture to it of some inert gas, entails the disappearance of the molecular “many-line” spectrum and the appearance of the Balmer atomic spectrum³).

From this point of view, all the results obtained earlier can also be easily explained. Thus, the mechanism of decomposition of hydrogen iodide will be represented by the perfectly clear equations:

\[ \mathrm{HJ} + h\nu = (\mathrm{HJ})^{*} \]

\[ (\mathrm{HJ})^{*} + \mathrm{HJ} = \mathrm{H}_{2} + \mathrm{J}_{2} \]

\[ 2\mathrm{HJ} + h\nu = \mathrm{H}_{2} + \mathrm{J}_{2}, \]

where the asterisk denotes an excited molecule.

For all its justification and plausibility from the physical point of view, the hypothesis of Stern and Volmer likewise proved to be in contradiction with certain facts. Thus, it is very difficult to explain, from the standpoint of this hypothesis, why the quantum yield in the dissociation of HJ remains constant, independently of the pressure of the gas and of admixtures of foreign gases.

From all that has been said it follows that none of the proposed theories is capable of explaining the entire totality of facts. Each of them excellently explains some group of phenomena, but at the same time is in contradiction with a number of others. It is perfectly clear that the question of the mechanism of the action of light on matter is most closely connected with the problem of the structure of the molecule. The study of the electronic and optical excitation of molecules and the substantial advances made in recent years through the investigation of molecular spectra have made it possible finally to unravel the contradictions that had arisen. However, before turning to a consideration of the most recent works, it is necessary briefly to recall the basic information from the theory of band spectra.

¹) G. Dieke und J. Hopfield, ZS. f. Phys., 40, 299, 1926.
²) V. v. Keussler, ZS. f. Phys., 15, 13, 1923.
³) V. Keussler, l. c.

II.

To avoid misunderstandings it should be stipulated that by band spectra in what follows we shall everywhere mean spectra belonging to molecules of a substance in the gaseous state. Externally these spectra are characterized by their extraordinary complexity, and also by the fact that in certain regions of the spectrum the lines crowd together, forming the so-called “bands,” often having on one side a sharp boundary, the so-called “edge,” and gradually blurring out on the other side. To give some idea of the extreme complexity of these spectra in comparison with atomic ones, it may be noted that a system of bands of a molecular spectrum, often comprising 1000 or more separate lines (for example, the cyanogen band system), corresponds to a single electronic transition, i.e. to only one spectral line of an atomic spectrum.

The reason for this complexity evidently lies in the fact that even the simplest molecule possesses a whole series of new degrees of freedom which the atom does not have. Indeed, the energy of a molecule may be divided into the following component parts: 1) the energy of rotation of the molecule \((E_m)\); 2) the energy of vibrations of the atoms in the molecule \((E_n')\); and 3) the energy of electronic jumps \((E_e)\). Thus:

\[ W = E_m + E_n' + E_e \]

All three terms of this sum are quantized, i.e. each of them may have not just any value, but a series of selected values determined by special quantum conditions \({}^{1})\). Absorption or emission of light by a molecule takes place only when it passes from one of these energy values to another; moreover, the frequency of the absorbed or emitted monochromatic light is determined by the well-known Bohr frequency rule:

\[ \nu = \frac{\Delta W}{h} = \frac{\Delta E_m}{h} + \frac{\Delta E_n'}{h} + \frac{\Delta E_e}{h} = \nu_m + \nu_n' + \nu_e \tag{1}. \]

Let us consider the simplest, completely symmetric diatomic molecule. Let the moment of inertia of such a molecule with respect to an axis perpendicular to the line connecting the centers of the nuclei be \(I\); the moment

\({}^{1})\) The fullest survey of the theoretical and experimental material relating to band spectra is given by the extensive (358 pp.) report of the committee on radiation in gases under the National Research Council, U. S. A.: Molecular Spectra in Gases. Washington, 1926. Among shorter surveys we shall mention: R. Mecke, Phys. ZS., 26, 217, 1926; R. Mecke und M. Guillery, Phys. ZS., 28, 479, 514, 1927; A. Sommerfeld, Atombau, 4th ed., p. 703 ff.; A. Kratzer, Ergebnisse d. exakt. Naturwiss., 1, 315, 1922; V. Kondrat'ev, U. F. N., 6, 1926.

inertia relative to this line is close to zero, the corresponding kinetic energy is also close to zero, and therefore we may disregard these rotations. We thus have:

\[ E_m=\frac{I\omega^2}{2}=\frac{(I\omega)^2}{2I}, \tag{2} \]

where \(\omega\) is the angular velocity of rotation. But \(I\omega\) is the angular momentum of the molecule. According to the rules of quantum theory it is precisely this quantity that must be quantized, and we may put, as usual,

\[ I\omega=m\frac{h}{2\pi}, \]

where \(m\) is an integer, the rotational quantum number. Taking this into account, from formula (2) we obtain

\[ E_m=\frac{h^2}{8\pi^2 I}m^2. \tag{3} \]

The optical term corresponding to this energy is obtained by dividing it by \(h\) \((E=h\nu)\), and will therefore be

\[ \frac{h}{8\pi^2 I}m^2=Bm^2,\quad \text{where } B=\frac{h}{8\pi^2 I}. \tag{4} \]

Let the absorption of light change only the rotational frequency of the molecule, i.e., let in formula (1) \(\Delta E_n=\Delta E'_e=0\). If in the initial (normal) state of the molecule the number of rotational quanta was \(m\), and in the excited state \(m'\), then the absorbed frequency, according to formulas (1) and (4), will be:

\[ \nu=B\,(m'^2-m^2). \]

The corresponding absorption spectrum is called rotational; it was discovered in 1913 by Rubens and Eva von Bahr in HCl, HBr, and others. Since the rotational quanta of the molecule are relatively very small (the frequencies of revolution of the molecule as a whole are very small compared with electronic frequencies), rotational spectra lie in the far infrared part of the spectrum—about \(100\)—\(130\,\mu\). It is easy to see that only polar molecules can have such spectra, for if the electric moment is absent, the electric field of the light quantum has nothing on which to exert an effect.

For a change of the quantum number \(m\) we initially indicated no restrictions. But the selection rules, following from the correspondence principle, require that \(m\) change only by \(\pm 1\)*):

\[ \Delta m=\pm 1. \]

*) In known cases a quantum transition corresponding to \(\Delta m=0\) is also possible. These cases, however, we shall not touch upon here.

In the case of purely rotational spectra one can speak only of such quantum jumps in which a change in \(m\) occurs corresponding to only one of the two signs. Thus, for example, in emission only a decrease in the number of quanta of rotation is possible, while in absorption only an increase of this number is possible.

Let us now suppose that the nuclei in our molecule execute vibrations relative to one another. If these vibrations are strictly harmonic, then our molecule will represent a linear oscillator—the very idealized object with which Planck operated in deriving the formula for the distribution of energy in the spectrum. The energy of such an oscillator, according to Planck, as is known, is equal to \(n h\omega_0\), where \(n\) is an integer and \(\omega_0\) is the frequency of the natural vibrations. Let the absorption of light change the number of vibrational quanta of the molecule from \(n\) to \(n'\). Then the change of energy will be

\[ \Delta W_n=(n'-n)h\omega_0, \]

and the frequency caused by this change will be

\[ (n'-n)\omega_0. \]

If the molecule, simultaneously with the vibrations of its nuclei, also rotates, then we shall have

\[ \nu=(n'-n)\omega_0+B(m'^2-m^2). \]

Here again, restrictions are imposed by the correspondence principle on the changes of the vibrational and rotational quantum numbers. Namely, if the molecule is a strictly harmonic vibrator, then it can change its energy only by one quantum of vibration:

\[ n'-n=\pm 1. \]

Furthermore, since \(\omega_0\) considerably exceeds \(B\), changes of both signs are admissible for \(m\) in the present case, i.e. \(m'-m=\pm 1\). Consequently:

\[ \nu=\omega_0+B(\pm 2m+1). \]

In accordance with the double sign at \(m\), we obtain in each band, corresponding to a definite state of vibration, two series of lines: one corresponds to transitions \(m\to m+1\), and the other to transitions \(m\to m-1\) 1.

If, however, the absorption of light leads to such a change in the bonds that the molecule ceases to be a harmonic vibrator and becomes an anharmonic vibrator, then the restriction imposed by the selection rules ceases to operate, and the molecule proves capable of absorbing any number of vibrational quanta. At the same time, the energy of such an anharmonic vibrator is expressed by a more complicated formula, into which the second and higher powers of the quantum number \(n\) enter. Namely, in the simplest case, when one may confine oneself only to the second power of \(n\), we shall have:

\[ E_n = nh\omega_0(1 - xn) = h(n\omega_0 - n^2 x\omega_0), \]

where the small quantity \(x\) characterizes the degree of departure of the vibrations from harmonicity. In spectroscopic works the formula written above is usually presented in a somewhat different form, corresponding to the so-called Deslandres formula (see p. 443):

\[ E_n = h(an - bn^2), \]

where, obviously, \(a = \omega_0\), and \(b = x\omega_0\).

The spectrum corresponding to the frequencies of the formula is called a rotational-vibrational spectrum. It still lies in the infrared region, though already in the near infrared, around \(10\)—\(15\,\mu\). This spectrum consists of a series of equally spaced lines with frequency difference

\[ \Delta \nu = 2B = \frac{h}{4\pi^2 I}. \]

Just like a purely rotational spectrum, it belongs to polar molecules, i.e. molecules possessing an electric moment.

Let, finally, an electronic transition be added to the change in rotational and vibrational energy. In such a case the spectrum is shifted from the infrared into the visible or even the ultraviolet region. Let us first consider the structure of an individual band, i.e. let us suppose that the electronic energy and the vibrational energy do not change, and that only the rotational energy changes. Since an electronic transition already causes a very profound change in the molecule, in particular a change in its configuration, the moment of inertia \(I\) in the initial and final states will, generally speaking, be different. Therefore the rotational frequencies can no longer be calculated by the simple formula \(B(m'^2 - m^2)\), but one must use a more general formula:

\[ \nu_m = B'm'^2 - Bm^2 = \frac{hm'^2}{8\pi^2 I'} - \frac{hm^2}{8\pi^2 I} = \frac{hm^2}{8\pi^2}\left(\frac{1}{I'} - \frac{1}{I}\right) + \frac{hm}{4\pi^2 I'} + \frac{h}{8\pi^2 I'}, \]

the vibrational quantum number \(n\) being replaced by \(n + \dfrac{1}{2}\). We use, however, the more customary formulas of the “classical” theory of molecular spectra, all the more since the physical meaning of the constants remains unchanged in either case.

where \(I\) is the moment of inertia in the initial state, and \(I'\) is the moment of inertia in the final state, and, as before, \(m'=m+1\). If we also add here the frequencies of vibrational and electronic origin, \(\nu_s+\nu_e\), then we obtain the general formula:

\[ \nu=A\pm 2Bm+Cm^2, \tag{5} \]

where

\[ A=\nu_e+\nu_s+\frac{h}{8\pi^2 I}, \]

\[ B=\frac{h}{8\pi^2 I'}, \]

\[ C=\frac{h}{8\pi^2}\left(\frac{1}{I'}-\frac{1}{I}\right). \]

Since \(m\) in formula (5) may take a series of integral values, each band splits up into a multitude of separate lines. These lines form two series, of which one corresponds to the upper sign before \(B\) (transition \(m\to m+1\)) and is usually called the positive branch; the other corresponds to the lower sign (transition \(m\to m-1\)) and is called the negative branch1.

Fig. 1.

The diagram in Fig. 1 clearly shows how the lines of the one and the other branch are distributed in the band. From this diagram it is quite clear how, as a result of this distribution, an accumulation of lines arises at the head, or edge, of the band. This accumulation is, consequently, due to a change in the moment of inertia of the molecule. Let us note that if the moment of inertia increases upon excitation, and the bonds are loosened, then the edges occur on the side of the short waves—the bands shade off toward the red side. Conversely, when the bonds are strengthened, the moment of inertia decreases, the bands

are quantized on the long-wave side and blur toward the violet side.

If we now imagine that the frequency of vibration of the nuclei in the molecule also changes, then instead of a single band we shall obtain an entire system of them, for each vibrational state will have its own band. The vibrational frequencies of the quanta of these bands (or, more precisely, of the so-called “zero lines”) obey the law of Deslandres

\[ \nu=\nu_e+(a'n'-b'n'^2)-(a''n''-b''n''^2), \]

where \(a, b\) are constants having a meaning already known to us, and \(n\) and \(n''\) are the quantum numbers of the initial and final vibrational states. The constants \(a\) and \(b\) are different in the initial and final states. This is because the change introduced by the electronic jump is so profound that, generally speaking, all the constants of the molecule—the moment of inertia, the natural vibrational frequency, the distance between the nuclei—change abruptly.

In order to give an idea of the numerical values of the constants, we give the formula representing the quanta of the ultraviolet absorption bands of oxygen:

\[ \nu=49359.3+(708\,n'-13n'^2)-(1565.37\,n''-11.37n''^2). \]

Fig. 2a. Violet bands of cyanogen.

Fig. 2b. Fine structure of an individual band in the negative group of nitrogen.

Here the quantum numbers \(n'\) refer to the excited state of the molecule, and the quantum numbers \(n''\) to the normal state. We see that the constant \(a\), equal to the vibrational frequency \(\omega\) at infinitely small amplitude, is reduced almost by half upon excitation. This indicates a very strong weakening of the bonds caused by the electronic jump.

In Fig. 2 there are shown, as an example, the system of violet bands of cyanogen and an individual band in the so-called negative group of nitrogen at very large dispersion.

III.

Let us now turn to the question of what the study of molecular spectra provides for recognizing the nature of elementary photochemical processes. From the preceding discussion we know that molecular spectra may be purely rotational, i.e. determined solely by the rotation of molecules; rotational-vibrational, when rotations are superposed on the vibrational motions of molecules; and, finally, spectra of electronic origin, in which we are dealing with electronic jumps complicated by vibrations of the nuclei and by rotation of the molecule as a whole. Purely rotational spectra, observed only in heteropolar molecules, are of little interest from the photochemical point of view. In principle, one can of course imagine that, with a sufficient increase in the rate of rotation, the molecule will be torn apart by the centrifugal forces thereby arising. In reality, however, purely rotational absorption spectra lie in the far infrared region; the corresponding periods of revolution are relatively very large, and the centrifugal forces developing during rotation are of an entirely different order of magnitude than the bonds holding the molecule together. Moreover, the change in rotational energy upon absorption of light, according to the correspondence principle, is always equal to only one quantum; and since the magnitude of this quantum, generally speaking, is very small (a few hundredths of a large calorie per gram-molecule), it cannot produce any substantial changes in the molecule.

The superposition of rotations on already existing electronic and vibrational frequencies can apparently rupture the molecule.¹ Spectroscopically this is manifested in the fact that the rotational lines, which determine the fine structure of a band, starting from a certain point, suddenly become weak in intensity, indistinct, and finally disappear altogether. In some cases (for example, in the hydrides of mercury, aluminum, and calcium) such a break in the rotational series occurs already at small values of the quantum number \(m\), whence it follows that these molecules become unstable even at relatively small rotational energies.

Approximately the same may be said of purely vibrational bands. It is quite obvious that, with a sufficient increase in the energy of vibration, the molecule must undergo decomposition; it is precisely in this way that thermal dissociation occurs. But a change in the energy of vibrations by means of the absorption of light is also restricted by selection rules, and so long as the molecule is still a harmonic vibrator it can change its energy only by one quantum. It follows from this that only in the case when the molecule is already vibrating strongly—

¹ H. Ludloff, ZS. f. Phys., 39, 523, 1926.

may take place, the new increase in the store of vibrational energy may lead to a change in the bonds, as a result of which the molecule will become an anharmonic vibrator and will prove capable of absorbing at once any number of vibrational quanta. Such a change in the bonds could also end in the dissociation of the molecules. However, at ordinary temperatures the store of vibrational energy within molecules is most often zero and in any case does not exceed one or two quanta, and accordingly the vibrational spectra do not indicate such a considerable weakening of the bonds1.

The most essential changes in the fate of a molecule are caused by those acts of absorption which are accompanied by electronic transitions. It is on these that we shall henceforth concentrate our attention.

Franck2 was the first to point out that the problem of the mechanism of elementary photochemical processes is most intimately intertwined with the question of the nature of chemical bonds. Following his example, and partly the historical development of the question, we shall consider separately homopolar and heteropolar molecules.

In homopolar molecules, which lack an electric moment, the presence of an electronic transition is in general a necessary prerequisite for the appearance of a band spectrum. The amounts of energy absorbed by molecules in such transitions are so great that they entail not only the displacement of the band spectrum from the infrared into the visible or even the ultraviolet region, but also a substantial change in the configuration of the molecule, as a result of which, as we have seen, an accumulation of lines arises at the head or edge of the band.

A natural question arises as to whether the transfer of this store of electronic energy and its conversion into the energy of the vibrating nuclei is possible. Lenz3 was the first to pose this problem and indicated a way to solve it, proceeding from the correspondence principle. The mechanism of this transfer of energy becomes, however, completely clear with the aid of the following purely mechanical picture indicated by Franck4.

Let the absorption of light cause an electronic transition. In that case the bonds in the molecule may change. We judge the character of this change by the appearance of the band spectrum: if the bonds are weakened—the distance between the nuclei and the moment of inertia increase—the bands are shaded on the side of the short waves and are washed out toward the red side; if the bonds grow stronger—the bands are washed out toward the violet side. Whatever, however, the sign and magnitude of this change may be, once it occurs, the average distance between the nuclei—

at equilibrium changes. Let a molecule absorb light in which the nuclei are at rest relative to one another. At the moment when excitation of the electronic system occurs, the nuclei, being far more massive than the electrons, still occupy their old equilibrium positions and, as a result, possess an excess of potential energy. In the next moment they rush toward the new equilibrium position and begin to oscillate about it, periodically converting their potential energy into kinetic energy and back again. It is quite natural that the quantitative measure of this transfer of electronic-excitation energy to the oscillating nuclei is determined by the magnitude of the change in the bonds. If the bonds undergo a strong change in the direction of their weakening, the increase in the potential energy of the nuclei, which then passes into the energy of their oscillations, may prove so considerable that the molecule breaks up in the primary act, i.e. without any subsequent collision.

Fig. 3 illustrates the process described. Here the distances between the nuclei are plotted along the axis of abscissae, and their potential energy along the axis of ordinates. The curve \(n\) refers to an unexcited molecule, in which no oscillations take place. The potential energy, as \(r\) decreases, at first decreases very slowly, then more rapidly, and, after passing through a minimum, increases more rapidly than it had previously decreased. This last circumstance is explained by the rapid increase of repulsive forces upon passage through a certain critical distance. The value \(r_0\), corresponding to the minimum of the potential energy, determines the distance between the nuclei at equilibrium. If an electronic jump has occurred in the molecule and if the bonds in it have thereby weakened, then the excited molecule will already correspond to the curve \(a\), whose minimum lies at \(r_1' > r_1\), and the work of dissociation \(D'\) will be less than \(D\). If, before absorption, no oscillations occur in the molecule, then upon excitation the nuclei will suddenly acquire an excess of potential energy \(U_1 - U_1'\), and, moreover, if this excess of potential energy proves greater than the work of dissociation of the molecule in the excited state, then obviously the bonds will be broken, the constituent parts of the molecule will separate with kinetic energy—the molecule will undergo dissociation in the primary act.

Let us now see how the processes described are reflected in the form of the molecular spectrum, and for this purpose we shall first of all dwell on the absorption spectrum of iodine vapor, which has been studied in very great detail.

Pringsheim1 found in this spectrum a whole series of band systems, and Mecke2 succeeded in distributing all the observed band edges among several series; in all the series the distance between the edges decreases as one passes to shorter waves. In Fig. 4 there is schematically represented the series that goes farthest toward the short-wave side (in order not to complicate the drawing, only the band edges are shown). As we see, the series extends from the red to the green part of the spectrum; at first the edges occur at equal distances, but then they all draw closer together and, finally, at about \(5000\) Å form a convergence limit, adjoining which is a continuous absorption spectrum. Franck3 was the first to give an ingenious interpretation of this peculiar spectrum. The bands in the iodine spectrum are shifted toward the red side. This means that, under electronic excitation, the bonds in the molecule are weakened. A quantitative measure of this weakening may be found on the basis of Mecke’s results, from which it follows that in the excited state the work of dissociation is half as great as in the normal state. Thus even an electronic jump in a molecule with nuclei at rest relative to one another leads to a strong “loosening” of the molecule. But it is well known that the strength of the bonds determines the mechanical frequency: the stronger the bonds, the faster the oscillations, and conversely, the looser the molecule, the slower the oscillations of the nuclei entering into it. If, as a rough approximation, we assume that the force binding the nuclei in the molecule is quasi-elastic, then the frequency of the harmonic oscillations arising under the action of this force is expressed by the familiar formula

\[ \omega_0=\frac{1}{2\pi}\sqrt{\frac{f}{\mu}}, \]

where \(f\) is the constant of the quasi-elastic force, and \(\mu\) is the “reduced” mass:

\[ \frac{1}{\mu}=\frac{1}{m_1}+\frac{1}{m_2}. \]

Let us consider the scheme of the energy levels of the molecule for the spectrum shown in Fig. 4. Here the level \(N\) (Fig. 5) represents the normal state of the unexcited molecule with nuclei at rest, \(A\) corresponds to the molecule that has undergone electronic excitation but is not oscillating; \(A_1\), \(A_2\), \(A_3,\ldots A_n\) depict the excited molecule with one, two, three, etc. quanta of oscillation. The distance between two neighboring levels—

Fig. 4.

…approximately corresponds to the mechanical frequency of the vibrations. Therefore, for an elastic harmonic vibrator the levels should be at equal distances. Meanwhile, in our case they gradually come closer together. This means that, as the vibrations of the nuclei increase, the frequencies continually decrease, and consequently the bonds become weaker and in the end reach zero: the energy levels approach one another until they merge.

Absorption series in the case of atomic spectra have an entirely analogous appearance: here too one sees a gradual convergence of the lines until they merge completely.

In the molecular spectrum of iodine vapor, as in atomic spectra, directly adjoining the place where the bands merge is a continuous absorption spectrum.

Fig. 5.

In the case of atomic spectra, the presence of a continuum is explained, as is known, by the process of disintegration, the ionization of the atom. Indeed, from Bohr’s frequency condition

\[ h\nu = W_1 - W_2 \]

it follows that a line absorption spectrum can arise only when the energies of the initial and final states \(W_1\) and \(W_2\) have selected, quantized values. But if one of these two quantities \(W_1\) or \(W_2\) is subject to no restrictions, then \(\nu\) will vary continuously. In the case of atomic spectra this will occur, for example, when an electron from some quantum orbit is ejected completely beyond the limits of the atom: under such a condition \(W_2\) will simply be kinetic energy, to which no quantum restrictions apply, and the absorption spectrum will be continuous. Quite analogously, according to Franck’s idea, the continuum adjoining the place where the bands crowd together indicates a process of dissociation of the molecule; for both the energy of the expelled electron and the kinetic energy with which the parts of the destroyed molecule fly apart may have a continuous series of arbitrary values.

This interpretation is very convincingly confirmed by the following experiment of Dymond1. Iodine vapor was successively illuminated with a series of wavelengths lying on either side of the place where the bands converge. So long as the wavelength of the exciting wave lay within the limits of discrete, band absorption \((\lambda > 4995\ \text{Å})\), iodine vapor intensely fluores—

fluoresced, emitting the molecular spectrum. Conversely, as soon as the exciting wave passed beyond the place of convergence of the quanta and entered the region of continuous absorption, all fluorescence disappeared. In the first case, as a result of absorption, excited iodine molecules were obtained, which, returning to the normal state, emitted light; in the second case the energy of excitation is expended on the rupture of molecular bonds, and no fluorescence was obtained.

If this interpretation is correct, then on the basis of the molecular spectrum one can calculate the heat of dissociation of the molecule. In fact, the frequency of the place of convergence of the quanta determines that boundary beyond which, upon absorption of light, the molecule breaks up into atoms flying apart with kinetic energy. If the band spectrum immediately gave us the energy levels of the unexcited molecule, then the heat of dissociation would simply be equal to the energy quantum \(h\nu_0\), corresponding to the frequency \(\nu_0\) of the place of convergence of the quanta. In reality, however, the absorption spectrum of a homoeopolar molecule gives the vibrational quanta of the molecule in the excited state. Therefore, in order to determine the heat of dissociation of the normal molecule, one must also know in what state the atoms separate upon dissociation. Thus, for example, the heat of dissociation of the iodine molecule, found by the thermal method, is equal to \(1.5\ \mathrm{V}\); the place of convergence of the quanta lies at \(4995\ \mathring{\mathrm A}\), which corresponds to a work of \(2.47\ \mathrm{V}\). A natural question arises: where does the excess energy of \(0.9\ \mathrm{V}\) go? Franck suggested that this excess is spent on the excitation of one of the atoms produced by dissociation. Discussion of the magnitude of the energy required for excitation of the various states of the iodine atom leads to the conclusion that in the present case one can speak only of the metastable state of the iodine atom (the spectroscopic symbol of the corresponding term is \({}^2P_1\))\(^{1}\). The normal state of iodine corresponds to the term \({}^2P_2\); therefore the difference \({}^2P_2 - {}^2P_1\) must be equal to approximately \(1\ \mathrm{V}\). Franck estimated it indirectly at \(0.9\ \mathrm{V}\), and Turner\(^{2}\) subsequently found this difference spectroscopically from observations of the arc spectrum of the haloids and showed that it is equal to \(0.937\ \mathrm{V}\). Thus, from this side as well, the explanation proposed by Franck received excellent support.

An analogous convergence of quanta in absorption spectra, and the continuum adjoining them, were subsequently found in a whole

\(^{1}\) J. Franck, l. c. This follows from the fact that the ground term of all haloids is a \(P\)-doublet, with the state \({}^2P_2\) being the stable state of the atom, and the state \({}^2P_1\) metastable. For the excitation of subsequent energy levels, much larger energies are required. Cf. Franck und Jordan. Handb. d. Phys. B. XXIII, p. 716.

\(^{2}\) H. Turner, Phys. Rev. 27, 397, 1926.

in a number of cases. Of this kind are the absorption spectra of chlorine and bromine ^1), oxygen (bands in the extreme ultraviolet region) ^2), hydrogen ^3), sulfur, selenium, and tellurium ^4). Moreover, in those cases where the place of convergence of the bands can be found directly, the band spectrum makes it possible to find the heat of dissociation of the molecule with spectroscopic accuracy. But even when the bands cannot be observed up to the point of their coalescence and the latter is determined by extrapolation, quite satisfactory figures for the work of dissociation are obtained in many cases ^5). Without dwelling here on this aspect of the question, which is of independent interest, we shall give, by way of example, only one table borrowed from Kuhn’s work ^6).

Table I.

Here, in column II, is given the full magnitude of the energy quantum corresponding to the place of convergence of the quanta; in III and IV—the work going to the excitation of one of the atoms formed (calculated indirectly by Franck and found directly by Turner); in V—the work of dissociation found from this; and in VI, for comparison, the same quantity found by thermal means. The agreement of the figures in the last two columns is highly satisfactory.

We may thus, from all that has been said, draw the conclusion that homeopolar molecules, when illuminated by light with a frequency exceeding the frequency of the place of convergence of the quanta, dissociate in the primary act, without a subsequent collision, into atoms, of which one is in the normal state and the other in an excited state.

^1) H. Kuhn, ZS. f. Phys., 39, 77, 1926.
^2) R. Birge and H. Sponer, Phys. Rev., 28, 260, 1926.
^3) Dieke and Hopfield, ZS. f. Phys., 40, 299, 1926.
^4) B. Rosen, ZS. f. Phys., 43, 69, 1927. It should be noted that in the case of the last three elements the bands approach one another, but even before their coalescence their line spectrum breaks off and is replaced by a continuous spectrum.
^5) R. Birge and H. Sponer, l. c.
^6) H. Kuhn, l. c.

Turning to the consideration of heteropolar molecules, we shall, following Franck, distinguish purely ionic molecules from atomic molecules possessing electrical polarity. Generally speaking, a molecule may be called ionic in the case when, upon continuous separation of its nuclei—for example, by gradually increasing the vibrations—the molecule adiabatically decomposes into two oppositely charged ions; and it may be called atomic when, under the same conditions, the molecule separates into two atoms1. In the latter case it is immaterial whether the molecule, owing to the asymmetry of the electron shell with respect to the nuclei, possesses an electric moment or not.

The possibility of optical dissociation of purely ionic molecules was discovered in an observation by Terenin2: attempting to produce optical excitation of sodium iodide vapor by illuminating it with ultraviolet rays of very short wavelength, Terenin found that, instead of molecular fluorescence, the sodium \(D\)-line is always emitted. Kondratyev3 and Terenin4 subsequently showed that this phenomenon is due to dissociation of the NaJ molecule in the primary act, i.e. as the result of absorption of light alone, and not through subsequent collisions of the excited molecule, as had originally been assumed. Theoretically, dissociation in the case of heteropolar molecules can be interpreted as follows: as a result of optical excitation, an electron jumps from the anion to the cation. It is quite evident that such a transition of the electron entails a sharp weakening of the bonds, and if this transition is, moreover, accompanied by a sufficient transfer of potential energy, the molecule decomposes. As Hund5 has shown, such a process does not contradict the principles of quantum mechanics. At the wavelengths with which Terenin and Kondratyev worked, the electronic transition takes place from the anion to excited states of the cation. But if such a transition is possible, then, evidently, in the limit a jump is also possible which transfers the electron from the anion to the normal state of the cation. In this case, with sufficient transfer of potential energy, the ionic molecule decomposes into two neutral unexcited atoms. Thus, in contrast to atomic molecules, in which decomposition always occurs into a normal and an excited atom, the first stage of dissociation of ionic molecules is decomposition into two neutral unexcited atoms.

All these considerations are confirmed by the study of the absorption spectra of alkali-halide compounds in the gaseous state. These spectra are, first of all, continuous, without any signs of line absorption1. It already follows from this that the electronic transition in such heteropolar molecules always ends in dissociation. Franck, Kuhn, and Rollefson2 showed, moreover, that the first stage of dissociation indeed leads to neutral, unexcited atoms. In fact, Table II shows that the boundary of the continuous spectrum on the long-wavelength side corresponds almost exactly to the heat of dissociation of the corresponding molecules into unexcited atoms.

TABLE II

A quantitative study of absorption led to the following results: the chlorides of the alkali metals have one maximum in the continuous absorption spectrum, the bromides—two, the iodides—also two and, in addition, apparently in the more distant ultraviolet part—one more. A detailed analysis shows that if the first maximum corresponds to decomposition into neutral unexcited atoms, then the second maximum corresponds to dissociation into a normal atom of the alkali metal and an excited (metastable state $^2P_1$) halogen atom: the distance between the maxima is, with a high degree of accuracy, equal to the work of excitation of one of the atoms. The third maximum, the transition to which is indicated in the spectrum of sodium iodide, according to all indications corresponds to decomposition into a normal iodine atom and an excited sodium atom. It is precisely in this third absorption region that the wavelengths used by Terenin in his experiments lie. There is reason to expect that, as one proceeds into ever

more distant ultraviolet regions of the absorption spectrum there will appear maxima corresponding to increasingly higher degrees of excitation of sodium and chlorine.

Here it is necessary to point out one further interesting consequence of optical dissociation. If the frequency of the exciting light somewhat exceeds that at which the molecules decompose,—for example, NaJ decomposes into a normal iodine atom and an excited sodium atom,—then the excess energy of the quantum corresponding to this frequency is obviously transformed into kinetic energy of the partners: the molecule not only dissociates, but the resulting atoms fly apart in different directions with considerable velocity. Thus, for example, in the case of sodium iodide one may calculate that the velocity with which the excited sodium atoms fly apart upon illumination of NaJ with light of \(\lambda = 2000\) Å is equal to \(2.9 \times 10^5\) cm/sec, whereas the mean velocity of thermal motion of the molecules at the temperature of the experiment (about \(650^\circ\)) is \(8 \times 10^4\). Such radiating atoms with supernormal velocity should exhibit a noticeable Doppler effect. And indeed, Hogness and Franck \(^{1}\) succeeded in showing the presence of a Doppler displacement in the optical dissociation of NaJ, accompanied by emission of the sodium \(D\)-line. Thus there was obtained a final, highly effective proof of the correctness of the ideas set forth.

Continuous absorption spectra have also been found for the molecules of silver iodide and silver bromide \(^{2}\). In this case, however, already the first stage of dissociation is decomposition into a normal silver atom and an excited iodine atom. Indeed, the work of dissociation of AgJ, found by the thermal method, is 47,000 cal; the excitation work of iodine (transition \(2^2P_2 — 2^2P_1\)) is 22,000 cal; the sum is 69,000 cal. Meanwhile, the energy corresponding to the beginning of continuous absorption is 76,000 cal. On the basis of this feature—decomposition into a normal and an excited atom—and of a whole series of other considerations, Franck considers it possible to assign AgJ, AgBr, and AgCl in the gaseous state not to ionic, but to atomic molecules possessing electrical polarity \(^{3}\).

The absorption spectrum of hydrogen iodide and hydrogen bromide in the gaseous state also proved to be continuous \(^{4}\). Considerations and calculations analogous to those just presented show that in this case as well dissociation proceeds into a normal hydrogen atom and an exci-

\(^{1}\) T. R. Hogness und J. Franck, ZS. f. Phys., 43, 26, 1927.

\(^{2}\) J. Franck und H. Kuhn, ZS. f. Phys., 43, 164, 1927; 44, 607, 1927.

\(^{3}\) Readers interested in the details of the argumentation are referred to the works cited on this and the preceding pages.

\(^{4}\) K. Bonhoeffer und W. Steiner, ZS. f. Phys. Chem., 122, 287, 1926; Tingey and Gerke. Journ. Am. Chem. Soc., 48, 1838, 1926.

an excited iodine atom. Franck and Kuhn1 draw from this the paradoxical conclusion that, in the gaseous state, hydrogen iodide also forms atomic, and not ionic, molecules2. A more detailed discussion of these highly interesting results would, however, take us too far from the subject that concerns us.

IV

Let us sum up and draw those concrete conclusions regarding the nature of elementary photochemical processes which follow from all that has been said. First of all, we must state that there does not exist a single mechanism of an elementary photochemical process. Not only do different substances use, in different ways, that excess of potential energy which they receive upon the absorption of light, but even one and the same molecule, under the action of waves of different length, may undergo different fates.

Band spectra testify to the fact that, as a result of the absorption of light, excited molecules most often arise.

We have seen above that even in the case where the magnitude of the absorbed quantum considerably exceeds the work of dissociation, the molecule, generally speaking, does not decompose in the primary act, but passes into an excited state. Thus, in accordance with the hypothesis of Stern and Volmer, the most frequently encountered elementary photochemical process is the excitation of the reacting molecule. The external sign of processes of this type is an absorption spectrum consisting of separate fine lines.

If a molecule has entered an excited state and the pressure is sufficiently low, then such a molecule most often returns to the normal state, giving up the excess energy in the form of fluorescence radiation. As the pressure increases, the probability of collision of the excited molecule with the surrounding molecules increases, and at the same time the fluorescence weakens: the well-known process of fluorescence quenching sets in3. The disturbance caused by impact leads to the molecule’s returning to the normal state without radiation, while it gives up the excess energy by an “impact of the second kind”4. The result of such an impact will be either an increase in the kinetic energy of the colliding

molecule, i.e. the conversion of optical energy into heat, or the excitation of the colliding molecule. The latter case is of particular interest to us in connection with the question of the mechanism of photochemical sensitization, to which we shall return below. Finally, there is also the possibility that a collision of the second kind will occur within the excited molecule itself. This means that, under the influence of a perturbation from the colliding molecule, the excitation energy, while remaining in the same molecule, will be redistributed among new degrees of freedom—in particular, it will pass into the energy of nuclear vibrations. If, in this process, the excess energy previously absorbed by the molecule exceeds the work of dissociation, then the molecule undergoes decomposition, i.e. a photochemical reaction takes place.

What fate befalls the excited molecule depends above all on the ratio between \(\tau\), the lifetime of the molecule in the excited state, and the interval between two collisions. The quantity \(\tau\) has repeatedly been measured by various methods and in all cases has proved to be of the order of \(10^{-7}\)—\(10^{-8}\) sec.¹) The time interval between two collisions is determined by the gas pressure. At normal pressure it is approximately \(10^{-9}\) sec, and the probability that the excited molecule will undergo a collision before it gives up its energy by radiation differs little from unity.²) In this case the probability of fluorescence appearing is practically equal to zero. The energy is utilized either for a photochemical reaction or is converted into heat.

Conversely, at low pressures the probability of a photochemical reaction is negligible; almost all the absorbed energy is given back in the form of fluorescence. This competition between the photochemical reaction and the emission of fluorescence is illustrated by a very interesting observation of Weigert:³) in the polymerization of anthracene into dianthracene, the yield depends on the concentration of anthracene. At low concentrations, intense fluorescence is observed, but the reaction is slow; conversely, at high concentrations the “yield” of the reaction increases, while the fluorescence becomes weak.

The photochemical law of equivalence requires that the number of molecules that have reacted be equal to the number of absorbed quanta of radiation. But even in the case when the reaction proceeds at high pressures or at high concentrations, i.e. when the probability of a subsequent collision of the excited molecule is almost equal to 1, by no means will every collision be effective in the sense of a photochemical reaction. Therefore, we must expect in advance that the quantum yield of the reaction will, generally speaking, be less than unity, as is in fact observed in practice.

¹) W. Wien, Ann. d. Phys., 60, 597, 1919; 66, 229, 1921; 76, 104, 1925; Göttling, Phys. Rev., 22, 566, 1923; E. Gaviola, ZS. f. Phys., 35, 748, 1926, etc.

²) V. Henri et R. Wurmser, Journ. d. Phys. 8, 289, 1927.

³) F. Weigert, Naturwiss. 15, 126, 1927.

in fact. Of course, we exclude here from consideration those cases in which the primary photochemical process is complicated by chains of side reactions; in these cases the quantum yield may also be an enormous number (the reaction of chlorine combining with hydrogen).

Only as one passes to ever shorter waves, i.e. to quanta of ever greater magnitude, should the “yield” approach the value indicated by the equivalence law. Indeed, the excess energy acquired by a molecule upon absorption of light need not necessarily be given up entirely in a collision. Therefore, the greater the magnitude of the absorbed quantum, the greater the probability that, despite a “useless” collision, the molecule will still retain a sufficient reserve of energy and undergo decomposition.

Fig. 6.

Fig. 7.

According to the equivalence law, the “yield” of the reaction, i.e. the number of molecules that have reacted per 1 cal of absorbed energy, decreases with decreasing wavelength. Thus the ideal curve of the dependence of the “yield” on the wavelength should have the form shown in Fig. 6 by curve 1: up to a certain wavelength \(\lambda=\lambda_0\), at which the quantum becomes equal to the work of dissociation, the reaction does not proceed at all; at \(\lambda=\lambda_0\) the reaction sets in and immediately gives the full yield, which decreases as the magnitude of the quantum further increases. The real dependence for the case under consideration, when the elementary process consists in excitation of the molecule, should be represented by curve 2, as follows directly from the preceding arguments. Thus, as the wavelength decreases, the yield relatively increases. This, apparently, is also the explanation of the generally known contradiction between ordinary observations and the requirements of the equivalence law: everyone knows that violet rays act more strongly than red ones, whereas curve 1 requires the opposite dependence.

Unfortunately, for not a single photochemical reaction has the corresponding curve been completely measured. But for fluorescence

there are interesting observations by Vavilov ¹), the results of which are presented in Fig. 7. Here the ideal curve is drawn as a dotted line (curve 1 of the preceding figure), while the solid curve represents the actually observed dependence. We see that the latter curve has exactly the same character as curve 2 in Fig. 6. Let us also note that in reality the phenomenon begins at somewhat longer wavelengths, i.e., at a somewhat smaller quantum energy, than could have been expected theoretically. This can be explained only by the fact that the missing energy is “made up” at the expense of thermal motion: the excited fluorescein molecule collides with an unexcited one and thereby receives the amount of energy which it lacks. A completely analogous process is sometimes observed also in photochemical reactions: such, for example, is the case of the decomposition of NH₃ under the action of \(\lambda = 207\,\mu\mu\) ²) or the decomposition of ozone under the action of \(\lambda = 253\,\mu\mu\) ³). In both cases the magnitude of the quantum is smaller than the work of dissociation of the molecule into atoms, and the missing energy is borrowed from the kinetic energy of thermal motions.

It is possible, however, that there is also such a case when a light quantum corresponding to a certain wavelength exceeds the work of dissociation of the molecule, but is not absorbed by this molecule. Such a case, as we saw at the beginning of the article, occurs in hydrogen. Thus, for example, a quantum of light corresponding to \(\lambda = 2537\,\overset{\circ}{A}\) is quite sufficient for the splitting of the hydrogen molecule, but in pure hydrogen decomposition does not occur because light of this wavelength is not absorbed by hydrogen. If, however, mercury vapor is admixed with hydrogen, which strongly absorbs \(\lambda = 2537\,\overset{\circ}{A}\), then dissociation occurs ⁴): the excited mercury atoms transfer their energy to the hydrogen molecules by collisions of the second kind. Thus, in the last two cases considered by us, we have in “sensitized” reactions a transitional stage from purely photochemical to purely thermal reactions ⁵). It follows

¹) S. I. Wawilow, ZS. f. Phys., 42, 311, 1927.
²) E. Warburg, Ber. d. Berl. Akad., 1911, S. 746.
³) E. Warburg, Ber. d. Berl. Akad., 1914, S. 881.
⁴) J. Franck und G. Cario, ZS. f. Phys., 11, 16, 1922; 17, 202, 1923. Cf. also J. Franck, U. F. N., 4, 62, 1924.
⁵) It should be borne in mind that photochemical sensitization is by no means in all cases explained by such a simple mechanism. Cases are not rare when the sensitization process consists of two or several stages, of which the first is the photochemical reaction of the sensitizer, and the subsequent ones are dark catalysis by the products of this reaction. Such, for example, is the mechanism of the decomposition of ozone sensitized by chlorine or bromine (K. Bonhoeffer, ZS. f. Phys. 13, 94, 1926), or the mechanism of sensitization of the actinometric liquid of Eder (cf. T. K. Molodyi and E. V. Shpolskii, Zhurn. Prikl. Fiz. 3, 57, 1926). In the case of gas reactions the condi-

It should be noted that the possibility of the existence of such reactions was first pointed out already in 1908 by Stark1, who proposed for them the name “thermophotochemical” reactions.

The limiting case of excitation is the ionization of the molecule. As we have seen, in a whole series of reactions we have grounds to expect that the elementary photochemical act consists in the formation of ions. As a rule, apparently, primary ionization is observed in all those cases in which the magnitude of the absorbed quantum considerably exceeds the work of dissociation and the ionization potential for the outer electrons—for example, in the case of the action of X-rays or γ-rays.

The next possibility for the mechanism of an elementary photochemical process is the dissociation of the molecule in the primary act, i.e. without a subsequent collision. Examples of such dissociation have been given and discussed in sufficient detail above. We shall therefore confine ourselves to only a few remarks. The condition for the possibility of dissociation in the primary act is a continuous absorption spectrum. Whether this spectrum is preceded by a discontinuous band spectrum ending in the coalescence of quanta, or whether only a continuous spectrum is obtained, or, finally, whether, quite the reverse, neither coalescence of quanta nor a continuous spectrum is observed at all—this is, of course, entirely determined by the structural peculiarities of the molecule. It is precisely on these peculiarities that it depends what part of the energy of electronic excitation will be transferred to the vibrating nuclei. The greater such transfer, the longer the system of bands, the greater the probability of a sufficient weakening of the bonds and of subsequent dissociation. Conversely, when the transfer of energy to the nuclei is small, a very short system of bands is obtained, the bonds in the molecule are almost unchanged, and dissociation does not occur. Molecules of the latter type may be exemplified by SiN molecules or cyanogen molecules (violet bands)2. Molecules of the first type may be exemplified by the halogen molecules: chlorine, bromine, and iodine. The amount of electronic-excitation energy transferred to the nuclei increases in the order: iodine, bromine, chlorine. In accordance with this, the maximum absorption for iodine lies in the continuous part of the spectrum, not far from the point of convergence of the quanta (at a distance of approximately 400 Å); for bromine it is considerably farther away (distance 900 Å), and, finally, for chlorine the absorption at the point of convergence of the quanta is negligible, while it reaches a maximum in the continuous part at a distance of 1440 Å from its beginning3. This means that, owing to the peculiarities

of the structure of the chlorine molecule, upon its excitation so considerable an energy is transferred to the vibrating nuclei that the molecule most probably decomposes into atoms flying apart with a large kinetic energy. It is evidently precisely this that explains the fact that, whereas the intense fluorescence of molecular iodine is well known and easily produced, in bromine Wood \(^{1}\), despite the use of the strongest light sources, was able to detect only traces of fluorescence, while chlorine gave no fluorescence at all. Undoubtedly all these facts must be taken into account in investigating the mechanism of the photochemical reactions of the halogens.

As regards the applicability of the law of equivalence in the case of primary dissociation, from the fact that every elementary act of absorption here immediately ends in a photochemical reaction it follows that the law of equivalence in this case must be strictly fulfilled. The facts confirm this very well, of course with the exception of those cases in which the process is complicated by side reactions \(^{2}\). Equally, the following remarkable fact becomes entirely intelligible: the quantum yield for the decomposition reaction of HI is always equal to 2, quite independently of the pressure. In the interval from very low pressures, when collisions between molecules are rare \(^{3}\), up to pressures of several hundred atmospheres—and even in liquid hydrogen iodide \(^{4}\)—for each absorbed quantum there always decompose two molecules of the substance. This fact, evidently, can be explained only by the fact that, whatever the pressure, the immediate result of the absorption of light is the optical decomposition of the HI molecule. And indeed, the absorption spectrum of hydrogen iodide, as we have already seen, is completely continuous, which fully confirms our conclusion.

We have thus considered two types of elementary photochemical processes: excitation and dissociation in the primary act. V. A. Henri \(^{5}\) points to the possibility of yet another, intermediate, mechanism: the transfer of the molecule from the normal state into a special unstable state, which Henri calls the state of “predissociation” (predissociation). The study of the absorption spectra of a large number of substances led Henri to the conclusion that in the ultraviolet region, as one passes to ever shorter waves, the appearance of the spectrum changes in a regular manner: instead of the usual bands, which split into an enormous num—

\(^{1}\) R. W. Wood, Phil. Mag., 33, 252, 1918.
\(^{2}\) Cf., for example, the review by R. Gerke. J. Am. Chem. Soc., Nov. 1927.
\(^{3}\) B. Lewis, Nature, April 2, 1927, p. 493.
\(^{4}\) Bodenstein und Lieneweg, ZS. f. Phys. Chym., 1926.
\(^{5}\) V. Henri et R. Wurmser, Journ. d. Phys., 8, 289, 1927.

a number of fine lines, beginning with a certain frequency, there appears a system of regularly distributed narrow bands (2–5 Å), which prove to be completely continuous. At still shorter wavelengths some substances give yet another system of broader (10–15 Å) bands, passing over into whole regions of continuous spectrum up to 100 Å wide. Such, for example, is the absorption spectrum of acrolein vapor

$$ \mathrm{CH_2{=}CH{-}C{-}H} \quad \begin{array}{c} \|\\ \mathrm{O} \end{array} $$

in the interval from 4130 Å to 3375 Å only ordinary bands, consisting of fine lines, are encountered; from 3375 Å to 2780 Å there is a system of equally spaced narrow continuous bands, gradually passing over into a continuous spectrum; finally, from approximately 2500 to 2000 Å there extends an extensive region of continuous absorption. The absorption spectra of phosgene, thiophosgene, benzene derivatives, and certain other substances have a similar character.

V. A. Henri attributes the disappearance of the fine structure of bands and the appearance, first, of narrow and then broad regions of continuous spectrum to the fact that, at a certain magnitude of the absorbed light quantum, the molecule passes into an unstable state, which he calls the state of “predissociation.”1 In this state the increase in the reserve of vibrational energy occurs in a quantum, discontinuous manner, and as a consequence a system of uniformly distributed bands is obtained. But in each of these vibrational states the molecule is so loose and labile that the further superposition of rotational energy already occurs in a continuous manner. The magnitude of the vibrational quanta (the distance between the bands), and consequently the corresponding frequency of nuclear vibrations, in the state of “predissociation” decreases in comparison with the normal state, which is the external indication of a loosening of the bonds. On the other hand, the dimensions of the molecules and, in particular, their chemical activity increase considerably. Thus, acetaldehyde has narrow continuous absorption bands beginning at \(\lambda = 28000\) Å, while at \(\lambda = 2350\) Å a broad absorption band begins. In accordance with this, rays of the first wavelength do not decompose the molecule, but considerably increase its chemical activity: the molecule becomes readily oxidizable; on the contrary, beginning with \(\lambda = 23000\) Å, the molecules of acetaldehyde decompose into molecules of methane and carbon monoxide. Here, in V. A. Henri’s opinion, a quite evident gradualness is observed in the destruction of the molecule: it

first passes into the “predissociation” state and only at a larger quantum value dissociates1.

The existence of transitional, unstable states has not, however, received definitive confirmation up to the present time. Henri’s investigations relate, in most cases, to complex organic substances, the theoretical interpretation of whose spectra is still far from complete. Nevertheless, the very fact of the existence of such spectra is of enormous interest from the photochemical point of view.

Thus we see that, although none of the three theories set forth in the first chapter can claim universal validity, all the processes that they indicate as elementary do in fact occur in various cases. Further advances in the interpretation of the mechanism of photochemical reactions are to be expected both from purely photochemical work and from the study of molecular structure—a line of investigation that in recent years has been developing with enormous rapidity.

1. “Structure des Molécules,” p. 100. ↩↩↩↩↩↩↩↩↩↩↩↩↩↩

2. H. Sponer, Ergebn. d. exakt. Naturwiss., 6, 81, 1927. ↩↩↩↩↩↩↩↩

3. H. Kuhn, Zs. f. Phys., 39, 77, 1926. ↩↩↩↩↩↩↩

4. Cf. J. Franck, Z. Phys. Chem., 1, 62, 1924; D. Coster, Z. Phys. Chem., 3, 1925. ↩↩↩

5. H. Hund, ZS. f. Phys., 40, 742, 1927. ↩