TRANSFER AND MIGRATION OF ENERGY IN BIOCHEMICAL PROCESSES. I

A. N. Terenin

1. INTRODUCTION

Over the last decade a number of interesting facts have accumulated, explained as a peculiar “action at a distance” of molecules in a biological medium. In particular, the possibility has been discovered of transferring portions of energy, substantial on the molecular scale, over considerable intermolecular distances, as well as the possibility of a local accumulation of energy as the result of the joint action of several molecular centers spatially remote from one another and excited by some source. Attempts to interpret the observed facts were first undertaken by the biochemists themselves, who discovered them, and then these phenomena came into the field of view of physicists, who found ready explanations for them. In doing so, both groups proceeded at first from a superficial similarity between the phenomena under consideration and physical processes in inorganic crystals; more recently an analogy has been drawn between the migration of energy in living objects and the intermolecular transfer of energy in concentrated solutions of organic dyes. The fundamental regularities of the latter phenomenon were elucidated in detail by S. I. Vavilov, who, together with his coworkers, carried out a series of exhaustive experimental investigations described below.

The attention that in recent years has been devoted to the question of energy migration in biological systems is evident from the large list, given below, of articles in biological, chemical, and physical journals. The present article is devoted to a critical review of the interpretations proposed*). The author has confined himself only to the biochemical side of the question, without touching upon the incomparably more complex physiological interrelations, in which he is not competent. Experience shows that already in the simplest biochemical

) The article published here constitutes the first part of such a review. See also A. N. Terenin and A. A. Krasnovskii, UFN 37*, issue 1, 65 (1949).

processes, qualitatively new relationships are revealed, not reducible to simpler physical and chemical regularities. Only certain, limited aspects of the phenomenon of energy transfer in biological systems are reproduced in physical and chemical experiments and are amenable to interpretation from this point of view. Of course, with such an approach one can speak only of objects closest to biochemical ones, i.e., of molecules of organic compounds, and not of phenomena in inorganic crystals. The latter topic is of great independent interest, but has no direct relation to the problem touched upon here.

By migration, or “wandering,” of energy are meant those phenomena in which a quantum of electronic excitation energy, imparted to one center of an extended system, for example as a result of absorption of a photon, is transferred—“travels”—without being expended to a second center, separated from the first by a considerable intermolecular distance. Having reached the second center, the quantum produces its entire effect—it is emitted as light or causes some physical or chemical reaction.

Another no less important feature of “long-range action” of this kind consists in the peculiar directionality, observed in some cases, of the displacement of the quantum, manifested externally in the fact that it seems to strive precisely toward those centers where it can be expended or used. These centers exert on the migrating quantum an attraction that is at first glance incomprehensible.

The mode of energy displacement described here differs from energy transfer by emission of a quantum in the form of radiation by one molecule and absorption of this quantum by another, far removed from the first. Nor can it be reduced to an exchange of energy between two particles occurring at the moment of collision when they approach one another by diffusion. The possibility of the first or second explanation is refuted each time by experiment. Thus, we are indeed dealing here with a distinctive phenomenon deserving a special name.

Here we should be especially interested in phenomena of energy transfer occurring in condensed phases, which are closest to the conditions of the biological medium.

2. CONCENTRATION EFFECTS IN DYE SOLUTIONS

In solutions of fluorescent organic dyes, when the concentration is raised above certain limits, two characteristic phenomena are observed: first, depolarization of the fluorescence light, and second, a decrease in the yield of emission—quenching of fluorescence. Both phenomena, as S. I. Vavilov showed, are closely connected with one another1; we shall consider them in more detail.

When viscous dye solutions are excited by linearly polarized light, the emitted fluorescence light is also linearly—

but polarized; moreover, in dilute solutions (concentrations less than \(10^{-4}\) mole/liter) the degree of polarization reaches \(40\%\) (not much below the limiting theoretical value of \(50\%\)). The polarization of light is explained by the fact that the electronic oscillator determining the absorption and emission of light by the molecule is anisotropic, and, in particular, the oscillation of the electronic charge in the molecule occurs along an axis rigidly connected with its skeleton.*)

Linearly polarized incident light excites predominantly those molecules whose oscillator axes approximately coincide with its direction of vibration (Fig. 1). In a viscous and still more in a glassy solvent, the possibility that the axis of the molecule will rotate during the short lifetime \(\tau\) of the excited state, of the order of \(10^{-8}\) sec, is excluded; this accounts for the high degree of polarization of the emitted light noted above.

Fig. 1. Schematic depiction of depolarization of fluorescence light as a result of energy transfer between molecules that have approached one another to distances smaller than the wavelength of light.

However, with increasing dye concentration, beginning at \(10^{-4}\) mole/liter, a decrease in the degree of polarization is observed, which at \(10^{-2}\) mole/liter for fluorescein in glycerin reaches a value amounting to 0.2 of the initial value, taken as unity (Fig. 2). In addition, as shown in the figure, the yield**) of emission decreases—self-quenching of fluorescence by the dye molecules. Rhodamines, trypaflavin, acridine orange, and others behave analogously to fluorescein\(^5\). At the concentration corresponding to the onset of depolarization (\(10^{-4}\) mole/liter), the average distance between dissolved dye molecules is 10 times greater than their linear dimension, approximately equal to \(5\,\text{\AA}\).

The phenomenon of depolarization described thus testifies to the increased sensitivity of an excited molecule

*) P. P. Feofilov brought great clarity to the question of the mutual connection between the oscillators of absorption and emission and their orientation in various fluorescing molecules\(^2\).

**) By yield is meant here the magnitude of the ratio of emitted energy to absorbed energy. If on the same graph one plots the molar absorption coefficient of the dye, then for the objects considered here it does not change with increasing concentration. In other words, the absorbed energy, referred to one and the same number of molecules, remains constant over the entire concentration interval.

of the dye molecule to the vicinity of a second unexcited molecule, beginning from a certain “critical” distance*). As calculation shows, in a solution of dyes there is no experimentally noticeable diffusion of fluorescence radiation from molecule to molecule by successive acts of optical excitation and emission. Consequently, this is not the cause of depolarization. The conclusion suggests itself that the excitation energy as such diffuses by being transferred directly from one molecule to another. Indeed, depolarization has received an exhaustive explanation based on the concept of resonance transfer**) of the quantum of excitation energy from the dye molecule that absorbed the light to another neighboring molecule; moreover, during the time \(\tau \simeq 10^{-8}\) sec before emission, the energy quantum manages to change carriers several times\(^{1,6}\). The difference in orientation of the final emitting molecule and its associated electronic oscillator from the orientation of the molecule that initially absorbed the light explains the decrease in the degree of polarization (Fig. 1).

Fig. 2. Decrease in the degree of polarization and in fluorescence yield with increasing concentration \(c\) of fluorescein in glycerin\(^{5}\).

In agreement with this interpretation is the interesting fact of the gradual depolarization of the emission as it decays in time, which was established on uranium glasses by the phosphoroscopic method, and for viscous solutions of dyes by means of a delicate fluorometric method that made it possible to follow the decrease in fluorescence intensity during \(10^{-8}\) sec.\(^{4}\) Indeed, as the decay proceeds, the “path” of the excitation quantum increases, and its emission occurs, as a rule, in a molecule oriented differently.

*) The sensitivity of dye molecules to perturbation by molecules of the same kind lies considerably lower than for atoms in vacuum. Thus, it was shown that an excited Na atom emitting polarized resonance radiation undergoes the depolarizing influence of another atom located at a distance of \(10^{4}\) atomic radii, i.e., at a vapor pressure of \(10^{-6}\) mm Hg.\(^{3}\) Meanwhile, the onset of concentration depolarization in dye molecules in solution occurs at a concentration equivalent to a dye-vapor pressure in vacuum on the order of 100 mm Hg.

**) The term “resonance” in this article has the generally accepted physical meaning of coincidence of light frequencies and energy levels and has no relation to the “theory of resonance” in chemistry.

In a theoretical treatment of the phenomenon, S. I. Vavilov did not introduce concrete model representations of the nature of the interaction between molecules, confining himself to general statistical premises concerning the probability of energy transfer, dependent on the time elapsed from the beginning of excitation. From these very general assumptions S. I. Vavilov obtained the following expression for the probability of energy transfer as a function of the concentration of molecules \(c\) and the time \(t\):

\[ q(c,t)=e^{-\lambda_0 c}\cdot e^{-\frac{ct}{K_2}}, \tag{1} \]

where \(\lambda_0\) and \(K_2\) are two constants depending on the properties of the molecules and of the medium; moreover, in most cases \(\lambda_0=0\).

S. I. Vavilov’s phenomenological theory embraces, from a single point of view, all the optical effects observed when the concentration is increased, and correctly reproduces all the established regularities.

The quenching phenomenon, observed along with depolarization, shows that the transfer of excitation energy is accompanied by a very effective dissipation of it into heat, increasing as the molecules approach one another. As S. I. Vavilov and his collaborators showed, the decrease in fluorescence yield is accompanied by a parallel shortening of the lifetime \(\tau\) of the excited state of the molecule. This is proved both by direct fluorometric measurements of the decay time and by indirect data based on determining the additional quenching action of extraneous, deliberately strongly quenching substances, such as, for example, iodide anions\(^6\).

The presence of concentration quenching strongly limits the “run” of the quantum, i.e., the distance over which it can move without loss. Thus, experiment shows\(^5\) that at a concentration of \(10^{-2}\) mole/liter, when the mean distance between dye molecules is about \(16\) Å, \(50\%\) of the excited molecules are unable to emit light (see Fig. 2). Calculation shows\(^ {15}\) that during the shortened excitation time the energy manages to change carriers 20 times; without quenching the latter number would have been 5 times greater. At a concentration of \(10^{-1}\) mole/liter, in the absence of quenching, energy transfer should have occurred 1000 times, whereas in fact at this concentration the fluorescence is almost completely quenched. In other words, the energy quantum has time to be dissipated as heat during the lifetime \(\tau\) of the excited state. Obviously, at such intermolecular distances the mutual perturbations of dye molecules lead not to transfer, but to degradation of the electronic excitation energy into kinetic degrees of freedom of the molecules.

The reason for such increased dissipation of excitation energy when molecules approach one another should be sought in the close interconnection

changes of the electronic state of the molecule with internal vibrational degrees of freedom. This interrelation, as is known, is already manifested in the external appearance of the absorption and emission spectra of dye molecules, which are diffuse, structureless, broad spectral bands with a uniform contour*).

The transfer of an excitation-energy quantum from one molecule to another would be very easy if this quantum, corresponding to the maximum of the fluorescence band, coincided with the maximum of the absorption band of the receiving molecule. Meanwhile these maxima are shifted relative to one another**) and the maximum of fluorescence falls in a spectral region of weak absorption and, consequently, of improbable excitation of the receiving molecule. It follows that energy transfer will be facilitated for those dyes in which the absorption and emission maxima are situated as close as possible and their maximum overlap occurs.

This conclusion is confirmed by the experiments of S. I. Vavilov and F. M. Pekerman on concentration effects in glycerol solutions of a number of dyes with different degrees of overlap of the absorption and emission spectra\(^{6}\).

From the presence of the parallel effect of strong self-quenching of emission and shortening of \(\tau\), it follows that the transfer of excitation energy, detected by the depolarization of light upon further convergence of the molecules, is accompanied by its degradation into heat. Evidently, the transfer of electronic excitation energy simultaneously affects also the vibrational state of the interacting molecules, a change of which, as is known, serves as a prerequisite for the conversion of electronic energy into heat\(^{7}\).

Some authors have proposed another explanation of concentration self-quenching\(^{8,15}\). It is assumed that with increasing concentration the number of associated paired dye molecules (dimers) increases; these, as is known, are incapable of fluorescing, since they effectively dissipate the excitation energy into heat. The presence of these dimers, also capable of absorbing an excitation quantum because of the proximity of their absorption spectrum to the spectrum of the monomer, is taken to be the cause of the strong quenching of fluorescence as the concentration is increased. However, this explanation is untenable because not all fluorescing dyes possess the property of giving such

*) On the question of the influence of the vibrational state on the form of the spectrum of complex molecules, see B. S. Neporent’s article in the issue of ZhETF devoted to S. I. Vavilov.

**) The maximum of the fluorescence band is shifted to the long-wavelength side relative to the maximum of the absorption spectrum (Stokes shift)\(^{7}\).

reversibly arising and decomposing double molecules. The formation of such dimers has been established for methylene blue and rhodamine, but they are absent in fluorescein, eosin, and other typical fluorescent dyes, which nevertheless exhibit concentration quenching. Moreover, the absorption maximum of the dimers is shifted toward higher frequencies relative to the absorption spectrum of single molecules, which, as stated above, makes energy transfer still more difficult and, possibly, reduces the latter practically to zero.

If the structural features of the molecules in the resonant transfer of electronic energy considered here are not of essential importance, then one should expect the most striking manifestation of the energy-transfer process when the magnitude of the emitted excitation quantum coincides with the maximum of the absorption spectrum of the acceptor, which must necessarily be of a different kind than the primarily excited molecule. In molecules of the same kind, the absorption and emission maxima, as was said above, do not coincide. Experiments recently carried out by Vavilov and Galanin ^9 did in fact establish that, if nonfluorescent molecules are added in increasing concentration to a fluorescent solution, then quenching of fluorescence is absent if the absorption-spectrum band of the added molecules does not overlap the emission-spectrum band of the fluorescent molecules, but the quenching increases sharply when the indicated two bands overlap. The experiments were carried out with the following objects (the fluorescent molecule is denoted by an asterisk): rhodamine—fuchsin, quinine—auramine, benzoflavin—chrysoidine, fluorescein—phenolphthalein (anion), rhodamine*—auramine. It was shown that, simultaneously and in parallel with quenching, the lifetime of the excited state \(\tau\) of the first molecules decreases, as measured directly by a fluorometer.

The necessity of strong perturbation of fluorescent molecules by other molecules that are in energetic resonance with them, and the possibility of exchange of energy between them, was pointed out by Jean Perrin as early as 1927, who called this phenomenon molecular or resonance “induction.” ^10

In these works J. Perrin also described experiments in which a nonfluorescent dye—methylene blue, with an absorption band exactly coinciding with the fluorescence band of another dye, “fluorescent blue”—strongly quenches the fluorescence of the latter. Moreover, the quenching proves to be more effective than with an equivalent increase in the concentration of the fluorescent dye itself. The same methylene blue weakly quenches the fluorescence of eosin, uranine (fluorescein), and still more weakly that of quinine sulfate, the emission bands

which do not give so complete a coincidence with the absorption maximum of methylene blue. Similarly, the fluorescence spectral band of uranine is quenched more strongly by eosin, with a coincident absorption band, than by increasing its own concentration or by adding esculin, with an ultraviolet absorption band. However, J. Perrin’s experiments were qualitative in character and required quantitative verification. In the study by Vavilov and Galanin, the fact of effective quenching of the emission of a dye molecule by a molecule of another kind was convincingly proved, provided there is sufficient overlap of the maximum of the emission band of the first molecule with the absorption band of the nonfluorescing second molecule. In this case both molecules are fixed at distances exceeding molecular dimensions but smaller than the wavelength of the emitted light (cf. Fig. 1).

In conclusion it should be noted that concentration quenching is not universal for all fluorescing compounds. It does not occur, for example, for acridine, pyrene, pinacryptol yellow, and others.^11 Many organic compounds, for example naphthalene and anthracene, in the crystalline solid state, when the molecules are closely packed in near proximity to one another, have a fluorescence yield practically no smaller than in dilute solutions.

3. THEORY OF TRANSFER OF EXCITATION ENERGY

The effects described above are not directly dependent on the viscosity of the solvent and change little on passing to glassy solutions, in which the dye molecules are deprived of mobility. For example, the concentration self-quenching of fluorescein has approximately the same magnitude both in water and in a glucose solution with a viscosity 2000 times greater, and even in solid ice.^12 Thus, the quenching considered here cannot be caused by diffusion of dye molecules and their direct contact during the time $\tau$ of existence of the excited state. Here, consequently, a certain “long-range action” is manifested, extending over a distance of the order of ten molecular diameters.

It is essential to note that the shape of the contours of the absorption and emission bands, with increasing concentration for the indicated objects, does not change. In other words, there is practically no mutual perturbation of the molecules leading to distortion of their electronic and vibrational states. And since the uniform normal contour of the emission spectral band of a dye is due to the establishment of an equilibrium thermal distribution of molecules over vibrational levels in a time of the order of $10^{-12}$ sec.,^7 it follows from this fact that the transfer of excitation energy takes place...

is accomplished over a longer time, lying, evidently, within the limits from \(10^{-12}\) to \(10^{-8}\) sec.—the lifetime \(\tau\) of the excited molecule before emission.

Jean Perrin was the first to point out the possibility of an electrodynamic interaction between the excited electronic oscillator of one molecule and the resting oscillator of another, and of the transfer of energy between them without the mediation of radiation\({}^{10}\). He proposed an interpretation of this phenomenon proceeding from the classical conception of inductive coupling between identical resonating oscillators. Such a treatment leads to the conclusion that the transfer of energy from one oscillator to another during the “damping time” of the oscillator, \(\tau \simeq 10^{-8}\) sec., is possible when they approach one another to distances smaller than a certain value \(R_0 \simeq \dfrac{\lambda}{2\pi}\), where \(\lambda\) is the wavelength of the radiation emitted by the oscillator.

Francis Perrin\({}^{13}\) gave a more profound quantum-mechanical theory of the phenomenon, basing himself on the previously proposed theoretical treatment of the transfer of electronic energy between gaseous atoms\({}^{14}\). In doing so he took into account the necessity of broadening the oscillation frequency of the oscillators, i.e. the presence of an extended spectral band of frequencies instead of a single line, as is actually observed for complex molecules of organic compounds. In F. Perrin’s theory this broadening was brought about by random violations of the regularity of the oscillations of the oscillators, occurring after an average interval of time \(\bar t \simeq 10^{-13}—10^{-14}\) sec.*).

For the critical distance at which either emission of a quantum or its transfer to a neighboring molecule becomes equally probable, according to F. Perrin’s theory one obtains the expression

\[ R_0 \simeq \frac{\lambda}{\pi}\sqrt[6]{\frac{\bar t}{\tau}} . \tag{2} \]

Both theories—the classical and the approximate quantum-mechanical—do not give numerical agreement with experiment, leading to excessively large distances \(R_0\) of critical approach. Thus, for fluorescein \((\tau = 5.07 \cdot 10^{-9}\ \text{sec.},\ \lambda \simeq 5000\ \text{Å})\), according to the classical theory one obtains \(R_0 \simeq 1000\ \text{Å}\), and according to the quantum-mechanical theory \(R_0 \simeq 200\ \text{Å}\). From the formula relating the average distance between molecules

*) According to F. Perrin, the disturbances are caused by collisions of dye molecules with solvent molecules. However, the fact, established in the author’s laboratory, that even in the gaseous state broadened spectral absorption bands are retained shows, beyond doubt, that the violations of the regularity of the oscillations of the electronic oscillator have an intramolecular origin and are due to the interaction of the electronic state with the vibrations of the molecular skeleton\({}^{7}\).

$R$ with their concentration:

\[ c=\left(\frac{7.35\cdot 10^{-8}}{R}\right)^3 \text{ mole/liter}, \]

it follows that the given value of the critical distance corresponds to concentrations $c$ of the order of $10^{-6}$ and $10^{-5}$ mole/liter, whereas concentration effects, according to the data of the preceding paragraph, set in only at a concentration of $10^{-3}$ mole/liter, when the mean distance between the dissolved molecules is only $50$ Å.

Moreover, according to F. Perrin, the probability of energy transfer between two oscillators is inversely proportional to the sixth power of the distance $R$. This should give a proportionality of the effect to the square of the concentration, whereas an exponential dependence has been established experimentally.

The reason for this discrepancy lies in the actual absence of exact energy resonance between the excited and unexcited dye molecules because of the presence of a Stokes shift, as was discussed above.

Recently Förster^15 has given a detailed quantum-mechanical theory of the transfer phenomenon, proceeding from the experimentally observed noncoincidence of the absorption and emission spectra. Assuming that the electrostatic interaction of moving electronic charges in two molecules situated at distances exceeding their dimensions, calculated by the methods of quantum mechanics, is analogous to the interaction produced by dispersion cohesive forces, and also taking into account the mutual overlap of mirror-symmetric absorption and emission spectra, Förster derives the following dependence of the probability of energy transfer $F(R)$ on the intermolecular distance $R$:

\[ F(R)=\frac{1}{\tau}\left(\frac{R_0}{R}\right)^6, \tag{3} \]

where $\tau$ is the lifetime of the excited state of the molecule, and $R_0$ is a constant. By $F(R)$ is meant the reciprocal of the time during which the energy quantum passes from one molecule to another. $R_0$ is that critical intermolecular distance at which transfer of the excitation quantum to a neighboring molecule is equally probable as its emission by the first molecule. Indeed, for $R=R_0$, $F(R)=\frac{1}{\tau}$. At a closer approach $R<R_0$, energy transfer must certainly take place during the lifetime of the excited state.

Consideration of the totality of electronic-vibrational transitions taking place in the emission and absorption of light by real dye molecules, which possess broad spectral bands, and detailed allowance for their mutual influence in two neighb-

... molecules lead to the following expression for \(R_0\):

\[ R_0^6=\frac{3\tau c J(\nu)}{8\pi^4 n^2 N' \nu_0^2}. \tag{4} \]

Here \(c\) is the velocity of light, \(n\) is the refractive index of the solvent, \(\nu_0\) is the frequency (in \(\mathrm{cm}^{-1}\)) of the vibrationless purely electronic transition of the molecule (the mean value of the frequencies of the maxima of the absorption and emission bands), \(N'=6.02\cdot 10^{20}\) is the number of molecules in a millimole, and \(J(\nu)\) is a measure of the mutual overlap of the absorption and emission bands of the molecule*).

From the expression given for \(R_0\), using known data on absorption spectra, we have for fluorescein \((\tau=5.07\cdot 10^{-9}\ \mathrm{sec}.)\) \(R_0=50\ \text{Å}\), for chlorophyll \((\tau \simeq 3\cdot 10^{-8}\ \mathrm{sec}.)\) \(R_0=80\ \text{Å}\), and for sulfuric-acid quinine \((\tau \simeq 4\cdot 10^{-8}\ \mathrm{sec}.)\) \(R_0=10\ \text{Å}\), in full agreement with those concentration values at which depolarization of fluorescence occurs in solutions for these compounds. In the case of quinine, as we see, there is no basis for assuming appreciable long-range action.

Diffusion of the excitation energy during the time \(\tau\) over a distance of \(50\ \text{Å}\) takes place faster than the Brownian diffusion motion of molecules, which covers about \(20\ \text{Å}\) in the same time.

However, from formulas (2) and (3) it follows that the probability of transfer of excitation energy between neighboring molecules also increases here in proportion to the square of the concentration, which, as was mentioned above, does not agree with experiment.

The question of the direct transfer of excitation energy between molecules located at distances smaller than the wavelength of the radiation arose and was subjected to theoretical consideration also apart from concentration phenomena in solutions of fluorescent dyes. Thus, in order to explain participation in photosynthesis, along with chlorophyll, of other pigments as well (which will be discussed in detail below), Oppenheimer proposed essentially the same interpretation\(^{16}\). In doing so he proceeded from an analogy between the transfer of excitation energy among dyes and the effect

*) In view of the fact that the absorption and emission bands have contours that are mirror-symmetric with respect to the vertical lying at \(\nu_0\), Förster, instead of the curve determined from the intensity distribution in the emission spectrum, takes the curve of the absorption coefficient \(\varepsilon(\nu)\) and, by replacing \(\nu\) by \(2\nu_0-\nu\), constructs from it the curve \(\varepsilon(2\nu_0-\nu)\), mirror-symmetric with respect to \(\nu_0\). The product \(\varepsilon(\nu)\cdot \varepsilon(2\nu_0-\nu)\) has its maximum value at the value \(\nu_0\), where the contours of absorption and emission completely intersect, and decreases on both sides. As a measure of the overlap of the bands, the integral

\[ J(\nu)=\mathrm{const.}\int_{0}^{\infty}\varepsilon(\nu)\cdot \varepsilon(2\nu_0-\nu)\,d\nu, \]

is adopted, which is obtained by graphical integration (see \(^{15}\)).

internal conversion of a γ-quantum of nuclear radiation into the energy of detachment of the deepest outer electrons of the atom. The efficiency of conversion considerably exceeds that which could have been expected from absorption of γ-radiation by an electron*).

To explain two such very heterogeneous facts from spheres of phenomena quite remote from one another, Oppenheimer, unaware of the works of Vavilov and Perrin, likewise assumes a direct coupling of the emitter and the acceptor of energy if they are at a distance smaller than the wavelength of the radiation, i.e. within the limits of the electrostatic field of the radiating oscillator. However, the author considers a very primitive classical picture of the electrostatic coupling of two identical oscillators, one of which emits per unit time a number of quanta:

\[ F=\frac{E}{h\nu}=\frac{16\pi^{2}\nu A^{2}}{3hc_n}, \]

where \(A\) is the amplitude of oscillation of the oscillator, \(\nu\) its frequency, \(c_n\) the speed of light in a medium with refractive index \(n\), and \(h\) Planck’s constant. The author calls the quantity \(F\) the “yield” of radiation. Taking into account that near a radiating dipole the electric field is inversely proportional to the third power of the distance, and not to the first power, as is the case for distances greater than the wavelength, Oppenheimer derives the following dependence of the probability \(T(R)\) of energy transfer to a neighboring oscillator on the distance \(R\) between them:

\[ T(R)=\frac{\sigma A^{2}c_n}{4\pi^{2}h\nu^{3}R^{6}}, \]

where \(\sigma\) is the molecular coefficient of absorption by the oscillator of light of frequency \(\nu\).

As a result of integration over a set of oscillators uniformly distributed in space with concentration \(N\) per unit volume and with all possible orientations around the first molecular oscillator with an “effective” radius \(R_m\), the following expression is obtained for the total probability, or rate, of energy transfer:

\[ T=\int_{R_m} NT(R)\,dV=\frac{\sigma A^{2}c_nN}{3\pi^{2}h\nu^{3}R_m^{3}}, \]

and for the ratio of the rate of energy transfer without radiation to the “yield” of radiation—the expression

\[ \rho=\frac{T}{F}=\frac{\sigma N}{R_m^{3}}\left(\frac{\lambda}{2\pi}\right)^4 . \]

\[ \underline{\hspace{2.5cm}} \]

*) Evidently, the same consideration must apply to the effect of internal conversion of the energy of X-ray radiation of an atom into the energy of detachment of an outer electron, i.e. to the internal photoelectric emission of an atom—the Auger effect.

The uncertainty of the radius \(R_m\), which differs from the “critical” value of the radius introduced above, does not permit any reliable conclusions. Taking \(R_m \simeq 10\) Å, which undoubtedly corresponds to direct contact of the molecules, Oppenheimer arrives at the conclusion that \(\rho \simeq 10^{11}\ \mathrm{sec.}^{-1}\). In other words, the transfer of the excitation energy quantum without radiation between pigments and chlorophyll is possible in \(10^{-11}\) sec. Oppenheimer’s extremely simplified theoretical approach deprives the numerical values he obtains of persuasiveness. His treatment takes into account neither the finite lifetime of the excited molecule nor the absence of coincidence of the absorption and emission spectra of real molecules, as other authors have done. The assignment to the phenomenon of energy transfer between dyes considered here of the name “internal conversion,” as Oppenheimer does, is unfortunate and misleading.

4. MIGRATION OF ELECTRONIC EXCITATION ENERGY IN MOLECULAR CRYSTALS

In constructing the general theory of photon absorption in a crystal, Ya. I. Frenkel, as early as 1931, came to the conclusion that localization of the excitation energy in one definite particle that has absorbed a photon, among a series of repeating identical particles, is impossible, since it does not give a stationary state of the system[^17]. Identical particles with the same positions of the electronic levels perturb one another, and this mutual influence must lead to displacement of the quantum of excitation energy together with a peculiar wave of the “probability of excitation” over all sites of the chain or lattice formed by the molecules.

The migrating quantum of electronic energy may be likened to a certain particle, called by Frenkel an “exciton,” with a mass greater than or equal to the mass of the electron.

The picture and terminology described here subsequently received broad recognition and application in the consideration of various photoprocesses occurring in crystalline lattices[^18].

For the possibility of displacement of the quantum of excitation energy through the crystal without its dissipation into heat, the interaction of the state of electronic excitation of the particle with the vibrational degrees of freedom of the system is of substantial importance.

The condition for free displacement of the exciton without its degradation into heat must be a weak interaction of the excited state with the vibrations of the lattice. In this case the exciton has time to pass to a neighboring lattice site before the latter assumes, around the site of excitation, a new equilibrium configuration corresponding to the changed electronic state of the excited site. It is assumed that the transition of the molecule into the excited elec-

the excited state at the site inevitably affects the forces of its interaction with the surroundings and leads to a local distortion of the lattice. Since the establishment of a new equilibrium configuration around the distorted site requires several atomic oscillations, completed in a time of the order of \(10^{-12}\) sec., the rate of exciton migration must be such that, in an even shorter time, it has already moved to the nearest lattice site, separated from it by a distance of the order of \(10^{-8}\) cm. For this, the rate of displacement of the exciton must exceed \(10^4\) cm/sec.

If the exciton does not have time to leave the place of its origin and the lattice rapidly assumes around it a new equilibrium configuration, which is equivalent to stabilization of the local distortion, then the exciton loses its mobility, becoming “stuck” at this site. The “stuck” exciton may disappear either by emission or by thermal degradation into small vibrational quanta of the lattice—“phonons,” in Frenkel’s terminology[^17].

The objects on which the hypothesis of exciton migration was experimentally tested were chiefly molecular crystals of polycyclic hydrocarbons: naphthalene, anthracene, naphthacene, tetracene, etc.[^22]

The absorption and fluorescence spectra of crystals of the simplest polycycles (naphthalene, anthracene, etc.) exhibit at low temperatures (\(-180\) and \(-253^\circ\)C), as shown by the investigations of Obreimov and Prikhot’ko, a remarkably fine structure, comparable with that given by isolated molecules of these compounds in the gaseous state.[^19] The theoretical analysis of the structure of the spectra of such crystals[^20] shows that the mutual perturbation of identical molecules appears in the displacement, splitting, and broadening of the electronic levels of free gaseous molecules. However, in these crystal lattices, bound by weak forces of cohesive nature, the molecules nevertheless retain to a considerable degree their individuality, as follows from the preservation of the principal features of the structural spectra and the frequencies of the vibrations of the molecular skeleton derived from this structure.

Absorption of monochromatic exciting radiation over a broad interval of the ultraviolet absorption spectrum leads, in the molecular crystals under consideration, to the emission of an always identical fluorescence spectrum with a uniform distribution of intensity and structure. It follows from the analysis that this emission spectrum is caused practically only by transitions from the very lowest non-vibrational electronic level of the excited state of the molecule.[^7] This result shows that the excess of vibrational energy, inevitably imparted to the molecules upon absorption of large quanta of ultraviolet light, is very rapidly expended in the lattice by the moment of emission, as shown by

studies carried out in the laboratory of the author of the present article on the fluorescence of gaseous and dissolved compounds21. The dissipation of excess vibrational energy in the condensed phase occurs already in the molecule that has absorbed the photon, in a time of the order of several vibrations, i.e., in \(10^{-12}\) sec. Thus, as in the case of dyes, only the vibrationless quantum of electronic energy of the molecule can migrate as an exciton.

Fig. 3. Schematic representation of the relative positions of the absorption and emission spectra of anthracene and naphthacene. The contours of the naphthacene spectra, for convenience of comparison, are plotted downward.

The concentration effect of self-quenching in polycyclic aromatic hydrocarbons is practically absent: their crystals fluoresce with practically the same yield as dilute solutions. The following fact compels one to assume the presence of exciton migration in their crystals.

The fluorescence of pure crystalline anthracene, excited by light with wavelengths close to \(3660\ \text{Å}\), is blue in color and exhibits, as in a solution of anthracene, several separate spectral maxima adjacent to the absorption spectrum and having an analogous structure (Fig. 3). The presence of a small impurity of naphthacene (tetracene), with a relative concentration of \(10^{-3}\)—\(10^{-5}\) by weight, is sufficient for the intrinsic fluorescence of anthracene to be suppressed and for an intense yellow-green fluorescence to appear, with a structural spectrum belonging to naphthacene (see Fig. 3)22. In the crystalline state, naphthacene itself fluoresces very weakly. In a benzene solution of anthracene with an impurity of up to \(1\%\)

naphthacene, joint emission of the spectra of both components is observed, and that of anthracene is brighter, in accordance with its greater concentration. The exciting spectral lines fall in spectral regions where light is absorbed by both components.

Thus, first, there occurs a specific strong quenching action of a small impurity on the fluorescence of the substance of the main crystal lattice and, second, the impurity fluoresces with a large yield, clearly exceeding that which it has at the same concentration in a mixed liquid solution. Hence the conclusion suggests itself that the energy of the photon imparted to the anthracene crystal is capable of moving unhindered through the crystal without emission and without being dissipated as heat, and if in the path of its migration there is encountered such a foreign inclusion as a naphthacene molecule, then the quantum of energy is transferred to the latter and is emitted in it. Without the naphthacene impurity, evidently, the luminescence of a pure anthracene crystal must occur at disturbances of the regular structure of the crystal lattice, i.e., at internal cracks or the external surface of microcrystals. Similar effects were also observed for a number of derivatives and substituted anthracenes into which naphthacene was introduced, and also in the naphthalene + anthracene system[^22]. The quantum yield of the ultraviolet fluorescence of crystalline naphthalene is 0.7; upon addition of 10% anthracene, the fluorescence yield of the latter in the naphthalene medium reaches 0.9, i.e., reaches the value observed for anthracene itself in the form of crystals.

Fig. 4. Quenching of anthracene fluorescence and ignition of naphthacene fluorescence with increasing concentration of the latter in a crystal of the former at two temperatures. Along the ordinate axis are plotted the values of the quantum yield of emission; along the abscissa axis, the common logarithm of the concentration of naphthacene, expressed in grams per gram of anthracene (with the minus sign): 7 denotes \(10^{-7}\) g of naphthacene per 1 g of anthracene.

In Fig. 4 is shown the dependence of the quantum yields of emission of anthracene and naphthacene upon increasing the concentration of the latter in a crystal of the former at \(+20^\circ\) and \(-180^\circ\) C. To measure the yield, and not simply the fluorescence intensity, the values of the absorption coefficients of anthracene and naphthacene known for solutions were used. The figure clearly shows, first of all, the strong fall in the fluorescence yield of the principal substance—anthracene—at an insignificant concentration of the impurity—naphthacene, and also the increase in the yield of the latter to a known maximum. Upon exceed-

...of a certain concentration, naphthacene, instead of a molecular solution, forms microcrystals which fluoresce weakly, as was said above. The weakly fluorescing polycyclic molecules acridine and phenazine in solutions, when added to anthracene, cause only quenching of its fluorescence, acting as a kind of energy trap, like the nonfluorescing dye dimers discussed in Section 2.

The observed quenching effects cannot be caused by the screening action of the impurity, although it does have an absorption spectrum overlapping the emission spectrum of the main crystal. Indeed, in mixed liquid solutions of the same relative concentration the peculiar effects described—quenching of one component and enhancement of the other—disappear completely.

Undoubtedly, in the facts set forth here we have confirmation of Frenkel’s theoretical ideas concerning the exciton and its migration. However, the limitation of the effect to a comparatively narrow class of objects, such as polycyclic aromatic hydrocarbons in the crystalline state, makes the extension of these ideas to the broad field of high-molecular noncrystalline compounds, to which protein belongs, premature and unfounded. Preliminary experiments by the author of the article with the fluorescence of thin layers obtained by the joint sublimation of a solvent and organic compounds onto a surface cooled by liquid air can also be interpreted as the migration of a large ultraviolet quantum in a frozen solvent—ammonia[^23].

It should also be noted in passing that the concept of the exciton has been incorrectly extended to phenomena that have no relation to it, and that clearly contrived explanations have been given with its aid. Thus, an experimental work has recently appeared on the luminescence of pure liquids and solutions of various aromatic compounds under the action of γ-radiation[^24]. From the fact that an admixture of an aromatic compound greatly increases the luminescence intensity of a pure solvent, clearly exceeding the effect expected from the direct action of the radiation on the impurity, the authors conclude that migration of the exciton takes place, i.e., of an energy quantum, from the center of excitation in the solvent to the dissolved molecules emitting light. The authors are not troubled by the circumstance that the nature of the solvent is immaterial and that the dissolved compounds luminesce equally well both in benzene, which has stable electronic excitation levels and is capable of receiving and giving up energy, and in ether or \( \mathrm{CCl}_4 \), which, judging from the absorption spectrum, do not possess discrete electronic levels and decompose upon excitation by ultraviolet light.

As is well known, the primary action of radioactive radiation on liquids leads to processes of ionization and dissociation of their molecules, with the formation of electrons, ions, and radicals. The kinetic energy, the energy of recombination, or the energy of reaction of these active diffusing particles formed in the bulk of the solvent is usually dissipated as heat. In the presence of molecules capable of luminescing, excitation by impact, recombination, or attachment to them of the indicated active particles is a sufficient cause of an increase in the light yield. The assumption of migration of a quantum of excitation energy in a liquid solvent is in this case a superfluous and artificial hypothesis.

A similar attempt to explain, by energy migration, chemical processes occurring in aqueous solutions under the action of X-rays proved untenable on examination. It was shown that energy is transferred by diffusing active particles^26.

5. SENSITIZED FLUORESCENCE OF DYES IN SOLUTIONS

The evidence cited above for energy transfer between molecules in solutions is to a significant extent indirect. The only impeccable and most convincing argument in favor of the existence of such a phenomenon can be the extinction of the spectrum of a foreign molecule lying in the path of migration of an energy quantum, as was shown above for molecular crystals.

A similar phenomenon is also known for mixtures of unlike atoms or molecules in vapors and gases under the name of sensitized fluorescence. It consists in the following: to optically excited, light-emitting gaseous particles \(A\) (for example, Hg vapor) are admixed vapors whose emission is not directly excited by the light acting on \(A\) (for example, Na vapor). In such a mixture, nevertheless, a characteristic emission is detected, one proper to the particles of the admixed component \(B\).

Such an observation is interpreted quite unambiguously as transfer of the energy of the excited particles \(A^*\) to particles \(B\), if the latter manage to collide with the former during the lifetime of their excited state \(\tau \simeq 10^{-8}\) sec.

Emission by the particles \(B\) occurs at the expense of “quenching” the equivalent number of particles \(A^*\). The process may be represented schematically as follows:

\[ \begin{gathered} A^* + B \longrightarrow (AB)^* \longrightarrow A + B^* .\\ \downarrow \hspace{3.6cm} \downarrow\\ h\nu_A \hspace{3.3cm} h\nu_B \end{gathered} \]

For the possibility of transfer of excitation energy to particle \(B\), the condition \(h\nu_A > h\nu_B\) must be satisfied. With a departure from exact energetic coincidence of the levels in particles \(A\) and \(B\), as theoretical calculations show, the efficiency of transfer drops sharply. At exact resonance, transfer occurs over distances considerably exceeding atomic radii \(^{14}\).

The existence of sensitized fluorescence also in the vapors of certain aromatic compounds was shown in the laboratory of the author of the present article in 1934 by N. A. Prilezhaeva. Subsequently the phenomenon was observed for a number of other fluorescing molecules in vapors \(^{26}\).

Of great fundamental significance for the problem considered here is the observation of sensitized fluorescence in dye solutions. In this connection, cases are of particular interest in which energy transfer occurs not as a result of the contact of particles \(A^*\) and \(B\) when they approach one another by diffusion, but when they are fixed at a sufficiently large distance from each other in a viscous or glassy medium.

In contrast to a mixture of atoms, which possess widely separated narrow absorption lines that permit selective excitation of atoms of one kind without affecting atoms of another kind, for a mixture of organic molecules the overlap of the broad regions of their absorption spectra is inevitable, and this substantially hinders selective excitation of only one participant. To prove the fact of energy transfer by means of sensitized fluorescence, in such cases careful spectrophotometric measurements of the spectra of the components and an accurate determination of the fraction of the energy of the exciting light absorbed by each of the components are necessary, in order to establish the relative yield of their emission.

Advancing the idea of intermolecular “induction” as the cause of concentration effects (see Section 2), J. Perrin \(^{10}\) also carried out qualitative experiments with a mixed solution of fluorescing dyes (phenosafranine + tetrabromofluorescein). An enhancement of the emission of the latter dye in the presence of the former was found. His experiments, however, were preliminary in character and did not provide a quantitative basis for a conclusion about energy transfer.

Similar experiments were recently repeated anew by Förster, first with a mixture of fluorescein and erythrosine in aqueous and water–alcohol solutions, and then with a mixture of trypaflavine and rhodamine in methanol \(^{27}\). Upon illumination through a light filter transmitting the exciting light within the absorption band of trypaflavine \((\lambda_T^a = 4600\ \text{Å})\), in an equimolar solution of the components there is observed only the blue-green fluorescence of trypaflavine \((\lambda_T^f = 5200\ \text{Å})\),

if the total concentration does not exceed approximately \(10^{-4}\) mole/liter.

At the same ratio of concentrations, but with a larger total concentration, the color of the fluorescence changes from white to orange, characteristic of the emission of rhodamine \((\lambda_R^f = 5800\,\text{\AA})\) (Fig. 5).

For a final conclusion about the presence of sensitized fluorescence and the transfer of energy from trypaflavine to rhodamine, it is necessary to be certain that there is neither direct excitation of rhodamine nor its excitation by absorption of the fluorescence light of trypaflavine, since the absorption band of the former \((\lambda_R^a = 5550\,\text{\AA})\) completely overlaps the fluorescence band of trypaflavine \((\lambda_T^f = 5200\,\text{\AA})\). Unfortunately, the author does not give a clear solution to this question, apparently because of the difficulty of measuring the emission yield. He confines himself to the conclusion that, along with the light-filter action, the addition of rhodamine causes strong quenching of the fluorescence of trypaflavine, identical with the effects described above in Section 2. The quenching is manifested already at concentrations below \(10^{-4}\) mole/liter, and at a concentration of \(10^{-3}\) mole/liter of rhodamine the intensity of the fluorescence of trypaflavine falls to one half of the initial value (without rhodamine).

Fig. 5. Mutual arrangement of the absorption and fluorescence bands of trypaflavine and rhodamine. For clarity, the maxima of the absorption bands are plotted downward from the wavelength scale in order to avoid overlap with the fluorescence bands, whose maxima are plotted upward.

According to Förster, the weakening of the fluorescence of trypaflavine by rhodamine is indeed quenching, and it cannot be attributed to the formation of any nonfluorescent dye associates arising independently of illumination.

Indeed, experiment reveals a shortening of the lifetime \(\tau\) of the excited state of trypaflavine in the presence of rhodamine, as it should if only excited molecules are affected. For this the author used the well-known method of additionally introducing into the dye mixture a universal strong quencher—iodide ion—capable of deactivating excited molecules at the very first encounter\({}^{28}\). Experiment shows that one and the same concentration of \(I^{-}\) ions in the presence of rhodamine (with concentration \(5 \cdot 10^{-3}\) mole/liter) quenches the fluo-

escence of trypaflavin not as strongly as in the absence or at a low concentration of rhodamine. Hence, as in concentration depolarization and quenching by identical molecules, one may confidently conclude that the presence of rhodamine reduces the mean lifetime $\tau$ of the excited state of trypaflavin molecules, eliminating the longest-lived states (cf. the experiments of Vavilov and Galanin in section 2).

Quenching of trypaflavin fluorescence by rhodamine does not depend on the introduction of glycerin into the solution, with a corresponding 15-fold increase in viscosity, and changes little with temperature. This proves that the phenomenon under consideration is not due to diffusion, but belongs to the effects of inductive long-range action discussed above.

From the value of the quencher concentration $(2.3\cdot 10^{-3}\ \mathrm{mol/liter})$ at which the intensity of trypaflavin fluorescence falls to one half, the author concludes that, in this case, the mean distance between these molecules is about $60\ \text{\AA}$*).

For other pairs of dyes the concentration for half-quenching has the following values: trypaflavin + methyl blue (in methanol)—$6\cdot 10^{-3}$, fluorescein + erythrosin—$7\cdot 10^{-4}\ \mathrm{mol/liter}$.

From the data of Vavilov and Galanin for the systems they studied, this concentration has approximately the same magnitude: for rhodamine 5G + fuchsin—$1\cdot 10^{-3}$, for quinine sulfate + auramine—$3\cdot 10^{-3}\ \mathrm{mol/liter}$.

Photometric measurements of the decrease of the fluorescence yield in mixed solutions of trypaflavin + rhodamine confirm the author’s conclusions.

*) Förster^27, on the basis of considerations analogous to those he used for concentration quenching^15, derives the following formula for the “critical” distance of transfer of excitation energy between molecules $A$ and $B$ (cf. above, section 3):

\[ R_0=\frac{\lambda_m}{2\pi n}\sqrt{\frac{3}{8}\frac{\eta_0}{\tau_0\Delta\nu}}, \]

where $\lambda_m$ is the mean wavelength between the maximum of the fluorescence of $A$ and the maximum of absorption of $B$, $n$ is the refractive index of the solvent, $\eta_0$ is the maximum fluorescence yield of $A$ in the absence of $B$, $\tau_0$ is the lifetime of the excited state of $A$, and the quantity $\Delta\nu$ serves as a measure of the overlap of the fluorescence band $f_A(\nu)$ of molecule $A$ and the absorption band $\varepsilon_B(\nu)$ of molecule $B$:

\[ \frac{1}{\Delta\nu}= \frac{\displaystyle\int f_A(\nu)\,\varepsilon_B(\nu)\,d\nu} {\displaystyle\int f_A(\nu)\,d\nu\int \varepsilon_B(\nu)\,d\nu}. \]

A. N. Terenin

Concentration quenching of chlorophylls $a$ and $b$ (separately and jointly) in liquid solvents was studied in detail quite recently[^39]. The authors established a decrease in fluorescence intensity in the same concentration range as for molecules of ordinary dyes. Of interest is the conclusion that the quenching of the fluorescence of chlorophyll $b$ by molecules of chlorophyll $a$ is more effective than the process of self-quenching of chlorophyll $a$ and $b$ molecules separately. Indeed, the narrow fluorescence band of chlorophyll $b$ with a maximum at 6485 Å is close to the absorption maximum of chlorophyll $a$ (6600 Å). On the basis of processing the data for separate and mixed solutions of both chlorophylls, the authors come to the conclusion that there is a certain excess (of the order of 25%) fluorescence intensity of chlorophyll $a$ in the presence of chlorophyll $b$ upon excitation with a wavelength of 4750 Å, which predominantly affects the latter. The authors see in this evidence for the existence of sensitized fluorescence caused by energy transfer from chlorophyll $b$ to chlorophyll $a$. However, as in the case of the Förster experiment described above, such an indirect conclusion, based on a simplified treatment of experimental data, cannot be considered convincing.

6. TRANSFER AND MIGRATION OF THE EXCITATION ENERGY OF CHLOROPHYLL IN PHOTOSYNTHESIS

The nature of the photochemical reactions in which the chlorophyll of the living leaf participates has not yet been clarified. A number of results obtained by Krasnovsky and co-workers in the laboratory headed by the author of this article point to the role of chlorophyll excited by light as a carrier of hydrogen, in agreement with the views of K. A. Timiryazev[^39]. From this point of view, chlorophyll itself directly participates in the chain of enzymatic oxidation-reduction reactions that remove hydrogen from water and attach it to carbon dioxide according to the overall equation

\[ \mathrm{CO}_2+\mathrm{H}_2\mathrm{O}\xrightarrow{+120\ \text{kcal}}\mathrm{O}_2+\frac{1}{x}(\mathrm{CH}_2\mathrm{O})_x . \tag{I} \]

Alongside this, abroad there has long existed another conception of the function of chlorophyll, namely, that it is assigned the role of a physical carrier of the energy of the absorbed quantum to the reacting molecules.

To carry out the overall reaction (I), 120 kcal/mole is required, i.e., no fewer than 4 quanta of light absorbed by chlorophyll (42 kcal). Measurement of the quantum yield of the total photosynthesis reaction, i.e., of the number of light quanta actually required for it, gives values from 4 to 12 quanta per unit reaction (I), which represents a good utilization of light energy, taking into account the complexity of the process.

If the chemical reaction of reduction of carbon dioxide in chloroplasts occurs only at a few centers, the number of which is significantly smaller than the number of chlorophyll molecules, and if the latter must deliver to these centers only energy, then the figure cited for the quantum yield indicates an astonishing productivity of the light absorbed by chlorophyll. From this it was concluded that there are special conditions for the propagation of energy in the chloroplast of a living leaf, under which: a) the quantum absorbed by each chlorophyll molecule is not dissipated as heat, but is capable of reaching the few centers, spatially distant from it, where the chemical reduction reaction occurs, and b) in this center the action of several different quanta may be combined in order to cover the energy balance of reaction (1). Thus arose the conception, defended by some authors abroad, of the migration of energy in photosynthesis.

The basis for the emergence of such a conception was provided by data on the light “saturation” of photosynthesis at high brightnesses. Under the clearest conditions this phenomenon was observed when green algae (Chlorella pyrenoidosa and Chlorella vulgaris) were illuminated by short spark flashes lasting \(10^{-5}\) sec, with longer dark pauses between them. Such illumination made it possible to establish that the rate of photosynthesis is limited by the “throughput capacity” of the subsequent dark reaction (Blackman reaction), which is completed only in \(0.01—0.02\) sec. If the dark pause is shorter than this time, the yield of the photosynthesis reaction does not attain that maximum value which it has when the dark pause is lengthened. The light stage of the reaction, however, proceeds incomparably faster.

Increasing the intensity of an individual spark flash leads to light saturation, i.e. to the attainment of a limiting value that does not depend on any further increase in the intensity of the light.

According to what has been said above, saturation is explained by the limited number of centers at which the slow (\(0.01\) sec) dark stage of the carbon dioxide reduction reaction proceeds. Until these centers have become free for their repeated use, increasing the intensity or increasing the frequency of light flashes is useless for the reaction. The limiting number of reduced \(\mathrm{CO_2}\) molecules under light saturation is taken as the number of centers of dark reduction. Comparison with the number of available chlorophyll molecules shows that the ratio of the number of such centers to the number of chlorophyll molecules, independently of the nature of the object, is approximately \(1:2000\). From this it was concluded that in the chloroplast there is a peculiar structural photosynthetic complex comprising 2000 chlorophyll molecules and one reduction center, forming—

forming a single integral system of bound molecules (a photosynthetic “unit”)^30. It is assumed that absorption of a photon by any chlorophyll molecule in the complex is inevitably accompanied by transfer of the quantum to the reduction center associated with the complex. On further refinement it proved necessary to limit the “functional” complex to several hundred chlorophyll molecules*).

The existence of a photosynthetic “unit” was subjected to criticism^31. In particular, it was pointed out that light saturation does not by any means necessarily imply the necessity of the presence of numerous reaction centers. The limited “throughput capacity” of the dark stage of the reaction may be due to the very kinetics of the forward and reverse reactions, which require about 0.01 sec for their completion.

Subsequently, the authors of the hypothesis described here had to abandon the notion of a geometric complex of closely situated chlorophyll molecules and to accept only their energetic linkage with one another, and also with the reduction center, through the intermediary of protein (see Rabinowitch^30).

The basis for such a modification of the hypothesis was provided by experiments with radioactive carbon dioxide containing the carbon isotope C^14, which established dark fixation of CO₂ in the chloroplast by an unknown compound containing no chlorophyll at all.

Thus, if one adheres to the hypothesis of a chlorophyll complex, then the migrating quantum of energy inevitably has to pass beyond the limits of the complex.

Meanwhile there is no need to invoke protein in order to explain the energetic linkage of chlorophyll molecules. Förster^32 drew attention to the fact that, according to the latest data, the concentration of chlorophyll in the chloroplast is very high, reaching values from \(6 \cdot 10^{-2}\) to \(10^{-1}\) mole/liter. This means that the considerations and conclusions which were given above (Sections 2 and 3) for concentration effects in dye solutions are applicable to chlorophyll in a living leaf.

Concentration depolarization and self-quenching of fluorescence, explained by migration of excitation energy, as was

*) If the hypothetical photosynthetic “unit” functions as a single electronic system, similar to the ordered polymerizate mentioned (see § 14, p. 4), then the absorption spectrum of such a system would differ strongly from the normal spectrum of chlorophyll. This is not the case, but it should be noted here that the maximum of the absorption spectrum of chlorophyll in a living leaf is shifted by 120 Å in comparison with the spectrum of a molecularly dispersed solution of chlorophyll and is closer to the maximum of the spectrum of chlorophyll aggregated in the form of a colloidal particle.

as noted earlier, appear starting at concentrations above \(10^{-4}\) mole/liter.

In chloroplasts the concentration of chlorophyll exceeds by hundreds of times the “critical” concentration at which the time of energy transfer is comparable with the lifetime \(\tau = 3 \cdot 10^{-8}\) sec of the excited state of chlorophyll. Indeed, chlorophyll fluoresces in the leaf with a very small yield.

From data on the overlap of the absorption and fluorescence spectra of chlorophyll \(a\) in ether solution and the value of \(\tau\), the “critical” distance between molecules proves to be \(R_0 = 80 \text{ Å}\).

Since, on the basis of the formulas given in Section 3, the probability of transfer of excitation energy is proportional to the square of the concentration, one should expect transfer of an excitation quantum to a neighboring molecule already within \(10^{-4}\) of the time \(\tau\). It follows that, during the lifetime of the excited state, the quantum could, before its disappearance (as a result of emission), “visit” \(10^4\) different chlorophyll molecules. Concentration self-quenching of fluorescence, which shortens \(\tau\) as a result of degradation of excitation energy into heat, in fact considerably limits the migration and path length of the quantum in comparison with this clearly overestimated estimate.

7. TRANSFER OF ENERGY FROM THE PIGMENTS OF THE LIVING LEAF TO CHLOROPHYLL

Along with chlorophyll, photosynthesizing cells contain, in greater or lesser concentration, pigments of another structure that absorb light in other regions of the visible spectrum, such as carotene, xanthophyll, fucoxanthin, phycobilins (phycocyanin, phycoerythrin), and others. In recent years a number of works have appeared clearly indicating that the light absorbed by these pigments is also used for photosynthesis, sometimes with an exceptionally high yield. The objects used for such studies are for the most part algae, since they contain large concentrations of accompanying pigments.

In 1941, on the alga Nitzschia closterium, a comparative determination was carried out of the quantum yield of photosynthesis in monochromatic light in the blue and green regions, where pigments predominantly absorb, and in the red region, where chlorophyll absorbs.\(^{33}\) The absorption of light by individual pigments was measured in solution after their chromatographic separation in an acetone extract from the alga. In spectral regions where the absorption of light by the pigments (carotene, fucoxanthin) predominates, the quantum yield of photosynthesis had practically the same value,

as in the regions where only chlorophyll absorbs (6650 Å)*. It should be noted that in solution the maxima of the absorption spectrum of the pigments are shifted toward the short-wavelength side by approximately 200 Å in comparison with the position of these maxima in suspensions of intact chloroplasts.

In 1942 a more detailed study on the blue-green alga Chroococcus showed that light absorbed by carotenoids is for the most part not used in photosynthesis, whereas light absorbed by the water-soluble chromoprotein—phycocyanin—is as effective as light absorbed by chlorophyll (Figs. 6a, 6b)^34. These results were confirmed by other authors^16, and it was shown that quanta of light absorbed only by phycocyanin are 90% as effective for photosynthesis as quanta absorbed by chlorophyll. This conclusion follows from the accompanying table^16,34.

If the unknown separate quantum yields of photosynthesis for chlorophyll and phycocyanin are denoted by $\varphi_{\mathrm{chl}}$ and $\varphi_{\mathrm{phc}}$, then from the two equations

$$ 0.085 = 0.94\varphi_{\mathrm{chl}} + 0.06\varphi_{\mathrm{phc}}, $$

$$ 0.078 = 0.20\varphi_{\mathrm{chl}} + 0.80\varphi_{\mathrm{phc}} $$

we have:

$$ \varphi_{\mathrm{chl}} = 0.086,\quad \varphi_{\mathrm{phc}} = 0.076 \quad \text{and} \quad \frac{\varphi_{\mathrm{phc}}}{\varphi_{\mathrm{chl}}} = 0.89. $$

This shows that the energy of light supplied to the accessory pigment—phycocyanin—is used for photosynthesis almost as well as the energy supplied to the main sensitizer of the reaction—chlorophyll.

An analogous result was obtained in 1943^34 on the classical object of photosynthetic research—the alga Chlorella pyrenoidosa.

* Here the quantum yield gives the number of reduced CO₂ molecules per one quantum of absorbed light.

Fig. 6a. Absorption spectra of extracted pigments of the alga Chroococcus in alcoholic solutions. The spectrum of phycocyanin is given for an aqueous solution.^34

Fig. 6b. Quantum yield of photosynthesis of the same alga. The solid curve is drawn through the experimental points, denoted by different symbols depending on the number of the experiment. The dotted curve gives the expected result under the assumption of an identical quantum yield, equal to 0.08 for chlorophyll and phycocyanin for all wavelengths, and of the absence of participation of carotenoids in photosynthesis.^34

Monochromatic measurements of the quantum yield over the entire extent of the absorption spectrum established that in the region 4900–5100 Å, where the accompanying yellow pigments (carotenoids and phycobilins) absorb 70% of the radiation, the quantum yield of photosynthesis falls only to 0.063, i.e. only 30% below the maximum value of the quantum yield (0.09) observed in the region of chlorophyll absorption (see ^29).

In view of the importance of this question, it has again been taken up in very recent investigations, with more careful measurements of the absorption spectra of pigments separated chromatographically from extracts. The experiments again confirmed identical photosynthetic activity over a broad region of the absorption spectrum, outside the absorption maxima of chlorophyll, and showed that light absorbed in diatoms by the pigment fucoxanthin is just as photosynthetically active as light absorbed by chlorophyll ^35.

From the fact of the high and identical photosynthetic activity of pigments very diverse in structure, such as chlorophyll and phycobilins, the conclusion suggests itself that there is a uniform, presumably physical, mechanism for the transfer of excitation energy from the other pigments to chlorophyll. The latter is in all cases accepted as the true sensitizer of the photosynthetic reaction.

The high concentration of pigments (\(10^{19}\) molecules in \(1\ \mathrm{cm}^3\), according to ^16), reaching as much as \(1/8\) of the concentration of chlorophyll in the chloroplast, ensures interaction of chlorophyll molecules with excited pigment molecules during the time of their excited state. It is therefore quite natural that both Förster ^32 and Oppenheimer with Arnold ^16 regard the fact cited above as an inductive transfer of energy from the electronic oscillator of the pigment molecule to a chlorophyll molecule located from it at a distance certainly smaller than the wavelength of light. Resonant transfer of energy from phycocyanin to chlorophyll is favored by the circumstance that the fluorescence band of phycocyanin is located in the region from 6200 to 6550 Å, i.e. near the maximum of the chlorophyll absorption band.

On the basis of very simplified calculations, Oppenheimer and Arnold ^16 come to the conclusion that the distance between phycocyanin and chlorophyll molecules lies within the limits from 7 to 40 Å (according to Förster ^32, about 80 Å), i.e. it is within those distances at which inductive energy transfer from an excited molecule of one substance to another is possible before emission. According to their calculation, from 45 to 95% of the excited phycocyanin molecules transfer their energy to chlorophyll before emission.

Some confirmation of this assumption is provided by the fact that the quantum yield of fluorescence of the phycocyanin complex

with the protein in aqueous solution is equal to 20%, whereas in the alga itself the quantum yield falls to 1–2%*).

In connection with this question, attempts to detect directly the transfer of excitation energy from pigments to chlorophyll by observing sensitized fluorescence in a living object acquire special interest. Preliminary experiments showed the presence of weak red fluorescence upon excitation of diatom algae by light absorbed by fucoxanthin^35. However, the spectral identity of this emission was not established. Moreover, without precise photometric measurements the question remains open, since there is the possibility of direct excitation of chlorophyll in its own absorption spectrum, overlapping the absorption maximum of fucoxanthin.

Similar experiments were carried out with red marine algae containing a fluorescent pigment—phycoerythrin^36. In living algae two principal maxima are observed in the absorption spectrum—6750 Å (chlorophyll) and 5500 Å (phycoerythrin). In the fluorescence spectrum of the alga there are three maxima—5750, 6500, and 7100 Å. Aqueous extracts containing predominantly the phycoerythrin compound with protein give an absorption maximum at 5500 Å and intense orange fluorescence with maxima at 5900, 6200, and 6750 Å.

Since the positions of the absorption maxima in aqueous extracts and in intact cells differ noticeably, the authors put forward the supposition that chlorophyll and phycoerythrin in the living cell are coupled into a single complex. A decisive conclusion about the transfer of energy from phycoerythrin to chlorophyll could not be drawn, since phycoerythrin itself has fluorescence bands in the red region of the spectrum. It could only be established that the red fluorescence of living cells is considerably more intense upon excitation by the green mercury line 5461 Å (in the region of predominant absorption of phycoerythrin) than upon excitation by red light (in the region of chlorophyll absorption). Phycoerythrin is spectrally complementary to chlorophyll, since it absorbs in the gap (4900–5700 Å) of the absorption spectrum of the latter, in contrast to carotenoids and phycocyanin, whose maxima overlap the short-wavelength maximum of chlorophyll in the blue part of the spectrum (Fig. 6a).

The hypothesis of the transfer of excitation energy from pigments to chlorophyll in photosynthesis has greatly lost its persuasiveness after a recently conducted careful study on photosynthesis

*) In chlorophyll in the leaf the quantum yield of fluorescence is 0.15%; thus, the indicated algae possess very bright fluorescence.

in various marine algae^37. Measurements of photosynthesis were carried out under the action of monochromatic beams of radiation of equal energy, isolated by a diffraction grating from a continuous spectrum, and were accompanied by photoelectric measurements of the absorption spectra of living algae and extracts*). Photosynthesis was measured by the evolution of oxygen, detected polarographically with a sensitive instrument. The authors compare the spectral curve of the rate of photosynthesis at different

Fig. 7. Absorption spectra and “photosynthetic action” of the red alga Porphyra nereocystis, for which phycoerythrin is the predominant pigment. The action-spectrum curve corresponds more closely to the absorption curve of an aqueous phycoerythrin extract than to the curves of chlorophyll and carotenoids^37.

wavelengths—the “action spectrum”—with the absorption spectrum of the alga for objects containing different concentration ratios of pigments and chlorophyll.

For green algae, the curve of the spectrum of photosynthetic “action” practically coincides with the absorption spectrum, showing distinct maxima at 6750 and 4900 Å, belonging to chlorophyll. The same coincidence occurs for the brown alga (Coilodesme), where it also extends to the region of the absorption spectrum of the carotenoid fucoxanthin. Thus, in these algae, light absorbed either by chlorophyll or by fucoxanthin is approximately equally effective**).

*) Flat algae are, in this respect, an object very convenient for spectrophotometric measurements.

**) This, however, does not refute Haxo’s assertion^38 that light absorbed by fucoxanthin is more effective.

A completely different picture has been established for a large number of red algae, which, along with chlorophyll and carotenoids, contain a large quantity of water-soluble phycobilins (phycoerythrin and phycocyanin). As one of the numerous results of this work shows, as presented in Fig. 7, it is the light absorbed specifically by phycoerythrin that has high photosynthetic activity in these algae, whereas in the region of the absorption maximum of chlorophyll photosynthesis decreases*). An analogous phenomenon is observed for algae containing an excess of phycocyanin. In all these algae photosynthesis is minimal at wavelengths of 4350 and 6750 Å, corresponding to the maximum absorption of chlorophyll. Chlorophyll and carotenoids are present here in concentrations of the same order as in green algae.

Until these interesting results are further confirmed by another, less specific method of measuring photosynthesis, one may draw the preliminary conclusion that other pigments by themselves can just as effectively induce photosynthesis, replacing chlorophyll. There is therefore no need, at least in red algae, to assume transfer of excitation energy to chlorophyll**).

In conclusion of this section of the article, we note that simple physical schemes of energy transfer from molecules initially excited by light to chlorophyll, or from it to the center of the chemical reaction, are wholly insufficient for understanding the mechanism of activation of elementary reactions in photosynthesis. For the latter, not every form of supplied energy is of significance. In particular, as is well known from the study of simpler chemical reactions, the supply even of large portions of energy in the form of quanta of electronic excitation is not in itself a sufficient condition for increasing the reactivity of molecules.

Thus, the interesting phenomena of energy transfer observed in dye solutions and in molecular crystals are insufficient for interpreting the regularities and mechanism of photosynthesis.

In the following article, methods of energy transfer that are more effective from the chemical point of view and that occur in biochemical reactions will be considered.

*) The spectrum of photosynthesis is very close to the absorption spectrum of a phycoerythrin extract, with three maxima (4950, 5400, and 5650 Å).

**) Apparently, in red algae the chlorophyll dissolved in the lipoid phase of the chloroplasts is not accessible to the enzymatic system responsible for the chemistry of photosynthesis, whereas the water-soluble phycobilins do have access to it. It is also possible that the protein to which phycoerythrin is bound is itself the enzyme for photosynthesis, whereas lipid-soluble chlorophyll is unable to combine with it.

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