FINE-STRUCTURE SPECTRA OF CHLOROPHYLL DIMERS A. P. Losev, R. V. Yaaniso, and I. N. Nichiporovich

UDC 535.379;547.979.7

The application of high-resolution optical spectroscopy [i] to the investigation of the electronic spectra of chlorophyll and its derivatives permits information inaccessible by other methods to be obtained on the localization of the weak S 2 + S o transition [2], the property of flexibility of the chlorophyll macrocycle to be detected [3], distinct spectral differences of NH-tautomers to be found in nonmetal-containing derivatives [3-4], and monoand disolvates in Mg-complexes [4-6], new data to be obtained on the state of aggregation of pigments in solutions and biosystems [7-8], the rate of charge separation in reaction centers to be estimated [9-11], and the characteristics of energy migration and the specifics of this process to be evaluated under conditions of removal of nonuniform broadening [12]. The hole burning method permits the detection of charge-transfer states in donor-acceptor complexes, since in such cases very broad holes (with a half-width of several hundred cm -I) are burned out. Investigations of chlorophyll dimers, as a structure modeling the native state of the pigments in the photosynthetic apparatus of plants, by methods of selective spectroscopy are promising in many respects. In [7] nonphotochemical burning of holes in the electronic spectra of a chlorophyll a dimer in polystyrene at 1.8 K was observed for the first time. In this work we investigated a chlorophyll dimer that is formed spontaneously in a nonpolar solvent when traces of water or other polar molecules are removed by a sodium mirror under vacuum. In this system, in our opinion, conditions are created for more complete aggregation of the pigment at a low concentration of it (105-104 M), which to a substantial degree eliminates the influence of unreacted monomeric pigment molecules on the results of the measurement. In this work a method is developed for the production of chlorophyll dimers in a nonpolar solvent, petroleum ether (T b = 70-I00~ which freezes "as a glass" at helium temperatures. The method consists of repeated redistillation of the solvent over a sodium mirror under high vacuum for chemical removal of traces of water. The chlorophyll film was exposed in a special evacuated cuvette at 70~ for 40 min to remove coordination-bound water, and then dry petroleum ether was redistilled under vacuum into the cuvette with the dried chlorophyll, and the cuvette was sealed off. The pigment dissolved, forming a dimer. Usually glass cuvettes with an optical path thickness of 1 mm were used. The fluorescence spectra were recorded on FICA-55 and SLM-4800 spectrofluorometers. The latter is equipped with a computer and a program for calculating the areas under the quantum fluorescence spectra. Measurements of the lifetime of the fluorescence were performed on a PRA-3000 pulse fluorometer, working in an accumulating system of photon counting. The error in the measurement of the fluorescence yield and lifetime was i0 and 2%, respectively. The absorption spectra were recorded on a Beckman-5270 spectrophotometer, and the circular dichroism spectra on a JASCO-20 instrument. A constant-pressure dye laser (Model 490 from Coherent on a dye mixture), the output power of which was stabilized by feedback to the feed current of the CR-3 pumping argon laser, to excite the fluorescence at helium temperatures. The spectra of the dyes covered the region of 570-690 nm with a generation line width 0.].-0.25 cm -I. The spectra were accumulated in an LP-4800 multichannel analyzer and processed on an EC-1010 computer. The radiation intensity on the sample during the hole burning, the duration of up to 3 min, did not exceed 3 mW/cm 2. In the m e a s u r e m e n t o f the fluorescence-excitation spectra, the intensity of the laser was weakened by two orders of magnitude in comparison with burning, so that the influence of burnout could be neglected. Spectral-Fluorescent Properties of the Chlorophyll Dimer in Dry Petroleum Ether. The presence of a chlorophyll dimer a in dehydrated petroleum ether follows from a number of

V. I. Stepanov Institute of Physics, Academy of Sciences of Belarus, Minsk. from Zhurnal Prikladnoi Spektroskopii, Vol. 57, Nos. 1-2, pp. 46-55, July-August, Original article submitted December 20, 1991.

564

0021-9037/92/0102-0564512.50

9 1993 Plenum Publishing Corporation

Translated 1992.

i

P

j I

Fig. i.

i

i

j

I

i J i r ]

Absorption and CD spectra of a chlorophyll dimer at 293 (i) and 77 K (2).

spectral data. The absorption spectrum contains bands belonging to two components of the dimer (Fig. I). In the region of the Qy transition the spectrum consists of two overlapping bands of approximately equal intensity with maxima at 666 and 676 nm. We shall call the transition with a greater energy D u (upper) and the one with a lower energy D~ (lower). The value of the energy gap E u - E~ = 220 cm -I A characteristic of the dimer is the closeness of the intensities of these transitions to equality. According to the data of [13], when larger oligomers (tri-, tetra-, etc.) are formed, the band D~ becomes predominant. The circular dichroism (CD) spectrum (Fig. i) of the dimer is also represented by two transitions of opposite signs but the same intensity. The force of rotation of each of the transitions is equal in absolute magnitude to the force of rotation of the monomer. This result agrees with the result of [14] and means that the CD spectrum is formed as the sum of the spectra of molecules possessing mutually perpendicular dipole moments of the transitions and agrees with the T-shaped structure proposed in the studies of Katz's group [13]. In this model the Mg atom of one dimer molecule (Du) is bonded to an oxygen atom of the isocyc]ic ring of another molecule (D~). In contrast to the monomer, which has a quantum yield and lifetime of the fluorescence of 0.35 and 6.0 nsec, the quantum yield of the fluorescence of the dimer is equal to 0.05 (according to our measurements relative to the monomer in ether), and the lifetime of the fluorescence is about 1 nsec. This result is evidence of the presence of an emissionless process in the dimer, which competes with the fluorescence process. According to these data we can calculate the total rate constant of deactivation of the singlet excited state of the chlorophyll monomer, equal to 1.6"108 sec -I, and assuming that the rate constant of emission of the molecule is unchanged by dimerization, we can estimate the rate constant of the emissionless process at Knr = 6KE = 1"109 sec -I However, it is possible that the observed fluorescence of the dimer is a secondary process of recombination of charges in the dimer. The process of separation of charges might occur far more rapidly. We shall return to this question in a discussion of the results on the burning of holes in the absorption spectrum of the dimer. The position of the fluorescence maximum of the dimer differ appreciably from the position of the fluorescence maximum of the monomer. The fluorescence spectrum of the dimer in the case of excitation into the band of the dimer at 450 nm has a band with maximum 686 nm (Fig. 2), belonging to the lower component of the dimer D~. Usually a shoulder is observed at 667 nm, which we might attempt to ascribe to the fluorescence from Du, if a small amount of undissociated monomer did not remain in solution. According to our data, the maximum of the 0-0 fluorescence band of the residual monomer lies precisely here, and the maximum of the fluorescence-excitation spectrum is found at 658 nm and was ascribed in [15] to the nonsolvated pigment with a coordination number of the Mg atom equal to four. Considering these data, we can assume that if fluorescence of the upper component of the dimer occurs, its fraction does not exceed 20-30% of the fluorescence intensity of D~. This conclusion agrees with the assumption of the presence of an inductive-resonance transfer of energy from D u to D~ with a rate constant no less than (4-6).108 sec -I The results examined above were obtained at 293 K. When the temperature of the solution is lowered to 77 K, the spectral-fluorescent properties of the dimer are changed. The values of the quantum yield and lifetime of the fluorescence are especially strikingly changed, increasing to the values characteristic of the

565

Ill , rel. units

J

i

6~fi

7Y0 A~ nm Fig. 2

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Fig. 3

Fig. 2. Fluorescence spectra of a solution of chlorophyll dimer a in the case of broad-band excitation: T = 293 (i, 2) and 77 K (3); lexcit = 430 (i), 455 (2), and 440 nm (3); &lexcit = 7.5 nm. Fig. 3. Fluorescence spectra of the chlorophyll dimerat 4.2 K a n d laser excitation in the vibronic region of the SI-S 0 transition: lexcit = 638.3 (i) and 640.2 nm (2). monomer, that is, 0.3 and 5.8 nsec. Thus, the energetics of the photophysical processes in the dimer do not differ from the energetics of monomer chlorophyll molecules at low temperature. Lowering the temperature suppresses the effective emissionless process of quenching of fluorescence that occurs under normal conditions in the dimer molecule. In addition, the absorption and CD spectra at 77 K are close to the spectra at 293 K (Fig. i), which is evidence against any substantial structural rearrangements in the dimer. When the temperature is lowered there is a shift of the absorption maxima in the long-wave direction. The fluorescence maximum is also analogously shifted (Fig. 2) by 7-8 nm, and, just as at 293 K, the spectrum is represented by a single band. This confirms the fact that emission occurs primarily from the lower component of the dimer. The preservation of the transfer of energy of electronic excitation from D u to D R was confirmed by the weak dependence of the fluorescence spectrum of the dimer on the wavelength of excitation, as well as by the fluorescence-excitation spectrum, which is analogous to the absorption spectrum and repeats all of its characteristics, in particular, the band at 450 nm, characteristic of the dimer. Thus, lowering the temperature evidently does not decrease the efficiency of charge transfer from D u to D R. According to these data we can estimate the efficiency of energy transfer from D u to D R as a = i - (i/i0) = 0.9. Considering that the total rate constant of deactivation of the S I state of chlorophyll in the absence of energy transfer is 1.6"108 sec -I, we can estimate the lower limit of the rate constant of emissionless energy transfer in the dimer Ket = KEa/l - a = 1.4.109 sec -I at 77 K. A weak band, assigned to the fluorescence of the equilibrium monomer, is also observed in the fluorescence spectrum. The maximum of the band is situated at 667 nm. In contrast to the bands of the dimer, this band is not shifted when the solution is frozen. The fluorescence-excitation spectrum corresponds to the absorption spectrum of the monomer. Considering that the Stokes shift of the fluorescence spectrum for the chlorophyll molecule is usually 8-10 nm, we can assume that the absorption maximum of this form of chlorophyll will lie at 657-659 nm. The maximum of the fluorescence-excitation spectrum of this form of chlorophyll has precisely this position when the fluorescence is recorded at the maximum situated at 908 nm [15]. We should mention that according to the data of [16, 17], two forms

566

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Fig. 5 Fig. 4. Fine-structure fluorescence-excitation spectrum of the unsolvated chlorophyll a monomer: lob s = 664.78 nm. Fig. 5. Fine-structure fluorescence-excitation spectrum of the chlorophyll dimer: lob s = 680.7 nm. with maxima in the region of 930-935 and 960-985 nm are observed in the fluorescence spectra of chlorophyll a, depending on the nature of the solvent, and should most likely be assigned to the mono- and dissolvates, respectively. On this basis the new form of chlorophyll, possessing a fluorescence maximum at 908 nm, was assigned to the unsolvated pigment with coordination number of the magnesium ion equal to four in [15]. An estimate showed that the content of this short-wave form of chlorophyll is several percent. If the assumption of an unsolvated form of chlorophyll is correct, then the fine-structure spectra of this form will differ from the analogous spectra of mono- and disolvates currently known. Fine-Structure Fluorescence Excitation Spectra of the Dimer. At helium temperature (4.2 K) with narrow-band laser excitation into the 0-i transition of the first electronic state, the fluorescence spectrum exhibits a fine structure of a number of 0-0 transitions against a background of the envelope line (Fig. 3). The narrow lines against a background of a structureless spectrum are related to selective excitation of the molecules possessing the same vibronic energy but a different reserve of electronic and vibrational energy. After vibrational relaxation, in the excited state these centers give a set of 0-0 lines at a distance from one another equal to the individual vibrational frequencies of the excited state [i]. The nature of the spectrum changes with changing excitation frequency, and thus a set of vibrational frequencies of the excited state that are obtained as the difference between

567

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Fig. 6. Hole burning in the spectrum of the chlorophyll dimer: a) Iburn = 684.46 nm; Iexci t = 0.3 mW/cm2; tburn = 25 sec; F = 0.58 • 0.04 cm-~; b) Iburn = 670.85 nm; Iexci t = 0.6 mW/cm2; tburn = 60 sec; F = 0.44 • 0.04 cm -I. Depth of the hole 5 (a) and 9% (b). the frequency of the excitation line and the 0-0 fluorescence line can be detected; however, it is more convenient to use the fluorescence excitation spectra for this purpose. The vibrational structure of the selectively recorded fluorescence-excitation spectrum is presented in Fig. 4 (in the case of recording at the wavelength of the unsolvated monomer). The spectrum contains a number of lines with half-widths of the order of i0 cm -I and numerous weaker, but readily reproducible lines, and it differs in position and intensity from the known spectra of the monosolvate and disolvate [4-5]. One of the essential differences is that the intensity ratio of the major vibrational lines in the spectrum of the unsolvated monomer differs from the ratio of lines in the spectra of the mono- and disolvate. In the unsolvated chlorophyll monomer, the intensities of the three major lines at 742, 983, and 1247 cm -I are related as 1.0:i.0:i.0, whereas in the mono- and disolvate the intensity ratio is equal to 0.7:1.0:0.7 [4] and 1.0:0.5:0.7 [5], respectively. The fine-structure fluorescence-excitation spectrum of the dimer differed substantially from both chlorophyll spectra mentioned (Fig. 5). Actually, for the dimer the most intense line is the line 1234 cm -~, the frequency of which differs appreciably from the frequency of the analogous line in the spectra of other chlorophyll forms. The intensity ratio of the major vibrational frequencies is specific for the dimer and equal to 0.7:0.5:].0. There are also other differences of the spectrum of the dimer, namely: An extremely intense band with maximum 923 cm -l, which is comparable with the intensity of the line 983 cm -I, appears; a satellite appears at 1267 cm -l near the 1234 cm -I line; a new line at 800 cm -l is observed close to the line second in intensity. The frequencies in the region of 1230-1250 cm -I were previously ascribed to the C-H vibrations of the methine bridges, and 740 and 983 cm -] to the vibrations of the pyrrole rings [4]. Consequently, dimer formation changes the electron density on the molecule that donates electrons to the magnesium atom of the other molecule, which is manifested in a change in the vibration frequencies of the pyrrole rings and methine bridges. We should mention an interesting characteristic of the excitation spectrum of the dimer, consisting of the fact that when fluorescence is recorded at the long-wave edge of the spectrum, the background in the excitation spectrum is significantly increased, but the spectrum itself becomes less sharp. The intensity of the background is commensurate with the intensity of the spectrum. This observation can be partially explained by the fact that at the long-wave edge of the fluorescence spectrum there is an interference of the phonon edges of a large number of fluorescence centers differing in frequency of the 0-0 transition, belonging to Ds However, a comparison with the excitation spectrum of a solution of monomeric chlorophyll under analogous conditions shows that the background is substantially greater in the case of the dimer. Evidently the increased background in the spectrum of the dimer is due to the contribution of the donor portion of the dimer to the absorption spectrum of the molecules, as a result of the transfer of energy of electronic excitation. A contribution

568

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720

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Fig. 7. Fine-structure fluorescence spectrum of the dimer in the case of excitation into a purely electronic transition: spectra before hole burning at i = 686.7] nm (i) and differential spectrum after hole burning (2). For a comparison of the frequencies cited for the ground state with the corresponding frequencies of the excited state, see Table i. of long-wave forms of the associates to the fluorescence also is not ruled out. The fluorescence spectrum Ds of the dimer, obtained according to the method of [18] as the difference between the fluorescence spectra before and after burnout of the pocket at the excitation wavelength 686.71 nm, shows a more pronounced structuring than is observed in the excitation spectrum of the dimer. Hole Burning in the Spectrum of the Dimer. If monochromatic light is resonance-absorbed in the region of a nonuniformly broadened spectra], band by photonless lines (PLL), and the excited molecules enter into a photochemical reaction, then the energy of the transition of these molecules is changed, and a hole with a width no less than 2F 0 appears in the spectrum (F 0 is the width of the purely electronic line). For chlorophyll a and its derivatives, a nonphotochemical hole burning is observed, a characteristic feature of which is reversible filling of the hole in the case of nonselective excitation [4]. Nonphotochemical hole burning can be represented as the result of the change in the configuration of the solvent matrix around the pigment molecules, which leads to a change in the pigment-matrix interaction and the resonance absorption frequency of the pigment molecules. Like numerous data on solutions of chlorophyll and other mono-dissolved pigments, we observed narrow holes in nonuniformly broadened dimer spectra at 4.2 K at any wavelength of burning in the region of the 0-0 transition of the dimer. Figure 6 presents as an example the results of hole burning at the absorption maxima D u and Ds by a laser line 0.i cm -l wide. From the data obtained it is evident that in both cases holes close in width but somewhat broader in Ds are burned out. The width of the lines F 0 = (F - Fs where F is the width of the hole in the spectrum and while Fs is the width of the laser line, is uniform. Thus, the uniform width of the burned out line is equal to 0.24 cm -I in Ds and 0.17 cm -I in D u. The latter value is virtually the same as that theoretically expected, if we assume that the uniform width of the PLL is negligible in comparison with Fs In this case, in agreement with [19], the width of the hole should be F = 2.Fs ~ = 1.4, Fs = 0.14 cm -I. The large width of the uniform line in Ds cannot be ascribed to energy transfer against the thermodynamic potential but may be associated with transfer of an electron from Ds to D u. However, the high quantum yield of the fluorescence of Ds is evidence against such an explanation. The width of the hole is known to be made up of the reciprocal of the rate of deactivation of the singlet excited state, including phototransfer of an electron I/T I and the rate of optical dephasing I/T2, determined by thermal fluctuations of the frequencies of optical

569

TABLE i. Vibrational Frequencies (cm -I) of the Unsolvated Chlorophyll a Monomer and Its Dimer in the S I and S o States at 4.2 K Monomer $1, kobs.-66,t,O nln

257,5 343 382 430 461 488 512 565 579 595 632 668 742,5 782 818 935 983,5 1004 1034

Dimer

Monomer

Dimer

S~, Xo b s -680,7 nm

So, ~ e x c i t : 6 8 0 , 7 nnl

51, Lobs~664,0 nlll

----. -426

176 259 352 403 447

1070 1095 1110 1121 1134 1168 1196

1070

1224 1247

1222

519 561 572 -710 742 760 800

923 983 1015 1031

532 590

757 813 935 999

1273 1312 1327 1347 1375 1402 1419

s,, k obs =680,7 rtl/i

So, ~excit ~680,7 nm 1064

1110 1117 1134

1174

1160 1204

1234

1236

1242 1267 1294 1328 1345 1375

1341

1414 1512 1538

transitions [19]. From estimates of the fluorescence lifetime DZ of the dimer and the lifetime of the excited state D u made earlier it is clear that the deactivation processes that determine them are capable of broadening the homogeneous line by a negligible amount, equal to F 0 = i/2~-c-T I = 3.10 -2 cm -I or more. Therefore, it seems interesting to evaluate the upper limit of the rate of the process according to the widths of the burned out hole. In the case of a homogeneous line width 0.17 cm -I, from the indeterminacy ratio we can estimate the rate of the process as I/T 1 = 2~-c.F 0 = 3"10 l~ sec -I. Consequently, in the T-shaped chlorophyll dimer there is not a very rapid transfer of energy from D u to Ds The case under consideration is very interesting from the standpoint of applicability of the theory of dipole-dipole inductive-resonance interaction to the dimer molecules. Actually, the distances between centers of dipole transitions D u and Ds are 0.85 nm, which is less than the diameter of the chlorophyll molecule. It can be assumed that in this case the electron clouds of the two molecules overlap appreciably, and exchange interaction may make a substantial contribution to the energy of interaction, as was assumed in [20]. The applicability of the ForsterGalanin theory to such short distances is justifiably doubtful. Despite the theoretical expectations, the experiment shows that energy transfer has a low rate and is fully explainable within the framework of the Forster-Galanin theory. Actually, the probability of energy transfer from the donor to the acceptor is equal to: Ket =

9000.1nlO.K2.B.J(v)/128.~.n~.N.~.Rt

where K 2 is an orientation vector; B is the quantum yield of the donor in the absence of transfer; J(v) is the overlapping integral of the absorption spectrum of the acceptor and the fluorescence spectrum of the donor; n is the index of refraction of the medium; N is Avogadro's number; 9 is the fluorescence lifetime; a n d R is the distance between the interacting dipoles. Almost all the quantities mentioned were measured or calculated according to the experimental data: B = 0.35, J(v) = 5.5"10 -13 mole-l-cm 6, n = 1.33, T = 6-i0 -s sec (R = 8.5-10 -8 cm [13]). Assuming that Ket does not exceed 3"10 I~ sec -~, which corresponds to the experimental data, we can determine the value of the factor K 2 according to the ForsterGalanin formula. The quantity K 2 = 1.25-10 -3 , and the angle between the dipole moments of the transitions is estimated at 88.0 ~ . If we assume Ket equal to 1.4.109 sec -i, which corresponds to the lower limit of the rate of energy transfer in the dimer, then the angle between the dipole moments of the transitions is found to be even closer to a right angle, 89.6 ~ . Thus, the Forster-Galanin theory is fully applicable to the calculation of the parameters of energy transfer in the chlorophyll dimer, predicting closeness to a 90 ~ angle between the dipole moments of the transitions of the interacting molecules. It seems to us that this result can be explained formally, considering that the length of the dipole, equal to 1.3 ~, found according to the dipole moment of the Qy transition of chlorophyll in the dimer [13],

570

is much less than the distance between the interacting dipoles. This conclusion supports our previous data on the correspondence of the curves of concentration depolarization of a chlorophyll solution in castor oil to the theory of inductive resonance all the way up to distances between molecules R = 15 ~ [21-22]. The method of hole burning yielded a uniform fluorescence spectrum of D~ in the case of selective excitation at the wavelength 686.71 nm. A uniform spectrum was obtained as the difference between the fluorescence spectrum at the excitation wavelength before and after hole burning and is presented in Fig. 7. A comparison of this spectrum with the fluorescence excitation spectrum of the dimer reveals many differences both in the positions of the major vibrational lines and in their intensities. The frequencies of the lines are compared in Table i. This result again shows that there is a perturbation of the D~ molecule by the D u molecule in the dimer. In view of the fact that the mutual positions of the D~ and D u molecules vary somewhat, mutual perturbation also varies and increases the spectral inhomogeneity of the components of the dimer. For this reason the uniform fluorescence spectrum of D~ is less sharp than, let us say, the spectrum of the monomer. Another vital difference in the selective properties of the excitation and fluorescence spectra is the absence of mirror symmetry - the excitation spectrum is substantially broader when the observed wavelength is approached than the fluorescence spectrum, which falls steeply at A > %excit (compare Fig. 5 and Fig. 7). This observation should again be related to the existence of energy transfer from D u to D~. A uniform fluorescence spectrum of D u cannot be recorded on account of the strong quenching of the fluorescence of D u as a result of the transfer of electronic energy to D~. LITERATURE CITED i. 2. 3. 4. 5. 6. 7. 8. 9. i0. ii. 12.

13. 14. 15. 16. 17.

18. 19. 20. 21. 22.

R. I. Personov, Selective Spectroscopy of Complex Molecules and Its Application [in Russian], Troitsk (1981). R. A. Avarmaa and A. P. Suisalu, Opt. Spektrosk., 56, 53-59 (1984). K. Kh. Mauring, I. V. Renge, and R. A. Avarmaa, Zh. Prikl. Spektrosk., 48, No. 3, 429436 (1988). R. Avarmaa and K. Rebane, Spectrosk. Acta, 41A, 1365-1380 (1985). I. Renge, K. Mauring, P. Sarv, and R. Avarmaa, J. Phys. Chem., 90, 6611-6616 (1986). I. Renge, K. Mauring, and R. Avarmaa, J. Lumin., 37, 207-214 (1987). T. P. Carter and G. 3. Small, J. Phys. Chem., 90, 1997-1998 (1986). R. Avarmaa, I. Renge, and K. Mauring, FEBS Lett., 167, 186-190 (1984). V. G. Maslov, A. S. Chunaev, and V. V. Tugarinov, Mol. Biol., 15, 788-79]. (]981). V. A. Shuvalov, A. Klevanik, A. O. Gonago, A. Ya. Shkuropatov, and V. S. Gubanov, FEBS Lett., 237, 57-60 (1988). J. K. Gillie, B. L. Fearey, J. M. Hayes, and G. J. Small, Chem. Phys. Lett., 134, 316323 (1987). R. Avarmaa, R. Jaaniso, K. Mauring, I. Renge, and R. Tamkivi, Mol. Phys., 57, 605-62] (1986). L. Shipman, M. Cotton, R. Norris, and J. Katz, J. Am. Chem. Soc., 9_88, 8222-8230 (1976). C. Houssier and K. Sauer, J. Am. Chem. Soc., 92, 779-791 (1979). A. P. Losev, I. N. Nichiporovich, E. I. Sagun, and G. D. Vasilenok, Dokl. Akad. Nauk BSSR, 31, 131-134 (1987). A. A. Krasnovskii (Krasnovsky), Jr., N. N. Lebedev, and F. F. Litvin, Studia Biophysics, 65, 81-89 (1977). S. S. Dvornikov, V. N. Knyukshto, K. N. Solov'ev, and M. P. Tsvirko, Opt. Spektrosk., 46, 689-695 (1979). R. V. Yaaniso and R. A. Avarmaa, Zh. P r i k l . S p e k t r o s k . , 44, No. 4, 601-606 ( ] 9 8 6 ) . H. Van der Laan, T. Schmidt, R. W. Visschers, K. J. Visschers, R. Van Grondlle, and S. Volker, Chem. Phys. Lett., 170, 231-238 (1990). A. Yu. Borisov, Biofizika, 32, No. 6, 1046-1061 (1987). E. I. Zen'kevich and A. P. Losev, Materials of the Conference of Young Scientists on Physics [in Russian], Minsk (1973), p. 24. A. P. Losev, Dissertation for the Degree of Doctor of Physicomathematical Sciences [in Russian], Minsk (1982).

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