Amplified emission of phthalocyanine isolated in cryogenic matrices

Laser induced fluorescence spectroscopy of free-base (H(2)Pc) and zinc (ZnPc) phthalocyanines trapped in rare gas and nitrogen matrices reveals a quite unexpected phenomenon with a moderate increase in the laser intensity. In all matrices except Xe, a huge increase occurs in the intensity of an emission band near 755 nm when pumping the S(1) <-- S(0) transition. The band involves a vibrational mode of the ground state, located at 1550 and 1525 cm(-1) for H(2)Pc and ZnPc, respectively. Many of the characteristics of amplified emission (AE) are exhibited by this vibronic transition. Excitation scans recorded for the AE band yield greatly enhanced site selectivity compared to what is obtained in normal fluorescence excitation scans.     

Amino-imino tautomerization reaction of the 4-aminopyrimidine/acetic acid system

The amino-imino tautomerization of the 4-aminopyrimidine (4APM)/acetic acid (AcOH) system through dual hydrogen bonding in n-hexane at room temperature was investigated using UV absorption and fluorescence spectroscopies, fluorescence time-profile measurements, and molecular orbital calculations, with those of the imino-model compound of 3-methyl-4(1H)-pyrimidinimine (3M4PMI). From the experimental results, it was confirmed that the imino-tautomer was formed in the first excited singlet state (S1) state through the double-proton transfer of the dual hydrogen-bonded complex of 4APM with AcOH. The fluorescences of the free 4APM monomer (band maximum at 353nm), imino-tautomer (at 414nm), and 3M4PMI monomer (at 437nm) exhibit the single-exponential decays of 98, 73, and 19ps time constants, respectively. The shorter decay time of the imino-tautomer fluorescence compared with the free monomer one is suggestive of the low activation energy process in the S1 state. From the result of the shortest decay time of the 3M4PMI fluorescence, it can be deduced that 3M4PMI has a non-planar structure in the S1 state. The theoretical calculations on the S0 and S1 state double-proton transfer for the 4APM/AcOH dual hydrogen-bonded system were performed with the use of formic acid (FoOH) in place of AcOH for the sake of simplicity. Only one peak of transition state was resolved in the S0 and S1 states. The energy barrier for the S1 state double-proton transfer of the 4APM/FoOH complex-->3H-4(1H)-pyrimidinimine/FoOH tautomer was estimated to be approximately 2kJmol(-1) using the CIS/6-31G(d) methods. On the other hand, the energy barrier for the S0 state reverse proton transfer of the 3H-4(1H)-pyrimidinimine/FoOH tautomer-->4APM/FoOH complex was estimated to be almost zero kJmol(-1) at B3LYP/6-31G(d) level.     

Vibrational energy relaxation of naphthalene in the S(1) state in various gases

Time-resolved fluorescence spectra of naphthalene in the S(1) state have been measured in various gases below 10(2) kPa. The band shape of the fluorescence changed in an earlier time region after the photoexcitation when an excess energy (3300 cm(-1)) above the 0-0 transition energy was given. The excitation energy dependence of the fluorescence band shape of an isolated naphthalene molecule was measured separately, and the time dependence of the fluorescence band shape in gases was found to be due to the vibrational energy relaxation in the S(1) state. We have succeeded in determining the transient excess vibrational energy by comparing the time-resolved fluorescence band shape with the excitation energy dependence of the fluorescence band shape. The excess vibrational energy decayed almost exponentially. From the slope of the decay rate against the buffer gas pressure, we have determined the collisional decay rate of the excess vibrational energy in various gases. The dependence of the vibrational energy relaxation rate on the buffer gas species was similar to the case of azulene. The comparisons with the results in the low temperature argon and the energy relaxation rate in the S(0) state in nitrogen were also discussed.     

Ultrafast photoinduced relaxation dynamics of the indoline dye D149 in organic solvents

The relaxation dynamics of the indoline dye D149, a well-known sensitizer for photoelectrochemical solar cells, have been extensively characterized in various organic solvents by combining results from ultrafast pump-supercontinuum probe (PSCP) spectroscopy, transient UV-pump VIS-probe spectroscopy, time-correlated single-photon counting (TCSPC) measurements as well as steady-state absorption and fluorescence. In the steady-state spectra, the position of the absorption maximum shows only a weak solvent dependence, whereas the fluorescence Stokes shift Δν?(F) correlates with solvent polarity. Photoexcitation at around 480 nm provides access to the S(1) state of D149 which exhibits solvation dynamics on characteristic timescales, as monitored by a red-shift of the stimulated emission and spectral development of the excited-state absorption in the transient PSCP spectra. In all cases, the spectral dynamics can be modeled by a global kinetic analysis using a time-dependent S(1) spectrum. The lifetime τ(1) of the S(1) state roughly correlates with polarity [acetonitrile (280 ps) < acetone (540 ps) < THF (720 ps) < chloroform (800 ps)], yet in alcohols it is much shorter [methanol (99 ps) < ethanol (178 ps) < acetonitrile (280 ps)], suggesting an appreciable influence of hydrogen bonding on the dynamics. A minor component with a characteristic time constant in the range 19-30 ps, readily observed in the PSCP spectra of D149 in acetonitrile and THF, is likely due to removal of vibrational excess energy from the S(1) state by collisions with solvent molecules. Additional weak fluorescence in the range 390-500 nm is observed upon excitation in the S(0)→S(2) band, which contains short-lived S(2)→S(0) emission of D149. Transient absorption signals after excitation at 377.5 nm yield an additional time constant in the subpicosecond range, representing the lifetime of the S(2) state. S(2) excitation also produces photoproducts.     

Early events in the photochemistry of 2-naphthyl azide from femtosecond UV/Vis spectroscopy and quantum chemical calculations: direct observation of a very short-lived singlet nitrene

Exposure of 2-naphthyl azide in acetonitrile at ambient temperature to femtosecond pulses of 266 nm light produces a transient absorption with maxima at 350 and 420 nm. The carrier of the 350 nm band decays more rapidly than that of the 420 nm band which has a lifetime of 1.8 ps. Analogous experiments with 1-chloro-2-naphthyl azide in methanol allow the assignment of the 350 nm band to a singlet excited state of 2-naphthyl azide and the carrier of the 420 nm band to singlet 2-naphthylnitrene. This reactive intermediate has the shortest lifetime of any singlet nitrene observed to date and is a true reactive intermediate. Computational studies at the RI-CC2 level of theory support these conclusions and suggest that initial excitation populates the S2 state of 2-naphthyl azide. The S2 state, best characterized as a pi --> (pi*, aryl) transition, has a geometry similar to S0. S2 of 2-naphthyl azide can then populate the S1 state, a pi --> (in-plane, pi*, azide) excitation, and in the S1 state, electron density is depleted along the proximal N-N bond. S1 is dissociative along that N-N coordinate to form the singlet nitrene, and with a barrier of only approximately 5 kcal/mol for N2 extrusion.     

Assignment of the lowest Qy-state and spectral dynamics of the CP29 chlorophyll a/b antenna complex of green plants: a hole-burning study

Low-temperature absorption, fluorescence and persistent non-photochemical hole-burned spectra are reported for the CP29 chlorophyll (Chl) a/b antenna complex of photosystem II of green plants. The absorption-origin band of the lowest Qy-state lies at 678.2 nm and carries a width of approximately 130 cm-1 that is dominated by inhomogeneous broadening at low temperatures. Its absorption intensity is equivalent to that of one of the six Chl a molecules of CP29. The absence of a significant satellite hole structure produced by hole burning, within the absorption band of the lowest state, indicates that the associated Chl a molecule is weakly coupled to the other Chl and, therefore, that the lowest-energy state is highly localized on a single Chl a molecule. The electron-phonon coupling of the 678.2 nm state is weak with a Huang-Rhys factor S of 0.5 and a peak phonon frequency (omega m) of approximately 20 cm-1. These values give a Stokes shift (2S omega m) in good agreement with the measured positions of the absorption band at 678.2 nm and a fluorescence-origin band at 679.1 nm. Zero-phonon holes associated with the lowest state have a width of approximately 0.05 cm-1 at 4.2 K, corresponding to a total effective dephasing time of approximately 400 ps. The temperature dependence of the zero-phonon holewidth indicates that this time constant is dominated at temperatures below 8 K by pure dephasing/spectral diffusion due to coupling of the optical transition to the glass-like two-level systems of the protein. Zero-phonon hole-widths obtained for the Chl b bands at 638.5 and 650.0 nm, at 4.2 K, lead to lower limits of 900 +/- 150 fs and 4.2 +/- 0.3 ps, respectively, for the Chl b-->Chl a energy-transfer times. Downward energy transfer from the Chl a state(s) at 665.0 nm occurs in 5.3 +/- 0.6 ps at 4.2 K.     

Polymer monolayers with a photosensitive crown‐ether

The mixed monolayers of a photosensitive crown‐ether (CE) and poly(maleic acid hexadecyl monoamide‐alt‐propylene) (P12) have been prepared and studied. Fluorescence spectra of CE have a strong band at 530–535 nm in solution (monomer) or at 593–603 nm in transferred monolayers (aggregates). Due to the interaction with polymer the fluorescence maximum of CE is shifted to 530 nm in the mixed monolayers with P12.     

The effect of decreasing temperature up to chilling values on the in vivo F685/F735 chlorophyll fluorescence ratio in Phaseolus vulgaris and Pisum sativum: the role of the photosystem I contribution to the 735 nm fluorescence band

The effect of leaf temperature (T), between 23 and 4 degrees C, on the chlorophyll (Chl) fluorescence spectral shape was investigated under moderate (200 microE m-2 s-1) and low (30-35 microE m-2 s-1) light intensities in Phaseolus vulgaris and Pisum sativum. With decreasing temperature, an increase in the fluorescence yield at both 685 and 735 nm was observed. A marked change occurred at the longer emission band resulting in a decrease in the Chl fluorescence ratio, F685/F735, with reducing T. Our fluorescence analysis suggests that this effect is due to a temperature-induced state 1-state 2 transition that decreases and increases photosystem II (PSII) and photosystem I (PSI) fluorescence, respectively. Time-resolved fluorescence life-time measurements support this interpretation. At a critical temperature (about 6 degrees C) and low light intensity a sudden decrease in fluorescence intensity was observed, with a larger effect at 685 than at 735 nm. This is probably linked to a modification of the thylakoid membranes, induced by chilling temperatures, which can alter the spill-over from PSII to PSI. The contribution of photosystem I to the long-wavelength Chl fluorescence band (735 nm) at room temperature was estimated by both time-resolved fluorescence lifetime and fluorescence yield measurements at 685 and 735 nm. We found that PSI contributes to the 735 nm fluorescence for about 40, 10 and 35% at the minimal (F0), maximal (Fm) and steady-state (Fs) levels, respectively. Therefore, PSI must be taken into account in the analysis of Chl fluorescence parameters that include the 735 nm band and to interpret the changes in the Chl fluorescence ratio that can be induced by different agents.     

Photophysical properties of oligo(2,3-thienyleneethynylene)s

Photophysical properties of oligo(2,3-thienyleneethynylene)s (nTE, n denotes the number of thiophene rings, n = 2, 3) in benzene were investigated using steady-state, time-resolved fluorescence, and transient absorption spectroscopies. For 2TE, generation of the radiative S2 and nonradiative S1 states was confirmed. Upon excitation, the S2 state was initially generated and deactivated to the S1 state within 10 ps. The S1 state exhibited the transient absorption band at 470 nm, of which the lifetime was estimated to be 5.3 ns. In the case of 3TE, on the other hand, it was revealed that the radiative S1 state with a transient absorption peak at 650 nm was generated upon excitation. The T1 states of nTE were generated from the S1 states. The quantum yields were estimated to be 0.52 and 0.54 for 2TE and 3TE, respectively. Extremely fast reactions in the higher triplet excited state were indicated for both 2TE and 3TE.     

Excited-state processes in the carotenoid zeaxanthin after excess energy excitation

Aiming for better understanding of the large complexity of excited-state processes in carotenoids, we have studied the excitation wavelength dependence of the relaxation dynamics in the carotenoid zeaxanthin. Excitation into the lowest vibrational band of the S2 state at 485 nm, into the 0-3 vibrational band of the S2 state at 400 nm, and into the 2B(u)+ state at 266 nm resulted in different relaxation patterns. While excitation at 485 nm produces the known four-state scheme (S2 --> hot S1 --> S1 --> S0), excess energy excitation led to additional dynamics occurring with a time constant of 2.8 ps (400 nm excitation) and 4.9 ps (266 nm excitation), respectively. This process is ascribed to a conformational relaxation of conformers generated by the excess energy excitation. The zeaxanthin S state was observed regardless of the excitation wavelength, but its population increased after 400 and 266 nm excitation, suggesting that conformers generated by the excess energy excitation are important for directing the population toward the S state. The S2-S1 internal conversion time was shortened from 135 to 70 fs when going from 485 to 400 nm excitation, as a result of competition between the S2-S1 internal conversion from the vibrationally hot S2 state and S2 vibrational relaxation. The S1 lifetime of zeaxanthin was within experimental error the same for all excitation wavelengths, yielding approximately 9 ps. No long-lived species have been observed after excitation by femtosecond pulses regardless of the excitation wavelength, but excitation by nanosecond pulses at 266 nm generated both zeaxanthin triplet state and cation radical.     

Excitation wavelength dependence of the proton-transfer reaction of the green fluorescent protein

Picosecond time-correlated single-photon counting was used to measure the proton-transfer rate of green fluorescent protein (GFP) excited by several wavelengths between 266 and 405 nm. When samples of GFP in water and D2O are excited at short wavelengths, lambda(ex) < 295 nm, the fluorescence properties are largely modified with respect to excitation at a wavelength around 400 nm, the peak of the absorption band of the S0 --> S1 transition of the ROH form of the chromophore. The shorter the excitation wavelength, the longer the decay time of the ROH emission band at 450 nm and the longer the rise time of the RO- emission band at 512 nm. The proton transfer is slower by an order of magnitude and about a factor of 3 when GFP in water and D2O are excited by 266 nm, respectively.     

Highly sensitive detection of discrete absorption and B-type delayed fluorescence of dibenzanthracene in PMMA

High resolution S0 --> Sn and T1 --> Tn electronic absorptions and B-type delayed fluorescence of 1,2,7,8-dibenzanthracene in polymethylmethacrylate (PMMA) were experimentally observed by flash and laser flash photolysis technique. Dibenzanthracene molecules were excited in a two-step process. In the first step, an excited singlet is created, which undergoes intersystem crossing to triplet state, then T-T absorption creates an excited triplet dibenzanthracene molecule, which returns to the first excited singlet level by intersystem crossing. The re-created first excited singlet of dibenzanthracene decays back to the ground state by emitting B-type of delayed fluorescence, which was observed at the same emission band of prompt (normal) fluorescence, and R-, E-, P-types of delayed fluorescences. For normal fluorescence, S1 state is decaying to S0 ground state. For E- and P-type of delayed fluorescences, T1 state is decaying to S0 via S1 state, and for B-type of delayed fluorescence, T2 state is decaying to S0 via S1 state.     

Time-resolved spectroscopy of the excited singlet states of tirapazamine and desoxytirapazamine

Laser flash photolysis (LFP, 400 nm excitation) of the anti-cancer drug tirapazamine (TPZ) in acetonitrile produces the singlet excited-state S1 with lambda(max) = 544 nm. The lifetime of this state is 130 ps, in good agreement with the reported fluorescence lifetime. The excited state is reduced to the corresponding radical anion by KSCN or KI. The spectrum of the radical anion is in good agreement with previously reported pulse radiolysis studies and time-dependent density functional theory (TD-DFT) calculations. LFP of desoxytirapazamine (dTPZ) also produces the first excited singlet state, S1. The fluorescence quantum yield and lifetime (5.4 ns) of the dTPZ singlet excited state are both much greater than the corresponding values of TPZ. This is explained by DFT calculations that predict that cyclization of TPZ to form an oxaziridine is thermodynamically facile but that cyclization of dTPZ to form an oxadiaziridine is not. Thus, the S1 state of TPZ has a short lifetime and low fluorescence quantum yield due to ready cyclization whereas the cyclization of the S1 state of dTPZ is unimportant and does not limit either the fluorescence quantum yield or the fluorescence lifetime. This conclusion is confirmed by studies of dTPZ', an isomer of dTPZ containing the C=N-O moiety which has a low quantum yield and short fluorescence lifetime similar to that of TPZ.     

Vibronic structure in the S1-S0 transition of jet-cooled dibenzofuran

Fluorescence excitation spectra of dibenzofuran in a supersonic jet are observed and the vibronic structure is analyzed for the S(1) (1)A(1) (pipi) and S(0) states. An observation of the rotational envelopes reveals that the band is a B-type band. However, it is shown that most of the strong vibronic bands are A-type bands. The intensity arises from vibronic coupling with the S(2) (1)B(2) state. We find a broad emission in the dispersed fluorescence spectrum for the excitation of the high vibrational levels in the S(1) state. This indicates that intramolecular vibrational redistribution (IVR) occurs efficiently in the isolated dibenzofuran molecule.     

Spectroscopic studies of a near-infrared absorbing pH sensitive aminodienone-carbocyanine dye system

Synthetic red and near-infrared absorbing dyes may be used as probe molecules in a large number of applications. Dyes exhibiting spectral changes with hydrogen ion concentration are useful as pH probes. Those dyes which have their absorption and fluorescence maxima in the long wavelength region of the visible spectral region are specially valuable because of decreased interference and semiconductor laser applications. In this paper we have evaluated an aminodienone dyes 1 which demostrates pH dependent absorption and fluorescence spectra as well as solvent polarity dependence. In organic solvents the long wavelength absorption band of the dye is in the reduced interference region. The absorption maximum is at 535 nm in neutral or alkaline solutions in methanol. The absorption spectra undergo a strong bathochromic shift in the presence of acids (lambda(max) = 709 nm) with a concomitant change in the fluorescence spectra. This pH sensitive dye was found to be specially especially useful for organic solvents. The analytical utility of this and similar near-infrared absorbing dyes is discussed.     

Spectral image adaptation and visual experience of DBA/PMMA

High resolution S0-->Sn and T1-->Tn electronic absorptions and B-type delayed fluorescence of 1,2,7,8-dibenzanthracene in polymethylmethacrylate (PMMA) were experimentally observed by flash and laser flash photolysis technique. Dibenzanthracene (hereafter DBA) molecules were excited in a two-step process. In the first step, an excited singlet is created, which undergoes intersystem crossing to triplet state, then T-T absorption creates an excited triplet dibenzanthracene molecule, which returns to the first excited singlet level by intersystem crossing. The re-created first excited singlet of dibenzanthracene decays back to the ground state by emitting B-type of delayed fluorescence, which was observed at the same emission band of prompt (normal) fluorescence, and R-, E-, P-types of delayed fluorescences. For normal fluorescence, S1 state is decaying to S0 ground state. For E- and P-type of delayed fluorescences, T1 state is decaying to S0 via S1 state, and for B-type of delayed fluorescence, T2 state is decaying to S0 via S1 state. The spectrum image showing the absorption/emission bands mentioned was also examined by image processing techniques in order to improve the visual experience of each band by localizing to a specific region of interest (ROI). Experimental results illustrate how the exact location of emission/absorption bands was clearly extracted from the spectral image and further improvements in the visual detection of absorption/emission bands.     

Solvent Polarity and pH Effects on the Spectroscopic Properties of Neutral Red: Application to Lysosomal Microenvironment Probing in Living Cells

Neutral red is a lysosomal probe and a biological pH indicator. In aqueous solutions, the protonated (NRW) and neutral (NR) forms of monomeric neutral red exhibit distinct absorption maxima (535 and 450 nm, respectively) but have the same fluorescence with a maximum at 637 nm and a quantum yield of 0.02. The similarity of the fluorescence spectra at acidic and basic pH suggests deprotonation of cationic species in the first singlet excited state. The NR fluorescence strongly depends on the solvent polarity as shown by addition of increasing amounts of water to pure dioxane, which gradually shifts the fluorescence maximum from 540 nm in pure dioxane to 637 nm in water. The fluorescence quantum yield increases from 0.17 in dioxane to 0.3 upon addition of 7% water and then decreases, reaching 0.02 in pure water. Immediately after incubation of human skin fibroblasts with neutral red, excitation with 435 nm light produces a fluorescence whose maximum is recorded at 575 nm. This fluorescence is located in the perinuclear region and originates from large fluorescent intracytoplasmic spots, suggesting staining of the endoplasmic reticulum-Golgi complex. At longer times, this fluorescence is shifted to 606 nm, suggesting slow diffusion of the lysosomotropic dye toward the more hydrated and acidic interior of ly-sosomes. Addition of a lysosomotropic detergent to cells previously incubated with neutral red shifts the fluorescence to the blue. Thus, in complex biological systems, this probe cannot be a good pH indicator but is a very sensitive probe of lysosomal rnicroenvironrnents.     

Spectroscopic characterization of intramolecular charge transfer of sodium 4-(N,N-dimethylamino)naphthalene-1-sulfonate

In this paper, a new dual fluorescent N,N-dimethylaminonaphthalene derivative, sodium 4-(N,N-dimethylamino)naphthalene-1-sulfonate (SDMDNS), was reported. It was found that SDMDNS emits dual fluorescence only in highly polar solvent water but not in organic solvents such as methanol, dioxane and acetonitrile. Only a single broad band emission at ca. 420 nm was observed in the short wavelength region in organic solvents. The dual fluorescence of SDMDNS in water was found at 423 and 520 nm, respectively. Introduction of organic solvent as ethanol into aqueous solution of SDMDNS leads to blue shift of the long-wavelength emission, and this was evidently supported by introduction of cyclodextrin or surfactant in the aqueous solution. It indicates that a highly polar solvent was required to bring out dual fluorescence; furthermore, the short wavelength fluorescence is emitted from locally excited (LE) state and the long wavelength fluorescence is emitted from charge transfer (CT) state. The pH dependence of the dual fluorescence of SDMDNS demonstrates that the neutral form of the molecular has a higher ratio of CT band intensity to LE band. Temperature effect on the excited state of SDMDNS was also examined and gave stabilization enthalpy (-DeltaH ) of the CT reaction 8.7 kJ mol(-1).     

Femtosecond fluorescence study of the reaction pathways and nature of the reactive S1 state of cis-stilbene

We report a femtosecond time-resolved fluorescence study of cis-stilbene, a prototypical molecule showing ultrafast olefinic photoisomerization and photocyclization. The time-resolved fluorescence signals were measured in a nonpolar solvent over a wide ultraviolet-visible region with excitation at 270 nm. The time-resolved fluorescence traces exhibit non-single exponential decays which are well fit with bi-exponential functions with time constants of τ(A) = 0.23 ps and τ(B) = 1.2 ps, and they are associated with the fluorescence emitted from different regions of the S(1) potential energy surface (PES) in the course of the structural change. Quantitative analysis revealed that the two fluorescent components exhibit similar intrinsic time-resolved spectra extending from 320 nm to 700 nm with the (fluorescence) oscillator strength of f(A) = 0.32 and f(B) = 0.21, respectively. It was concluded that the first component is assignable to the fluorescence from the untwisted S(1) PES region where the molecule reaches immediately after the initial elongation of the central C[double bond, length as m-dash]C bond, while the second component is the fluorescence from the substantially twisted region around a shallow S(1) potential minimum. The quantitative analysis of the femtosecond fluorescence data clearly showed that the whole isomerization process proceeds in the one-photon allowed S(1) state, thereby resolving a recent controversy in quantum chemical calculations about the reactive S(1) state. In addition, the evaluated oscillator strengths suggest that the population branching into the isomerization/cyclization pathways occurs in a very early stage when the S(1) molecule still retains a planar Ph-C[double bond, length as m-dash]C-Ph skeletal structure. On the basis of the results obtained, we discuss the dynamics and mechanism of the isomerization/cyclization reactions of cis-stilbene, as well as the electronic structure of the reaction precursor.     

INTERACTIONS AMONG PHOTOSYNTHETIC ANTENNA EXCITED STATES

Abstract. The data of Kung and DeVault (1978) showing high-order fluorescence from chromatophores of photosynthetic bacteria are analyzed in relation to other data on first-order fluorescence of photosynthetic systems, particularly that of Monger and Parson (1977). The wavelengths of emission observed (down to 445 nm) require energy equivalent to two lowest singlet-excited states. The dependence on excitation intensity is best explained by any of the following third-order processes: (a) 3 S ₁→3 S ₀; (b) 2 S ₁+ T , → 2 S ₀+ T ₁; (c) S ₁+ 2 T ₁→ 3 S ₀. However, (c) is ruled out because it predicts heavy T ₁-destruction which is not observed. Contribution from the second order process: 2 S ₁→ S ₀ is probable, but even the data of Monger and Parson show that it is insufficient by itself. Two-photon absorption: S ₀+ hv ₁→ S ₁; S ₁+ hv ₁→ S _n; S _n S ₀+ hv ₂ could also account for the high-order fluorescence and its dependence on excitation intensity. [ S ₀, S ₁ S _n are ground, first excited and a higher excited singlet states, respectively, of antenna bacteriochlorophyll, T _t is the lowest triplet state, c/v , is the exciting wavelength (694 or 868 nm) and c/v ₂ the wavelength of the high-order fluorescence (445, 535. or 600 nm), where c = velocity of light.] Maximum values are estimated for some of the rate constants.