TRIPLET LIFETIME DEPENDENCE ON VIBRATIONAL ENERGY FOR GAS-PHASE

CARBONYL AROMATIC COMPOUNDS: BENZOPHENONE AND FLUORENONE

G.A. Zalesskaya*, D.L. Yakovlev, E.G. Sambor

Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus,

Scaryna Av. 70, 220072 Minsk, Belarus

zalesskaya@imaph.bas-net.by

A strong increase in triplet decay rates by over three orders of magnitude under IR laser excitation of gas phase triplet molecules was revealed. The dependences of intensities and decay rates of CO₂ laser induced delayed fluorescence on vibrational energy and bath gas pressure were used to study dominant relaxation pathways in the lowest triplet state T₁ within a wide range of vibrational energy E_vib. With this end in view, the excess energy dependence for decay rates of all nonradiative relaxation processes in T₁ such as the intersystem crossing from the triplet state T₁ to the ground state S₀, the reversible intersystem crossing between excited singlet S₁ and triplet T₁, as well as a rate of competiting intermolecular vibrational relaxation were compared. It was found that under vibrational equilibrium at high vibrational temperature (T_vib>>T) the experimentally observed nonexponential dependence of the gas phase triplet molecule decay time on E_vib reflected the excess vibrational energy (in T₁) dependence of intersystem crossing rate from T₁ to S₀ that was well approximated by Arrhenius’ activated type rate equation in contrast to exponential decay for an isolated molecule.

Introduction

            The photochemical and photophysical properties of carbonyl aromatic compounds in the triplet state are currently of interest due to their ability to participate in many important photochemical reactions sensitized by triplet ketones such as hydrogen atom, electron and proton transfer. Many aspects of these reactions are important for understanding of the fundamental processes in chemical and biological systems.

            Much attention has been paid to decay processes in triplet states. In fact, great care was taken to study the sensitivity of triplet state decay time to both the intrinsic molecular parameters and environment properties in different media. Laser spectroscopy study of gas phase systems over a wide range of vibrational energies permitted us to obtain the important information about dominant pathways of triplet molecule relaxation. The additional data for the bath gas influence on the intensities and the decay rates of delayed fluorescence of vibrationally excited triplet molecules link spectroscopic information of an isolated molecule and a molecule in the dense medium. Gas phase data can be utilized to provide the prediction of the photophysics of complex molecules under study in a condensed phase over a broad temperature range.

            In works [1,2], we demonstrated that delayed fluorescence (DF) induced by direct infrared multiphoton excitation (IRMPE) of triplet state molecules by CO₂ laser radiation can be successfully used to study the excess energy dependence of nonradiative relaxation rates in the triplet state T₁. It was noted that the advantage of this method was the possibility to change the vibrational energy of triplet molecules over a wide range because the intensity and decay rate of DF of vibrationally excited molecules proved to be very sensitive to a laser energy density.

Methods

            In the present work, by utilizing the method for triplet molecule IRMPE we have studied the excess energy dependence for the intersystem crossing (ISC) rate from the triplet state T₁ to the ground state S₀, for the rates of the reversible ISC between the singlet state S₁ and the triplet state T₁ as well as the rates of competitive process of intermolecular vibrational relaxation in the state T₁ within a wide vibrational energy interval. Such a complex study of nonradiative transitions permits the determination of the fate both of an isolated triplet molecule and a collisional perturbed one.

            The chosen molecules of benzophenone (C₁₃H₁₀O), fluorenone (C₁₃H₈O) have IR absorption bands in the CO₂ laser radiation region and can be IRMPE by CO₂  laser radiation both in the ground electronic and in the triplet state T₁. They process a high average vibrational energy áE_vibñ = 3100 cm^-1 at an initial temperature of 380K for benzophenone and áE_vibñ = 3000 cm^-1 at 428K for fluorenone and emit long–lived luminescence in the gas phase due to efficient singlet–triplet interaction between the first excited singlet S₁ and triplet T₁. At the initial temperature of experiment the delayed emissions mainly correspond to delayed fluorescence with a decay time of 160 ms for benzophenone (T=380K) and 420 ms for fluorenone (T=428K). It is worth noting, whereas benzophenone is characterized by a low electron energy gap, DE_ST @ 2000 cm^-1, between S₁ and T₁, the corresponding value for fluorenone is much larger (5400<DE_ST<7000 cm^-1).

            The experimental technique used in the present work was described previously [1,2]. Rapid ISC of molecules under study was exploited to prepare them in the triplet state T₁. The nitrogen laser was used to excite a molecule to the singlet state S₁. IR excitation of triplet molecules was produced by TEA CO₂ laser radiation that was focused by lenses from blenched Ge and was passed through a cell beam to a beam with visible light. The samples to be irradiated were prepared in a high vacuum line–provided cylindrical heated cell with NaCl windows. Zone refined substances were stored in the side arm of the quartz cell. A vapor pressure was controlled by a temperature of the thermostated side reservoir. Vapors were diluted with a large quantity of bath gases: He³, Kr, N₂ (0<P_bg<20 Torr). Luminescence was observed in the direction normal to excitation. A signal of the photomultiplier placed behind the monochromator slit came to the digital oscilloscope and was averaged over several pulses by a computer.

Results and discussion

            For relaxation processes within a wide interval of the vibrational energy of the triplet molecules and bath gas pressure to be analyzed, the following results are of special importance.

1. CO₂ laser activated emissions were observed only in the spectral regions of usual luminescence. The spectra were slightly shifted to the high–frequency region as compared to those of thermally activated molecules. This effect was caused by reducing of the role of “hot” phosphorescence and observed in other cases at nonequilibrium vibrational excitation of the triplet molecules.

2. As discussed in our previous works [1,2], the decay of CO₂ laser induced DF proved to be nonexponential and exhibited two exponential decay behaviors characterized by two distinct decay rates:

I(n,t)=I₁×exp(-K₁t)+ I₂×exp(-K₂t)

where K₁ and K₂ were equal to 10⁶, 10⁴ s^-1 and 10³, 10² s^-1, respectively. The decay rates of DF are independent of the observation wavelength for l_ob = 400–580 nm, as it is typical for DF of molecular systems characterized by the efficient ISC. The decay rates of a fast component of both benzophenone and fluorenone increased by several orders of magnitude with a rise of CO₂ laser energy density E_CO2. The dependence of K₁ on E_CO2 was essentially distinguishable at different bath gas pressure.

3. At energy densities E_CO2 sufficient to induce DF of fluorenone the decay rates of the fast component of DF linearly increased with increasing bath gas pressure P_bg only in a limited range of pressures. At a higher pressure, the decay rates remained unaltered. The added bath gas caused the decrease of benzophenone DF decay rates K₁ at low E_CO2 and the increase at E_CO2>1.2 J/cm².

Intermolecular relaxation at MPE of triplet molecules.

            To consider photophysical processes in the state T₁ at high E_vib, let us analyze the features of intermolecular vibrational relaxation as a main competitive process after the MPE of triplet molecules. (1) An important feature of multiphoton excited molecules that have more than 60 vibrational degrees of freedom, is a rapid redistribution of excitation energy from the levels of excited vibration to the triplet manifold of vibrational states during an IR laser pulse. A time resolution of experiment permits us to study vibration–translation (V–T) relaxation and is insufficient to determine the decay rates of vibration–vibration (V–V) relaxation. (2) MPE of triplet molecules causes a population of quasicontinuum states. Therefore, the excitation process should be reliably considered to be incoherent. Thus, the time variation of vibrational level population may be obtained from solving a set of coupled rate equations for radiative pumping in a quasicontinuum. That is why, we can easily predict a vibrational level population and evaluate an average vibrational energy of triplet molecules. (3) In vapors at a pressure of 10^-3<P_V<0.15 Torr, when only several collisions may occur during a full IR laser pulse, we can neglect the influence of collisions on the population distribution. Maximum vibrational temperatures, T_vib, achieved at MPE were estimated from comparison of intensities and decay rates of laser activated and thermally activated DF. (4) Collisions between excited molecules and bath gas particles change the MPE conditions that now depend on E_CO2 and P_bg. By varying these values, we can control the condition of establishing vibrational distribution during the laser pulse. As P_bg increases and E_CO2 decreases, the population distribution over vibrational levels in the triplet states is shifted to the region of low energies. It is worth noting that at the achieved excitation rates, K_ex, the bath gas pressures used were insufficient to establish the steady state regime (K_ex=K_V), at which E_vib does not any more increase.

            Intermolecular vibrational relaxation in mixtures of vibrationally excited molecules and bath gases reduces some part of the triplet molecules excited above the singlet state S₁. As a result, the time–resolved intensities, I(n,t), of the fast component decrease and its decay rates K₁ increase with P_bg. This experimental information was adopted to determine the quantitative characteristics of vibrational energy transfer such as a collisional efficiency b=K_col/Z=DK₁/DP×Z and average energy transferred per one collision áDEñ=E_vib×b as well as their excess energy dependence. Here K_col and Z are the rate constants of intermolecular vibrational relaxation and gas kinetic collisions, respectively. It was found that b and áDEñ have small values typical for the vibration–translation process. In mixtures with Kr, He³, N₂ at vibrational energies used they change over the range 10^-4<b<3×10^-4 and 3<áDEñ<20 cm^-1, thereby increasing with E_vib in just the same way as the rate of intermolecular vibrational relaxation. Conversion of vibrational energy to translational one involves as much as 10³–10⁴ collisions.

The vibrational energy dependence of T₁S₀ ISC rate

            The decay rates of DF are determined by a sum of radiationless transitions that usually exceed radiative ones. Depending on excitation energy, vapor or bath gas pressures, possible processes that can promote deactivation of vibrationally excited triplet molecules are intermolecular vibrational relaxation at a rate K_V=K₀+K_col×P, or intersystem crossing T₁S₀ of vibrationally excited and thermalized triplet molecules at rates of K^*_TS0 or K_TS0, respectively. The intersystem crossing T₁S₀, whose rate K_TS0 is a strongly increasing function of E_vib, may be rate determining for the decay process under some experimental conditions. For the considered molecules, this situation is implemented both at low pressures, when intermolecular vibrational relaxation is not yet important for the decay processes, and over the pressures range with K_V>K_TS0. In the intermediate pressure interval collisional energy transfer is rate determining. Thus, the competition of these processes manifests itself in changes of bath gas pressure dependence of time–resolved and time integrated intensities on E_CO2. Initially, the intensities increase with E_vib due to high vibrational level population of T₁ and then mainly decrease with increasing an ISC rates. In addition, it was tested carefully that bimolecular processes such as triplet–triplet annihilation, triplet – ground state interactions and photochemical processes did not alter the triplet state concentration. The dependences of I_int on E_CO2 in fluorenone mixed with Kr demonstrate (Fig. 1) that after adding a bath gas the ISC T₁S₀ becomes rate determining for DF decay at a significantly higher E_CO2. In such a case, the range of the laser energy densities corresponding to the increase in the time–integrated intensity with E_CO2 extends in the direction of high values of E_CO2. This result is due to lowering of maximum T_vib and E_vib in mixtures of excited molecules and bath gases in comparison with pure vapors. Estimations show that I_int starts to decease at

different E_CO2 but at the same vibrational energy (E_vib@22000 cm^-1) in all cases.

            The similar results are obtained for benzophenone. The dependences of K₁ and I(n,t) on P_bg indicate that decreasing decay rates as well as leveling–off intensities take place at the same E_vib@17000cm^-1. At higher energies the time–integrated intensities and decay rates of fast and slow components of DF do not change mor

e with P_bg (Table 2). This is statistical limit behavior characterized by the absence of nonradiative relaxation rate dependence on pressure. Above the estimated E_vib, the quasicontinuum conditions are fulfilled and DF decay is determined by intramolecular processes in T₁. At vibrational energy under consideration, the collisional (Dn_col@h×K_col×P=10^-6 cm^-1) and laser broadening widths (Dn_ex@h×t_P/sI_L=10^-4 cm^-1) are much higher than a level energy difference because at this E_vib we have a density of vibration levels as high as 10^{10 1}/_cm-1. Vibrational level densities higher than 10^{6 1}/_cm-1 are necessary but insufficient to form quasicontinuum. It is good evidence that unharmonic coupling may exist only between specific modes of large complex molecules, but seems to be negligible for many other modes.

            It is a well–known fact that the temperature dependence of thermally activated DF decay rates is determined by the process of ISC to the ground state, which has significant activation energies with a barrier height determined by energy corresponding to the crossing point between the potential surfaces involved in the transition. At vibrational equilibrium the triplet decay rates for chosen molecules increase by over several orders of magnitude as vibrational energy, E_vib, ranges from 3000 cm^-1 to 20000 cm^-1. Over a wide interval of vibrational energies as well as over a more narrow one that was attainable in the previous study, these dependences (K_dec on E_vib) are nonexponential and, as seen from Fig. 2, are well described by Arrhenius’ activated type rate equation which gives an activation energy of 4093 cm^-1 and 2547 cm^-1, pre–exponentials of 3.4×10⁹ s^-1 and 1.3×10⁷ s^-1 for benzophenone and fluorenone, respectively. Thus, the nonexponential behavior like Arrhenius’ one which was found in many works for the temperature dependence of DF and phosphorescence decay rates proves to be correct for the vibrational energy dependence under vibrational equilibrium at T_vib>>T. The additional data also plotted in Figure 2 are the known triplet decay rates for benzophenone and fluorenone in crystals, solutions as well as decay rates obtained from temperature static gas phase measurement of delayed emission. It should be emphasized that at the lowest temperature in a gas phase the lifetime approaches that obtained in solutions, and the latter correlates with the lifetime in glasses at very low temperatures (77K). This is further evidence of the common nature of the triplet lifetime decrease with temperature in a neutral medium stipulated by the process of ISC T₁S₀. The triplet decay rate dependence on vibrational energy was a simple exponential function at a low vapor pressure, when the conditions are close to collision–free ones, and also at low bath gas pressure if K_TS0>K_V.

The vibrational energy dependence of ISC T₁S₀ rate for isolated molecule

            The thermally averaged decay rate K(T) experimentally obtained under the conditions of high rates of intermolecular relaxation can be expressed in terms of a level density N(E) and microscopic decay rates of independently decaying levels, K_j, so that:

            K(T) = òdEN_i(E_j)exp(-E/kT)K_i(E_j) / òdEN_i(E_j)exp(-E/kT).           (1)

Thus, Eq. (1) couples microscopic time–resolved spectroscopic information about an isolated molecule with kinetic information in a dense medium and vice versa. In the present work, to predict the rates of relaxation processes for an isolated molecule the solution was obtained for the relevant set of coupled rate equations describing the population changes in the states S₀, S₁ and T₁. In order to avoid unnecessary complications, the simplified kinetic scheme was used. The vibrational levels of the triplet state were presented as a set of equidistant levels with an energy gap of 0.1 cm^-1. Only one level was suggested in S₁. Assuming also that the rates of reversible S₁T₁ ISC are determined by the density of vibrational levels in the final electronic states. In addition, K_TS0 was approximated by the relation: K_TS0 = C₁× exp(C₂×E_j). In such a case, the necessary differential equations can be written as:

where n_T = n₀, n_S1 = n_S0 = 0 are the total populations in the states T₁, S₁ and S₀ at t=0, n_m is the population of the vibration level m, r_m is the population distribution function satisfying the condition

 l is the number of a vibrational level in the triplet state region where the triplet vibrational level does not yet interact with the vibrational level of the singlet state, i.e. DE_ST = 0.1(l+1) cm^-1 (DE_ST @ 2000 cm^-1 for benzophenone and DE_ST @6000 cm-1 for fluorenone were used). Temperature dependences of intensities and decay rates of thermally activated DF were employed to determine varying parameters l, C₁ and C₂. By utilizing the density of states calculated for benzophenone and for fluorenone and well-known radiative rates: K_S0 = 3.3×10⁵ с^-1, K_T0 = 1.4×10² с^-1 for benzophenone and K_S0 = 3×10⁶ с^-1, K_T0 = 5 с^-1 for fluorenone, we can predict absolute values of nonradiative process rates and their energy dependences.

1)      Nonradiative rate K_T1S1 increases rapidly in an almost exponential fashion over a wide vibrational energy range.

2)      K_T1S0 appears to increase with vibrational energy of triplet molecules that is typical for radiationless transition rates.

3)      K_S1T1 decreases slowly with vibrational energy mainly due to a decrease of such a governing factor as the ratio N_T(E)/N_S(E) in a vibrational energy region under study. On the other hand, the coupling matrix element of singlet–triplet interaction is smeared out over a greater number of vibrational states, thus decreasing it as the density of vibrational states goes up with E_vib. This collection of data was checked by utilizing the microscopic experimental data for decay rates of fluorenone DF obtained in a low pressure gas phase as well as by comparing the calculated DF pulse for benzophenone at given E_vib with experimental one initiated by CO₂ laser radiation. Experimental and calculated values prove to be in good agreement (Fig. 4).

Conclusions

The energy dependence of nonradiative transition rates for the vibrationally excited triplet molecules was determined within the wide range of vibrational energies up to 20000 cm^-1 (in T₁). For gas phase benzophenone and fluorenone the rates of DF decay apparently varied by over several orders of magnitude as vibrational energy of the triplet molecules, E_vib, ranged from 3000 cm^-1 to 20000 cm^-1.

V–T relaxation was found to be responsible for the pressure dependence of the DF decay rates after MPE of the triplet molecules by CO₂ laser pulse (a half width of about 50 ns). The values of vibrational energies were estimated corresponding to the statistical limit conditions when the triplet molecule decay can be ascribed only by the unimolecular decay rates.

One of the most interesting conclusion to emerge from this investigation was that under vibrational equilibrium (K_V> K_TS0) at T_vib>>T for gas phase benzophenone and fluorenone the ISC T₁S₀ rate dependences on E_vib were well approximated by Arrhenius’ activated type rate equation as well as it was found in many works for the temperature dependence triplet molecule decay rates in condense neutral media.

Within the same vibrational energy range the energetic dependences of the rates K_S1T1 and K_T1S1 for reversible ISC between S₁ and T₁ demonstrated different behaviour for an isolated molecule: as the rate K_T1S1 was an exponential function of E_vib, whereas the rate K_S1T1 decreased with E_vib.

The results obtained may be important to understand the nature of triplet relaxation process and provide the prediction of the sensitivity of triplet molecule decay rates to intrinsic molecule parameters and ambient medium properties.

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