Stochastic model for triplet yields

A stochastic model of triplet yields is considered where the singlet S₁ is initially excited and subsequently feeds the triplet T₁. Both S₁ and T₁ have Montroll—Shuler step ladder vibrational relaxation mechanisms and radiative and non-radiative decay rates that vary linearly with increasing vibrational energy. Assuming the S₁ → T₁ rates also have this linear variation, the kinetic model is exactly solved in terms of integrals of simple functions of hyperbolic functions. The predictions of the model are illustrated by application to naphthalene. The model parameters are chosen; wherever possible, from experimental data. The predictions are in gross qualitative agreement with available experiments on triplet yields, and they indicate more detailed future experiments to separate the S₁ → T₁ and S₁ → S₀ (ground singlet) decays (and their energy dependence) in aromatic hydrocarbons.     

The study of the intramolecular heavy atom effect in 9,10-dichlorophenanthrene and 1,2,3,4-tetrachloronaphthalene using PMDR techniques

Using PMDR techniques, the top two zero-field triplet levels in 9,10-dichlorophenanthrene and 1,2,3,4-tetrachloronaphthalene are shown to be most favoured by S₁ → T₁ ISC and T₁ → S₀ phosphorescence. Spin—orbit vibronic coupling via CCl out-of-plane modes and static distortions of the heavy atom are responsible for such behaviour respectively.     

Collision induced intersystem crossing the photophysics of glyoxal vapor excited at 4358 Å

The yields, lifetimes and spectra of singlet ¹A_u (S₁) and triplet ³A_u (T₁) emissions from glyoxal vapor (0.003 to 10 torr) have been measured after initially pumping levels about 1000 cm^?1 above the S₁ zero-point level with the 4358 A Hg line and with flash excitation centered at 4345 A. Only S₁ emission is observed at the lowest pressures. The singlet fluorescence contains appreciable structure from the zero-point level even when the hard sphere collision interval exceeds the radiative lifetime calculated from the absorption coefficient. Implications of long lifetimes (due to S₁ - T₁ vibronic interactions) are not confirmed by pulsed excitation studies. Both S₁ and T₁ emissions are observed at pressures above about 0.1 tert and both are self-quenched. However, added gases such as cyclohexane, argon, and helium selectively quench only S₁ emission. This quenching is collision-induced S₁→T₁ intersystem crossing with cross sections of order 0.1 hard sphere for transitions from the S₁ zero-point level. The triplet yield in 0.2 torr of pure glyoxal is probably near unity, and the subsequent crossing T₁ → S₀, if it occurs, lies in the statistical limit. Indications of fast nonradiative decay from high triplet vibrational levels are seen in the phosphorescence yields. Self-quenching of the triplet state appears to be associated with the photochemical activity of glyoxal.     

Evidence for a non-RRKM photochemical decay. Triplet state behavior of alicyclic ketones

By means of triplet-triplet energy transfer to biacetyl, the population of the vibrationally relaxed triplet state T⁰₁ of the alicyclic ketones cycloheptanone, cyclohexanone, and cyclopentanone was examined as a function of the excitation wavelength. This population, as measured in terms of the ketone triplet yield φ_T(λ), was compared with the excitation energy dependence of the photochemical quantum yield. This comparison demonstrated that the main photochemical path of these ketones originates from higher vibrational levels of T₁. Thus, φ^T(λ) reflects the branching ratio between a non-RRKM photochemical decay and the vibrational relaxation process to T₁. Moreover, φ_T(λ) was found to decrease significantly in the order cycloheptanone > cyclohexanone > cyclopentanone. This observation reflects, at least in part, the influence of the internal degrees of freedom on the vibrational relaxation rate.     

The appearance of fine structure in the phosphorescence spectra of organic molecules in solid solutions under T1 ← S0 laser excitation

Phosphorescence spectra of coronene. 1,2-benzypyrene and chrysene in bromobutyl at 4.2 K under laser excitation directly in the region of the T₁ ← S₀ transition have been studied. Under these conditions, the phosphorescence spectra acquire a line structure. Vibrational analysis of the spectra has been performed and the frequencies of the normal vibrations of the investigated molecules in the S₀ state have been determined. A “multiplet” structure of the phosphorescence spectra appearing for monochromatic excitation to vibrational sublevels of the T₁ state has been studied. It is shown that the frequencies of the molecular vibrations in a triplet state can be found from an analysis of this structure.     

Selective excitation effects in microwave optical double resonance and phosphorescence spectroscopy of molecular crystals

The photoexcitation routes used to produce molecular crystal, triplet states are shown to have important optical and microwave spectral consequences. 2-benzoylpyridine crystals at 4.2 K have T₁ → S₀ phosphorescence spectra showing line width dependence on whether initial production of the T₁ state is through direct T₁ → S₀ absorption, or through S₁ ← S₀ absorption followed by S₁ → T₁ intersystem crossing. Striking differences are seen in the optically detected zero-field resonance spectra.     

Delayed fluorescence S2 → S0 of azulene in isopentane,due to hetero-triplet—triplet annihilation of 3azulene* and 3fluoranthene*

The lowest triplet state of azulene, T₁(Az), can be populated efficiently by triplet energy transfer from the lowest triplet state of fluoranthene, T₁(F1). In isopentane at temperatures 120 K ? T ? 193 K a delayed fluorescence S₂(Az) → S₀(Az) is found, caused by hetero-triplet—triplet annihilation T₁(Az) + T₁(Fl) → S₂(Az) + S₀(F1).     

Simulated T ← S spectrum of 2,4,5-trimethylbenzaldehyde in durene

The T_1,2 ← S₀ phosphorescence excitation spectrum of 2,4,5-trimethylbenzaldehyde in durene has been simulated using forty-five zero-order Born-Oppenheimer product states of which thirty-two belong to T₁ (ππ*), the others to T₂ (nπ*). The spectrum is very complicated in the region 400–600 cm^?1 above the T₁ (ππ*) ←3 S₀ origin band at 24150 cm^?1. In this tangled region conventional vibrational analysis is not useful. Several comments on the physical properties of the excited triplet states of 2,4,5-trimethylbenzaldehyde are given.     

List of subject

We report the high resolution emission (S₁ → S₀, T₁ → S₀) and laser single site singlet excitation (S₁ ← S₀) spectra for the various insertion sites of coronene in n-heptane cooled to 1.5 K. The observation of site splitting of doubly degenerate vibrations and weak electric dipole forbidden 0, 0 bands in the S₁ → S₀ and T₁ → S₀ spectra indicates that the ground state, the first excited singlet and lowest triplet states are all distorted. In these spectra, the intensity distribution of the various sites in the 0, 0 bands suggests that the distortion is different from site to site but similar in S₀, S₁ and T₁. Identical ordering of the sites in S₁ S₀ and S₁ S₀ spectra as well as the observation of weak shifts in the vibrational frequencies in the two states implies the absence of strong pseudo Jahn-Teller forces in the first excited singlet state. We propose, further, that this is also true for the triplet state. This conclusion is supported by the similarity in zero-field splitting parameters of coronene and deuterated coronene. Taken together, these results indicate strongly that the distortion of coronene in n-heptane is primarily crystal field induced and is not greatly changed upon excitation of the molecule to its lowest excited states.     

The triplet state decay (T1(nπ*) → S0) of benzaldehydes in the dilute gas phase

The triplet T₁(nπ^*) decay of benzaldehyde (B) and its isotopomers

and

were investigated in the dilute vapour phase (≤0.5 Torr) at room temperature. Following

excitation the quantum yields of the phosphorescence and photodecomposition, and the rate constants of the phosphorescence and the radiationless T₁ → S_o process were determined. Based on these results and in conjunction with theoretical calculations of T₁ → S_o rates and previous data obtained on propynal, the decay mechanism of benzaldehyde was analyzed. It is shown that the important accepting modes of the non-radiative T₁ → S_a decay are the

wagging and the CO stretching modes. In spite of the close vicinity of the T₂(ππ^*) and the T₁(nπ^*) states, the non-adiabatic coupling (communication between ring and carbonyl vibrations is not sufficient to influence the relaxed T₁(nπ^*) decay significantly.     

Selective Population of the n, π* and π, π* Triplet States of 1-Indanones

The two components of the dual phosphorescence of 1-indanone ( 1 ) and six related ketones ( 2–7 ) possess different excitation spectra exhibiting the vibrational progression characteristic of the S₀ → S₁ (n, π*) transition (shorter-lived emission) and two bands of the S₀ → S_{2 and 3} (π,π*) 0–0 transitions, respectively. The most favorable intersystem crossing routes are S₁ (n, π*) → T (n, π*) and S_2,3 (π*) → T (π, π*). Internal conversion to S₁ competes more effectively with S (π, π*) → T (π, π*) intersystem crossing only from higher vibrational levels of the S₂ and S₃ states.     

Photophysical Properties of Pyrazinopsoralen,A New Monofunctional Psoralen*

Abstract— Pyrazinopsoralen (PzPs), a new monofunctional psoralen, has a UV absorption spectrum similar to other psoralens except that it absorbs more strongly in the long-UVA than 8-methoxypsoralen. The solvent effects on the UV absorption and fluorescence emission spectra indicate that the lowest excited singlet state is the π,π* state like other psoralen derivatives. It shows a much lower fluorescence quantum yield (0.0008 in ethanol at room temperature) than the other psoralens as expected by the increased proximity effect (vibronic perturbation) due to close ¹(n,π*) to ¹(π,π*) states. The fluorescence lifetime was 1.05 ns in methylcyclohexane with a single exponential decay, while more than two components were observed in other solvents with the short-lived component being the major (>95%). The triplet state of PzPs could not be detected by phosphorescence, laser flash excitation (T-T absorption) and singlet oxygen formation probably due to very low φ_isc, or short lifetime of the triplet state (τ_T) caused by the fast T₁→ S₀ intersystem crossing.     

Reversible intersystem crossing,fluorescence lifetime lengthening and collisionally induced phosphorescence in biacetyl

The emissions of biacetyl excited at 4200 Å were studied at pressures down to 10^?3 torr. Apart from the well-known nanosecond fluorescence, a new emission of the same spectral composition was found with a non-exponential decay in the microsecond range. Furthermore the phosphorescence, as defined by its spectral composition, was found to be collisionally induced.The results imply that after excitation, the molecule rapidly transfers (rate constant k_S→T) to the triplet state, giving rise to the nanosecond decay time; and can then transfer back to the singlet state (rate constant k_T→S), giving rise to the microsecond emission. At the same time internal conversion can occur (k_S→S0). From an analysis of the data we find for k_S→S0 = 2.4 × 10⁷ sec^?1, k_S→T = 7.6 × 10⁷ sec^?1, k_T→S = 1.9 × 10⁵ sec^?1. The kinetic treatment can be transformed to a quantum mechanical one, yielding values for the triplet level density (?_T), the coupling element V_ST and the number of triplet states (N) coupled to the singlet excited. At 4200 Å we find ?_T = 6.3 × 10⁵cm, V_ST = 1.0 × 10^?5 cm^?1, N = 400.Phosphorescence occurs only when the molecule is deactivated by collisions to a vibronic triplet state below the vibrationless excited singlet state. The efficiency of biacetyl collisions is 0.54.     

The phosphorescence of 4h-pyran-4-thione: large quantum yields from room-temperature fluid solutions

The spectra, phosphorescence quantum yields and triplet lifetimes of 4H-pyran-4-thione (PT) in fluid solution at room temperature have been measured. In inert perfluoroalkane solvents at 293 K, the phosphorescence quantum yield of PT is 0.33 on excitation to S₂ and 0.47 on direct excitation to T₁. The reasons for these extremely large radiative yields are discussed.     

Theoretical study of the absorption and emission spectrum and non-adiabatic excited state dynamics of gas-phase xanthone

The ground, singlet, and triplet excited state structures (S₁, S₂, T₁, and T₂) of xanthone have been calculated and characterized in the adiabatic representation by using time-dependent density functional theory (TDDFT). However, the fast intramolecular transition mechanisms of xanthone are still under debate, and so we perform non-adiabatic excited state dynamics of the photochemistry of xanthone gas phase and find that it follows El-Sayed's rule. Electronic transition mechanism of xanthone is sequential from the S₂ state: the singlet internal conversion (IC) time from S₂ (¹ππ*) to S₁ (¹nπ*) is 3.85 ps, the intersystem crossing (ISC) from S₁ (¹nπ*) to T₂ (³ππ*) takes 4.76 ps, and the triplet internal conversion from T₂ (³ππ*) to T₁ (³nπ*) takes 472 fs. The displaced oscillator, Franck–Condon approximation, and one-photon excitation equations were used to simulate the absorption spectra of S₀ → S₂ transition, with v₅₅ being most crucial for S₀ structure; the fluorescence spectra of S₁ → S₀ transition with v₄₇ for S₁; and the phosphorescence spectra of T₁ → S₀ transition with v₄ for T₁. Our method can reproduce the experimental absorption, fluorescence, and phosphorescence spectra of gas-phase xanthone.     

Photophysical Properties of Some Methyl-Substituted Angelicins: Fluorometric and Flash Photolytic Studies

This paper describes the results of a study of the photophysical properties of various methyl-angelicins (MA) in solvents of different polarity and proticity. The behavior of their excited singlet and triplet states was investigated by fluorometry and nanosecond laser flash photolysis. On the basis of semiempirical (ZINDO/S-CI) calculations and the solvent effect on the absorption and fluorescence properties, the lowest excited singlet state (S₁) is assigned to a partially allowed π, π* state. The close lying S₂ state is n,π* in nature. The efficiency of the decay pathways of S₁ (fluorescence, intersystem crossing and internal conversion) strongly depends on the energy gap between the S₁ and S₂ states consistent with the manifestation of “proximity effect.” Thus, MA in cyclohexane decay only through S₁→ S₀ internal conversion, while in acetonitrile and ethanol, where the n, π* state is located at higher energy, their fluorescence and intersystem crossing increase significantly. The lowest excited triplet states (T₁) were characterized in terms of their absorption spectra, decay kinetics, molar absorption coefficients and formation quantum yields. The interaction of T₁ MA with molecular oxygen leads to an efficient formation of singlet oxygen, as evidenced by the appearance of characteristic IR phosphorescence centered at 1269 nm.     

Nonradiative decay processes in benzene

We investigate the behavior of single vibronic level nonradiative decay rates in benzene and benzene-d₆. The effects of excitation in a promoting mode which undergoes frequency and geometry changes in the S₁ relaxation (to T₁ or S₀) are considered in detail. Calculated relative nonradiative decay rates are compared with experimental values and are used to assign triplet state vibrational frequencies to the ν_s, ν₁₀ and ν₁₆ vibrations. This comparison also indicates that none of these modes, nor the modes ν₁ and ν6, are likely to be the dominant promoting modes for the S₁ → T₁ decay. Some simple expressions are given which provide good estimates of the vibronic state dependence of the non-radiative decay rates. In conjuction with experimental decay rate data, these estimates can aid in guiding spectral assignments of vibronic bands. Simple but general theoretical criteria are derived which are useful in determining those vibrations which are poor (or good) accepting modes. Our previous theory is generalized to consider absolute nonradiative decay rates. The results are used to suggest a possible mechanism for the “channel three” decay process observed by Callomon . Although the numerical applications presented here are to benzene electronic relaxation processes, the theoretical developments also apply to and the calcultions illustrate general features of nonradiative decay in the statistical limit.     

Nuclear Coordinate dependence of electronic transition moments in orbitally forbidden transitions: A new interpretation of deuterium isotope effects

The nuclear coordinate dependence of electronic transtion moments has been investigated for the purpose of finding new interpretations of deuterium isotope effects on spectral intensities and radiative decay rates in orbitally forbidden electronic transitions. By using “AO following nuclei” wavefunctions as the building block for the electronic wavefunction in the adiabatic BO vibronic wavefunction, the spin-free hamiltonian is diagonalized to generate eigenfunctions and eigen-energies. It is found that the electronic transtion moments based on these eigenfunctions show dependences upon the vibrational modes which are not directly involved in vibronic coupling. This leads to interpretations of the deuterium isotope effects in T₁ → S₀ radiative transitions of aromatic hydrocarbons and S₀ → S₁ absorption in pyrazine which are not based on the conventional Herzberg—Teller or non-BO coupling.     

Theoretical DFT study of phosphorescence from porphyrins

Geometrical structure of free-base porphin (H₂P) and Mg- and Zn-porphyrins together with their vibrational frequencies and vibronic intensities in phosphorescence are investigated by density functions theory (DFT) with the standard B3LYP functional. These molecules have a closed-shell singlet ground state (S₀) and low-lying triplet (T₁) excited states of ππ* type. The S₀–T₁ transition probability and radiative lifetime of phosphorescence (τ_p) of these molecules are calculated by time-dependent DFT utilizing quadratic response functions for account of spin–orbit coupling (SOC) and electric-dipole transition moments including displacements along active vibrational modes. The infrared and Raman spectra in the ground singlet and first excited triplet states are also studied for proper assignment of vibronic patterns. The long radiative lifetime of free-base porphin phosphorescence (τ_p ∼ 360 s at low temperature limit, 4.2 K) gets considerably shorter for the metalloporphyrins. An order of magnitude reduction of τ_p is predicted for Mg-porphyrin but no change of phosphorescence polarization is found. A forty times enhancement of the radiative phosphorescence rate constant is obtained for Zn-porphyrin in comparison with the H₂P molecule which is accompanied by a strong change of polarization and spin-sublevel radiative activity. A strong vibronic activity of free-base porphin phosphorescence is found for the b_2g mode at 430 cm⁻¹, while the 679 and 715 cm⁻¹ vibronic bands of b_3g symmetry are less active. These and other out-of-plane vibrations produce considerable changes in the radiative constants of different spin sublevels of the triplet state; they also promote the S₁ → T₁ intersystem crossing. Among the in-plane vibrations the a_g mode at 1614 cm⁻¹ is found very active; it produces a long progression in the phosphorescence spectrum. The time-dependent DFT calculations explain the effects of the transition metal atom on phosphorescence of porphyrins and reproduce differences in their phosphorescence and EPR spectra.     

Theoretical study of the photochemical reaction mechanism of bicyclo[4.1.0]hept‐2‐ene upon direct photolysis

Ab initio multiconfigurational CASSCF/MP2 method with the 6‐31G* basis set has been employed in studying the photochemistry of bicyclo[4.1.0]hept‐2‐ene upon direct photolysis. Our calculations involve the ground state (S₀) and excited states (S₁, T₁, and T₂). The ground‐state reaction pathways corresponding to the formation of the six products derived from bicyclo[4.1.0]hept‐2‐ene via two important diradical intermediates (D1 and D2) were mapped. It was found that there are various crossing points (conical intersections and singlet–triplet crossings) in the regions near D1 and D2. These crossing points imply that direct photolysis can lead to two possible radiationless relaxation routes: (1) S₁ → S₀, (2) S₁ → T₂ → T₁ → S₀. Computation indicates that the second route is not a competitive path with the first route during direct photolysis. The first route is initiated by barrierless cyclopropane bond cleavage to form two singlet excited diradical intermediates, followed by efficient decay to the ground‐state surface via three S₁/S₀ conical intersections in the regions near the diradical intermediates. All six ground‐state products can be formed via the three conical intersections almost without barrier after the decays. The barriers separating the diradical minima on S₁ from the S₁/S₀ conical intersections were found to be very small with respect to the vertical excitation energy, which can explain why the product distribution is independent of excitation wavelength. Triplet surfaces are not involved in the first route, which agrees with the fact that the product contribution was unchanged by the addition of naphthalene. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005