Polarization of phosphorescence transitions and probabilities of intramolecular nonradiative deactivation of the lowest triplet state of aromatic molecules

This study continues the experimental testing of the validity of the inductive resonance theory of dipole-dipole energy transfer from the T ₁→S ₀ transition dipole to stretching vibrations of intramolecular CH bonds of naphthalene and its hydroxy derivatives. To this end, in the series of compounds under study, the range of variation of the geometrical parameter [Φ(CH)]² of the Förster theory, which accounts for the mutual orientation of the energy donor and acceptor, is estimated. Preliminarily, the angles between the transition dipole moments of the radiative and absorptive electronic transitions (T ₁→S ₀ and S ₀→S ₁; T ₁→S ₀ and S ₀→S ₂; S ₁→S ₀ and S ₀ →S ₁; and S ₁→S ₀ and S ₀→S ₂) are measured at 77 K by the method of polarization photoselection. From the polarization measurements, the angles between the phosphorescence transition dipole moment and the plane of a molecule are determined. It was found that, upon passage from naphthalene to its β derivatives, the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule markedly changes, with the in-plane component of the dipole moment being increased by an order of magnitude. The experimentally determined rate constants of nonradiative deactivation of the T ₁ state averaged over the CH groups of the naphthalene ring system, k _nr(CH), are compared with the rate constants [Φ(CH)]² of the inductive resonance energy transfer from the dipole of the T ₁→S ₀ transition to the dipole of the CH vibrations polarized in the plane of a molecule, calculated with regard to the orientational factor [Φ(CH)]². This comparison showed that, in the series of compounds under study, a change in the orientation of the dipole moment of the radiative T ₁→S ₀ transition relative to the plane of a molecule does not affect the rate of the nonradiative T ₁?S ₀ transition. This inference is confirmed by the absence of a correlation between the rate constants k _dd(CH) calculated by us (with regard to [Φ(CH)]²) and the well-known rate constants k _nr(CH) of individual sublevels of the T ₁ state measured at T≤1.35 K for a number of organic molecules. The possible sources of discrepancy between the experimental data that k _nr(CH) is independent of [Φ(CH)]² and the predictions of the theory are considered. A conclusion is made that the electronic-vibrational energy transfer between electric dipoles is the most probable mechanism of the T ₁?S ₀ transitions, but the rate constant of the dipole-dipole energy transfer upon interaction of the electronic and vibrational dipoles in a molecule does not depend on their orientations.     

Nonradiative deactivation of the lowest triplet state of tetrachlorodibenzo-p-dioxin

In the nonadiabatic approximation, we have studied how the shape of promoting out-of-plane vibrational modes and vibronically induced spin-orbit interactions in structural elements of the 2,3,7,8-tetrachlorodibenzo-p-dioxin molecule affect the energy degradation rate constants K _dg ^s of triplet T ₁ ^s sublevels.     

The effect of the heteroatom on the radiative deactivation of the lowest triplet state in heterocyclic analogues of fluorene

The vibronic transition strengths F _VSO ^s for the transitions from the spin sublevels s of the triplet state T₁ to the energy levels of the nontotally symmetric vibrations of dibenzothiophene (DB(S)) are calculated. For a series of heterocyclic analogues of fluorene (DB(S) and previously studied carbazole, dibenzofuran, and phenyldibenzophosphole), the regular features of the effect of the valence state of the heteroatom and of the spin-orbit interactions in individual atomic groups of the molecule are revealed. The factors affecting changes in the radiative deactivation rate constant of the T₁ state of the molecules studied are established. The intensity distribution of the vibronic lines in the Herzberg-Teller component of the fine structure phosphorescence spectrum of phenyldibenzophosphole is calculated taking into account different populations of the triplet sublevels.     

The lowest singlet and triplet excited states of pyrazine

The phosphoresence, fluorescence and absorption spectra of pyrazine-h₄ and -d₄ have been obtained at 4°K in a benzene matrix. For comparison, those of the isotopically mixed crystal pyrazine-h₄ in d₄ were also taken. All these spectra show extremely sharp and well-resolved lines and reveal detailed vibronic structure.The coincidence of origins of absorption and emission shows that the lowest singlet state is an allowed transition, properly designated as ${}^1\text{B}{}_{\mathrm{3u}}\text{←}{}^1\text{A}{}_{\mathrm{1g}}$. The forbidden component ¹B_2g, predicted by both “exciton” and MO theories to be below the allowed component, must lie higher. Its exact location still remains uncertain.The phosphorescence spectrum, when compared with the singlet-triplet excitation spectrum, indicates that the lowest triplet state is also symmetry allowed, showing a strong 0-0 band and the coincidence of origins of absorption and emission. In accordance with previous work, the triplet state is designated as ³B_3u.The vibronic structure of the phosphorescence spectrum is very complicated. The first work on the analysis of this spectrum concluded that a simple progression of ν_6a exists. Under the high resolution attainable in the present experiments, the supposed ν_6a progression proves to have a composite structure, starting from the second member of the progression. Not only is the ν_9a hydrogen-bending mode present as shown by the appearance of the CD bending mode in the d₄ spectrum, but a band assigned as 2ν_6b was also identified. The latter's anomalous intensity in the phosphorescence spectrum is interpreted as due to the Fermi resonance with 2ν_6a and ν_9a bands. To help resolve the present controversy over the origin of the phosphoresence spectrum observed in crystalline pyrazine, detailed vibrational analyses of the emission spectra were made. The fluorescence spectrum has essentially the same vibronic structure as the phosphorescence spectrum.     

Intramolecular interactions and deuteration effect in nonradiative deactivation of lowest triplet state of anthracene and naphthalene

In the approximation of nonadiabatic interactions and considering all out-of-plane vibrational modes to be promoting ones, we calculate changes in the rate constants T _s K _dg ^s of the nonradiative degradation T ₁ ^s ⇝ S ₀ of in-plane spin (s) triplet states as a result of the complete deuteration of anthracene and naphthalene molecules. We examine how the deuteration, the frequency factor, and the shape of promoting vibrational modes affect the squared matrix elements of both nonadiabatic coupling and adiabatic vibronically induced spin-orbit (VISO) coupling of electronic states. The compensation effect of spin-orbit interactions in structural elements of the carbon backbone of the anthracene molecule is ascertained.     

Heavy atom effect on photophysical deactivation of molecular triplet states

The decrease in the spin-orbit (SO) interaction with increasing number of chlorine atoms in molecules of dibenzo-p-dioxine derivatives is found and explained. The heavy atom effect on components of the rate constant of phosphorescence k _ph=_{k SO}+_{k VSO} related to SO and vibronic-spin-orbit (VSO) interactions is quantitatively estimated.     

Nonradiative deactivation of the lowest triplet state of naphthalene and its hydroxy derivatives at 77 K

The validity of an inductive resonance theory of energy transfer from the T ₁→S ₀ transition dipole to overtone vibrations of molecular groups containing H and D atoms is experimentally tested for a series of compounds whose conjugation systems are similar in size. To this end, by using kinetic, spectral, and luminescent methods (measurements of the phosphorescence decay times, phosphorescence spectra, ratios between the quantum yields of phosphorescence and fluorescence at 77 K, total quantum yields of fluorescence at 293 K, and ratios between the quantum yields of fluorescence at 293 and 77 K), the deactivation processes of the lowest excited T ₁ and S ₁ states of seven emitting centers (naphthalene, its hydroxy and dihydroxy derivatives, and their monoanions) in solutions in ethanol-h ₆, ethanol-d ₆, and their 2: 1 mixtures with diethyl ether are studied. For all the compounds studied, the rate constants k _r of the radiative T ₁→S ₀ transition and the changes in the overlap integrals of the spectra of phosphorescence and absorption of overtones of CH stretching vibrations are determined. The rate constants of energy transfer k _dd(CH) from the T ₁→S ₀ transition dipole to the stretching vibrations of the CH bonds are calculated without regard for the changes in the localization and orientation of this transition dipole in the compounds under study. The contribution of an individual CH group k _nr(CH) to the total rate constant of nonradiative deactivation of the T ₁ state averaged over the CH groups of the naphthalene ring system is ascertained. A good correlation between the changes in the constants k _nr(CH) and k _dd(CH) in the series of the hydroxy derivatives of naphthalene is found, which is indicative of the inductive resonance mechanism of the energy degradation of the T ₁ state. The deviations from proportionality between the changes in these constants upon passing from naphthalene to its hydroxy derivatives, which correlate with a marked increase in the radiative constant k _nr of the hydroxy derivatives in comparison with naphthalene, indicate changes in the strength and localization of the T ₁→S ₀ transition dipole moment and in its orientation with respect to the plane of the molecule that occur due to introduction of a heteroatom, oxygen, whose lone pair of electrons enters into conjugation with the πelectrons of the naphthalene ring system.     

Semi-empirical calculations of the zero-field-splitting parameters of the lowest triplet states of aromatic ketones

Semi-empirical calculations of zero-field-splitting parameters have been performed for the lowest triplet states of aromatic ketones, the mixing between the nearly degenerate n, π* and π, π* triplet states through the vibronic and spin-orbit interactions being considered. The results show that the mixing through the spin-orbit interaction is important to explain the absolute values and signs of the zero-field-splitting parameters observed for acetophenone, p-chlorobenzaldehyde, and benzophenone. The observed and calculated D values are -0·1943 cm^-1 and -0·180 cm^-1 for the lowest triplet state of p-chlorobenzalhyde in p-dibromobenzene.     

The role played by some factors of intramolecular interaction in nonradiative deactivation of the lowest triplet state of octachlorodibenzo-p-dioxin

We have studied how intramolecular interactions, such as vibronically induced spin-orbit (VISO) and nonadiabatic interactions, which are governed by different structural elements of the octachlorodibenzo-p-dioxin (OCDD) molecule, affect the deactivation of its lowest triplet state. In the nonadiabatic approximation, taking into account out-of-plane vibrational modes as promoting ones, we have estimated the values of rate constant K _dg ^s of the nonradiative energy deactivation of in-plane triplet sublevels (s = z, y) of the triplet state of the OCDD molecule.     

类硅离子精细结构能级和辐射寿命

用全相对论多组态自洽场方法,计算了类硅离子的1s、2s、2p-、2p 、3s、3p-、3p、3d-、3d、4s、4p-、4p、4d-、4d、4f-、4f、5s、5p-、5p、 5d-、5d、5f-、5f、5g-、5g、6s、6p-、6p轨道的912个精细结构能级和辐射寿命以及各种跃迁参数.能级的计算值和实验值符合得很好.从计算结果中发现了一些亚稳态能级.     

HgII离子精细结构能级和辐射寿命

用全相对论多组态自洽场方法,计算了HgII离子的5d10nl、5d96s2、5d9nsnp、5d96p2和5d86s26p等组态的3840个精细结构能级和辐射寿命以及各种跃迁参数.能级的计算值和实验值符合得较好.同时,我们还发现了一些长寿命亚稳态能级.     

类钴离子精细结构能级和辐射寿命

用全相对论多组态自洽场方法,计算了类钴离子MoⅩⅥ和Fm LⅩⅩⅣ的1s、2s、2p-、2p、3s、3p-、3p、3d-、3d、4s、4p-、4p、4d-、4d、4f-、4f、5s、5p-、5p、5d-、5d轨道的1014个精细结构能级和辐射寿命以及其他各种跃迁参数,能级的计算值和实验值符合得较好.另外,还发现了一些寿命较长的亚稳态能级.     

Studies of hyperfine splittings and spin distributions of the lowest excited triplet states of substituted benzenes and pyridines

Hyperfine splittings and linewidths of the E.P.R. spectra of the lowest excited triplet states of several cyano-substituted benzenes, pyridines and 1,2,4,5-tetrachlorobenzene were studied, and spin distributions were estimated. These spin distributions as well as the zero field parameters were discussed in terms of the modified benzene π electron MO. It is shown that one excited configuration dominates in the studied systems, but a small amount of configuration mixing is necessary in order to explain ZFS. The experimentally determined spin densities were compared with those calculated from UHF methods in the case of benzonitrile and phenylacetylene. The calculated spin densities agree well with those estimated experimentally when proper choice of integral is made. It is also shown that the spin distributions in triplet state and radical anions are similar in the systems studied here. The geometries of the excited triplet states of substituted benzenes are also investigated from UHF calculation.     

Instability of the lowest triplet state of benzene under environmental perturbations : zero-field splitting and radiative properties of the spin components

Coupling is considered between the lower ³ B _1u and ³ E _1u states of benzene under the combined influence of substituents and the crystal field. A model is derived in which the value of the E.S.R. parameter E, the orientation of the zero-field axes relative to the molecular frame and the radiative properties of the upper two spin components of the lowest triplet state are interpreted in terms of an electronic wavefunction.

With the model the reduced intensity of the 0-0 band relative to the 8₁ ⁰ band in the phosphorescence spectra of a number of benzene-like systems is explained. Further the radiative properties of the zero-field spin components of toluene in a benzene host are interpreted; in this system the angle between the in-plane zero-field axes and the molecular axes appears to be 74° (±6°).     

Roles played by an oxygen atom and out-of-plane high-frequency vibrational modes of a dibenzofuran molecule in the nonradiative deactivation of the lowest triplet state

We have studied the deactivation of the triplet sublevels s = z, y, and x of the lowest triplet state T ₁ ^s of the dibenzofuran molecule, which is determined by radiative (dipole) and nonradiative (degradation) transitions with the rate constants K _rad ^s and K _dg ^s . The main attention is paid to the nonradiative transitions T ₁ ^s ? S ₀ from the in-plane spin states (s = z, y), which are determined by the intramolecular interaction along the coordinates of out-of-plane vibrational modes. The roles played by the many-electron atom (oxygen) and high-frequency out-of-plane vibrational modes in the intramolecular interaction have been evaluated theoretically. Estimates of K _dg ^s based on three known approaches (three models) that describe the nonradiative transition in the approximation of adiabatic and nonadiabatic interactions are presented.     

Radiative deactivation of the lowest triplet state of dibenzo-<Emphasis Type="Italic">p</Emphasis>-dioxine

A theoretical evaluation of the dipole moments of vibronic transitions (which are governed by vibronic spin-orbit interactions) was carried out for dibenzo-p-dioxin molecules. On the basis of the comparison of the obtained results with the data on the distribution of line intensities in a fine-structure phosphorescence spectrum of dibenzo-p-dioxin at 4.2 K, it is inferred that radiative deactivation of the lowest triplet state T ₁ (ππ*) occurs from one of the triplet sublevels. For the molecules of dibenzo-p-dioxin and one of the isomers of tetrachlorodibenzo-p-dioxin, the effect of the form of vibrational modes and individual constants of the spin-orbit coupling in O and Cl atoms on vibronic spin-orbit interactions is discussed.     

Symmetries in the triplet superconducting states

Depending upon the point-group symmetry of the system several phases occur within the superconducting state. The gap parameter for four different point group symmetries is calculated.     

Fine-structure splittings of excited P-and D-wave states in charmonium

It is shown that, in the relativistic case, the fine-structure splittings of the excited 2³ P _J and 3³ P _J states in charmonium are as large as those of the 1³ P _J state if the same value of α_s(μ)≈0.36 is used. The predicted mass of M(2³ P ₀)=3.84 GeV appears to be 120 MeV lower than the center of gravity of the 2³ P _J multiplet and lies below the D $\bar D$ ^* threshold. Our value of M(2³ P ₀) is nearly 80 MeV lower than that from the Godfrey and Isgur article [Phys. Rev. D 32, 189 (1985)], while the differences in other masses are not greater than 20 MeV.