Radiationless Transition Probabilities Research Articles

Assessing Excited State Energy Gaps with Time-Dependent Density Functional Theory on Ru(II) Complexes.

A set of density functionals coming from different rungs on Jacob's ladder is employed to evaluate the electronic excited states of three Ru(II) complexes. While most studies on the performance of density functionals compare the vertical excitation energies, in this work we focus on the energy gaps between the electronic excited states, of the same and different multiplicity. Excited state energy gaps are important for example to determine radiationless transition probabilities. Besides energies, a functional should deliver the correct state character and state ordering. Therefore, wave function overlaps are introduced to systematically evaluate the effect of different functionals on the character of the excited states. As a reference, the energies and state characters from multistate second-order perturbation theory complete active space (MS-CASPT2) are used. In comparison to MS-CASPT2, it is found that while hybrid functionals provide better vertical excitation energies, pure functionals typically give more accurate excited state energy gaps. Pure functionals are also found to reproduce the state character and ordering in closer agreement to MS-CASPT2 than the hybrid functionals.

Relativistic calculations of K-, L- and M-shell X-ray production cross-sections by electron impact for Ne, Ar, Kr, Xe, Rn and Uuo

In this work, we derive X-ray production cross-sections from electron-impact ionization cross-sections for Ne, Ar, Kr, Xe, Rn, and Uuo, calculated in the modified relativistic binary-encounter-Bethe model, and using as the only input parameter the binding energies obtained in the Dirac-Fock approach. Radiative and radiationless transition probabilities necessary to compute the inter- and intra-shell atomic yields were calculated in the same approach. Shell electron-impact ionization cross-sections and X-ray production cross-sections are compared with the corresponding cross-sections retrieved from the National Institute of Standards and Technology Reference Database and available experimental data.

Relativistic M-subshell radiationless transition probabilities and energies for Zn, Cd and Hg

Theoretical calculations of radiationless transition probabilities and energies for M-subshell vacancies in Zn, Cd, and Hg are tabulated using the Dirac–Fock method. Transition probabilities between an initial vacancy state and a final two-vacancies state are presented for each initial and final atomic angular momentum quantum number. Calculations were performed in the single configuration approach with the Breit interaction, self-energy and (Uehling) vacuum polarization corrections included in the self-consistent method. Higher-order retardation corrections and QED effects were also included as perturbations.

Relativistic calculations of M-shell decay rates and yields in Zn, Cd and Hg

In this work, we calculate the radiative and radiationless transition probabilities of M-shell vacancies in Zn, Cd and Hg atoms using the Dirac–Fock method. The obtained transition probability values are then used to calculate the corresponding fluorescence, Auger and Coster–Kronig yields for each subshell that are compared to existing theoretical calculations. Average M-shell fluorescence yields are derived and compared with semi-empirical and experimental results.

Measurement of K to L shell vacancy transfer probabilities for the elements 46≤ Z≤55 by photoionization

The K to L shell vacancy transfer probabilities for nine elements in the atomic region 46≤ Z≤55 were determined by measuring the L X-ray yields from targets excited by 5.96 and 59.5 keV photons and using the theoretical K and L shell photoionization cross-sections. The L X-rays from different targets were detected with an Ultra-LEGe detector with very thin polymer window. Present experimental results were compared with the semi empirical values tabulated by Rao et al. [Atomic vacancy distributions product by inner shellionization, Phys. Rev. A 5 (1972) 997–1002] and theoretically calculated values using radiative and radiationless transitions. The radiative transitions of these elements were observed from the relativistic Hartree–Slater model, which was proposed by Scofield [Relativistic Hartree–Slater values for K and L shell X-ray emission rates, At. Data Nucl. Data Tables 14 (1974) 121–137]. The radiationless transitions were observed from the Dirac–Hartree–Slater model, which was proposed by Chen et al. [Relativistic radiationless transition probabilities for atomic K- and L-shells, At. Data Nucl. Data Tables 24 (1979) 13–37]. To the best of our knowledge, these vacancy transfer probabilities are reported for the first time.

Significant Quenching of the Photoinduced Charge Separated State of Aminophenyl(phenyl)acetylene and N,N-Dimethylaminophenyl(phenyl)acetylene in Protic Solvents

By using picosecond transient absorption and fluorescence lifetime measurement techniques, we have investigated intramolecular charge separation and charge recombination processes of aminophenyl(phenyl)acetylene and N,N-dimethylaminophenyl(phenyl)acetylene in various polar solvents. Significant quenching of the intramolecular charge separated state was observed in protic solvents and both the triplet and fluorescence yields were much lower than those in aprotic polar solvents. Such enhancement of the charge recombination was explained by the increase of the radiationless transition probability to the ground electronic state caused by the structural deformation around the amino nitrogen atom. Interaction between the amino nitrogen atom and the oxygen atom of the solvent molecule, which is the hydrogen-bond donor terminal of the network, should play an important role.

Solvent effects on intramolecular charge separation

Solvent polarity effects on the energetics of charge separation processes, in particular on proton transfer in 1-morpholinomethyl-2-naphthol (M2N), were studied and discussed in the frame of a continuum model. The obtained results were compared to electron transfer (TICT) inp-cyano-N,N-dimethylaniline (CDMA). Solvatochromic shifts of M2N were explained by an increase of the molecular dipole moment on excitation, but more importantly by a rotation of its direction. A minimum in the excited state lifetime in an intermediate polarity region was attributed to a maximum radiationless transition probability.

Generalized potential surfaces under inclusion of nuclear motion

AbstractA new method for the solution of the vibronic Schrödinger equation is presented. The proposed approach allows the preservation of the concept of potential surfaces under inclusion of nuclear motion. The dynamical interaction of electrons and nuclei is partially included in the equation determining the potential surfaces. The corresponding electronic wave functions can be used as a basis for a generalized representation. Since the variation principle is involved for the determination of the potential surfaces, the proposed representation may be considered as a generalization of the adiabatic one. As a consequence the vibrational wave equation and the calculation of radiationless transition probabilities is simplified.

Use of the local harmonic approximation in the theory of radiationless transitions

The possibility of applying the «local harmonic approximation» to the calculation of the generating functions used in the theory of radiationless transitions has been investigated. The approximation attempts to «adapt» point by point the generating function to the curvature of the potential, varying the oscillator frequency in a suitable manner. In the simple case of two identical Morse oscillators separated by a constant energy gap ΔE, the radiationless transition probability has been computed for a wide range of ΔE values. The results are compared with those obtained by summing over the exact bound states of a Morse oscillator. It is found that the line shape is qualitatively correct although some spurious negative contribution is introduced by the approximation.

ChemInform Abstract: S‐TETRAZINE: COUPLING OF THE S0 TO THE S1 ELECTRONIC STATE BY TWO OUT‐OF‐PLANE B3U VIBRATIONS

Large effects of vibronic coupling upon vibrational levels of the ground and first excited singlet states of s‐tetraazabenzene‐d0 and d2 are successfully modelled. The model is used also in discussing observed large radiationless transition probabilities and some anomalous infrared and visible transition probabilities.

S-tetrazine: Coupling of the S to the S1 electronic state by two out-of-plane b3u vibrations

Large effects of vibronic coupling upon vibrational levels of the ground and first excited singlet states of s-tetraazabenzene-d0 and d2 are successfully modelled. The model is used also in discussing observed large radiationless transition probabilities and some anomalous infrared and visible transition probabilities.

Relativistic Auger and x-ray deexcitation rates of highly stripped atoms

Radiative and radiationless transition probabilities have been computed relativistically for Li-, N-, F-, K-, and Co-like ions with atomic numbers up to $Z=92$ and with initial configurations consisting of a few closed inner shells with one deep-lying vacancy. Relativity is found to have a pronounced effect on the Auger rates of these highly ionized systems. Radiationless-transition rates are seen to increase with degree of ionization; the stripping of outer shells has a much smaller effect than creation of an empty inner shell of spectator holes. Fluorescence yields are found to increase with the degree of ionization. In the radiative decay of $1s2{s}^{2}$ Li-like ions, initial-state correlation and configuration interaction boost the fluorescence yield by six orders of magnitude at low and medium $Z$.

Electronic spectra and luminescence properties of 1,2-benzotetraphene in crystalline matrices at 77 K

Quasilinear absorption and luminescence spectra of 1,2-benzotetraphene were obtained in polycrystalline matrices at 77 K. Tne energies of successive excited singlet states as well as the energy of the lowest excited triplet state were found experimentally and compared with those calculated by the PPP CI method. The fluorescence lifetime and quantum yield were determined experimentally. Moreover, the radiationless transition probabilities, lifetime of triplet state and phosphorescence quantum yield were estimated employing the Siebrand-Williams model. The results obtained suggest that radiationless ISC processes are the main deactivation channel of the S 1 and T 1 states. The vibrational analysis of quasilinear absorption and luminescence spectra was performed and fundamental frequencies of ground and first excited singlet states were determined.

RelativisticM-shell radiationless transitions

The first relativistic calculations of radiationless transition probabilities for the filling of vacancies in atomic $M$ shells are reported. For eight elements with atomic numbers $70\ensuremath{\le}Z\ensuremath{\le}100$, radiationless ${M}_{4}$- and ${M}_{5}$-subshell transition rates, $M$-subshell fluorescence and Coster-Kronig yields, and $L{\ensuremath{\alpha}}_{1,2}$ and $L{\ensuremath{\beta}}_{1}$ x-ray linewidths were computed with Dirac-Hartree-Slater wave functions using the M\o{}ller two-electron operator. The inclusion of relativity is found to affect strong Auger transitions by 10-20%, and weak transitions by as much as a factor of 2, mostly because of the difference between relativistic and nonrelativistic wave functions. The new theoretical results agree substantially better with experimental data than the results of older, nonrelativistic calculations.

The photoacoustic determination of fluorescence yields of dye solutions

A new method for the measurement of the primary fluorescence quantum yield of dye solutions is presented. The method is conceptually and experimentally simple, relying of the Sn → S1 transition probability as an internal standard for comparison with the S1 radiationless transition probability, both probabilities being measured by photoacoustic spectroscopy.

Fluorescence Quantum Yield Measurements.

Four molecular fluorescence parameters describe the behaviour of a fluorescent molecule in very dilute (~ 10−6M) solution: the fluorescence spectrum ;the fluorescence polarization PM;the radiative transition probability kFM; andthe radiationless transition probability kIM.These parameters and their temperature and solvent dependence are those of primary interest to the photophysicist and photochemist. and PM can be determined directly, but kFM and kIM can only be found indirectly from measurements of the secondary parameters,the fluorescence lifetime τM, andthe fluorescence quantum efficiency qFM,where kFM=qFM/τM and kIM=(1–qFM) τM.The real fluorescence parameters , τ and ϕF of more concentrated (c > 10−5 M) solutions usually differ from the molecular parameters , τM and qFM due to concentration (self) quenching, so that τ > τM and ϕF < qFM. The concentration quenching is due to excimer formation and dissociation (rates kDMc and kMD, respectively) and it is often accompanied by the appearance of an excimer fluorescence spectrum in addition to , so that has two components. The excimer fluorescence parameters , PD, kFD and kID together with kDM and kMD, and their solvent and temperature dependence, are also of primary scientific interest.The observed (technical) fluorescence parameters , τT and in more concentrated solutions usually differ from the real parameters , τ and ϕF, due to the effects of self-absorption and secondary fluorescence. The technical parameters also depend on the optical geometry and the excitation wavelength. The problems of determining the real parameters from the observed, and the molecular parameters from the real, will be discussed.Methods are available for the accurate determination of and τT. The usual method of determining involves comparison with a reference solution R, although a few calorimetric and other absolute determinations have been made. For two solutions excited under identical conditions and observed at normal incidence ϕFTϕFRT=n2∫FT(v¯)dv¯nR2∫FRT(v¯)dv¯where n is the solvent refractive index.Two reference solution standards have been proposed, quinine sulphate in N H2SO4 which has no self-absorption, and 9,10-diphenylanthracene in cyclohexane which has no self-quenching. The relative merits of these solutions will be discussed, and possible candidates for an “ideal” fluorescence standard with no self-absorption and no self-quenching will be considered.

Radiationless transitions in complexes

A theoretical study is presented for the possible changes in radiationless transition probability from the first excited states to the ground state when a molecule enters a complex. An expression is derived that incorporates the contribution from the totally symmetric intermolecular vibration of the donor relative to the acceptor. The bond-length change has been calculated for a molecule entering a complex and on excitation of the latter in the chargetransfer band and also in states localized in the donor. It is found that there should not be large changes in probability for transitions localized in the donor.

Deuterium effects on radiationless electronic transitions of xanthene dyes in aqueous and alcoholic solutions

Solvent deuteration effects on internal conversion (S 1 ∼→ S 0) and intersystem crossing (S 1 ∼→ T 1) in 6-hydroxy-9-phenylfluoron and fluorescein were determined from fluorescence and triplet quantum yield measurements in alkaline solutions of H 2O, D 2O, CH 3OH, CH 3OD, C 2H 5OH, and C 2D 5OD. Deuterium substitution of the oxygen-bonded hydrogens of these solvenis reduces both the internal conversion (by approximately 1.6) and the intersystem crossing (by approximately 1.2) rate constants; the additional deuteration of the alkyl groups of the alcohols does not produce any further effect. The effect of solvent deuteration was negligible for fluorescein. Deuteration of the xanthene groups of the dyes does not influence the radiationless transition probabilities to any significant extent.

Width of AtomicL2andL3Vacancy States nearZ=30

Consequences of the discontinuity at $Z=30$ in the Coster---Kronig transition probability ${f}_{23}$ have been investigated by Auger and photoelectron spectroscopy. The $\frac{{L}_{3}\ensuremath{-}{M}_{45}{M}_{45}}{{L}_{2}\ensuremath{-}{M}_{45}{M}_{45}}$ Auger intensity ratio is found to undergo a sudden decrease at $Z=30$. Relative ${L}_{2}$ and ${L}_{3}$ level widths of Cu and Zn are derived from photoelectron spectra; while the ${L}_{3}$ width increases from Cu to Zn, the ${L}_{2}$ width of Cu is greater than that of Zn, contrary to the general trend. The data agree qualitatively with earlier calculations of radiationless-transition probabilities based on hydrogenic wave functions, but substantial quantitative discrepancies are found. New calculations have been performed with numerical single-particle wave functions based on Green's atomic independent-particle model. With suitable assumptions regarding Cu and Zn ${M}_{4}$ and ${M}_{5}$ electron binding energies in the presence of an ${L}_{2}$ vacancy, reasonable agreement between calculated and observed Auger-electron intensity ratios and $L$-subshell level widths is attained.

Effect of Temperature on Radiationless Transitions

The temperature dependence of the transition probability of radiationless transitions has been discussed by using the golden rule expression for the radiationless transition probability derived from the view-point of the nonstationary character of the Born—Oppenheimer adiabatic approximation. It is shown that the rate constant of radiationless processes depends on temperature as knr/knr 0=1 + ∑ k Ak exp(− ℏ ωk ′/kT).Ak's have been shown to be related to the changes in normal coordinates and frequencies in the equilibrium configuration of the two electronic states in which the radiationless transition takes place.