Theory Of Nonradiative Transitions Research Articles

Nonradiative Transitions in Media of Different Polarities and Their Modeling for 12′-Apo-β-Caroten-12′-Al and 8′-Apo-β-Caroten-8′-Al

The theory of nonradiative transitions, based on the model of orientational broadening of electronic levels, is used to interpret known data on the effect of the polarity of the medium and temperature on the lifetime of the S 1(A − ) state for 12′-apo-β-caroten-12′-al and 8′-apo-β-caroten-8′-al. The effect of promoting vibrations on the rate constant for nonradiative transitions is considered. The results make it possible to hypothesize that the internal electric field created by the environment strongly perturbs the pigment molecules. Consequently, in the excited S 1(A − ) state, both pigments exist as different conformers I and II. Their structures differ by a 180° rotation of the cyclohexene ring relative to the polyene chain. Conformer II predominates in polar media, and is found in an intramolecular charge-transfer state S 1(A − /ICT). In addition, as a result of fluctuations in the internal electric field, it can also be found in a charge-separated state S 1(A − /CS).

Specific features of photoprocesses in molecules with a styryl group

Rate constants of photophysical processes are calculated for molecules with a styryl group (stilbene (styrylbenzene), 4-trans-styrylbiphenyl, 4-trans-styrylterphenyl, and 1,4-distyrylbenzene) using an original method based on the theory of nonradiative transitions. The values for calculations are obtained using a software package based on the method of intermediate neglect of differential overlap with spectroscopic parametrization. The results make it possible to numerically estimate the molecular parameters and effect of substituents. Torsional and twist rotations are simulated in the fluorescence structure of trans-stilbene, and the effect of these rotations on the rates of photoprocesses is analyzed. The results additionally contribute to the interpretation of excitation-energy relaxation and photoisomerization of stilbene.

The role of intermolecular vibrations and reorganization of a reaction system in tunneling reactions with H atom transfer. A Debye model for the medium

Mechanisms of temperature dependence of the rate constants for two types of solid-state tunneling chemical reactions, namely, transfer of an H atom between two molecules and intramolecular transfer, are analyzed. To this end, an analytical expression for the rate constant for tunneling atom transfer in solids is derived in the framework of a modified theory of nonradiative transitions. The mechanisms of the temperature dependence of the rate constant considered in this work include oscillations of the potential barrier to chemical reaction in intermolecular fluctuations and reorganization of the medium. The effect of pressure on the distance between reactants and on the frequency of intermolecular vibrations is taken into account. The theory developed is used to interpret experimental data on tunneling transfer of an H atom in two reactions: a) intramolecular hydrogen transfer in a matrix-isolated formic acid molecule entrapped in an argon crystal and b) H atom transfer from a fluorene molecule to an excited acridine molecule in a fluorene crystal.

Electronic States and Photoprocesses in Bichromophore Systems

We present the results of quantum‐chemical investigation of energy transfer in organic molecules and systems and the inferences drawn. The Forster theory has been subjected to a critical analysis in order that the energy transfer could be described in the context of the current theory of nonradiative transitions and the incorrectness of the basic premises of the Forster theory has been demonstrated. A new variant of the mechanism of electronic energy transfer on the basis of the theory of electron transitions and of the quantum mechanics of molecules has been suggested. It is shown that the interaction of the molecules of the donor and acceptor perturbs the electronic states of isolated molecules even before the excitation of the donor molecule. A characteristic feature of the manifestation of intermolecular interaction is the spatial delocalization of the wave functions of the electronic states of interacting molecules, leading to the possibility of occurrence of conventional photophysical processes with participation of the electronic states of various molecules of the bimolecular system. In experimental investigations, the result of the intermolecular nonradiative transition is recorded as evidence of the spatial transfer of the energy of electronic excitation from the donor molecule to the acceptor molecule.

Non-radiative transitions in the oscillating field model

The model of energy levels crossing in the theory of non-radiative transitions (NRT) has been developed. In the framework of this model NRT are due to the crossing of purely electron energy states of the impurity ion caused by ligands thermal vibrations. Analytical expressions describing the temperature dependence of the NRT probabilities are obtained. The results of calculation of the 3T 2→ 3A 2 NRT for the tetrahedrally coordinated Cr 4+ ion are reported. An accordance between the theoretical calculations and experimental data is discussed.

On the theory of nonradiative transitions in optical excitation of gaseous media

A new approach and a theoretical model for describing experimentally observed nonradiative effects are considered. Nonradiative transitions in an ensemble of polyatomic molecules are interpreted as conversion of absorbed energy of optical radiation to energy of thermal translational motion of gas molecules. The model includes explicit account for intermolecular interactions. The form of the corresponding model Hamiltonian in the approximation of pairwise interactions of molecules and methods for its calculation are proposed. It is shown that all required matrix elements of the theory are easy to calculate, and the method is suitable for both qualitative and quantitative analysis of nonradiative effects.

A Theory of Electronic Energy Transfer in Complex Molecular Systems

The Forster theory for energy transfer is critically reviewed in the context of the present-day theory of nonradiative transitions, and the fundamental tenets of the Forster theory are shown to be erroneous. A new theory of electronic energy transfer is constructed taking into account the electronic transition theory. The intermolecular interaction between donor and acceptor molecules is assumed to perturb electron states of isolated molecules before the donor-molecule excitation. A distinguishing characteristic of the intermolecular interaction is spatial delocalization of the wave functions of electron states of the interacting molecules. It is this fact that has made it possible to realize ordinary photophysical processes between electron states of various molecules in a bimolecular system. In the experiments under study, the result of the intermolecular nonradiative photoprocess is given as evidence of electronic energy transfer from the donor molecule to the acceptor molecule.

Analytical treatment of a two-level system with transitive and displacive vibronic coupling

The eigenvalue problem of a Hamiltonian which has been used as a model in exciton dynamics and in the theory of nonradiative transitions is formulated in Bargmann's Hilbert space of analytical functions (1962). For particle combinations of the parameters of the Hamiltonian one finds exact solutions which are elementary transcendental functions. In the general case the eigenvalues and the eigenfunctions are determined by matrix continued fractions. The eigenfunctions can be represented accurately by Neumann expansions with very few terms.

Theory of non-radiative transitions in molecules and solids

Abstract An extension of a previously proposed theory of non-radiative transitions is presented. It takes account of both strong and weak electron-phonon interaction. A single-frequency oscillator model is used to derive expressions for the transition probability at constant energy on the basis of the adiabatic approximation. The restrictions of both the perturbation theory (weak electronic coupling) and the quasi-classical approximation to nuclear tunneling are removed. Formulae for the transition probability in the high and low energy ranges are derived which are valid for any electronic coupling strength, i.e. for the whole range between the limits of non-adiabatic and adiabatic transitions, for the conditions of both strong and weak electron-phonon interaction.

Temperature effects on the fluorescence kinetics of excited cyclohexane

In agreement with the results reported by Lipsky, emission from cyclohexane depends on the temperature T and on the nature of the phase (liquid or solid). Determination of the lifetimes of the fluorescent state with a single photon counting apparatus gives similar results. Our experimental work shows that the rate constant of fluorescence for the solid phase I (face-centered cubic cell) practically does not depend on temperature. Variations of lifetime vs. T cannot easily be interpreted only with the classical theory of non-radiative transitions.

Non-radiative transitions: competing interaction models

In the theory of non-radiative transitions, as in all internal transition theories, many different choices for the transition Hamiltonian are possible. The main emphasis of the paper is to show that different choices may yield transition rates which differ by orders of magnitude. Unitary transformations prove a natural means to mediate different interaction forms. Six different approximations are compared ('static', 'Condon', and four 'non-Condon' approaches). It is suggested that the lowest rate has to be taken, if more than a single result is valid for any given coupling strength.

The effect of intramolecular modes on the velocity of non-radiative transitions in a polar medium

The theory of non-radiative transitions in a polar medium, describing both the case of perturbation theory and that of strong interaction causing the transition and taking into account intramolecular degrees of freedom, is developed. Master equations governing the system kinetics are derived. The general result is analysed in the special case of quasiresonant non-radiative transitions. It is shown that in the case of strong interaction only the orientational mobility of solvent dipolar particles controls the velocity of non-radiative transitions. Attention is paid to the fact that the presence of isotope effect may serve as the criterion of the conditions under which the reaction is proceeding.

The numerical evaluations of the density of states weighted Franck–Condon factor in large molecules. Effects of frequency changes

The numerical integration method (NIM) is applied to calculations of the density of states weighted Franck–Condon (DWFC) factor which plays an important role in the theory of nonradiative transitions. The 200 point Legendre–Gauss quadrature formula is used to save computing time. Values of the integrand are given with the quadruple precision to avoid accumulated errors occuring in the numerical integration. The illustrative calculations are carried out for the T1→S0 intersystem crossing in benzene. If frequency changes of all vibrational modes are taken into account, the energy gap law applies very well, but it fails without frequency changes. This fact suggests that the ordinary saddle point method based on the harmonic displaced potential surface model is inaccurate. The DWFC factor is sensitive to frequency changes of a high frequency mode which plays an important role in nonradiative transition. When low and medium frequency modes are added, as a group, to high frequency ones, they give a significant effect upon the DWFC factor. If a frequency change of a low frequency mode is hypothetically reduced to an extremely low value, the DWFC factor rapidly increases. This relates to the proximity effect by Wassam and Lim in the nonradiative transition in N-heterocyclic aromatic hydrocarbons. Finally, Metz’s method is discussed.

The role of accepting modes in the theory of nonradiative transitions

We treat explicitly the role of geometry and frequency changes in the nonradiative decay of individual vibrational levels in isolated large molecules, and present new results appropriate to the case of small effective energy gaps.

On the Theory of Nonradiative Transitions in Polar Media II. Processes with “Nixing” of Quantum and Classical Degrees of Freedom

AbstractThe probability of radiationless transition between two multidimensional parabolic terms is calculated for the processes with “mixing” of quantum and classical degrees of freedom. The dependence of the transition probability on the heat of the process is investigated. The transition is shown to be of quasi‐activation less and quasi‐barrier less character at large values (modulo) of the heat of the process.

On the Theory of Nonradiative Transitions in Polar Media I. Processes without “Mixing” of Quantum and Classical Degrees of Freedom

AbstractThe probability of radiationless transitions between two multi‐dimensional parabolic terms is calculated. The dependence of transition probability on temperature and heat of the processes is investigated. It is shown that all the degrees of freedom of the system may be divided into “classical” and “quantum” degrees of freedom in dependence of their behaviour during process. The activation dependence of the transition probability on the temperature is associated with the motion along the classical degrees of freedom only. The change of states of quantum degrees of freedom leads to the appearance of an exponential non‐temperature factor in the transition probability. The transition is shown to be of activationless or barrierless character at large values (modulo) of the heat of process for the processes without “mixing” of classical and quantum degrees of freedom.

The absolute rates of radiative and of nonradiative decay from three vibronic levels in isolated 1B 2u benzene molecules

Absolute rate constants for radiative and for nonradiative decay from three single vibronic levels of isolated 1B 2u benzene molecules are derived from experimental data. Both rate constants show sensitivity to the vibrational state of the excited molecule. Their correspondence with the theory of vibronically induced radiative transitions and with the theory of nonradiative transitions in large molecules is discussed.

Theory of non-radiative transitions in molecules

Reports a study of the effect on photon absorption cross sections of non-radiative transitions (damping) in molecules. The analysis is carried out in the Heisenberg representation in which the time dependence of the dynamical variables used is that given by Senitzky's theory of the damped quantum oscillator and the damped two-level system. The formulation of the non-radiative problem presented is used to study the effect of damping of molecular vibrations, damping of vibronic states, and internal conversion or intersystem crossing followed by radiative re-emission-fluorescence or phosphorescence. In all cases examined the effect of damping appears as a Lorentzian line shape. Integration over the envelope of Lorentzian energies yields the total transition probability for a photon absorption.

Mechanism of emission processes in nickel-doped II-VI compounds

A phenomenological model of non-radiative transitions for certain nickel-doped II-VI compounds is developed. The predictions of the model are shown to account for the apparent irrationality of the observed luminescence properties of these particular phosphors. Further experiments are suggested, the information from which should supply sufficient data to provide a rigorous check on any proposed theory of non-radiative transitions between impurity energy levels. The analysis also concerns the validity of conclusions about the nature of the luminescence transitions based on the configurational co-ordinate diagram.