Transitions In Large Molecules Research Articles

Dynamics of radiationless transitions in large molecules: 4. An ensemble of molecules occurring in condensed medium at a finite temperature

Statistically averaged vibration-phonon (VP) states of large molecules occurring in a condensed medium are represented by superpositions of lower excited states of high-frequency intramolecular vibrations and phonons in the state of thermal equilibrium. The dynamics of amplitudes of these states is described by an ensemble of Hamiltonians, wherein the distribution of their parameters characterizes the configuration distribution of the medium and determines the broadening and shift of absorption bands and the time evolution of the ensemble population. The equations of motion for statistically averaged amplitudes, as found by second-order cumulant expansion, coincide with those found by solving the secular equation, which takes into account both intramolecular and VP interactions. The relative contribution of the decay and decoherence to the evolution of the amplitudes has been considered. Critical values at which the transition from regular recurrence cycles to stochastic dynamics takes place have been found for the VP coupling parameters. The ergodicity of VP systems and the conditions of separation of the intramolecular and phonon-stimulated dynamics have been considered.

Dynamics of radiationless transitions in large molecules: 3. Decay of vibration-phonon states

The statistical operator of the ensemble of high-frequency intramolecular vibrations associated with the phonon reservoir depends on the phonon occupation numbers under thermal equilibrium conditions. The eigenvalues of energy of statistically averaged vibration-phonon (VP) states are complex quantities. In the case of weak VP coupling, only one- and two-phonon transitions are taken into consideration for calculating the decay rate constant, in which the difference of phonon energies compensates for the difference in energy between the initial and final intramolecular states. Although the fast evolution of amplitudes of VP states is due to intramolecular redistribution of energy and is not reduced to exponential decay of the initial state, the imaginary components of the eigenvalues coincide with those predicted by Fermi’s golden rule. The relative contribution of two-phonon (combination) transitions compared with one-phonon transitions increases with an increase in the density of intramolecular states and temperature, becoming prevalent for large molecules at T ≥ D ≫ Δ0 (D = 100–200 K (70–140 cm−1) is the Debye temperature and Δ0∼10 cm−1 is the spacing between neighboring intramolecular vibration levels). When T ≥ D, the decay rate constant is K ∝ T2.

Dynamics of radiationless transitions in large molecules: 2. Recurrence cycles in population evolution of the initial state

Evolution of the population of the initial state S is due to radiationless transitions into a dense discrete spectrum of intramolecular vibrations {Rn} (reservoir R) and spontaneous decay of S and Rn by virtue of coupling with a continuous spectrum of intermolecular vibrations (reservoir Q). An exact solution to the dynamic problem has been found, which indicates that in contrast to the Fermi approximation, which reproduces only the exponential decay of S, the evolution consists of recurrence cycles such that Loschmidt echo (partial recovery of the population of S via back transitions from Rn) appears in each cycle. The width and number of echo components depend upon average characteristics of the spectrum of R. With an equidistant spectrum and the same coupling constants of S with all R states, the decay of S is exponential in the initial cycle and the number of echo components and echo width increase proportionally to the cycle number in subsequent cycles. The increase in the width causes mixing of the echo components and the transition from regular to quasi-stochastic dynamics. Deformation of the equidistant spectrum leads to nonexponential decay in the initial cycle, an increase in the number of components, and a reduction in the number of cycles with regular dynamics.

Dynamics of radiationless transitions in large molecules: 1. Absorption spectra of adjoin reservoir states

The dynamics of radiationless transitions in large molecules interacting with the surroundings is determined by the dense discrete spectrum of final states {Rn}, close in energy to the initial state s, and by the sets of SR-coupling matrix elements and the decay rate constants of S and {Rn}. It has been shown that the shape and the fine structure of the absorption band of the optical transition from the ground to the initial state S ← S0 makes it possible to find the characteristic function of these three distributions. The transformation of the regular spectrum into the stochastic one has been considered.

Fate of Excited States in Jet-Cooled Aromatic Molecules: Bifurcating Pathways and Very Long Lived Species from the S1 Excitation of Phenylacetylene and Benzonitrile

Pump-probe delayed ionization studies on phenylacetylene and benzonitrile in a supersonic beam reveal the production of a low-ionization-potential (approximately 5.7 eV) species lasting more than hundreds of microseconds after excitation to the S1 state. Excitation of the molecules was done with a frequency-doubled, Fourier transform-limited, pulse-amplified cw laser, and the rotationally resolved structure of the S1-S0 transition ensures that the excited molecules are monomers. Excited-state photoelectron spectroscopy shows that the long-lived species are formed during the light pulse but not by transfer from the fluorescing S1 population after the pulse, even though the S1 spectral signature is present in the long-lived action spectrum. This behavior differs greatly from that found in benzene and with most commonly held pictures of radiationless transitions in large molecules.

Shapes and correlations as observational discriminants for the origin of diffuse bands

Observations are made of the diffuse interstellar bands in heavily reddened early-type stars in three associations (Cas OB6, Be 87, and Cyg OB2) where the extinction is attributed mostly to material at intermediate densities between molecular clouds and the diffuse medium. The degree of correlation with E(B-V) separates the lines into at least two groups. Detailed analysis of line profiles reveals diversity in the outline of wings ranging from a nearly symmetric Lorentzian shape for 6284 A to an extended long-wavelength wing in 6269 A. It is suggested that the origin of the lines can be explained by the vibronic transitions in large molecules. 58 references.

The Role of the Promoting Mode in Nonradiative Transitions in Large Molecules

Abstract A rate expression for the intramolecular nonradiative transition where a promoting mode acts also as an accepting mode at the same time has been derived within the statistical limit. The dependence of the nonradiative transition rate on the shift of the equilibrium point of the promoting mode in the relevant electronic states, Δp, has been examined for two cases, i) excited \ightsquigarrow ground states and ii) excited \ightsquigarrow excited states, in aromatic hydrocarbons which satisfy the above condition.

Effects of anharmonicities on radiationless transitions in large molecules

A new computational method to account for the effect of anharmonicities on non-radiative decay rates of large molecules in the statistical limit is given by using expansions of the generating functions which have been used successfully in multiphonon processes. This method is free from the ambiguity which, as in previous conventional methods, arises from the factorization which separates the decay rate into a product of an electronic term, a Franck-Condon factor and a density of final states. The rate expression is asymmetric with respect to the sign of the displacement of the accepting modes. Actual calculations are performed for a model molecule which closely resembles benzene. The numerical data for the decay rate exceed the results of the harmonic approximation by about two orders of magnitude.

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.

The energy gap law for radiationless transitions in large molecules

In this paper we present a unified treatment of non-radiative decay processes in large molecules which involve either electronic relaxation between two electronic states or unimolecular rearrangeme...