On the relation between non adiabatic unimolecular reactions and radiationless processes

In this paper we present the results of a theoretical study of non adiabatic unimolecular dissociation processes with applications to the decomposition of N₂O(¹ ) to yield N₂(¹ ₉ ) and O(³ P). Such unimolecular reactions which involve a change in the electronic state can be handled by the theory of thermally excited intramolecular radiâtionless decay processes in analogy to molecular predissociation and electronic relaxation in the statistical limit. General criteria were advanced for describing the decay probability of a single vibronic level in terms of Fermi's golden rule and for specifying the (high pressure) unimolecular rate constant in terms of a thermally averaged transition probability. The quantum mechanical rate constant for the non adiabatic reaction is characterized by a pre-exponential factor determined by the interstate coupling matrix element and by a temperature dependent activation energy. At low temperatures the activation energy is equal to the continuum onset, and the reaction involves a tunnelling process. In the high temperature limit a general demonstration of the Franck Condon principle for thermal reactions was provided, whereupon the non radiative transition occurs at the intersection of the potential surfaces. Numerical calculations for a one dimensional model system for the thermal decomposition of N₂O were performed utilizing the semiclassical approximation and confirm our general conclusions. A two dimensional linear model has been developed representing the rate constant in terms of a convolution of two generalized line shape functions, which enabled us to study the distribution of vibrational energy among the diatomic N₂ molecules resulting from the thermal decomposition of N₂O. Some predictions concerning the determination of single level decay probabilities and vibrational distribution of the molecular products are presented.

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Zusammenfassung In dieser Arbeit werden die Ergebnisse einer theoretischen Untersuchung nicht adiabatischer unimolekularer Zerfallsreaktionen mitgeteilt und auf den Zerfall von N₂O(¹ ) zu N₂(¹ _g ) und O(³P) angewandt. Solche unimolekularen Reaktionen, bei denen sich der Elektronenzustand ändert, können mit der Theorie thermisch angeregter intramolekularer strahlungsloser Zerfallsprozesse in Analogie zu molekularer Prädissoziation und elektronischer Relaxation im statistischen Limit behandelt werden. Kriterien zur Beschreibung der Zerfallswahrscheinlichkeiten eines einzelnen Vibrationszustands unter Berücksichtigung von Fermis Golden Rule werden entwickelt sowie die unimolekulare Geschwindigkeitskonstante (im Hochdruckbereich), wobei thermisch gemittelte Übergangswahrscheinlichkeiten berücksichtigt werden, mitgeteilt. Die quantenmechanische Geschwindigkeitskonstante für die nicht adiabatische Reaktion wird durch einen präexponentialen Faktor, der durch die Matrixelemente der Kopplung beider Zustände bestimmt ist und durch eine temperaturabhängige Aktivierungsenergie charakterisiert. Bei tiefer Temperatur stimmt die Aktivierungsenergie mit der Energie der Kontinuumsgrenze überein, die Reaktion verläuft über einen Tunneleffekt. Für hohe Temperaturen wurde ein allgemeiner Beweis des Franck-Condon-Prinzips für thermische Reaktionen gegeben, wonach der strahlungslose Übergang beim Schnittpunkt der Potentialflächen auftritt. Rechnungen für ein eindimensionales Modell des N₂O Zerfalls wurden in der semiklassischen Näherung durchgeführt und bestätigen unsere Folgerungen. Ein zweidimensionales Modell wurde entwickelt, das die Geschwindigkeitskonstante als Faltungsintegral zweier verallgemeinerter Linienformintegrale wiedergibt. Dadurch wurde es ermöglicht, die Verteilung der Vibrationsenergie auf die zweiatomigen N₂ Moleküle, die bei dem thermischen Zerfall von N₂O enstehen, zu studieren. Einige Voraussagen über die Bestimmung der Zerfallswahrscheinlichkeiten eines Vibrationszustandes und die Vibrationsverteilung der molekularen Produkte werden mitgeteilt.

     

Effect of viscosity on the singlet-excited state dynamics of some hemicyanine dyes

Photophysical properties of hemicyanine dyes (1 - 3) were investigated in solvents of varying polarity and viscosity. Hemicyanines possess relatively low fluorescence quantum yields (1%) in polar solvents. A significant increase in fluorescence quantum yield and lifetimes was observed with increase in viscosity of the solvent medium. The radiative, as well as nonradiative decay channels from the singlet-excited state were investigated by varying the viscosity of the medium. The viscosity-dependent radiationless relaxation observed in hemicyanine dyes is suggestive of a restricted rotor motion in the singlet excited state.     

Driven Chain Macromolecule in a Heterogeneous Membrane-Like Medium

Monte Carlo simulations are performed to study the conformational relaxation of a large polymer chain driven into a heterogeneous (membranelike) substrate on a discrete lattice. Chains are created on trails of constrained self-avoiding walks (SAW) on the lattice. Kink–jump, crank–shaft, and reptation moves are used to move segments of chains. Short chains of length L _sc are driven by a field E ₁ toward an impenetrable substrate to design a membrane medium with mobile chain segments. A long chain of length L _lc is then driven by a field E ₂ into the membrane medium and is subsequently allowed to relax in a field E ₃. Radius of gyration R _g and end-to-end distance R _e of the long chain are examined. The relaxation of the conformation of the long chain and its magnitude is found to depend on the initial (predeposition) conformation of the chain, i.e., on E ₂. For a relatively relaxed initial conformation (at E ₂ = 0.1), the longitudinal component of the radius of gyration (R _gz ) is found to decay with the driving field E ₃ with a power law, R _gz E ₃ where 0.1 at low field (E ₃ 0.1) and 1/3 at high field E ₃ 0.1.     

Theoretical insight into the photodeactivation pathway of the tetradentate Pt (II) complex with different inductive substituents

Density functional theory (DFT) and time‐dependent density functional theory (TD‐DFT) both were used to explore the impacts of different inductive substituents on the photophysical properties, radiative/nonradiative processes and photodeactivation mechanism for the Pt (II) complex with novel spiro‐arranged tetradentate ligand. Spectrum simulations show that the electron donor methoxyl (‐OCH₃) group can cause the emission wavelength to red‐shift but have little effect on the absorption spectrum. In the simulation of the radiative decay process for the tetradentate Pt (II) complex, the singlet‐triplet splitting energy is reduced by the introduction of substituents with strong electron‐releasing capability (i.e., from the original trifluoromethyl (‐CF₃) group to ‐OCH₃ group), accompanied with a lower radiative rate constant (k_r). The analyses of non‐radiative decay processes show that the substitution of ‐OCH₃ group on azole rings reduces the energy barriers of thermally activated non‐radiative photodeactivation pathway, which in turn increases the temperature‐dependent non‐radiative rate constants (k_nr(T)). In addition, the substitution of ‐CF₃ by ‐OCH₃ group slightly weakens molecular rigidity and enhances the Huang‐Rhys factor, but decreases the SOC between the triplex excited (T) state and the ground (S₀) state. Thereby, the two complexes may have the similar temperature‐independent non‐radiative rate constant (k_nr’). This work offers theoretical guidance for the design and optimization of the efficient organic light emitting diode (OLED) materials based on the structure of tetradentate Pt (II) complexes.     

Determination of Some Parameters of a Porous Medium–Liquid System by the Pulsed Field Gradient NMR

A possibility was considered to estimate the parameter of a porous medium S/V _p, whereSand V _p are the surface area and the volume of pores, respectively, as well as the power of nuclear magnetic energy sinks of a porous medium–liquid system by the example of randomly packed glass spheres 53–63 m in diameter and acetone, water, or decane as a liquid medium. Estimates were made by analyzing the time dependences of the effective self-diffusion coefficient D(t) and P(t), the probability of return of a molecule to its initial position by time t. It was shown that the short-time parts of D(t) dependence allow us to obtain parameters S/V _p and , whereas those of P(t), only the S/V _p parameter. The values of , obtained from D(t), and from the time of relaxation of longitudinal nuclear magnetization, differ from each other by an order of magnitude. As expected, the value of S/V _p, obtained for a given porous medium, is independent of the nature of introduced liquid.     

Electronic relaxation of small molecules in a dense medium

In this paper we present a theoretical study of radiationless transitions in a small molecule embedded in a dense inert medium. Two extreme situations of the molecule-medium coupling were considered, involving the case of zero displacements of the medium modes between the two electronic states (i.e. the Shpolskii matrix) and the limit of strong molecule-medium coupling. The Fourier transform of the non radiative decay probability of a small molecule in a Shpolskii matrix involves exponential damping, while for the strong coupling situation Gaussian damping is involved. In the case of the Shpolskii matrix the decay rate of a small molecule can be expressed in terms of an infinite series where each term corresponds to a product of an (intramolecular) Poisson distribution and a (medium induced) Lorentzian distribution. The Lorentzian widths were explicitly expressed in terms of the vibrational relaxation widths. The Robinson-Frosch formula can be obtained for the extreme case of near degeneracy in a Shpolskii matrix. In the limit of strong molecule-medium coupling the decay rate of a small molecule can be recast in terms of an infinite sum where each term involves a superposition of a Poisson distribution and a Gaussian distribution. The medium induced Gaussian distribution is determined by intramolecular phonon broadening. We have elucidated some new features of the electronic relaxation of a small molecule in a dense medium pertaining to the problem of off-resonance intramolecular coupling which modifies the energy gap law and the deuterium isotope effect.

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Zusammenfassung Strahlungslose Übergänge in einem kleinen Molekül, das von einem dichten inerten Medium umgeben ist, werden untersucht, wobei zwei Grenzfälle bei der Kopplung Molekül/Medium zugrunde gelegt werden: keine Verschiebungen der Medium-Bewegungen beim Übergang (d.h. der Shpolskii-Matrix) einerseits und starke Kopplung Molekül/Medium andererseits. Die Fouriertransformierte für die Wahrscheinlichkeit des strahlungslosen Zerfalls eines kleinen Moleküls in Form einer Shpolskii-Matrix schließt exponentielle Dämpfung ein, wohingegen bei starker Kopplung die Dämpfung einer Gauss-Funktion entspricht. Im ersteren Fall läßt sich der Zerfall als unendliche Reihe von Produkten einer intramolekularen Poisson-Verteilung mit einer vom Medium induzierten Lorentz-Verteilung formulieren, wobei die Lorentz-Breite explizit mittels der Schwingungsrelaxationsbreiten angegeben wird. Die Robin-Frosch-Formel ergibt sich für den Grenzfall der Fastentartung der Shpolskii-Matrix. Bei starker Molekül-Medium-Kopplung laßt sich der Zerfallsverlauf als unendliche Summe von Überlagerungen von Poisson- und Gaussverteilungen angeben. Dabei wird die Medium-induzierte Gauss-Verteilung durch die intramolekulare Phononen-Verbreiterung bestimmt. In diesem Zusammenhang zeigten sich einige neue Gesichtspunkte für die elektronische Relaxation kleiner Moleküle in dichten Medien, wie z. B. das Problem von Nicht-Resonanz bei intramolekularer Kopplung, wo der Satz vom Energie-Sprung und der Deuterium-Isotopie-Effekt modifiziert werden müssen.

     

Linear viscoelastic behaviour of complex polymeric materials: a fractional mode representation

A rheological constitutive equation for complex polymeric materials is derived starting from a special formulation of the relaxation function. This relaxation function contains six parameters and is divided into three regions: the plateau region, an intermediate power-law region and the terminal region of rapid stress decay. Material functions like the complex modulusG ^* and the logarithmic density function of the relaxation time spectrum H and of the retardation time spectrum L respectively are derived. Material parameters like the zero shear viscosity ₀ and the equilibrium shear complianceJ _e are also calculated. The comparison of the measured dynamic moduli of H-shaped polystyrenes, associating terminally functionalized polyisoprenes and randomly associating polybutadienes with the theoretical predictions of the proposed phenomenological model shows an excellent agreement.     

Vibrational relaxation by collision in polyatomic molecules

A model of a harmonic oscillator with friction is used to discuss the conversion of translational energy to vibrational by collision of an atom with a polyatomic molecule. It is shown that adiabatic conversion implies that E ² may substantially exceed the value calculated, neglecting the interaction of the bond with the rest of the molecule.     

The phosphorescence of benzene obtained byab initio and semi-empirical calculations

Summary Radiative decay and phosphorescence of triplet stare benzene is doubly -orbital and spin- forbidden and is only activated through vibronic coupling among the manifold of triplet states. For this reason the determination of lifetime and transition moments for the decay of triplet benzene has posed a considerable challenge to both theory and experiment. In the present work we have addressed the triplet benzene problem at several levels of theory; by truncated perturbation theory and semiempirical, CNDO/S-CI, calculations; by complete sum-over-state calculations as implemented in recentab initio multiconfiguration quadratic response (MCQR) theory; and by direct MCQR calculations of vibronic phosphorescence. The vibronic coupling is in the two former cases treated by the Herzberg-Teller (H-T) perturbation theory, involving four main mechanisms for the phosphorescent decay of triplet benzene. The results and interpretations given by these approaches as well as their merits and limitations are presented and discussed in some detail. Our calculations indicate that the phosphorescent decay of the³ B _1u state takes place predominantly through vibronic coupling along thee _2g mode. We obtain a phosphorescence that is almost completely out-of-plane polarized, which is in line with more recent measurements by the microwave-induced delayed phosphorescence technique, and could reproduce quite well the intensity ratios for different vibronic bands obtained in that experiment. The final triplet state lifetime is the result of a delicate sum of contributions from several vibronic degenerate and non-degenerate modes. The direct vibronic phosphorescence calculations predict a long lifetime, about one minute — 68 seconds for the best wavefunction — and seem to focus on a doubling of the assumed, albeit not established, best experimental value for the radiative lifetime of triplet benzene; 30 seconds.Dedicated to Inga Fischer-Hjalmars on her 75th birthday     

Effect of strongly interacting solutes on group rotational correlation functions in ethanol

Proton magnetic relaxation rates of solutions of LiCl and LiI in isotopically labelled ethanols CH₃CD₃OD, CD₃CH₂OD and CD₃CD₂OH have been measured as functions of temperature and concentration mostly at v=30 MHz, where 21. The data were reduced in a way that revealed that CH₃ and CH₂ relaxation curves contained a residuum from the slow motion of the OH group in many cases. Thus, the rotational time correlation function of the CH₃ and CH₂ groups contain a residuum term stemming from the slow motion within the same molecule. The data show a threshold of the rotational energy which has to be exceeded in order to make the effect observable.     

Molecular Structure and Internal Rotation Potential of Dimethylphenylphosphine, According to Gas-Phase Electron Diffraction Data and Quantum-Chemical Calculations

Geometric parameters of dimethylphenylphosphine molecule were determined by gas-phase electron diffraction using a dynamic model in which the rotation of the PMe₂ group is treated as large-amplitude motion. Refinement of the structural parameters and parameters of the potential function was performed taking into account the geometry relaxation on the basis of HF/6-311++G** calculations. The internal rotation potential has a single minimum at 0° ( is the angle between the bisector of the MePMe angle and the phenyl ring plane) and may be described by the function of the form V() = 0.5V ₂(1 - cos2), where V ₂ = 0.38±0.36 kcal mol^{- 1}. The data obtained are compared with those for related molecules. Steric effects affect the geometry of the phenylphosphine molecule more significantly than does p- interaction.     

Electronic structures and photophysical properties of phosphorescent platinum (II) complexes with tridentate C^N*N cyclometalated ligands

To get an insight into the structure–property relationships in a series of strongly phosphorescent platinum(II) complexes with tridentate C^N*N cyclometalated ligands, their electronic structures and electroluminescence properties were systematically investigated via density functional theory and time‐dependent density functional theory. Moreover, the factors related to the radiative and non‐radiative decay process, including the transition electric dipole moment μ(S_n), the energy difference between singlet and lowest triplet excited states ΔE(S_n–T₁) and the spin–orbital coupling matrix elements $?S_n\left|{\stackrel{?}{H}}_{\mathrm{SOC}}\right|T_1?$, as well as the energy gap between T₁ and S₀ states ΔE(T₁–S₀) and absorption–emission Stokes shifts have been calculated. Fine emission color tuning and high phosphorescence quantum yield of phosphorescent complexes may be achieved through introducing five–six‐membered metallacycle geometries and linking a substituent (such as phenyl) at bridge atoms. Additionally, phosphorescent properties of these complexes show a clear dependence on the electronegativity of bridge atoms.     

Rheology of polystyrene solutions around the coil overlapping concentration: A phenomenological description of stresses in simple shear flow

Linear viscoelasticity behavior is described with the sum of two terms for polystyrene solutions in tricresyl phosphate around the coil overlapping concentration (K. Osaki, T. Inoue, & T. Uematsu, J Polym Sci Part B: Polym Phys 2001, 39, 211). One is a Rouse–Zimm (RZ) term represented by the Zimm theory with arbitrarily chosen values of the hydrodynamic interaction parameter and the longest relaxation time (τ_RZ). The other (the L term) consists of a relaxation mode with a single relaxation time (τ_L > τ_RZ) and a high‐frequency limiting modulus proportional to the square of the concentration. In this study, we describe the viscosity (η) and first normal stress coefficient (Ψ₁) in steady shear with simple formulas. The stress due to the L term is assumed to be given by a Kaye, Bernstein, Kearsley, and Zapas (K‐BKZ) equation with the damping function h(γ) = (1 + 0.2γ²)^?1/2, where γ is the magnitude of shear. Contributions to η and Ψ₁ from the RZ term are derived from the RZ model, in which the relaxation time in steady flow is given by τ_st = τ + (τ_RZ ? τ)/(1 + 0.35τ_RZ γ˙) instead of τ_RZ. Here, γ˙ is the rate of shear, and τ is the τ_RZ value at the infinite dilution limit. η and Ψ₁ at various concentrations for two polystyrene samples (with molecular weights of 2890 and 8420 kg mol^?1) are well described with parameters derived from dynamic viscoelasticity. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1038–1045, 2002     

Dynamic light scattering of CTAB:NaSal threadlike micelles in the semidilute regime. II. effect of surfactant concentration

Dynamic light scattering measurements are made on networks formed by elongated threadlike micelles of cetyltrimethylammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at 25°C. The surfactant concentrationC _D of the samples is varied from 0.006 to 0.3 M and the ratio of the salt concentrationC _s toC _D is fixed at unity. The time correlation functionA _q (t) of light intensity scattered from the solutions exhibits transition from the unimodal to the bimodal distribution of the decay rate at aroundC _D=0.05 M. The dependence of the first cumulant _e on the scattering vectorq for the samples withC _D0.03 M is described by the dynamic scaling law. The cooperative diffusion coefficientD _c is obtained from extrapolation of _e/q² for the samples withC _D0.03 M and of _f/q² forC _D0.05 M where _f is the first cumulant from the fast mode. TheD _c is found in proportion toC _D ^0.45, being in agreement with the theoretical prediction for a rigid rod in the semidilute regime by the scaling law. The decay rate _s characteristic of the slow mode is independent ofq, and _s ^–1 roughly agrees with the mechanical relaxation time estimated from a fit of the dynamic viscoelastic data of the same samples by a Maxwell type of model with the single relaxation time .     

A representation of the polarization term in the interaction energy between a molecule and a point-like charge

The interaction energy of a molecule M with a point-like charge q can be partitioned into simpler contributions, two of which can be expressed in terms of the charge distribution _M of the sole M. The first term, qV(r), represents the interaction of q with the undistorted charge _M ⁰ of M while the second q ² P(r) gives the additional contributions due to the polarization of _M ⁰ under the influence of the charge q placed at the point r. In this paper we investigate the possibility of getting an inexpensive and sufficiently accurate analytical representation of P(r) over the whole space outside the van der Waals volume of M.     

An application of the virial theorem to study AH2 structures II. Use of CNDO/2 wavefunctions

The simple form for the virial theorem for polyatomic molecules takes the form W=–t _i where t _i is an orbital kinetic energy. It is applied to study shapes of molecules of AH₂ type. Kinetic-energy-versus-angle diagrams are constructed with CNDO/2 wavefunctions that satisfy the virial theorem. The shapes of the molecules can be explained with the aid of the diagrams.     

Orientational dynamics of C70 molecules in chlorobenzene

Dynamics of anisotropy relaxation of C₇₀ singlet excited molecules in chlorobenzene was measured at room temperature by the picosecond transient grating technique. The time-ependent diffraction efficiency exhibits a two-stage decay: a fast component (₁ = 12±5 ps), which is comparable with the corresponding signal of C₆₀ in chlorobenzene ( = 8±2 ps), and a slow one (₂ = 30±5 ps). It is supposed that relaxation of anisotropy is related to the orientational mobility of excited C₇₀ molecules relative to two axes of the molecular framework. The results obtained cannot be described by the Einstein-Stokes-Debye theory. The Hynes-Kapral-Weinberg theory, which takes into account microscopic interactions between molecules upon collisions, agrees satisfactorily with the experiment. The influence of dielectric friction on the orientational mobility of C₇₀ in chlorobenzene was estimated.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 601–604, March, 1996.     

Gaussian basis sets for CO2 molecule generated with the molecular improved generator coordinate Hartree–Fock method

The molecular improved generator coordinate Hartree–Fock (MIGCHF) method is used to generate increasing size atom-centered Gaussian basis sets for the CO₂ molecule. From these basis sets total HF energies and second-order correlation energies were calculated and compared with results obtained with other approaches. Considering our largest basis set, the HF energy is in error by 98 hartree and the second-order correlation energy corresponds to 95.6% of an estimate of the limiting value. The relevance of the present calculations is to show the accuracy that can be achieved in studies of small polyatomic molecules with the MIGCHF method.Acknowledgement We acknowledge the financial support of CNPq (Brazilian Agency). We employed computational facilities at Universidade Federal do Espírito Santo and Universidade Estadual Paulista (IQ Araraquara).     

On the decay modes of hydrogen-helium mesic molecules

Radiative, Auger and two-particle dissociation modes of hydrogen-helium mesic molecules are considered. Auger rate is shown to be independent of the isotopic content of the molecule and amounts to 25% of radiative one. Two-particle decay rate strongly depends on the isotopic content and for light isotopes is an order of magnitude higher than the radiative rate.