Application of the energy gap law to the decay of charge transfer excited states,solvent effects

Values of non-radiative decay rate constants (k_nr) and emission energies (E_cm) have been obtained for Os(Phen₃)²⁺ in a series of solvents and the results are consistent with the energy gap law. For hydroxylic solvents like water or methanol related studies suggest the existence of strong, specific contributions to the vibrational trapping energy of the solvent.     

From A to B in free energy space

The authors present a new method for searching low free energy paths in complex molecular systems at finite temperature. They introduce two variables that are able to describe the position of a point in configurational space relative to a preassigned path. With the help of these two variables the authors combine features of approaches such as metadynamics or umbrella sampling with those of path based methods. This allows global searches in the space of paths to be performed and a new variational principle for the determination of low free energy paths to be established. Contrary to metadynamics or umbrella sampling the path can be described by an arbitrary large number of variables, still the energy profile along the path can be calculated. The authors exemplify the method numerically by studying the conformational changes of alanine dipeptide.     

The energy gap law for triplet states in Pt-containing conjugated polymers and monomers

The energy gap law established for aromatic hydrocarbons and rare earth ions relates the nonradiative decay rate to the energy gap of a transition through a multiphonon emission process. We show that this energy gap law can be applied to the phosphoresce of a series of conjugated polymers and monomers for which the radiative decay rate has been enhanced through incorporation of a heavy metal. We find that the nonradiative decay rate from the triplet state T(1) increases exponentially with decreasing T(1)-S(0) gap for the polymers and monomers at 300 and 20 K. Comparison of the nonradiative decay of polymers with that of their corresponding monomers highlights the role of electron-lattice coupling.     

Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.     

A novel approach to the calculation of the free energy due to molecular flexibility

The contribution of the molecular flexibility to the solvation excess free energy is expressed in terms of probabilities of reaching hard limits on intramolecular coordinates in a series of calculations successively relaxing those limits. Numerical tests on the harmonic oscillator are also presented and used to make suggestion about computational issues.     

Extension of the diffusional kinetics models involving changes in activation energy

On the basis of previous modifications of the Zhuravlev and Ginstling-Brounshtein models, a generalization of kinetic diffusional models is proposed. With the assumption that the rate of the activation energy change during the reaction is inversely proportional to the reaction time, it has been shown that all diffusional kinetic equations in heterogeneous systems take the formF()=KT ⁿ , whereF() is a function of the degree of conversion andK andn are constants related to the rate constant.

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Zusammenfassung Auf Grund vorangegangener Modifikationen der Modelle von Zhuravlev und Ginstling-Brounshtein wird eine Verallgemeinerung der kinetischen Diffusionsmodelle vorgeschlagen. Mit der Annahme, daß die Geschwindigkeit der Änderung der Aktivierungsenergie während der Reaktion umgekehrt proportional der Reaktionszeit ist, wird gezeigt, daß alle kinetischen Diffusionsgleichungen für heterogene Systeme die FormF()=KT ⁿ haben, woF() eine Funktion des Konversionsgrades undK undn mit der Geschwindigkeitskonstante in Beziehung stehende Konstanten sind.

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- . , , , F()=KT ⁿ , F() — , K n — .

     

Distribution-function approach to free energy computation

Connections are explored between the free energy difference of two systems and the microscopic distribution functions of the energy difference. On the basis of a rigorous relationship between the energy distribution functions and the free energy, the scheme of error minimization is introduced to derive accurate and simple methods of free energy computation. A set of distribution-function approaches are then examined against model systems, and the newly derived methods exhibit state-of-art performance. It is shown that the notion of error minimization is powerful to improve the free energy calculation using distribution functions.     

A recipe for the computation of the free energy barrier and the lowest free energy path of concerted reactions

The recently introduced hills method (Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) is a powerful tool to compute the multidimensional free energy surface of intrinsically concerted reactions. We have extended this method by focusing our attention on localizing the lowest free energy path that connects the stable reactant and product states. This path represents the most probable reaction mechanism, similar to the zero temperature intrinsic reaction coordinate, but also includes finite temperature effects. The transformation of the multidimensional problem to a one-dimensional reaction coordinate allows for accurate convergence of the free energy profile along the lowest free energy path using standard free energy methods. Here we apply the hills method, our lowest free energy path search algorithm, and umbrella sampling to the prototype S(N)2 reaction. The hills method replaces the in many cases difficult problem of finding a good reaction coordinate with choosing relatively simple collective variables, such as the bond lengths of the broken and formed chemical bonds. The second part of the paper presents a guide to using the hills method, in which we test and fine-tune the method for optimal accuracy and efficiency using the umbrella sampling results as a reference.     

The role of large conformational changes in efficient ultrafast internal conversion: deviations from the energy gap law

Conversion of electronic excitation energy into vibrational energy was investigated for photochromic spiropyran molecules, using femtosecond UV-mid-IR pump-probe spectroscopy. We observe a weaker energy gap dependence than demanded by the "energy gap law". We demonstrate that large conformational changes accompanying the optical excitation can explain the observed time scale and energy gap dependence of ultrafast S(1) --> S(0) internal conversion processes. The possibility of dramatic deviations from standard energy gap law behavior is predicted. We conclude that controlling molecular conformations by rigid environments can have a substantial impact on photophysical and (bio)chemical processes.     

Radiationless decay of the second excited singlet states of aromatic thiones: Experimental verification of the energy gap law

S₂ → S₀ fluorescence quantum yields and S₂ lifetimes of eight aromatic thiones in inert perfluoroalkane solutions at room temperature have been measured using picosecond laser techniques. Photostable, structurally rigid thiones undergo S₂ → S₁ internal conversion at rates consistent with the energy gap law of radiationless transitions. An average electronic coupling matrix element of 1.9 × 10² cm^?1 is found.     

Comparison between Gibbs free energy minimization and mass action law for a multitemperature plasma with application to nitrogen

This paper gives all the necessary physical equations to determine the composition and the thermodynamic properties in a multitemperature plasma utilizing two different methods: the first method is based on Gibbs free energy minimization and the second is based on the resolution of the mass action law. The lowering terms of the ionization potential and thermodynamic properties are given for a multitemperature plasma using the Debye-Hückel approximation. Numerical application is made to a nitrogen plasma.     

A model for the free energy of adsorption on low energy surfaces.

In constructing a generalized thermodynamics for the fluid-vapor-solid equilibrium in poorly wetted systems the specific free energy of adsorption at saturation vapor pressure is a basic and elusive term. If the adsorbed phase is modeled as a two dimensional gas, systems for which a complete spectrum of data is available can serve as an empirical basis for constructing and testing adsorption-contact angle relationships. From the extension of such relationship other often inassessible terms can be estimated. Such a construct is reported here and extended to the estimation of the excess adsorption entropy at saturation vapor pressure in non-wetting systems     

Application of the multiensemble sampling to the hydration free energy

We demonstrate the feasibility of using multiensemble sampling method (MESM) to determine the free energy difference between two far states for which the configurational distributions do not overlap at all. The MESM is a recently developed non‐Boltzmann sampling technique. The free energy of charging a sodium ion in water is accurately calculated in a single simulation, introducing nine intermediate ionic states. This is due to the ability of the method to explore the relevant parts of configuration space equally for every state, and this ability comes from the universality of weighting function W and the simplicity in adjusting its parameters. Detailed procedures of adjusting the parameters are presented. The comparison with a free energy perturbation method (FEPM) shows that the MESM is more reliable and efficient. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1004–1009, 2001     

The free energy gap and temperature dependence of the electronic transmission coefficient in electron-transfer reactions of the solvated electron

We have investigated the dependence of the electronic factor in electron-transfer rate constants on the energy gap and temperature by minimizing the electronic energy with respect to the instantaneous non-equilibrium solvent polarization. The electronic charge billows out and shrinks in the “normal” and strongly exothermic free energy region, respectively, but the effect is only comparable to the variation of the nuclear factor for low temperatures and strongly exothermic processes.     

Modeling the cavitation free energy

A new expression to compute the cavitation free energy has been derived by integrating a new model to fit its derivative with respect to the cavity radius. The derivatives were obtained from Monte Carlo simulations data of the contact values of distribution functions for hard-sphere solutes in TIP4P water at 298 K and 1 atm. The new expression, formulated in the framework of the thermodynamics of surfaces and unlike the classical simple models, gives good results also for very small cavities with a radius of approximately 1 A. The contribution to the free energy of a term, which depends on the excess number of molecules at the dividing surface, has been taken into account and discussed for the assumed dependence on r of the surface tension. The asymptotic behavior of the derivative has thus been considered, and a function t(r), which is 0 at r = 0 and 1 at infinity, has been introduced to describe the transition from small to large length regimes. The value of the surface tension obtained by fitting is in very good agreement with that obtained from a simulation of the liquid/vapor interface by using the TIP4P model.     

Effect of high-frequency modes and hot transitions on free energy gap dependence of charge recombination rate

The charge recombination (CR) dynamics of geminate ion pairs formed by excitation of the ground-state donor-acceptor complexes in polar solvent have been investigated within the framework of stochastic approach. It is shown that for low exergonic reactions these dynamics critically depend on the reorganization energy of intramolecular high-frequency mode. Even moderate reorganization energies (0.1-0.2 eV) significantly accelerate the excited-state population decay making it nearly exponential. In the solvent-controlled regime, the majority of the excited donor-acceptor complexes recombine at nonthermal (hot) stage when the nonequilibrium initial wave packet passes through a number of term crossings corresponding to the transitions with creation of several vibrational quanta. Analysis of this mechanism allows to conclude (i) the CR in viscous solvents proceeds much faster than the diffusive relaxation of solvent, (ii) under certain conditions, the CR rate becomes practically independent of the diffusive component of solvent relaxation which is determined by solvent viscosity, (iii) in contrast to predictions of Marcus theory, the CR rate decreases monotonically with the rise of reaction exergonicity even at small free energy gaps, in accordance with experimental results. Two semiquantitative approaches providing rather simple analytical expressions for the hot charge recombination dynamics are suggested. These approximations give a good reproduction of the excited-state decay in the wide area of model parameters.     

A method to estimate the Gibbs free energy of non-equilibrium alloys by thermal analysis

A method has been developed to estimate the Gibbs free energy $ \left( {G_{\text{S}}^{\text{NE}} } \right) $ of the non-equilibrium solid alloys with multicomponents based on differential scanning calorimetry (DSC) analysis. In this method, the DSC curves of the non-equilibrium and equilibrium alloys during heating up to fully melting and those of the alloys during solidifying were measured. Then the thermal effects of the solid phase transformations from non-equilibrium to equilibrium states and the equilibrium solidification could be calculated. By evolving the traditional equal-G curve principle to equal-G point, the Gibbs free energy of the equilibrium solid alloy with multicomponents could be obtained on condition that the free energy of the liquid alloy was known. Considering the thermal effects of the solid phase transformations from non-equilibrium to equilibrium states, the Gibbs free energy value of the non-equilibrium alloys with a given composition could be achieved although the phase constitution of the equilibrium solid alloys and the Gibbs free energy of each phase were not known, and the calculation errors could be reduced by dividing the alloys into many infinitesimal virtual pure metals. The Gibbs free energy of the non-equilibrium Al?CSi?CMn alloys was calculated by using this method, confirming the validity of this method.     

Nanoparticle films as electrodes: voltammetric sensitivity to the nanoparticle energy gap

Electron-transfer reactions of redox solutes at electrode/solution interfaces are facilitated when their formal potentials match, or are close to, the energy of an electronic state of the electrode. Metal electrodes have a continuum of electronic levels, and redox reactions occur without restraint over a wide span of electrode potentials. This paper shows that reactions on electrodes composed of films of metal nanoparticles do have constraints when the nanoparticles are sufficiently small and molecule-like so as to exhibit energy gaps, and resist electron transfers with redox solutes at potentials within the energy gap. When solute formal potentials are near the electronic states of the nanoparticles in the film, electron-transfer reactions can occur. The electronic states of the nanoparticle film electrodes are reflected in the formal potentials of the electrochemical reactions of the dissolved nanoparticles at naked metal electrodes. These ideas are demonstrated by voltammetry of aqueous solutions of the redox solutes methyl viologen, ruthenium hexammine, and two ferrocene derivatives at films on electrodes of 1.1 nm core diameter Au nanoparticles coated with protecting monolayers of phenylethanethiolate ligands. The methyl viologen solute is unreactive at the nanoparticle film electrode, having a formal potential lying in the nanoparticle's energy gap. The other solutes exhibit electron transfers, albeit slowed by the electron hopping resistance of the nanoparticle film. The nanoparticles are not linked together, being insoluble in the aqueous medium; a small amount of an organic additive (acetonitrile) facilitates observing the redox solute voltammetry.