Excluded volume effect for large and small solutes in water

The cavitation effect, i.e., the process of the creation of a void of excluded volume in bulk solvent (a cavity), is considered. The cavitation free energy is treated in terms of the information theory (IT) approach [Hummer, G.; Garde, S.; Garcia, A. E.; Paulaitis, M. E.; Pratt, L. R. J. Phys. Chem. B 1998, 102, 10469]. The binomial cell model suggested earlier is applied as the IT default distribution p(m) for the number m of solute (water) particles occupying a cavity of given size and shape. In the present work, this model is extended to cover the entire range of cavity size between small ordinary molecular solutes and bulky biomolecular structures. The resulting distribution consists of two binomial peaks responsible for producing the free energy contributions, which are proportional respectively to the volume and to the surface area of a cavity. The surface peak dominates in the large cavity limit, when the two peaks are well separated. The volume effects become decisive in the opposite limit of small cavities, when the two peaks reduce to a single-peak distribution as considered in our earlier work. With a proper interpolation procedure connecting these two regimes, the MC simulation results for model spherical solutes with radii increasing up to R = 10 A [Huang, D. H.; Geissler, P. L.; Chandler, D. J. Phys. Chem. B 2001, 105, 6704] are well reproduced. The large cavity limit conforms to macroscopic properties of bulk water solvent, such as surface tension, isothermal compressibility and Tolman length. The computations are extended to include nonspherical solutes (hydrocarbons C1-C6).     

A semi-empirical calculation of the potential surface for the CH 3 . +CH2=CH2 reaction

A model for the reaction CH ₃ ^. +CH₂=CH₂ is studied including the hybridization change of the reaction center. The interaction energy is devided into two parts. The first is a stabilization energy — the contribution due to the -electron delocalization (including the hybridization effects). It is computed by the PPP method. The second part is an exchange repulsion due to all valence electrons of the three carbon atoms. Correlation corrections are considered. A potential energy surface is constructed, giving a saddle point value close to the experimental activation energy. A discussion is given of the approximations involved. The method suggested is a generalization of the reactivity indices method of the theory of chemical reactivity. It can be regarded as a justification of this more empirical approach.

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Zusammenfassung Ein Modell für die Reaktion CH ₃ ^. +CH₂=CH₂ wird untersucht, einschließlich der Änderung der Hybridisation des Reaktionszentrums. Die Wechselwirkungsenergie wird in zwei Teile zerlegt. Der erste Teil ist eine Stabilisationsenergie — der Beitrag, der der Delokalisierung des -Elektrons (einschließlich Hybridisationseffekte) entspricht. Der zweite Teil ist eine Austauschabstoßung, die von allen Valenzelektronen der drei Kohlenstoffatome herrührt. Korrellationskorrekturen werden berücksichtigt. Eine Fläche der potentiellen Energie wird konstruiert mit einem Sattelpunktswert, der dicht an der experimentellen Aktivierungsenergie liegt. Die verwendeten Näherungsmethoden werden diskutiert. Die vorgeführte Methode ist eine Verallgemeinerung der Methode der Reaktivitätsindices aus der Theorie der chemischen Reaktivität. Sie kann als eine Rechtfertigung dieser mehr empirischen Näherung angesehen werden.

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Résumé Etude d'un modèle pour la réaction CH ₃ ^. +CH₂=CH₂ où l'on tient compte du changement d'hybridation du centre réactif. L'énergie d'interaction est divisée en deux termes. Le premier est une énergie de stabilisation; c'est la contribution dela délocalisation des électrons (effets d'hybridation compris). Il est calculé par la méthode PPP. Le second terme est une répulsion d'échange dûe à tous les électrons de valence des trois atomes de carbone. Les corrections de corrélation sont introduites.Une surface d'énergie potentielle est construite; elle fournit une valeur de l'énergie d'activation proche de celle obtenue expérimentalement. Les approximations utilisées sont discutées. La méthode proposée est une généralisation de celles des indices de réactivité. On peut la considérer comme justifiant cette approche plus empirique.

     

Calculations on the mechanism of ion polymerization in the formaldehyde crystal

A number of possible crystal structures of formaldehyde are calculated using an atom—atom scheme in order to explain some phenomena observed in the low-temperature solid-state polymerization of this and related systems. The structures whose molecular packing favours the polymerization are shown to represent local energy minima. Studies of various molecular motions in so calculated crystals support the hypothesis that polymer chains move spontaneously at the propagation stage. Main peculiarities of the solid-state polymerization mechanism are formulated on the basis of the present and previous calculations.     

Exact solution for the quasi-classical model of vibrational population inversion in exothermal exchange reactions

An exact solution is found for the quasi-classical model of population inversion in exothermal exchange reactions. The model is formulated using natural reaction coordinates and is based on the following assumptions: (1) The chemical systems under study should have a small parameter, namely, the product of the curvature of the reaction path by the classical amplitude of the transversal vibrational motion. (2) Classical turning points are absent within the interaction region for the vibrational levels involved in nonadiabatic transitions. An analytical expression is derived for the vibrational transition probabilities P_mn under these restrictions. In particular, for the transitions from a zero level and probabilities P_on form a two-parameter binomial distribution, whereas a more simple model devised by Hofacker and Levine results in a one-parameter Poisson distribution.     

Potential of mean force for ion pairs in non-aqueous solvents. Comparison of polarizable and non-polarizable MD simulations

Potentials of mean force (PMF) are calculated for two model ion pairs in two non-aqueous solvents. Standard non-polarizable molecular dynamics simulation (NPMD) and approximate polarizable simulation (PMD) are implemented and compared as tools for monitoring PMF profiles. For the polar solvent (dimethylsulfoxide, DMSO) the PMF generated in terms of the NPMD reproduces fairly well the refined PMD–PMF profile. For the non-polar solvent (benzene) the conventional NPMD computation proves to be deficient. The validity of the correction found in terms of the approximate PMD approach is verified by its comparison with the result of the explicit PMD computation in benzene. The shapes of the PMF profiles in DMSO and in benzene are quite different. In DMSO, owing to dielectric screening, the PMF presents a flat plot with a shallow minimum positioned in the vicinity of the van der Waals contact of the ion pair. For the benzene case, the observed minimum proves to be unexpectedly deep, which manifests the formation of a tightly-binded contact ion pair. This remarkable effect arises owing to the strong electrostatic interaction that is incompletely screened by a non-polar medium. The PMFs for the binary benzene/DMSO mixtures display intermediate behaviour depending on the DMSO content.     

Computation of hydration free energies of organic solutes with an implicit water model

A new approach for computing hydration free energies DeltaG(solv) of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component DeltaG(el) of DeltaG(solv) and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (DeltaG(nel)). The novel features include the following: (a) two different cavities are used for treating DeltaG(el) and DeltaG(nel). For the latter case the cavity is larger and based on thermal atomic radii (i.e., slightly reduced van der Waals radii). (b) The cavitation component of DeltaG(nel) is taken to be proportional to the volume of the large cavity. (c) In the treatment of van der Waals interactions, all solute atoms are counted explicitly. The corresponding interaction energies are computed as integrals over the surface of the larger cavity; they are based on Lennard Jones (LJ) type potentials for individual solute atoms. The weighting coefficients of these LJ terms are considered as fitting parameters. Testing this method on a collection of 278 uncharged organic solutes gave satisfactory results. The average error (RMSD) between calculated and experimental free energy values varies between 0.15 and 0.5 kcal/mol for different classes of solutes. The larger deviations found for the case of oxygen compounds are probably due to a poor approximation of H-bonding in terms of LJ potentials. For the seven compounds with poorest fit to experiment, the error exceeds 1.5 kcal/mol; these outlier points were not included in the parameterization procedure. Several possible origins of these errors are discussed.     

The charge-carrier mobility in disordered organic materials: the long-range one-dimensional diffusion with the memory effect

The transport of charge carriers in disordered organic materials is considered based on the techniques of generalized Langevin equation. We simulate the one-dimensional diffusion of a charge in the ensemble of molecular chains interacting with the acoustic phonon subsystem of bulk environment. The random local charge transitions between chain links are mutually correlated. The full computation of the zero-field charge mobility for the N, N-di(1-naphthyl)-N, N-diphenyl-(1,1-biphenyl)-4,4-diamine (\(\alpha \)-NPD) is performed as an illustration. Several models for the probabilities of local transitions are tested. The individual local diffusion constants are randomly varied along a molecular chain within several orders of magnitude. The stationary diffusion regime establishes for every chain the temperature-dependent partial charge mobility as a frequency-dependent complex-valued response function. It is averaged over the chain ensemble. The computational scheme is simple and efficient. The importance of the memory effect depends on specific properties of a given material. This dependence in terms of the system parameters is discussed.     

Momentum representation of the solute/bath interaction in the dynamic theory of chemical processes in condensed phase

For the system consisting of the chemically reactive solute immersed in the oscillator bath, we consider an approach based on the solute/medium interaction expressed in terms of momenta rather than coordinates. In the adiabatic representation the medium reorganization effects are suppressed, being hidden in the solute renormalized potential and new spectral density function. The advantage proposed by the bilinear interaction in momentum representation is its spatial uniformity important for approximate dynamical treatments. The procedure of explicit transforming a standard spectral density (coordinate representation of interaction) into the spectral density in adiabatic representation (momentum representation of interaction) is the main new result of the present study. Illustrative calculations for several types of spectral functions are performed. Special discussion is devoted to clarifying the nature of the slow diffusion coordinate, to which the present approach is mainly addressed.     

The potential surfaces for the addition reactions of π-systems

A semi-empirical MO method is used to calculate potential energy surfaces for the addition reaction of methyl radical with ethylene and butadiene and the Diels-Alder reaction (ethylene + butadiene). The heights of the potential barriers found agree well with the experimental activation energy values. The reaction model involves explicit consideration of the hybridization changes of the reaction centre and the changes of the intermolecular bond lengths. Using Diels-Alder reaction as an example a significance of the proper choice of basic hybride AO's is examined in detail. It is stressed that the reaction model is to be chosen accurate enough when complex organic systems are studied with the great number of internal nuclear degrees of freedom.

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Zusammenfassung Zur Berechnung von Potentialhyperflächen für die Anlagerung von Methylradikalen an Äthylen und Butadien und für die Diels-Alder-Reaktion wird ein semiempirisches MO-Verfahren angegeben. Die gefundenen Potentialschwellen stimmen gut mit den experimentellen Aktivierungsenergien überein. Das Modell berücksichtigt explizit die Änderung der Hybridisierung an den Reaktionszentren und die der Bindungslängen. Der Einfluß der Basiswahl wird im Fall der Diels-Alder-Reaktion untersucht. Dabei ergibt sich, daß das Verfahren auch ausreichend genau ist für die Behandlung von Systemen mit mehr Freiheitsgraden.

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Résumé Une méthode d'O.M. semi-empirique est utilisée pour calculer les surfaces d'énergie potentielle pour la réaction d'addition du radical méthyle à l'éthylène et au butadiene ainsi que pour la réaction de Diels-Alder (éthylène + butadiène). Les hauteurs des barrières de potentiel obtenues sont en bon accord avec les valeurs expérimentales des énergies d'activation. Le modèle de la réaction contient explicitement les variations d'hybridation sur le centre réactif et les variations des longueurs de liaison intermoléculaires. En prenant la réaction de Diels-Alder comme exemple la signification d'un choix approprié des orbitales atomiques hydrides est examiné en détail. Les approximations de la méthode de calcul sont discutées. On souligne que le modèle de la réaction doit être choisi avec suffisamment de précision lorsque l'on étudie des systèmes organiques complexes avec un grand nombre de degrés de liberté nucléaire internes.