Thermodynamics potential energy surfaces

Batteries Critical Data in Physics and Chemistry Electrochemistry Electrolyte Solutions, Thermodynamics Potential Energy Surfaces... 

Catalytic reactions occur on active centers at surfaces distinction between physisorption and chemisorption Kinetic mechanisms of heterogeneous catalytic reactions Langmuir-Hinshelwood kinetics Basis of non-equilibrium thermodynamics Potential energy surface for the reaction H + H2 Transition-state theory... 

It should be stressed that although these symmetry considerations may allow one to anticipate barriers on reaction potential energy surfaces, they have nothing to do with the thermodynamic energy differences of such reactions. Symmetry says whether there will be symmetry-imposed barriers above and beyond any thermodynamic energy differences. The enthalpies of formation of reactants and products contain the information about the reaction s overall energy balance. 

Secondly, it is usual to calculate only a few points which are assumed to be characteristic with full optimization of geometry instead of the complete potential energy surface 48). For a pure thermodynamical view it is enough to know the minima of the educts and products, but kinetic assertions require the knowledge of the educts and the activated complex as a saddle point at the potential energy surface (see also part 3.1). 

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

In a recent development, Corcelli et al. [110] introduced a convenient bias function with general applicability that promises to accelerate the convergence of rate calculations in systems with large enthalpy barriers. They apply a puddle potential (used previously by the same group to enhance thermodynamic averaging [69]) that changes the potential energy surface from which the trajectories are initiated to become... 

From the chemical point of view, the solvent in which the CL experiment is carried out can have a dramatic influence on the efficiency of the CL reaction as solvation can alter the shapes, the depths, and the densities of the vibrational states of the potential surfaces representing the ground states of products and reactants and the lowest excited singlet state of the potential fluorophore. The alteration of the intersections of these potential energy surfaces can affect the enthalpies of reaction and the enthalpies of activation for dark and lumigenic reactions. In some cases, these changes will favor CL (if AH decreases relative to AHa) and in some cases, they will make it thermodynamically unfavorable for CL to occur. 

The empirical valence bond (EVB) method of Warshel [19] has features of both the structurally and thermodynamically coupled QM/MM method. In the EVB method the different states of the process studied are described in terms of relevant covalent and ionic resonance structures. The potential energy surface of the QM system is calibrated to reproduce the known experimental... 

The potential energy surface for the hydroformylation of ethylene has been mapped out for several catalytic model systems at various levels of theory. In 1997, Morokuma and co-workers [17], considering HRh(CO)2(PH3) as the unsaturated catalytic species that coordinates alkene, reported free energies for the full catalytic cycle at the ab initio MP2//RHF level. Recently, in 2001, Decker and Cundari [18] published CCSD(T)//B3LYP results for the HRh(CO)(PH3)2 catalytic complex, which would persist under high phosphine concentrations. Potential energy surfaces for both Rh-catalyzed model systems were qualitatively very similar. The catalytic cycle has no large barriers or deep thermodynamic wells to trap the... 

The thermodynamic stabilities of phenonium ions have been determined based on bromide-transfer equilibria in the gas phase and, depending on the substituents, the bridged species (1) has been proposed as an intermediate or transition state on the potential-energy surface for the 1,2-aryl rearrangement of triarylvinyl cations (see Scheme 1). Phenonium ion (3) has been presented as an intermediate to account for the fact that lactonization of methyl 4-aryl-5-tosyloxy hexanoate (2) produces y-lactone (4) selectively under thermodynamic conditions, but affords 5-lactone (5) preferentially under kinetic conditions. It has been shown that anodic oxidation of frany-stilbene in alcohols in the presence of KF or BU4NBF4 is accompanied by its electro-oxidative rearrangement into diphenylacetaldehyde acetals. The mechanism outlined in Scheme 2 has been proposed" for the transformation. 

In transition-state theory, the absolute rate of a reaction is directly proportional to the concentration of the activated complex at a given temperature and pressure. The rate of the reaction is equal to the concentration of the activated complex times the average frequency with which a complex moves across the potential energy surface to the product side. If one assumes that the activated complex is in equilibrium with the unactivated reactants, the calculation of the concentration of this complex is greatly simplified. Except in the cases of extremely fast reactions, this equilibrium can be treated with standard thermodynamics or statistical mechanics . The case of... 

This relation is credited to Svante Arrhenius and is called the Arrhenius temperature dependence. Arrhenius was mainly concerned with thermodynamics and chemical equilibrium. Some time later Michael Polanyi and Eugene Wigner showed that simple molecular arguments lead to this temperature dependence, and this form of the rate is frequently called the Polanyi-Wigner relation. They described chemical reactions as the process of crossing a potential energy surface between reactants and products (see Figure 2-3), where f and... 

Chapter 1 introduces Potential Energy Surfaces as the connection between structure and energetics, and shows how molecular equilibrium and transition-state geometry as well as thermodynamic and kinetic information follow from interpretation of potential energy surfaces. Following this, the guide is divided into four sections ... 

Auerbach et al. (101) used a variant of the TST model of diffusion to characterize the motion of benzene in NaY zeolite. The computational efficiency of this method, as already discussed for the diffusion of Xe in NaY zeolite (72), means that long-time-scale motions such as intercage jumps can be investigated. Auerbach et al. used a zeolite-hydrocarbon potential energy surface that they recently developed themselves. A Si/Al ratio of 3.0 was assumed and the potential parameters were fitted to reproduce crystallographic and thermodynamic data for the benzene-NaY zeolite system. The functional form of the potential was similar to all others, including a Lennard-Jones function to describe the short-range interactions and a Coulombic repulsion term calculated by Ewald summation. 

Potential energy surfaces or profiles are descriptions of reactions at the molecular level. In practice, experimental observations are usually of the behaviour of very large numbers of molecules in solid, liquid, gas or solution phases. The link between molecular descriptions and macroscopic measurements is provided by transition state theory, whose premise is that activated complexes which form from reactants are in equilibrium with the reactants, both in quantity and in distribution of internal energies, so that the conventional relationships of thermodynamics can be applied to the hypothetical assembly of transition structures. 

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