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P3_Reaction Energies

P3_Reaction Energies - Chapter P3 Energies of Chemical...

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1 Chapter P3: Energies of Chemical Reactions In addition to its geometry, the internal energy of a molecule is its most fundamental property. Differences in internal energies between the products and reactants of a reaction (reaction enthalpies) indicate whether the reaction will be favorable ( exothermic ) or unfavorable ( endothermic ). Combined with the entropy, which may be calculated from knowledge of equilibrium geometry and vibrational frequencies, reaction enthalpy may be used to provide the Gibbs energy. Our first objective in this chapter will be to establish the ability of each of the three classes of models that have now been introduced: Hartree-Fock, B3LYP density functional and MP2 models, to reproduce the energies for different types of chemical reactions. We will employ a very-large basis set to explore the limits of each model and to attempt to separate the LCAO approximation from the underlying treatment of electron correlation. While we cannot hope to actually achieve these limits, by repeating the calculations with a somewhat smaller basis set we can hope to put bounds on the magnitude of the error caused by the LCAO approximation. Our second objective will be to establish the performance of the same three classes of methods with smaller, more practical basis sets. This will allow us to provide much greater numbers and diversity of examples and to construct meaningful problems. The third objective will be to define combinations of theoretical models (“recipes”) that are able to provide accurate heats of formation to be used in thermochemical comparisons. We will consider both recipes with and without empirical parameters. The final objective of the chapter will be to address the calculation of entropy and subsequent determination of the Gibbs energy. Problems throughout this chapter are intended to exemplify the types of questions that may be posed to modern quantum chemical methods and the types and quality of responses that can be expected. Some will need only a few seconds or minutes of computer time, while others may require several hours.
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2 Total Energy vs. Heat of Formation The heat of formation typically reported in an experimental study differs in three ways from the total energy obtained from a quantum chemical calculation. The obvious difference is that enthalpy and energy are not the same, but are related through a pressure-volume term. H = E + (PV) or at constant pressure H = E+ P V However, except where comparisons involve experiments that have been carried out under very high pressures, the energy and enthalpy of a reaction can be safely assumed to be identical. Reactions can be (and have been) carried out as a function of pressure and provide information about differences in the volumes of reactants and products. A more interesting involves extracting the volumes of transition states (relative to those of reactants) from the pressure dependence of activation energies. This will be discussed in Chapter P4 .
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