First-principles thermochemistry

Note that the FPA can be used for more than spectroscopic applications. In fact it has helped to redefine first-principles thermochemistry, see the HEAT (High-accuracy Extrapolated Ah initio Thermochemistry) [63,64] and Wn (Weizmann-n) [65] protocols and Refs. [37,66,67], for example. 

In Section 2.1, we remarked that classical thermodynamics does not offer us a means of determining absolute values of thermodynamic state functions. Fortunately, first-principles (FP), or ab initio, methods based on the density-functional theory (DFT) provide a way of calculating thermodynamic properties at 0 K, where one can normally neglect zero-point vibrations. At finite temperatures, vibrational contributions must be added to the zero-kelvin DFT results. To understand how ab initio thermodynamics (not to be confused with the term computational thermochemistry used in Section 2.1) is possible, we first need to discuss the statistical mechanical interpretation of absolute internal energy, so that we can relate it to concepts from ab initio methods. 

Dixon, D. A. Feller, D. Peterson, K. A. A practical guide to reliable first principles computational thermochemistry predictions across the periodic table, In Annual Reports in Computational Chemistry Wheeler, R. A., Ed. Elsevier 2012 Vol. 8, p 1-28. 

Recent advances in computational chemistry have made it possible to calculate enthalpies of formation from quantum mechanical first principles for rather large unsaturated molecules, some of which are outside the practical range of combustion thermochemistry. Quantum mechanical calculations of molecular thermochemical properties are, of necessity, approximate. Composite quantum mechanical procedures may employ approximations at each of several computational steps and may have an empirical factor to correct for the cumulative error. Approximate methods are useful only insofar as the error due to the various approximations is known within narrow limits. Error due to approximation is determined by comparison with a known value, but the question of the accuracy of the known value immediately arises because the uncertainty of the comparison is determined by the combined uncertainty of the approximate quantum mechanical result and the standard to which it is compared. 

Advances in computational chemistry and molecular simulation have also reached the stage whereby they can be used to develop more advanced and robust kinetic models for catalytic systems. First-principle quantum chemical methods, for example, are being used to routinely calculate thermochemistry and kinetics for gas phase chemistry with accuracies on the order of... 

J.M.L. (2008) Highly accurate first-principles benchmark data sets for the parametrization and validation of density functional and other approximate methods. Derivation of a robust, generally applicable, double-hybrid functional for thermochemistry and thermochemical kinetics.. Phys. Chem. A, 112, 12868-12886. 

Verevkin SP, Emel yanenko VN, Zaitsau DH, Heintz A, Muzny CD, Frenkel M (2010) Thermochemistry of imidazolium-based ionic liquids experiment and first-principles Calculations. Phys Chem Chem Phys 12 14994-15000... 

The first law of thermodynamics leads to a broad array of physical and chemical consequences. In the following Sections 3.6.1-3.6.8, we describe the formal theory of heat capacity and the enthalpy function, the measurements of heating effects that clarified the energy and enthalpy changes in real and ideal gases under isothermal or adiabatic conditions, and the general first-law principles that underlie the theory and practice of thermochemistry, the measurement of heat effects in chemical reactions. 

Chemical reactions are the changes (A) of greatest interest to chemists. The heat liberated or absorbed in chemical reactions (i.e., reaction enthalpy A//rxn, under the usual conditions of open laboratory vessels) has been the subject of intense interest and quantitative calorimetric study from the dawn of the modem chemical era. In the present section, we merely wish to sketch how first-law principles underlie the entire theory and practice of modem thermochemistry, without entering the domain of practical applications, which are usually discussed in introductory chemistry textbooks. 

Calorimetry is the basic experimental method employed in thermochemistry and thermal physics which enables the measurement of the difference in the energy U or enthalpy of a system as a result of some process being done on the system. The instrument that is used to measure this energy or enthalpy difference (At/ or A//) is called a calorimeter. In the first section the relationships between the thermodynamic functions and calorimetry are established. The second section gives a general classification of calorimeters in terms of the principle of operation. The third section describes selected calorimeters used to measure thermodynamic properties such as heat capacity, enthalpies of phase change, reaction, solution and adsorption. 

This laN was first formulated by the Swiss-Russian chemist Germain Henri Hess (180 "" 1 50), who is generally regarded as the founder of the field of thermochemistry. The law follows from the principle of conservation of energy. Thus, if reactions (a) arid (bf occur there is a net evolution of 30 fccal when 1 mol of Y is produced. We can then reconvert Y into 2A + B by the reverse of reaction (c). If the heat required to do this differed from 30 kcal, we would have obtained the starting materials with a net gain or loss of heat, which would violate the principle of conservation of energy. 

The usual way to determine the aromaticity of a compound is to determine its heat of formation, and compare this with an idealized calculated value, where there is no resonance. The actual path followed in the case of triquinacene was much more convoluted. To describe this history, we first need to say a little bit about thermochemistry and heats of formation. These topics will be discussed in more detail in Chapter 11, we will just give a brief outline here. The ideas are quite straightforward in principle, and the difficulty comes at the practical level. It is easy to imagine doing these things with high precision, but that is not so easy experimentally. 

Now that we have analyzed some hypothetical applications of the first law of thermodynamics we should ask how these principles apply to chemistry and chemical reactions. The key concept is that elements react to form compounds, presumably to form lower energy situations, but that is not always the case as we will see in the next chapter. Even so, most reactions do result in a lower energy. Since energy is involved, we may think that Af7 is the key to thermochemistry, but we have already mentioned that often pressure and/or volume changes occur during a reaction. Even though these may be small effects, we know that we should work with A//. Thus, a question for an experimental science like chemistry is How can we measure A// Calorimetry involves mostly simple mathematics but is really the main part of thermochemistry. Careful measurements of Affcomb are the backbone of thermochemistry. 

This chapter is composed of three parts. The first covers principles of thermochemistry that are fundamental to the comprehension of the mechanisms involved in spectral interpretation electronegativity, chemical bonds, acidity and basicity, inductive and mesomeric effects, the Audier-Stevenson rule, and stability rules for radicals in the gas phase. 

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