Approximation methods thermochemical properties

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. 

Different ab initio methods can be characterized by their treatment of electron-electron interactions, called electron correlation. The first practical ab initio method was the HF (Hartree-Fock) method, which treats each electron as if it exists in a nniform field made from the total charge and space occnpied by the other electrons. This treatment is only an approximation to the interactions between electrons as point charges in a dynamics system and exclndes the contribution of excited electronic configurations. This neglect of electron correlation can lead to significant error in determining thermochemical properties. 

Zeleznik and Gordon [77] invented the method of simultaneous regression of the thermochemical properties so that more than one property can be approximated by a single polynomial. This work ended up with the famous NASA seven-term polynomials first published by Zeleznik and Gordon [77] and McBride et al. [15], which cover heat capacity Cp, enthalpy, and entropy. 

The kinetic method is an approximate scheme to determine relative thermochemical properties based on the rates of competitive dissociation of mass-selected cluster ions. As an example, consider the proton-bound dimer system ... 

Most of the semiempirical MO methods currently used are based on SCF theory and differ in the approximations that are made so as to simplify the evaluation of the two-electron repulsion integrals. The approximations are then corrected for by parametrization, wherein parameters are included in the fundamental protocol to make the results match ab initio calculations on known systems. Examples of these semiempirical methods are CNDO (complete neglect of differential overlap), INDO (intermediate neglect of differential overlap), and NDDO (neglect of diatomic differential overlap). An alternative approach is to parameterize the calculations to optimize agreement with measured molecular properties, such as thermochemical, structural, or spectral data. 

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