Experimental atomization energies

Th ere are sim ilar expression s for sym m etry related in tegrals (sslyy), etc. For direct comparison with CNDO, F is computed as in CNDO. The other INDO parameters, and F, are generally obtained [J. I. Slater, Quantum Theory of Atomic Structure, McGraw-Hill Book Company, Vol. 1, New York, I960.] from fits to experimental atomic energy levels, although other sources for these Slater-Con don parameters are available. The parameter file CINDO.ABP contains the values of G and F (columns 9 and 10) in addition to the CNDO parameters. 

Present knowledge about atomic charges of sp systems is unfortunately insufficient it does not permit direct evaluations of m. Extensive numerical analyses, namely, comparisons of experimental atomization energies with their all-theoretical formulation leaving m as the only unknown parameter, were thus carried out. They indicated that [109,129,192]... 

Equation (14.9) lends itself to numerical tests (see Table 14.1). The first two terms are well known they are those described for the saturated carbons (see Table 10.4) hence Ai = 0.0356 and A2 = 0.0529kcalmol ppm . We also know that flHC 7.393 kcal/mol. Using this theoretical input and the appropriate sums, —A , in comparisons with experimental atomization energies, one obtains and A and the empirical estimates of the two terms in brackets... 

TABLE 14.3. Comparison between Calculated and Experimental Atomization Energies of Selected Dienes (kcal/mol)... 

A very popular functional, optimized to reproduce experimental atomization energies, is the "hybrid" exchange-correlation B3LYP functional (= Becke, three-parameter, Lee, Yang, and Parr) ... 

De = D° + o>e is the experimental atomization energy of XH observed from molecular spectra. Then ... 

The valence-bond approach plays a very important role in the qualitative discussion of chemical bonding. It provides the basis for the two most important semi-empirical methods of calculating potential energy surfaces (LEPS and DIM methods, see below), and is also the starting point for the semi-theoretical atoms-in-molecules method. This latter method attempts to use experimental atomic energies to correct for the known atomic errors in a molecular calculation. Despite its success as a qualitative theory the valence-bond method has been used only rarely in quantitative applications. The reason for this lies in the so-called non-orthogonality problem, which refers to the difficulty of calculating the Hamiltonian matrix elements between valence-bond structures. 

Table I. Theoretical vs Experimental Atomic Energy Separations, AE(eV) of Sc and B atoms.

Figure 7 The correlation between the F12 contributions obtained at the CCSD(F12) and MP2-F12 levels of theory. The MP2-F12 values were scaled with the interference factor /int = 0.78 determined by minimizing the deviations between the calculated and experimental atomization energies. The CCSD(F12) values contain the correction associated with the improvements made in the (T) contribution. The dashed line refers to the linear function fitted to the presented data and the dotted line reflects the hypothetical perfect correlation.

The coefficients in this expression, co = 0.20, cx = 0.72 and cc = 0.81, were obtained by fitting the results of B3-LYP calculations to a test set of experimental atomization energies, electron affinities, and ionization potentials. 

The composite methods Wl, W2, W3, and W4 (where the W stands for the Weiz-mann Institute, where the methods were developed) use high-level coupled-cluster calculations to achieve extraordinary accuracy in thermochemical quantities [A. Karton et al., J. Chem. Phys., 125,144108 (2006) and references cited therein]. Wl has one empirically determined parameter, but W2, W3, and W4 have no empirical parameters. Wl and W2 use CCSD(T) and CCSD calculations with correlation-consistent basis sets, do exttapo-lations to the complete basis-set limit, and include relativistic corrections. W3 and W4 include CCSDT and CCSDTQ calculations, and W4 includes a CCSDTQ5 calculation with a small basis set. For various test sets of small molecules, the mean absolute deviation from experimental atomization energies or heats of formation is 0.6 kcal/mol for Wl, 0.5 kcal/mol for W2, 0.2 kcal/mol for W3, and 0.1 kcal/mol for W4. W4 also gives highly accurate bond distances, harmonic vibrational frequencies, vibrational anharmonic-ity constants, and dipole moments for small molecules [A. Karton and M. L. Marlin, J. Chem. Phys., 133, 144102 (2010) arxiv.org/abs/1008.4163]. These methods are limited to small molecules. 

The calorimetric measurement of heats of formation and atomization energies is a classical discipline of chemistry and a number of compilations of such data exist. In Table 15.20, we have listed the experimental atomization energies for the molecules in Table 15.1. 

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