Disagreement with experiment

But similar calculations for the iron-group ions show marked disagreement with experiment, and many attempts were made to explain the discrepancies. The explanation is simple in many condensed systems the perturbing effect of the atoms or molecules surrounding a magnetic atom destroys the contribution of the orbital momentum to the magnetic moment, which is produced entirely by the spin moments of unpaired electrons.40... 

For a subset of 27 G2-2 molecules with fairly small experimental uncertainties, W1 theory had MAD of 0.7 kcal/mol, compared to the average experimental uncertainty of 0.4 kcal/mol. Some systems exhibit deviations from experiment in excess of 1 kcal/mol in the cases of BF3 andCF4, very slow basis set convergence is responsible, and W2 calculations in fact remove nearly all remaining disagreement with experiment for the latter system. (The best available value for BF3 is itself a theoretical one, so a comparison would involve circular reasoning.) Other molecules (N02 and C1NO) suffer from severe multireference effects. 

A.J. Ardell. Precipitate coarsening in solids Modern theories, chronic disagreement with experiment. In G.W. Lorimer, editor, Phase Transformations 87, pages 485-490, London, 1988. Institute of Metals. 

However this disagreement with experiment is explained not by an error in the calculations, but by the fact that a condition of the applicability of the calculation assumed beforehand is not fulfilled in the thermal balance of a laboratory burner we certainly cannot neglect the amount of heat given off by radiation. 

A brief list of basic assumptions used in the ACF method precedes the detailed analysis of the results of calculations. The derivation of the formula for the spectral function is given at the end of the section. The calculations demonstrate a substantial progress as compared with the hat-flat model but also reveal two drawbacks related to disagreement with experiment of (i) the form of the FIR absorption spectrum and (ii) the complex-permittivity spectrum in the submillimeter wavelength region. We try to overcome these drawbacks in the next two sections, to which Fig. 2c refers. 

However, the so-corrected hat-curved model still does not give a perfect agreement with the experiment, since it does not allow us to eliminate the second drawback (ii), namely, disagreement with experiment of the calculated complex permittivity in the submillimeter wavelength region. 

In writing equation (4.6), we have assumed that the nuclei can be treated as Dirac particles, that is, particles which are described by the Dirac equation and behave in the same way as electrons. This is a fairly desperate assumption because it suggests, for example, that all nuclei have a spin of 1 /2. This is clearly not correct a wide range of values, integral and half-integral, is observed in practice. Furthermore, nuclei with integral spins are bosons and do not even obey Fermi Dirac statistics. Despite this, if we proceed on the basis that the nuclei are Dirac particles but that most of them have anomalous spins, the resultant theory is not in disagreement with experiment. If the problem is treated by quantum electrodynamics, the approach can be shown to be justified provided that only terms of order (nuclear mass) 1 are retained. 

To conclude the analysis of the approximations noted, it is possible to state that, from the point of view of chemical applications, they represent very subtle effects. The experience shows that if ab initio calculations are in disagreement with experiment, it is in most cases not due to the approximations noted. As will be shown in next chapters, the crucial point in ab initio calculations is the basis set effect and, if the calculations are at the SCF level, also the correlation energy. The only exceptional case we shall meet in this book concerns ionization potentials for core electrons in molecules containing heavy atoms. Here the relativistic effects are very important. 

MO methods have calculated that the bond order of the C(5)-C(6) bond in the first triplet of a series of pyrimidines is lower than in the first excited singlets of the corresponding molecules, and have concluded that dimerization of the bases occurs via the triplet state. They divided the pyrimidines into three groups the pyrimidines which are known to be easily dimerizable (uracil, 6-methyluracil, thymine, orotic acid—for these molecules the Pse values in their T state are of the order of 0.09-0.12), those which dimerize not so easily (5-aminouracil, cytosine, 5-methylcytosine—Pge 0.13-0.17), and the bases which do not dimerize at all or only with considerable difficulty (2-thiothymine, Pgg = 0.31 isocytosine, Pgg = 0.39 and 5-nitrouracil). The relative distribution of the bases within groups leads sometimes to only limited agreement with available experimental data. For instance, as the Pgg = 0.085 in T of uracil is lower than Pgg = 0.106 in T of thymine, uracil should dimerize more easily than thymine, a conclusion in disagreement with experiment. ... 

In view of the small number of degrees of freedom involved in reactions (1), (4), (5) and (6) these processes will be in their pressure-dependent regions. Both H and CH3 are p radicals, so that the choice of any chain-ending step leads to recombination, which with second-order initiation corresponds to three-halves-order reaction (cf. Table 11), in disagreement with experiment. For example, the mechanism... 

To summarize, ionization and excitation energies support the familiar picture of unsaturated molecules in terms of it electrons. Nevertheless, we wish to stress the point that agreement or disagreement with experiment by no means proves or disproves an approximate theory. There is often an alternative explanation for the characteristics of unsaturated compounds in Chapt. 4.5, we haved noted that the properties related to the delocalization of it electrons (ring currents etc... ) could be interpreted in a different way, even for benzene. Curiously enough, the electronic transition of benzene can be reproduced by a GMS treatment involving the a electrons of C—C and C—H bonds instead of the it electrons of the ring 109). 

This applies in particular to the so-called a—n interaction, which is often introduced generically to explain away the fact that pure -electron theories sometimes fail to explain facts or give serious quantitative disagreement with experiment. 

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