Comparing Theoretical and Experimental Results

After having summarized the experimental and theoretical results obtained for the transmetalation of 1 with ZnMc2, the only thing that is left is to compare them 

The quantitative comparison of experimental and theoretical Gibbs energy barriers can be only strictly made for the concerted mechanisms, since only the lower (for 5+) and higher (for 4+) limits for the ionic mechanisms could be estimated experimentally. Thus, according to the computed barriers for the concerted mechanisms 

These values were calculated using the reaction rates derived from the kinetic model a adopted in the experiments. Note that the experimental values for the concerted mechanisms are the quantitative kinetic results, whereas for the ionic mechanisms the values plotted correspond to the estimated maximum (i.e. L = THF) or minimum (i.e. L = PMePh2) values compatible with the experimental observations. 

All the results obtained in this combined experimental and theoretical study are summarized in the catalytic cycle depicted in Fig. 4.22. 

de Meijere, A., Diedrich, F. (eds.) Metal-Catalyzed Cross-Coupling Reactions (2nd edn). Wiley-VCH, Weinheim (2004) 

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This paper summarizes the theoretical analysis of some new molecules with methylsulfonyl group as the electron acceptor group, describes the syntheses of new stilbene and azobenzene systems, and presents the measurements of their optical spectra, ground-state dipole-moments, and molecular hyperpolarizability coefficients, p. We compare theoretical and experimental results and comment on the potential usefulness of these chromophores as components for NLO materials. The incorporation of sulfonyl-containing chromophores into polymers, and the NLO properties of the resulting materials, will be discussed in our forthcoming paper (9). 

So that we may gain some idea of the value of our predictions for molecules for which experimental information is not available, it is important to compare theoretical and experimental results in the cases where the latter is known. We present here such a comparison for geometries and energies. 

Similar work from the former Soviet Union used Hiickel calculations to predict theUV/VIS spectra of lignin substructures [63], In later papers, all-electron CNDO/S calculations were reported which were in good agreement with experiment [64], Shevchenko et al. [65] showed the influence of conformation on UV spectra and also reported on the agreement between calculation and experiment. In work related to that of Remko, Burlakov et al. [66] compared theoretical and experimental results for quinone methides. 

Atomic spectroscopy is a powerful tool to investigate also nuclear properties, and studies comparing theoretical and experimental results can provide a calibration of nuclear structure calculations, needed e.g., for the interpretation of experiments involving parity non-conservation [63], electric dipole... 

Nowadays, nanoparticles have been widely used as fillers and compatibilizers. They exert certain effect on the miscibility of blends. Ginzburg applied a simple theory to study the effect of nanoparticles on the miscibility of PVA/PMMA blends and compared theoretical and experimental results for the same system with fillers and without fillers (Ginzburg 2005) when nanoparticle radius is smaller than polymer radius of g5n ation, the addition of nanoparticles increases the critical value of Xn and stabilizes the homogeneity (Fig. 10.38). 

Comparing theoretical and experimental results allows us to understand the realistic behavior of these innovative materials. In particular, considering the cost of these materials, traditional composite materials are more competitive in terms of economic value and properties. This is a critical aspect with reference to the large dimensions of aerospace components and structures. 

The molecular mechanics or quantum mechanics energy at an energy minimum corresponds to a hypothetical, motionless state at OK. Experimental measurements are made on molecules at a finite temperature when the molecules undergo translational, rotational and vibration motion. To compare the theoretical and experimental results it is... 

Calculate some points on the theoretical titration curve before performing the experiment. Then compare the theoretical and experimental results. Also note the coincidence of the potentiometric and visual end points. 

The methods for the direct measurement of tropospheric hydroxyl radical, HO, are reviewed, and the technical hurdles that remain to be surmounted are discussed in the light of theoretical and experimental results. Sensitivities, advantages, and disadvantages of several HO methods are compared, and a way to compare many of the existing HO methods experimentally is presented. 

The basis of the high selectivity in this system, confirmed by both theoretical and experimental results, is that the active catalyst [XHg]+ reacts at least 1000 times faster with the C-H bonds of methane than with those of CH3OH, which exists primarily as the protonated, or sulfated forms, [CH3OH2]+ or CH30-S03H, respectively, in sulfuric acid. This greater reactivity of the methane C-H bonds compared with those of methanol can be traced to substantially lower reac-... 

The theoretical and experimental results for a fuel-lean methane-air flame are given in Figures 5-7. These results include temperature and major species compositions. The experimental and theoretical results are compared by matching the abcissas of the temperature profiles. The model very accurately predicts the slope of the temperature profile but predicts a larger final flame temperature than is measured. This is a consequence of heat lost to the cooled, gold-coated burner wall that is 1.5 mm away from the positions where data were taken. 

Wetmore et al. have achieved impressive results with the use of Density Functional Theory (DFT) calculations on the primary oxidation and reduction products observed in irradiated single crystals of Thymine [78], Cytosine [79], Guanine [80], and Adenine [81], The theoretical calculations included in these works estimated the spin densities and isotropic and anisotropic hyperfine couplings of numerous free radicals which were compared with the experimental results discussed above. The calculations involve a single point calculation on the optimized structure using triple-zeta plus polarization functions (B3LYP/6-31 lG(2df,p)). In many cases the theoretical and experimental results agree rather well. In a few cases there are discrepancies between the theoretical and experimental results. 

An analogous relation holds for /3 (—w w,0). The solute-solvent interactions are treated here on the level of dipolar reaction fields. Such effects are increasingly taken into account in quantum chemical calculations on linear and non-linear optical properties of molecules (Karelson and Zerner, 1992 Willets and Rice, 1993 Bishop, 1994a Di Bella etai, 1994 Tomasi and Persico, 1994). Therefore, the solute polarizabilities represent a natural level at which theoretical and experimental results should be compared. Expressions (90)-(92) allow us to identify the major terms that are missing when results of NLO solution experiments are compared with theoretical calculations for molecules in the gas phase. It turns out that the contributions induced by the reaction field are substantial and often even larger than those of the isolated molecule (Mikkelsen et al., 1993). 

Some disagreement that is observed between the theoretical and experimental results can be attributed to the variability of ion activity coefficients and their effea on the assessment of dissociation constants. However, it is difficult and sometimes inadvisable to blame these factors because disagreement in the concentration distribution curves lead to only small differences in the kinetic rates [46]. For example satisfactory agreement between the experimental and calculated values was observed on comparing the rates of the forward Ni-RjZn and reverse Zn-R Ni exchanges. The Tq 5 (forw)/To 5 (rev) ratios are 7.8 and 6.5 for the experimental and calculated values, respectively. 

Fig. 2.2. (a) STM image of small Au clusters on Ti02. Vacancies are marked with squares, (b) Simulated STM image of a single Au atom trapped in an oxygen vacancy, (c) Line profiles comparing DFT theoretical and experimental results. Reproduced from [34]. Copyright 2003 American Physical Society... 

The aim of the present review is first to summarize what is known about the primary radiation induced defects in nucleic acid constituents from detailed EPR/ENDOR experiments, then to explore the use of theoretical calculations to assist in making free radical assignments. The theoretical calculations include estimates of spin densities and isotropic and anisotropic hyperfine couplings which can be compared with the experimental results. In many cases the theoretical and experimental results agree rather well. In other cases there are discrepancies between the theoretical and experimental results. The successes and failures of DFT to calculate spin densities and hyperfine couplings of more than twenty primary radiation induced radicals observed in the nucleobases are discussed. Some unsolved problems and suggestions for future work are also discussed. 

The dimension estimation can be carried out with the help of Eq. (1.4) and the value (p can be calculated according to Eq. (1.7). The results of the dimension theoretical calculation according to Eq. (1.29) are shown in Table 1.2, from which the theoretical and experimental results show good agreement. Eq. (1.29) indicates unequivocally the cause of a filler s different behavior in nano and microcomposites. The high (close to 3, see Table 1.2) values of d for nanoparticles and relatively small d = 2.17 for graphite) values of d for microparticles at comparable values of cp will be more discussed in the following sections. 

Calculations for finite nuclei will be discussed which demonstrate that the distribution of sp strength in the experimentally accessible energy region can be qualitatively understood. In addition, it becomes possible to interpret both theoretical and experimental results in terms of quasiparticle excitations, the basic concept of Landau s theory of Fermi liquids [19-21]. In contrast to an infinite liquid, the sp basis must be appropriate for the finite system under study and is not composed of the sp momentum states. Apart from this obvious requirement, most notions carry over rather straightforwardly. The ability to calculate the sp strength distribution and compare to experimental data presents an advantage over the approach initiated by Migdal [22,23]. 

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