Comparison with Theoretical Calculations

The binding enthalpy, is given by Equation 7.19 (explained in Chapter 1)  

Because AE i is the dominant term in the enthalpy expression, single-point electronic energy calculations were performed at higher levels than the level of geometry optimization. As expected and shown in Table 7.6, the negative enthalpy increases with the level of computation. 

A satisfactory convergence to a common gas-phase calculated value of -34.7 kJ mor is observed in Table 7.6 when both the computational level and the gas-phase-like behaviour of the medium increases. 

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Fig. 59.—Differential weight distribution for poly-(methyl methacrylate), as deduced from curve in Fig. 58, in comparison with theoretically calculated curve. (Baxendale, Bywater, and Evans. )...

Graph 1. Hydrogen capacity for Pt-MnCb (bar of black check on white background) in comparison with theoretically calculated amount of gas adsorbed by Pt (plain bar) and support (bar with white diamonds on black background). 

Knowledge of the sample pressure is essential in all high-pressure experiments. It is vital for determinations of equations of state, for comparisons with other experimental studies and for comparisons with theoretical calculations. Unfortunately, one cannot determine the sample pressure directly from the applied force on the anvils and their cross-sectional area, as losses due to friction and elastic deformation cannot be accurately accounted for. While an absolute pressure scale can be obtained from the volume and compressibility, by integration of the bulk modulus [109], the most commonly-employed methods to determine pressures in crystallographic experiments are to use a luminescent pressure sensor, or the known equation of state of a calibrant placed into the sample chamber with the sample. W.B. Holzapfel has recently reviewed both fluorescence and calibrant data with the aim of realising a practical pressure scale to 300 GPa [138]. 

In order to increase the experimental benchmarks available for comparison with theoretical calculation, Mcllroy et al., determined the singlet triplet energy splitting in a diaminosubstituted nitrenium ion, 1,3-dimethylbenzotriazolium ion 37 (Fig. 13.22). This species can be viewed a nitrenium ion by virtue of mesomer 37a, which places a positive charge on the central nitrogen. Because this species... 

Additional spectroscopic data were available, which have, however, less frequently been used for comparison with theoretical calculations. These comprise the UV spectrum. Ref. 20, and the microwave spectrum of 4 (a) R. D. Brown, P. D. Godfrey, and M. J. Rodler, J. Am. Chem. Soc. 1986, 108, 1296. The dipolar C NMR spectrum of 1,2-[ C]2-4 in an argon matrix was measured and analyzed in order to determine the C=C distance., cf. Ref. 24. A detailed comparison of measured and calculated chemical shifts is given in (b) H. Jiao, P. v. R. Schleyer, B. R. Beno, K. N. Houk, and R. Warmuth, Angew. Chem. 1997, 109, 2929 Angew. Chem. Int. Ed. Engl. 1997, 36, 2761. 

Fig. 10. Concentration dependence of the diffusion coefficient of Dye I in Nylon 6 determined from diffusion profiles (film-roll method), in comparison with theoretical calculations from Eq. (25) with DT2 = 1.5 x lO-10 cm2/s and DT2/DX] =0.7 (full line) 82-84>. The individual contributions of the first and second terms of Eq. (25) are shown by the broken lines A and B respectively...

L.B. Knight et al., Laser vaporization generation of the SiB and SiAl radicals for matrix isolation electron spin resonance studies comparison with theoretical calculations and assignment of their electronic ground states as X 4Z. J. Chem. Phys. 98, 6749-6757... 

Comparison with Theoretical Calculations. It appears that the polymer valence bands are (very) difficult to interpret without the aid of a theoretical basis, or a model, or of the use of a reference spectrum obtained from a model compound. Indeed, Quantum Chemical theory is nowadays able to calculate band structure and density of states for polymers, to simulate the limited resolution of the spectrometer, and to modulate these theoretical density of states to account for the photoionization cross sections that vary considerably for valence bands of polymers containing different types of atoms, and electrons with various symmetries. Consequently, one is able now to predict theoretically the energies of the various molecular orbitals, but also... 

Quahtative information on the structme of the colored corrinoids in solution can be extracted rapidly from UV/Vis and CD spectra most of the spectroscopic features can be rationalized nowadays by comparison with theoretically calculated spectra. For more precise constitutional information, some of the newly developed methods of mass spectrometry allow the analysis even of the involatile Bi2-derivatives. Modem one-and two-dimensional proton, carbon, nitrogen, and phosphoms NMR spectroscopy has proven a powerful instrument for the delineation of the stmcture of diamagnetic cobalt-corrins in solution. ESR-spectroscopy has given important information on paramagnetic corrinoid Co"-complexes, whether in frozen solutions or bound in corrinoid enzymes. X-ray adsorption fine spectroscopy (EXAFS) spectroscopy and vibrational (IR and Raman) spectroscopy are other spectroscopic techniques used more frequently now in the B12 field. 

Similar results have been obtained for Ni(100)c(2 x 2)-CO and Ni(100)c(2 X 2)-0. For CO best agreement between theory and experiment is found for the adsorbate bonded in the atop or terminal position, in agreement with LEED observations. It has been emphasized by Plummer and Gustafsson that at present the interpretation of experimental data depends heavily on comparison with theoretical calculations for each individual adsorbate-surface combination. General symmetry arguments (selection rules), however, are now being formulated which should allow identification of the symmetry of the initial-state orbital or adsorption site, without complicated calculations. 

Gold nanoparticles prepared within mesoporous silica monolith showed red-shift of the Mie-resonance absorption band with decreasing the Au particle size. Comparison with theoretical calculations of Mie-resonance for particles of... 

Figure 23.2. (a) Dependence of the band gap of nc-Si determined from the onset of the PL excitation spectra (shown in (b)) in comparison with theoretical calculations and the position of the maximum of the "red" PL from nc-Si/SiOj. 

An example of a more recent experiment is the smdy of hyperfine structure of highly excited levels of neutral copper atoms, which yielded the magnetic-dipole and electric-quadmpole interaction constants. The experimental results allowed a comparison with theoretical calculations based on multiconfiguration Hartree-Fock methods [858]. Measurements of lifetimes [859] and of state multipoles using level-crossing techniques can be found in [860]. 

It is probably worth emphasizing that serial correlations among time correlation functions computed in molecular dynamics calculations are commonly present and should be taken into account when making comparisons with theoretical calculations and with other similar calculational results. 

FIGU RE 5.9 Two-color ladder-type optical-optical double-resonance PA spectra via the Og (4p3/2) v = Q,J = 2 level. The panels show the spectra just below the 4s--bos asymptote (top), the 44 -F 5d asymptote (middle) and the 4s + 6d asymptote (bottom). Comparison with theoretical calculations suggests that the absolute vibrational quantum numbering is as shown, with u = 0 [22]. (From Normand, B. and Stwalley, W.C., J. Chem. Phys., 121, 285, 2004. With permission.)... 

Furthermore, comparison between theory and experiment for the equilibrium geometries of the complexes (shown for n = 1 — 3 in Fig. 5.2) and vibrational redshifts provide critical tests of theoretical potentials. Furthermore, the spectroscopic data implicitly include the effects of nonpairwise interactions, and comparison with theoretical calculations using accurate pairwise potentials permits the quantitative determination of their sign and magnitude. 

Z.-S. Li, J. Norin, A. Persson, C.-G. Wahlstrom, S. Svanberg, P.S. Doidge, E. Biemont Radiative properties of neutral germcuiium obtained from excited state lifetime and branching ratio mecisurements and comparison with theoretical calculations. Phys. Rev. A 60, 198 (1999)... 

The necessary steps for data reduction from raw data to comparison with theoretically calculated wavefunctions. In the left hand site are the corrections for absolute studies measurements, in the right hand site for comparative studies. In the first case the (q) is reduced... 

A potentiodynamic kinetic model of Pt oxide formation that is consistent with CV data over a wide range of scan rates and for different catalyst surface structures is an important step in understanding Pt oxide formation and reduction. Evaluation of the model against a range of electrochemical and spectroscopic data and comparison with theoretical calculations of reaction pathways and energetics could help furnishing details of reaction mechanisms. 

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