Theoretical studies calculations

In theoretical studies, calculations are usually given for loss of heat along the well column and from there into the top and bottom of the oil-bearing formation. These losses do indeed occur in any thermal process, but they increase significantly in petroliferous formations that consist of micro- and macroporosity reservoirs. In such formations the injected heat carrier cannot be retained locally because it easily escapes along high permeability channels. Continuous area steam flooding in such cases becomes ineffective as an EOR technique because the process itself cannot be adequately controlled. 

Dobbyn A J, Stumpf M, Keller H-M and Schinke R 1996 Theoretical study of the unimolecular dissociation HO2—>H+02. II. Calculation of resonant states, dissociation rates, and O2 product state distributions J. Chem. Phys. 104 8357-81... 

By using this approach, it is possible to calculate vibrational state-selected cross-sections from minimal END trajectories obtained with a classical description of the nuclei. We have studied vibrationally excited H2(v) molecules produced in collisions with 30-eV protons [42,43]. The relevant experiments were performed by Toennies et al. [46] with comparisons to theoretical studies using the trajectory surface hopping model [11,47] fTSHM). This system has also stimulated a quantum mechanical study [48] using diatomics-in-molecule (DIM) surfaces [49] and invoicing the infinite-onler sudden approximation (lOSA). 

Theoretical methods ranging from the now obsolete HMO studies to ab initio calculations have been used extensively on pyrazoles. Although not emphasized in earlier reviews (66AHC(6)347,67HC(22)l), the most recent publications (B-76MI40402,79RCR289) contain several references to theoretical studies. Some publications related to structural studies are to be found in the following sections, especially in connection with NMR spectroscopy (Section 4.04.1.3.4), UV spectroscopy (Section 4.04.1.3.6), PE spectroscopy (Section 4.04.1.3.9) and tautomerism (Section 4.04.1.5). 

Whereas oxaziridine and diaziridine were partial subjects of comprehensive theoretical studies on cyclic compounds (73MI50800), diazirine and some of its simple derivatives were the special target of quantum chemical investigations. Since diazirine, the lowest molecular weight heterocycle, has only five atoms and is of high symmetry, there was a chance for ab initio calculations, which followed some semiempirical studies. 

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

As already mentioned, there are two so called "dead volumes" that are important in both theoretical studies and practical chromatographic measurements, namely, the kinetic dead volume and the thermodynamic dead volume. The kinetic dead volume is used to calculate linear mobUe phase velocities and capacity ratios in studies of peak variance. The thermodynamic dead volume is relevant in the collection of retention data and, in particular, data for constructing vant Hoff curves. 

Abstract—Experimental and theoretical studies of the vibrational modes of carbon nanotubes are reviewed. The closing of a 2D graphene sheet into a tubule is found to lead to several new infrared (IR)- and Raman-active modes. The number of these modes is found to depend on the tubule symmetry and not on the diameter. Their diameter-dependent frequencies are calculated using a zone-folding model. Results of Raman scattering studies on arc-derived carbons containing nested or single-wall nanotubes are discussed. They are compared to theory and to that observed for other sp carbons also present in the sample. 

In this chapter the pressure drop for pneumatic conveying pipe flow is studied. The conventional calculation method is based on the use of an additional pressure loss coefficient of the solid particles. The advantage of this classical method is that in principle it can be applied to any type of pneumatic flow. On the other hand, its great disadvantage is that the additional pressure loss coefficient is a complicated function of the density and the velocity of the conveying gas. z lso, it is difficult to illustrate the additional pressure loss coefficient and this makes the theoretical study of it troublesome. 

Experimental and theoretical studies on the benzyl radical (Figure 18.7) have long figured in the literature. The agreement with experiment is acceptable at the BLYP/EPR-II level of theory — much better than that produced by standard Ul-IF calculations. 

Theoretical studies of the relative stabilities of tautomers 14a and 14b were carried out mostly at the semiempirical level. AMI and PM3 calculations [98JST(T)249] of the relative stabilities carried out for a series of 4(5)-substituted imidazoles 14 (R = H, R = H, CH3, OH, F, NO2, Ph) are mostly in accord with the conclusion based on the Charton s equation. From the comparison of the electronic spectra of 4(5)-phenylimidazole 14 (R2 = Ph, R = R3 = H) and 2,4(5)-diphenylimidazole 14 (R = R = Ph, R = H) in ethanol with those calculated by using ir-electron PPP method for each of the tautomeric forms, it follows that calculations for type 14a tautomers match the experimentally observed spectra better (86ZC378). The AMI calculations [92JCS(P1)2779] of enthalpies of formation of 4(5)-aminoimidazole 14 (R = NH2, R = R = H) and 4(5)-nitroimidazole 14 (R = NO2, R = R = H) point to tautomers 14a and 14b respectively as being energetically preferred in the gas phase. Both predictions are in disagreement with expectations based on Charton s equation and the data related to basicity measurements (Table III). These inconsistencies may be... 

A theoretical ab initio study of the gas-phase basicities of methyldiazoles (90JA1303) included a discussion of the 4(5)-methylimidazole tautomer-ism. The RHF/4-31G calculations led to the conclusion that the 4-methyl tautomeric form 14a (R = Me, R = R = H) is 5.2 kJ moP more stable than its 5-methyl counterpart 14b. It was emphasized that this result is to be considered as basic-set dependent. However, a recent theoretical study [94JST(T)45] showed that, starting from the RHF/6-31G level, all the more accurate approximations indicate a higher intrinsic stability for the 4-methyl tautomer. At the MP2/6-31G level, the total energy of the 4-methyl tautomer is 0.7 kJ mol lower than that of the 5-methyl tautomer. Inclusion of solvation effects can, thus, strongly affect the position of the tautomeric equilibrium 14a 14b. Recently, a systematic theoretical study... 

Hydroxyfurazans exist solely in the hydroxy form. This is in accord with quantum chemical calculations (Scheme 167). Density functional theoretical studies (B3LYP/6-311- -G(2d,p)) indicate that 3-hydroxyfurazan is more stable than the... 

In agreement with the previously reported theoretical study, the results of semi-empirical calculations showed that the formation of the Dewar isomer is favored [99H(50)1115]. Probably, the observed formation of the azirine derives from a thermal isomerization of the first photoproduct, in line with that described in the case of furan and thiophene derivatives (Fig. 11). 

The first systematic theoretical study on dihydro-1,2,4-triazines was recently carried out (98JOC5824) the stabilities of all the possible unsubstituted dihydro-1,2,4-triazines were calculated using various theoretical methods, all reliable calculation methods consistently show that the 2,5-dihydro isomer 98 is the most stable. This is in perfect agreement with the experimental observations all the synthetic methods used for the preparation of dihydro-1,2,4-triazines result in 2,5-dihydro isomer 98, provided the structures of the reactants and the reaction mechanism allow its formation. Thus, although Metze and Scherowsky (59CB2481) claimed the formation of 1,2-dihydro-1,2,4-triazine 92 (R = = Ph) in the reduction... 

A theoretical study based on PM3 frontier molecular orbital (FMO) and potential energy surface (PES) analysis at the RHF/6-31-I-G level was performed to examine the reaction of l-amino-2-ethoxycarbonylpyridinium mesitylenesulfonate and acrylonitrile in the presence of Hiinig s base leading to the formation of 3-cyano-4-hydroxy-l,2-dihydropyrido[l,2-ft]pyridazi-nium inner salt (54) (99JOC9001). The calculations indicated that both the... 

Viswanadhan and Matticc278 carried out calculations aimed at rationalizing the relative frequency of backbiting in these and other polymerizations in terms of the ease of adopting the required conformation for intramolecular abstraction (see 2.4.4), More recent theoretical studies generally support these conclusions and provide more quantitative estimates of the Arrhenius parameters for the... 

On the basis of these studies we decided to carry out a series of AMI and IMA experiments (2) with the TMPCl/EtAlCl2/DtBP combination. Figures 1 and 2 show the results. The M versus Wp (g of poly(P-PIN) formed) plots and the N (number of moles of poly(P-PIN) formed) versus Wp plots (insets) indicate increasing deviation from the theoretical values (calculated for Ieff = 100%). According to these results chain transfer proceeds in these polymerizations, i.e., the systems are nonliving. Further experimentation would be necessary to develop satisfactory living conditions, in particular to investigate the effect of solvent polarity, temperature and electron donors on the mechanism. 

Very recently there has been an experimental and theoretical study of electronic substituent effects in 4-aminoaryl (4-substituted aryl) sulfones146. PMR, 13C NMR and infrared measurements were involved and semi-empirical all-valence CNDO/2 calculations, with and without sulfur d orbitals, were carried out. Various correlations between spectral results and substituent constants are presented. There is good agreement between experimental and theoretical data, which does not depend on the inclusion or exclusion of the sulfur d orbitals from the calculations. 

Fischer-type carbene complexes, generally characterized by the formula (CO)5M=C(X)R (M=Cr, Mo, W X=7r-donor substitutent, R=alkyl, aryl or unsaturated alkenyl and alkynyl), have been known now for about 40 years. They have been widely used in synthetic reactions [37,51-58] and show a very good reactivity especially in cycloaddition reactions [59-64]. As described above, Fischer-type carbene complexes are characterized by a formal metal-carbon double bond to a low-valent transition metal which is usually stabilized by 7r-acceptor substituents such as CO, PPh3 or Cp. The electronic structure of the metal-carbene bond is of great interest because it determines the reactivity of the complex [65-68]. Several theoretical studies have addressed this problem by means of semiempirical [69-73], Hartree-Fock (HF) [74-79] and post-HF [80-83] calculations and lately also by density functional theory (DFT) calculations [67, 84-94]. Often these studies also compared Fischer-type and... 

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