Calculation scheme

X-ray analysis of 2-phenylmethylaraino-5-phenyl-A-2-thiazoline-4-one (176), which exists in the keto form in the solid state (420), and of 4,4 -diacetoxy-5,5 -dimethy]-2,2 bithiazolyl (177) (419) are available as model compounds for theoretical calculations (Scheme 92). 

On pages 232-234 is an example in the other extreme, where a high-pressure, fast reaction is studied on an industrial size catalyst. The layout and calculation schemes are the same as in the NOx example, so these are not repeated here. 

On page 235-241 is the explicit solution used in Excel format to make studies, or mathematical experiments, of any desired and possible nature. The same organization is used here as in previous Excel applications. Column A is the name of the variable, the same as in the FORTRAN program. Column B is the corresponding notation and Column C is the calculation scheme. This holds until line 24. From line 27 the intermediate calculation steps are in coded form. This agrees with the notation used toward the end of the FORTRAN listing. An exception is at the A, B, and C constants for the final quadratic equation. The expression for B was too long that we had to cut it in two. Therefore, after the expression for A, another forD is included that is then included in B. 

Both of these substitution pathways in MeCN solution have been simulated using the Onsager model (Tables IV and V). Whereas pathway b is favored in the gas phase, inclusion of solvent effects in the calculations causes pathway a to be energetically favored. Substitution of Cl via pathway a is now 1.6 kcal/mol more favorable. In addition, TS(X)/TS(Pyr) calculations (Scheme 15) for the OMe (40) and OSiMes (41) cations have been performed. TS(X) of both 40 and 41 remain significantly disfavored (+66.9 kcal/mol and +46.6 kcakmol, respectively), thus indicating that pathway b should be preferred in MeCN.Tliese calculations are in complete agreement with experimental observations. 

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... 

The structures of pyrrolo[l,2-c]pyrimidine 139 and its N-protonated form 140 were obtained from MP2/6-31G calculations (Scheme 92) [99JOC7788]. Proton affinities computed at the same level reveal that N-protonation is slightly preferred over protonation at the C7 position. The most stable tautomers of 2-substituted 5-methyl-7-hydroxy-l,2,4-tiiazolo[l,5-a]pyrimidine 141 were... 

The molecular orbital energy-level diagrams of heteronuclear diatomic molecules are much harder to predict qualitatitvely and we have to calculate each one explicitly because the atomic orbitals contribute differently to each one. Figure 3.35 shows the calculated scheme typically found for CO and NO. We can use this diagram to state the electron configuration by using the same procedure as for homonuclear diatomic molecules. 

Wallqvist A, Ahlstrom P, Karlstrom G (1990) A new intermolecular energy calculation scheme -applications to potential surface and liquid properties of water. J Phys Chem 94(4) 1649-1656... 

A major objective in developing these risk estimation procedures was to provide a method capable of evaluating hundreds of properties in several communities within the DOE Uranium Mill Tailings Remedial Action Program in a timely manner. Therefore, we chose a calculation scheme that could be performed using commercially available database software (dBASE II, a trademark of Ashton-Tate, Culver City, CA), but that at the same time would be flexible enough that assessments for other contaminants could be readily incorporated. 

This effect has recently been explained by considering that under microwave irradiation the route involving direct reaction between the acyl chloride and the imine competes efficiently with the ketene-imine reaction pathway, a situation highlighted by theoretical calculations (Scheme 9.69) [42 a],... 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

Essentially all of the engineering thermodynamic correlations used in pollution control models and synthesis gas phase equilibria, chemical equilibria, and enthalpy calculation schemes have their foundations in fundamental theory. Experimental data, in addition to being directly useful to designers, allows the correlation developer to assess the validity and suitability of his model. Included within the third section (Properties of Aqueous Solutions—Theory, Experiment, and Prediction) are chapters providing both comprehensive reviews and detailed descriptions of specific areas of concern in the theory and properties of aqueous solutions. 

The simplified module model and the calculation scheme will be shown later in Figure 7 to 8 and Table 3 ... 

Similarly, [(Bu CH2)2Mo(=NAr)(=CHCMe2R)] reacts with the silanols group of a silica or a molecular silanol to yield [(=SiO)Mo(=NAr)(=CHCMe2R)(CH2Bu )] via direct electrophilic cleavage of the Mo-C bond, according to mass balance analysis, NMR and calculations (Scheme 2.27) [72, 73]. 

The cluster studied in this work is shown in Figure 1 with its neighbors in a unit cell based on yttrium ions. With this choice, the ions Cul, Cu2 and 04 each have all their nearest neighbors included into the cluster. We did not correct the influence of nearest point charges on the boundary ions 01, 02, and 03, by introducing pseudopotentials, as in the ICECAP program, see [38]. An account of such corrections complicates the calculation scheme used. The real influence of this effect will be checked in fiiture studies. The interionic distances were taken from Jorgensen et al. [50]. 

The DRE calculation scheme takes into account only two types of CC bonds, not accounting for the fact that the energy of an acyclic polyene depends on its branching. The 7r-energy of a branched acyclic polyene Ev (BP) is related to the energy of an isomeric linear polyene E (LP) by (75JCP3399)... 

So, SRPA and EOM with the Hamiltonian (23)-(24) are equivalent. This allows to to establish the connection between the SRPA and couled-cluster EOM method with the single reference (see for reviews [32-35]). SRPA uses the excitation operators involving only singles (Iph) and so generally carries less correlations than EOM-CC. At the same time, SRPA delivers very elegant and physically transparent calculations scheme and, as is shown in our calculations, the correlations included to the SRPA are often quite... 

In ab initio methods the HER approximation is used for build-up of initial estimate for and which have to be further improved by methods of configurational interaction in the complete active space (CAS) [39], or by Mpller-Plesset perturbation theory (MPn) of order n, or by the coupled clusters [40,41] methods. In fact, any reasonable result within the ab initio QC requires at least minimal involvement of electron correlation. All the technical tricks invented to go beyond the HFR calculation scheme in terms of different forms of the trial wave function or various perturbative procedures represent in fact attempts to estimate somehow the second term of Eq. (5) - the cumulant % of the two-particle density matrix. 

It is shown that the simplified calculational scheme discussed in Parts I and II of this series accomodates the total body of inexact and often self-contradictory experimental information almost as well as might reasonably be expected of any computational method. Some possibly systematic discrepancies in the reported experimental C-J pressures are discussed on the basis of methods used to carry out and interpret the measurements in the various laboratories. 

The internal dynamics of a short sequence in a chain is studied according to the dynamic RIS scheme. Conformational transitions with dynamic pair correlations are considered. Resistance to dynamic rearrangements resulting from environmental effects and constraints operating at the ends of a sequence are incorporated into the calculation scheme. Calculations for a short sequence in a PE chain show that pair correlations do not significantly affect the orientational relaxation of a vector affixed to a bond in the sequence. Contributions from constraints, on the other hand, are dominant and slow down the orientational motions. 

This calculational scheme has been applied to the Small Boy detonation. The test was made to compare fractionation data from this well-studied event (2) with calculated values. Using 25 particle size fractions that approximate the fallout from the event and the time-temperature history given in Table III, which was derived from generalized time-temperature event histories, the fission product contents of the nuclide chains 80 through 150 in the particle size fractions were calcu-... 

To avoid lengthy calculations, let us confine ourselves to the implicit calculation scheme. Introducing discretization tj = iAt, rm = mAr, g(rm, U) = glm, one gets... 

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