Simple Additions

Clearly, simple additivity of atom properties will no longer suffice, as the contribution of an atom will diminish the hirther it is away from the atom whose property has to be estimated. In the following, we present two methods of accounting for the influence of one atom on another, attenuated over the distance between the two atoms. 

The simple addition of acrolein to enamines derived from aldehydes to give substituted glutardialdehydes has also been observed (54). 

Let us first of all consider the simple additive rule R90, defined by 

Rings can either stabilize or destabilize molecules beyond what is to be expected from a simple additivity scheme. Stabilization comes from aromatic ring systems 

Thus, nitric oxide seems to react in a complex manner. Simple addition to existing ions and initiation of new reactions, which might involve even carbon bond scission, seem to occur. At present our study of this system is incomplete. We have not been able to reconcile the complexity of the spectra with the findings of Meisels which are otherwise supported by our rate constant determinations. 

Kang and Jhon [9] showed that mean molecular polarizabiHties, a, can be estimated om atomic hybrid polarizabihties, by a simple additivity scheme summing over all N atoms (Eq. (6)). 

Kohli et al. [27], for instance, showed that the tensile modulus of a highly drawn PC-TLCP composite could be modeled effectively by the simple additivity rule of mixtures, while the compression molded composite samples with a spherical TLCP morphology had moduli according to the inverse rule. In both cases, the tensile modulus of the TLCP (Ei,c) itself was assumed to be a constant value determined from a tensile test of the pure TLCP samples. But whether or not the dispersed TLCP fibers and deformed droplets have the same modulus as the bulk TLCP samples remains a question. 

The importance of FMO theory hes in the fact that good results may be obtained even if the frontier molecular orbitals are calculated by rather simple, approximate quantum mechanical methods such as perturbation theory. Even simple additivity schemes have been developed for estimating the energies and the orbital coefficients of frontier molecular orbitals [6]. 

VVe now need to consider how the form of the wavefunction varies with k. The first situation we consider corresponds to fc = 0, where the exponential terms are all equal to 1 and the overall wavefunction becomes a simple additive linear combination of the atomic orbitals  

Optical parametric oscillator (OPO, see 20) is the real equivalent to the radio frequency shifter however OPO can be replaced by a simple addition of a local oscillator (e.g. laser) through a beam splitter. Multiplication takes place at the level of detectors. For sake of S5mimetry, detectors can be placed at both output of the beam splitter, the intermediate frequency is then the output of the differential amplifier. 

In 2,1-benzisoxazoles, halogenation with CI2 or Br2 leads to substitution in the 5-position, although the reaction appears to behave as a simple addition across a double bond. A 

The high efficiency of conversion of the diesel generator immediately restricts its potential improvement compared with gas turbines. With the simple addition of a boiler, the gas turbine can give a heat/power ratio of 2 1 compared with the diesel s 0.6 1. (The diesel heat/power 

To balance equations 10.2 and 10.3 in terms of electrical charge it has been necessary to add four electrons to the right-hand side of equation 10.2 and to the left-hand-side of equation 10.3. However, simple addition and rationalisation of equations 10.2 and 10.3 yields equation 10.1. 

For each failure time, calculate the corresponding cumulative hazard value, which is the sum of its hazard value and the hazard values of all preceding failure times. This calculation is done recursively by simple addition. For example, for the generator fan failure at 

Treatment of natural rubber with chlorine gives a product, chlorinated rubber, with a maximum chlorine content of 65% corresponding to the empirical formula C10H11CI7. Such a compound corresponds neither to a hypothetical simple addition to the double bond (Figure 30.6 (I)) nor to a product with a-methylenic substitution in addition (II). 

The conversion of carboxylic acid derivatives (halides, esters and lactones, tertiary amides and lactams, nitriles) into aldehydes can be achieved with bulky aluminum hydrides (e.g. DIBAL = diisobutylaluminum hydride, lithium trialkoxyalanates). Simple addition of three equivalents of an alcohol to LiAlH, in THF solution produces those deactivated and selective reagents, e.g. lithium triisopropoxyalanate, LiAlH(OPr )j (J. Malek, 1972). 

Fluoride ion produced from the nucleophilic addition-elimination reactions of fluoroolefins can cataly7e isomerizations and rearrangements The reaction of per fluoro-3-methyl-l-butene with dimethylamine gives as products 1-/V,/Vdimeth-ylamino-1,1,2,2,4,4,4-heptafluoro-3-trifluoromethylbutane, N,W-dimetliyl-2,2,4,4,4-pentafluoro 3 trifluoromethylbutyramide, and approximately 3% of an unidentified olefin [10] The butylamide results from hydrolysis of the observed tertiary amine, and thus they share a common intermediate, l-Al,A -dimethylamino-l,l 24 44-hexafluoro-3-trifluoromethyl-2-butene, the product from the initial addition-elimination reaction (equation 4) The expected product from simple addition was not found 

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