Decomposition schemes

In order to improve parallelism and load balancing, a hybrid force-spatial decomposition scheme was adopted in NAMD 2. Rather than decomposing the nonbonded computation into regions of space or pairwise atomic interactions, the basic unit of work was chosen to be interactions between atoms... 

Lack of any peaks corresponding to oxygen-containing components in the mass spectra of CoNbOF5 (see Fig. 93, C) leads to the conclusion that the compound decomposes without releasing NbOF3 molecules. Hence, the decomposition scheme can be represented by the following interactions ... 

Diacyl peroxides are particularly prone to induced decomposition (Scheme 3.16). Transfer to initiator is of greatest importance for polymerizations taken to high conversion or when the ratio of initiator to monomer is high. It has been shown that, during the polymerization of S initiated by BPO, transfer to initiator can be the major pathway for the termination of chains.7,41... 

The byproducts of decomposition of certain dialkyldiazcncs can be a concern. Consider the case of AIBN decomposition (Scheme 3.13). The major byproduct is the ketenimine (lO).61 100"102 This compound is itself thermally labile and reverts to cyanoisopropyl radicals at a rate constant similar lo that for AIBN thermolysis.59,60 102 This complicates any analysis of the kinetics of initiation/2,60... 

Even though AIBN has a low transfer constant, the ketenimine formed by combination of cyanoisopropyl radicals (Scheme 3.13) is anticipated to be more susceptible to induced decomposition (Scheme 3.22).1Cb... 

A number of mechanisms for thermal decomposition of persulfate in neutral aqueous solution have been proposed.232 They include unimolccular decomposition (Scheme 3.40) and various bimolecular pathways for the disappearance of persulfate involving a water molecule and concomitant formation of hydroxy radicals (Scheme 3.41). The formation of polymers with negligible hydroxy end groups is evidence that the unimolecular process dominates in neutral solution. Heterolytic pathways for persulfate decomposition can he important in acidic media. 

Compounds with a thiocarbonyl a to the S-S bond such as the dithiuram (e.g. 8f2Al and xanthogen disulfides (e.g. 9)M have transfer constants that are much higher than other disulfides. In part, this may be due to the availability of another mechanism for induced decomposition (Scheme 6.9) involving addition to the C S double bond and subsequent fragmentation. Thiocarbonyl double bonds are very reactive towards addition and an addition-fragmentation mechanism has been demonstrated for related compounds (Section 6.2.3.5). 

Leadbeater described the use of Ni(CN)2 for the microwave-assisted cyanation of (hetero)aryl bromides [81]. The use of 0.6equiv of Ni(CN)2 was found to be optimal. Unfortunately, the heteroaryl bromides reported in the study gave relatively low yields due to significant decomposition (Scheme 70). 

Multiple M=P bonding in (OC)5M=PR becomes evident with ADF s bond energy analysis in terms of electrostatic interactions, Pauli repulsion, and orbital interactions from which the a,Ti-separation is obtained using a symmetry decomposition scheme [21]. For singlet (OC)5Cr=PR, which has a BDEst of 40.5 kcal/mol, the a- and n-components are 62.4 and 40.9 kcal/mol, respectively. 

Intermolecular Energy Decomposition Schemes Equivalence Between Terms... 

Figure 6-1. Notations for usual energy decomposition schemes...

Kitaura K, Morokuma K (1976) A new energy decomposition scheme for molecular interactions within the Hartree-Fock approximation. Int J Quantum Chem 10 325... 

The volume confined by the surface < )(r) = < )0 can be calculated more precisely if the surface has been triangulated within one of the simplex decomposition schemes. Having the surface represented by the polygons inside a simplex, the volumes of the geometrical object specified by the polygons can be... 

In order to apply the PSM, the surface must first be triangulated by using one of the simplex decomposition scheme. The vectors normal to each vertex of the polygons are calculated as... 

Fig. 36 Structure of meso- and (+ )-azobis[6-(6-cyanododecanoic acid)] and their decomposition scheme.

The mode of decomposition of Oi -alkylated diazeniumdiolates bound to carbonyls is also exceptional because they can undergo rearrangement to hyponitrites before decomposition (Scheme 3.15) [163]. 

Shore and coworkers—nuclearity studies over Ru carbonyl catalysts. Shore et al.64 studied reactions of K[DRu3(CO)n] + CO + H20 <- HD + Ru3(CO)i2 + KOH. They found that, at room temperature and 1 atm pressure of Pco, HD is rapidly evolved. In the absence of CO, however, the HD was formed only in trace quantities. They proposed two possible mechanisms to account for this behavior, (a) a concerted mechanism where CO promotes hydride decomposition (Scheme 28), or (b) an associative mechanism involving a complex-CO adduct, which decomposes with H20 (Scheme 29). 

Jackson JR, Grossmann IE (2003) Temporal Decomposition Scheme for Nonlinear Multisite Production Planning and Distribution Models. Industrial Engineering Chemistry Research 42 3045-3055... 

Certain desirable features are sought in and certain limitations are imposed on any effective decomposition scheme. These are ... 

The obtained obs values are reported as a fimction of the complex concentration (Fig. 8), and a good linear correlation between obs and the complex concentration was observed for both oxidation forms of iron complexes. From the slope of the plot of obs vs. catalyst concentration the catalytic rate constants ( cat) i29) were determined to be (3.7 0.5) X 10 M- s and (3.9 0.5) x 10 M s for [Fe (dapsox)(-H20)2]C104 and [Fe (H2dapsox)(H20)2](NOs)2, respectively 49). It is important to note that, it does not matter whether we start from the Fe(III) or Fe(II) form of the complex, identical spectral changes (Fig. 6a and 6b) and kinetic behavior (Fig. 8) for these two complexes is observed upon reaction with, which is consistent with the redox cychng of the complex during O2 decomposition (Scheme 9). 

A major advantage of the orbital decomposition scheme of the KT is its ability to deal with orbital contributions to Se from molecular targets. This virtue has been particularly useful to theoretically analyze [25,33,40,41] the origin of the experimentally observed chemical binding effects and physical phase-state effects in the stopping power of light ions in compounds in the gas or in the condensed phase [20-24]. 

Function approximation comes naturally with the Fourier transition. Since tiny details of a function in real space relate to high-frequency components in Fourier space, restricting to low-order components when transforming back to real space (low-pass filtering) effectively smoothes the function to any desirable degree. There are special function decomposition schemes, like spherical harmonics, which especially build on this ability [128]. 

Jackson, J.R. and Grossmann, I.E. (2003) Temporal decomposition scheme for nonlinear multisite production planning and distribution models. Industrial el Engineering Chemistry Research, 42, 3045. 

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