Writing parallel structure

Bonded atoms can share more than one electron pair. A double bond occurs when bonded atoms share two electron pairs in a triple bond, three pairs of electrons are shared. In ethylene (Q2H4) and acetylene (QHJ, the carbon atoms are linked by a double bond and triple bond, respectively. Using two parallel lines to represent a double bond and three for a triple bond, we write the structures of these molecules as... 

Because the electron density we seek is a complicated periodic function, it can be described as a Fourier series. Do the many structure-factor equations, each a sum of wave equations describing one reflection in the diffraction pattern, have any connection with the Fourier series that describes the electron density As mentioned earlier, each structure-factor equation can be written as a sum in which each term describes diffraction from one atom in the unit cell. But this is only one of many ways to write a structure-factor equation. Another way is to imagine dividing the electron density in the unit cell into many small volume elements by inserting planes parallel to the cell edges (Fig. 2.16). 

Each diffracted ray is a complicated wave, the sum of diffractive contributions from all atoms in the unit cell. For a unit cell containing n atoms, the structure factor Fhkl is the sum of all the atomic fhkl values for individual atoms. Thus, in parallel with Eq. (2.3), we write the structure factor for reflection Fhkl as follows ... 

Parallelism. Because much of the data in an NDA involves comparisons of one group to another, parallel structure is important in presenting the data. Style books for scientific writing will supply good examples of this concept. 

In prior sections of this chapter, we discussed a variety of programming languages, as well as program structuring techniques that have been found useful for writing parallel computational chemistry codes. Some parallel systems are described in the chapter appendix. In this section, we delve more deeply into the more specific topics of ... 

Various ways of writing the formula to describe a moiety parallel the amount of information known about that moiety. For example, consider the two molecules illustrated in Figure 1. One can not tell from the molecular formula , C2H60, which isomer is being described. The structural formula , on the other hand, advises precisely which atoms are attached to each other. 

CUDA abstracts the hierarchical GPU hardware structure outlined, into a programming framework, requiring the coder to write in an intrinsically parallel fashion. The small numerically intensive subroutines of code that run specifically on the GPU are termed kernels. These are executed in blocks where each block contains multiple instances of the kernel, termed threads. 

The structure of halloysite is equivalent to that of kaolinite, but has a layer of water molecules between each pair of silica and alumina layers (see Chap. 9 Deer et al. 1992). Writing halloysite dissolution in the same form as in Eq. (7.35) for kaolinite, its solubility product is = 10 - (Hem et al. 1973 Stecfel and van Cappellen 1990), versus = 10" for kaolinite. In other words, halloysite is about 80 times more soluble than kaolinite. If plotted in Fig. 7.9, also assuming Si02(aq) = 17 ppm, the solubility curve for halloysite is parallel to but 1.9 log units above the curve for kaolinite at any pH. 

Now in an ice crystal each proton jump over a distance 2/ as in fig. 9.12 effectively moves the defect concerned through some larger distance, say r. From fig. 9.6 these two distances can be related to characteristic spacings in the lattice for either the direct jumps associated with ion states or the oblique jumps characteristic of valence defects. More than this, however, not all jump directions make the same angle with the field, though in the unpolarized ice structure there is always a possible jump with a component in the field direction. This average is simply performed and leads to an average defect displacement parallel to the field which we can write as . From (9.61) the classical mobility is then... 

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