Stick notation

This notation uses atomic symbols or group abbreviations joined by single, double or triple lines to represent single, double or triple covalent bonds. All atoms are included in a stylised manner at an 

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In stick notation we write these reactions as shown in Figure 2-17. We described the steps by which cmde oil is converted into aromatics such as p-xylene previously. Here we discuss the production of ethylene glycol from ethane. 

Figure 2. The ligand common to all molybdenum and tungsten enzymes, MPT, is shown here in several formats (a) in common stick notation (b) as a ball and stick (c) an orientation rotated 90° from view (b) to emphasize the spacial relationship between the pterin plane and the dithiolene-pyran ring portion (d) MGD in common stick notation and for comparison, (e ) FAD, a common electron-transfer prosthetic group. Coordinates for the views in (b) and (c) are taken from the data deposited in the Protein Data Bank (PDB) for the 1.3-A resolution structure of DMSO reductase from Rhodobacter sphaeroides.

A second approach also considers three populations free (unquenched) donors No, free acceptors NA, and a population engaged in FRET pairs Ns that transfer energy with characteristic efficiency E (between 0 and 1). However, in this case, the Ns population emits both donor fluorescence (quenched by a fraction (1 - E)) and sensitized emission (proportional to ENS). To keep in line with the treatment and terminology in other chapters in this volume, this latter approach will be followed here. Note, however, that in other chapters the population of FRET pairs is indicated by the subscript DA whereas we stick to the notation Ns to indicate that this quantity is based on photons emitted from sensitized emission (S image) and to keep the close synonymy with the former approach. Thus, our Io-s equals Ida and Is +1 a equals IAo- Both ways yield essentially identical results. 

Care is needed with notation at this point some texts call an inert electrode operating in this context a redox electrode. However, we will stick with the terminology developed over the previous chapters. 

We can see the different structural features of n-pentane, Ao-pentane, and neo-pentane more clearly by drawing the molecules in two dimensions, as shown in the middle row of Figure 12.1. Alternatively, we can represent them by the stick structures shown in the bottom row. A stick structure is a commonly used, shorthand notation for representing an organic molecule. Each line (stick)... 

Fig. 7.4 11 L8 PDB structure. Chain A is represented in green cartoons and chain B in stick CPK notation.

Bent Geometry Molecules belonging to the geometry classes AX2E2 are bent or nonlinear. In this notation, A is still the central atom, and X is still a stick-on group. The E s represent lone pairs of electrons on the central atom (A). Water is... 

The effective communication of chemical structure is essential for all chemists. Over the years many different types of structure representation have been developed. Before the use of computers, chemists drew structures manually, often using a linear text notation. As more sophisticated methods for drawing have become available, the trend has been toward two-dimensional stick structures, such as the zigzag Natta projection (Figure 8.1). 

Figure 2 Structure of the human hepatic cytochrome P450 CYP3A4 (18) is shown from the distal site of the heme in cartoon representation. The spacious substrate-binding cavity is represented as a mesh. The heme is shown in sticks, which can be observed under the mesh grid. Helices are labeled by letters according to the common notation for all cytochromes P450 that share the same fold (17). Prepared using PyMol (Defano Scientific ffC, San Carlos, CA)...

In the following, we will discuss DMC simulations on the CO oxidation on the Pt(lOO) surface, that were done in our laboratories. The simulations show oscillations in the CO2 production rate as well as several types of spatio-temporal pattern formation. In essence, it is an extension of the ZGB model with desorption and diffusion of A, finite reaction rates and surface reconstruction. We will discuss it to illustrate the complexity of the models with which DMC simulations can be done nowadays. For clarity, we will stick to the A and B2 notation employed in the previous section. Species A corresponds to CO and B2 corresponds to 02- Furthermore, we will speak in terms of reaction rates instead of relative reaction probabilities. This terminology is entirely justified in the DMC approach that we used. 

It should be noted that instead of dressing the molecular states g and s by 1 and 0 photons, respectively, we could use any photon numbers p and p — 1. The corresponding matrix elements are than proportional to p. In processes pertaining to linear spectroscopy it is convenient to stick with photon populations 1 and 0, keeping in mind that all observed fluxes should be proportional to the incident photon numberp or, more physically, to the incident field intensity fo P- With this in mind we will henceforth use the notation g, k) (or g, m if the incident direction is not important for the discussion) as a substitute for g, Ik)-... 

Solutions of macromolecules are often sufficiently dilute that Eq. (13.5.21) applies. Moreover for large molecules can be computed from hydrodynamics. For a sphere with stick boundary conditions Cs = 6jirjas. Thus in dilute solutions D° and thereby as, the particle radius, can be determined (see Chapters 5 and 8). Since D° depends on the temperature and the solvent, it is important to report the data in a standardized manner. Usually the measurements are performed at room temperature and are extrapolated to inifinite dilution. Thus for example the notation D%0,a denotes the diffusion coefficient of the solute at 20°C in the solvent H20 extrapolated to infinite dilution. For nonideal solutions... 

Figure 1. Representative polyoxometalates in polyhedral notation. A. the isopolyanion decatungstate (Wio032 ) (C>4h point group symmetry) and B. the heteropolyanion family, (TM)PWii039 , where TM is a first row divalent transition metal ion, P is the heteroatom (Cs point group symmetry). In the latter class of complexes, which constitute functional oxidatively resistant inorganic metalloporphyrin analogs, P is one of many elements that can function as the heteroatom. The darker octahedron on the surface and the veiy dark internal tetrahedron of B represent the TM ion and the heteroatom, respectively. In polyhedral notation a complementary notation to ball-and-stick or bond representations, the vertices of the polyhedra, principally W06 octahedra, are the nuclei of the oxygen atoms. The metal atoms lie inside each polyhedron.

This process bears the respectable name of "self-dissociation of water and is pre-smned to be an equihbrium reaction, because it concludes when the species indicated on the left and right side of this chemical equation (reactants and products) are present at the same time. This means the order of the reactants and products in the above chemical equation could even be reversed. The reaction itself is also called reversible. In pure water, the same amounts of hydrogen (H+) ions and hydroxide ions (OH ) form. The notation used for hydrogen ion is still a matter of debate in today s science. Some experts stubbornly stick to the notation HjO which is called oxonium or hydroxonium ion (—> 4.10). It is difficult to formulate justice here, as reality itself is much more complex than any single chemical formula could express. But as far as notations go, using the simpler one seems... well, simpler. 

Later, in discussion of optimal mechanism design, we will fall back on the more general framework of randomized allocation rules and expected payments. For now we choose to stick with deterministic allocations and payments to keep the notation as simple as possible. 

SI unit of activity. Since 1975, the internationally recommended unit is the becquerel (Bq) defined as 1 disintegration per second (1 dps), but workers in nuclear and radiochemistry, especially those handling high activities, still stick to the old unit curie. Some authors prefer the notation dps to Bq and the acronym dpm (meaning decays per minute) also occurs as a unit of activity. 

Fig. X.l. The coordinate system used in the multipole expansion, (a) Interparticle distances. The large black dots denote the origins of the two Cartesian coordinate q/stems, labelled a and b, respectively. We assume particle 1 always resides close to a. particle 2 always close to b. The figure gives a notation related to the distances considered, (b) Tvo Cartesian coordinate systems (and their polar counterparts) one associated with the centre a, the second one with centre b (the x and y axes are parallel in both systems, the x axes are collinear). Note that the two coordinate systems are not on the same footing the z axis of a points towards b, while the coordinate system b does not point to a. Sometimes in the literature we introduce an alternative coordinate system with equal footing by changing zj —zj (then the two coordinate systems point to each other), but this leads to different handedness ( right- or left-handed ) of the systems and subsequently to complications for chiral molecules. Let us stick to the non-equivalent choice .

In the literature, many forms of the unitary matrix in Eq. (11.27) can be found and are not easy to be recognized as the same — often also because the notation is varied and authors chose not to stick to historically older conventions. To demonstrate how these different forms can be interconverted we may consider some of them explicitly in the following. An often employed version of Uq, identical to the one above, is the exponential form. 

For the sake of brevity, we stick to the notation fioKHn also for the (2x2)-block diagonal operators (up to this point, these operators denoted sums of block-diagonal (4x4) even operators). Up to fourth-order (n=4), the (2x2)-dimensional DKH Hamiltonians... 

A) Ball-and-stick model.fSj Shorthand notation. Note that N N represents ethylenediamine. 

For the sake of simplicity, we have used the symbol to depict the dissociating proton. In reality, the free proton does not exist in solution, but is always associated with the electron pair of another species present, typically the solvent. As we have seen, in water, is represented by the hydronium ion, HsO. In methanol, it wonld be methoxonium ion CH30H2, in methoxymethane (Figure 1-22B) it would be (CH3)20H, and so on. We shall see later that in many organic reactions carried out under acidic conditions, there are several potential recipients of a dissociating proton, and it becomes cumbersome to show them all. In these cases, we will stick with the short notation H. ... 

The time rate of change of shear strain, y (or dyidt, the dot is Newton s notation for the time derivative), is the so-called shear rate. Since the order in which the mixed second derivative is taken is immaterial (note that by sticking to two dimensions, we can write total rather than partial derivatives), then... 

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