First sphere

A hierarchy is thereby achieved, that will lead to a reaction file structure, where each entry is referenced through the various levels of specificity up to the R-categories. Queries can be entered at any degree of generality. 

ACS Symposium Series Ameriean Chemieal Soeiety Washington, DC, 1977. 

It is worth remarking that the different R-categories govern widely different populations of known reactions. One obvious example is the simple four center reaction of the kind A-B + C-D = A-C + B-D, which is incidentally represented by the simplest R-matrix in closed shell chemistry that has a zero diagonal. 

We have started the design of a model program to extract irreducible R-matrices from known reactions, to put them into canonical order, and to set the sequence of references in a hierarchical file, that is organized in a similar way as substructure files described in (5.1.3). 

Gasteiger, C. Gillespie, P. Gillespie, I. Ugi in Computer Representation and Manipulation of Chemical Information , Ed. W.T. Wipke, S. Heller R. Feldmann, E. Hyde, Wiley, N.Y. (197 ). 

---

The extended connectivity (EC) value of an atom of the first sphere (i) results from the number (n) of neighboring atoms (NA) according to Eq, (7) ... 

When all the EC values of the atoms have been calculated, the number of equivalent classes (e) for the first sphere is determined. The number of classes is equivalent to the number of different EC values. 

At 2 20 A M., another explosion occurred, the BLEVE of sphere 407. Its fireball was less intense than the earlier one. The sphere s top section traveled 190 m (620 ft) and caused the destruction of a firewater tank and one of the plant s fire pumps. Other sections further damaged other units. The pressure relief valve of this sphere traveled 500 m (1600 ft). The damage from projectiles was much greater than that caused by the first sphere failure because they traveled farther and in more damaging directions. 

In the relative coordinate system in which the first sphere is at rest, a collision can occur only if the center of the second sphere lies within the collision cylinder" as shown in figure 9.6. Now, the volume of the cylinder is equal to b d4> db u 5t. Prom figure 9.6 it should be clear that... 

A more detailed analysis of the first sphere of 12 Ga atoms shows that the cluster bears a resemblance not only to the anti-cuboctahedron. In the arrangement... 

The smaller contribution to solvent proton relaxation due to the slow exchanging regime also allows detection of second and outer sphere contributions (62). In fact outer-sphere and/or second sphere protons contribute less than 5% of proton relaxivity for the highest temperature profile, and to about 30% for the lowest temperature profile. The fact that they affect differently the profiles acquired at different temperature influences the best-fit values of all parameters with respect to the values obtained without including outer and second sphere contributions, and not only the value of the first sphere proton-metal ion distance (as it usually happens for the other metal aqua ions). A simultaneous fit of longitudinal and transverse relaxation rates provides the values of the distance of the 12 water protons from the metal ion (2.71 A), of the transient ZFS (0.11 cm ), of the correlation time for electron relaxation (about 2 x 10 s at room temperature), of the reorienta-tional time (about 70 x 10 s at room temperature), of the lifetime (about 7 x 10 s at room temperature), of the constant of contact interaction (2.1 MHz). A second coordination sphere was considered with 26 fast exchanging water protons at 4.5 A from the metal ion (99), and the distance of closest approach was fixed in the range between 5.5 and 6.5 A. 

Definition) All atoms of the ligands to be compared arc ordered according to their topologic distance (number of bonds to the stereogenic center). All atoms of equal topologic distance are said to form a sphere, The atoms in the first sphere are called proximal atoms (p). The atoms of spheres II, III,. . N.. are bound to the stereogenic center via 2, 3. , N.. bonds. 

Rule) The ranking of an atom within a sphere (N) firstly depends on the rank of the atom in the lower sphere (N-l) to which it is bonded. The numbering of atoms as shown above is very helpful. The first sphere is occupied by the proximal atoms p, p, those in the second sphere are numbered 1, 2, 3,., ., and those in the third sphere 11, 12, 13, 21, 22, 23,. .. etc. The smaller the number, the higher the relative ranking. 

Levich (1970) suggested a molecular model to rationalize the phrase outer sphere activation." Thus, the lack in Marcus s original (1956) model of any explicit accounting for the influence of the first hydration layer led to the idea that the activation must arise outside the first sphere. ... 

In writing the formula of a "coordinated complex", the "coordinated group , called "nucleus" or the "first sphere" is enclosed in square brackets, while the acid radicals are placed outside in the so-called "second or ionization sphere". For instance in the formula [m Rm], M is a metal (such as Cd,... 

Theorem 10.5.1 The only ( 3,4, 4)-spheres that are 3R2 are either APrism4, or the infinite family of r-elongated octahedra (first spheres on Figures 10.11, 10.12 correspond to cases t = 1,2). 

A ( 5,7), 3)-sphere with a -cycle of 5-gons and n < 31 has at most 19 7-gons. Hence, one of its (7,3)-polycycles has less than nine 7-gons. We enumerated all (7,3)-polycycles up to nine 7-gons, and found only two spheres depicted on Figure 15.5. The first sphere was in [DGr02], while the second coincides with the one found in [HaSo07],... 

FIGURE5.il A liquid is characterized by some short-range order but no long-range order Here we see an ordered structure within the first sphere of neighbors, but a less ordered arrangement within the next sphere of neighbors. 

In writing the formula of a "coordinated complex , the "coordinated group , called "nucleus or the "first sphere is enclosed in square brackets, while the acid radicals are placed outside in the so-called "second or ionization sphere . For instance in the formula [M Rml X, M is a metal (such as Cd, Co, Cr, Cu, Fe, Hg, Mn, Ni or Zn), R is a non-ionic(neutral) radical(such as NH3, H20, ethylenediamine, diethylenetriamine, pyridine, etc), m is "coordination number of M, X is a negative(acidic) radical(such as Cl, CN, ... 

The term r is the upper limit of the integral in Eq. (5) and the smaller and the larger values indicate the ranges of the first and second coordination spheres, respectively. These are defined in the present work as r, = (l/V2)rL and 2rL for ions with different and the same charges, respectively, in the first sphere coordination sphere, and r2 = (V3/2)rL and rL for different the same charges, respectively, in the second coordination sphere. The term rL denotes the lattice constant, and m stands for mol (kg H20) 1. 

Including the stereoisomer shown, the number of possible stereoisomers is x = 27 = 128 since there are six chirality centres and one double bond which can be either E- or Z-configured. The absolute configuration of the carbon atom at position 4 cannot be determined until the third sphere. In the first sphere there are three carbon atoms, in the second all carbon atoms are attached to two carbon atoms and one hydrogen atom. In the third sphere the priority order is 0,C,C > C,C,(C) > C,C,H and therefore this chirality centre is S- configured. 

Most free-volume models for diffusion in polymers follow the phenomenological basis set in (55) where the self-diffusion of an ideal liquid of hard spheres ( molecules ) has been analysed. These molecules are confined - for most of the time - in a cage formed by their immediate neighbours. A local fluctuation in density may open a hole within a cage, large enough to permit a considerable displacement of the sphere contained by it. This displacement gives rise to diffusion only if another sphere jumps into the hole before the first sphere returns to its initial position. Diffusion occurs not as a result of an activation process in the ordinary sense but rather as a result of the redistribution of the free-volume within the liquid of hard spheres. 

Our calculation on defect vibrations enables the assignment of the EA spectrum features. For example, one is found at a frequency of 10.0 THz from the zero phonon line and falls in the region between the acoustic and optical bands of the phonon spectrum of the ZnO crystal. Perhaps it is due to an Ai-motion of the Ni ion, the O ions of the first sphere and the Zn ions of the second sphere. According to our calculation, the EA spectrum for ZnO Ni corresponds to the nickel acceptor exciton [d h]. 

---