Definition of coordinates

However, for alternative definitions of coordination and coordination numbers, see the following paragraphs. 

Definition of coordination number. The coordination number of an ion is the number of ions to which it is linked by electrostatic flux. 

FIG. 4.15 Flow of polymer solutions (a) velocity gradient through the center of mass of a polymer chain (b) definition of coordinates for /th segment of rotating chain. The distance r = r, is the distance of the /th segment from the center of mass. (Redrawn with permission from Hiemenz 1984.)... 

FIG. 6.4 Definition of coordinates describing the displacement of an element of curved surface ABCDioA B C D. ... 

FIG. 6.14 Definition of coordinates for describing surfaces with an axis of symmetry (OP). 

No strict definition of coordination compound will be followed for the compounds of these two groups, but coverage will be concentrated on those compounds where inter-group relationships are most obvious. In particular, the halogen oxides and derived oxo ions will not be considered. 

Fig. 5.1. Time dependence of a typical classical trajectory in the photodissociation of C1CN — Cl 4- CN(j). (a) R(t) (solid line) is the Cl-CN separation and 7(t) (dashed line) is the orientation angle of CN with respect to the scattering vector R (for the definition of coordinates see Figure 3.1). (b) The angular momentum j(t) of CN (solid line) and the torque F1 = -dV/dj (dashed line).

Since this method has been described in the literature[16] we provide here only a brief outline of the numerical algorithm, but then discuss aspects of it in some detail. The application to H2O in Section HI should clarify the implementation and performance of the method. The algorithm has three parts definition of coordinates and coordinate groups and zero order Hamiltonians for each generation of an ESB from solutions of the zero order Hamiltonians and solution of the Schrodinger equation for many vibrational states efficiently by iterative methods. 

In solid state chemistry where there are often a number of equal short interatomic contacts, the simplest definition of coordination number is the number of nearest neighbours. In coordination chemistry (solid, solntion and gas phases) a more practical definition of coordination number is the number of atoms or ligating groups (such as a C=C double bond) bound to a metal. Thus in [CoCl4] the coordination nnmber is four. The majority of coordination complexes are either 4- or 6-coordinate. For... 

Figure Al.3 The rotation method. Definition of coordinate systems.

ECoN is a useful generalization of the classical definition of coordination number (number of anions in contact with a cation) it considers the lengths of the bonds (Hoppe... 

In an novel approach, a metal ion mediated self-assembly process [6] is used in the spirit of the new inclusive definition of coordination chemistry. Peptides or amino acids can be covalently linked to a metal-binding ligand. 

The definition of coordination isomerism depends on the context. Historically, a complete series of coordination isomers required at least two metals. The ligandimetal ratio remains the same, but the ligands attached to a specific metal ion change. For the empirical formula Pt(NH3)2Cl2, there are three coordination isomer possibilities that contain Pt(II). 

Robot, Fig. 5 ISO definitions of coordinate systems for industrial robots (ISO 9787 1990)... 

Here, r,R are (for example) mass scaled diatom and atom to center of mass of diatom distances (cf. Eqs. 1,8,9) and y the Tbend) angle between r and R. Actually r,R,y may represent a much wider definition of coordinates. For example, ,R may be the heliocentric coordinates of Smith. 

O Keeffe, M. (1979). A Proposed Rigorous Definition of Coordination Number. Acta Crystallogr. A35,772-775. 

Brunner GO (1977) A definition of coordination and its relevance in the structure types AIB2 and NiAs. Acta Cryst A33 226-227... 

The perspectives provided by Lehn s supramolecular chemistry (3,7) and Cram s host/guest complexation (4) do indeed broaden the realm of coordination chemistry, but the focus still remains on a molecular coordination entity. On the other hand, the coordination polyhedron has lost its pivotal position in the broad definition of coordination chemistry. Furthermore, all manner of intermolecular interactions and interacting pairs are included, and the forces included range from van der Waals and subtle hydrophobic interactions through strong covalent bonds. Coordination chemistry demands only that the molecular entities that unite to form the complex still be recognizable substructures within the complex (6). It is particularly instructive, at this point, to examine examples of coordination entities formed by various modes of interaction that were not recognized in traditional coordination chemistry. 

Unfortunately, the definition of coordination number and geometry i less clear-cut for organometallic species, such as Cp2pe. Is this molecule 2-coordinate (there are two ligands), 6-coordinate (there are six electron pairs involved in metal-ligand bonding), or 10-coordinatc (the 10 C atoms arc all within bonding... 

One widely accepted definition of coordination is "the act of managing dependencies between entities and the joint effort of entities working together towards mutually defined goals" (Malone and Crowston, 1993, 4). Arshinder et ah (2008) identify the following difficulties in coordinating SC ... 

Expeiimental data, definitions of coordinates, molecular geomehy data, and L and P3 matrices for med l chloride are given in section 3.3. The calculated atomic polar tensor matrix is given below (in units of D A ) [124]. 

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