General Definition of Complexes

According to the lUPAC, a coordination entity, or complex, is composed of a central atom, usually a metal atom, to which is attached a surrounding array of other atoms or groups of atoms, each of which is called a ligand. The central atom is also called the nucleus. 

22 General Definitions Concerning Complexes Rules of Nomenclature and Writing 

for example, in the complex ion hexamminecobalt(III), [Co (NH3)6] + (Werner s luteocobaltic complex), the central nucleus is the cobalt atom and the ammoniac molecules are the ligands. We can already notice that in the formula of a complex, the complex is written between brackets (for details about the writing and nomenclature of complexes, see Sect. 22.4). 

The lUPAC definition of a complex necessitates the following comments  

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What is complexity There is no good general definition of complexity, though there are many. Intuitively, complexity lies somewhere between order and disorder, between regularity and randomness, between perfect crystal and gas. Complexity has been measured by logical depth, metric entropy, information content (Shannon s entropy), fluctuation complexity, and many other techniques some of them are discussed below. These measures are well suited to specific physical or chemical applications, but none describe the general features of complexity. Obviously, the lack of a definition of complexity does not prevent researchers from using the term. 

What is complexity There is no good general definition of complexity, though there are many attempts to define it. ... 

The general definition of complexes, which we ve already seen, can be somewhat refined in fhe confext of the chemical analysis. For this purpose, we can say that... 

Schuster S et al. A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nature Biotechnol 2000 18 326-332. 

In reality, different classes of derivatives contribute the general definition of bis-dithiolene metal complexes, Scheme 8.72... 

In a critical and definitive review of this area (de Kruif et al.. 2004), the following general features of complex coacervation were asserted ... 

The term piezoelectric nonlinearity is used here to describe relationship between mechanical and electrical fields (charge density D vs. stress a, strain x vs. electric field E) in which the proportionality constant d, is dependent on the driving field, Figure 13.1. Thus, for the direct piezoelectric effect one may write D = d(a)a and for the converse effect x = d(E)E. Similar relationships may be defined for other piezoelectric coefficients (g, h, and e) and combination of electro-mechanical variables. The piezoelectric nonlinearity is usually accompanied by the electro-mechanical (D vs. a or x vs. E) hysteresis, as shown in Figure 13.2. By hysteresis we shall simply mean, in the first approximation, that there is a phase lag between the driving field and the response. This phase lag may be accompanied by complex nonlinear processes leading to a more general definition of the hysteresis [2],... 

Complexity has a straightforward intuitive meaning (it is the opposite of simplicity), but its scientific history is littered with the corpses of discarded definitions. There simply is no hope of achieving a general consensus on a comprehensive definition of complexity, and this implies that any attempt to give a mathematical formulation to the problem of epigenesis is apparently crippled at the very beginning by lack of a definition. 

A more general definition of the FCWD includes overlap integrals of quantum nuclear modes. The definition given by Eq. [19] includes only classical solvent modes (superscript s ) for which these overlap integrals are identically equal to unity. An extension of Eq. [19] to the case of quantum intramolecular excitations of the donor-acceptor complex is given below in the section discussing optical Franck-Condon factors. 

The scope of the project includes not only the definition of the final product deliverable but the level of work effort required to complete this project. For example, a new pharmaceutical drug will be used to reduce long-term intractable pain, will be in an injectable form, and will use existing packaging configurations in defined concentrations and formulations. This is an initial, general definition of the product scope. The project scope, however, is much more time consuming and complex to develop and would include ... 

If one considers machines that react on many interface inputs, as they are needed in a general definition of signature schemes, one can choose to measure complexity as a function of the sum of the lengths of the interface inputs that occurred so far, or still of the initial state only. In particular situations, one might even make more special requirements, such as considering the time needed until the next output as a function of the most recent input only. ... 

A general definition of the Quantum Molecular Similarity Measure is reported. Particular cases of this definition are discussed, drawing special attention to the new definition of Gravitational-like Quantum Molecular Similarity Measures. Applications to the study of fluoromethanes and chloro-methanes, the Carbonic Anhydrase enzyme, and the Hammond postulate are presented. Our calculations fully support the use of Quantum Molecular Similarity Measums as an efficient molecular engineering tool in order to predict physical properties, lMok>gical and pbarraacdogical activities, as well as to interpret complex chemical problems. 

Since many averaging processes might be thought of, we first give a general definition of an invariant mean (or invariant averaging process ) on G. Let " (G) be the C -algebra of all complex valued, continuous, bounded functions on G, equipped with the usual operations ... 

For a general definition of sensors, see - Chemical and Biochemical Sensors. The term sensor denotes a small specialized device that operates selectively on several analytes [167], Optical sensors are certainly competitive with ion-selective electrodes becau.se they are now less complex than in the past and miniaturization promises further success in the future. Furthermore, optical sensors have advantages [168] in remote sensing and by utilization of the spectral information, especially in the case of sensor arrays. 

See Key Terms for more general definitions of high spin complex and low spin complex. 

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