Bond number, definition

FIG. 13 Average number of hydrogen bonds (for definition see text) as a function of p in five simulations at different levels of hydration in a Vycor pore. Full hues show the number of water-water bonds, long-dashed hnes show the number of bonds between water molecules and Vycor, and short-dashed lines denote the sum of the two. From top to bottom, the frames correspond to a water content of about 96, 74, 55, 37, and 19% of the maximum possible (corresponding to 2600, 2000,1500, 1000, and 500 water molecules in a cylindrical cavity of about 4nm diameter and 7.13 nm length). (From Ref. 24.)... 

Restricted to an individual bond the definition of a g function is a function cylinder symmetrical round the bond axis (angular moment zero), a tz function has a component of unity along this axis comp, s and p states with values for the subsidiary or azimuthal quantum number l equal to o and i, respectively (P. 11). 

In the first and second groups of the periodic table the 8 — N rule does not give the number of possible covalent bonds, furthermore the elements of these groups, together with those of the transition groups do not form homo-polar or ionic bonds but a metallic bond possessing definite characteristics. 

At present a large variety of solid compounds are called Zintl phases. The name Zintl phase was introduced by Laves According to Laves, Zintl phases are those intermetallic compounds which crystallize in typical non-metal crystal structures. For these compounds one expects an ionic contribution to the chemical bond. This definition has been extended to a large number of solid compounds formed by alkali or alkaline earth metals with metallic or semimetallic elements of the fourth, fifth and partly third group of the Periodic Table for which common structural and bonding properties have been found. The crystal structures and chemical properties of these compounds have been studied extensively . ... 

E = valence electron number per formula unit N = average bond number per semi-metal atom in a chosen defect-free reference structure N = additional electrons to be introduced upon formation of one defect in the reference structure, e.g. a defect in the diamond structure type localizes four electrons to form four lone electron pairs in the neighborhood of the defect Ec = electrons located in electron-poor clusters which, for example, may be determined according to Wade-Mingos rules or according to the 18e rule Ec = electron number in electron-poor cluster(s) composed of semi-metal atoms Ec = electron number in electron-poor cluster(s) composed of metal atoms). By definition, Zintl phases do not contain metal-centered occupied electronic states for these cases (1) may be rewritten as ... 

The Bond and capillary numbers definition might differ in different sources according to the problem under consideration, but the basic concept (relative importance of gravity vs. viscosity and capillarity vs. viscosity) is always the same. Sometimes, the ratio for capillary number is inverted. 

The flow in fluid-fluid microstructured channels is characterized using dimensionless numbers. The most important dimensionless number for characterization of all types of flows is the Re number that relates inertial force to viscous force. Due to low flow velocities and characteristic dimension in the micrometer range, Re is often less than 1 meaning that viscous force is dominant over inertial force. The capillary number Ca is the ratio of viscous to interfacial forces. The range of Ca in a typical microchannel is lO " to 10 . Multiplying both numbers. Re and Ca, results in the Weber number We, which represents the ratio between inertial and interfacial forces. The importance of gravity vhth respect to interfacial forces is characterized by the Bond number Bo. The definitions of the dimensionless numbers are summarized in Table 2.2. 

The surface tension gradient driven flow system in Figure 6.1.7(b) has different heights of the liquid fUm, h z), at different locations along the z-coordinate. Gravitational force will tend to eliminate it. The relative influence of the two forces is indicated by the Bond number, Bo, defined earlier by equation (6.1.17). The characteristic length dimension of the system to be used in the definition of Bo is any particular value of h(z) ... 

Two different bonding indiees will be used in this book, namely bond-number and bond-order. The bond number refers to the number of pairs of electrons that form a covalent bond. It may be calculated from the weights of the valence-bond structures that are used to describe the electronic structure of the molecule, as is demonstrated above for N2O. The bond-order is a molecular orbital index of bonding. For the purpose of qualitative discussion of diatomic bonding, we shall define the bond-order to be /4 (No. of bonding electrons) - (No. of antibonding electrons). Another definition of bond-order will be introduced in Chapter 14. 

The most well-known and at the same time the earliest computer model for a molecular structure representation is a wire frame model (Figure 2-123a). This model is also known under other names such as line model or Drciding model [199]. It shows the individual bonds and the angles formed between these bonds. The bonds of a molecule are represented by colored vector lines and the color is derived from the atom type definition. This simple method does not display atoms, but atom positions can be derived from the end and branching points of the wire frame model. In addition, the bond orders between two atoms can be expressed by the number of lines. 

Because it is desirable to break a peptide this way, some flexibility is required in the rigorous definition of sp -sp single bond. In particular, the dative Cqj-N bond in the backbone of a peptide is considered to be such a bond since the definition is based on the number of neighbors — four for carbon, three for nitrogen, two for Oxygen, etc. If this were not the case, you couldn t break a protein into classical and quantum regions at all. 

On the assumption that the pairs of electrons in the valency shell of a bonded atom in a molecule are arranged in a definite way which depends on the number of electron pairs (coordination number), the geometrical arrangement or shape of molecules may be predicted. A multiple bond is regarded as equivalent to a single bond as far as molecular shape is concerned. 

Another fundamental property of chemical bonds is polarity. In general, it is to be expected that the distribution of the pair of electrons in a covalent bond will favor one of the two atoms. The tendency of an atom to attract electrons is called electronegativity. There are a number of different approaches to assigning electronegativity, and most are numerically scaled to a definition originally proposed by Pauling. Part A of Table 1.6... 

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