Valency defined

In order to establish Eqn. II.2, it is in fact unnecessary to introduce valences defined according to Defs. II.7 and II.8. The key parameters are... 

The word covalent was coined in 1919 when the great American Chemist Irving Langmuir said, it is proposed to define valence as the number of pairs of electrons which a given atom shares with others. In view of the fact. .. that valence is very often used to express something quite different, it is recommended that the word covalence be used to denote valence defined as above. He added, In [ionic] sodium chloride, the covalence of both sodium and chlorine is zero . 

In open-shell systems, the sum of the bond orders of all bonds in which atom A participates differs from the valence defined according to Equation 22.2 the difference accounts for the unsatisfied bonding capability of the atom, the free valence, expressed as... 

In order to take into account all valence electrons of the ith atom, the vertex degree is replaced by the valence vertex degree 61 (also called the vertex valence) defined as ... 

One should strictly make a distinction between ideal bond valence defined theoretically from the bond graph in Section 10.3.2 and experimental bond valence determined from the observed bond lengths using Equations 10.1 or 10.2. Except in the situations described in Section 10.6, tbe two differ only by the experimental uncertainty... 

Sometimes confusion has been caused by taking valence linkings to represent some form of combining power or stability. This question must be made clear and the meaning of valence defined carefully for a proper understanding of the questions to be taken up. In order to do this, chemical energy will be taken up for a moment and the relation between it and valence described. 

Reciprocal lattice vectors are usefiil in defining periodic fimctions. For example, the valence charge density, p (r), can be expressed as... 

Since and depend only on die valence charge densities, they can be detennined once the valence pseudo- wavefiinctions are known. Because the pseudo-wavefiinctions are nodeless, the resulting pseudopotential is well defined despite the last temi in equation Al.3.78. Once the pseudopotential has been constructed from the atom, it can be transferred to the condensed matter system of interest. For example, the ionic pseudopotential defined by equation Al.3.78 from an atomistic calculation can be transferred to condensed matter phases without any significant loss of accuracy. 

Several factors detennine how efficient impurity atoms will be in altering the electronic properties of a semiconductor. For example, the size of the band gap, the shape of the energy bands near the gap and the ability of the valence electrons to screen the impurity atom are all important. The process of adding controlled impurity atoms to semiconductors is called doping. The ability to produce well defined doping levels in semiconductors is one reason for the revolutionary developments in the construction of solid-state electronic devices. 

Under the assumption that the matrix elements can be treated as constants, they can be factored out of the integral. This is a good approximation for most crystals. By comparison with equation Al.3.84. it is possible to define a fiinction similar to the density of states. In this case, since both valence and conduction band states are included, the fiinction is called the joint density of states ... 

The concept of biradicals and biradicaloids was often used in attempts to account for the mechanism of photochemical reactions [2,20,129-131]. A biradical (or diradical) may be defined as [132] an even-electron molecule that has one bond less than the number permitted by the standard rules of valence. 

The concept of oxidation states is best applied only to germanium, tin and lead, for the chemistry of carbon and silicon is almost wholly defined in terms of covalency with the carbon and silicon atoms sharing all their four outer quantum level electrons. These are often tetrahedrally arranged around the central atom. There are compounds of carbon in which the valency appears to be less than... 

In formulating a mathematical representation of molecules, it is necessary to define a reference system that is defined as having zero energy. This zero of energy is different from one approximation to the next. For ah initio or density functional theory (DFT) methods, which model all the electrons in a system, zero energy corresponds to having all nuclei and electrons at an infinite distance from one another. Most semiempirical methods use a valence energy that cor-... 

MM methods are defined atom by atom. Thus, having a carbon atom without all its bonds does not have a significant affect on other atoms in the system. In contrast, QM calculations use a wave function that can incorporate second atom effects. An atom with a nonfilled valence will behave differently than with the valence filled. Because of this, the researcher must consider the way in which the QM portion of the calculation is truncated. 

When writing a Lewis structure we restrict a molecule s electrons to certain well defined locations either linking two atoms by a covalent bond or as unshared electrons on a sm gle atom Sometimes more than one Lewis structure can be written for a molecule espe cially those that contain multiple bonds An example often cited m introductory chem istry courses is ozone (O3) Ozone occurs naturally m large quantities m the upper atmosphere where it screens the surface of the earth from much of the sun s ultraviolet rays Were it not for this ozone layer most forms of surface life on earth would be dam aged or even destroyed by the rays of the sun The following Lewis structure for ozone satisfies fhe ocfef rule all fhree oxygens have eighf elecfrons m fheir valence shell... 

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

You start building propanal using an sp C from the model kit Note that five dif ferent types of carbon are available Each is defined by a particular number of unfilled valences (these are used to make bonds) and a particular idealized geometry Valences that are not used for bonds are automatically turned into hydrogen atoms so it is nor mally unnecessary to build hydrogens into a model... 

Since the basis set is obtained from atomic calculations, it is still desirable to scale exponents for the molecular environment. This is accomplished by defining an inner valence scale factor and an outer valence scale factor ( double zeta ) and multiplying the corresponding inner and outer a s by the square of these factors. Only the valence shells are scaled. 

Direct and Indirect Energy Gap. The radiative recombination rate is dramatically affected by the nature of the energy gap, E, of the semiconductor. The energy gap is defined as the difference in energy between the minimum of the conduction band and the maximum of the valence band in momentum, k, space. Eor almost all semiconductors, the maximum of the valence band occurs where holes have zero momentum, k = 0. Direct semiconductors possess a conduction band minimum at the same location, k = O T point, where electrons also have zero momentum as shown in Eigure la. Thus radiative transitions that occur in direct semiconductors satisfy the law of conservation of momentum. 

The impurity atoms used to form the p—n junction form well-defined energy levels within the band gap. These levels are shallow in the sense that the donor levels He close to the conduction band (Fig. lb) and the acceptor levels are close to the valence band (Fig. Ic). The thermal energy at room temperature is large enough for most of the dopant atoms contributing to the impurity levels to become ionized. Thus, in the -type region, some electrons in the valence band have sufficient thermal energy to be excited into the acceptor level and leave mobile holes in the valence band. Similar excitation occurs for electrons from the donor to conduction bands of the n-ty e material. The electrons in the conduction band of the n-ty e semiconductor and the holes in the valence band of the -type semiconductor are called majority carriers. Likewise, holes in the -type, and electrons in the -type semiconductor are called minority carriers. 

Faraday s Law of electrolysis states that the amount of chemical change, ie, amount dissolved or deposited, produced by an electric current is proportional to the quantity of electricity passed, as measured in coulombs and that the amounts of different materials deposited or dissolved by the same quantity of electricity are proportional to their gram-equivalent weights (GEW) defined as the atomic weight divided by the valence. The weight in grams of material deposited, IF, is given by... 

The possible number of valence stmctures for a given boron hydride has been defined exacdy using three general equations of balance. For a borane... 

E = dV/dx defined as V/m. The ions and electrons reestablish equilibrium by moving in the field which results in a net electric current density j defined as C/(m -s) or A/m. An electron or an electron hole has a unit charge, e = 1.601 x 10 C an ion has this unit charge times its valence Thus the... 

Hydroxide. Freshly precipitated cerous hydroxide [15785-09-8] Ce(OH)2, is readily oxidized by air or oxygenated water, through poorly defined violet-tinged mixed valence intermediates, to the tetravalent buff colored ceric hydroxide [12014-56-17, Ce(OH)4. The precipitate, which can prove difficult to filter, is amorphous and on drying converts to hydrated ceric oxide, Ce02 2H20. This commercial material, cerium hydrate [23322-64-7] behaves essentially as a reactive cerium oxide. 

Electrons excited into the conduction band tend to stay in the conduction band, returning only slowly to the valence band. The corresponding missing electrons in the valence band are called holes. Holes tend to remain in the valence band. The conduction band electrons can estabUsh an equihbrium at a defined chemical potential, and electrons in the valence band can have an equiUbrium at a second, different chemical potential. Chemical potential can be regarded as a sort of available voltage from that subsystem. Instead of having one single chemical potential, ie, a Fermi level, for all the electrons in the material, the possibiUty exists for two separate quasi-Fermi levels in the same crystal. 

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