The Covalent Bond in

The covalent bond is made from electrons, which are the elementary particles residing in the atoms and hovering around the nucleus, where the protons and neutrons are encapsulated. Any covalent molecule, even the largest possible, is made from a collection of covalent bonds, which are created by clicking electrons. 

Why does the rule allow electron pairing but not larger groupings of electrons We sort of alluded to this selection rule in the Retouches to Lecture 1. There is in fact a highly sophisticated theory called Quantum Mechanics (QM), which explains why the pairing is the choice for covalent bonding (see Retouches section 2.R.2.). We are not going to learn this theory in the course. And in all truth, this idea of electron 

SCHEME 2.3 The covalent bond in H2. The red line connecting the two H atoms on the right symbolizes an electron-pair bond, also known as a covalent bond. 

FIGURE 2.2 The caricature of Gilbert Newton Lewis pointing to the CI2 molecule with an electron pair between the atoms (the caricature is reproduced with kind permission from its artist, the historian W. B. Jensen). Note that the Lewis representation for the bond, C1 C1, is different than the one we use, Cl-Cl. His C1 C1 representation tells precisely that the bond is made from an electron pair. But this representation is less convenient for large molecules. Just imagine having to dot 100 different bonds... Therefore, the line binding the two atoms replaced this electron dot representation. 

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Chemists refer to the bond in a molecule like sodium chloride as ionic , meaning that its electron pair resides entirely on chlorine. At the other extreme is the covalent bond in the hydrogen molecule, where the electron pair is shared equally between the two hydrogens. Intermediate cases, such as the bond in hydrogen fluoride which is clearly polarized toward fluorine, are generally referred to as polar covalent bonds (rather than partially ionic bonds). Are these situations really all different or do they instead represent different degrees of the same thing ... 

Earlier we referred to the forces that hold nonmetal atoms to one another, covalent bonds. These bonds consist of an electron pair shared between two atoms. To represent the covalent bond in the H2 molecule, two structures can be written ... 

In Chapter 7, we used valence bond theory to explain bonding in molecules. It accounts, at least qualitatively, for the stability of the covalent bond in terms of the overlap of atomic orbitals. By invoking hybridization, valence bond theory can account for the molecular geometries predicted by electron-pair repulsion. Where Lewis structures are inadequate, as in S02, the concept of resonance allows us to explain the observed properties. 

Because nonmetals do not form monatomic cations, the nature of bonds between atoms of nonmetals puzzled scientists until 1916, when Lewis published his explanation. With brilliant insight, and before anyone knew about quantum mechanics or orbitals, Lewis proposed that a covalent bond is a pair of electrons shared between two atoms (3). The rest of this chapter and the next develop Lewis s vision of the covalent bond. In this chapter, we consider the types, numbers, and properties of bonds that can be formed by sharing pairs of electrons. In Chapter 3, we revisit Lewis s concept and see how to understand it in terms of orbitals. 

The specific reaction of a conduritol epoxide requires, in addition to the acidic group for the protonation of the oxirane, a nucleophile for the formation of the covalent bond. In all cases studied so far, this is the carboxylate... 

The energy for the fission of the covalent bond in organic contaminants is normally supplied thermally using thermodynamically accessible chemical or biochemical reactions, or by the introduction of catalysts to lower the activation energy of the reactions. There has been interest, however, in using electrical energy in a number of forms to carry out these reactions. A selection of processes for the destruction of contaminant is noted with some illustrative examples. 

The atoms in the molecules of these pain relievers are covalently bonded. Electrons are shared between atoms in a series of single and double covalent bonds. The covalent bonds in aspirin, acetaminophen, and ibuprofen are similar to those found in methane and carbon dioxide. 

A suitable approach to the equilibration of an amorphous polymer system at bulk density becomes much more likely when the fully atomistic model in continuous space is replaced by an equivalent coarse-grained model on a lattice with sufficient conformational flexibility. Different strategies, which seek results at different levels of detail, can be employed to create an appropriate coarse-grained model. Section 4 (Doruker, Mattice) describes an approach which attempts to retain a connection with the covalent bonds in the polymer. The rotational isomeric state (RIS) [35,36] model for the chain is mapped into... 

The covalent bonding in organic compounds can be described by means of the electron dot notation (Chap. 5). The carbon atoms has four electrons in its outermost shell ... 

Chain stretching is governed by the covalent bonds in the chain and is therefore considered a purely elastic deformation, whereas the intermolecular secondary bonds govern the shear deformation. Hence, the time or frequency dependency of the tensile properties of a polymer fibre can be represented by introducing the time- or frequency-dependent internal shear modulus g(t) or g(v). According to the continuous chain model the fibre modulus is given by the formula... 

Covalent bonding is the sharing of one or more pairs of electrons by two atoms. The covalent bonds in a molecule a covalently bonded compound are represented by a dash. Each dash is a shared pair of electrons. These covalent bonds may be single bonds, one pair of shared electrons as in H-H double bonds, two shared pairs of electrons as in H2C=CH2 or triple bonds, three shared pairs of electrons, N=N . It is the same driving force to form a covalent bond as an ionic bond—completion of the atom s octet. In the case of the covalent bond, the sharing of electrons leads to both atom utilizing the electrons towards their octet. 

In ethylene, there are two types of bonds. Sigma (tr) bonds have the overlap of the orbitals on a line between the two atoms involved in the covalent bond. In ethylene, the C-H bonds and one of the C-C bonds are sigma bonds. Pi (ir) bonds have the overlap of orbitals above and below a line through the two nuclei of the atoms involved in the bond. A double bond is always composed of one sigma and one pi bond. A carbon-to-carbon triple bond results from the... 

Another type of bond is the covalent bond, in which one, two, or more pairs of electrons are shared by two or more atoms. Unlike ionic bonds, covalent bonds involve the sharing of electrons by atoms. The simplest example of covalent bonding occurs when two atoms of hydrogen bond to form a diatomic hydrogen molecule (H + H yield H H, or H ). 

Isomer shift data obtained from Mossbauer spectral studies of Eu" and Dy " complexes of edta, salicylaldehydatoethylenedi-imine, and 8-hydroxy-quinoline have indicated that the covalent bonding in these species is small (ca. 4 % of the total) and is attributable to electron transfer from the ligands to the partly filled 4/ shell. 

The hydrogen and chlorine atoms each donate one electron to the covalent bond. In the molecule, the hydrogen has completed its valence shell with 2 electrons, and the chlorine has a full shell with 8 valence electrons. 

For the covalent bonds in the diatomic molecules studied by Bader and Essen (1984), values of ky and k2 vary from —25 to —45 eA-s, while /3 is positive in the range of 0-45 eA-5. The sum of the curvatures, V2p, is invariably negative, indicating the concentration of electron density in the internuclear region. But for second-row atoms, the larger positive value of A3 may dominate the Laplacian. 

The weakness of the covalent bond in dilithium is understandable in terms of the low effective nuclear charge, which allows the 2s orbital to be very diffuse. The addition of an electron to the lithium atom is exothermic only to the extent of 59.8 kJ mol-1, which indicates the weakness of the attraction for the extra electron. By comparison, the exother-micity of electron attachment to the fluorine atom is 333 kJ mol-1. The diffuseness of the 2s orbital of lithium is indicated by the large bond length (267 pm) in the dilithium molecule. The metal exists in the form of a body-centred cubic lattice in which the radius of the lithium atoms is 152 pm again a very high value, indicative of the low cohesiveness of the metallic structure. The metallic lattice is preferred to the diatomic molecule as the more stable state of lithium. 

The nature of the covalent bonds in the polypeptide backbone places constraints on structure. The peptide bond has a partial doublebond character that keeps the entire six-atom peptide group in a rigid planar configuration. The N—C and Ca—C bonds can rotate to assume bond angles of (p and ip, respectively. 

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