Bond axis

Most of the molecules we shall be interested in are polyatomic. In polyatomic molecules, each atom is held in place by one or more chemical bonds. Each chemical bond may be modeled as a harmonic oscillator in a space defined by its potential energy as a function of the degree of stretching or compression of the bond along its axis (Fig. 4-3). The potential energy function V = kx j2 from Eq. (4-8), or W = ki/2) ri — riof in temis of internal coordinates, is a parabola open upward in the V vs. r plane, where r replaces x as the extension of the rth chemical bond. The force constant ki and the equilibrium bond distance riQ, unique to each chemical bond, are typical force field parameters. Because there are many bonds, the potential energy-bond axis space is a many-dimensional space. 

Figure 4-18 The Potential Energy for Rotation of n-Butane About its Central Bond Axis. The anti conformer in the center is slightly lower in energy than the two gauche conformers.

The hydrogen atom attached to an alkane molecule vibrates along the bond axis at a frequency of about 3000 cm. What wavelength of electromagnetic radiation is resonant with this vibration What is the frequency in hertz What is the force constant of the C II bond if the alkane is taken to be a stationary mass because of its size and the H atom is assumed to execute simple harmonic motion ... 

For a diatomie speeies, the vibration-rotation (V/R) kinetie energy operator ean be expressed as follows in terms of the bond length R and the angles 0 and (j) that deseribe the orientation of the bond axis relative to a laboratory-fixed eoordinate system ... 

The O atom uses one of its sp or sp hybrids to form the CO a bond and antibond. When sp hybrids are used in conceptualizing the bonding, the other sp hybrid forms a lone pair orbital directed away from the CO bond axis one of the atomic p orbitals is involved in the CO n and 71 orbitals, while the other forms an in-plane non-bonding orbital. Alternatively, when sp hybrids are used, the two sp hybrids that do not interact with the C-atom sp2 orbital form the two non-bonding orbitals. Hence, the final picture of bonding, non-bonding, and antibonding orbitals does not depend on which hybrids one uses as intermediates. 

Acyclic Compounds. Different conformations of acyclic compounds are best viewed by construction of ball-and-stick molecules or by use of Newman projections (see Fig. 1.2). Both types of representations are shown for ethane. Atoms or groups that are attached at opposite ends of a single bond should be viewed along the bond axis. If two atoms or groups attached at opposite ends of the bond appear one directly behind the other, these atoms or groups are described as eclipsed. That portion of the molecule is described as being in the eclipsed conformation. If not eclipsed, the atoms... 

Nitroparaffias (or nitroaLkanes) are derivatives of the alkanes ia which one hydrogen or more is replaced by the electronegative nitro group, which is attached to carbon through nitrogen. The nitroparaffins are isomeric with alkyl nitrites, RONO, which are esters of nitrous acid. The nitro group ia a nitroparaffin has been shown to be symmetrical about the R—N bond axis, and may be represented as a resonance hybrid ... 

The unhybridized electron pairs associated with multiple bonds occupy orbitals of a quite different shape, called pi (it) bonding orbitals. Such an orbital consists of two lobes, one above the bond axis, the other below it. 

Along the bond axis itself, the electron density is zero. The electron pair of a pi (tt) bond occupies a pi bonding orbital. There is one tt bond in the C2H4 molecule, two in QH The geometries of the bonding orbitals in ethylene and acetylene are shown in Figure 7.13. 

The valence atomic orbitals which are available to form the orbitals of a CC single bond, directed along the x axis, are the 2s and 2px atomic orbitals on each carbon atom. Their admixture—in proportions which depend on the number of neighbors at each carbon and on the subsequent hybridization—creates two (s, p ) hybrids on each atom. One of these hybrids points away from the other atom and can be used for bonding to additional atoms. The pair of hybrids which point at each other overlap and interact in the conventional fashion [we symbolize the non-interacting orbitals by an interruption of the bond axis (Fig. 1)]. The two bond orbitals which are formed in this manner both have [Pg.3]

Fig. 8-6. Conformation of phenyldiazenyl radicals with the N=N group rotating about the C-N bond axis (after Suehiro et al., 1986).

Now consider the alkynes, hydrocarbons with carbon-carbon triple bonds. The Lewis structure of the linear molecule ethyne (acetylene) is H—O C- H. To describe the bonding in a linear molecule, we need a hybridization scheme that produces two equivalent orbitals at 180° from each other this is sp hybridization. Each C atom has one electron in each of its two sp hybrid orbitals and one electron in each of its two perpendicular unhybridized 2p-orbitals (43). The electrons in the sp hybrid orbitals on the two carbon atoms pair and form a carbon—carbon tr-bond. The electrons in the remaining sp hybrid orbitals pair with hydrogen Ls-elec-trons to form two carbon—hydrogen o-bonds. The electrons in the two perpendicular sets of 2/z-orbitals pair with a side-by-side overlap, forming two ir-honds at 90° to each other. As in the N2 molecule, the electron density in the o-bonds forms a cylinder about the C—C bond axis. The resulting bonding pattern is shown in Fig. 3.23. 

The bond in F2 forms from orbital overlap between a pair of fluorine 2 p orbitals that point along the bond axis. 

As Figure 10-19 shows, bonds that form from the side-by-side overlap of atomic p orbitals have different electron density profdes than a bonds. A p orbital has zero electron density—a node—in a plane passing through the nucleus, so bonds that form from side-by-side overlap have no electron density directly on the bond axis. High electron density exists between the bonded atoms, but it is concentrated above and below the bond axis. A bond of this type is called a pi ( r) bond, and a bonding orbital that describes a ttbond is a tt orbital. 

A a bond has high electron density distributed symmetrically along the bond axis. A 71 bond has high electron density concentrated above and below the bond axis. 

Figure 10-30 shows the constmction of the 2 -based molecular orbitals. One pair of MOs forms from the p orbitals that point toward each other along the bond axis. By convention, we label this as the z-axis. This end-on overlap gives Cp and

Severai common poi /atomic oxoanions, inciuding suifate, perchiorate, and phosphate, have inner atoms from the third row of the periodic tabie. In these anions, vaience d orbitais are avaiiable to participate in bonding. Figure 10-47 shows how a n orbitai can form through side-by-side overiap of a d orbital on one atom with a.7, p orbital on another atom. As with other itt bonds, electron density is concentrated above and below the bond axis. 

A carbon-carbon double bond is a reactive functional group because of its iz electrons. Remember from Chapter 10 that ethylene has a CDC bond made up of one a bond plus one itt bond. As shown in Figure 13-1. the electrons in the iTrbond are located off the bond axis, making them more readily available for chemical reactions. Moreover, 71 electrons are less tightly bound than a electrons. Consequently, the reactivity patterns of ethylene are dominated by the chemistry of its n electrons. Polyethylene is one familiar polymer whose monomer is ethylene. We describe the polymerization reaction of ethylene and other monomers containing CDC bonds in Section 13-1. 

We first consider what happens when comparing directly the optimum orbital of H2, the un-optimised orbital of (i.e. the sum of the two Is orbitals of the H atoms) and the orbitals of the H atom itself. The comparison between the values of these orbitals along the bond axis is presented on the fig. (7). 

Fig.7. Values of different orbitals of a.nd H along the bond axis of. The r distance is given in Bohr units r=0 corresponds to the position of one of the H nuclei, r > 0 corresponds to the region between the two nuclei.

As discussed above, XBs tend to be Unear, namely to be formed along the C - X bond axis on the XB donor module and along the lone pair axis of the heteroatom on the XB acceptor module. The angles between these axes determine the halogen-bonded adducts geometry. 

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