Overlap lateral

Here the indices a and b stand for the valence orbitals on the two atoms as before, n is a number operator, c+ and c are creation and annihilation operators, and cr is the spin index. The third and fourth terms in the parentheses effect electron exchange and are responsible for the bonding between the two atoms, while the last two terms stand for the Coulomb repulsion between electrons of opposite spin on the same orbital. As is common in tight binding theory, we assume that the two orbitals a and b are orthogonal we shall correct for this neglect of overlap later. The coupling Vab can be taken as real we set Vab = P < 0. 

A cr orbital can be formed either from two s atomic orbitals, or from one s and one p atomic orbital, or from two p atomic orbitals having a collinear axis of symmetry. The bond formed in this way is called a a bond. A n orbital is formed from two p atomic orbitals overlapping laterally. The resulting bond is called a n bond. For example in ethylene (CH2=CH2), the two carbon atoms are linked by one a and one n bond. Absorption of a photon of appropriate energy can promote one of the n electrons to an antibonding orbital denoted by n. The transition is then called Ti —> 7i. The promotion of a a electron requires a much higher energy (absorption in the far UV) and will not be considered here. 

The atomic orbitals overlap laterally or side-on and form a pi (ti) bond. 

See Fig. 10-7. The C s use sp hybrid atomic orbitals to form tr bonds with each other and with the H s. The remaining p orbitals at right angles to the plane of the C s overlap laterally to form a tt electron cloud. 

Prior art discloses range overlapping later claimed range. 

The benzenonium ion is a type of allylic cation [see Problem 8.24(/ )]. The five remaining C s using sp -hybridized orbitals each have a p orbital capable of overlapping laterally to give a delocalized n structure, or a complex ... 

The 2p and 2py orbitals from the two atoms do not approach head-on in this confignration, but rather side by side. Therefore, the positive lobes of the 2p orbitals can overlap laterally, as can the negative lobes. Together, they form a TT bond, which has a node through the plane containing the bond axis with electron density concentrated above and below the plane. The wave function for the bond pair is... 

Each carbon atom will also have an unused 2pz orbital, partly filled, and the lobes of these will extend above and below the plane of the a bonded framework (Figure 196). We can consider two adjacent lp9] lobes to overlap laterally, giving three tt bonds, but as it is obvious that any particular 2pz orbital could overlap laterally with the orbital on either side of it, we consider the bonding to result from the overlapping of all the 2pz orbitals taken together. 

Nitrogen molecule (Nj) Nitrogen atom has the electron configuration Is 2s 2pj 2p 2p. There are three half-filled p orbitals. As in the formation of oxygen molecule one of the p orbitals on each N atom of same symmetry overlap along the bond axis forming a CT bond. The other two half-filled orbitals on each N atom overlap laterally to form two pi bonds. Thus a triple bond (one a and two n) is present between two N atoms in a molecule of nitrogen. 

Two p orbitals may also overlap laterally (side-to-side) to form a PI (tt) bond (Fig. 18.9). The bonding ir MO consists of two electron charge clouds concentrated above and below the axis joining the two nuclei. The MO has a nodal plane (in which the electron density is zero) incorporating the bond axis as shown in Fig. 18,9a. The antibonding MO is depicted in Fig. 18.9b. A strong rt bond can result... 

A linear shape indicates that each C uses sp hybrid AO s (Table 19.1). The energy levels of an sp hybridized C are shown in Fig. 19.7d. Figure 19,9 shows the assembly of 2 H atoms, each with a Is atomic orbital, and 2 C atoms, each with two sp hybrid orbitals and a p and p orbital. Each C atom forms two cr bonds, one by overlapping an sp hybrid orbital with the other C atom, and one by overlapping an sp orbital with the s orbital of a H atom. The p orbitals overlap laterally to form a ir... 

Linearity means the O—C—O bond angle is 180 we therefore assume that the carbon uses p hybridized orbitals to farm a (r bond to each O atom (Fig. 19.10). The C atom also has two p orbitals, each of which overlaps laterally with a p orbital of an adjacent oxygen atom to give two TT bonds. Each tt bond holds a pair of electrons, one from each atom, and therefore the octet requirement for C is satisfied. The separate TT bonds are in planes perpendicular to each other. Since each O atom bonds to only one other atom, there is no bond angle with O at the center to tell us about the kind of AO used by the O atoms. However, we assume that the unshared pairs of electrons are in hybrid orbitals and then bodi O atoms are sp hybridized. 

The difference in energy between the localized (Kekule) and delocal-ized models is called DELOCALIZATION ENERGY. The more extensive the delocalization of p electrons, the greater is the delocalization energy and the more stable is the molecule. The term aromatic is now used to describe those substances with large delocalization energies. All aromatic substances have p orbitals overlapping laterally in a cyclic fashion. They are all less reactive chemically than isomers without this... 

The extended system arises om the overlapping lateral p orbitals as shown in Fig. 24.6b. The relationship between the number of alternating C=C groups and the absorbed wavelength, is given in the comparison below ... 

Median extrascapular overlap median extrascapular overlapped by lateral extrascapulars (0) median extrascapular overlapping lateral extrascapulars (1) median extrascapular abutting lateral extrascapulars (2). 

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