Orbitals, overlapping

There are two mechanisms by which a phase change on the ground-state surface can take place. One, the orbital overlap mechanism, was extensively discussed by both MO [55] and VB [47] formulations, and involves the creation of a negative overlap between two adjacent atomic orbitals during the reaction (or an odd number of negative overlaps). This case was temied a phase dislocation by other workers [43,45,46]. A reaction in which this happens is... 

Figure 2.8. The iwo orbitals overlap giving a covalent bond and ihe tvvv electrons are (>ir in a molecular orbital. (If the t o nuclei could be pushed together completely, the...

An extended Huckel calculation is a simple means for modeling the valence orbitals based on the orbital overlaps and experimental electron affinities and ionization potentials. In some of the physics literature, this is referred to as a tight binding calculation. Orbital overlaps can be obtained from a simplified single STO representation based on the atomic radius. The advantage of extended Huckel calculations over Huckel calculations is that they model all the valence orbitals. 

The Born model is based on electrostatic interactions, dielectric permitivity, and orbital overlaps. It has the advantage of being fairly straightforward and adaptable to computational methods. The free energy for the polarization of the solute is expressed as... 

Another question is whether the filled orbitals are of a bonding or antibonding character. This is displayed on a crystal orbital overlap population (COOP) plot as shown in Figure 34.3. Typically, the positive bonding region is plotted to the right of the zero line. 

FIGURE 34.3 Crystal orbital overlap plot for CoNb4Si. 

COOP (crystal orbital overlap population) a plot analogous to population analysis for band-structure calculations... 

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

A bond m which the orbitals overlap along a line connecting the atoms (the inter nuclear axis) is called a sigma (a) bond The electron distribution m a ct bond is cylm drically symmetric were we to slice through a ct bond perpendicular to the mternuclear axis Its cross section would appear as a circle Another way to see the shape of the elec tron distribution is to view the molecule end on... 

Orbitals overlap along a line connecting the two atoms... 

Describe the bonding in ammonia assuming sp hybridization of nitrogen In what kind of orbital is the unshared pair What orbital overlaps are involved in the N—H bonds , ... 

FIGURE 2 9 Each half filled sp orbital overlaps with a half filled hydrogen Is or bital along a line between them giving a tetrahedral arrangement of four ct bonds Only the major lobe of each sp orbital is shown Each orbital contains a smaller back lobe which has been omitted for clarity... 

Identify the orbital overlaps involved in the indicated bond in the compound shown (propene) Is this a tt bond or a ct bond ... 

The hydrocarbon shown called vmylacetylene is used in the syn neoprene a synthetic rubber Identify the orbital overlaps involved in How many cr bonds are there in vmylacetylene How many... 

Section 2 6 Bonding m methane is most often described by an orbital hybridization model which is a modified form of valence bond theory Four equiva lent sp hybrid orbitals of carbon are generated by mixing the 2s 2p 2py and 2p orbitals Overlap of each half filled sp hybrid orbital with a half filled hydrogen Is orbital gives a ct bond... 

Of the overlaps between an s and a p orbital as shown in the illustration one is bonding one IS antibonding and the third is nonbonding (neither bonding nor antibonding) Which orbital overlap corresponds to which interaction" Why" ... 

An orbital overlap description of electron delocalization mil dimethylallyl cation H2C=CH—C(CH3)2 is given m Figure 10 2 Figure 10 2a shows the rr bond and the vacant p orbital as independent units Figure 10 2b shows how the units can overlap to give an extended rr orbital that encompasses all three carbons This permits the two rr electrons to be delocalized over three carbons and disperses the positive charge... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

Additionally sp hybridization of the hydroxyl oxygen allows one of its unshared electron pairs to be delocalized by orbital overlap with the tt system of the carbonyl group (Figure 19 1) In resonance terms this electron delocalization is represented as... 

Figure 7.12 Orbital overlap between transition metal and olefin (a) d 2 y2 and TT and (b) d y and rr. ...

Fig. 4. Orbital overlap for conduction molecular orbitals and molecular stacking in tetrathiafulvalene (TTF).

Syn- and anti-orientations are possible and there is evidence that the anti-orientation does not favor orbital overlap such an orientation is favored with larger branched-chain substituents. A C-nmr study found that the TT-electron density on the vinyl P-carbon is lower as the reactivity of the monomer increases (20). Methyl vinyl ether exists almost entirely ia the syn-stmcture, a favorable orbital overlap situation, and MVE for this reason is less reactive to both polymerization and hydrolysis (21). 

Dienes would be expected to adopt conformations in which the double bonds are coplanar, so as to permit effective orbital overlap and electron delocalization. The two alternative planar eonformations for 1,3-butadiene are referred to as s-trans and s-cis. In addition to the two planar conformations, there is a third conformation, referred to as the skew conformation, which is cisoid but not planar. Various types of studies have shown that the s-trans conformation is the most stable one for 1,3-butadiene. A small amount of one of the skew conformations is also present in equilibrium with the major conformer. The planar s-cis conformation incorporates a van der Waals repulsion between the hydrogens on C—1 and C—4. This is relieved in the skew conformation. 

The deviation from planarity that is present in a structure such as 1 raises the question of how severely a conjugated system can be distorted from the ideal coplanar alignment of p orbitals and still retain aromaticity. This problem has been analyzed by determining the degree of rehybridization necessary to maximize p orbital overlap in 1. It is found that rehybridization to incorporate fractional amounts of s character can improve orbital alignment substantially. Orbitals with about 6% s character are suggested to be involved... 

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