Orbital Effect of Overlap

Using the simplest picture (and neglecting the effect of overlap on the normalization), this doubly occupied og spatial molecular orbital can be thought of as being the symmetric linear combination of the two Is atomic orbitals on the left and right hydrogens, HL and Hr... 

Answer to 9 and 10. The orbital interaction diagram for the bonding is shown in Figure B3.8. The geometric changes described for ethylene, its cation radical, and its excited state reinforce our conclusions regarding the effect of overlap, namely that... 

The effectiveness of overlap of bonding orbitals of ihe same symmetry appears to decrease as the principal quantum number increases and as the difference between the principal quantum numbers increases. This is reflected in the bond strengths shown in Table 10, The covalent radius of hydrogen is especially subject to effects of this kind, and has the values 0.3707, 0.362, 0.306. 0.284 and 0.293 A respectively in H2. HF. HCI. HBr and HI. The apparent anomaly of the P-P, S-S. and Cl-Cl bonds being stronger than the N—N. O-O. and F—F bonds has been considered in paragraph (I). 

Fig. 2.16. The 3d members of the Rydberg series of (a) H2O and (b) D2O, showing the enormous complexity of rovibronic detail and the effect of overlap with orbitals of different molecular symmetry (after J.-P. Connerade et al. [92]).

The final energy component is charge transfer (5), which is a quantum mechanical term arising from electron delocalization from the occupied orbitals of one molecule into unoccupied molecules of the other. This energy component depends on the overlap between these orbitals, which has an approximate exponential dependence on the atom-atom distance and has a directional dependence which depends on how the orientation of the orbitals effects their overlap. 

Figure 7-13 Symmetry orbitals constructed from s- and p-type AOs. (a) Sketches according to an idealized convention that ignores overlap between AOs on A and B. (b) Effects of overlap. Note that the pa — Pob combination is bonding. This depends on our having chosen a common z axis for both atoms. Sometimes the z axes are chosen to point from each atom toward the other. In that case, Pa A PaB becomes antibonding.

When elements in Period 2 form covalent bonds, the 2s and 2p orbitals can be mixed or hybridised to form new, hybrid orbitals each of which has. effectively, a single-pear shape, well suited for overlap with the orbital of another atom. Taking carbon as an example the four orbitals 2s.2p.2p.2p can all be mixed to form four new hybrid orbitals (called sp because they are formed from one s and three p) these new orbitals appear as in Figure 2.9. i.e. they... 

The second summation is over all the orbitals of the system. This equation is used in IlyperChem ah imiio calculations to generate contour plots of electrostatic potential, [fwe choose the approximation whereby we n eglect the effects of the diatomic differen tial overlap (NDDO). then the electrostatic potential can be rewritten... 

The Extended Hiickel method neglects all electron-electron interactions. More accurate calculations are possible with HyperChem by using methods that neglect some, but not all, of the electron-electron interactions. These methods are called Neglect of Differential Overlap or NDO methods. In some parts of the calculation they neglect the effects of any overlap density between atomic orbitals. This reduces the number of electron-electron interaction integrals to calculate, which would otherwise be too time-consuming for all but the smallest molecules. 

The NDDO (Neglect of Diatomic Differential Overlap) approximation is the basis for the MNDO, AMI, and PM3 methods. In addition to the integralsused in the INDO methods, they have an additional class of electron repulsion integrals. This class includes the overlap density between two orbitals centered on the same atom interacting with the overlap density between two orbitals also centered on a single (but possibly different) atom. This is a significant step toward calculatin g th e effects of electron -electron in teraction s on different atoms. 

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