S-P type interaction

Figure 2. Relations between transition probabilities and impact parameter R for A + A — A + A (S-P type interaction). Pf, P, and Pc are the transfer probabilities where the initial F-state angular momenta have the direction , n, and ...

Velocity Dependence of the Cross Section. For S-P type interaction, the excitation transfer cross section was proportional to V1 for Case 1, and to tT2/5 for Case 3. For Case 2 the velocity dependence was not as simple. Here the ratio of the angular frequency of the resonant defect [a> = (Ei — Ef/tl) to the relative incident velocity (v)—i.e.> a = to/v is the most important parameter. If the ratio is small compared with the reciprocal of the interaction range a"1, the transfer will approach that of Case 1 (exact resonance). The cross ection will decrease monotonically with t at higher velocities. If a a"1, the cross section will be fairly small compared with that of exact resonance. Further, in the limit of t 0, the cross section would be zero, and would increase with v at low velocity region. Then, it will reach a maximum in between these regions for Case 2. This feature will hold for all inter-multipole types of interaction including the S-P type. However, the detailed and quantitative discussion on the velocity dependence for Case 2 is not this simple. On the other hand, the velocity dependence of the cross section for the resonance type excitation transfer (Cases 1 and 3) can be discussed more straightforwardly, not only for the S-P interaction case but also for other interaction cases (48, 69). 

Figure 3.4. An s- and p-type interaction between p orbitals The s orbitals are further apart and less polarized than the p orbitals. Also, Ae. — Aea > Ae — As . ...

IlypcrCChcm oITcrs an easy way to Interactively add certain basis functions to a molecular system, The Extra Basis Eiinction dialo > box can be used to add an S, P. D, SP. or SPD shell to the selected atom(si. These extra basis functions are primitives with no con-traction s, Th IIs, the extra basis functions are unic uely defined by the shell type and the value of the exponen t. 

In reality there are subtle deviations from this simple picture. The energy levels shift somewhat from element to element, and different structure types have different band structures that become more or less favorable depending on the valence electron concentration. Furthermore, in the COOP diagram of Fig. 10.13 the s-p, s-d and p-d interactions were not taken into account, although they cannot be neglected. A more exact calculation shows that only antibonding contributions are to be expected from the eleventh valence electron onwards. 

Also the a-n interaction in Diels-Alder additions, which occurs with sy -fashion with regard to both diene and dienophile, is explained (Fig. 7.38). For the first place, the p-a type interaction is allowed, by the selection rule already mentioned, between the jr-part of butadiene and the ji-part of ethylene. Once this weak p-a type interaction starts, the p AO part forms a six-electron system. The HO of this -part will come from HO of butadiene jr-part interacting with LU of ethylene jr-part will interact with er-LU s of both butadiene and ethylene. The mode of interaction is as indicated in Fig. 7.38. 

Pj orbitals that are oriented perpendicular to the square lattice interact in the same way as the s orbitals, but the r-type interactions are inferior and correspondingly the band width is smaller. For and orbitals the situation is somewhat more complicated, because [Pg.101]

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