Overlap integral Promotion

The chemical reactions through cyclic transition states are controlled by the symmetry of the frontier orbitals [11]. At the symmetrical (Cs) six-membered ring transition state of Diels-Alder reaction between butadiene and ethylene, the HOMO of butadiene and the LUMO of ethylene (Scheme 18) are antisymmetric with respect to the reflection in the mirror plane (Scheme 24). The symmetry allows the frontier orbitals to have the same signs of the overlap integrals between the p-or-bital components at both reaction sites. The simultaneous interactions at the both sites promotes the frontier orbital interaction more than the interaction at one site of an acyclic transition state. This is also the case with interaction between the HOMO of ethylene and the LUMO of butadiene. The Diels-Alder reactions occur through the cyclic transition states in a concerted and stereospecific manner with retention of configuration of the reactants. 

The presence of the HRI coating induces an increase in the effective refractive index of the cladding modes and thus a decrease in the resonance wavelengths. In addition, the spatial shift of the cladding mode field profile toward the HRI overlay promotes a decrease of the overlap integral with the core mode and so of the transmission loss peak. The subsequent evaporation of the solvent molecules from the nano-cavities results in a reduction of its refractive index. This explains the partial... 

However, a more significant elfect is expected on the first excited A-state complex, in which one of the iIq electrons is promoted into the ti system. About half the H-bonding attraction ( 3 kcal/mol — 1000 cm ) is lost by removal of the Uq oh interaction in the 0 spin set, but this is partially compensated by the reverse oh delocalization that is thereby opened by emptying of the tIq orbital. From the relative pre-NBO overlap integrals for the two interactions (S /S o — 0.6) and the expected MuUiken-type proportionality to energetic (Fock/Kohn-Sham) matrix elements, we might expect that the residual -40% elfect on the vertical A<— X promotion energy corresponds to a blue-shift on the order of -400 cmThe calculated vertical X A blue shifts AVn-bond at the CIS/6-311-H-G " (450 cm ) or CASNBO(7,5)/6-311-i-i-G " (250 cm ) levels are consistent with this simple estimate. 

Before we examine further the behavior of the generating function G2(t), let us return to Equation 3.16 for the transition probability. To this end, we have yet to obtain the expression for the factor which includes the d/dgri overlap integral arising from the promoting mode (3.14). Proceeding as in the previous manner and writing Equation 3.14 explicitly with the help of Equation 3.18, we find that... 

The analysis of these relations shows how much the charge transfer depends on the frontier functions. In this case, an integral of the Fukui functions with a large orbital overlapping, has the role to reduce the inhibitory effects induced by the chemical strengths of the two chemical systems and to promote the charges transfer. 

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