Weak interactions expectation energy

Electronic Effects. Because of more favorable overlap, the interaction of the carbon 2p orbital with substituent p or ti orbitals is expected to dominate. The a (rp ) orbital that lies in the nodal plane of the substituent p or ti orbital will only interact with substituent a orbitals, and then only weakly. Thus its energy is mostly unperturbed by the substituent. A simple way to analyze the effect of the perturbation by substitution is to superimpose the orbitals of a prototypal carbene on those of the 71 system of the substituent. 

This is smaller than the coefficient —3.2 x 10+3 nm6 kT already estimated for the zero-frequency contribution and therefore again indicates very weak interaction energy. Inclusion of the significant degree of retardation screening expected at these separations would have yielded still smaller energies. 

In the IR absorption spectrum of ACN (Fig. 5) there is a small relatively sharp transition at 3150 cm-1. This transition has previously been assigned as a combination of C-C stretch (918 cm-1) and C N(2253 cm-1) stretch (84). Since the combination transition overlaps the higher energy tail of the C-H stretch fundamental, pumping at this frequency is expected to produce vibrationally excited molecules where all three vibrations interact. The excitations may be viewed as weakly interacting independent vibrations (47). The weak interaction is assured since the anharmonicity is relatively small (<0.3% of the vibrational frequency). Any coherent vibrational states produced by the pump pulse will lose coherence very rapidly, since the dephasing time constant (T2 0.5 ps) (51) is much faster than the VER lifetime. 

In the case of weak interactions, according to the wide band approximation an analytical expression for the total expectation of the energy is obtained ""... 

Eq. 94 can be used to analyze the effect of errors in the approximate quantities (functionals and potentials) on the interaction energy in weakly interacting complexes. The first six terms represent the zeroth-order contribution to the error i.e. do not account for the complexation induced change of the electron densities of the isolated monomers. Such terms can be expected to be dominant for weak complexes in the absence of strong electrostatic and polarization effects. Terms from the seventh to ninth represent the first-order contribution. Their relative significance increases... 

---