Distance dependence quadrupole interactions

Examination of the various contributors to ES reveals that the dipole-dipole R"3 term is particularly sensitive to angular distortions. Whereas the dipole-quadrupole interactions contained in the R 4 term are also sizable, it is important to note that they behave differently depending upon which molecule is rotated. That is, the R 4 term produces a net stabilization if the donor is turned but adds to the destabilization of R-3 if the rotation occurs in the acceptor. Overall, the multipole series, truncated at R 5, provides a reasonable approximation of the full ES distortion energy, particularly at the longer distance. 

Thus for two polarizable dipole molecules in the gas phase all attractive interactions depend on the inverse of the sixth power of their mutual distance. For two identical molecules, neglecting higher terms (quadrupole interactions etc.). 

K+, Rb+ and Cs+, respectively) and, on the other hand, to the nonlinear distance dependencies of electrostatic interactions. The latter fall off sharply in proportion to R 2 for ion-dipole, R3 for ion-quadrupole and R 4 for ion-induced dipole interactions. 

In VO(TPP) CHCly-toluene the measured hf values of the pyrrole protons are found to be 1.38 MHz and -0.26 MHz (in-plane) and -0.26 MHz (out-of-plane). The hfe tensor may be separated into a contact contribution = 0.29 MHz and an axial dipolar contribution A = 1.10 MHz which conesponds to a V-H distance of 5.24 A. The axial-ity of the dipolar tensor indicates that the spin density on the nitrogen ligands is very small in VO(TPP) (in agreement with the N hfs data), in contrast to Ag(TPP), where the unpaired electron is significantly delocalized and strongly rhombic pyrrole proton tensors have been observed. No interpretation of the N quadrupole interaction has been given. As found in VO(acac)2, the proton resonances in VO(TPP) show a considerable solvent dependence. Since interpretation of this effect is highly speculative at present, we shall not discuss this problem. 

If all interactions between multipoles up to quadrupoles are included, then only some of the interactions having i " and R distance dependencies are accounted for. Alternatively, if the distance dependence is taken as the deciding factor, then quadrupoles are required for including all interaction of order R or lower, but the dipole-quadrupole and quadrupole-quadrupole interactions should not be included. 

Fig. 12. Schematic of three mechanisms which can lead to lattice modulations (a) distance dependent exchange, (b) quadrupole in a crystal field, and (c) quadrupole-quadrupole interaction. (From Bohr et al. 1989.)...

Monopole-quadrupole. Exemplified by interactions of the type ss pp ), these terms have significant value at only very small distances. As with the dipole-dipole terms, the distance dependence is r. ... 

All interaction terms are negative (favorable) and inversely proportional to temperature. As the order of the multipole increases the distance dependence becomes increasingly severe, and interactions beyond quadrupole-quadrupole do not provide a significant contribution to overall interaction energies. 

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