Quadrupole model, evaluated

Quadrupole model, evaluated, 109 Reciprocal length, in ionic cloud theory, 248... 

Numerous X-ray investigations have unravelled the solid state structure of contact and solvent-separated ion pairs. It was therefore considered to be of interest to evaluate also the potential of solid state NMR as a tool for the investigation of this structural problem. In addition to the study of chemical shifts discussed above (Section II.B), the quadrupole coupling constant of the nuclide Li, x( Li), was expected to be an ideal sensor for the bonding situation around the lithium cation because, due to its dependence on the electric field gradient, the quadrupolar interaction for this spin-3/2 nucleus is strongly influenced by local symmetry, as exemplified in Section II.C.3. This is also shown with some model calculations in Section ILF. 

The muon g — 2 value has been determined in a series of experiments at CERN [45,46]. The primary purpose of the new muon g — 2 experiment at Brookhaven National Laboratory is to improve the precision of the experiment by about a factor 20 and verify the presence of the electroweak effect which has been evaluated to two loop orders in the Standard Model. In this experiment, polarized muons from pion decays are captured in a storage ring with a uniform magnetic field and a weak-focusing electric quadrupole field. For a muon momentum of 3.09 GeV/c and 7 = 29.3 the muon spin motion is unaffected by the electric quadrupole field and the difference frequency uia is given by... 

Both rms and rrms are sensitive to the choice of grid point locations where the QM potential is evaluated. Typical values of rms and rrms are 1 to 3 kJ/mol and 3 to 9% with 6-3IG" wavefunctions. The fit generally worsens as grid points are placed closer to the molecule. In certain cases (e.g., strong lone pair effect) worse fits may be obtained with net atomic charge models. Models utilizing additional nonatomic sites, site dipoles, and/or quadrupoles usually give a much better fit. 

The table shows that the M + D + Q atomic multipole expansion is sufficient for most purposes. The largest rms value is just 0.03 kj/mol. So the curve fitting exercise is successful when carried to atomic quadrupole level, satisfying mathematical requirements of accuracy and convergence. But what about chemical reasonableness and transferability. Judged by these criteria, the M a- D -I- Q model is poor. As a practical matter, it may be necessary to always evaluate M + D -I- Q parameters for the specific molecule being considered and not expect the parameter values to have any obvious intuitive chemical meaning. 

A recent account by Matile et al. [62] can be considered as the first experimental example of the use of anion-tt interactions for the design of a synthetic anion channel. Matile and co-workers report the design, synthesis, and evaluation of jt-acidic, shape-persistent ohgo-(p-phenylene)-N,N-naphthalenediimide (0-NDI) rods that can transport anions across lipid bilayer membranes with a rare selectivity Cl" > F" > Br" > I" and a substantial anomalous mole fraction effect. DFT calculations revealed a global quadrupole moment Qzz =+ 19.4 B for a model NDI. By comparison with... 

The point-charge model can be improved by considering the effects of higher multipole moments in eq. (46). Dipole and quadrupole contributions (terms with k - and 2 in eq. (46)) have been evaluated for PrCL (Hutchings and Ray, 1963). It is possible to include the dipole contributions to the crystal field in a self-consistent manner (Morrison, 1976) in that treatment, point charge and dipole contributions to the electric field at various lattice sites are evaluated, and the dipole moments at these sites... 

By comparing experimental or accurate theoretical results with others based on approximate models, it is possible to determine which among those models offers the best approximate constants of the motion and quantum numbers to describe particular states. This approach is used to evaluate and compare the extent of validity of independent-particle, Hartree-Fock and collective, molecule-like descriptions of atoms with two valence electrons. The comparisons are made on the basis of overlaps, oscillator strengths, momentum correlation and quadrupole moments. The criterion for each evaluation is the extent of agreement with results obtained from well-converged Sturmian Configuration Interaction wave functions. 

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