Point-dipole approximation

For two stacks having the same molecular orientations, the numerical factor 3 (2) in formula (3.3.15) should be substituted by 2 as a result, with

parameters indicated above, the frequency shift yielded in the point-dipole approximation is 2 = - 445 cm"1. On the other hand, the computer simulation of two parallel stacks, each consisting of ten BTCC molecules, gave the frequency... 

The intrachain dipole-dipole interactions of BTCC molecules are responsible for the frequency shift contributing to the first of Eqs. (3.3.8) as (3)//(l -3cos2sign changing at

Coulomb interactions show this boundary angle to be equal to 30°.132 Thus, as far as intrastack interactions of dye molecules are concerned, the point-dipole approximation introduces large errors into the treatment. 

Summing the first and second order contributions (5.9), (5.5) and (5.12a), the total hf matrix for a proton (ligand atom N) in the point-dipole approximation is given by... 

In early work, Spiesecke and Schneider (59) pointed out that inductive effects alone cannot account for a- and -signal shifts. They held diamagnetic neighbor-anisotropy effects (63) arising from anisotropic electron-charge distributions responsible for the deviations in the electronegativity correlations. For bonds with conical symmetry they applied McConnell s magnetic point-dipole approximation (64) for the estimation of this contribution, Act ... 

In this section, we discuss the work inquiring into the meaning of r/s, the distance between the two dipoles in Eqs. (12) and (13). The simplest approximation is to assume that r/s is equal to the internuclear distance between the nucleus in the ligand, the relaxation of which is being studied, and the metal ion. This amounts to the point-dipole approximation for both the nuclear and the electron spins. While such an approximation is perfectly... 

The effective distances obtained by Nordenskiold et al. (40) are compared with the internuclear distances in Table I. Clearly, the point dipole approximation is reasonable for the hydrogen nuclei in these complexes, while substantial deviations are observed for the oxygen nuclei. The findings of these early quantum chemical studies were confirmed by Sahoo and Das (41-43). Wilkens et al. have reported DFT calculations using Eq. (16) for a 104 atom model for high-spin Fe(III) rubredoxin (44). Large discrepancies between the effective distances and the input distances for the calculations were found for the hyperfine-shifted nitrogen-15 resonances, as well as for proton and carbon-13 nuclei in cysteines bound to the iron center. 

If the solute molecule has a dipole moment, it is expected to differ in various electronic energy states because of the differences in charge distribution. If the solvent is nonpolar, then the rough description of the interaction is dipole-induced dipole type. In polar solvents, dipole-dipole interactions also become important. The London forces are always present. For the calculation of dipole-dipole interaction energy, point dipole approximations are made which are poor description for large extended molecules. 

Kowalewski analyzed the validity of the point dipole approximation in a series of complexes and found that the effective distance from the ligand nucleus to the unpaired spin agreed well with the internuclear distance for XH nuclei. Large deviations from the point dipole approximation have been found for the ligand nuclei directly bound to the metal. 57 J 59... 

This contribution to the shift is quite difficult to evaluate, because in general the spin density distribution all over the space is not known. The approach to this problem should be stepwise. We first consider that the unpaired electron is localized on the metal nucleus in a paramagnetic metal complex. We refer to this as to the metal-centered point-dipole approximation. Surely this contribution will always be present and often dominant. Then we will discuss the consequences of relaxing this condition. Even in the metal-centered approximation several cases should be discussed. 

The accuracy of the present point-dipole approximation with respect to a model with delocalized unpaired electrons (Section 2.2.2) has also been evaluated for f" systems [80]. The deviations have been found to be substantially smaller than those estimated for 3d metal ions. 

As anticipated in Sections 2.2.2 and 3.1, the unpaired electrons should not be considered as point-dipoles centered on the metal ion. They are at the least delocalized over the atomic orbitals of the metal ion itself. The effect of the deviation from the point-dipole approximation under these conditions is estimated to be negligible for nuclei already 3-4 A away [31]. Electron delocalization onto the ligands, however, may heavily affect the overall relaxation phenomena. In this case the experimental Rm may be higher than expected, and the ratios between the Rim values of different nuclei does not follow the sixth power of the ratios between metal to nucleus distances. In the case of hexaaqua metal complexes the point-dipole approximation provides shorter distances than observed in the solid state (Table 3.2) for both H and 170. This implies spin density delocalization on the oxygen atom. Ab initio calculations of R m have been performed for both H and 170 nuclei in a series of hexaaqua complexes (Table 3.2). The calculated metal nucleus distances in the assumption of a purely metal-centered dipolar relaxation mechanism are sizably smaller than the crystallographic values for 170, and the difference dramatically increases from 3d5 to 3d9 metal ions [32]. The differences for protons are quite smaller [32]. 

The TDC method takes into account the shape of the molecules in detail, and its accuracy in the calculation of the Coulomb coupling depends only on the size of the volume elements used in the grid (the cube ). In this way, the TDC method has proven extremely useful in understanding the limitations of the point dipole approximation (PDA) in a variety of systems. In particular, how the PDA fails to describe the coupling when the interchromophoric center-to-center distance is comparable to the molecular dimensions, a situation found, for example, in many of the relevant interactions present in natural light-harvesting antennas. [50]... 

Riplinger, C., Kao, J. P. Y., Rosen, G. M., Kathirvelu, V., Eaton, G. R., Eaton, S. S., Kutateladze, A., and Neese, F. (2009). Interaction of radical pairs through-bond and through-space Scope and limitations of the point-dipole approximation in electron paramagnetic resonance spectroscopy. J. Am. Chem. Soc. 131, 10092—10106. Schiemann, O., and Prisner, T. F. (2007). Applications of electron paramagnetic resonance to distance measurements in biomolecules. Q. Rev. Biophys. 40, 1—53. 

At large distances compared with the size of the molecules, the dipolar transitions may be treated with point dipoles. This approximation is not valid for intermolecular distances met with in condensed phases. However, the point-dipole approximation allows one to discuss the various levels of interaction and proves very useful for the discussion of the general case, as illustrated in Section II. Historically, the point-dipole approximation was the first to be applied to molecular-crystal excitations.17-20... 

Figure 1.2. Excitonic dispersion curves for the first singlet state of the anthracene crystal. These curves are calculated in the point-dipole approximation, the transitions to upper states being accounted for by a constant dielectric permittivity.13,37...

When the point-dipole approximation is no longer valid, the exact distribution of transition charges on the molecule is introduced. The difference between this distribution and that of the point dipoles is important only in short-range interactions and modifies only the analytic part of the dispersion. In particular, the retarded interactions (and the associated properties) are not modified. 

The values of the ion shifts were estimated in the point charges point dipoles approximation of the EFGs calculation both in the PSN and PMN. 

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