Susceptibility molecular

The molecular susceptibility Xm gives therefore directly the root-mean-square radiusyrms of the electron-cloud in 1918 and earlier years this formula provided one of the best ways of estimating atomic radii" (14) which are obviously electron-cloud radii y and not structural radii r. 

The spectral simulation procedure is described in more detail elsewhere.[3] Here, we introduce briefly the basic equations. The rotationally-sensitive part of a general fs DFWM signal is expressed through the third order molecular susceptibility %(t) as follows [4,5]... 

Fig. 9. Relationship of two symmetry-related molecular susceptibility tensors to monoclinic crystal axes. (b) Definitions of principal crystal susceptibilities in monoclinic crystals.

Turning from the more practical side of recent advances, let us consider the routine aspect of the calculation of molecular susceptibilities from the eigenvalues and eigenvectors produced by some ligand field model. The usual procedure, using Van Vleck s equation... 

The principal molecular susceptibilities, calculated as the penultimate step in reproducing the experimental crystal susceptibilities, were found to lie far from any M-L bond directions or from any suitable bisectors of these vectors nor did the magnitudes of the principal molecular susceptibilities describe anything like an axially symmetric susceptibility tensor. It is clear why so much difficulty was experienced earlier in the interpretation of the crystal susceptibilities. 

A similar study has been performed on the isomorphous iron(II) analogue of this system (31). The experimental susceptibilities were different, of course. The basis functions for the calculations were different also in mz s-Fe(py)4 (NCS)2 the d6 configuration gives a SD term as the only level of maximum spin multiplicity. Otherwise the procedures followed those adopted for the cobalt analogue. Except that in this case the principal molecular susceptibilities were calculated to lie in entirely different but uninformative directions, all the results from the ferrous system virtually coincided with those from the cobalt one. This... 

The magnetic susceptibility which can be calculated through (1) is the molecular susceptibility while the one which can be experimentally measured is the crystal susceptibility the two are identical only when the site symmetry of the metal ion is equal to the point symmetry of the crystal space group. When the site symmetry is lower the molecular susceptibility can be obtained only through some indirect procedure39. ... 

In a series of comprehensive magnetochcmical investigations, Pascal (501,602) found that the molecular susceptibility of diamagnetic, organic compounds can be closely represented by... 

Construction of a bulk material possessing a large bulk susceptibility requires not only molecular constituents with large microscopic susceptibilities but a noncentrosymmetric system where the orientation of the molecular species results in additivity of the molecular susceptibilities. 

The molecular susceptibility (— Xm x 10 /cm mol) of pyrazine has been determined as 37.7 (576) or 38.0 (577) these show large differences from those of pyrimidine (43.1) and pyridazine (40.5). The nature of these differences suggests that they result from delocalization of the lone-pair orbitals of the nitrogen atoms in these compounds (577). 

Burke and Lauterbur noted the enhanced shieldings both of and of cyclopropane with respect to other cycloalkanes, and they considered the existence of a ring current to rationalize these, and also the enhanced molecular susceptibility. 

Anisotropic molecules show optically isotropic behavior in the bulk when they are disordered and randomly oriented, for instance in solutions or liquid crystal above the transition temperature. Under the influence of a strong beam, the induced dipole moment of the molecules feels a torque that tends to orient the molecule. The reorientation of the molecular dipoles induces a change in the refractive index. The typical values for molecular susceptibilities and the time-responses vary depending on the type of systems. For small anisotropic molecular systems, x 10 esu, with a time response 10 s. However, in the nematic phase, liquid crystal molecules are strongly correlated, resulting in much higher values, x 10 esu,... 

At the molecular level the third-order nonlinear polarization ju, is correlated to the local electric fields (/) through the third-order nonlinear molecular susceptibility y ... 

N.m.r. line-broadening and shift effects have been investigated for CoL [L = (12)] in H2O, MeOH, and DMT. " Crystalline and molecular susceptibilities and their orientations of cobalt(ii) phthalocyanine [Co(pc)], bis(pentane-2,4-dithionate)cobalt(ii) [Co(pdt)2], and the analogous copper(ii) complexes have been reported. E.s.r. has been used to show that addition of DMF or DMSO to aqueous solutions of cobalt(ii)tetraphenylporphyrintetrasulphonate [Co(tpps)] results in a... 

The total molecular susceptibility has now been expressed as a sum over operators localized on the various atomic nuclei. But they operate on wave functions that extend over the whole molecule. If the average values of these atomic operators are not greatly dependent on parts of the wave function far removed from the nucleus in question and if the relevant properties of the electron distribution around each nucleus are not much different for a given type of atom in different molecules, the terms within each sum over n in Eq. (41) will be independent and constant. They will, in short, be additive atomic susceptibilities that can be evaluated from measured molecules and used to predict the susceptibility of any desired molecule. We have already demonstrated the additivity of the diamagnetic susceptibilities [Eq. (37)]. 

For convenience in application we have obtained both atom and bond values. In the atom approach we have assumed that an atom in a particular bonding situation (particular hybridization) will always contribute the same amount to the molecular susceptibility. This contribution consists of the three principal components as shown in Table 8 under atom susceptibilities. To evaluate the molecular susceptibility, the atom or bond values in Table 8, which are principal values, are rotated into the principal inertial axis system (a, b, and c) of the molecule. The atom and bond susceptibilities were determined by least squares fitting the experimental molecular susceptibility components of the 14 common nonstrained, nonaromatic molecules shown in Table 7. 

It is evident from the results in Table 7 that the molecular susceptibilities obtained from the local values in Table 8 are in good agreement with experimental results. These local values can now be used to predict the molecular susceptibility of nonstrained, nonaromatic compounds on which measurements are not available. In conclusion we have extended the well-known Pascal s rules for bulk susceptibility to the individual diagonal elements in the molecular magnetic susceptibility tensor. Of course, the diagonal sums of the values given in Table 8 also allow a prediction of the bulk susceptibilities. 

It still remains to be determined whether or not the group susceptibility anisotropies and principal susceptibilities are transferable to any large extent among different molecules. If the concept of bond susceptibilities is valid, it should be possible to establish sets of these quantities, which, when combined, are able to reproduce the molecular susceptibility components and anisotropies.55 Of course, it would be necessary to classify the bonds according to the environment, as ApSimon et al.53,54 did. 

For our purposes, A designates the anisotropic chemical shift (CS), dipolar (D) interactions. The chemical shift implicitly contains the anisotropic molecular susceptibility which places a natural limit on the resolution of proton NMR of solids under conditions of high resolution as discussed by VanderHart [12]. 

Fig. 1.2. The field induced magnetic moment is depicted schematically in this drawing. This effect is most pronounced in aromatic molecules such as fluorobenzene, where comparatively strong electron ring currents may be induced, leading to a field induced, molecular magnetic dipole moment which opposes the exterior field. Trying to align the induced moment, the exterior field will exert a torque ind X H on the molecule and will thus perturb the overall rotation. This perturbation is seen as a splitting in the rotational spectra. Since there will be a torque only in the case that md and H are not aligned, i.e., if Jg is anisotropic, only the anisotropies of the molecular susceptibility tensor can be obtained from the splittings of the rotational lines...

Table II.3. Diagonal values of molecular susceptibilities referred to the principal inertial axis system in units of 10 S erg/(G2 mole). In each case the first reference is for the susceptibilities, the second for the structure. The local values Xaa(loc), Xbb(loc), Jfcc(ioc) have been calculated according to Eq. (11.12), using the known structure and the atom susceptibilities listed in Table II.2...

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