Diamagnetic susceptibility Correction

Added February 10, 1927.—J. H. Van Vleck in Proc. Nat. Acad. America, vol. 12, p. 662 (December, 1926), has discussed the mole refraction and the diamagnetic susceptibility of hydrogen-like atoms with the use of the wave mechanics, obtaining results identical with our equations (24) and (34). He also considered the effect of the relativity corrections (which is equivalent to the effect of a central field) and concluded that equation (24), derived by the use of parabolic instead of spherical co-ordinates, is not invalidated.]... 

Aromatic ring currents[45, 46] or the charge stiffness[47] provide a related application of correction vectors, now associated with magnetic fields. Ring currents are the diamagnetic susceptibility of 4n+2 systems. The correction vector in monocycles is obtained from... 

Table 2. The factors q mx1- n V f°r maSnetic induced corrections to the matrix elements of radiative 7r-transitions in the Lyman nOA-) —> Is) and Balmer series nOA- —> 12s) and nmA+) — 2pm) with m = 0,1. The upper level index A is determined by ordering the absolute values of diamagnetic susceptibility, reP ...

For a homonuclear molecule, D = d, so that the second term in (8.131) vanishes. Corrections to (8.131) for molecular vibration and centrifugal stretching have been given by Ramsey [18], The above result means that if the rotational magnetic moment fi, is measured, the high-frequency part of the diamagnetic susceptibility can be determined. 

Acceptor number (or acceptivity), AN — is an empirical quantity for characterizing the electrophilic properties (-> Lewis acid-base theory) of a solvent A that expresses the solvent ability to accepting an electron pair of a donor atom from a solute molecule. AN is defined as the limiting value of the NMR shift, S, of the 31P atom in triethylphosphine oxide, Et3P=0, at infinite dilution in the solvent, relative to n-hexane, corrected for the diamagnetic susceptibility of the solvent, and normalized ... 

In comparing the work of Schneider and co workers to that of Huggins, Pimentel, and Shoolery, we should note a different use of reference standards. Schneider and Reeves discuss their use of an external reference sample (1705). In this use, it is generally assumed that the volume susceptibilities of solution components are additive. This assumption is made doubtful by the existence of solvent-solute complex formation. Huggins et al, on the other hand, use an internal reference, i.e., a reference solute dissolved in the solution of interest. Thus a correction for bulk diamagnetic susceptibility is obviated by putting the solute in the same mag netic environment as the species of interest. 

Table 10.1. The molar diamagnetic susceptibility calculated by group contributions, the correction index N s used in the correlation equation, and the fitted or predicted (fit/pre) values of m, for 125 polymers. For 15 of these polymers, cannot be calculated via group contributions, but can be calculated by using the new correlation. The values of °%v used in the correlation equation are all listed in Table 2.2. is expressed in units of IQ-6 cc/mole.

In spherically symmetric systems the induced diamagnetism depends primarily on the mean square radius of the valence electrons as the small contribution from the inner-shell electron core can usually be neglected 1 ). In the case of molecules with symmetry lower than cubic, the quantum mechanical treatment by Van Vleck 23> indicates that another term must be added to the Larmor-Langevin expression in order to calculate correctly diamagnetic susceptibilities. This second term arises because the electrons now suffer a resistance to precession in certain directions due to the deviations of the atomic potential from centric symmetry. The induced moment will now be dependent on the orientation of the molecule in the applied magnetic field and thus in general the diamagnetic susceptibility will not be an isotropic quantity 19-a8>. 

A (diamagnetic susceptibility exaltation parameter) = Am—Am, all in units of —10- cm3 mol-1. Am is the experimentally determined molar susceptibility, Am- is the susceptibility estimated for a model cyclopolyene (neglecting ring current corrections) 28>. 

Also, corrections to special constituents such as multiple bonds, lone pairs, rings, atoms in special positions, groups of atoms etc. can be introduced. The above expression is a basis for the successful empirical calculations of diamagnetic susceptibilities on the basis of constitutive increments. The best known and the most widely used scheme refers to the Pascal method [31], although some other schemes are available [32]. A set of Pascal constants is collected in Appendix 4. 

We carried out the converse operation. The experimental values of the diamagnetic susceptibility were compared with the calculated values obtained using various approximations. It was found that the measured values of Xd differed severalfold from the values calculated on the assumption that neutral atoms were present in lithium fluoride crystals. However, when we assumed that these crystals consisted of ions, we found that the calculated and the experimental values were practically identical. This indicated that our approximations of the f curves for ions were correct. 

The same contributions appear in the expression of the bulk susceptibility (corrected for diamagnetism)... 

But as everything has a diamagnetic susceptibility, this must be corrected by subtracting the total diamagnetic susceptibility, Xm negative quantity) ... 

Here, n, is the number of atoms of kind i, x fbeir susceptibility per gram-atom, and the sum extends over all atoms in the molecule. In addition, is the number of certain structural elements of kind j, Apj their contribution to the susceptibility, and the sum is over all these contributions. The quantities Xai and /Ipj are called the Pascal constants and the constitutive corrections, respectively. The most frequently used constants Za and constitutive corrections Ap are listed in Tab. 7. In general, the diamagnetic susceptibility of an organic substance may be estimated on the basis of the tabulated values with an accuracy of a few percent. Even though the Pascal scheme was established purely on an empirical basis, it is justified by more recent calculations involving molecular orbital theory [170]. Critical discussions and reviews on the subject are available in the literature [118, 167] and illuminating examples for the calculation of susceptibilities within the Pascal scheme are included in various textbooks [2,8,14]. 

It is often found that the Curie law Eq. (21) is followed by many magnetically dilute substances other than free atoms or ions. There is, in addition, a second-order contribution to the paramagnetic susceptibility, the so-called temperature-independent paramagnetism Not. (also abbreviated TIP, cf. section 1,1.3.6) which arises from states separated from the ground state by an energy k T It follows that the molar susceptibility corrected for diamagnetism may be frequently represented by the Langevin-Debye expression... 

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