Explaining the trends of Nuclear Shielding caused by Magnetic moments related to Susceptibilties Copy

The 2nd Alpine Conference on Solid-State NMR ,Chamonix Mont-Blanc, France Sept 9-13,2001

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A WebPage where the particulars about participation in the 3rd Alpine Conference on Solid State NMR are being posted. This is the next in sequence to the 2nd Alpine Conference. 3rd Alpine Conference also being held at the same venue in France at Chamonix Mont-Blanc, during September 14-18,2003

A webpage of this site  https://saravamudhan.tripod.com/id12.html (see the left side links-panel: "other related webpages")consists of a list of the contributions in pususance of the title"Explaining the trends of Nuclear Shielding caused by Magnetic moments related to Susceptibilties"

The events which followed after (year 2003) the reports at the above link of "id12.html" are listed and particulars are posted at the tripod site: http://nehuacin.tripod.com/


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The poster presentation at the 2nd Alpine Conference had 20 Sheets displayed the poster space. The text of the contents of Sheet #1,#2 & #20 are copied here below which is indicative of the results which appeared on the poster

                                                      contents of SHEET#1
The contents of this paper are based on the sequence of contributions at the annual National Symposia in India during the previous 3-4 years including an International Biophysics Congress held in India in Sept.1999. It is intended to convey here a possible comparitive advantages & limitations, for various experimental NMR requirements, of the present method and the already known methods for the induced field calculations and hence the demagnetizing factors also.This contribution would put forward the results in a comprehensive perspective in which it has not been reported hither to.
This present method resulted when the calculartion of intermolecular contributionmto the shielding tensor values by a lattice-summing method effectively(1) accounted for the deviations of the experimentally measured tensor parameters and hence an intensive effort was made to arrive at a possibility for extending it to a summing over the entire extent of the macroscopic specimen.
(a) This method can be explained as the very simple magnetic-dipole equations and summing over the large number of contributions where as earlier methodsa required in some form or the other classical electrodynamic considerations and resulting complications of using difficult integrals to arrive at equations.
(b) Since it is only a summing over semi-micro volume elements along a radial vector of polar coordinates r,q & j and making a second summation over the different lengths and polar angles to possibly cover the entire material of the magnetized specimen, this does not require the classical equations from the electrodynamic considerations and the associated difficult integrals to evaluate.
(c) Because of this simplicity it becomes easily programmable method for computation and even arbitrary shapes can be included without complications arising in the already known methods.
(d) In the following presentation of results the demagnetization factors calculated by the present method are compared with the already reported table of values  from the earlier methods to illustrate the efficacy & reliability of the method used as per the descriptions given here
Reference(1) Multiple-pulse line-narrowing experiments for High Resolution Proton Magnetic Resonance Spectra and the measurements of proton shielding tensor parameters in single crystals of PMDA,calcium-,barium-,and lead-formates by the research group of Prof.U.Haeberlen at the Max-planck institute,Abteilung Molekulare Physik,Heidelberg.
 A cursory reading of the  sheet 20  even before proceeding from sheet 3 onwards could be helpful.
For necessary compactness in presenting the contents some of the sheets have the materials reduced to such smaller sizes as is not usual for reading. These materials in their "un-reduced" sizes are available with the presenter.
                                                   contents of SHEET#2
Sheet   1.   Title page with an abstract
Sheet   2.   Salient features of the presentation
Sheet   3.  An excerpt from a project report -An introductory page
Sheet   4.   Simplified equation for the field induced by a dipole originating from a spherical volume element with uniform magnetic susceptibility, its radius in relation to the distance to the point where the indiced field is relevant. This radius-distance consideration for packing the spheres along a vector length.And the equation for the number of such dipoles along the close-packing direction.
Sheet   5.  Extension of the above considerations to two and three dimensional expanses to cover the entire material of a macroscopic specimen.
Sheet   6.  Equation for the Shielding constant(induced field analog) s for the contribution from along a vector,two dimensional packing of the vectors and similar three dimensional depiction.
Sheet   7.  Tabulation of calculated values.
Sheet   8.  Results for the various locations of the center of the inner cavity.
Sheet   9.  Results for the case of ellipsoidal shapes.
Sheet   10. A presentation of the case of possible application to NMR studies of membrane transport.
Sheet   11. Polar coordinate definitions and trends of the various factors appearing in the equations.
Sheet   12. ELLIPSOIDS- a pocket calculator calculation and tabulation of computer calculated values for extended sets of cavity center locationssimilar to sheet 8.
Sheet   13. Calculation of induced fields by the same method in regions inside and outside the magnetized specimen.
Sheet   14. Methods based on bulk susceptibility differences.
Sheet   15. Various sample shapes in membrane transport context and other NMR situations.
Sheet   16. A typical feasibility demonstration of simplicity of this procedure to such contexts as in sheet 15.
Sheet   17. Computer program results of ellipsoids of different a/b ratios for demagnetization factors.
Sheet   18. Similarity of figures & drawings/plots obtained by this induced field calculations and the reproduced images of objects by NMR imaging.
Sheet   19. Various shapes encountered in NMR where this procedure of induced field calculation seems to be conveniently applicable.
Sheet   20. Summary and references
contents of SHEET#20
The considerations of possibilities of calculating demagnetization factors(1) by the methods similar to lattice summing provide a possibility to calculate these factors using even a simple pocket calculator(12) for the standard shapes of homogeneously magnetized specimens.This enables the calculation of induced magnetic fields inside the specimen at various points conveniently and also how these contributions at a given point differ depending on the polar and azimuthal angles(5,11) of the contributing elements from within the specimen.There are experimental situations(10,14,19) where inhomogeneities present in the sample are advantageously used(13,16) for assigning the NMR signal characteristics from different regions of the sample. It is also being pointed out that these induced field distributions expressed as field inhomogeneities(13,18) within the sample can be calculated more discretely by the above methods and can be adding to the methods available for optimizing contrasts in images if necessary with added susceptibility modifying reagents and these depend on the shapes of the samples and that of the regions considered within the sample. The demagnetization factors calculated for a few standard shapes are reported(17) for comparison with the standard tabulated values. An effort is made  to depict the pointwise induced field values from the perspectives of image-representations to make it appreciable that such pictures can be visually indicative18 of the actual modifications required for a given situation to reduce the necessity for the enormous numerical tabulations(7,17,13) which would render even this simplified calculations relatively tedious.

Readings for a better perspective of the microscopic and macroscopic aspects

1. Local-field Effects and Effective-medium theory: A Microscopic perspective D.E.Aspnes, American Journal of Physics, 50(8),1982, pages 704 to 708
2. Local Fields in Solids:microscopic aspects of dielectrics                 S.E.Schnatterly and C.Tario,Reviews of Modern Physics, vol 64,1992,   pages 619-622.
3. Lattice-sum Methods for Calculating Electrostatic
Interactions in Molecular Simulations,  Brock A.Luty, Ilaro G.Tironi  and  Wilfred  F.van Gunsteren
Demagnetization Factor Calculations,Induced Field Effects

1. Effect Of Demagnetization On Magnetic Resonance Line Shapes In Bulk Samples: Apploication To Tungston , George Mozurkewich, H.I.Ringermacher and D.I.Bolef, Physical Review B, Vol 20(1), 1979 Pages 33-38.
2. Rapid Computation Of Magnetic Anomalies And Demagnetization Effects Caused By Bodies Of Arbitrary Shapes, P.Vallabh Sharma, J. Geophysical Research, Vol.64 1966/11, Pages 89-107.

After a poster presentation (on the calculations of intramolecular shielding tensor at aromatic proton in benzene molecule )at the joint ISMAR-CA '98 (Aug.1998 at TU Berlin), the induced field calculations are now being extended to calculating a tensor-form shielding contribution due to the ring current in benzene!
Benzene Molecule with the Delocalized Aromatic Charge cloud

Benzene proton being depicted for intra molecular shielding calculations



The Benzene Molecule is being depicted as the delocalized charge cloud with one plane of delocalization above the molecular plane and the other below the molecular plane.Further the charge cloud contributed Sucseptibility tensor is considered as sum of contributing elements which can be summedup.


As can be seen in the figure the charge circulations of the delocalised pi electrons can be associated with the Susceptibility Tensor values as can be expertimentally measured for aromatic systems and this total susceptibility can be giving rise to a dipole moment at the centre of the benzene molecule, which is the molecular centre of symmetry.
The circulating charge cloud can be subdivided into several small volumes of clouds ("how far are these subdivisions realistic?"is a question which can be ascertained by the quality of the comparability of the calculated quantity with the experimentally measured Shielding constant/tensor values ) and each volume element with Susceptibility values apportioned to it from the total molecular value and these individual (voulme elemental susceptibility)component values when added tensorially should conserve the total value. Now these individual costituent element can be associated with a point within that volume for the originating point for the dipolemoment arising due to the elemental volume susceptibility.These elements' contributuion to Shielding calculated at the proton in benzene- all contributing at the same proton site inthe molecule. These individual contributions can be subjected to the tensorial addition to give the total shielding contribution.