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

Shielding- and Demagnetization-factor Calculations
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An Abstract Submitted for oral presentation at the 8th NMRS Meeting,20th-24th JAN.2002, at the SGPGI, Lucknow

APPROACHES ATTEMPTING TO REVALIDATE A FAILING POINT-DIPOLE APPROXIMATION BY REPLACING THE FULL CHARGE-CLOUD VOLUME WITH FRAGMENTED/CLOSELY-PACKED SEMI-MICRO VOLUME ELEMENTS

S.Aravamudhan
Department Of Chemistry
North Eastern Hill University
Shillong 793022
Meghalaya INDIA
Email: saravamudhan@nehu.ac.in



In one of the very early papers while interpreting the results of the High Resolution PMR results in single crystalline solid-state it was suggested1 that for calculating intermolecular contributions to the shielding tensor it is convenient to consider a given molecule as made up of fragments and apply the point dipole approximations more effectively. It was found that even for calculating intra molecular shielding tensor such a fragmented molecule approach does seem to facilitate the use of the magnetic dipole model and for intramolecular total shielding values simple summation over the contributions of various fragments yields results reasonably well2. As reported recently3 considering a given macroscopic magnetized specimen as made up of closely packed volume elements can lead to a simple procedure of summing the induced field contributions from these semi-micro volume elements to reproduce the already availble demagnetization factor values for various standard shapes. All these results have made it possible that the simple considerations given for the Neighbour Group Anisotropy Effects4 can be even more extensively validated and in several contexts, particularly for the Chemical consequences, this procedure seems to make more contributing factors conveniently and understandably tractable for intrpretation.
With the above foreground, in this contribution it is being further emphasized that this approach seem to yield a simple procedure for calculating the induced field due to a macroscopic magnetized specimen at points outside the specimen but even at such closer distances where till now the application of the simple point dipole approximation had been found unreliable.

Thus the overall trend in adapting this procedure of summing up induced field contributions is that in the case of Shielding Tensor Calculations from the confidence gained by the application to intermolecular case the approach could be found reasonable for even the intramolecular values, which means internal to the molecular specimen.On the otherhand with the confidence gained by the application to the Demagnetization factor calculations which is a case of contributions internal to the specimen and hence the semi-micro volume elements and their contributions to the induced fields are all centred inside the magnetized specimen,the procedure is now being found as an effective one for considerng the fields around the same magnetized specimens for which Demagnetization factors were calculated. A comprehensive realisation of the simplicity of this procedure would be enabled by applying these considerations to the various contexts where induced field contributiuons,their origin and the values, have to be ascertained. These considerations would be reviewed to emphasize that this simple procedure, of summing up contributions by dividing and fragmenting the contributing-whole, provides an approach leading the approximations to yield the actual limiting values.
REFERENCES:
1. Pyromellitic Acid dianhydride: Crystal Structure and Anisotropic Proton Shielding. S.Aravamudhan, U.Haeberlen,H.Irngartinger and C.Krieger. Molecular Physics, 38, 241 (1979).
2. (a) Use of Magnetic Dipole Model for Calculation of Shielding Tensors. S.Aravamudhan and A.Tomba Singh, 3rd NMRS Symposium, Feb., 1997, I.I.T.,Delhi. (b) Implications of Calculating the Full Shielding Tensor of Protons in Benzene Molecule Using a Magnetic Dipole Approximation. S.Aravamudhan and A.Tomba Singh, 4th NMRS Symposium, Feb., 1998, I.I.Sc., Bangalore. (c) Investigating the Feasibility of Calculating Intramolecular Shielding Tensors Using a Magnetic Dipole Model. S.Aravamudhan, Proceedings of the Joint 29th Ampere-International Conference on Magnetic Resonance and Related Phenomena, Technische Universitat Berlin,Berlin,page 501, August 1998.
3. (a) A Report on the Demagnetizing Factor and Induced Field Calculations for Standard Sample Shapes. S.Aravamudhan, Symposium on Spatially Resolved Magnetic Resonance & 7th NMRS Symposium, Feb. 2001, C.L.R.I/I.I.T.,Madras,CHENNAI. (b) Induced Fields Due to a Magnetized Specimen. S.Aravamudhan, 2nd Alpine Conference on Solid State NMR,Chamonix Mont-Blanc,France . Poster 2 Sept.2001.
4. The reader may please look-up the various comments and the applicablity of the early approach suggested by Harden M.McConnel ,the reference to which may be found in the Reference (1) cited above in this abstract and others as also the discussions on Ring Current Effects in Aromatic & Conjugated systems.e.g., Stephen J.Perkins, Application of Ring Current Calculations to the Proton NMR of Proteins and RNA in Biological Magnetic Resonance,vol.4 ,page 193., Edited by Lawrence J.Berliner & J.Reuben, Plenum Press (1992).

The Following is an Abridged Version of the Same Abstract Given Above

MOLECULAR FRAGMENTS MAKING UP THE WHOLE MOLECULE ;
CLOSE-PACKED VOLUME ELEMENTS MAKING UP THE WHOLE SPECIMEN


In this contribution, by calculating the induced field due to a macroscopic magnetized specimen at points outside the specimen using the summing procedure3 even at such closer distances where till now the application of the simple point dipole approximation had been found unreliable, it is intended to point out that this procedure seems to make the trends of shielding factors more conveniently and understandably tractable for interpretation.
Thus the overall trend in adapting this procedure of summing up induced field contributions is that in the case of Shielding Tensor Calculations, from the confidence gained by the application1 to intermolecular case the approach could be found reasonable for even the intramolecular values2, which means internal to the specified molecule.On the otherhand with the confidence gained by the application3 to the Demagnetization factor calculations which is a case of contributions internal to the macroscopic specimen - and hence the semi-micro volume elements and their contributions to the induced fields are all centred inside the magnetized specimen,the procedure is now being found as an effective one for considerng the fields due to aspecimen around (outside) the same magnetized specimens for which Demagnetization factors were calculated. A comprehensive realisation of the simplicity of this procedure would be enabled by applying these considerations to the various contexts where induced field contributiuons,their origin and the values, have to be ascertained. These considerations would be reviewed to emphasize that this simple procedure, of summing up contributions by dividing and fragmenting the contributing-whole, provides an approach leading the approximations to yield the actual limiting values.
REFERENCES:
1. Pyromellitic Acid dianhydride: Crystal Structure and Anisotropic Proton Shielding. S.Aravamudhan, U.Haeberlen,H.Irngartinger and C.Krieger. Molecular Physics, 38, 241 (1979).
2. Investigating the Feasibility of Calculating Intramolecular Shielding Tensors Using a Magnetic Dipole Model. S.Aravamudhan, Proceedings of the Joint 29th Ampere-International Conference on Magnetic Resonance and Related Phenomena, Technische Universitat Berlin,Berlin,page 501, August 1998.
3. Induced Fields Due to a Magnetized Specimen. S.Aravamudhan, 2nd Alpine Conference on Solid State NMR,Chamonix Mont-Blanc,France . Poster 2 Sept.2001
.




The Running Title for the pages in this website included here(below) as well for a quick side reference-though a repetition

The Foreground and the current trends of research activities by Dr.S.Aravamudhan , Department of Chemistry, North Eastern Hill University, Shillong


The present subject of research has inception at the instance which made a breakthrough in the explanations of discrepancies repeatedly encountered while trying to account for the results of experimental proton shielding tensor measurements by the Multiple Pulse Selective Averaging methods in Solid State
NMR. This work ,particularly on the single crystals of Pyromellitic Acid Dianhydride, opened up -as was pointed out in the Discussions of the published paper-two pronged investigation of the consequences:
1) To study the possibilities of calculating INTRA (in exclusion of the INTER)molecular contribution to the shielding tensors as arising due to the induced fields by simple point dipole contributions.
And 2) to find methods of extending the considerations of intermolecular calculations to the whole macroscopic extent of the specimen instead of the only semi-microscopic (of about 100 Angstroms extent) elements.These should enable the simple basis of dipole (point dipole approximation) contributions to be understood more comprehensively from the intra- to intermolecular consequences without the acompanying obscurities due to the involved mathematical procedures which render all the explanations to be beset with a kind of abstractness which causes discomfitures while applying in Chemical contexts.
On the aspect (1) a poster presentation could result at the Joint ISMAR-CA'98 at the Technische Universitat in Berlin during August 1998.
The aspect (2) above is the matter dealt with in the presentation at the 2nd alpine conference. All these aspects have been presented (in steps) at the annual Symposia of the National Magnetic Resonance Society,INDIA
Hence the present achievement is founded firmly on the results of the work as Post Doctoral Fellow during 1975-77,and the informations gathered by literature survey while being at the NCL,Pune and the further supplementary assistance available in obtaining published reference materials from CSIR labs.The earlier efforts to realise were all in the form of several M.Sc.,Project Works(each of only six months duration) at the NEHU,Chemistry. A great deal remains to be inferred by intensive efforts and communicate them as publications in Journals. The possible applications of these simple calculation procedureshave beenpointed out broadly in the poster presentation at the Internatinal Biophysics Congress in held in New Delhi in September 1999 and this participation was funded by the INSA Grant.