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Prevailing Forms of Equations and the Proposed Use of Tensor Form for the Shielding of Nuclei
S.Aravamudhan
Department of Chemistry
North Eastern Hill University
Shillong (Meghalaya) 793022
INDIA
There are four important models for describing the diamagnetic anisotropy of aromatic ring systems[1]. There are detailed considerations of the equations based on these models in the reviews available till now[2]. Without mentioning much of the details of the methods for obtaining these equations it can be pointed out at the outset that the resulting equation for the proton shieldings (chemical shifts) are for the isotropic values and depend on the anisotropy of the diamagnetic susceptibility of the aromatic ring. Hence there can be the ring current susceptibility only as the component perpendicular to the plane of the aromatic ring.
A consideration of using the Susceptibility tensor of the various bonds (C-H,C-C,C=C etc.,) and the contribution of aromatic delocalised π electron system seemed encouraging even for calculating the intramolecular shielding effects[3]. Some of these considerations as applicable to biomolecular systems were illustarted in the previous contributions at the meetings of the Indian Biophysical Society[4]. A more explicit consideration of the equations prevailing in the context of Biomolecular proton NMR would be presented with the advantages which may be of significance when calculations are made with the Full Tensor form instead of the equations obtained for only the trace of the Tensor for the consequences of Aromatic Ring Current Effects.
[1] �NMR in Medicine and Biology�, K.H.Hausser and H.R.Kalbitzer, p102, Springer Verlag (1991).
[2] �Application of Ring Current effects��,Stephen J.Perkins in �Biological magnetic resonance Vol.4� p193, Edited by Lawrence J.Berliner and Jaques Reuben, Plenum Press(1982)
[3] �Investigating the Feasibility �� by S.Aravamudhan page 501, Proceedings of the Joint 29th Ampere-13th ISMAR International Conference,TU Berlin 1998.
[4] Poster presentations by S.Aravamudhan at the Annual Meetings of IBS at UOM Chennai in 2002 and at IIT Roorkee in 2003.
INTRODUCTION :
For the Biomolecular structure determination, NMR Chemical shifts induced by the Aromatic Ring Current effects become important parameters in conjunction with the X-ray methods. It becomes necessary hence, to be able to calculate this aromatic ring cuureent effect contributions to verify the structural parameters. The equations prevailing at present are all for the calculation of isotropic chemical shift values and the different variations of this equations are to improve for the way the induced magnetic moment localized or distributed in the molecular system particularly the aromatic delocalisation of the elctronic charge cloud, the ardius of the aromatic ring in comparison to the distances at which its influence is calculated. The effort has been to improve the validity of the point-dipole approximation.
Eventhough the NMR methods have been very effective in this context, there have been several inadequacies and hence the reliability could not be improved to the required degree. Part of this predicament could be discerned as due to the inherent �averaging out� while deriving the equations for the isotropic shifts. With the experiences in handling the Full tensor Form Shielding tensor Calculations, it is being pointed out in this presentation that the explicit calculation of shielding tensor for the context followed by the necessary processing of the set of tensors with averaging and merging appropriately, the NMR methods could become an inherently informative tool for the structure determination.
An elementary calculation of the NMR isotropic chemical shift in the vicinity of the benzene molecule has been illustrated in these posters which is basically a calculation of the relevant Shielding tensors and then obtain the trace of the tensors for comparison with the calculated results available till now using the equations for the isotropic shifts.
INDEX TO THE POSTER SHEETS [displayed at ibs2004] :
SHEET-1: An Introduction and Index
SHEET-2: An illustration of the Benzene Ring Environement : The Ring Current in Magnetic Field; Thus Induced Magnetic Moment; And, the Relevant Systems of Coordinates Used in Ring current effect Calculations.
SHEET-3 & SHEET-4: Prevailing Equations Used in the Chemical Shifts due to the Aromatic Ring Current Effects
SHEET-5: The Equation for the Shielding Tensor on the Basis of a Magnetic Dipole Model with Diamagnetic Magnetic Susceptibility and the Proton Position as the Inputs
SHEET-6: TheTotal Molecular Magnetic Susceptibility Tensorof Benzene with an Illustration of the Corresponding Principal Axis System.
SHEET-7 & SHEET-8: The Total Susceptibility Tensor and its Break up as the Susceptibility Tensors of the Fragmented Groups/ Bonds/ Atoms/localized and delocalised contributions.
SHEET-9: Results of calculations of Shielding Tensor : Further calculation of the Trace for the isotropic shifts for comparison with the prevailing Calculated results in literature.
SHEET-10 & SHEET-11: The Use of the Tensor Form of the equations to Calculate the Tensor for circulating Currents above and below the Plane of the Benzene ring for Various proton positions in the surrounding: Illustration of the possible plot-patterns which can be visually indicative of the trends in structures.
SHEET-12: The Essential Differences and Distinctions in the Variety of Rigid rotations to partially Rigid and the Simultaneous Inedependent Motions indicating the requirement of a consideration at the unaveraged tensors to account for the relevant relative motions within the System.
SHEET-13: The Magnetic Moment; Field directions and the resulting dipolar field distributions. ;Click Here to Display a Webpage containing downloadable "SHEET#s" relevant for the contents
SHEET-14: Another Perspective for this Context.
SHEET-15: A Segment of actual Biological Molecular system where in the Aromatic Ring has a favourable disposition for Large Ring Current shifts.
SHEET-16: A Flow Chart of a Computer Program to indicate the stage where the modifications can be introduced to adapt the full-tensor Calculatuion Procedures.
SHEET-17,18,19, & 20 The variety of sstructural situations where the chemical shifts would have to be averaged with better discretion and hence the requirement of a standby procedure for shielding tensor calculations as envisaged here in this poster presenation.
Shielding by Ring Current Effect Contributions
Isotropic Shielding Values by the Traditional Equations and from the Full Tensor Calculations
Department of Chemistry
North Eastern Hill University
Shillong 793022 Meghalaya
The efforts to find the advantages- which might be added when full shielding tensor calculations are obtained, while trying to interpret the Biomolecular Structures on the basis of the ring current effects- have been leading to the necessity to obtain the isotropic values of the shielding by calculating the trace of the Full Shielding Tensor calculated from an equation based on the magnetic dipole model[1]. The contents of the Webpage http://geocities.com/inboxnehu_sa/NSCMB2004.htmlwould indicate that a preliminary effort could lead to the conclusion that the comparison of values of isotropic shielding by this approach and the values listed earlier based on the traditional equations for the isotropic shielding parameter has been encouraging. A more detailed effort to use the magnetic dipole model and calculate the Shielding Tensor as a function of the distances around the aromatic ring would be reported in this contributions with the highlights on the additional advantages of such effort.
REFERENCE:
1.http://saravamudhan.tripod.com/
2.http://geocities.com/amudhan20012000/Confview_link.html