1. MRSFall 2006 Meeting Nov.27-Dec.1, 2006 Boston USA
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MRSFall 2006 Meeting Nov.27-Dec.1, 2006 Boston USA
By ARAVAMUDHAN, Sankarampadi Department of Chemistry North Eastern Hill University SHILLONG INDIA Session MM17.2: December 1, :00AM
Title of the Talk: Line Shapes in Magnetic Resonance and the Average Static Magnetic Field in the Medium: The Role of Discreteness and Continuum within the Material
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2/24/ :50:09 AM
MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM

2. MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM
The task would be to calculate the induced field inside the cavity σcavity
Organic Molecular single crystal : a specimen of arbitrary shape
I.V.E Sphere
Induced field calculation by discrete summation σinter
Continuum
σIVE = σinter + σM
Discrete
I.V.E. Cavity
Added σinter
Shifts the
line position
σcavity = σBulk +σM O
Inner Volume Element I.V.E H O
σintra / σM O O
4 point star indicates the molecule at a central location. Structure of a typical molecule on the right
σIVE(S) σM O H
In-homogeneity can cause line shape alterations: O
not simply shifts only
Proton Site with σintra
single sharp line
2/24/ :50:09 AM
MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM

3. Intra molecular Shielding σ=‘σM’
Line (position) shifts & Line shape changes
NMR Line for only
Intra molecular Shielding σ=‘σM’
Added intermolecular : σInter Contributions causes a shift downfield or up field σ = ‘σM’+‘σInter’ ’+‘σB (homogeneous)’
Homogeneous no line shape alterations
Slightly inhomogeneous
Nearly spherical
& shifted
& shifted
Highly inhomogeneous
Cylindrical
Inhomogeneous Magnetization can cause line shape alterationsσ = ‘σM’+‘σInter’ ’+‘σB (in-homogeneous)’
2/24/ :50:09 AM
MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM

4. MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM
(1-3.cos2θ) term causes +ve & -ve contributing zones
See drawing below
Lattice
summation
Shell by Shell
Induced field varies as R-3
Number of molecules in successive shells increase as R2
Magnetic Field
Product of above two vary as R-1
Each moment contributes to induced field
The above distance dependences can be depicted graphically
Dashed lines: convergence limit
2 A˚ equal spacing
Benzene
Molecule &
Its magnetic
moment
When the R becomes large, the R-1 term contribution becomes smaller and smaller to become insignificant
-ve zone
{χM . (1-3.COS2θ)}/(RM)3
+ve
Magnetic field direction
2/24/ :50:09 AM
MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM

5. MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM
First and Foremost it is to be pointed out that trying to sum the induced field contributions in the discrete region by taking the molecule by molecule contributions from the neighborhood, results in a convergence of the summed value to a total sum, which can be termed as Intermolecular contributions. This convergence is depicted below in the actual single crystalline case of an Organic molecular single crystalline system.
The summed up contributions from within Lorentz sphere as a function of the radius of the sphere. The sum reaches a Limiting Value at around 50Aº. These are values reported in a M.Sc., Project (1990) submitted to N.E.H.University. T.C. stands for (shielding) Tensor Component .Convergence occurred in this particular case at 50 Aº radius.
2/24/ :50:09 AM
MRSFall 2006-I: Dec.1,2006: MM17.2: 11:00AM