O O O O O O H H Proton Site with σ intra Organic Molecular single crystal : a specimen of arbitrary shape 4 point star indicates the molecule at a central location. Structure of a typical molecule on the right Induced field calculation by discrete summation σ inter Added σ inter Shifts the line position single sharp line Inner Volume Element I.V.E I.V.E. Cavity I.V.E Sphere σMσM σ IVE(S ) Discrete Continuu m The task would be to calculate the induced field inside the cavity σ cavity In-homogeneity can cause line shape alterations: not simply shifts only σ intra / σ M σ IVE = σ inter + σ M σ cavit y = σ Bulk + σ M

The top or a Spindle Shaped object comes under the category of Shapes within which the Induced field distribution would be Inhomogeneous even if the Susceptibility is uniformly the same over the entire sample NMR Line for only Intra molecular Shielding Added intermolecular Contribultions causes a shift downfield or upfield homogeneous Inhomogeneous Magnetization can Cause Line shape alterations 4. The case of Shape dependence for homogeneously magnetized sample, and consideration of in-homogeneously magnetized material.

A cylinder shaped specimen (Blue line in the plot below) Zero ind. Field Points Not to be discussed in this presentation The points on the Blue line would be specified and at these Calculated field values an NMR line would be placed after adding the sum total of intra and intermolecular contributions to induced fields. Calculations at 9 points along the axis Distance along the axis

No intra molecular Value; inter- molecular value (in I.V.E) set=0 in subsequent plots; only cavity field is used to generate line shapes Cylinder By Calculation Trend line interpolation E E E E-07-1E E E E E-086.8E E E-081E E E-086.8E E E E E-07-1E E E E-07 Only inter molecular value 5.80E-07 can be set = 0 “Only” inter-molecular value 5.80E-07 was added and the line shape was plotted with those values : NEXT GRAPHICAL PLOT A Graph of the data in table Lines at interpolat ed values Overlapping last three lines Add to all Values down the column

Same graph as displayed in previous slide Gradual increase of component lines broadens the lines and can cause the change in the appearance of overall shape. Illustration with 4 different width values Same width as above Width twice that of red Width twice that of blue 10 times that of red Width 2.5 times that of green

Line at σ IVE

Add to all Values down the column