O

O

OO

O

O H

H

Proton Site with σintra

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 σinter

i=ii /R3i [1-(3.RRi /R5

i)]Added σinter

Shifts the

line position

single sharp line

Inner Volume Element I.V.E

I.V.E. Cavity

I.V.E Sphere

σMσIVE(S)

Discrete

Continuum

The task would be to calculate the induced field inside the cavity σcavity

In-homogeneity can cause line shape alterations:

not simply shifts only

σintra / σM

σIVE =

σinter + σM

σcavity =

σBulk +σM

In d c d F i e l d a t t h e C e n t e r o f a 'T O P "

- 4 .0 0 E - 0 7

- 2 .0 0 E - 0 7

0 .0 0 E + 0 0

2 .0 0 E - 0 7

4 .0 0 E - 0 7

6 .0 0 E - 0 7

8 .0 0 E - 0 7

7 .0 6 .0 5 .0 4 .0 3 .0 2 .0 1 .0 0 .0 1 .0 - 2 .0 - 3 .0 - 4 .0 - 5 .0 - 6 .0 - 7 .0

D i s t 'Y ' f r o m C e n t e r ' 0 '

Indc

d Fi

elds

at c

ente

r

I n d c d ie ld a t th e C e n t e r x = y = 8 In d f ie ld C n t r e x = 1 6 y = 8

T h e T O P S h a p e

- 1 0

- 8

- 6

- 4

- 2

0

2

4

6

8

1 0

8 .0 6 .0 4 .0 2 .0 0 .0 - 2 .0 -4 .0 -6 .0 - 8 .0

X C o o r d in a te V a lu e

Y C

oor

din

ate

Val

ue

S e r i e s 1 S e r ie s 2

‘Y ’ V a lu e In d F ie ld

7 7 . 2 8 E - 0 7

5 4 . 6 2 E - 0 7

4 1 . 6 4 E - 0 7

2 - 2 . 6 6 E - 0 9

0 - 6 . 6 8 E - 0 8

- 2 - 2 . 6 6 E - 0 9

- 4 1 . 6 4 E - 0 7

- 5 4 . 6 2 E - 0 7

- 7 7 . 2 8 E - 0 7

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 CauseLine 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 Spindle or Top shapedSpecimen (Green line in the plot below)

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.

Indcd Field at the Center of a 'TOP"

-4.00E-07

-2.00E-07

0.00E+00

2.00E-07

4.00E-07

6.00E-07

8.00E-07

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0Dist 'Y' from Center ' 0 '

Indc

d Fi

elds

at c

ente

r

ind Field Cylinder x=y=8 Indcd ield at the Center x=y=8

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

A graphical plot for data in TABLE-I

-3.00E-07

-2.00E-07

-1.00E-07

0.00E+00

1.00E-07

2.00E-07

7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7

position along the axial line from center

indu

ced

field

val

ueCylinder Series2

specified point w ise induced filed and nmrlines

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

2.50E-07 3.25E-07 4.00E-07 4.75E-07 5.50E-07 6.25E-07 7.00E-07 7.75E-07

induced field value

inte

nsity

arb

uni

ts

nmrlines at specied points

Cylinder

By Calculation Trend line interpolation

7 -2.87E-07 -2.9E-07

6 -1.9E-07

5 -1.87E-07 -1E-074 3.25E-08 -2.8E-08

3 2.8E-08

2 6.45E-08 6.8E-08

1 9.2E-08

0 9.35E-08 1E-07

-1 9.2E-08

-2 6.45E-08 6.8E-08

-3 2.8E-08

-4 3.25E-08 -2.8E-08-5 -1.87E-07 -1E-07

-6 -1.9E-07

-7 -2.87E-07 -2.9E-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 interpola

ted values

Overlapping last three

lines

Add to all Values down the column

NMR lines at induced field values of specified points in material

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

-3.50E-07 -2.50E-07 -1.50E-07 -5.00E-08 5.00E-08 1.50E-07 2.50E-07 3.50E-07

calculated induced field values

ampl

itude

arb

uni

ts

Lineshapes

NMRlines at induced field values of specified points in material

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

-3.50E-07 -2.50E-07 -1.50E-07 -5.00E-08 5.00E-08 1.50E-07 2.50E-07 3.50E-07

calculated induced field values

ampl

itude

arb

uni

ts

Lineshapes

Same graph as displayed in previous slide

Broadening of overallshape of line

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

-3.50E-07 -2.50E-07 -1.50E-07 -5.00E-08 5.00E-08 1.50E-07 2.50E-07 3.50E-07

calculated induced field values

Ampl

itude

arb

uni

ts

width=5.0E-09 width=1.0E-08 width=2.0E-08 width=5.0E-08

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

Sharp line homogeneous/brodened lineshape inhomogeneous

0.00E+001.00E+022.00E+023.00E+024.00E+025.00E+026.00E+027.00E+028.00E+029.00E+02

-3.50E-07 -2.50E-07 -1.50E-07 -5.00E-08 5.00E-08 1.50E-07 2.50E-07 3.50E-07

induced field

ampl

itude

arb

uni

ts

Cylindrical w eight/w idth2.0E-08 w idth=2.0E-08 & spindle w eightfactors Only Intra Molecular

widhth 2.0E-08/No Weight factors

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

-3.50E-07 -2.50E-07 -1.50E-07 -5.00E-08 5.00E-08 1.50E-07 2.50E-07 3.50E-07

Line at σIVE

Add to all Values down the column