## First-order quadrupole interaction for static crystal. Contributor: R. Hajjar

Home and Applets > Quadrupole Interaction > Definition > V(2,0) in Static NMR

## Analytical expression of V(2,0) for static crystal in NMR

The first-order quadrupole interaction is related to V(2,0):

In static NMR experiment, V(2,0) is defined by:

Its analytical expression can be determined as follows:

(1) Select and copy the following green lines; then paste them into a cell of Mathematica, a software for numerical and symbolic calculations.

(2) Press "Ctrl-A" for select all; then press "Shift-enter" for evaluate cells.
(Or in the menu bar, select Kernel > Evaluation > Evaluate Cells)

Using Mathematica-5 running with a 3-GHz processor, the analytical expression of V(2,0) is obtained in 5 seconds.

```(* V2pas is a row-matrix with 3 columns
containing the 3 nonzero eigenvalues of the EFG
expressed as a 2-nd rang spherical tensor, in eq unit *)

V2pas = {{eta/2, Sqrt[3/2], eta/2}};

(* D2 is a reduced form (3 rows x 1 column) of the 2-nd order
Wigner active rotation matrix *)

D2 = {

{Sqrt[3/8]*Sin[beta1]^2*E^(-2*I*alpha1)},

{(-1 + 3*Cos[beta1]^2)/2},

{Sqrt[3/8]*Sin[beta1]^2*E^(2*I*alpha1)}

};

(* V20static is an expression *)
V20static = FullSimplify[V2pas.ComplexExpand[D2]];

(* suppression of the double curve brackets {{}} of V20static *)
Print[V20static[[1, 1]]];

Remove[V2pas, eta, D2, alpha1, beta1, V20static];
```

(top)

[Contact me] - Last updated December 16, 2012
Solid-state NMR bibliography for
Aluminum-27
Antimony-121/123
Arsenic-75
Barium-135/137
Beryllium-9
Bismuth-209
Boron-11
Bromine-79/81
Calcium-43
Cesium-133
Chlorine-35/37
Chromium-53
Cobalt-59
Copper-63/65
Deuterium-2
Gallium-69/71
Germanium-73
Gold-197
Hafnium-177/179
Indium-113/115
Iodine-127
Iridium-191/193
Krypton-83
Lanthanum-139
Lithium-7
Magnesium-25
Manganese-55
Mercury-201
Molybdenum-95/97
Neon-21
Nickel-61
Niobium-93
Nitrogen-14
Osmium-189
Oxygen-17
Palladium-105
Potassium-39/41
Rhenium-185/187
Rubidium-85/87
Ruthenium-99/101
Scandium-45
Sodium-23
Strontium-87
Sulfur-33
Tantalum-181
Titanium-47/49
Vanadium-51
Xenon-131
Zinc-67
Zirconium-91

Copyright © 2002- pascal-man.com. All rights reserved.