Nuclear Quadrupole Resonance Spectroscopy (NQR) is a chemical analysis technique that detects nuclear energy level transitions in the absence of a magnetic field through the absorption of radio frequency radiation. NQR is applicable to solids due to the quadrupole moment averaging to zero in liquids and gases. The interaction between a nucleus's quadrupole moment and the electric field gradient of its surroundings results in quantized energy levels. Transitions between these levels are detected as NQR spectra and provide information about electronic structure, hybridization, and charge distribution. NQR finds applications in studying charge transfer complexes, detecting crystal imperfections, and locating land mines.

1. Dr.P.GOVINDARAJ
Associate Professor & Head , Department of Chemistry
SAIVA BHANU KSHATRIYA COLLEGE
ARUPPUKOTTAI - 626101
Virudhunagar District, Tamil Nadu, India
Nuclear Quadrupole Resonance Spectroscopy (NQR)

2. Nuclear Quadrupole Resonance Spectroscopy (NQR)
• NQR spectroscopy is a chemical analysis technique like NMR, in which the transitions of
nuclear energy levels can be detected in the absence of a magnetic field by the absorption
of radio frequency radiation.
• The nuclear energy levels are formed due to the interaction between nuclear quadrupole
moment and electric field gradient
• NQR is applicable only to solids and not for liquids and gases, because the quadrupole moment
average was found to zero
Definition

3. Nuclear Quadrupole Resonance Spectroscopy (NQR)
• A nucleus with I > ½ lack the spherical system along the spin axis resulted elongated
(prolate spheroid) shape and compressed (oblate spheroid) shape along the spin axis
Nuclear quadrupole moment and electric field gradient

4. Nuclear Quadrupole Resonance Spectroscopy (NQR)
• The distorted shape generate electric (or nuclear) quadrupole moment (e Q) and it is
defined by
e Q =  𝑥,𝑦,𝑧 𝑟2(3 cos 2( − 1))d --------------(1)
where
 𝑥,𝑦,𝑧 is the charge density at (x,y,z)
r is the distance of the volume element d from the nucleus
 is the angle which the radius vector r makes with the nuclear spin axis

5. Nuclear Quadrupole Resonance Spectroscopy (NQR)
• The nuclear quadrupole moment (eQ) is a measure of the departure from spherical symmetry
of the nuclear charge and it will be greater than zero for prolate molecules and less than zero
for oblate molecules
• The electric field gradient (EFG) designated as q (or eQ ), created at the quadrupolar
nucleus by the asymmetric charge distribution arising from the extra nuclear electrons or
the non-bonding electrons in the molecule of which the nucleus from a part
• The time-averaged electrostatic potential (V) is produced at the nucleus by all charges
outside it. The electric field of all these charges is
E = Ex 𝑖 + Ey 𝑗+ Ez 𝑘 -------------(2)

6. Nuclear Quadrupole Resonance Spectroscopy (NQR)
• Where 𝑖 , 𝑗 , 𝑘 are the unit vectors which specify the directions of the axes x, y and z
respectively. The components of the electric field are defined as
Ex = −
𝜕𝑉
𝜕𝑥
; Ey = −
𝜕𝑉
𝜕𝑦
; Ez = −
𝜕𝑉
𝜕𝑧
• The electric field gradient components are defined as
qxx = −
𝜕𝐸𝑥
𝜕𝑥
=
𝜕2
𝑉
𝜕𝑥2
qyy = −
𝜕𝐸𝑦
𝜕𝑦
=
𝜕2
𝑉
𝜕𝑦2
qzz = −
𝜕𝐸𝑧
𝜕𝑧
=
𝜕2
𝑉
𝜕𝑧2
and also qxy =
𝜕2
𝑉
𝜕𝑥𝜕𝑦
; qyz =
𝜕2
𝑉
𝜕𝑦𝜕𝑧
etc.,

7. Nuclear Quadrupole Resonance Spectroscopy (NQR)
• When qxx = qyy = qzz then the electric field gradient is said to be spherical and there is
no interaction of nuclear quadrupole moment with the electronic charge distribution
• When qxx ≠ qyy ≠ qzz then the electric field gradient is said to be non spherical and there is
an interaction of nuclear quadrupole moment with the electronic charge distribution
resulted NQR spectra by the absorption of radio frequency radiation
Principle of NQR
• A nucleus with I >½ is said to be quadrupole nucleus and have different nuclear
orientation caused by the interaction between the nuclear quadrupole moment of a nucleus
and the electric field gradient, giving rise to a set of quantized energy levels

8. Nuclear Quadrupole Resonance Spectroscopy (NQR)
• The energy of interaction between the nuclear quadrupole moment of the nucleus and the
electric field gradient is
Em =
𝑒2
𝑞𝑄[3𝑚2
𝐼 −𝐼(𝐼+1)]
4𝐼(2𝐼−1)
------------(3)
where
I is the nuclear spin quantum number
eq (=
𝜕2
𝑉
𝜕𝑧2 ) is the magnitude of electric field gradient in the direction of the axis of symmetry
eQ is the nuclear quadrupole moment
mI is the magnetic quantum number which takes the (2I+1) values i.e, mI = I, I-1,…..-I

9. Nuclear Quadrupole Resonance Spectroscopy (NQR)
• The states +mI and –mI are degenerate as mI appears as mI
2 in the equation (3)
• The selection rule for magnetic dipole transition is ∆ mI = ±1
• The frequency of the (mI - 1)→ mI transition is given by
 =
3𝑒2
𝑞𝑄
4𝐼 2𝐼−1 ℎ
2 𝑚𝐼 −1 --------------(4)
where
eQ is the nuclear quadrupole moment
eq is the electric field gradient
e2qQ/h is the nuclear quadrupole coupling constant
• The NQR frequencies of nuclei lie in the range 100 KHz – 1000 MHz

10. Nuclear Quadrupole Resonance Spectroscopy (NQR)
Example:
1. For nuclei having spin I =3/2 (35Cl, 79Br) there will be two energy levels as per equation (3)
and the equation (4) allows only a single transition of frequency  =
e2qQ
2ℎ
shown in
the diagram

11. Nuclear Quadrupole Resonance Spectroscopy (NQR)
2. For nuclei having spin I = 5/2 (127I, 121Sb) there will be three energy levels as per equation (3)
and the equation (4) allows two transition of frequencies 1 and 2 shown in the figure
 1=
3e2qQ
20ℎ
;  2=
6e2qQ
20ℎ

12. Application of Nuclear Quadrupole Resonance Spectroscopy (NQR)
• NQR has been used principally for investigating the electronic structure of molecules
• Information regarding hybridization and the ionic character of the bond can be determined
by comparing the quadrupole coupling constant in atomic and molecular state in the
same nuclei
• Study of the structure of charge transfer complexes
• Detection of crystal imperfections small imperfections destroy symmetry of internal
electric field, lead to splitting or broadening of NQR lines.
• This technique is suitable for detecting land mines, an application for which it would be
difficult to project a uniform magnetic field into the ground.

13. THANK YOU