Nuclear quadrupole resonance spectroscopy or NQR is a chemical analysis technique related to nuclear magnetic resonance (NMR). Unlike NMR, NQR transitions of nuclei can be detected in the absence of a magnetic field, and for this reason NQR spectroscopy is referred to as "zero Field NMR". The NQR resonance is mediated by the interaction of the electric field gradient (EFG) with the quadrupole moment of the nuclear charge distribution. Unlike NMR, NQR is applicable only to solids and not liquids, because in liquids the electric field gradient at the nucleus averages to zero (the EFG tensor has trace zero). Because the EFG at the location of a nucleus in a given substance is determined primarily by the valence electrons involved in the particular bond with other nearby nuclei, the NQR frequency at which transitions occur is unique for a given substance. A particular NQR frequency in a compound or crystal is proportional to the product of the nuclear quadrupole moment, a property of the nucleus, and the EFG in the neighborhood of the nucleus. It is this product which is termed the nuclear quadrupole coupling constant for a given isotope in a material and can be found in tables of known NQR transitions. In NMR, an analogous but not identical phenomenon is the coupling constant, which is also the result of an internuclear interaction between nuclei in the analyte.
Principle Any nucleus with more than one unpaired nuclear particle (protons or neutrons) will have a charge distribution which results in an electric quadrupole moment. Allowed nuclear energy levels are shifted unequally due to the interaction of the nuclear charge with an electric field gradient supplied by the non-uniform distribution of electron density (e.g. from bonding electrons) and/or surrounding ions. As in the case of NMR, irradiation of the nucleus with a burst of RF electromagnetic radiation may result in absorption of some energy by the nucleus which can be viewed as a perturbation of the quadrupole energy level. Unlike the NMR case, NQR absorption takes place in the absence of an external magnetic field. Application of an external static field to a quadrupolar nucleus splits the quadrupole levels by the energy predicted from the Zeeman interaction. The technique is very sensitive to the nature and symmetry of the bonding around the nucleus. It can characterize phase transitions in solids when performed at varying temperature. Due to symmetry, the shifts become averaged to zero in the liquid phase, so NQR spectra can only be measured for solids.
Analogy with NMR In the case of NMR, nuclei with spin ≥ 1/2 have a magnetic dipole moment so that their energies are split by a magnetic field, allowing resonance absorption of energy related to the Larmor frequency:
where γ {\displaystyle \gamma } is the gyromagnetic ratio and B {\displaystyle B} is the (normally applied) magnetic field external to the nucleus. In the case of NQR, nuclei with spin ≥ 1, such as 14N (spin 1), 17O (spin 5/2), 35Cl (spin 3/2) and 63Cu (spin 3/2), also have an electric quadrupole moment Q which has energy levels between which resonance can be observed, even in the absence of a magnetic field. Nuclei with spin 1 or 3/2 give only a single resonance line, but a nucleus with spin 5/2 gives two resonance lines, one at double the frequency of the other. The nuclear quadrupole moment is associated with non-spherical nuclear charge distributions. As such it is a measure of the degree to which the nuclear charge distribution deviates from that of a sphere; that is, the prolate or oblate shape of the nucleus. NQR is a direct observation of the interaction of the quadrupole moment with the local electric field gradient (EFG) created by the electronic structure of its environment. The NQR transition frequencies are proportional to the product of the electric quadrupole moment of the nucleus and a measure of the strength of the local EFG:
where q is related to the largest principal component of the EFG tensor at the nucleus. C q {\displaystyle C_{q}} is referred to as the quadrupole coupling constant. In principle, the NQR experimenter could apply a specified EFG in order to influence ω Q {\displaystyle \omega _{Q}} just as the NMR experimenter is free to choose the Larmor frequency by adjusting the magnetic field. However, in solids, the strength of the EFG is many kV/m^2, making the application of EFG's for NQR in the manner that external magnetic fields are chosen for NMR impractical. Consequently, the NQR spectrum of a substance is specific to the substance - and NQR spectrum is a so called "chemical fingerprint." Because NQR frequencies are not chosen by the experimenter, they can be difficult to find making NQR a technically difficult technique to carry out. Since NQR is done in an environment without a static (or DC) magnetic field, it is sometimes called "zero field NMR". Many NQR transition frequencies depend strongly upon temperature.
Derivation of resonance frequency Source: Consider a nucleus with a non-zero quadrupole moment Q {\textstyle {\textbf {Q}}} and charge density ρ ( r ) {\textstyle \rho ({\textbf {r}})} , which is surrounded by a potential V ( r ) {\textstyle V({\textbf {r}})} . This potential may be produced by the electrons as stated above, whose probability distribution might be non-isotropic in general. The potential energy in this system equals to the integral over the charge distribution ρ ( r ) {\textstyle \rho ({\textbf {r}})} and the potential V ( r ) {\textstyle V({\textbf {r}})} within a domain D {\textstyle {\mathcal {D}}} :
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