Nuclear quadrupole resonance spectroscopy or NQR is a
chemical analysis
Analytical chemistry studies and uses instruments and methods to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire analysis or be combined with another method. Separati ...
technique related to nuclear magnetic resonance (
NMR
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with ...
). Unlike NMR, NQR transitions of nuclei can be detected in the absence of a
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
, and for this reason NQR spectroscopy is referred to as "
zero Field NMR
Zero- to ultralow-field (ZULF) NMR is the acquisition of nuclear magnetic resonance (NMR) spectra of chemicals with magnetically active nuclei ( spins 1/2 and greater) in an environment carefully screened from magnetic fields (including from the ...
". The NQR resonance is mediated by the interaction of the
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
gradient (EFG) with the
quadrupole moment
A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure refl ...
of the nuclear
charge distribution
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...
. Unlike NMR, NQR is applicable only to solids and not liquids, because in liquids the quadrupole moment averages out. Because the EFG at the location of a nucleus in a given substance is determined primarily by the
valence electrons
In chemistry and physics, a valence electron is an electron in the outer shell associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed. In a single covalent bond, a shared pair forms ...
involved in the particular bond with other nearby nuclei, the NQR
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
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
Perturbation or perturb may refer to:
* Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly
* Perturbation (geology), changes in the nature of alluvial deposits over time
* Perturbatio ...
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
Spin or spinning most often refers to:
* Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning
* Spin, the rotation of an object around a central axis
* Spin (propaganda), an intentionally b ...
≥ 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
In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moment of an object about an external magnetic field. The phenomenon is conceptually similar to the precession of a tilted classical gyroscope in an extern ...
:
where
is the
gyromagnetic ratio
In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol , gamma. Its SI u ...
and
is the (normally applied) magnetic field external to the nucleus.
In the case of NQR, nuclei with spin ≥ 1, such as
14 N,
17O,
35 Cl and
63 Cu, also have an
electric quadrupole moment. 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
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circu ...
or
oblate
In Christianity (especially in the Roman Catholic, Orthodox, Anglican and Methodist traditions), an oblate is a person who is specifically dedicated to God or to God's service.
Oblates are individuals, either laypersons or clergy, normally livi ...
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.
is referred to as the quadrupole coupling constant.
In principle, the NQR experimenter could apply a specified EFG in order to influence
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
Zero- to ultralow-field (ZULF) NMR is the acquisition of nuclear magnetic resonance (NMR) spectra of chemicals with magnetically active nuclei ( spins 1/2 and greater) in an environment carefully screened from magnetic fields (including from the ...
". Many NQR transition frequencies depend strongly upon temperature.
Derivation of resonance frequency
Consider a nucleus with a non-zero quadrupole moment
and charge density
, which is surrounded by a potential
. 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
and the potential
within a domain
:
One can write the potential as a
Taylor-expansion at the center of the considered nucleus. This method corresponds to the
multipole expansion
A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, \R^3. Similarly ...
in cartesian coordinates (note that the equations below use the Einstein sum-convention):
The first term involving
will not be relevant and can therefore be omitted. Since nuclei do not have an
electric dipole moment
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The ...
, which would interact with the electric field
, the first derivatives can also be neglected. One is therefore left with all nine combinations of second derivatives. However if one deals with a homogeneous oblate or prolate nucleus the matrix
will be diagonal and elements with
vanish. This leads to a simplification because the equation for the potential energy now contains only the second derivatives in respect to the same variable: