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Spin Quantum Number, I

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A quantum number describing the overall spin of a nucleus. Due to the very complex vector summation properties of p protons and n neutrons for an individual nucleus, I cannot be determined from theory, but instead is an empirical quantity defined for various nuclear configurations.

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Spin I = 0 Nuclei

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Refers to nuclei with zero spin angular momenta, and are therefore magnetically invisible to the NMR experiment. Occurs for nuclei with even atomic mass, and even atomic numbers. Examples include 12C and 16O.

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Spin I = ½ Nuclei

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Refers to nuclei with non-zero spin angular momenta, and that posse a spherical shape with uniform charge distribution. I = ½ nuclei possess 2 energy states. Occurs for nuclei with odd atomic mass, and odd or even atomic numbers. Examples include nuclei such as 1H, 13 C, 15N, and 31P.

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Spin I = 1 Nuclei

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Refers to nuclei with non-zero spin angular momenta, and that posse a non-spherical, ellipsoid shape. I =1 nuclei possess 3 energy states. Occurs for nuclei with even atomic mass, and odd atomic numbers. Examples include nuclei such as 2 H, 14 N, and 17O.

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Quadrupolar Nuclei

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Magnetic nuclei with non-zero spin angular momenta, and a non-spherical, ellipsoidal shape that have I > ½ .

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Nuclear Angular Momentum, P

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Vector describing the magnitude and direction of the spin angular momentum of a nucleus

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Magnetic Quantum Number, m

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The number of possible orientations of the angular momentum in a magnetic field, given by m = I, I −1,..., − (I −1), − I ; the total number of possible orientations is equal to 2 I + 1 .

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Nuclear Magnetic Moment, µ

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Magnetic dipole moment that arises from the circular electric current induced by a nucleus spinning about its axis; µ is oriented along the spin axis of the nucleus; µ can be defined relative to P as follows: µ = γ P .

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Magnetogyric Ratio, γ

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Proportionality constant between µ and P such that µ = γ P ; a fundamental property of any given nucleus; units = rad T-1s-1 ; also known as the gyromagnetic ratio.

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Directional Quantization

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Behavior of the nuclear angular momentum P such that its components Pz must point only along a reference direction, e.g. the z direction; Pz must be integral if I = integer, or halfintegral if I = half-integer, Pz is related to the z component of the magnetic quantum number m as follows: Pz = mz ; also refers to the directional components of the magnetic moment µ along z : µz = mz γ .

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α Spin State

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Refers to a nuclear dipole aligned with the external applied B0 field; this is the state of lower energy; corresponds to m = + ½ for an I = ½ nucleus.

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β Spin State

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Refers to a nuclear dipole aligned opposed to the external applied B0 field; this is the state of higher energy; corresponds to m = - ½ for an I = ½ nucleus.

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Nuclear Precession

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The phenomenon where a spinning nucleus in an external magnetic field experiences a torque on its magnetic moment µ imposed by the applied B0 field; this torque causes the axis of the spinning nucleus to move in a circular motion, and at a constant angle, about the direction of the applied B0 field.

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Larmor Precessional Frequency

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The frequency of the precession of a spinning nucleus in an applied B0 magnetic field; defined as ν L = γ 2 π ⋅ B0 .

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Nuclear Magnetic Resonance

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The coherent exchange of energy between an applied external electromagnetic field B1 having an associated frequency ν1 , and a nucleus having a Larmor frequency of ν L ; the resonance condition occurs when ν1 = ν L ; resonance supplies the energy that allows transitions between ground and excited nuclear energy states to occur.

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Net Magnetization Vector, M0

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The vector summation of the z components of all nuclear dipole moments in a sample to give a bulk, or net, magnetization vector pointing along the +z direction.

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Saturated NMR Signal

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The situation that occurs when the NMR ground and excited states become equally populated; this leads to no net difference in absorption vs. emission, and thus no observable NMR signal.

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Spin-Lattice or T1 Relaxation

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Dissipation of excess spin energy in excited state nuclei by equilibration with the surrounding sample environment, i.e. the lattice; absorbed energy is dissipated as heat throughout the lattice; T1 relaxation refers to the return to thermal equilibrium that re-establishes the equilibrium Nα and Nβ values; first-order process characterized by the return of net magnetization along the z′ axis with relaxation time T1 ; strongly affected by mobility of the lattice.

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Spin-Spin or T2 Relaxation

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Dissipation of excess spin energy in excited state nuclei by exchange of spin with other surrounding ground-state nuclei; T2 relaxation refers to the loss of phase coherence in the transverse (x′ - y′) plane; first-order process characterized by relaxation time T2 ; T2 relaxation times are usually shorter than T1 relaxation times, therefore transverse relaxation is faster than longitudinal relaxation; thus, T2 is the primary influence on line broadening in NMR spectra.

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Superconducting Magnet

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Electromagnets that maintain a magnetic field, i.e. an electrical current in the coils of the electromagnet, by keeping the coils of the magnet at or below 4 K, where the material comprising the coils is superconducting; no external current is needed - superconductivity is maintained at 4 K using liquid He; field strengths of 1.4 T - 21.1 T (60 - 900 MHz) are commercially available.

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Field-Frequency Lock

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Method of maintaining the homogeneity of the magnetic field in superconducting magnets; a reference nucleus (typically 2 H) is continuously irradiated; since the ratio of B0 to ν L is constant, any drift in ν L is automatically compensated via a feedback circuit, thereby keeping B0 stable.

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Shim Coils

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Method of maintaining the homogeneity of the magnetic field in superconducting magnets; shim coils are wires through which current is passed, producing small magnetic fields; these fields are used to compensate for inhomogeneity in the main B0 field.

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Sample Spinning

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Method of maintaining the homogeneity of the magnetic field in superconducting magnets; B0 inhomogeneity is damped by spinning the sample using an air turbine at 20 - 50 rpm along the longitudinal axis of the sample NMR tube.

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Continuous Wave NMR

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Technique that uses a radiofrequency sweep to excite the Larmor frequencies of the nuclei in the sample; older NMR technique that is not currently widely used.

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Pulsed Fourier Transform NMR

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Technique that excites the Larmor frequencies of the nuclei in a sample; nuclei in static B0 field are subjected to periodic, short, high power, radiofrequency pulses from a second B1 magnetic field; the RF pulse provides a bandwidth of frequencies centered around a particular frequency, ν1 , thereby exciting the Larmor frequencies of all nuclei in the sample simultaneously; most modern NMR instruments are pulsed FT-NMR.

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Pulse Width, τp

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The length of time the B1 field interacts with the sample; τp is usually very short, i.e. 1 - 10 µs; also known as the pulse length or pulse duration.

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Pulse Amplitude

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The measure of the power with which the pulse is applied; determines the strength of the B1 field.

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Interpulse Delay

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The time delay between pulses; can be in the range of 1 - 10 seconds.

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Rotating Frame of Reference

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The concept of a transformed coordinate system that rotates about the laboratory z axis at the Larmor frequency; a net magnetization vector M0 rotating at the Larmor frequency in a laboratory coordinate system appears stationary in a frame of reference rotating about the z axis at ν L ; the rotating coordinate system is distinguished from the x, y, and z laboratory coordinate system by primes on the axes, i.e. x′ , y′ , z′ .

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Free Induction Decay

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In the NMR experiment, an RF pulse is applied to nuclei with τp and ν1 ; this rotates M0 away from the z′ axis into the transverse (x′ - y′) plane; during the interpulse delay, an oscillating RF signal is emitted by the nuclei as they return to the ground state; this oscillating signal decays as a function of time as the phase coherence among the precessing magnetic dipoles is lost; this is the free induction decay (FID), and represents the time domain NMR signal.

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Diamagnetic Circulation

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When placed in a B0 field, electrons surrounding the nucleus circulate in direction that produces a magnetic field that opposes the applied B0 field.

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Screening or Shielding Constant, σ

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Quantity that describes the magnetic shielding of a nucleus by its surrounding electronic and magnetic environment, leading the nucleus to experience a smaller, "effective" magnetic field Beff = B0 (1−σ ) ; the shielding constant accounts for local charge density and opposes B0, leading to a new resonance value ν L = γ^2 π ⋅ B0 (1−σ ) ; σ is a dimensionless quantity that may be theoretically calculated and is on the order of 10-6 for protons; σ values are molecular constants that do not depend on the B0 field and are solely determined by electronic and magnetic environment of a particular nucleus.

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Chemical Shift, δ

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The difference in the NMR absorption frequency of protons bound to chemically distinct groups in molecules; δ is a dimensionless quantity defined in relation to an internal standard reference frequency as follows: δ = ν sample −νreference /νreference ×106 ; units = ppm; denominator can be replaced with the spectrometer frequency as follows: δ = Δν /spectrometer frequency×106 ; δ is independent of B0 field strength; important factors influencing chemical shift are electron density, electronegativity of neighboring groups, and anisotropic-induced magnetic field effects.

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Internal Standard

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Use of a reference molecule to act as a frequency standard for calculation of chemical shifts; in 1 H and 13C NMR spectroscopy, tetramethylsilane (CH3)4Si is commonly used since it contains 12 highly shielded protons resulting in a single, sharp NMR peak occurring at low resonance frequency; by convention, NMR spectra are displayed with the magnetic field strength increasing from the left to right; therefore, the TMS resonance, defined as ppm = 0, lies at the far right of the spectrum.

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Upfield

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NMR naming convention that corresponds to the region of the NMR chemical shift spectrum with higher diamagnetic shielding and lower resonance frequencies; indicates a shift towards smaller values of the chemical shift parameter, δ .

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Downfield

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NMR naming convention that corresponds to the region of the NMR chemical shift spectrum with lower diamagnetic shielding and higher resonance frequencies; indicates a shift towards larger values of the chemical shift parameter, δ .

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Diamagnetic Component of Shielding Constant, σdiag

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The type of nuclear shielding that is dependent on the spherical charge density of the s electrons near the nucleus.

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Inductive Effects

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The chemical shift values that directly correlate with the deshielding of the nucleus by the electronegativity effects of the neighboring groups.

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Magnetic Anisotropy Effects

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Anomalous chemical shift values that are not explained by electronegativity arguments, and are due to the anisotropic magnetic properties of multiply bonded and/or aromatic compounds.

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Ring Currents

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Secondary fields arising in aromatic compounds that act in opposition to the B0 applied magnetic field.

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Paramagnetic Component of Shielding Constant, σpara

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A term that accounts for nuclear shielding that is dependent on non-spherical charge density effects.

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Spin-Spin Coupling

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A term that describes the effect that two nuclei have when they are sufficiently close in space that they can exert a magnetic effect on one another; this magnetic effect is manifested through the observed splitting of their NMR resonances - the splitting is caused by the presence of the 2nd nucleus; the origin of spin-spin interactions takes place through the interactions of nuclei and bonding electrons - not through space; also known as through-bond coupling, scalar coupling, indirect coupling, or J-coupling.

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Coupling Constant, J

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The spacings between the multiplet splitting patterns seen in the NMR resonances that are observed in spin-spin coupling; units = Hz; when measured in Hz, J is independent of the magnitude of B0 .

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Fermi Contact Term

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Describes the mechanism of spin-spin coupling; direct interaction between the magnetic moments of nuclei and those of the bonding electrons in s states; seen in the striking dependence on the s character, i.e. the hybridization of the bonds between the nuclei.

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First-Order NMR Spectra

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NMR spectra in which the chemical shift between molecular resonances is large compared to the coupling constant; practical definition of first-order NMR spectra is Δν/J>10 .

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Pascal's Triangle

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Triangular array of binomial coefficients; also corresponds to the relative areas of a spin-spin splitting multiplet in NMR spectroscopy; areas of the split resonances are symmetric around the midpoint of the peak and proportional to the coefficients of the terms in Pascal's triangle; i.e. an NMR resonance will be split by n magnetically equivalent protons into n + 1 peaks whose relative intensities are given by the ratio contained in the nth row of Pascal's triangle.

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