Symbols for NMR
Symbol  Meaning  Symbol  Meaning 

Roman alphabet  
a or A  Hyperfine (electronnucleus) coupling constant  A_{ql,m}  The mth component of an irreducible tensor of order l representing the nuclear spin operator for an interaction of type q 
B  Magnetic Field (strictly the magnetic flux density or magnetic induction)  B_{0}  Static magnetic field of an NMR spectrometer 
B_{1},B_{2}  Radiofrequency magnetic fields associated with frequencies ν_{1}, ν_{2}  B_{L}  Local magnetic field (components B_{xL}. B_{yL}, B_{zL}) of random field or dipolar origin 
C  Spinrotation interaction tensor  C_{x}  Spinrotation coupling constant of nuclide X 
D  Dipolar interaction tensor  D  Dipolar coupling constant between two nuclei (say 1 and 2), (μ_{0}/4π)γ_{1}γ_{2}(h/2π)r_{12}^{3}in frequency units (footnote 1). 
D^{C}  Nuclear receptivity relative to that of the carbon13 nucleus  D^{P}  Nuclear receptivity relative to that of the proton (hydrogen1 nucleus) 
E  Electric field strength  F  Spectral width 
F_{1}, F_{2} (or f_{1},f_{2}  The two frequency dimensions of a twodimensional spectrum (use F_{3} etc., for higher orders)  
F_{G}  Magnetic quantum number associated with  g  Nuclear or electronic g factor (Landé splitting factor) 
G  Magnetic field gradient amplitude  H_{ij}  Element of matrix representation of Hamiltonian operator (in energy units) ; superscripts indicate the nature of the operator 
Î_{j}  Nuclear spin operator for nucleus j (components Î_{jx}, Î_{jy}, Î_{jz})  Î_{j+}, Î_{j}  'Raising' and 'lowering' spin operators for nucleus j 
I_{j}  Magnetic quantum number associated with Î_{j}  J  Indirect coupling tensor 
^{n}J  Nuclear spinspin coupling constant through n bonds (usually given in frequency units). Parentheses may be used (for example) to indicate the species of nuclei coupled, e.g. J(13C, 1H) or, additionally, the coupling path, e.g. J(POCF). Where no ambiguity arises, the elements involved can be, alternatively, given as subscripts, e.g. J_{CH}. The nucleus of higher mass should be given first  J(ω)  Spectral density of fluctuations at angular frequency ω. Subscripts and superscripts to J may be used to indicate the relevant quantum number change (0, 1 or 2) or the order and component of the relevant tensor quantities. 
^{n}K  Reduced nuclear spinspin coupling constant (see the notes concerning ^{n}J), K_{jk}= 4π^{2}J_{jk}/hγ_{j}γ_{k}  L  Angular momentum 
m_{j}  Eigenvalue of Î_{jz} (magnetic component quantum number) (footnote 2)  m_{tot}  Total magnetic component quantum number for a spin system (eigenvalue of Σ_{j}Î_{jz})(footnote 2) 
m_{tot}(X)  Total magnetic component quantum number for Xtype nuclei (footnote 2)  M_{0}  Equilibrium macroscopic magnetization per volume of a spin system in the presence of B_{0} 
M_{X}, M_{Y}, M_{Z}  Components of macroscopic magnetization per volume.  M_{n}  nth moment of spectrum (M_{2} = second moment, etc.) 
n_{α}, n_{β}  Populations of the α and β spin states  N  Total number of nuclei of a given type per volume in the sample 
q  Electric field gradient tensor in units of the elementary charge (principal components q_{xx}, q_{yy}, q_{zz}) (see also V)  Q  eQ is the nuclear quadrupole moment, where e is the elementary charge 
R^{X}_{1}  Spinlattice (longitudinal) relaxation rate constant for nucleus X  R^{X}_{2}  Spinspin (transverse) relaxation rate constant for nucleus X 
R^{X}_{1ρ}  Spinlattice relaxation rate constant in the rotating frame for nucleus X  S  Signal intensity 
Electron (or, occasionally, nuclear) spin operator; cf. Î  t_{1}, t_{2}  Time dimensions for twodimensional NMR 

T_{C}  Coalescence temperature for signals in an NMR spectrum  T^{X}_{1}  Spinlattice (longitudinal) relaxation time of the X nucleus (further subscripts refer to the relaxation mechanism) 
T^{X}_{2}  Spinspin (transverse) relaxation time of the X nucleus (further subscripts refer to the relaxation mechanism)  T^{*}_{2}  Net dephasing time for M_{X} or M_{y} (including contribution from magnetic field inhomogeneity) 
T^{X}_{1ρ}  Spinlattice relaxation time of the X nucleus in the frame of reference rotating with B_{1}  T_{d}  Pulse (recycle) delay 
T_{ac}  Acquisition time  T^{(l,m)}_{q}  The mth component of an irreducible tensor of order l representing the strength of an interaction of type q 
V  Electric field gradient tensor. V = eq, where e is the elementary charge  V_{α,β}  Elements of Cartesian electric field gradient tensor 
W_{0}, W_{1},W_{2}  Relaxation rate constants (transition probabilities per time) between energy levels differing by 0, 1, and 2 (respectively) in m_{tot} especially, but not uniquely, for systems of two spin 1/2 nuclei  W_{r}  Transition probability between spin states r and s 
Greek alphabet  
α  Nuclear spin wavefunction (eigenfunction of Î_{jz}) for the m_{I}=+1/2 state of a spin1/2 nucleus  α_{E}  The Ernst angle (for optimum sensitivity) 
β  Nuclear spin wavefunction (eigenfunction of Î_{jz}) for the m_{I}=1/2 state of a spin1/2 nucleus  γ_{X}  Magnetogyric ratio of nucleus X 
δ_{X}  Chemical shift (for the resonance) of nucleus of element X (positive when the sample resonates to high frequency of the reference). Usually in ppm (footnote 3). Further information regarding solvent, references or nucleus of interest may be given by superscripts or subscripts or in parentheses.  Δn  Population difference between nuclear states (Δn_{0} Boltzmann equilibrium) 
Δδ  Change or difference in δ  Δν_{1/2}  Full width in frequency units of a resonance line at halfheight 
Δσ  Anisotropy in σ [Δσ = σ_{zz}  1/2(σ_{xx} + σ_{yy}] (footnote 4). (see also ζ  Δχ  (i) Susceptibility anisotropy (Δχ = χ_{}  χ_{⊥} (II) difference in electronegativities 
ε_{0}  Permittivity of a vacuum  ζ  Anisotropy in shielding (footnote 4), expressed as σ_{zz}  σiso. (see also Δσ) 
η  (i) Nuclear Overhauser enhancement (so that the nuclear Overhauser effect is 1 + η); (ii) tensor asymmetry factor (e.g. in σ); (iii) viscosity  κ  Skew of a tensor. (See also footnote 7) 
&theta:  Angle, especially for that between a given vector and B_{0}  μ  (i) Magnetic dipole moment (component μ_{z} along B_{0}); (ii) electric dipole moment 
σ_{0}  Permeability of a vacuum  σ_{B}  Bohr magneton 
σ_{N}  Nuclear magneton  ν_{j}  Larmor precession frequency of nucleus j (usually given in MHz) 
ν_{0}  (i) Spectrometer operating frequency; (ii) Larmor precession frequency (general, or of bare nucleus)  ν_{1}  Frequency of 'observing' RF magnetic Field B_{1} (to be distinguished from its strength, γB_{1}, for which the symbol Ω_{1} is recommended) 
ν_{2}  Frequency of 'irradiating' RF magnetic Field B_{2} (to be distinguished from its strength, γB_{2}, for which the symbol Ω_{2} is recommended)  Ξ_{x}  Resonance frequency for the nucleus of element X in a magnetic Field such that the protons in tetramethylsilane (TMS) resonate at exactly 100 MHz 
ρ  Density matrix  Density operator  
ρ_{ij}  Element of matrix representation of  σ  Shielding tensor (footnotes 5 and 6) 
σ_{j}  Isotropic) shielding constant of nucleus j. Usually given in ppm. Subscripts may alternatively indicate contributions to σ  σ_{}, σ_{⊥}  Components of shielding tensor σ parallel and perpendicular to the symmetry axis (axiallysymmetric case) (footnote 5) 
Reduced density operator  τ  (i) Time between RF pulses (general symbol) (ii) lifetime in dynamic NMR usage 

τ_{c}  Correlation time for molecularlevel motion, especially for isotropic molecular tumbling  τ_{d}  Dwell time 
τ_{null}  Recovery time sufficing to give zero signal after a 180° pulse  τ_{p}  Pulse duration 
τ_{sc}  Correlation time for relaxation by the scalar mechanism  τ_{sr}  Correlation time for spinrotation relaxation 
τ_{}, τ_{perp}  Correlation times for molecular tumbling parallel and perpendicular to the symmetry axis (axially symmetric case)  Χ  (i) Magnetic susceptibility (footnote 7) ; (ii) nuclear quadrupole coupling constant (Χ = e^{2}q_{zz}Q/h) 
ω_{j}, ω_{0}, ω_{1}, ω_{2}  As for ν_{j}, ν_{0}, ν_{1}, ν_{2} but for angular frequencies  Ω  Span of a Tensor 
Ω_{1}, Ω_{2}  R.f. magnetic Fields, expressed in angular frequency units for a nucleus of magnetogyric ratio γ (Ω_{1} = γB_{1}, Ω_{2} = γB_{2} 
Parameters and Symbols for Use in Nuclear Magnetic Resonance (IUPAC Recommendations 1997)
^{1}Note that confusion might arise when the socalled alphabet expansion is used for D, since this includes a term D which is not the dipolar coupling constant.
^{2}M rather than m is frequently recommended, but most NMR practitioners use m so as to avoid confusion with magnetization.
^{3}Whereas earlier IUPAC recommendations give a definition of δ which requires that the “unit" ppm is not stated when values are quoted, this is largely ignored and a change of recommendation is under consideration.
^{4}ζ = 2Δδ/3
^{5}The symbols σ (and related terms for components), σ_{j}, σ_{}, σ_{⊥} should refer to shielding on absolute scale (for theoretical work). For shielding relative to a reference, symbols such as σ_{}  &sigma_{ref} should be used.
^{6} For tensors, doubled subscript capital letters X, Y and Z should generally be used for principal components, e.g. σ_{XX}, σ_{YY} and σ _{ZZ} for shielding. Alternatively, numerical subscripts may be used (e.g. σ_{11}, σ_{22}, σ_{33}).
^{7} The symbol κ may also be used for magnetic susceptibility, some authors reserving χ for unrationalized units.
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