SYMBOLS AND ABBREVIATIONS ROMAN SYMBOLS Electron (hyperfine) interaction constant with nucleus N Natural abundance of nucleus N/% Magnetic field strength (flux density) in tesla: 1T = 104 gauss Static magnetic field strength of NMR spectrometer Magnetic field strength of radiofrequencies applied to the sample; B1 , observing field; B2 , perturbing field eN Spin-rotation tensor of nucleus N C II , C-L Spin-rotation components for axial symmetry D Direct dipolar coupling tensor DIS (Mutual) translational diffusion constant for spins I and S e Elementary charge e2qQ/h Nuclear quadrupole coupling constant (NQCC) in frequency units ge Electronic g factor (Lande splitting factor) gN Nuclear g factor ( = Jl N/ IN) G(!) = f( t) f( t + !) = autocorrelation function of f( t) h Planck's constant Ii h/2n :it Hamiltonian operator i J=1 I Nuclear spin angular momentum IN Spin quantum number of nucleus N I Moment of inertia J Spin-spin (scalar, indirect) coupling tensor nJAB , nJ(AB) Spin-spin coupling constant over n bonds between nuclei A and B; 3 J(ABeD) shows a coupling path Fermi contact contribution to J Spin-dipolar contribution to J r Orbital contribution to J J(w) Spectral density at angular frequency w Reduced spin-spin coupling constant (as above) nKAB = n~AB e:)(~:) INA -2 m-3 L Line-broadening factor for quadrupolar nucleus N L = f(lN) Qt, where f(lN) = (2IN + 3)//t(2IN-1) me Electron mass mp Proton mass MI Magnetic quantum number M Bulk magnetization of nuclear spins 615 616 SYMBOLS AND ABBREVIATIONS q or eq Electric field gradient (efg) Q or eQ Nuclear electric quadrupole moment S 1. Another spin interacting with I 2. Order parameter in partially oriented systems Temperature Tesla: 1 T = 104 gauss Pulse width (length, duration) Longitudinal (spin-lattice) relaxation time TI in frame of reference rotating with B I Transverse (spin-spin) relaxation time Observed value of T2 (= l/n W I/2 ), including effects of magnetic field inhomogeneity Quadrupolar relaxation time Pulse interval In-phase (dispersion mode) signal Out-of-phase (absorption mode) signal Linewidth at half-height Transition probability of nucleus I GREEK SYMBOLS 0(0 Pulse angle (flip angle) 0(,/3 Spin states (± 1/2) Y Magnetogyric ratio of nucleus N/rad T -I S-I l' y/2n Yoo Sternheimer antishielding factor {) Chemical shift/ppm A Difference (e.g., A{)) Aa Shielding anisotropy = a II - a -L for axial symmetry AX Magnetic susceptibility anisotropy = XII - X-L for axial symmetry eo Permittivity of a vacuum , Spin orbit coupling constant 1/ 1. NO E factor 2. Asymmetry of shielding tensor = (a 22 - all )/( a 33 - a av) 3. Asymmetry of efg tensor = (qxx - qyy)/qm where Iqzzl ~ Iqyyl ~ Iqxxl 4. Viscosity Magnetic moment Permeability of a vacuum Bohr magneton Nuclear magneton 1. Operating frequency of spectrometer 2. Larmor frequency/Hz Frequency of observing rf field B I in Hz Frequency of perturbing rf field B2 in Hz Resonance frequency of standard substance for nucleus X at a magnetic field giving a resonance frequency of precisely 100 MHz for TMS protons under standard conditions Nuclear magnetic shielding tensor Shielding tensor components for axial symmetry, otherwise all' a22, a33, where a 33 ~ a22 ~ all SYMBOLS AND ABBREVIATIONS 617 t Evolution time between rf pulses Correlation time for molecular tumbling Correlation time for spin-rotation relaxation x 1. Magnetic susceptibility 2. Nuclear quadrupole coupling constant = e2qQ/h (for X in Hz) Volume magnetic susceptibility Larmor frequency/rad s ~l = 2nvo Angular frequencies of B 1 , B2 rf fields in rad S~l ABBREVIATIONS A- {M,X} Observation of nucleus A with irradiation also of nuclei M, X ASIS Aromatic solvent-induced shifts CIDNP Chemically induced dynamic nuclear polarisation COSY Correlated two-dimensional (2D) NMR spectroscopy CSA Chemical shift anisotropy = SA CP Cross-polarization CW Continuous wave DD,dd Direct dipolar (or dipole~dipole) interaction DEFT Driven equilibrium FT DEPT Distortionless enhancement by polarization transfer ENDOR Electron-nuclear double resonance efg Electric field gradient ESR Electron spin resonance FID Free induction decay FT Fourier transform HOMO High-lying occupied molecular orbital INDOR Internuclear double resonance INEPT Insensitive nucleus enhancement by polarization transfer JCP J cross-polarization LUMO Low-lying unoccupied molecular orbital MAS Magic angle spinning MO Molecular orbital NMR Nuclear magnetic resonance NOE Nuclear Overhauser effect NOESY Two-dimensional NOE spectroscopy NQCC Nuclear quadrupole coupling constant NQR Nuclear quadrupole resonance ppm Parts per million ppt Parts per thousand rf Radiofrequency SA, sa Shielding anisotropy SECSY Spin echo correlated 2D NMR spectroscopy S:N Signal-to-noise ratio SPI Selective population inversion SPT Selective population transfer SR, sr Spin-rotation interaction TMS Tetrameth ylsilane WAHUHA Pulse sequence of Waugh, Huber, and Haeberlen SI UNITS AND FUNDAMENTAL CONSTANTS These tables use the recommended SI (Systeme International) units, with some indication of their relation to other units in the literature, including electromagnetic units (e.m.u.) and the less common electrostatic units (e.s.u.), both in the centimeter gram second system (CGS). (1,2) The relationships are complex: four systems of equations have been used, and each of these has been written in nonrationalized and now rationalized forms. (3) With rationalization, explicit values and dimensions are given to the permittivity eo of a vacuum, which was taken as unity and dimensionless in the e.m.u. system, and to the permeability Ilo, taken as unity and dimensionless in the e.s.u. system. (These two systems are mutually inconsistent: on the Maxwell theory the product eollo is equal to c- 2, where c is the speed of light, approximately 3 . 108 m s -1.) The physical relationships of the different systems of electrical and magnetic units have been ably described. (4) The SI uses the unit of current (ampere) as fundamental unit (whereas for e.m.u. it is a unit magnetic pole, with flo = 1, and for e.s.u. a unit charge, with eo = l). It is a pity that what NMR spectroscopists call the magnetic field, Bltesla, is officially named the magnetic flux density, whereas the magnetic force (HI A m -\) has been named the magnetic field intensity. The two are related by H = Bill, where IlINA -2 is the permeability of the medium. Although internationally agreed upon in 1960, the SI and the rationalizations are still not fully implemented; new editions or reprints of standard works in NMR, and even some current work, still use the old systems. Crooks's conclusion(4) is particularly relevant (now that we have the tesla as well !): "Many authors, especially in the older literature, skip lightly from e.m.u. to e.s.u., from gauss to oersted, with an agility born of long experience and deep understanding. Students who attempt to follow their reasoning must do so with care, or they will stumble into confusion." Such caution is needed with some of the "other units" given in the Tables. Far better is consistent use of the SI. Unfortunately there is confusion also as to units and symbols that may be used with the SI. Although base units such as the kilogram and the meter have been used in the tables, all the decimal multiples (g; em, mm, nm, pm, etc.) are also part of the SI, and may be used as convenient. Units recognized for continued use with the SI include the electron volt eV, a degree of angle, the minute, hour, and day. Names which are still in use for decimal multiples of SI units, although their continued use is dis­ couraged, include the angstrom, barn, dyne, bar, erg, and poise. Definitions of these quantities in SI units are included in the tables. The Fundamental Constants are the revised values of 1986. (5) 619 620 SI UNITS AND FUNDAMENTAL CONSTANTS UNITS Physical quantity Symbol SI Unit" Symbol/definition Other units Length, distance I, r meter m 1 A= 10 pm Time t second Plane angle il,O,tP degree radian rad = 360°/2n 1/2n cycles Frequency v,f hertz HZ=S-I 1 cps or cis (cycle per second) Angular frequency w = 2nv radian rad Mass m kilogram kg Reduced mass Jl kg Jl=m l m2/(m l +m2) Momentum p=mu kgms- I =N s Velocity u ms- I Angular momentum L=rxp kgm2s-I =Js Wavelength A=C/V meter m Period, relaxation time, T, 1: = l/v second correlation time Energy U joule J =kgm2 S-2 1 erg = 10-7 J 1 NBS cal = 4.184 J lint. cal = 4.186 J 1 eV = 1.602 19 10-19 J Entropy S J kg-I K- I le.u.=calg- IOC-I Temperature T kelvin K deg or °C (Celsius) o °C = 273.15 K Force F newton N=kgms-2 1 dyne = 10-5 N =Jm-I Pressure P,p pascal Pa=kgm-I s-2 1 atm = 101 325 Pa =Nm-2 1 torr = 1 atm/760 =Jm-3 ~ 1 mmHg 1 bar = 105 Pa Viscosity 1'/ poise p =0.1 Pa s e.m.u.jS! e.s.u./e.m.u. Electric current I ampere A=Cs-I 10 l/c Electric charge Q,q coulomb C=As 10 l/c Electric potential V volt V=kgm2s- 3 A-I 10-8 c difference =JA-Is-I =JC- I Power W watt W=kgm2s- 3 (1 W=107 ergs- l ) =Js-I Electric field strength E Vm- I 10-6 c Magnetic flux f/J weber Wb=Vs 10-8 c maxwell Magnetic flux density B tesla T=Vsm-2 1 G= 1O- 4 T c (induction field) =kg A -I S-2 gauss Magnetic field intensity H amperem- I Am-I 1 Oe = 10 3/4n l/c oersted Self inductance L henry H=WbA-I 10-9 c2 Magnetization M = (B/Jlo) - H Am-I 103 Magnetic dipole moment Jl amperem2 Am2 10-3 Magnetogyric ratio Y= Jl/!h rad T-I S-I 10-4 rad G-I S-I Nuclear electric Q (barn) 10-28 m2 quadrupole moment Reduced spin-spin KNN· = 4n2J NN.jhy NY N· N A -2 m -3 10 cm-3 coupling constant a SI-prefixed decimal multiples and fractions are acceptable also (despite widespread belief to the contrary).