Symbols and abbreviations Free

These lists contain the symbols and abbreviations most frequently used in this volume, but they are not expected to be exhaustive. Some specialized notation is only defined in the relevant chapter. An attempt has been made to standardize usage throughout the volume as far as is feasible, but it must be borne in mind that the original research literature certainly is not standardized in this way, and some difficulties may arise from this fact. Trivial use of subscripts etc. is not always mentioned in the symbols listed below. Some of the other symbols used in the text, e.g. for physical constants such as h or π, or for the thermodynamic quantities such as H or S, are not included in the list since they are considered to follow completely accepted usage.

a_N

hyperline (electron–nucleus) interaction constant

A

• (i) hyperfine (electron–nucleus) interaction constant

• (ii) parameter relating to electric field effects on nuclear shielding

B

• (i) magnetic induction field (magnetic flux density)

• (ii) parameter relating to electric field effects on nuclear shielding

B₀

static magnetic field of NMR or ESR spectrometer

B₁, B₂

r.f. magnetic fields associated with v₁, v₂

C_x

spin-rotation coupling constant of nucleus X (used sometimes in tensor form): C²=1/3(C$||2$+2C$⊥2$)

C_||, C_⊥

components of C parallel and perpendicular to a molecular symmetry axis

D

• (i) self-diffusion coefficient

• (ii) zero-field splitting constant

D

rotational diffusion tensor

D_||, D_⊥

components of D parallel and perpendicular to a molecular symmetry axis

D_int

internal diffusion coefficient

D₀

overall isotropic diffusion coefficient

E

electric field

E_n

eigenvalue of ̂ (or a contribution to ̂)

g

nuclear or electronic g-factor

G

magnetic field gradient

H_ij

element of matrix representation of 



Hamiltonian operator-subscripts indicate its nature

I_i

nuclear spin operator for nucleus i

I_ix, I_iy, I_iz

components of I_i

I

• (i) ionization potential

• (ii) moment of inertia

ⁿJ

nuclear spin–spin coupling constant through n bonds (in Hz). Further information may be given by subscripts or in brackets. Brackets are used for indicating the species of nuclei coupled, e.g. J (¹³C, ¹H) or additionally, the coupling path, e.g. J(POCF)

J_r

reduced splitting observed in a double resonance experiment

J

rotational quantum number

ⁿK

reduced nuclear spin–spin coupling constant (see the notes concerning ⁿJ)

m_i

eigenvalue of I_iz (magnetic component quantum number)

M₀

equilibrium macroscopic magnetization of a spin system in the presence of B₀

M_x, M_y, M_z

components of macroscopic magnetization

M_n

the number of average mol. wt.

P_A

valence p orbital of atom A

P_i

fractional population (or rotamers etc.)

P_uv

element of bond-order, charge-density matrix

q

electric field gradient

Q

• (i) nuclear quadrupole moment

• (ii) quality factor for an r.f. coil

s_A

valence s-orbital of atom A

S$A2$(0)

electron density in S_A at nuclear A

S

• (i) singlet state

• (ii) electron (or, occasionally, nuclear spin) cf. I

• (iii) ordering parameter for oriented systems

• (iv) overlap integral between molecular orbitals

t

elapsed time

T

• (i) temperature

• (ii) triplet state

T_c

coalescence temperature for an NMR spectrum

T_g

the glass transition temperature (of a polymer)

T$1X$

spin–lattice relaxation time of the X nuclei (further subscripts refer to the relaxation mechanism)

T$2X$

spin–spin relaxation time of the X nucleus (further subscripts refer to the relaxation mechanism)

T$1′$

inhomogeneity contribution to dephasing time for M_x or M_y

T$1*$

total dephasing time for M_x or M_y; (T$2*$)⁻¹=T₂⁻¹+ (T₂′)⁻¹

T₃

decay time following 90₀–τ–90₉₀ pulse sequences

T$1pX$,T$2pX$

spin–lattice and spin–spin relaxation time of the X nuclei in the frame of reference rotating with B₁

T_1D

dipolar spin–lattice relaxation time

X_i

mole fraction of compound

Z_A

atomic number of atom A

α

• (i) nuclear spin wavefunction (eigenfunction of I_z) for a spin –1/2 nucleus

• (ii) polarizability

β

nuclear spin wavefunction (eigenfunction of I_z) for a spin−½ nucleus

γ_X

magnetogyric ratio of nucleus X

δ_X

chemical shift of a nucleus of element X (positive when the sample resonates to high frequency of the reference). Usually in p.p.m.

δ_ij

Kronecker delta (=1 if i=j, and =0 otherwise)

δ(r_KA)

Dirac delta operator

Δ

• (i) time between field gradient pulses

• (ii) spectral width

ΔJ

anisotropy in J(ΔJ=J_||J_⊥, for axial symmetry)

Δn

population difference between nuclear states

Δδ

change of difference in δ

Δ_V½

full width (in Hz) of a resonance line at half-height

Δσ

• (i) anisotropy in σ(Δσ=σ_||–σ_⊥, for axial symmetry)

• (ii) differences in σ for two different situations

Δχ

• (i) susceptibility anisotropy (Δ_χ=χ_||–χ_⊥, for axial symmetry)

• (ii) differences in electronegativities

ɛ_r

relative permittivity

ɛ₀

permittivity of a vacuum

η

• (i) nuclear Overhauser effect

• (ii) asymmetry factor (e.g. in e²qQ/h)

• (iii) refractive index

• (iv) viscosity

μ

magnetic dipole moment

μ₀

permeability of a vacuum

μ_B

Bohr magneton

μ_N

nuclear magneton

v_i

Larmor precession frequency of nucleus i (in Hz)

v₀

• (i) spectrometer operating frequency

• (ii) Larmor precession frequency (general, or of bare nucleus)

v₁

frequency of ‘observing’ r.f. magnetic field

v₂

frequency of ‘irradiating’ r.f. magnetic field

σ_i

shielding parameter of nucleus i (used sometimes in tensor form). Usually in p.p.m. Subscripts may alternatively indicate contributions to σ.

σ_||, σ_⊥

components of σ parallel and perpendicular to a molecular symmetry axis

σ^d

diagrammatic contribution to σ

σ^p

paramagnetic contribution to σ

τ

• (i) pre-exchange lifetime of molecular species

• (ii) time between r.f. pulses (general symbol)

τ_c

correlation time

τ_coll

mean time between molecular collisions in the liquid state

τ_j

angular momentum correlation time

τ_p

pulse duration

τ_t

translational magnetic relaxation correlation time

χ

• (i) magnetic susceptibility

• (ii) electronegativity

• (iii) nuclear quadrupole coupling constant (=e₂qQ/h)

ω

carrier frequency in rad s⁻¹

ω_i, ω₀, ω₁, ω₂

as for v_i, v₀, v₁, v₂ but in rad s⁻¹

ω_m

modulation angular frequency (in rad s⁻¹)

ω_r

sample rotation (rad ⁻¹)

a.f.

audiofrequency

a.u.

atomic unit

a.m.

amplitude modulation

b.c.c.

body-centred cubic

c.m.c.

critical micelle concentration

e.d.

electron diffraction

e.f.g.

electric field gradient

f.c.c.

face-centred cubic

f.m.

frequency modulation

h.c.p.

hexagonal close-packed

h.f.

hyperfine

i.d.

inside diameter

i.f.

intermediate frequency

l.c.

liquid crystalline

mol.wt.

molecular weight

o.d.

outside diameter

p.p.m.

parts per million

r.f.

radiofrequency

r.m.s.

root mean square

s.h.f.

super-high frequency

u.h.f.

ultra-high frequency

ADC

analogue-to-digital converter

AEE

average excitation energy approximation

AQ

acquire

ARP

adiabatic rapid passage

BIRD

bilinear rotation decoupling

CCPPA

coupled cluster polarization propagator approximation

CH-COSY

carbon–hydrogen correlation spectroscopy

CHESS

chemical shift selection

CHF

coupled Hartree–Fock molecular orbital calculations

CIDEP

chemically induced dynamic electron polarization

CIDNP

chemically induced dynamic nuclear polarization

COSY

correlation spectroscopy

CP

cross polarization

CPMG

Carr–Purcell pulse sequence. Meiboom–Gill modification

CSA

chemical shielding anisotropy

CSI

chemical shift imaging

CW

continuous wave

DAC

digital-to-analogue converter

DD

dipole–dipole (interaction or relaxation mechanism)

DEPT

distortionless enhancement by polarization transfer

DLB

differential line broadening

DNP

dynamic nuclear polarization

DQ

double quantum

DQF

double quantum filter

ECOSY

exclusive correlation spectroscopy

EHT

extended Hückel molecular orbital theory

ENDOR

electron–nucleus double resonance

EOM

equations of motion

ESR

electron spin resonance

EXSY

exchange spectroscopy

FC

Fermi contact

FID

free induction decay

FLASH

fast low angle shot

FPT

finite perturbation theory

FT

Fourier transform

GIAO

gauge included atomic orbitals

HMQ

heteronuclear multiquantum

HOHAHA

homonuclear Hartman–Hahn

HRPA

higher random phased approximation

IDESS

improved depth selective single surface coil spectroscopy

IGLO

individual gauge for different localized orbitals

INADE-QUATE

incredible natural abundance double quantum transfer experiment

INDO

intermediate neglect of differential overlap

INDO/S

intermediate neglect of differential overlap calculations for spectroscopy

INDOR

internuclear double resonance

INEPT

insensitive nuclei enhanced by polarization transfer

IR

infrared

ISIS

image selected in vivo spectroscopy

LIS

lanthanide induced shift

LORG

local origin

LSR

lanthanide shift reagent

MASS

magic angle sample spinning

MBPT

many body perturbation theory

MEM

maximum entropy method

MINDO

modified INDO

MQ

multiple quantum

MQC

multiple quantum coherence

MQF

multiple quantum filter

NMR

nuclear magnetic resonance

NOE

nuclear Overhauser enhancement

NOESY

nuclear Overhauser enhancement spectroscopy

NQCC

nuclear quadrupole coupling constant

NQR

nuclear quadrupole resonance

PFG

pulsed field gradient

PRE

proton relaxation enhancement

QF

quadrupole moment/field gradient

QPD

quadrature phase detection

REX

relativistically extended Hückel molecular orbital theory

ROESY

rotating frame Overhauser enhancement spectroscopy

RPA

random phase approximation

SCPT

self consistent perturbation theory

SD

spin dipolar

SECSY

spin echo correlation spectroscopy

SEFT

spin echo Fourier transform

SLITDRESS

slice interleaved depth resolved surface coil spectroscopy

SOPPA

second order polarization propagator approach

SPI

selective population inversion

SPT

selective population transfer

SR

spin rotation (interaction or relaxation mechanism)

TART

tip angle reduced T1 imaging

TOCSY

total correlation spectroscopy

UV

ultraviolet

WAHUHA

Waugh, Huber and Häberlen (cycle of pulses)

ZQ

zero quantum

ZQC

zero quantum coherence

acac

acetylacetonato

ACTH

adrenocorticotropic hormone (corticotropin)

ADP

adenosine diphosphate

AMP

adenosine monophosphate

ATP

adenosine triphosphate

BSA

bovine serum albumin

CMP

cytidine monophosphate

cp

cyclopentadienyl

DAP

dodecylammonium propionate

DME

1,2-dimethoxyethane

DMF

dimethylformamide

DML

dimyristoyl-lecithin

DMS

dimethylsiloxane

DMSO

dimethyl sulfoxide

DNA

deoxyribonucleic acid

DPG

2,3-diphosphoglycerate

DPI

dipalmitoyl-lecithin

dpm

dipivaloylmethanato

DPPH

diphenylpicrylhydrazyl

DSS

2,2-dimethyl-2-silapentane-5-sulfonate (usually as the sodium salt)

DTBN

di-t-butyl nitroxide

EBBA

N-(p-ethoxybenzylidene)-p-butylaniline

EDTA

ethylenediaminetetra-acetic acid

EVA

ethylene-vinyl acetate

fod

1,1,1,2,2,3,3-heptafluoro-7,7-dimethyloctane-4,6-dionato

HAB

4,4′-bis(heptyl)azoxybenzene

HMPA

hexamethylphosphoramide

HOAB

p-n-heptyloxyazoxybenzene

IHP

inositolhexaphosphate

KDP

potassium dihydrogen phosphate

MBBA

N-(p-methoxybenzylidene)-p-butylaniline

NADH(P)

nicotinamide adenine dinucleotide (phosphate)

NMF

N-methylformamide

PAA

p-azoxyanisole

PBA

pyrene butyric acid

PBLG

poly(l-benzyl μ-glutamate)

PC

phosphatidyl choline (lecithin)

PCB

polychlorinated biphenyl

PDMS

polydimethylsiloxane

PMA

poly(methacrylic acid)

PMMA

poly(methyl methacrylate)

POM

poly(oxymethylene)

PS

phosphatidylserine

PTFE

polytetrafluoroethylene

PVC

poly(vinyl chloride)

PVF

poly(vinyl fluoride)

PVP

poly(vinyl pyrrolidone)

RNA

ribonucleic acid (tRNA, transfer RNA)

SDS

sodium dodecyl sulfate

TAB

trimethylammonium bromide

TCNQ

tetracyanoquinodimethane

TFA

trifluoroacetic acid

THF

tetrahydrofuran

TMS

tetramethylsilane

UTP

uridine triphosphate