a. Quantum Numbers 

J  Resultant total angular momentum quantum number, excluding nuclear spins. 
N  Rotational angular momentum quantum number, excluding electron and nuclear spins, in the case where electron spin is present. 
K  Projection of J (or N) on the symmetry axis in the limiting prolate or oblate symmetric top. 
F_{1}  Resultant angular momentum quantum number including nuclear spin for one nucleus. 
F  Resultant total angular momentum quantum number. 
λ or ε  Quantum number employed when F_{1} is not a good quantum number. This value simply numbers the levels from lowest to highest energy for the same F quantum number. 
ν_{1},ν_{2},ν_{3} v_{1}v_{2}v_{3} 
Vibrational modes (ν) and quantum numbers (v). ν_{1} is the highest energy symmetric stretching mode, ν_{2} is the bending mode, and ν_{3} is the asymmetric stretch for XY_{2} molecules or lowest energy stretch for XYZ molecules. 
U or L  Upper or lower energy level or transition frequency. 
′ or ″  Prime or double prime is used to distinguish the upper (′) and lower (″) levels in a transition. They occur as superscripts on the quantum numbers. 
ℓ  Quantum number for vibrational angular momentum. 
I or (I_{i })  Angular momentum quantum number of nuclear spin for one (or i^{th}) nucleus. 
S  Resultant angular momentum number of electron spins. Σ is the projection of S on the molecular axis. 
Λ  Absolute values of the projection of the resultant orbital angular momentum on the molecular axis. 
Ω  Absolute value of the projection of the total electronic angular momentum on the molecular axis. 
Σ, Π, Δ  Electronic state designation for which 
b. Molecular Constants 

A, B, C ^{ } 
Rotational constants (MHz). These are related to the principal moments of inertia: 
$${\bar B}$$  Bbar equals (B + C)/2. 
τ, Δ, δ, D  Quartic centrifugal distortion constants (MHz or kHz). 
H, h  Sextic centrifugal distortion constants (MHz or kHz). 
L, ℓ, G, g  Octic centrifugal distortion constants (MHz). 
P, p, F  Dectic centrifugal distortion constants (MHz). 
χ_{aa}(X), ... 
Nuclear electric quadrupole coupling constant along principal axis indicated for nucleus X (MHz). 
Product of the nuclear quadrupole coupling constant and the asymmetry parameter for the bending vibrational state.  
µ_{a,b}  Components of the electric dipole moment along the a or bprincipal axes. 
α_{v }, γ_{vv}  Rotationvibration coefficients in the power series representing B_{v} (eq 3). 
q_{v}  ℓdoubling constant (MHz). 
σ_{} , σ_{⊥}  Components of the magnetic shielding tensor which are parallel and perpendicular to the molecular axis, respectively. 
Q  Molecular quadrupole moment relative to the center of mass (esu · cm^{2}). 
Electric polarizability anisotropy (cm^{3}).  
χ_{⊥ }, χ_{}  Components of the magnetic susceptibility tensor which are, respectively, perpendicular and parallel to the molecular axis (erg/G^{2} · mol). 
χ_{xx}  χ_{yy}  Magnetic susceptibility anisotropy. 
g_{⊥} , g_{}  Components of the molecular G tensor which are, respectively, perpendicular and parallel to the molecular axis. g_{⊥} is sometimes denoted g or g_{J} for linear molecules in the ground state (µ_{N}). 
g_{xx}  g_{yy}  Anisotropy of the molecular G tensor perpendicular to the molecular axis (µ_{N}). 
c_{X} or M  Spin rotation constant related to nucleus X (kHz). 
S_{XY}  Spinspin interaction constant between nucleus X and nucleus Y (kHz). 
α_{p} , β_{p}  Ωtype doubling parameters,
$$ \alpha_p = 4\Sigma(1)^S \times~ \frac{\langle \Pi\, (A+2B) L_y\, (eq 14) $$ \beta_p = 4\Sigma(1)^S \times ~ \frac (eq 15)

p_{eff}  Λtype doubling constant in the ^{2}Π_{1/2} state (MHz). 
a, b, c, d 
Magnetic hyperfine coupling constants (MHz) where,
$$ a = 2\mu_{\rm B} g_{\rm N}\mu_{\rm N} \langle 1/r^3\rangle $$ (eq 16) $$ b =  \mu_{\rm B}g_{\rm N}\mu_{\rm N} ~\left\langle (eq 17) $$ c = 3\mu_{\rm B}g_{\rm N}\mu_{\rm N} ~\left\langle (eq 18) $$ d = 3\mu_{\rm B}g_{\rm N}\mu_{\rm N} ~\left\langle (eq 19) Here µ_{B} is the Bohr magneton, µ_{N} is the nuclear magneton, and g_{N} is the nuclear gvalue. 
A  Spinorbit coupling constants defined by the power series expansion, 
(O)_{S}  Spinrotation interaction constant (ref [21]). Coefficient in the Hamiltonian term 
(ij)_{S},T_{ij}  Spinrotation interaction constants where i and j are a, b, or c and the Hamiltonian term is Σ(ij)_{S}N_{i}S_{j}. See Curl and Kinsey [21] and Bowater et al. [22] (for T_{ij} notation) for correspondence to the notation of other workers. 
(O)_{I},a_{I}  Fermi interaction constant and coefficient of the 
(ij)_{I}  Magnetic dipoledipole interaction constant in the Hamiltonian term 
(ij)_{Q}  Nuclear electric quadrupole interaction constant in the term 
A_{S}, B_{S}, C_{S}  Combination of spinrotation constants where 
c. Other 

*  Asterisks in the uncertainty column indicate that the transition frequency is calculated rather than measured. 
(...)  Parentheses in the numerical listings contain measured or estimated uncertainties. For example, the value 1.407(83) should be interpreted as 
a,b,c  Designate principal axes corresponding to A, B, and C, respectively. 
r(XY)  Distance between centers of mass of atoms X and Y (Å). 
∠XYZ  Angle formed by atoms X, Y, and Z (degrees). 