54
3 Diatomic Molecules
Table 3.1 List of constants and parameters used in this chapter
Symbol Quantity [unit]
Equations
B
Rotational constant [MHz or cm –1 ]
(3.23)
B e
Equilibrium state rotational constant
(3.23, 3.39, 3.76)
B υ
Rotational constant for vibrational state υ
(3.39)
˜
D e
Dissociation energy [J]
(3.1)
D e
Quartic centrifugal distortion constant [kHz]
(3.47, 3.48)
H e
Sextic centrifugal distortion constant [Hz]
(3.49)
I
Moment of inertia [kg m 2 or u Å 2 ]
(3.17)
J
Rotational quantum number: 0, 1, 2, …
(3.22)
U lk
Dunham isotope-independent parameter
(3.72)
V A
lk
Correction parameter for the point-like nucleus [fm −2 ]
(3.83)
Y lk
Dunham constant [cm −1 ]
(3.71)
a
Morse anharmonicity constant
(3.13)
a 0
Quadratic potential constant [cm −1 ]
(3.14, 3.73a)
a i , i > 0 Higher-order potential constant [dimensionless]
(3.14, 3.73a–3.73d)
g J
Rotational g factor [dimensionless]
(3.55)
h
Planck constant
k
Harmonic force constant [dyn cm –1 = 10 −3 N m −1 ]
(3.1)
m A
Atomic mass of atom A [kg or u]
m e
Electron rest mass
M p
Proton rest mass
r
Bond length [pm or Å]
r e
Equilibrium value calculated from Y 01
(3.56)
r BO
e
Isotopically independent Born–Oppenheimer bond length
(3.83)
r z
Zero-point average structure
(3.68)
r 0
Effective structure
(3.58)
r s
Substitution structure
(3.64)
u
Unified atomic mass unit = 1.660 538 782(83) × 10 −27 kg
υ
Vibrational quantum number: 0, 1, 2, …
(3.10)
A
lk
Correction parameter for the Born–Oppenheimer approximation (3.78, 3.79, 3.82)
α e
Rotation–vibration interaction constant [MHz or cm −1 ]
(3.40, 3.49)
γ e
Higher-order rotation–vibration interaction constant [kHz]
(3.49)
μ
Reduced mass
(3.8)
μ D
Electric dipole moment [C m or D, 1 D = 3.335 64 × 10 −30 C m] (3.80)
(continued)
3 Diatomic Molecules
Table 3.1 List of constants and parameters used in this chapter
Symbol Quantity [unit]
Equations
B
Rotational constant [MHz or cm –1 ]
(3.23)
B e
Equilibrium state rotational constant
(3.23, 3.39, 3.76)
B υ
Rotational constant for vibrational state υ
(3.39)
˜
D e
Dissociation energy [J]
(3.1)
D e
Quartic centrifugal distortion constant [kHz]
(3.47, 3.48)
H e
Sextic centrifugal distortion constant [Hz]
(3.49)
I
Moment of inertia [kg m 2 or u Å 2 ]
(3.17)
J
Rotational quantum number: 0, 1, 2, …
(3.22)
U lk
Dunham isotope-independent parameter
(3.72)
V A
lk
Correction parameter for the point-like nucleus [fm −2 ]
(3.83)
Y lk
Dunham constant [cm −1 ]
(3.71)
a
Morse anharmonicity constant
(3.13)
a 0
Quadratic potential constant [cm −1 ]
(3.14, 3.73a)
a i , i > 0 Higher-order potential constant [dimensionless]
(3.14, 3.73a–3.73d)
g J
Rotational g factor [dimensionless]
(3.55)
h
Planck constant
k
Harmonic force constant [dyn cm –1 = 10 −3 N m −1 ]
(3.1)
m A
Atomic mass of atom A [kg or u]
m e
Electron rest mass
M p
Proton rest mass
r
Bond length [pm or Å]
r e
Equilibrium value calculated from Y 01
(3.56)
r BO
e
Isotopically independent Born–Oppenheimer bond length
(3.83)
r z
Zero-point average structure
(3.68)
r 0
Effective structure
(3.58)
r s
Substitution structure
(3.64)
u
Unified atomic mass unit = 1.660 538 782(83) × 10 −27 kg
υ
Vibrational quantum number: 0, 1, 2, …
(3.10)
A
lk
Correction parameter for the Born–Oppenheimer approximation (3.78, 3.79, 3.82)
α e
Rotation–vibration interaction constant [MHz or cm −1 ]
(3.40, 3.49)
γ e
Higher-order rotation–vibration interaction constant [kHz]
(3.49)
μ
Reduced mass
(3.8)
μ D
Electric dipole moment [C m or D, 1 D = 3.335 64 × 10 −30 C m] (3.80)
(continued)