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Quantum numbers formats

Methylamine vibration-rotation-tunneling energy levels in the Ohashi-Hougen formalism

Code:
Ohashi-Ilyushin code for methylamine
Output Format:
J K Sym, J K Sym F

Details: Each energy level is characterized by the quantum numbers J and K = Ka, together with the overall torsion–wagging–rotation symmetry species Γ, corresponding to an irreducible representation of the permutation–inversion group G12. To distinguish between the two components of doubly degenerate levels of E1 or E2 symmetry with identical J and K values, the labels E1+1 and E1−1, or E2+1 and E2−1 are employed, where the +1 and −1 components correspond to k = +K and k = −K, respectively. When table includes hyperfine levels, the standard quantum number F = J + I is included in the level designation.

The correspondence between the integer symmetry identifier Sym used in the .cat file and the symmetry species Γ is summarized in the table below.

Sym 3 -3 4 -4 1 -1 2 -2
Γ A1 A2 B1 B2 E1+1 E1-1 E2+1 E2-1

Energy levels of an asymmetric top with a single internal rotor of C3v symmetry

Code:
RAM36/RAM36hf, BELGI-Cs
Output Format:
J Ka Kc m, J Ka Kc m F

Details: Each energy level is characterized by the asymmetric-top quantum numbers J, Ka, and Kc, together with the free-rotor quantum number m. When table includes hyperfine levels, the standard quantum number F = J + I is included in the level designation.

The correspondence between the m quantum number used in the .cat file and the vibrational–torsional quantum number vt, as well as the associated symmetry species Γ = A or E of the C3v point group, is summarized in the table below.

m 0 1 -3 -2 3 4 -6 -5 6 7
vt 0 0 1 1 2 2 3 3 4 4
Γ A E A E A E A E A E

Energy levels of an asymmetric top with two internal rotors of C3v symmetry

Code:
ERHAM
Output Format:
J Ka Kc Sym, J Ka Kc Sym F, J Ka Kc s

Details: Each level is characterized by the asymmetric top quantum numbers J, Ka, and Kc, together symmetry number σ. A combination of (σ1,σ2) values of upper and lower levels corresponds to a combination of symmetry species Γ1Γ2 of C3v symmetry point group. The correspondence is summarized in the table below.

(σ1,σ2) (0,0) (0,1) (1,0) (1,1) (1,2)
Γ1Γ2 AA AE EA EE EE'

Methylamine vibration-rotation-tunneling energy levels in the Kleiner-Hougen formalism

Code:
Kleiner-Hougen code for methylamine
Output Format:
J Ka Kc Sym, J Ka Kc Sym F

Details: Each energy level is characterized by the asymmetric-top quantum numbers J, Ka, and Kc, together with the overall torsion–wagging–rotation symmetry species Γ, corresponding to an irreducible representation of the permutation–inversion group G12. When table includes hyperfine levels, the standard quantum number F = J + I is included in the level designation.

The correspondence between the integer symmetry identifier Sym used in the .cat file and the symmetry species Γ is summarized in the table below.

Sym 1 2 3 -3 4 -4
Γ E1 E2 A1 A2 B1 B2