Molecule Types Symmetric Tops Samples

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The pure rotational spectrum of the ground state of NH₃/ND₃ and the Stark effect

NH₃

The data files given here were constructed by fitting to the line positions and intensities in the HITRAN 2008 (http://www.hitran.com) database. The fit was restricted to J < 16, and is sufficient to reproduce the line positions to better than 0.001 cm^-1 and the intensities to better than 10^-20  cm² cm^-1 Molecule^-1. There are two points that are slightly non-standard:

1. The point group used is D_3h, rather than C_3v. This is necessary to account for the inversion doubling in the ground state, which appears in the data file as two vibrational states:
• s/0+ with A₁' symmetry
• a/0- with A₂" symmetry
2. To fit the K = 3n levels requires three perturbation operators:
• <0+|J+-^6|0+> = J₊⁶ + J_-⁶
• <0+|J^2J+-^6|0+> = J²(J₊⁶ + J_-⁶)
• <0+|J+-^12|0+> = J₊¹² + J_-¹²

The Stark Effect

   M  Sym   #    g Population Name J K (kl) Sym M         Energy Linear         Dipole     Err  Quadratic       Err  Two Level Delta     C              Dipole2    Err
   0    -   1    4 .660533316 a  0  0 A2"  0             0.7933 -5.20523347e-9 -.0309983 15.8% -1.0409798e-15 .02 %
   0    -   2    2 .036129526 s  1  1 E"  0             16.1730 -1.47243024e-9 -.0087686 15.8% -2.9448374e-16 .002%
   0    -   3    2 .032246486 a  1  1 E'  0             16.9632 -1.53137719e-9 -.0091197 15.8% -3.0627282e-16 .002%
   0    -   4    4 .042329414 s  1  0 A2'  0            19.8899 3.241105275e-9 .01930147 15.8% 6.48153456e-16 .033%
   1    -   1    2 .036129526 s  1  1 E"  1             16.1730 -7.02797997e-8 -.4185312 13.9% -1.3786935e-14 5.18% 16.583449 .82098935 -1.25126674e-7 -.7451561 .013%
   1    -   2    2 .032246486 a  1  1 E'  1             16.9632 6.802667704e-8 .40511341 13.9% 1.33363101e-14 5.36% 16.583784 .75886528 1.190970869e-7 .70924861 .015%
   1    -   3    4 .042329414 s  1  0 A2'  1            19.8899 -1.47290548e-9 -.0087715 15.8% -2.9457878e-16 .002%

ND₃

• nd3x0.pgo, similar to the nh3x0.pgo file above. This was derived by from an unweighted fit to all lines in the CDMS linelist with J < 16, which gave an average error of 7×10^-5 cm^-1 and a maximum error of 0.003 cm^-1. This has the two ground state inversion doublets in different manifolds, giving a simpler description than in the next file.
• nd3x0one.pgo, equivalent to the nh3x0one.pgo file above, with both ground state inversion doublets in the same manifold to allow the Stark effect to be simulated. This uses exactly the Hamiltonian and constants used in the Fusina and Murzin paper. This includes perturbations acting between the two inversion doublets, though note that the sign of the α_J and α_K constants must be changed in PGOPHER to give consistent matrix elements. The line positions agree with the CDMS linelist to < 0.006 cm^-1 (< 0.0005 cm^-1 for J < 15). The operators mixing states are:
• <0-|JzJ+-^3|0+> = [J₊³ + J_-³, J_z]₊ (term in α)
• <0+|J^2JzJ+-^3|0+> = J²[J₊³ + J_-³, J_z]₊ (-term in α_J)
• <0+|Jz^3J+-^3|0+> = [J₊³ + J_-³, J_z³]₊ (-term in α_K)
• nd3x0hyp.pgo which has the hyperfine structure due to the nitrogen nucleus added to the simulation, giving a linelist consistent with the Coudert and Roueff paper.