Remarks on fitting vinylamine, C2H3NH2
Because of the tunneling of the NH2 group, vinylamine has a
double minimum potential. The 0– tunneling state is
45.18 cm–1 or 1.35 THz higher in energy than
the 0+ state.
Strong a-type and weak b-type transitions occur
within the states while strong c-type transitions are allowed
between the states. These selection rules dictate that both states may
be coupled via b- and a-type Coriolis interaction.
Only even order Coriolis operators are generally employed for pure
inversion problems. Alternatively, only odd order operators
are sometimes used.
The lowest order Coriolis parameters for vinylamine are Fac
and Fac. The signs of these parameters can not be determined
in the fit, but the relative signs of the centrifugal distortion corrections
will be determined in the fit. However, the signs of the lowest order parameters
relative to those of the dipole moment components may be derived from
relative intensity measurements of suitible transitions.
Stark measurements may be employed also provided there is a sufficiently large
dependence of the Stark shifts on the signs of the lowest order Coriolis
parameters (or on signs of the dipole moment components).
The latter method has been used, for example, in
E. A. Cohen and H. M. Pickett,
The Rotation-Inversion Spectra and Vibration-Rotation Interaction in
NH2D,
J. Mol. Spectrosc. 92 (1982) 83–100. View
abstract;
and, with tentative results, in
D. Christen, L. H. Coudert, R. D. Suenram, and F. J. Lovas,
The Rotational/Concerted Torsional Spectrum of the g'Ga Conformer
of Ethylene Glycol,
J. Mol. Spectrosc. 172 (1995) 57–77. View
abstract.
The former method was employed, e.g., in
D. Christen and H. S. P. Müller,
The Millimeter Wave Spectrum of aGg' Ethylene Glycol:
The Quest for Higher Precision,
Phys. Chem. Chem. Phys. 5 (2003) 3600–3605. View
abstract;
and in
H. S. P. Müller and D. Christen,
Millimeter and Submillimeter Wave Spectroscopic Investigations into the
Rotation-Tunneling Spectrum of gGg' Ethylene Glycol, HOCH2CH2OH,
J. Mol. Spectrosc. 172 (1995) 57–77. View
abstract.
The lines within the 0+ and 0– states of
vinylamine have been summarized by
R. D. Brown, P. D. Godfrey, B. Kleibomer, A. P. Pierlot, and D. McNaughton,
Submillimeter-Wave Spectrum, Far-Infrared Spectrum, and Inversion
Potential of Vinylamine,
J. Mol. Spectrosc. 142 (1990) 195–204. View
abstract.
Transitions between the states have been described in
D. McNaughton and E. G. Robertson,
The Far-Infrared Inversion Transition of Vinylamine,
J. Mol. Spectrosc. 163 (1994) 80–85. View
abstract.
I do not know of any attempts to determine the signs of the
Coriolis interaction parameters with respect to those of the
dipole moment components. As part of the transitions within and
between the states occur in overlapping frequency regions
(see spectral simulations), the relative signs can be determined in theory.
The number of spectroscopic parameters is exactly the same as in the
latter publication on vinylamine. They used two sets of rotational and
quartic centrifugal distortion constants, and two HKJ
for each tunneling state the energy difference and Fac.
Slightly different parameters were used here and for the creation of the
catalog entries: one set of rotational and quartic centrifugal distortion
parameters along with HKJ and HJK;
three quadratic distortion corrections to the energy which may be viewed as
differences of the two tunneling states from the average rotational
parameters, three quartic corrections which may be viewed as corresponding
differences for the diagonal quartic distortion parameters; and finally
Fac, FacJ,
and Fbc.
As can be seen below, omission of the last one or two parameters affects
the others only slightly and causes modest, but significant deteriorations
of the fit.
Fit with 20 parameters:
NEW PARAMETER (EST. ERROR)
1 1099 A-(B+C)/2 46811.822(145)
2 199 (B+C) 9299.85947( 60)
3 40099 (B-C)/4 366.187203(118)
4 2099 -DK -0.82599( 45)
5 1199 -DJK 0.0519636(165)
6 299 -DJ -6.45671(175)E-03
7 40199 d1 -1.41197(165)E-03
8 50099 d2 -0.09143(173)E-03
9 2199 HKJ -3.366( 54)E-06
10 1299 HJK -0.1599(315)E-06
11 11 E 1354537.25(283)
12 1000 EK 208.4373(204)
13 100 EJ 0.01528( 46)
14 40000 E2 1.264494( 53)
15 2000 EKK -0.029324( 86)
16 1100 EJK 0.6467( 59)E-03
17 200 EJJ 0.02539(116)E-03
18 410001 Fac 65.3887(108)
19 410101 FacJ -0.2169(202)E-03
20 210001 Fbc 2.647( 94)
MICROWAVE AVG = -0.073045 MHz,
MICROWAVE RMS = 38.506376 MHz,
END OF ITERATION 1 OLD, NEW RMS ERROR= 0.79733
Fit with 19 parameters:
NEW PARAMETER (EST. ERROR)
1 1099 A-(B+C)/2 46811.798(145)
2 199 (B+C) 9299.85943( 60)
3 40099 (B-C)/4 366.187216(118)
4 2099 -DK -0.82636( 45)
5 1199 -DJK 0.0519693(165)
6 299 -DJ -6.45640(175)E-03
7 40199 d1 -1.41209(165)E-03
8 50099 d2 -0.09168(173)E-03
9 2199 HKJ -3.301( 53)E-06
10 1299 HJK -0.1840(314)E-06
11 11 E 1354536.62(283)
12 1000 EK 208.4551(203)
13 100 EJ 0.01443( 45)
14 40000 E2 1.264509( 53)
15 2000 EKK -0.029484( 85)
16 1100 EJK 0.6383( 59)E-03
17 200 EJJ 0.02841(113)E-03
18 410001 Fac 65.27577(248)
19 210001 Fbc 2.765( 89)
MICROWAVE AVG = -0.019019 MHz,
MICROWAVE RMS = 42.708157 MHz,
END OF ITERATION 1 OLD, NEW RMS ERROR= 0.86501
Fit with 18 parameters:
NEW PARAMETER (EST. ERROR)
1 1099 A-(B+C)/2 46811.655(145)
2 199 (B+C) 9299.85956( 60)
3 40099 (B-C)/4 366.187251(118)
4 2099 -DK -0.82546( 45)
5 1199 -DJK 0.0519225(162)
6 299 -DJ -6.45618(175)E-03
7 40199 d1 -1.41203(165)E-03
8 50099 d2 -0.09315(172)E-03
9 2199 HKJ -3.338( 53)E-06
10 1299 HJK -0.1118(310)E-06
11 11 E 1354533.41(282)
12 1000 EK 208.3688(195)
13 100 EJ 0.01284( 44)
14 40000 E2 1.264613( 53)
15 2000 EKK -0.029131( 82)
16 1100 EJK 0.6532( 58)E-03
17 200 EJJ 0.02813(113)E-03
18 410001 Fac 65.27495(248)
MICROWAVE AVG = 0.309704 MHz,
MICROWAVE RMS = 44.639992 MHz,
END OF ITERATION 1 OLD, NEW RMS ERROR= 0.99097