Coding conventions for ARTSCAT, version4, Column 29 (Vibrational and rotational assignments).
Conventions are species specific.

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Water molecule

Vibrational and rotational coding for Water

v: v1v2v3   vibrational quantum numbers
J Ka Kc: rotational quantum numbers
Up: upper
lo: lower


WARNING: the upper and lower g have a "strange" value in HITRAN. 
There is no physical reason. However, these "strange" values were kept because they are consistent with the Einstein factor. 
  g_upper=(2*J'+1)xfactor   g_lower=(2*J"+1)xfactor  
  
  This factor ??? is set to
  factor= 1 for the (010) vibration state
  factor= 3 for the (020) vibration state
  factor= 6 all other vibrational state

                              up  low    up       lo
                               v   v   J Ka Kc   J Ka Kc
@    H2O-162     209914679.09    90.0     90.0 000 000  7  5  2   7  5  3 
@    H2O-162     486533180.09    66.0     66.0 000 000  5  4  1   5  4  2 
@    H2O-182     512255372.98    66.0     66.0 000 000  5  4  1   5  4  2 
@    H2O-162     824669093.47    42.0     42.0 000 000  3  3  0   3  3  1 
@    H2O-182     853539107.17    42.0     42.0 000 000  3  3  0   3  3  1 
@    H2O-162     892302271.99   102.0    102.0 000 000  8  5  3   8  5  4 
@    H2O-182     956307961.77   102.0    102.0 000 000  8  5  3   8  5  4 
@    H2O-181    1603829691.81    11.0      9.0 010 010  5  1  5   4  2  2 
@    H2O-161    2160274473.10     9.0     11.0 010 010  4  2  2   5  1  5 
@    H2O-162    2394562279.03    78.0     78.0 000 000  6  4  2   6  4  3 
@    H2O-182    2521554364.24    78.0     78.0 000 000  6  4  2   6  4  3 
@    H2O-162    2973941183.36   150.0    150.0 000 000 12  6  6  12  6  7 
                                 
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Methane  CH4-211 and CH4-311
See HITRAN for the notation

g_upper=factor_sym x(2*J'+1)  g_lower=factor_sym x(2*J"+1)
with  factor_sym= 5 (A1 or A2 sym), factor_sym=3 (F1, F2) and factor_sym=2 (E sym)

     The J is just on the left-hand side of the "E F2 A1 etc..." symetries                                                       
                                                up            low           up        low  
                                             <vibration > < vibration><.......Rotation.....>  
                                                                          J           J 
@    CH4-211    31867938.29    21.0     21.0  0 0 0 0 1A1  0 0 0 0 1A1    3F2  1      3F1  1   
@    CH4-211    44848951.72    81.0     81.0  0 0 0 0 1A1  0 0 0 0 1A1   13F2  1     13F1  1   
@    CH4-211    70391269.14    69.0     69.0  0 0 0 0 1A1  0 0 0 0 1A1   11F2  1     11F1  1   
@    CH4-211   101449767.79    57.0     57.0  0 0 0 0 1A1  0 0 0 0 1A1    9F2  1      9F1  1   
@    CH4-211   106756094.29    45.0     45.0  0 0 0 0 1A1  0 0 0 0 1A1    7F2  1      7F1  1   
@    CH4-211   107595513.18    33.0     33.0  0 0 0 0 1A1  0 0 0 0 1A1    5F2  1      5F1  1   
     

     

 
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 Methane   CH4-212   (in fact CH3D)
                                  upper       lower   upper      lower
                                  Vib         vib    J  K sym    J  K sym  
 CH4-212 1161860780518.88       GROUND       GROUND  5  4  E     4  4  E    
 
 CH4-212 1162427238368.27       GROUND       GROUND  5  1  E     4  1  E    
 CH4-212 1162464952259.49       GROUND       GROUND  5  0  A2    4  0  A1   


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CO2

All transitions are within the ground vibrational state

For CO2, this depends on the isotopic species:
CO2-628: no hyperfine structure. 
CO2-627  hyperfine structure, we have to indicate F' and F" (upper and lower F values) 

J": lower J value
X=R means that the upper J is equal to J"


g_upper=(2*J'+1)  g_lower=(2*J"+1)

For CO2-627, one has to deal with hyperfine structure 
g_upper=2*F'+1  g_lower=2*F"+1

CO2 molecule
                                                      F'      X  J"  F" 
@    CO2-628   22075787833.70     3.0      1.0                R  0e     
@    CO2-627   22700465394.94     6.0      6.0        2.5     R  0e  2.5
@    CO2-627   22701244855.35     8.0      6.0        3.5     R  0e  2.5
@    CO2-627   22701634585.56     4.0      6.0        1.5     R  0e  2.5
@    CO2-628   44151455750.42     5.0      3.0                R  1e     
@    CO2-627   45401260561.60     6.0      4.0        2.5     R  1e  1.5
@    CO2-627   45401410457.83     8.0      8.0        3.5     R  1e  3.5
@    CO2-627   45401590333.31     6.0      8.0        2.5     R  1e  3.5
@    CO2-627   45401800188.04     4.0      4.0        1.5     R  1e  1.5
                                 
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CO molecule 
vib=001 transition within the first vibrational state
vib=000 transition within the ground state
                                       g_upper  g_lower  vib  J' J"    
@    CO-38	  103803078624.01       6.0      2.0     001  1  0
@    CO-38	  104711359834.01       6.0      2.0     000  1  0
@    CO-28	  108806914540.49       3.0      1.0     001  1  0
@    CO-36	  109220478236.30       6.0      2.0     001  1  0



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H2CO, or H2S  or SO2 or H2SO4
  
  g_upper=2*J'+1  g_lower=2*J"+1  

                                g_upper  g_lower   J'Ka'Kc' J"Ka"Kc"  

@    H2S-121   89497042486.74     45.0     39.0    7  1  6   6  4  3
@    H2S-121  119665157535.28      9.0     11.0    4  2  2   5  1  5
@    H2S-121  149662390882.76     63.0     57.0   10  3  8   9  4  5  

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H2O2

For H2O2, we have to deal with the torsion=v4 (represented by two quantumnumbers) and the vibration (v1-v3 and v5-v6)

    0 0 002 0 0   is for v1=0, v2==0, v3=0  v4=(02) v5=0, v6=0
    
    The rotational numbers J Ka Kc are "classical"


                                    upper         lower        upper          lower
                                   vib tor vib    vib tor vib  J Ka Kc        J Ka Kc                                     
@  H2O2-1661    1292405286.44      0 0 002 0 0    0 0 004 0 0 21  1 20       20  2 18
@  H2O2-1661    1585302517.90      0 0 001 0 0    0 0 003 0 0 35  2 34       34  3 32
@  H2O2-1661    2237351114.05      0 0 001 0 0    0 0 003 0 0  8  2  6        9  1  8
@  H2O2-1661    2752994141.81      0 0 003 0 0    0 0 001 0 0 10  1 10        9  2  8
@  H2O2-1661    3965954426.88      0 0 014 0 0    0 0 022 0 0 14 10  5       13  9  5
@  H2O2-1661    4647082891.46      0 0 001 0 0    0 0 003 0 0 13  0 13       12  1 11

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HO2
See Saito, J. Mol. Spectr 65 pp229-235 (1977)

One has to deal with the spin-rotation structure and of the hyperfine structure
J= N+1/2 or J=N-1/2
F=J+1/2  or F=J-1/2

So:

N, Ka Kc are the "classical" rotational quantum numbers
j=- if J=N-1/2 and j=+ if J=N+/2


Example
23  1 22   22- 22  2 21   21-
[N',Ka',Kc']=[23,1,22]  F'=22, J'=21.5, --- [N",Ka",Kc"]=[23,1,22] F"=21, J3=22.5

The g_upper and g_lower degeneracy are related to 
g_upper=(2xF'+1)  g_lower=(2xF"+1)





                                 g_upper  g_lower       <...upper.....><..lower.......>
                                                         N Ka Kc   F j  N Ka Kc    F j 
@  HO2-166      5179094587.42      5.0      5.0          2  1  1    2+  2  1  2    2+ 
@  HO2-166      5182931930.89      7.0      7.0          2  1  1    3+  2  1  2    3+ 
@  HO2-166      5757544135.14      5.0      5.0          2  1  1    2-  2  1  2    2- 
@  HO2-166      5771904193.87      3.0      3.0          2  1  1    1-  2  1  2    1- 
@  HO2-166      9279535910.97     47.0     45.0         23  1 22   23- 22  2 21   22- 
@  HO2-166      9283043482.72     45.0     43.0         23  1 22   22- 22  2 21   21- 
@  HO2-166     10144886840.98     31.0     31.0         15  2 13   15+ 15  2 14   15+ 
@  HO2-166     10145456446.65     33.0     33.0         15  2 13   16+ 15  2 14   16+ 
@  HO2-166     10404956798.30     31.0     31.0         15  2 13   15- 15  2 14   15- 
@  HO2-166     10405796217.18     29.0     29.0         15  2 13   14- 15  2 14   14- 

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HCL and HF
v' v"= when v'=v"=1, this transition is within the fisrt excited state
v' v"= when v'=v"=0, this transition is within the ground state

N' and N" = upper and lower N value
J' and J": upper and lower J value
R: means that  N'-N"=1


For v=0:
g_upper=2x(2J'+1)  
g-lower=2x(2J"+1)

For v=1 (no hyperfine structure)
g_upper=8x(2N'+1)  
g-lower=8x(2N"+1)

                                  g_upper  g_lower    v'   v"  J'         N"   J"
@  HCl-17     606789048682.72      24.0      8.0      1    1           R  0       
@  HCl-15     607688216202.00      24.0      8.0      1    1           R  0       
@  HCl-17     624964356179.17       8.0      8.0      0    0   1.5     R  0    1.5
@  HCl-17     624977816860.53      12.0      8.0      0    0   2.5     R  0    1.5
@  HCl-17     624988309596.56       4.0      8.0      0    0   0.5     R  0    1.5
@  HCl-15     625901597340.61       8.0      8.0      0    0   1.5     R  0    1.5
@  HCl-15     625918745469.21      12.0      8.0      0    0   2.5     R  0    1.5
@  HCl-15     625931996295.86       4.0      8.0      0    0   0.5     R  0    1.5
@  HCl-17    1213205065609.96      40.0     24.0      1    1           R  1       
@  HCl-15    1215002231457.93      40.0     24.0      1    1           R  1       
@  HCl-17    1249558618568.94      12.0     12.0      0    0   2.5     R  1    2.5
@  HCl-17    1249558618568.94       8.0      4.0      0    0   1.5     R  1    0.5


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Ozone


g_upper=2*J'+1  g_lower=2*J"+1

For ozone, one has to deal with hyperfine structure for the 17O species
for O3-676 and O3-667 g_upper=2*F'+1  g_lower=2*F"+1


                                 g_upper  g_lower   v' v"   J'Ka'Kc' J"Ka"Kc"  F'  F" 
                
@    O3-666      789694600.00     63.0     65.0    000 000 31  5 27  32  4 28            
@    O3-666     1087764800.00     67.0     65.0    000 000 33  4 30  32  5 27            
@    O3-666     2488277401.40     41.0     43.0    010 010 20  3 17  21  2 20            
@    O3-666     2594073500.00     93.0     95.0    000 000 46  7 39  47  6 42            
@    O3-666     5027519520.66     21.0     19.0    010 010 10  1  9   9  2  8            
@    O3-676     6380003215.68     36.0     38.0    000 000 15  3 13  16  2 14   17.5 18.5
@    O3-676     6380153111.91     26.0     28.0    000 000 15  3 13  16  2 14   12.5 13.5
@    O3-676     6380482883.61     34.0     36.0    000 000 15  3 13  16  2 14   16.5 17.5
@    O3-676     6380512862.86     28.0     30.0    000 000 15  3 13  16  2 14   13.5 14.5
@    O3-676     6380692738.33     30.0     32.0    000 000 15  3 13  16  2 14   14.5 15.5
@    O3-676     6380692738.33     32.0     34.0    000 000 15  3 13  16  2 14   15.5 16.5
@    O3-676     8348560411.89     38.0     40.0    000 000 18  3 15  19  2 18   18.5 19.5
@    O3-676     8348590391.14     40.0     42.0    000 000 18  3 15  19  2 18   19.5 20.5
@    O3-676     8348650349.63     36.0     38.0    000 000 18  3 15  19  2 18   17.5 18.5
@    O3-676     8348770266.61     42.0     44.0    000 000 18  3 15  19  2 18   20.5 21.5
@    O3-676     8348830225.10     34.0     36.0    000 000 18  3 15  19  2 18   16.5 17.5
@    O3-676     8349070059.07     32.0     34.0    000 000 18  3 15  19  2 18   15.5 16.5
@    O3-667     8665111268.29     10.0      8.0    000 000  4  0  4   3  1  3    4.5  3.5
@    O3-667     8665890728.69     12.0     10.0    000 000  4  0  4   3  1  3    5.5  4.5
@    O3-667     8665950687.18      8.0      6.0    000 000  4  0  4   3  1  3    3.5  2.5
@    O3-667     8666969981.53     14.0     12.0    000 000  4  0  4   3  1  3    6.5  5.5
@    O3-667     8895711626.99     38.0     40.0    000 000 16  3 14  17  2 15   18.5 19.5
@    O3-667     8895771585.48     28.0     30.0    000 000 16  3 14  17  2 15   13.5 14.5


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OCS 

g_upper=2*J'+1  g_lower=2*J"+1  

@   O2-67             9000.00 0.31677E-40 296  0.29204470751E-19 0.000E+00     62.0     65.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 000   32  32  31   32  32  30
@   O2-67            23500.00 0.13629E-39 296  0.31020807195E-19 0.000E+00     62.0     67.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 000   33  33  31   33  33  32
@   O2-68            40100.00 0.35804E-43 296  0.97600307854E-19 0.000E+00    121.0    121.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 000   60           60        
@   O2-68            40500.00 0.79894E-43 296  0.94437532676E-19 0.000E+00    119.0    119.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 000   59           59        
@   O2-66            40800.00 0.21511E-43 296  0.99915319645E-19 0.000E+00    119.0    119.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 000   59           59        
@   O2-66            40800.00 0.14795E-46 296  0.12971846739E-18 0.000E+00    119.0    119.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 001   59           59        
@   O2-68            40900.00 0.17528E-42 296  0.91325060263E-19 0.000E+00    117.0    117.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 000   58           58        
@   O2-68            41400.00 0.38235E-42 296  0.88263015761E-19 0.000E+00    115.0    115.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 000   57           57        
@   O2-66            41700.00 0.75730E-46 296  0.12326345242E-18 0.000E+00    115.0    115.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 001   57           57        
@   O2-66            41700.00 0.11210E-42 296  0.93386498285E-19 0.000E+00    115.0    115.0  16726.000  16839.000  16726.000  18901.000  16726.000  27550.000  12151.000   0.75   0.75   0.75   0.75   0.00   0.70   0.30  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00  0.000E+00 000   57           57        
                                 G-upper  g_lower   J' J"
@    OCS-822   11409711522.71     3.0      1.0      1  0
@    OCS-632   11865725842.62     3.0      1.0      1  0
@    OCS-624   12123847155.78     6.0      2.0      1  0
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Molecular oxygen

===>  For O16-O16  and O16-O18, 
We just have a spin structure. So the J value can take 3 values which are:  J=N,N-1 and N+1  
Condition:  J  cannot be negative (of course)
we do not have to deal with an hyperfine stucture
So, there is no F_upper  or F_lower rotational quantum numbers.
 (In fact, F_upper=J_upper and F_lower=J_lower)

==========================================================================

===>  For O16-O17, we have to deal with I(O17)=5.2. 
The J value can take 3 values which are:  J=N,N-1 and N+1  
Condition:  J  cannot be negative (of course)
In addition, one has to deal with the hyperfine structure. (I(O17)=5/2
For this reason, F_upper (and F_lower) can take 6 different values, which are:
 F_upper= J_upper-5/2,  J_upper-3/2, J_upper-1/2, J_upper+1/2, J_upper+3/2 and J_upper+5/2
Condition: one should ALWAYS have   J  and F cannot be negative (of course)

ATTENTION: Here, I have coded   F+.5 (as in the JPL catalog)



=================================================================

G_upper= (2*F_upper+1)  for O16-O17

G_upper= (2*J_upper+1)  for O16-O16  and O16-O18

===================================================================

Vib:  VIB=000  for transitions within the ground state
      Vib=001  for transitions withing the v=1 (first excited) vibrational state

                                                                                                                                  UPPER        LOWER
                sigma                                                           G_sup   G_inf                              Vib
                                                                                                                                  N   J  F+.5  N   J  F+.5
@   O2-67      693475.3277E+06 0.18006E-30 296  0.36837841351E-21 0.000E+00      8.0     10.0  16726.000  ----   0.000E+00 000    5   6   4    3   3   5     F'=3.5   F"=4.5   G_upper=2*3.5+1   G_lower=2*4.5+1
@   O2-67      693489.8026E+06 0.28171E-29 296  0.36836848128E-21 0.000E+00      8.0      8.0  16726.000  ----   0.000E+00 000    5   6   4    3   3   4     F'=3.5   F"=3.5   G_upper=2*3.5+1   G_lower=2*4.5+1
@   O2-67      693500.5568E+06 0.70179E-29 296  0.36836252194E-21 0.000E+00      8.0      6.0  16726.000  ----   0.000E+00 000    5   6   4    3   3   3
@   O2-66      706775.4249E+06 0.99085E-22 296  0.31277392416E-19 0.000E+00      9.0      7.0  16726.000  ----   0.000E+00 001    5   4        3   3           G_upper=2*4+1   G_lower=2*3+1  
@   O2-66      715392.9800E+06 0.19038E-18 296  0.36425852508E-21 0.000E+00      9.0      7.0  16726.000  ----   0.000E+00 000    5   4        3   3
@   O2-68      731186.6780E+06 0.57846E-18 296  0.32073351285E-21 0.000E+00      9.0      9.0  16726.000  ----   0.000E+00 000    5   4        3   4
@   O2-67      750637.9001E+06 0.31905E-19 296  0.32975594932E-21 0.000E+00      4.0      4.0  16726.000  ----   0.000E+00 000    5   4   2    3   4   2
@   O2-67      750693.0711E+06 0.10641E-19 296  0.32972019329E-21 0.000E+00      4.0      6.0  16726.000  ----   0.000E+00 000    5   4   2    3   4   3
@   O2-67      750696.2538E+06 0.10641E-19 296  0.32975594932E-21 0.000E+00      6.0      4.0  16726.000  ----   0.000E+00 000    5   4   3    3   4   2
@   O2-67      750751.4248E+06 0.36455E-19 296  0.32972019329E-21 0.000E+00      6.0      6.0  16726.000  ----   0.000E+00 000    5   4   3    3   4   3
@   O2-67      750828.3467E+06 0.16725E-19 296  0.32966854571E-21 0.000E+00      6.0      8.0  16726.000  ----   0.000E+00 000    5   4   3    3   4   4



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g-upper or lower = (2xJ+1)xfactor
 
 factor= 6 for K=0, 1, 2, 4,5 etc..
 factor=12 for K=3, 6, 9 etc.. 

                                  g_up     g_low     vib_up         vib-low  rot_up         rot_low
                                                                             J'  K'         J" K" 
@  NH3-4111     1745091898.02     372.0    372.0    0 0 0 0 a      0 0 0 0 s 15  3 0  a     15  3 0  s    12
@  NH3-4111     2434224821.22     540.0    540.0    0 0 0 0 a      0 0 0 0 s 22  9 0  a     22  9 0  s    12
@  NH3-4111     2443608325.16     270.0    270.0    0 0 0 0 a      0 0 0 0 s 22  8 0  a     22  8 0  s     6 
@  NH3-4111     2455000438.56     258.0    258.0    0 0 0 0 a      0 0 0 0 s 21  7 0  a     21  7 0  s      
@  NH3-4111     2458987678.25     246.0    246.0    0 0 0 0 a      0 0 0 0 s 20  4 0  a     20  4 0  s 
@  NH3-4111     2479013814.45     246.0    246.0    0 0 0 0 a      0 0 0 0 s 20  2 0  a     20  2 0  s 
@  NH3-4111     2497690884.58     246.0    246.0    0 0 0 0 a      0 0 0 0 s 20  1 0  a     20  1 0  s      


@  NH3-4111  2152466258616.61     186.0    174.0    0 0 0 0 a      0 0 0 0 a 15  8 0  a     14  1 0  a      6 
@  NH3-4111  2160667201222.18     186.0    186.0    0 1 0 0 s      0 1 0 0 a 15  1 0  s     15  5 0  a      6
@  NH3-4111  2165669778010.33      42.0     30.0    0 1 0 0 s      0 1 0 0 s  3  1 0  s      2  2 0  s      6


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PH3
                                      J' K'  J" K" 
@   PH3-4111         62200.00          3  3  3  -3
@   PH3-4111         93900.00         12 -6 12   6
@   PH3-4111        255900.00         13  6 13  -6
@   PH3-4111        434100.00          4 -3  4   3
@   PH3-4111        642300.00         14 -6 14   6
@   PH3-4111       1504800.00         15  6 15  -6 

@   PH3-4111 2157318355700.00          9  4  8   1
@   PH3-4111 2174976899000.00          8  1  7   2
@   PH3-4111 2197496458700.00          7  2  6   5
@   PH3-4111 2208598847800.00         11  9 10  -6
@   PH3-4111 2208598857000.00         11 -9 10   6
@   PH3-4111 2233155054600.00         10 -6  9   3


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Propane

t' and t" are for the torsion
                                  J'Ka'Kc' t' J"Ka"Kc"  t" 
@    C3H8       1371415700.00    20  7 14  0  19  8 11  0
@    C3H8       1371776600.00    20  7 14  1  19  8 12  1
@    C3H8       1371828200.00    20  7 14  5  19  8 11  5
@    C3H8       1372379400.00    20  7 13  0  19  8 12  0
@    C3H8       1372430900.00    20  7 13  2  19  8 11  2
@    C3H8       1764296700.00    28 10 18  2  27 11 16  2
@    C3H8       1764368800.00    28 10 19  0  27 11 16  0
@    C3H8       1764373000.00    28 10 18  0  27 11 17  0


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