Molecule Types Asymmetric Tops Samples <Prev Next>

The microwave spectrum and electric field focusing of (NO)2

For the purposes of this example a completely blank mixture will be taken for the starting point, though it would also be possible to start from the default asymmetric top. The data is taken from "Molecular beam electric resonance spectroscopy of the nitric oxide dimer", C. M. Western, P. R. R .Langridge-Smith,  B. J. Howard, and S. E. Novick, Molecular Physics, 44, 145 (1981),

Setting up the simulation

To produce a basic simulation in PGOPHER:
  1. Click on File, New, Empty Mixture.
  2. Select View, Constants
  3. Right Click on the unlabeled mixture item at the top and select "Add New...", "Species".
  4. You will probably want to rename the new species (NO)2 - right click and select "Rename"
  5. Next create a molecule object - right click on (NO)2 and select "Asymmetric Molecule"
  6. Again you will probably want to rename the new molecule (NO)2 - right click and select "Rename"
  7. The following settings need to be made at the molecule level:
    1. PointGroup = "C2v"
    2. C2zAxis = b. See figure 1 of the paper and Symmetry and Axis Systems.
    3. For the purposes of the current example we will ignore the hyperfine structure, so nNuclei will be left at 0.
    4. This implies the statistical weights should be set if correct intensities are required. In this case only the spin 1 nitrogen nuclei need be considered, so the required settings are eeWt = ooWt = 6, eoWt = oeWt = 3.
  8. Next create the ground manifold - right click on the molecule and select "Add New...", "Asymmetric Manifold". You might want to rename it to "X". As this manifold will be the initial state for all transitions, set:
    1. Initial = True
  9. Next create the ground vibrational state; right click on the manifold and select "Add New...", "Asymmetric Top". A good name for this is "v=0".
  10. Enter the rotational constants from the paper: A = 25829.4803, B = 5614.30927 and C = 4605.4396. As these are in MHz, make sure the units are showing "MHz" at the top of the constants window by clicking "Convert Units".
  11. To simulate a microwave spectrum, a dipole moment must be entered. First create a Transition Moments object to contain the dipole moment: Right click on the molecule and select "Add New...", "Transition Moments". No settings need be made for this.
  12. Now the dipole moment itself can be added. Right click on the transition moments object and select "Add New...", "Cartesian Transition Moment". The paper has μb = 0.171197 Debye so set:
    1. Axis = b to indicate that the dipole is along the b axis.
    2. Strength = 0.171197

This should be enough for a basic simulation of the microwave spectrum; press the simulate button (Simulate) and then the all button (all) and you should see a simulation. The rotational temperature is not specified in the paper, but 5 K is more likely for a van der Waals complex in a molecular beam than the default of 300 K. Changing the plot units to MHz ("Plot", "Units" "MHz") is also more reasonable for a microwave spectrum. Adjusting the frequency scale allows the three microwave transitions mentioned in the paper to be identified (at 187.5, 21224 and 22270 MHz), along with many others. The completed data file is in nodimer.pgo

Focusing in an electric field

The paper includes a plot of energy levels as a function of field, as deflection of the molecule in an electric field was essential in measuring the spectrum. The essential features of the plot can be generated as follows, starting with the file as generated above.
  1. Use "View", "Levels" to open the energy level plot window.
  2. Check the Field box to switch the mode to Electric or Magnetic Field Plots
  3. A default plot will in principle be generated, but will take rather a long time with the default settings as above. To speed things up, press "Abort" if the calculation hasn't finished and reduce the J range of the calculation. With the default settings, the maximum J will be taken from the species object, and defaults to 25. Try setting Jmax to 5.
  4. The paper used a maximum field of 80 kV/cm, so set the maximum field to 8000000 V/m
  5. Setting Top to 65e3, Bottom to -10e3 MHz, Shift Mult to 10 and unchecking Track Quanta will duplicate the figure fairly closely, though not so neatly as the states are not separated by Ka.
  6. Ka can be selected by with the Ka control.
  7. The plot below is obtained with the plot range set to just cover the states with the biggest Stark shifts, with Shift Mult reset to 1. The plot labels are added by setting Position to End. The quantum numbers on the labels are J Ka Kc M. The nodimerplot.pgo file has the plot settings included within it.

Hyperfine Structure

The hyperfine structure mentioned in the paper can also be simulated. Starting from the end of the first section:
  1. At the molecule level, set nNuclei = 2. To avoid an error message, you will also need to set JAdjustSym to false.
  2. (Optional) Rename the "Nucleus1" and "Nucleus2" items that appear to "N1" and "N2"
  3. Set the Spin of each nucleus to 1. (The spin of the nitrogen nucleus).
  4. Set AsNext for the first nucleus to true - this flags that the two nuclei are equivalent.
  5. For correct intensities, the statistical weights due to the remaining nuclei must be set. In this case this is the oxygen nuclei (with I = 0) so the required settings are eeWt = ooWt = 1, eoWt = oeWt = 0. Note versions before 7.1.145 required all 4 weights non zero, but did not handle the case of more than one pair of equivalent nuclei correctly.
  6. The hyperfine constants can now be entered into either of the nuclei. As AsNext is set, the constants are automatically copied to the other nucleus. The required values are: CHIzz = -4.06522, CHIxxmyy = -8.54983, Caa = 0.01043, Cbb = 0.01384, Ccc 0.00075. Note that these values assume that the z axis is identified with the a axis and x with b; this is controlled by the representation used and Ir is the default.
The simulation will now include hyperfine structure. You will need to zoom in to a single rotational line to see it. The completed data file is in nodimerhyp.pgo