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), http://dx.doi.org/10.1080/00268978100102341.
Setting up the simulation
To produce a basic simulation in PGOPHER:
- Click on File, New,
- Select View, Constants
- Right Click on the unlabeled mixture item at the top and
select "Add New...", "Species".
- You will probably want to rename the new species (NO)2 - right
click and select "Rename"
- Next create a molecule object - right click on (NO)2 and
select "Asymmetric Molecule"
- Again you will probably want to rename the new molecule (NO)2
- right click and select "Rename"
- The following settings need to be made at the molecule level:
- PointGroup =
- C2zAxis = b.
See figure 1 of the paper and Symmetry
and Axis Systems.
- For the purposes of the current example we will ignore the
hyperfine structure, so nNuclei will be
left at 0.
- 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.
- 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:
- Initial = True
- 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".
- 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".
- 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.
- 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:
- Axis = b to
indicate that the dipole is along the b axis.
- Strength = 0.171197
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.
This should be enough for a basic simulation of the microwave
spectrum; press the simulate button () and then the all button () 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
- Use "View", "Levels" to open the energy
- Check the Field
box to switch the mode to Electric or
Magnetic Field Plots
- 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
- The paper used a maximum field of 80 kV/cm, so set the maximum
field to 8000000 V/m
- 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.
- Ka can be selected by with the Ka control.
- 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.
The hyperfine structure mentioned in the paper can also be
simulated. Starting from the end of the first section:
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
- At the molecule level, set nNuclei = 2. To
avoid an error message, you will also need to set JAdjustSym to
- (Optional) Rename the "Nucleus1" and "Nucleus2" items that
appear to "N1" and "N2"
- Set the Spin of each nucleus to 1. (The spin of the nitrogen
- Set AsNext for the
first nucleus to true - this flags that the two nuclei are
- 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.
- 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.