Worked Example - Predicting the Photoelectron Spectrum of H2O
using ab initio
ab into programs can
be used to calculate the normal mode information required to
simulate electronic spectra including Franck-Condon factors. The
key parameters required for are summarized in Making a data file for simulating
vibrational structure from l
matrices. The steps below provide a worked example for the
first band in the photoelectron spectrum of water, using ab into
calculations for the required values. See the related worked
example, The Photoelectron Spectrum of
H2O for an alternative approach using
The ab into
For this exercise Molpro
is used, though many ab
initio programs will produce the same information. A
calculation including normal modes can be performed with the
following control file:
This performs a geometry optimization and normal mode
calculation for the ground state of the ion using both
Hartree-Fock and CASSCF. The same file will also work for the
ground state of the neutral if the "wf,9,2" line is removed. The more recent
versions of Molpro output in XML format that PGOPHER can read
directly; alternatively add a "put molden,H2O.molden" command after the frequencies step. This
writes out the normal mode (and other) information that PGOPHER can also read
The normal mode output that is required looks like this for the
FREQUENCIES * CALCULATION OF NORMAL MODES FOR CASSCF000
Nr Atom Charge X Y Z
1 H1 1.00 0.000000000 -1.417298632 1.034331878
2 O1 8.00 0.000000000 0.000000000 -0.130322946
3 H2 1.00 0.000000000 1.417298632 1.034331878
Frequencies dumped to record 5400.2
Gradient norm at reference geometry: 0.46187D-03
1 A1 2 A1 3 B2
Wavenumbers [cm-1] 1715.28 3721.36 3833.40
Intensities [km/mol] 53.05 2.68 14.45
Intensities [relative] 100.00 5.06 27.23
H1X1 0.00000 0.00000 0.00000
H1Y1 0.42031 0.56516 0.52478
H1Z1 0.53260 -0.39609 -0.43124
O1X2 0.00000 0.00000 0.00000
O1Y2 0.00000 0.00000 -0.06612
O1Z2 -0.06711 0.04991 0.00000
H2X3 0.00000 0.00000 0.00000
H2Y3 -0.42031 -0.56516 0.52478
H2Z3 0.53260 -0.39609 0.43124
Note the optimized equilibrium geometry (in atomic units), the
normal mode frequencies and the l matrix elements at the end. The latter
are the relative motion of each atom in a particular mode.
Setting up the simulation
There is now enough information to produce a basic simulation in PGOPHER. The Molpro output files are available
as H2OCAS.out (neutral molecule)
and H2OplusCAS.out (ion).
- Click on File, Import, l
Matrix... and select the ab initio output file generated as above. The
description below assumes you start with the output file
generated as above for the neutral molecule.
- Select View, Constants.
You will note that two states have been generated (S0 and S1), corresponding to
the HF and CASSCF stages of the calculation respectively. Only
one of these is required; to use the CASSCF calculation right
click on the first S0
and select "Delete".
(Respond "Yes to All" to the delete linked nodes
- Check that the imported values are reasonable using the l
matrix window, which displays the geometry and normal
modes. Bring this up by right clicking on the lower S1
label, and select "l matrix...". Click on "yz" to select the
correct plane for plotting, and display the normal modes by
clicking on the corresponding columns in the top grid. Note that
the numbering and symmetries will not be right at this stage,
but this is best fixed after importing the ion information. "Operate", "Print" will print
checks for the centre of mass (should be at the origin) and the
orthogonality of the normal modes, together with a lot of other
information. It is normal for rounding errors to produce numbers
slightly different from 0 and 1, but larger differences may
indicate a problem with the import. "Operate", "Orthogonalize" will force the checks to be
- For clarity, rename some of the items to more meaningful
names. Right click on the item and select "Rename" to do this. The
manifold and state, currently "S1" should both be something like "Neutral", and the "LmatrixImport" items
could be "Water"
(upper item) and "H2O" (lower item). (This structure
permits isotopically substituted species in the same file - a "D2O"
item could be added at the same level as "H2O").
- We need to set this state as the initial state in the
simulation - click on the upper "Neutral" object (the
manifold) and ensure "Initial" is set to true.
- Now import the calculations for the ion. Ensure that "Merge" is selected
under the "File" menu, so that the import does not
overwrite the steps above, then use File,
Import, l Matrix... again for the ion calculations.
Turn "Merge" off
after doing this, to avoid later confusion.
- A second "LmatrixImport"
species with two states beneath it will have been generated by
the import. As above, the second is required, so delete the "SO"
objects as before. For clarity, rename both "S1" items to "Ion".
- Copy the "Ion"
manifold to the first molecule generated above, "H2O".
To do this, right click on the "Ion" manifold (the uppermost Ion item) and select
copy. Next right click on the destination molecule (the H2O item) and select
paste. The remaining import items can then be deleted - right
click on the upper "LmatrixImport"
and select delete. The final structure aimed for is shown to the
- Now check the upper state as in state 3 above, using "Operate", "Orthogonalize" if
- The two states must now be connected by a multidimensional Franck-Condon
factor. Right click on the H2O molecule and select "Add New", "Transition Moments". A
dialog will pop up asking which states you want to connect;
select "Ion" as the
bra and "Neutral" as the ket. Now right click on
the new item, <Ion|mu|Neutral>
and select "Add New",
be set to true for this item, so that the imported l matrices are used.
- At this point, check that the atom layout and numbering is
consistent between the two imports; different choices can easily
be made, especially if the imported data is for more than one
source. Bring up the Dushinsky
Transformation Window by right clicking on the multidimensional Franck-Condon
factor, the lower <Ion|FCF|Neutral>,
and selecting "Dushinsky
matrix...". This plots equilibrium geometries for the
two states on top of each other, and any problems should be
clear from this plot.
- The symmetry can now be set; it is not imported automatically
as full symmetry is often not used in ab initio calculations. Click on the molecule
item, H2O, and
- PointGroup =
- Click on each mode in the neutral ground state in turn (v1, v2 and v3 under Neutral) and enter:
- Symmetry - the
symmetry of the mode, which you will only need to change (to
B2) for the asymmetric stretch. The l matrix window
will show that this has been imported as the first vibrational
- vMax = 0. This
selects the maximum vibrational quantum number to be
considered in each mode. The default (3 or 5) will lead to
rather a slow simulation; setting to 0 means that
vibrationally excited states are excluded.
- To rearrange the modes to the standard order, right click on
any mode and select "Sort".
will sort the modes by symmetry and then descending order of
frequency. Other menu options allow individual modes to be move
up or down; note the "global
shift" operations affect all the states in the
molecule, whereas the "Move"
operations just affect the selected state.
- Set the ionization energy by clicking on the ion ground state,
the lower "Ion",
- Origin =
86800 cm-1 = 10.7 eV. (The calculations described
above suggested an energy difference of 0.395 atomic units.)
- You should also set Symmetry
= B1 for the electronic ground state of the ion.
- Note the spin, S
should be left as zero rather than ½ as PGOPHER does not have
a specific calculation mode for ionization. Ignoring spin
effects will be a reasonable approximation unless spin
splittings are large.
- As a final step you may want to adjust the range of
vibrational quantum numbers in the excited state considered.
Click on each mode in the ion in turn (v1, v2
and v3 under Neutral) to see them;
if the product of all the vMax
is 100 or more the calculation is likely to become rather slow
in the current version of the program.
Press the simulate button () and
then the all button () and you should see a
simulation. Comparison with the empirical spectrum generated in
the related worked example, The
Photoelectron Spectrum of H2O shows that the
intensities are reasonable, though both the ionization energy
and vibrational frequencies need adjustment.
The resulting file is available as H2OCAS.pgo.