Molecule Types Vibrational Structure Vibrational Energy Levels and Franck-Condon Factors | <Prev Next> |

The key parameters required for a simulation of a vibrational
spectrum are summarized in Making a
basic data file for simulating vibrational structure. The
steps below show how to do this for the first band in the
photoelectron spectrum of water, using literature values for
constants where available. See the related worked example, Predicting the Photoelectron Spectrum
of H_{2}O using ab
inito Calculations for an alternative approach.

An excellent compilation of spectroscopy constants for can be
found in the NIST Chemistry web book at http://webbook.nist.gov/chemistry/.
A formula search on H_{2}O with ions not excluded yields
information on several isotopes; selecting the main isotope and
then "Vibrational and/or electronic energy levels" yields for H_{2}O:

Sym Species |
No | Approximate type of mode |
Selected Freq |

a1 |
1 |
Sym str |
3657 |

a1 |
2 |
Bend |
1595 |

b1 |
3 |
Anti str |
3756 |

Confusingly the asymmetric stretch, v_{3}, is shown as
having b_{1} symmetry in this table, though the modern
convention is to classify this mode as b_{2}. The b_{2}
symmetry follows if the out of plane axis is chosen to be the x axis, the current
convention, while b_{1} symmetry follows if the out of
plane axis is chosen to be the y axis. The choice is not
necessarily important for the simulation, but it is important to
be consistent.

Selecting "Gas phase ion energetics data" gives an ionization
potential of 12.621 eV; see below for some discussion of this
value.

For the ion information on several states is available; taking
just the most recent ground state (X state) gas phase values:

Vib Sym |
No | Approximate type of mode |
cm^{-1} |

a1 |
1 |
Sym stretch |
3197.97 |

a1 |
2 |
Bend |
1408.42 |

b2 |
3 |
Asym Stretch |
3253.91 |

Note that the asymmetric stretch is shown as b_{2}
here. More detailed simulations would have to consider
anharmonicities.

- Click on File, New, Vibrational Spectrum.
- Select View, Constants
- Click on "
`VibratingMolecule`". This sets the parameters common to all states, and the ones that need to be changed from the default values are:

- PointGroup = "C2v"
- nModes = 3. This is the number of vibrational modes. Note that you should not set the number of atoms (nNuclei) unless you want to input an l matrix for each state.
- No changes need to be made at the manifold level for the
neutral, "Ground",
though you may want to rename it to "Neutral", by right clicking on it and
selecting "Rename".

- Click on each mode in the neutral ground state in turn (v1, v2 and v3 under X) and enter:
- Omega - the frequency from the first table above.
- Symmetry - the
symmetry of the mode, which you will only need to change for
the asymmetric stretch, v
_{3}. - 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.

- The manifold labeled "Excited" corresponds to the ion; no changes need to be made here, though you may want to rename it to "Ion".
- Click on the ion ground state, "A" and set:
- Symmetry = B1 - the symmetry of the electronic ground state of the ion.
- Origin =
101795 cm
^{-1}= 12.621 eV. This is the energy of the ground state of the ion with respect to that of the ground state of the neutral, the ionization energy. (Strictly this is the difference in energy between the minima of the potential energy curves for the two states.) Tip: to avoid having to convert the value from eV, click on the Convert Units button until the units show "eV", enter the value in eV and then click on the button again until cm^{-1}appears. - You may want to rename the state to X or perhaps IonX, as it is the ground state of the ion, rather than the A state.
- 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.
- Click on each mode in the ion ground state in turn (v1, v2 and v3) and enter:
- Omega - the frequency from the second table above.
- (The symmetry will have been set in step 5.2 above.)
- Leave vMax as the default here; you may need to adjust this depending on the length of the vibrational progressions.
- The default geometry change is too large; as the ionization here is from a non-bonding orbital an initial assumption of no change would be more reasonable. Click on each normal mode under the multidimensional Franck-Condon factor, <IonX|FCF|X> and ensure:
- Displacement
= 0. This represents the change in each normal mode.

This should be enough for a basic simulation; press the
simulate button () and then the all
button () and you should see a simulation,
though it will essentially have only one peak as we are assuming
no geometry change on ionization.

It is important to check simulations, not only because it is easy to make mistakes in the steps above, but also because there can be differences in the definitions of the constants or other factors, such as the different choice of symmetry for the asymmetric stretch described above. Checking against tabulated line positions or published spectra is an effective check; note the facility for overlaying pictures (from a Journal for example) onto a simulation.

In this case an experimental simulation is
available from R. N. Dixon, G. Duxbury, J. W. Rabalais and L.
Åsbrink, "Ro-vibronic structure in the photoelectron
spectra of H_{2}O, D_{2}O and HDO", Molecular
Physics, 31, 423, http://dx.doi.org/10.1080/00268977600100311.
This shows that, while the first peak is indeed the strongest,
about ¼ of the intensity is in the other peaks. Manually
adjusting the vibrational displacements to v1 = 0.07, v2 = 0.07
gives a reasonable match for the observed intensities. As a
final point, the peaks are all shifted from the simulation - the
strongest peak is simulated at 12.550 eV but measured at 12.624
eV. The difference here (0.074) is likely to be the zero point
energy; this could be checked by looking at the individual
vibrational levels - selecting "View", "States". Adding 0.074eV = 600 cm^{-1}
to the ion origin brings the spectra into line, as shown in the
plot below.

To obtain the plot the plot units were set to eV ("Plot", "Units", "eV") and a Gaussian width of 0.04 eV was selected (The "Gau" box on the main window toolbar). The completed file is available as H2OPES.pgo.