Vibrational progression of an OLED phosphorescent emitter

Triplet harvesting in OLEDs by transition metal complexes increases the maximum efficiency from 25% to 100%. Singlet excitons are rapidly converted to triplet excited states and fast phosphorescence can be achieved by strong spin-orbit coupling. In this example we calculate the frequencies of the T1 and S0 state of Pt(4,6-dFppy)(acac) in the gas phase to determine the vibronic fine structure from the Franck-Condon factors. We compare these with the experimental results from the Yersin group, who studied Pt(4,6-dFppy)(acac) in n-octane. [1] The sample command line input files can be downloaded here.

To calculate the overlap of the vibronic wave functions, we first need to calculate the frequencies of the two electronic states involved, followed by the Franck-Condon calculation. So we have three steps:

  1. Optimize the lowest singlet state (S0) and calculate frequencies
  2. Optimize the lowest triplet state (T1) and calculate frequencies
  3. Calculation of the Franck-Condon Spectrum

You can start straight away with the example input files or read further to learn how to set up these three calculations in the GUI for your own complexes.

1. Optimize lowest singlet state (S0)

First, the geometry of the complex (in its lowest singlet state) must be optimized by performing the following steps. (Another basis set and functional can be used as well.)

Remark: Pt(4,6-dFppy)(acac) has Cs-symmetry. The use of symmetry may speed up the calculation and may improve the analysis of the results.

1. SCM → New Input
2. In AMSinput make the complex by copying the xyz coordinates
3. Click the Symmetrize button SymmTool
4. Select the Task Geometry Optimization
5. Tick the Frequencies box
6. Set the XC functional to GGA:BP86
7. Set the Basis Set to TZP
8. Set the Frozen core to Small and the Numerical quality to Good
9. Run the calculation (File → Run)
/scm-uploads/doc.2021/Tutorials/_images/GO_S0.png

2. Optimize lowest triplet state (T1)

For calculating the complex in its T1 state, the same DFT settings should be applied as for S0, but an unrestricted calculation needs to be performed.

Remark: An open shell electronic configuration may break symmetry. In this case Pt(4,6-dFppy)(acac) also has Cs-symmetry in the lowest triplet state, as one may check if one looks at the results of the frequency calculation. In general, however, one may have to break symmetry in the starting geometry, in order to get a non-symmetric optimized geometry.

1. SCM → New Input
2. In AMSinput make the complex by copying the xyz coordinates
3. Click the Symmetrize button SymmTool
4. Select the Task Geometry Optimization
5. Tick the Frequencies box
6. Tick the Unrestricted box
7. Change the Spin Polarization to 2
8. Set the XC functional to GGA:BP86
9. Set the Basis Set to TZP
10. Set the Frozen core to Small and the Numerical quality to Good
11. Run the calculation
/scm-uploads/doc.2021/Tutorials/_images/GO_T1.png
The energy of the T1 state can be found at the bottom of the logfile or in the output
The difference in energy of the T1 state with respect to the S0 state can be calculated now

This difference in energy should be about 2.5 eV which is in reasonable agreement with the experimental result for the 0-0 transition, which is 21461 cm-1 (2.66 eV) for Pt(4,6-dFppy)(acac) in n-octane. [1].

3. Calculation of the Franck-Condon Spectrum

Next the Franck-Condon spectrum will be calculated. Important is to make a new AMSinput file.

1. SCM → New Input
2. On the main panel choose Properties Only as the Task
3. Make sure that the Frequencies box is ticked
4. In the panel bar, select Details → Files (Restart)
5. Choose in Properties only for the results folder of the T1 calculation (for instance T1_GeoFreq.results)
6. In the panel bar, select Properties → Franck-Condon Spectrum
7. Tick the Calculate Franck-Condon spectrum box
8. Select as the Reference state the adf.rkf file from the S0 calculation (e.g. in the S1_GeoFreq.results folder)
9. In Quanta reference state enter 5 and in Quanta current state enter 0
10. Fill in the Frequencies range: from -10000… 0 cm-1
11. Run the calculation
/scm-uploads/doc.2021/Tutorials/_images/FCF_settings.png

In this example we do not consider vibrational excitations in the T1 state (i.e. “hot states”). We therefore set the number of quanta for the T1 state to zero and only allow quanta in the S0 state. (The number of 5 quanta in S0 should be enough the get a converged spectrum, but you can try fewer/more to see if the spectrum changes.) More information about the calculation of Franck-Condon spectra can be found in the AH-FC: Adiabetic Hessian Franck-Condon section.

The output will list the spectral intensity from -10000 cm-1 to 0 cm-1 (relative to the 0-0 transition) by taking into account the overlap of the vibronic wavefunction (Franck-Condon factors). The FCF spectrum can be visualized at SCM → Spectra. The lines can be Gaussian-broadened to take into account thermal broadening.

1. SCM → Spectra
2. |Axis| → Flip Horizontal
3. Enter 300 for the Width
4. Enter 21461 (experimental 0-0 transition) for the Offset (makes the spectrum unvisible)
5. Double-click on the x-axis to open the Graph options window
6. Enter 17000 for Minimum value and 22500 for Maximum value
7. Close with OK in Graph options window (spectrum should be visible again)
/scm-uploads/doc.2021/Tutorials/_images/FCspectrum.png

References

[1](1, 2) A. F. Rausch, M. E. Thompson, H. Yersin, Triplet state relaxation processes of the OLED emitter Pt(4,6-dFppy)(acac), Chemical Physics Letters 468, 46 (2009)