Optoelectronics Properties

This topic describes the optoelectronic properties generated in an optoelectronics calculation, and the methods used for the calculation. The calculations can be set up in the Optoelectronics Calculations Panel.

All calculations begin with a gas phase optimization of the ground state, neutral molecule. This calculation is only performed once and used for all properties. All successive calculations are run with the same method and basis set. If calculations on the cation or anion are required for more than one property, they are only calculated once. For the anion calculations, it may be advisable to add diffuse functions to the basis set.

Screening Calculations

The Screening calculation method is intended to produce high quality results with a small basis set. This method uses the MIDI! basis set (Jaguar basis MIDIX). Because this basis set lacks d functions on carbon atoms, calculations generally run much faster with this basis set than with more common basis sets such as 6-31G*. Because d functions are included on other heavy atoms including N, O and F, results are similar to 6-31G* in quality and significantly improved over 3-21G(*). However, MIDI! does not have coverage for many elements in the periodic table, so by default the following algorithm is used to assign the basis set for screening calculations so that they can be run over most of the periodic table. For any element for which MIDI! is not defined, 6-31G* is used if it is defined for that element; if 6-31G* is not defined for that element, LACV3P is used. If the basis set for screening is changed to any basis set other than MIDI! (basis=midix), this algorithm is not applied.

Oxidation and Reduction Potentials

Two different methods can be used for oxidation and reduction potentials: a Koopmans' approximation and an adiabatic method. The selection of the methods can be made in the Advanced Options dialog box of the Optoelectronics Calculations panel.

For the Koopmans Approximation, the potential is calculated with the following formula.

Potential = slope * Orbital_energy + intercept

The value of Orbital_energy is taken to be the HOMO energy from the neutral molecule for the oxidation potential, and the LUMO energy for the reduction potential. The values of the slope and intercept were obtained by linear regression against experimental oxidation and reduction potentials over a wide range of OLED materials, including hole and electron transporting materials, emitting materials, organics and organometallic complexes. These values were developed using B3LYP with the default basis set for screening calculations (see Screening Calculations above) and are not directly applicable to other methods and basis sets.

Koopmans' approximation only requires a single calculation on the neutral molecule in the ground state. It is the default method for Screening calculations. It is significantly faster and more robust than the adiabatic method. In addition, because it has been parameterized to experimental data, it is likely to produce results that are as good as or better than the adiabatic method.

The adiabatic potentials are calculated with the following formulae:

Oxidation Potential = E_electrode + E_electron + E_cation − E_neutral
Reduction Potential = E_electrode + E_electron + E_neutral − E_anion

This method requires calculations on the neutral species and the ions. The ion geometries are optimized in the gas phase, just as for the neutral molecule. Single-point calculations are performed with aqueous continuum solvation (PBF) at the optimized gas-phase geometries. E_electron is taken as -4.28 eV and E_electrode is the potential of the electrode chosen in the Advanced Options dialog box.

It may be advisable to include diffuse functions in the basis set when calculating reduction potentials with the adiabatic method.

The properties are shown in Maestro as optelec Oxidation Potential (eV) and optelec Reduction Potential (eV).

Scaled HOMO and LUMO Values

HOMO and LUMO energies are often derived from experimental redox potentials, using the following expressions:

Absolute_Electrode = NHE_Energy + Electrode_Potential
Orbital_Energy = Absolute_Electrode − Redox_Potential

where NHE_Energy is the energy of the NHE electrode in water, taken to be −4.28 V [3], and Electrode_Potential is the potential of the chosen electrode relative to NHE.

The HOMO and LUMO energies so obtained are rarely comparable to computed HOMO and LUMO energies. However, computed redox data (particularly from the default Screening mode) are comparable to experimental redox data. So "scaled" HOMO and LUMO energies are calculated from the computed redox data using the same expressions, for comparison with those derived from experiment.

The properties are shown in Maestro as optelec Scaled HOMO (eV) and optelec Scaled LUMO (eV).

Hole and Electron Reorganization Energies

The reorganization energy is the sum of the energy for the neutral molecule to relax from the ion geometry to the neutral geometry and the energy for the ion to relax from the neutral geometry to the ion geometry.

E_reorg = (E_vert_neutral − E_opt_neutral) + (E_vert_ion − E_opt_ion)

Geometry optimizations are performed on the neutral and the ionic species, and single-point calculations for the neutral at the ion geometry (E_vert_neutral) and the ion at the neutral geometry (E_vert_ion) are then performed, all in the gas phase.

The properties are shown in Maestro as optelec Hole Reorganization Energy (eV) and optelec Electron Reorganization Energy (eV).

In addition to the reorganization energy, extraction potentials and small-polaron stabilization energies are computed, as follows:

E_extract = (E_opt_ion − E_vert_neutral)

E_stabil = (E_vert_ion − E_opt_ion)

These properties are shown in Maestro as optelec Hole Extraction Potential (eV), optelec Electron Extraction Potential (eV), optelec Hole Small Polaron Stabilization Energy (eV) and optelec Electron Small Polaron Stabilization Energy (eV).

Triplet Energy and Triplet Reorganization Energy

The triplet energy property is the energy of the relaxed lowest triplet state relative to the energy of the relaxed ground state. The formula used includes corrections that can be parametrized:

E_trip = slope * (E_triplet_state − E_ground_state) + intercept

The energy of the triplet state is calculated using unrestricted DFT (UDFT) to optimize its geometry. The slope and intercept were parametrized for the Screening calculation method, using B3LYP and the default screening basis set. The energy without the parametrization is reported as optelec T1 Raw Triplet Energy (eV).

The triplet reorganization energy is defined in a similar manner to the hole and electron reorganization energies:

E_trip_reorg = (E_vert_ground − E_opt_ground) + (E_vert_triplet − E_opt_triplet)

Similarly, the triplet stabilization energy is defined as:

Geometry optimizations are performed on the ground state and the triplet state, and single-point calculations for the ground state at the triplet geometry (E_vert_ground) and the triplet at the ground state geometry (E_vert_triplet) are then performed, all in the gas phase.

The properties are shown in Maestro as optelec Triplet Energy (eV) and optelec Triplet Reorganization Energy (eV).

When the triplet reorganization energy is calculated, three other properties are also calculated:

E_trip_abs = (E_vert_triplet − E_opt_ground)

E_trip_emisson = (E_opt_triplet − E_vert_ground)

E_trip_stabil = (E_vert_triplet − E_opt_triplet)

These properties are reported as optelec T1 Vertical Absorption (eV), optelec T1 Vertical Emission (eV), and optelec Triplet Stabilization Energy (eV).

Absorption Spectrum

The absorption spectrum is calculated from vertical excitation energies computed with TD-DFT (itddft=1) in the Tamm-Dancoff approximation (itda=1 ) at the neutral molecule geometry. Five states are calculated (nroot=5). The spectrum can be viewed in the Spectrum Plot panel, accessible from Quantum Mechanics → Plot Spectra.

In addition, this calculation computes properties based on the full spectrum. This full spectrum is obtained by line-broadening the computed transitions. The broadening is done by placing a Lorentzian curve centered on each transition. Each curve has a line width of 40 nm and a height equal to the oscillator strength of the transition. The sum of all curves is then taken to form the full absorption spectrum. The same method is used when plotting the spectrum on the Spectrum Plot panel. From this full spectrum, the following properties are computed.

• Lmax—The wavelength in the visible region for which the spectrum has the highest intensity. This might not correspond to the wavelength of the lowest energy transition because a) a higher energy transition may have higher intensity, or b) two transitions may add together to form a peak centered on neither transition. Since 390 nm is considered the short wavelength cutoff of the visible spectrum, an absorption spectrum with no or only trivial peaks in the visible spectrum will typically show an Lmax value of 390. This property is shown in Maestro as optelec Lmax (nm).

• Red Area/Green Area/Blue Area—These are the integrated areas under the absorption spectrum in the stated red, green or blue region. For the purposes of these properties, the region definitions are:

  blue: 390-490
  green: 490-590
  red: 590-750

  These areas are useful in a relative comparison of the shifting absorption window between structures. They can, for instance, offer a quick analysis of which structure in a series has the most (or least) absorption in the green region. Since the spectra are scaled by the computed oscillator strength of the transitions, a change in area can occur due to a change in intensity or a shifting of the peak to shorter or longer wavelengths. The integrated areas are shown in Maestro as optelec Blue Area, optelec Green Area, and optelec Red Area.

Excited Singlet Energies and S1-Tx Energy Separations

The nth excited singlet state energy is shown in Maestro as optoelec Sn at S0 (eV). The corresponding transition dipole moment of these excitations are shown in Maestro as optelec Sn at S0 Transition Dipole (D). The energy gap between the lowest three triplet states (T1, T2, and T3) and the first excited singlet state (S1) state is calculated using TDDFT, using the S0 (ground) state as the reference. The gap can be calculated either at the equilibrium geometry of the T1 state or the equilibrium geometry of the S0 state. This gap is useful for assessing the possibility of thermally-activated delayed fluorescence. The properties are shown in Maestro as optelec S1-Tn Gap (eV).

Fluorescence

The energy of the first excited singlet state (S1) is optimized using TDDFT, and the wavelength of the fluorescence maximum and the integrated areas in the red, green, and blue regions are calculated. These are defined in the same way as for the absorption spectrum. No spectrum file is generated, as there is only a single transition under consideration, and no account is taken of the oscillator strength for the transition. The emission wavelength is shown in Maestro as optelec Emax (nm), and the integrated areas are shown in Maestro as optelec Emission Blue Area, optelec Emission Green Area, and optelec Emission Red Area.