Singlet-Triplet Intersystem Crossing Rate

Tutorial Created with Software Release: 2024-4
Topics: Organic Electronics
Methodology: Molecular Quantum Mechanics
Products Used: Jaguar, MS Maestro

Tutorial files

2 MB
This tutorial is written for use with a 3-button mouse with a scroll wheel.
Words found in the Glossary of Terms are shown like this: Workspacethe 3D display area in the center of the main window, where molecular structures are displayed

 

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Abstract:

 

In this tutorial, we will learn how to compute the singlet-triplet intersystem crossing rate for a system of organic optoelectronics.

 

Tutorial Content

  1. Introduction to Singlet-Triplet Intersystem Crossing

  1. Creating Projects and Importing Structures

  1. Calculating and Analyzing the Singlet-Triplet Intersystem Crossing Rate

  1. Conclusion and References

  1. Glossary of Terms

1. Introduction to Singlet-Triplet Intersystem Crossing

Organic light-emitting diodes (OLEDs) are key components in modern display and lighting technologies, with their efficiency and performance strongly dependent on the excited-state dynamics of the emitting materials. Two critical processes in these dynamics are intersystem crossing (ISC) and reverse intersystem crossing (RISC), both of which involve transitions between states of different spin multiplicities.

Intersystem crossing is the non-radiative transition from a singlet excited state to a triplet state, shown below. This process is crucial in phosphorescent OLEDs, where triplet states are harvested to increase efficiency. On the other hand, RISC is the transition from a triplet state back to a singlet state, enabling triplet excitons to contribute to light emission in thermally activated delayed fluorescence (TADF) materials, which are a promising class for next-generation OLEDs due to their ability to achieve nearly 100% internal quantum efficiency.

Estimating the rates of ISC and RISC is essential to understanding the efficiency of OLED emitters. Digital chemistry plays a vital role in predicting these rates, providing insights into molecular properties that control the underlying electronic transitions. Two widely used models in this context are Marcus theory and the semiclassical Marcus-Levich-Jortner (MLJ) model, both of which are grounded in the theory of electron transfer.

Marcus theory, originally developed for electron transfer, has been adapted to describe non-radiative transitions such as ISC and RISC in OLEDs. This theory treats these transitions as charge-transfer-like processes, where the rate depends on the reorganization energy (λ),the driving force (ΔG), as well as the coupling between the initial and final states. Marcus theory provides a framework for calculating ISC and RISC rates by linking them to the energy difference between singlet and triplet states (ΔEST), spin-orbit coupling, and reorganization effects.

The semiclassical Marcus-Levich-Jortner model extends Marcus theory by incorporating quantum mechanical effects of molecular vibrations. This model is particularly useful for systems where high-frequency vibrations (e.g., C–H and C–C stretching modes) significantly influence the transition rates. By accounting for both classical and quantum vibrational modes, the MLJ model offers a more detailed description of ISC and RISC, capturing the subtleties of molecular interactions that impact OLED efficiency.

Incorporating these models into computational workflows, combined with methods such as density functional theory (DFT) and time-dependent DFT (TD-DFT), allows for predictions of ISC and RISC rates (kISC and kRISC). These tools enable the exploration of material properties such as energy gaps (ΔEST) and spin-orbit coupling constants, and guide the rational design of next-generation OLED materials with enhanced emission efficiency.

In this tutorial, we apply the Marcus theory and Marcus-Levich-Jortner model to estimate the rates of kISC and kRISC, taking as representative example a neat film of 4CzDPO (2,5-bis(2,6-di(9H-carbazol-9-yl)phenyl)-1,3,4-oxadiazole), a TADF emitter. We will calculate the rates using the Optoelectronic Film Properties panel and analyze them using the Optoelectronic Film Properties Viewer.

This tutorial does not cover building the 4CzDPO system. See the Disordered System Building and Molecular Dynamics Multistage Workflows tutorial for practice building an optoelectronic film morphology system. If interested in using the Optoelectronic Film Properties panel to calculate other optoelectronic film properties see the Calculating Transition Dipole Moments (TDM), TDM Distributions, and Order Parameter, the Singlet Excitation Energy Transfer, or the Computational Ellipsometry tutorial.

2. Creating Projects and Importing Structures

At the start of the session, change the file path to your chosen Working Directorythe location where files are saved in MS Maestro to make file navigation easier. Each session in MS Maestro begins with a default Scratch Projecta temporary project in which work is not saved, closing a scratch project removes all current work and begins a new scratch project, which is not saved. A MS Maestro project stores all your data and has a .prj extension. A project may contain numerous entries corresponding to imported structures, as well as the output of modeling-related tasks. Once a project is saved, the project is automatically saved each time a change is made.

Structures can be built in MS Maestro or can be imported using File > Import Structures (or drag-and-dropped), and are added to the Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion and Project Tabledisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data. The Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion is located to the left of the Workspacethe 3D display area in the center of the main window, where molecular structures are displayed. The Project Tabledisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data can be accessed by Ctrl+T (Cmd+T) or Window > Project Table if you would like to see an expanded view of your project data.

  1. Double-click the Materials Science icon

Figure 2-1. Change Working Directory option.

  1. Go to File > Change Working Directory
  2. Find your directory, and click Choose
  3. Pre-generated files are included for running jobs or examining output. Download the zip file here: schrodinger.com/sites/default/files/s3/release/current/Tutorials/zip/isc.zip
  4. After downloading the zip file, unzip the contents in your Working Directorythe location where files are saved for ease of access throughout the tutorial

Figure 2-2. Save Project panel.

  1. Go to File > Save Project As
  2. Change the File name to isc_tutorial, click Save
    • The project is now named isc_tutorial.prj

 

Figure 2-3. The input structure entry.

  1. Go to File > Import Structures
  2. Navigate to where you downloaded the provided tutorial files, choose input.maegz and click Open

The imported entry 4CzDPO is now available in the entry list. This amorphous system is composed of 100 molecules of 4CzDPO. This system is initially built using the Disordered System Builder panel. To equilibrate the morphology, an energy minimization was followed by a 10ns molecular dynamics (MD) simulation.

3. Calculating and Analyzing the Singlet-Triplet Intersystem Crossing Rate

In this section, we will calculate the ISC / RISC rates of 4CzDPO molecules in a MD equilibrated box using the Optoelectronic Film Properties panel and visualize the results with the Optoelectronic Film Properties Viewer panel.

Figure 3-1. Opening the Optoelectronic Film Properties panel.

  1. In the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion, includethe entry is represented in the Workspace, the circle in the In column is blue and select(1) the atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection". Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries the 4CzDPO entry
  2. Go to Tasks > Materials > Quantum Mechanics > Optoelectronic Film Properties > Optoelectronic Film Properties

Figure 3-2. Setting up the Optoelectronic Film Properties panel for a ISC / RISC calculation.

  1. Ensure that Use structures from shows Workspace (included entry)
  2. Check the Singlet-triplet intersystem crossing rate option
    • Uncheck all other options
  3. Click Jaguar Options to open the Jaguar Options panel

This panel allows you to determine various optoelectronic film properties, such as order parameter (emitting dipole orientation), singlet exciton energy transfer rate, singlet-triplet intersystem crossing rate, refractive index, and extinction coefficient. See the Calculating Transition Dipole Moments (TDM), TDM Distributions, and Order Parameter, Singlet Excitation Energy Transfer, or Computational Ellipsometry tutorial for more details on performing various property calculations. Here, the singlet-triplet intersystem crossing rate tab options are explored.

Singlet-Triplet Intersystem Crossing Rate tab: Specify the molecule and corresponding parameters for the singlet-triplet intersystem crossing rate calculation.

Compute rate for these molecules option menu: Select the molecule type for which the intersystem crossing rate should be computed.

Intersystem crossing reorganization energy text box: The energy required to reorganize the molecular geometry and surrounding environment as the molecule of interest transitions from singlet to triplet electronic state during ISC, accounting for the relaxation of nuclear and solvent coordinates before and after the transition.

Reverse intersystem crossing reorganization energy text box: The energy required to reorganize the molecular geometry and surrounding environment as the molecule of interest transitions from singlet to triplet electronic state during RISC, accounting for the relaxation of nuclear and solvent coordinates before and after the transition.

Quantum mechanical reorganization energy text box: The quantum-mechanical contribution to the reorganization energy in the Marcus-Levich-Jortner (MLJ) model refers to the portion of the total reorganization energy associated with high-frequency vibrational modes, which is used to calculate the Huang-Rhys parameters.

For detailed information about the various parameters in the panel, see the help documentation.

Figure 3-3. Setting the Jaguar Options.

  1. Change the Basis set to 6-31G**
  2. Check the Excited state (TDDFT) option
  3. Click OK to close the panel

Figure 3-4. Running the ISC / RISC calculation.

  1. Keep all default options
    • Default values were used for simplicity. However, for accurate prediction of the ISC / RISC rates one is recommended to estimate the reorganization energies associated with the ISC and RISC transitions  using the potential energy surfaces of the related triplet and singlet states.
  2. Change the Job name to opto_film_props_4CzDPO
  3. Adjust the job settings () as needed
    • This job requires a CPU host and can be completed in about 8 hours on 8 processors
  4. If running the job, proceed to click Run. If you would prefer to proceed with imported files, please proceed to the next steps.
  5. Close the Optoelectronic Film Properties panel

Figure 3-5. The calculation output.

Let’s import the results:

  1. Go to File > Import Structures
  2. Navigate to where you downloaded the provided tutorial files, choose Section_03 > opto_film_props_4CzDPO > opto_film_props_4CzDPO-out.maegz
  3. Select(1) the atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection". Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries and includethe entry is represented in the Workspace, the circle in the In column is blue the output in the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion and workspacethe 3D display area in the center of the main window, where molecular structures are displayed, respectively.
    • Note that the structure will resemble the input structure, but now also contains the data from the Optoelectronic Film Properties calculation
  4. Use the WAM (workflow action menu) button () to open the Optoelectronic Film Properties Viewer
    • Alternatively, access the panel via Tasks > Materials > Quantum Mechanics > Optoelectronic Film Properties > Optoelectronic Film Properties Viewer

Figure 3-6. Viewing the Optoelectronic Film Properties result.

  1. Ensure that the Singlet-triplet intersystem crossing rate tab is selected
    • ISC (S1 → T1) Marcus rate is 9.38 × 107 ± 1.38 × 108 1/s
    • The Marcus and Marcus-Levich-Jortner rates are dependent on the underlying DFT functional (including various modifications) and reorganization energy values
  2. Select Marcus RISC from the Property drop down menu

 

Figure 3-7. Viewing the Marcus RISC results.

The calculated RISC (S1 → T1) Marcus rate is 1.05 × 106 ± 1.87 × 106 1/s

  1. Select Singlet Energy from the Property drop down menu

Figure 3-8. Viewing the Singlet Energy.

The S1 excited state energy is 2.99 ± 0.15 eV, which is the middle of the gaussian curve plotted in the viewer.

Feel free to explore the rest of the panel and property options before closing the viewer.

4. Conclusion and References

In this tutorial, we learned how to compute the singlet-triplet intersystem crossing rate for optoelectronic materials using MS Maestro.

For further learning:

For introductory content, focused on navigating the Schrödinger Materials Science interface, an Introduction to Materials Science Maestro tutorial is available. Please visit the materials science training website for access to 80+ tutorials. For scientific inquiries or technical troubleshooting, submit a ticket to our Technical Support Scientists at help@schrodinger.com.

For self-paced, asynchronous, online courses in Materials Science modeling, including access to Schrödinger software, please visit the Schrödinger Online Learning portal on our website.

For some related practice, proceed to explore other relevant tutorials:

For further reading:

 

 

5. Glossary of Terms

Entry List - a simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion

Included - the entry is represented in the Workspace, the circle in the In column is blue

Project Table - displays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data

Recent actions - This is a list of your recent actions, which you can use to reopen a panel, displayed below the Browse row. (Right-click to delete.)

Scratch Project - a temporary project in which work is not saved, closing a scratch project removes all current work and begins a new scratch project

Selected - (1) the atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection". Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries

Working Directory - the location where files are saved

Workspace - the 3D display area in the center of the main window, where molecular structures are displayed