1. Double-click the Materials Science icon
   • (No icon? See Starting Maestro)

Figure 2-1. Change Working Directory option.

2. Go to File > Change Working Directory
3. Find your directory, and click Choose
4. 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/intercalation.zip
5. 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.

6. Go to File > Save Project As
7. Change the File name to intercalation_tutorial, click Save
   • The project is now named intercalation_tutorial.prj

Figure 2-3. Import structure file.

8. Go to File > Import Structures
9. Navigate to where you downloaded the provided tutorial files, choose Section_02 > spinel_LiTiS2.mae and click Open

Figure 2-4. The spinel LiTiS₂ structure in ball-and-stick representation.

The imported entry is now available in the workspace. This experimental crystal structure is available from The Materials Project Database using the searchable “Query Materials Project Database” where then the file can be Downloaded. This structure has ID mp-755414. This asymmetric unit does not need any further preparation and is ready for QE simulations.

10. 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 spinel structure
11. Change the representation to ball-and-stick by clicking on the Style menu () and choosing Apply ball-and-stick representation

To add more bonds to Li (as shown here) go to Materials Science > Preferences, then under Workspace select Materials Science. Check Ignore atomic valences when calculating bonds. Close the Preferences window. In the bottom right corner of the workspace, open the periodic structure tool window. Click Build Cell. Check Recalculate Connectivity and Recalculate Bond Orders then click Apply.

Figure 3-1. Quantum ESPRESSO Calculations panel settings.

For the convergence tests, we will use the Material Project structure of spinel LiTiS₂ imported in Section 2, see References for the database

1. With spinel LiTiS₂ includedthe entry is represented in the Workspace, the circle in the In column is blue in the workspacethe 3D display area in the center of the main window, where molecular structures are displayed and 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 in the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion, go to Tasks > Materials > Quantum Mechanics > Quantum ESPRESSO > Quantum ESPRESSO Calculations
   • The Quantum ESPRESSO Calculations panel opens
2. Ensure that Use structures from shows Project Table (1 selected entry)
3. Check the Convergence tests box
4. Go to Pseudopotentials
   • Quantum ESPRESSO Calculations - Pseudopotentials panel opens

Figure 3-2. Selecting pseudopotentials.

5. In Path click Browse
6. Navigate to where you saved the tutorial file and choose the all_pbe_UPF_v1.5 directory
   • The Pseudopotentials panel is automatically filled with the paths to the directory and to the Li, Ti and S specific pseudopotential files
   • Pseudopotentials are not included with the Quantum ESPRESSO installation and must be downloaded separately. There are several libraries available (see this link for more information). The pseudopotentials used in this tutorial can be downloaded from the GBRV pseudopotential site
7. Click OK to close the Pseudopotentials panel
   • A message appears that the energy cutoffs were not defined. Click OK.

Note: This warning can be ignored  since we will define the energy cutoffs from the result of the convergence test.

Figure 3-3. Opening the Advanced Options panel.

8. Go to Advanced Options

Figure 3-4. Advanced Options, Theory tab settings.

9. In the Theory tab, ensure the following are selected:
   • Spin-polarized for Spin treatment
     1. This is chosen because the compound of interest is magnetic
   • GGA for Density functional type
   • PBE for Density functional
   • Uncheck Use symmetry

For more information about parameter settings, see the Electronic Structure Calculations of Bulk Crystals Using Quantum ESPRESSO tutorial and the Quantum ESPRESSO Calculations documentation

Figure 3-5. Advanced Options, SCF tab settings.

10. Switch to the SCF tab
11. For Smearing, input 0.003

Figure 3-6. Advanced Options, Convergence tests tab settings.

12. Switch to the Convergence tests tab
13. Make the following selections:
    • Minimum energy cutoff to 40 Ry
    • Maximum energy cutoff to 120 Ry
    • Step size to 20 Ry
    • Charge density multiplier to 5
      1. For this system, a charge density multiplier of 5 is sufficient but can range from 8-12 in specific cases. For very accurate simulations, testing is highly recommended.
    • Check Grid plane distance, with the following settings:
      1. Max: 0.05
      2. Decrement: 0.01
      3. Steps: 4
      4. Check Include Γ-point
14. Click Save to return to the Quantum ESPRESSO Calculations panel

Figure 3-7. Starting the convergence calculation.

15. Change the Job Name to convergence_LiTiS2
16. Adjust the job settings () as needed
    • This job requires a CPU host. The job can be completed in approximately 3 days on a CPU host with 8 CPUs

Note: With the current settings the workflow will perform a number of fixed cell and frozen atom QE calculations with different energy cutoff and k-point grid combinations. The ranges for the tested values have been specified in the Convergence Test subpanel. Each calculation will be performed on 8 threads with a maximum of 1 calculation running simultaneously. So, the workflow will request 8 CPU cores assuming the machine has 8 cores and the Job Settings have not been changed. 

17. If you would like to run the job, click Run. Otherwise, we will proceed with pre-generated results
18. Close the Quantum ESPRESSO Calculations panel

Figure 3-8. Importing Structures.

By analyzing the convergence calculations, we can select reasonable values for the wavefunction energy cutoff and the k-point grid parameters to ensure required accuracy in further calculations

19. To import the pre-generated results from the main menu, choose File > Import Structures
20. Navigate to where you downloaded the tutorial file and choose convergence_LiTiS2.maegz file
21. Click Open
    • A new group with 18 structures is added to the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. The entire group is automatically 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 and the first entry includedthe entry is represented in the Workspace, the circle in the In column is blue in the workspacethe 3D display area in the center of the main window, where molecular structures are displayed
    • Maintain the entire entry group selection

Figure 3-9. Launching Convergence Tests Viewer panel.

22. From Tasks in the toolbar, search for convergence
    • Alternatively, go to Tasks > Materials > Quantum Mechanics > Quantum ESPRESSO > Convergence Tests Viewer
23. Choose Convergence Tests Viewer from the list
    • The Convergence Tests Viewer panel opens

Figure 3-10. Loading data from Workspace.

The Convergence Tests Viewer panel will be used to analyze the results of the convergence calculations

24. Click Load data from Workspace
    • This loads in the selected entry group
25. Check Convert energy to eV
26. Check Show relative energy
    • Energy values are now displayed relative to the lowest energy value in the data set

Figure 3-11. Convergence with the wavefunction cutoffs.

27. In Wavefunction cutoffs (Ry) column, shift-click all entries
    • The graph shows convergence with k-points for the different wavefunction cutoffs. We observe that a K-point grid of 3 x 3 x 3 (14 K-points) meets our convergence criteria of 1 meV/atom. There are only 14 K-points due to symmetry reduction
    • A 1 meV/atom relative energy convergence criteria is sufficient, to obtain this value we take the values graphed and divide by the number of atoms in the structure

Figure 3-12. Convergence with the wavefunction cutoff for a given k-point grid.

28. In # of K-points column, shift-click all entries
    • The graph shows convergence with wavefunction cutoff for the different k-point grids. We observe that a wavefunction cutoff of 80 Ry meets our convergence criteria of less than or equal to 1 meV/atom
    • The cutoff for the charge density is determined from the wavefunction cutoff and the multiplicator, which was defined as 5 during the convergence test

For our optimization calculation, we can proceed with a wavefunction cutoff of 80 Ry and a K-point grid of 3x3x3. For more information on running convergence calculations, see the Electronic Structure Calculations of Bulk Crystals Using Quantum ESPRESSO tutorial.

Figure 4-1. Spinel LiTiS₂ structure.

For the optimization calculation, we will use the Materials Project Database structure of spinel LiTiS₂ imported in Section 2.

1. With spinel LiTiS₂ includedthe entry is represented in the Workspace, the circle in the In column is blue and 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 in the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion, go to Tasks > Materials > Quantum Mechanics > Quantum ESPRESSO > Quantum ESPRESSO Calculations
   • The Quantum ESPRESSO Calculations panel opens

Figure 4-2. Quantum ESPRESSO Calculations panel settings.

2. Ensure that Use structures from shows Project Table (1 selected entry)
3. Check the Optimize atomic positions and cell box and uncheck all other boxes
4. Click Pseudopotentials
   • Quantum ESPRESSO Calculations - Pseudopotentials panel opens  

Figure 4-3. Selecting pseudopotentials.

The pseudopotential panel should have remembered the location of the pseudopotentials used in the convergence calculation. If this is not the case, use the next several steps to set them once again

5. In Path click Browse
6. Navigate to where you saved the tutorial file and choose the all_pbe_UPF_v1.5 directory
   • The Pseudopotentials panel is automatically filled with the paths to the directory and to the Li, Ti, and S specific pseudopotential files
7. Click OK to close the Pseudopotentials panel
   • A message appears that the energy cutoffs were not defined. Click OK.

Figure 4-4. Opening the Advanced Options.

8. Click Advanced Options

Figure 4-5. Advanced Options, Theory tab.

9. In the Theory tab, ensure the following are selected:
   • Spin-polarized for Spin treatment
   • GGA for Density functional type
   • PBE for Density functional
   • Uncheck Use symmetry
10. Set the Grid plane distance to 0.04000, check Include Γ-point, and click Update K-point mesh to update the Monkhorst-Pack grid values
    • The relationship between the density and the Monkhorst Pack definition can be checked with the Update K-point mesh option
    • A grid plane density of 0.04/Å relates to a 3x3x3 Monkhorst-Pack grid for this particular system

Figure 4-6. Advanced Options, SCF tab settings.

11. Go to the SCF tab
12. For Custom energy cutoff for wavefunctions, input 80
13. For Custom energy cutoff for charge density, input 400
14. For Max steps in SCF, input 200
15. For Smearing, input 0.003 for increased accuracy compared to the default setting

Figure 4-7. Advanced Options, Optimization tab settings.

16. Go to the Optimization tab
17. Make the following selections:
    • Number of steps to 200
    • Total energy threshold to 1e-06 Ry
    • Force threshold to 0.00050 Ry/Bohr
18. Click Save to return to the Quantum ESPRESSO Calculations panel

Figure 4-8. Starting the optimization calculation.

19. Change the Job Name to optimization_LiTiS2
20. Adjust the job settings () as needed
    • This job requires a CPU host. The job can be completed in approximately 3 days using 8 CPUs
21. If you would like to run the job, click Run. Otherwise, we will proceed with pre-generated results
22. Close the Quantum ESPRESSO Calculations panel

Figure 4-9. DFT-relaxed spinel LiTiS₂ in the workspace.

23. If you did not run the optimization yourself, from the main menu, choose File > Import Structures
24. Navigate to where you downloaded the tutorial file and choose the optimization_LiTiS2.maegz file
25. Click Open
    • A new entry group is added to the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion

Figure 5-1. DFT-relaxed spinel LiTiS₂ in the workspace.

1. With spinel LiTiS₂ includedthe entry is represented in the Workspace, the circle in the In column is blue and 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 in the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion, go to Tasks > Materials > Enumeration > Periodic Systems
   • The Enumerate Periodic Structure panel opens

Figure 5-2. Enumerate Periodic Structure panel.

Before enumerating the system, we need to define our selected atoms. We want to select all Li atoms in order to define the positions where a Li-vacancy can be generated. This can be done in many ways. Here we will use the Atom Selection menu.

2. Ensure that Use structures from shows Workspace (included entry)

Figure 5-3. The Define tool in the top toolbar.

3. Click Define in the top toolbar to open the Atom Selection panel

Figure 5-4. The Atom Selection panel.

4. In the Atom tab, choose Element, then Li
5. Add the selection
6. Click OK to close the panel

Figure 5-5. All 16 Li ions selected.

All 16 Li atoms should now be selected in the workspace

Figure 5-6. Enumerate Periodic Structure panel.

7. All 16 Li atoms are listed as the Atom Set
   • You can also type an atom name after Atom Set in case there are more sets to be defined
8. Click Add Transmutation and a row of controls for defining the transmutation is displayed

Figure 5-7. Choosing the vacancy.

9. Click Set Element to open the Choose Element dialogue
10. Select Vacancy
11. Click OK to close the panel
    • When the Choose Element panel is closed you will see that Set Element says DU

Figure 5-8. Saving the vacancy option.

12. Change the DU Concentration min value to 1 and the max value to 1
    • These values represent the minimum and maximum number of atoms to transmute from the atom selection
    • For creating Li-vacancies, we want these values to be the same to create structures with a constant number of Li-vacancies but with varying arrangement
    • For this setup, one Li atom will be removed from the spinel system creating 1 Li-vacancy
13. Click Save

Figure 5-9. Running the Enumerate Periodic Structure panel.

Under Transmutations we now see Atom set

14. Change the job Name to enumerate_Li_vacancy_1
15. Adjust the job settings () as needed
    • This job requires a CPU host. The job can be completed in approximately 5 minutes on a CPU host
16. Click Run
17. Close the Enumerate Periodic Structures panel

Figure 5-10. Spinel LiTiS₂ structure with 1 Li-vacancy.

18. When the job is finished enumerate_Li_vacancy_1 (1) will be added to the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion containing 1 structure with 1 Li vacancy
    • Due to symmetry only one unique vacancy structure is generated

We want to repeat this process to generate structures with 2, 4, 6, 8, 10, 12, 14, and 16 Li-vacancies. Follow the steps above for each of the even numbered vacancies. Make sure to delete any old transmutations in the Enumerate Periodic Structure Panel before proceeding with the next Li-vacancy structure.

Figure 5-11. All Li-vacancy structures built.

Once all the vacancy structures have been generated, 9 groups will have been added to the entry list. Many of these vacancy groups contain several possible structures.

Since we have an abundance of possible vacancy structures at most vacancy concentrations, in the next section, we are going to select a subset of structures for further calculations.

Figure 6-1. LiTiS₂ structure with one Li-vacancy.

This section will walk through the optimization of the structure with 1 Li vacancy, but note that all optimized structures at every Li-concentration are provided in the tutorial files and are necessary to produce the final voltage curve.

1. With enumerate_Li_vacancy_1 includedthe entry is represented in the Workspace, the circle in the In column is blue and 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 in the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion, go to Tasks > Materials > Quantum Mechanics > Quantum ESPRESSO > Quantum ESPRESSO Calculations
   • The Quantum ESPRESSO Calculations panel opens

Figure 6-2. Quantum ESPRESSO Calculations panel settings.

2. Ensure that Use structures from shows Project Table (1 selected entry)
3. Check the Optimize atomic positions and cell box and uncheck all other boxes
4. All optimization settings (including pseudopotentials) for the Li-vacancy structures should be identical to those in Section 4. Follow the calculation setup steps 4-31 in Section 4 

Figure 6-3. Starting the calculation.

5. Change the JobName to optimization_Li_vacancy_1
6. Adjust the job settings () as needed
   • This job requires a CPU host. The job can be completed in approximately 2 days on 8 CPUs
7. If you would like to run the job, click Run. Otherwise, we will proceed with pre-generated results
8. Close the Quantum ESPRESSO Calculations panel

Figure 6-4. DFT-relaxed spinel LiTiS₂ in the workspace.

9. If you did not run the optimization yourself, from the main menu, choose File > Import Structures
10. Navigate to where you downloaded the tutorial file and choose the optimization_Li_vacancy_1.maegz
11. Click Open
    • A new entry group is added to the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion

Figure 6-5. All possible Li-vacancy structures.

Every Li-vacancy structure created in Section 5 needs to be optimized using the same setup as described in this section. These optimizations can be run as individual jobs or in one large batch. For the purposes of the tutorial you can instead import the pre-generated provided files:

12. Import all the Li-vacant optimized structures included in the provided tutorial files
    • Including the file imported in step 24, there are 58 different optimized Li-vacancy structures
    • When the Li-vacancy structure possibilities exceeded 10 structures, only 10 different structures were selected for performing a geometry optimization

Figure 7-1. Opening the Project Table.

To plot the formation energy, we need to collect the total energy for each optimized structure from the Project Table. We will have 59 total energy values, one from the original optimized spinel LiTiS₂ structure and then 58 values from the Li-vacancy structures.

1. Open the Project Table

Figure 7-2. Opening the Property Tree.

2. Open the Property Tree by clicking Window > Property Tree

Figure 7-3. Extending the menus.

3. Expand the All menu
4. Expand the Material Science menu
5. Expand the Secondary drop down menu

Figure 7-4. Adding the Etot (Ry) values.

6. Add Etot (Ry) from the Secondary menu

The total energy values are now shown for all optimized structures, we will need each value copied into a spreadsheet or you can export the energy values from the project table by going to Data → Export → Spreadsheet

A spreadsheet with all total energy values is included in the provided files

7. Open spinelLiTiS2.xlsx with any spreadsheet program that you have available

Figure 7-5. Spinel LiTiS₂ spreadsheet.

This spreadsheet has 2 tabs. Click the Formation_Energy tab. There are 4 columns in this tab.

• Column A: Number of Li vacancies in the system
• Column B: The concentration of Li in the system, with 1 being 100%
• Column C: The total energy in Ry from the Project Table
• Column D: The formation energy (E_f)
  • E_f was calculated using Equation 1 (below)
  • Clicking on any value in Column D will show which cells were used in the formation energy calculation

Figure 7-6. Formation energy vs Li Concentration.

The calculated formation energy (column D) vs. Li concentration (column B) is plotted here.

The convex hull plot of the formation energy determines the lowest energy structure for each Li-vacancy concentration (recognizing that we only performed the calculation on a small subset for each concentration).

Feel free to visualize the corresponding low-energy structures in the workspace.

Figure 7-7. The spreadsheet showcasing the lowest energy structure.

You will notice one value for each Li concentration bolded in the spreadsheet. This is the lowest energy structure from the selected subset at each concentration. These structures will be used to calculate the voltage curve in the final section.

Figure 8-1. The optimized Li crystal structure.

Before we can approximate the voltage curve of Li_xTiS₂ against the Li metal anode, we need to calculate the total energy of the bulk Li crystal. We took the experimental bcc Li crystal structure and performed a convergence test before running a geometry optimization. Here, we will import the optimized structure, but for a more detailed explanation on optimizing bulk crystal structures using Quantum ESPRESSO, see the Electronic Structure Calculations of Bulk Crystals Using Quantum ESPRESSO tutorial

1. To import the optimized Li crystal structure file, go to File > Import Structures
2. Navigate to where you downloaded the provided tutorial files, choose Li.maegz and click Open

The optimized Li crystal structure is now in the workspace

Figure 8-2. Obtaining the Etot energy for the bulk Li crystal.

3. To obtain the total energy of the bulk Li crystal, open the Project Table and scroll until you see Etot (Ry) for the periodic_dft_import_Li entry
   • These Etot (Ry) values are already copied into the provided spreadsheet

Figure 8-3. Voltage curve tab in the provided spreadsheet.

4. Return to the provided spreadsheet, spinelLiTiS2.xlsx, and navigate to the Voltage_Curve tab  

These columns demonstrate the various steps for calculating the voltage curve from the DFT total energies