Nudged Elastic Band (NEB)

DFTB Catalysis AMS Driver Nudged Elastic Band (NEB) Transition state Reaction barrier PLAMS

In this tutorial we will use the climbing-image Nudged Elastic Band method (NEB) to identify the minimum energy path of:

• a chemical reaction in vacuum

• ionic diffusion in a solid

Transition state of a chemical reaction

In this first example, we will find the minimum energy reaction path and transition state of the following reaction:

We will be using the DFTB engine with the GFN1-xTB model. This is a computationally fast method (which is convenient for the purposes of a tutorial) but it is not very accurate in predicting reaction energies. For better accuracy, using the DFT engine ADF (or BAND) is recommended.

Setting up and running the calculation

You can set up and run the calculations for this tutorial using either the Graphical User Interface (GUI), the python library PLAMS or a bash script.

GUI

Start AMSjobs

1. in the menu bar select SCM → New input

This will open a new AMSinput window.

In AMSinput:

1. Switch to the DFTB panel: →

2. Select Task → NEB

We will use the GFN1-xTB model, which is the default model as of the AMS2020 release. Your AMSinput window should look like this:

When setting up an NEB calculation we need to specify two systems: the initial and final states of the reaction. The NEB algorithm will then generate a set of images by interpolating between the initial and final systems. This will be the initial approximation of the reaction path, which will be optimized during the NEB calculation.

1. Download the following xyz files: file NEB_initial.xyz and NEB_final.xyz

2. Import the coordinates of the initial system: in the menu bar, select File → Import Coordinates (System)… and select the file NEB_initial.xyz

3. Create a new molecule-tab: in the menu bar, select Edit → New Molecule…

4. Import the coordinates of the final system in the newly created molecule tab: in the menu bar, select File → Import Coordinates (System)… and select the file NEB_final.xyz

You can easily switch between molecule tabs using the arrows at the bottom of the molecule drawing area. Here, you’ll also see the molecule names, such as C2H4N2O for the first molecule and NEB_final for the second. Note that the GUI has the following naming convention:

• Main System: The first molecule is considered the main system, and is often automatically assigned its chemical formula as the name.

• Additional Molecules: For any additional molecules, the GUI uses by default the name from their original XYZ files.

Important

In NEB calculations, the order of the atoms in the initial and final system should be the same (if you provide an intermediate system, you should use a consistent atom-ordering for that too). The order of the atoms should be consistent because the images-interpolation algorithm maps the n-th atom of the initial system to the n-th atom of the final system.

You can see the indices of the atoms by clicking in the menu bar on Properties → Atom Info → Name → Show. It is possible to change the order of the atoms in the Coordinates panel (in the panel bar: Model → Coordinates) using the Move atom(s) option.

Now, go to the NEB details panel where we will set up the NEB calculation:

1. Click on next to Task → NEB to go to the NEB details panel

2. From the drop-down menu next to initial system, select C2H4N2O or NEB_initial depending on the name (may differ between AMS versions).

3. From the drop-down menu next to final system, select NEB_final

4. Check the Characterize PES point checkbox

Your AMSinput window should look like this:

Tip

From most AMSinput panels you can jump to the relevant section of the user manual by clicking on , which is located in the top-right corner of the panel.

We are now ready to run the calculation:

In AMSinput:

1. In the menu bar, click on File → Save and give it the name “NEB_tutorial”

2. In the menu bar, click on File → Run . This will bring the AMSjobs window to the front

3. Wait for the calculation to finish. It should take just a few seconds

In the logfile you can monitor the progress of your NEB calculation:

In AMSjobs:

1. Select the job “NEB_tutorial” and in the menu bar click on SCM → Logfile. This will open the logfile

A NEB calculation consists of several steps, which are automatically executed one after the other:

• first, the two end points (the initial and final molecules) are optimized (in the logfile, look for Optimizing initial state and Optimizing final state)

• then the NEB reaction path will be optimized (in the logfile, look for NEB Path Optimization). During the reaction path optimization, the highest-energy image on the path will climb to the transition state

• finally, a single point calculation for the TS is performed (in the logfile: Final calculation for highest-energy image). If the option Characterize PES point is on, then the lowest-lying normal modes will be calculated in order to validate the TS (the TS should have exactly one imaginary frequency). Some information on the reaction path is printed at the end of the logfile:

  NEB found a transition state!
  TS barrier height from the left           0.02576078 Hartree
                                           16.165 kcal/mol
                                           67.635 kJ/mol
  TS barrier height from the right          0.08632064 Hartree
                                           54.167 kcal/mol
                                          226.635 kJ/mol
  

Bash script

The following bash script performs an NEB calculation using the AMS driver and the DFTB engine. The input options for the AMS driver described in the AMS driver manual, while the DFTB manual describes the input options for the DFTB Engine block.

#!/bin/sh

"$AMSBIN/ams" << eor

Task NEB

Properties
    PESPointCharacter Yes
End

# The initial system (no header)
System
    Atoms
        N  1.88630912 -0.34204867 -1.59424245
        N  1.14203025 -1.15084766 -1.95458206
        O  0.07639739 -1.27682918 -1.40578886
        C  0.74766633  1.24132374  1.29097263
        C -0.52735637  0.87051548  1.20080269
        H  1.08791192  2.15092371  0.80682956
        H -1.23438622  1.47569873  0.64278673
        H -0.86675778 -0.04061999  1.68265930
        H  1.45534611  0.63457332  1.84647164
    End
End

# The final system should be called 'final'
System final
    Atoms
        N  1.44280525  0.39326405  0.02115802
        N  0.56588608 -0.32983790 -0.53167497
        O -0.68785300 -0.26603404 -0.00725496
        C  0.86550207  1.12517445  1.10513146
        C -0.57889386  0.65549932  1.05974328
        H  0.94852175  2.21696742  0.91684905
        H -1.26384434  1.51200042  0.88137995
        H -0.85746564  0.15513847  2.01191277
        H  1.35845740  0.84559176  2.06071421
    End
End

Engine DFTB
    Model GFN1-xTB
EndEngine
eor

Important

In NEB calculations, the order of the atoms in the initial and final system should be the same (if you provide an intermediate system, you should use a consistent atom-ordering for that too). The order of the atoms should be consistent because the images-interpolation algorithm maps the n-th atom of the initial system to the n-th atom of the final system.

To run the calculation:

1. Save the above script in a file called NEB.run

2. Make the script executable: in a terminal, type chmod +x NEB.run

3. Run it interactively and redirect the output to a file: in a terminal, type ./NEB.run > out

Python

See the NEB scripting example.

To improve the initial approximation of the reaction path in an NEB calculation, you can (optionally) provide an intermediate system.

Another important NEB option is the number of images. In case of problematic NEB path optimization convergence, using more images might help (note that the computation time increases with the number of images used).

You can read more about the various NEB options in the AMS manual.

Results of the calculation

GUI

Now, let’s visualize the reaction path computed by NEB:

In AMSjobs:

1. Select the job “NEB_tutorial” and, in the menu bar, click on SCM → Movie. This will open the AMSmovie module

In AMSmovie, you can click on play (or drag the slide-bar) so see the reaction happening. On right-hand side, the energy and gradients of the images in the NEB reaction path are plotted.

The transition state is characterized by having one imaginary frequency. Let’s visualize the normal modes of the transition state geometry with AMSspectra:

In AMSmovie:

1. click on SCM → Spectra. This will open the AMSspectra

Here you will see the computed normal modes for the TS geometry. Notice that there is one negative frequency (imaginary frequency are shown as negative numbers).

In AMSspectra:

1. In the table, click on the line with the negative frequency

The corresponding normal mode will be displayed in the molecule-visualization area. This normal mode gives you an idea of how the atoms are moving as they cross the transition state.

Bash script

In the folder where you executed your script you will find a file out, which contains the text-output of the calculation, and a folder called ams.results containing binary results of the calculation.

At the end of the output file out you will find a section summarizing the results of the NEB calculation:

NEB found a transition state!


------------------------------------------------------------
TS barrier height from the left           0.02581511 Hartree
                                         16.199 kcal/mol
                                         67.778 kJ/mol
TS barrier height from the right          0.08637041 Hartree
                                         54.198 kcal/mol
                                        226.765 kJ/mol
Reaction energy                          -0.06055530 Hartree
                                        -37.999 kcal/mol
                                       -158.988 kJ/mol
------------------------------------------------------------
        Transition state geometry

--------
Geometry
--------

Atoms
Index Symbol   x (angstrom)   y (angstrom)   z (angstrom)
   1      N     1.76794468     0.02199401    -0.76530642
   2      N     0.86568320    -0.56021023    -1.14090273
   3      O    -0.28459962    -0.76023024    -0.92163051
   4      C     0.89983351     0.97770099     0.84893165
   5      C    -0.38912967     0.55813520     0.80607959
   6      H     1.18303105     1.94163319     0.44757192
   7      H    -1.15509240     1.14579400     0.31965225
   8      H    -0.73127815    -0.27639812     1.40152984
   9      H     1.61076814     0.51427067     1.51998360

The folder ams.results contains:

• a text file called ams.log containing a very concise summary of the calculation’s progress during the run.

• the main binary results file ams.rkf, containing the reaction path computed in the NEB calculation.

• the engine results file NEB_TS_final.rkf corresponding a single point calculation at the transition state geometry. It contains, among other properties, the normal modes.

You can explore the content of the rkf binary results files using the kfbrowser utility.

In a terminal, type: $AMSBIN/kfbrowser ams.results/NEB_TS_final.rkf

The binary results of the calculation can also be visualized with the GUI modules:

In a terminal, type: $AMSBIN/amsmovie ams.results/ams.rkf

In a terminal, type: $AMSBIN/amsspectra ams.results/NEB_TS_final.rkf

Ionic diffusion in a solid

In this second example, we will determine the minimum energy path and the activation energy of Li diffusion in a typical cathode materials LiTiS₂.

We will use the ML potential engine with the M3GNet universal machine learning potential. Although M3GNet was trained to reproduce ground state structures of the Materials Project database, it can also be accurate to describe transition states, as we will demonstrate in this tutorial. This tutorial can be reproduced with the periodic DFT engine BAND.

Important

First, make sure to install the M3GNet package inside AMS as described in the M3GNet tutorial.

Note

When using M3GNet, you can include dispersion via an “engine addon” option. In the following, D3 dispersion will be included throughout.

Layer LiTiS₂ cathode material

In some Li-based cathode materials, the diffusion of Li ions is tightly connected to the content of Li in the materials. We would like to demonstrate this by computing

• the diffusion barrier of Li in LiTiS₂ with 1 Li vacancy, and

• the diffusion barrier of Li in LiTiS₂ with 2 Li vacancies.

In LiTiS₂, the lithium ions are octahedrally coordinated between the S−Ti−S sandwich layers.

Li diffusion in LiTiS₂ with 1 vacancy

To perform the NEB calculation we will use the graphical user interface. Either

• build the systems manually (next step), or

• import them directly (skip to the next section)

Build LiTiS₂ initial and final structures with 1 vacancy

We will start with a supercell of crystalline LiTiS₂, constructed from the optimized lattice parameters, and then introduce a vacancy.

Import the pristine system

Start AMSinput: SCM → New Input

Now, either

• download LiTiS2_supercell_pristine.in and import it (File → Import coordinates…), or

• copy-paste the below coordinates into AMSinput.

  Reveal copy-pastable coordinates

  System
      Atoms
          Li 1.71915 2.9776551458 6.174905 
          Ti 1.71915 2.9776551458 3.0874525 
          S 1.71915 4.9627585764 4.5513282748 
          S 3.4383 3.9702068611 7.7984817252 
          Li 3.4383 5.9553102917 0.0 
          Ti 3.4383 5.9553102917 9.2623575 
          S 3.4383 7.9404137222 10.7262332748 
          S 5.15745 6.947862007 1.6235767252 
          Li 3.4383 5.9553102917 6.174905 
          Ti 3.4383 5.9553102917 3.0874525 
          S 3.4383 7.9404137222 4.5513282748 
          S 5.15745 6.947862007 7.7984817252 
          Li 6.8766 0.0 0.0 
          Ti 6.8766 0.0 9.2623575 
          S 6.8766 1.9851034305 10.7262332748 
          S 8.595750000000001 0.9925517153 1.6235767252 
          Li 6.8766 0.0 6.174905 
          Ti 6.8766 0.0 3.0874525 
          S 6.8766 1.9851034305 4.5513282748 
          S 8.595750000000001 0.9925517153 7.7984817252 
          Li 5.15745 2.9776551458 0.0 
          Ti 5.15745 2.9776551458 9.2623575 
          S 5.15745 4.9627585764 10.7262332748 
          S 6.8766 3.9702068611 1.6235767252 
          Li 5.15745 2.9776551458 6.174905 
          Ti 5.15745 2.9776551458 3.0874525 
          S 5.15745 4.9627585764 4.5513282748 
          S 6.8766 3.9702068611 7.7984817252 
          Li -3.4383 5.9553102917 0.0 
          Ti -3.4383 5.9553102917 9.2623575 
          S -3.4383 7.9404137222 10.7262332748 
          S -1.71915 6.947862007 1.6235767252 
          Li -3.4383 5.9553102917 6.174905 
          Ti -3.4383 5.9553102917 3.0874525 
          S -3.4383 7.9404137222 4.5513282748 
          S -1.71915 6.947862007 7.7984817252 
          Li 0.0 0.0 0.0 
          Ti 0.0 0.0 9.2623575 
          S 0.0 1.9851034305 10.7262332748 
          S 1.71915 0.9925517153 1.6235767252 
          Li 0.0 0.0 6.174905 
          Ti 0.0 0.0 3.0874525 
          S 0.0 1.9851034305 4.5513282748 
          S 1.71915 0.9925517153 7.7984817252 
          Li -1.71915 2.9776551458 0.0 
          Ti -1.71915 2.9776551458 9.2623575 
          S -1.71915 4.9627585764 10.7262332748 
          S 0.0 3.9702068611 1.6235767252 
          Li -1.71915 2.9776551458 6.174905 
          Ti -1.71915 2.9776551458 3.0874525 
          S -1.71915 4.9627585764 4.5513282748 
          S 0.0 3.9702068611 7.7984817252 
          Li 0.0 5.9553102917 0.0 
          Ti 0.0 5.9553102917 9.2623575 
          S 0.0 7.9404137222 10.7262332748 
          S 1.71915 6.947862007 1.6235767252 
          Li 0.0 5.9553102917 6.174905 
          Ti 0.0 5.9553102917 3.0874525 
          S 0.0 7.9404137222 4.5513282748 
          S 1.71915 6.947862007 7.7984817252 
          Li 3.4383 0.0 0.0 
          Ti 3.4383 0.0 9.2623575 
          S 3.4383 1.9851034305 10.7262332748 
          S 5.15745 0.9925517153 1.6235767252 
          Li 3.4383 0.0 6.174905 
          Ti 3.4383 0.0 3.0874525 
          S 3.4383 1.9851034305 4.5513282748 
          S 5.15745 0.9925517153 7.7984817252 
          Li 1.71915 2.9776551458 0.0 
          Ti 1.71915 2.9776551458 9.2623575 
          S 1.71915 4.9627585764 10.7262332748 
          S 3.4383 3.9702068611 1.6235767252 
      End
      Lattice
          10.3149 0.0 0.0
          -5.15745 8.9329654375 0.0
          0.0 0.0 12.34981
      End
  End
  
  

Create the “initial” system for NEB with a Li vacancy

Orient the crystal along the x-axis (Ctrl+1), then rotate the view slightly the molecule for a better view of the middle Li atom in the top layer (index 25).

Select → Select By Index → 25

In the bottom right corner, you see the coordinates for this atom. Write them down because you will need them later: 5.157 2.978 6.175

Atoms → Delete Atom(s) (or press the ‘Delete’ key on your keyboard)

In the bottom right corner, verify that the stoichiometry is Li17 S36 Ti18 (one fewer Li than Ti).

The Li atom that will diffuse has index 1. Let’s highlight it with a region for better visibility. Regions can be used to affect the calculation, but here we just use it to better see the diffusing atom.

Click outside any atoms so that no atom is selected

Select → Select by Index → 1

Atoms → New Region From Selected Atoms

This will highlight atom 1 with a colored orb around it.

Now export this structure to a .in file, so that we do not accidentally lose it:

File → Export coordinates → .in

Save it with the filename LiTiS2_vacancy_initial.in

Create the “final” system for NEB with a Li vacancy

NEB calculations have both a starting point (initial system) and an end point (final system).

We will create the final system by changing the coordinates of atom 1 to the coordinates of the atom that was removed.

You can either do this

• manually by first selecting atom 1 and then right-click-dragging the atom into the approximate position of the previous vacancy, or

• just set the coordinates directly:

  In the panel bar, go to Model → Coordinates

  Change the coordinates of the first atom to 5.157 2.978 6.175 (the values for the atom you removed earlier)

  File → Export coordinates → .in

  Use the file name LiTiS2_vacancy_final.in

Set up the NEB calculation

Import the initial and final systems

Note

• By default, the NEB task will optimize both the initial and final points before interpolating between them.

• Make sure that the initial and final structures are close to their respective local minima!

• Best practice is to explicitly optimize them and verify that the structures look good before running the NEB.

• When you perform NEB in a crystal it is recommended to keep the cell dimension between the initial and final states.

Create a new clean input:

SCM → New Input

Now, either

• File → Import Coordinates → LiTiS2_vacancy_initial.in (download or use your own), or

• Reveal copy-pasteable coordinates (LiTiS2_vacancy_initial.in)

  System
      Atoms
          Li 1.71915 2.9776551458 6.174905 region=Region_1
          Ti 1.71915 2.9776551458 3.0874525 
          S 1.71915 4.9627585764 4.5513282748 
          S 3.4383 3.9702068611 7.7984817252 
          Li 3.4383 5.9553102917 0.0 
          Ti 3.4383 5.9553102917 9.2623575 
          S 3.4383 7.9404137222 10.7262332748 
          S 5.15745 6.947862007 1.6235767252 
          Li 3.4383 5.9553102917 6.174905 
          Ti 3.4383 5.9553102917 3.0874525 
          S 3.4383 7.9404137222 4.5513282748 
          S 5.15745 6.947862007 7.7984817252 
          Li 6.8766 0.0 0.0 
          Ti 6.8766 0.0 9.2623575 
          S 6.8766 1.9851034305 10.7262332748 
          S 8.595750000000001 0.9925517153 1.6235767252 
          Li 6.8766 0.0 6.174905 
          Ti 6.8766 0.0 3.0874525 
          S 6.8766 1.9851034305 4.5513282748 
          S 8.595750000000001 0.9925517153 7.7984817252 
          Li 5.15745 2.9776551458 0.0 
          Ti 5.15745 2.9776551458 9.2623575 
          S 5.15745 4.9627585764 10.7262332748 
          S 6.8766 3.9702068611 1.6235767252 
          Ti 5.15745 2.9776551458 3.0874525 
          S 5.15745 4.9627585764 4.5513282748 
          S 6.8766 3.9702068611 7.7984817252 
          Li -3.4383 5.9553102917 0.0 
          Ti -3.4383 5.9553102917 9.2623575 
          S -3.4383 7.9404137222 10.7262332748 
          S -1.71915 6.947862007 1.6235767252 
          Li -3.4383 5.9553102917 6.174905 
          Ti -3.4383 5.9553102917 3.0874525 
          S -3.4383 7.9404137222 4.5513282748 
          S -1.71915 6.947862007 7.7984817252 
          Li 0.0 0.0 0.0 
          Ti 0.0 0.0 9.2623575 
          S 0.0 1.9851034305 10.7262332748 
          S 1.71915 0.9925517153 1.6235767252 
          Li 0.0 0.0 6.174905 
          Ti 0.0 0.0 3.0874525 
          S 0.0 1.9851034305 4.5513282748 
          S 1.71915 0.9925517153 7.7984817252 
          Li -1.71915 2.9776551458 0.0 
          Ti -1.71915 2.9776551458 9.2623575 
          S -1.71915 4.9627585764 10.7262332748 
          S 0.0 3.9702068611 1.6235767252 
          Li -1.71915 2.9776551458 6.174905 
          Ti -1.71915 2.9776551458 3.0874525 
          S -1.71915 4.9627585764 4.5513282748 
          S 0.0 3.9702068611 7.7984817252 
          Li 0.0 5.9553102917 0.0 
          Ti 0.0 5.9553102917 9.2623575 
          S 0.0 7.9404137222 10.7262332748 
          S 1.71915 6.947862007 1.6235767252 
          Li 0.0 5.9553102917 6.174905 
          Ti 0.0 5.9553102917 3.0874525 
          S 0.0 7.9404137222 4.5513282748 
          S 1.71915 6.947862007 7.7984817252 
          Li 3.4383 0.0 0.0 
          Ti 3.4383 0.0 9.2623575 
          S 3.4383 1.9851034305 10.7262332748 
          S 5.15745 0.9925517153 1.6235767252 
          Li 3.4383 0.0 6.174905 
          Ti 3.4383 0.0 3.0874525 
          S 3.4383 1.9851034305 4.5513282748 
          S 5.15745 0.9925517153 7.7984817252 
          Li 1.71915 2.9776551458 0.0 
          Ti 1.71915 2.9776551458 9.2623575 
          S 1.71915 4.9627585764 10.7262332748 
          S 3.4383 3.9702068611 1.6235767252 
      End
      Lattice
          10.3149 0.0 0.0
          -5.15745 8.9329654375 0.0
          0.0 0.0 12.34981
      End
  End
  
  

Create a new “molecule” in AMSinput for the final state:

Edit → New Molecule

Now, either

• File → Import Coordinates → LiTiS2_vacancy_final.in (download or use your own), or

• Reveal copy-pasteable coordinates (LiTiS2_vacancy_final.in)

  System
      Atoms
          Li 5.157 2.9776551458 6.174905 region=Region_1
          Ti 1.71915 2.9776551458 3.0874525 
          S 1.71915 4.9627585764 4.5513282748 
          S 3.4383 3.9702068611 7.7984817252 
          Li 3.4383 5.9553102917 0.0 
          Ti 3.4383 5.9553102917 9.2623575 
          S 3.4383 7.9404137222 10.7262332748 
          S 5.15745 6.947862007 1.6235767252 
          Li 3.4383 5.9553102917 6.174905 
          Ti 3.4383 5.9553102917 3.0874525 
          S 3.4383 7.9404137222 4.5513282748 
          S 5.15745 6.947862007 7.7984817252 
          Li 6.8766 0.0 0.0 
          Ti 6.8766 0.0 9.2623575 
          S 6.8766 1.9851034305 10.7262332748 
          S 8.595750000000001 0.9925517149999999 1.6235767252 
          Li 6.8766 0.0 6.174905 
          Ti 6.8766 0.0 3.0874525 
          S 6.8766 1.9851034305 4.5513282748 
          S 8.595750000000001 0.9925517149999999 7.7984817252 
          Li 5.15745 2.9776551458 0.0 
          Ti 5.15745 2.9776551458 9.2623575 
          S 5.15745 4.9627585764 10.7262332748 
          S 6.8766 3.9702068611 1.6235767252 
          Ti 5.15745 2.9776551458 3.0874525 
          S 5.15745 4.9627585764 4.5513282748 
          S 6.8766 3.9702068611 7.7984817252 
          Li -3.4383 5.9553102917 0.0 
          Ti -3.4383 5.9553102917 9.2623575 
          S -3.4383 7.9404137222 10.7262332748 
          S -1.71915 6.947862007 1.6235767252 
          Li -3.4383 5.9553102917 6.174905 
          Ti -3.4383 5.9553102917 3.0874525 
          S -3.4383 7.9404137222 4.5513282748 
          S -1.71915 6.947862007 7.7984817252 
          Li 0.0 0.0 0.0 
          Ti 0.0 0.0 9.2623575 
          S 0.0 1.9851034305 10.7262332748 
          S 1.71915 0.9925517149999999 1.6235767252 
          Li 0.0 0.0 6.174905 
          Ti 0.0 0.0 3.0874525 
          S 0.0 1.9851034305 4.5513282748 
          S 1.71915 0.9925517149999999 7.7984817252 
          Li -1.71915 2.9776551458 0.0 
          Ti -1.71915 2.9776551458 9.2623575 
          S -1.71915 4.9627585764 10.7262332748 
          S 0.0 3.9702068611 1.6235767252 
          Li -1.71915 2.9776551458 6.174905 
          Ti -1.71915 2.9776551458 3.0874525 
          S -1.71915 4.9627585764 4.5513282748 
          S 0.0 3.9702068611 7.7984817252 
          Li 0.0 5.9553102917 0.0 
          Ti 0.0 5.9553102917 9.2623575 
          S 0.0 7.9404137222 10.7262332748 
          S 1.71915 6.947862007 1.6235767252 
          Li 0.0 5.9553102917 6.174905 
          Ti 0.0 5.9553102917 3.0874525 
          S 0.0 7.9404137222 4.5513282748 
          S 1.71915 6.947862007 7.7984817252 
          Li 3.4383 0.0 0.0 
          Ti 3.4383 0.0 9.2623575 
          S 3.4383 1.9851034305 10.7262332748 
          S 5.15745 0.9925517149999999 1.6235767252 
          Li 3.4383 0.0 6.174905 
          Ti 3.4383 0.0 3.0874525 
          S 3.4383 1.9851034305 4.5513282748 
          S 5.15745 0.9925517149999999 7.7984817252 
          Li 1.71915 2.9776551458 0.0 
          Ti 1.71915 2.9776551458 9.2623575 
          S 1.71915 4.9627585764 10.7262332748 
          S 3.4383 3.9702068611 1.6235767252 
      End
      Lattice
          10.3149 0.0 0.0
          -5.15745 8.9329654375 0.0
          0.0 0.0 12.34981
      End
  End
  
  

You can toggle between the initial and final structures using the arrows below the 3D area.

Set up the engine M3GNet settings

In the yellow dropdown, switch to

Set Model → M3GNet → M3GNet-UP-2022

On the panel bar, go to Details → Engine Addons

Tick the D3 Dispersion → Yes

Set up the NEB settings

1. From the Main tab, select the Task → NEB

2. Click the next to Task → NEB

3. Set the Maximum number of iterations to 100

4. Set the Number of images to 19

5. Set Initial system to LiTiS2_vacancy_initial (or it may be called Mol-1)

6. Set Final system to LiTiS2_vacancy_final (or it may be called Mol-2)

The NEB is now ready. Save the calculation. This will automatically rename the molecules as initial and final.

Run the calculation. This might take a few more minutes as AMS will perform a simultaneous optimization of all the 17 images by minimizing the forces parallel to the reaction path.

Once the calculation is finished, select LiTiS2_NEB in AMSjobs and click SCM → Movie. You can re-orient the crystal and use the slidebar under the molecule area to appreciate the diffusion along the minimum energy path. If you double click the y-axis label of the graph, you can switch to your prefered units. We found the activation energy E_A = 0.59 eV.

NEB with Python

See the Li diffusion NEB scripting example.

Li diffusion in Li_xTiS₂

To explore the effect of lithium concentration on diffusion, begin with the structures from step 3. Remove the Li atom with index 9 for both the initial and final structures and at the end increase the NEB iterations to 500.

This change reduce the activation energy by approximately a factor of 2.

• In the first case, the lithium migration trajectory was roughly linear.

• The presence of the additional Li vacancy causes the path to curve, passing through a tetrahedral site and creating a shallow energy minimum.