Battery Cathodes: Intercalation Potential and Volume Change

Batteries Cathode materials Intercalation potential Volume change MLPotential

Note: This tutorial is intended for AMS2026 with access to the UMA-S-1.2-OMat machine learning potential.

This tutorial will teach you how to:

• Optimize the lithiated and delithiated crystal structures of LiFePO₄.

• Compute the intercalation potential from the two total energies.

• Compute the relative volume change upon delithiation.

• Consider how the workflow can be adapted to explore doped cathodes as well as sodium analogues.

If you follow this tutorial, you will be able to calculate the properties of the materials cited in Ref. [1].

Table 9 Comparison of the calculated average intercalation potential (IP, in V vs. Li/Li⁺) and the relative volume change upon delithiation (VC, in %) with the experimental data from Tables II and IV of Ref. [1].

Structure	Expt. IP	Calc. IP	Expt. VC	Calc. VC
LiCoO2	4.10	3.926	-7.958	-2.102
LiNiO2	3.90	4.014	-9.422	-8.461
LiTiS2	2.10	1.972	-10.605	-8.849
LiMn2O4	4.10	3.913	-5.051	-5.939
LiMnPO4	4.10	3.872	-9.046	-8.534
LiFePO4	3.50	3.573	-6.534	-5.764
LiCoPO4	4.80	4.412	-1.846	-4.310

Fig. 27 Calculated versus experimental benchmark values for the materials in Table II and Table IV of Ref. [1]. Blue circles show the intercalation potential (IP, in V vs. Li/Li⁺) and red crosses show the relative volume change upon delithiation (VC, in %). The dashed diagonal corresponds to y = x.

Note

Overall, UMA-S-1.2-OMat reproduces these properties very well, with noticeable deviations observed only for the Co-based materials.

Introduction

Olivine phosphate materials are widely studied as battery cathodes because they can combine good stability with high operating voltage. In this tutorial, we use LiFePO₄ as a starting point and evaluate two simple descriptors for cathode performance:

• the intercalation potential

• the volume change upon charging

The basic idea is to optimize two crystal structures:

• the lithiated material LiFePO₄

• the delithiated material FePO₄

From these calculations, you can estimate the average lithium intercalation potential and the relative volume change.

\[V = \frac{E(\mathrm{FePO_4}) + E(\mathrm{Li}) - E(\mathrm{LiFePO_4})}{F}\]

In practice, you should use a consistent reference energy for lithium metal when evaluating the voltage.

The volume change is computed from the optimized cell volumes:

\[\Delta V (\%) = 100 \times \frac{V_{\mathrm{delithiated}} - V_{\mathrm{lithiated}}}{V_{\mathrm{lithiated}}}\]

You should therefore review 10 Ways to Get the Energy and Other Properties. Looking at the output of a geometry optimization job, you will find at the end the Energy (hartree) and right above the Unit cell volume (angstrom^3) (when the lattice is optimized), which can be used to extract the relevant data for this tutorial.

Tip

We recommend creating a table to store the total energies and volumes of each calculation you perform below.

For comparison, the experimental values for LiFePO₄ and FePO₄ from Tables II and IV of Ref. [1] are:

Property	Experimental value
LiFePO4 volume (Å3 /f.u.)	72.85
FePO4 volume (Å3 /f.u.)	68.09
Relative volume change upon delithiation (%)	-6.534
Average intercalation potential (V vs. Li/Li+)	3.5

This tutorial focuses on the GUI workflow. A companion Jupyter notebook can be used for the same workflow in Python.

Part A: LiFePO₄

Part A focuses on pristine LiFePO₄. You will first calculate the lithium reference energy needed to compute the intercalation potential.

Setting the Lithium Reference Energy

Build and optimize bulk lithium in AMSinput.

1. Create a new job: SCM → New Input

2. Build the crystal: Builders → Crystal Structure → Cubic → bcc

3. Select Li from the element presets and click OK

4. Switch to the machine learning potential engine: →

5. Set Model to UMA-S-1.2-OMat

6. Set Task to Geometry Optimization

7. Go to Details → Engine Add-ons

8. Enable the same D4 setting used for the cathode calculations

9. Go to Details → GeometryOptimization

10. Set Optimize lattice to Yes

11. Save the job as, for example, Li_bcc_opt

12. Run the calculation

We found a lithium reference energy of E(Li) = -0.070836 Ha per atom.

Set up and run the LiFePO₄ calculations

You will now optimize the fully lithiated structure and then create and optimize the delithiated structure.

Set up the geometry optimization for LiFePO₄ in AMSinput.

1. Open AMSinput: SCM → New Input

2. Import the crystal structure: File → Import Coordinates (System) and select LiFePO4.cif

3. Switch to the machine learning potential engine: →

4. Set Model to UMA-S-1.2-OMat

5. Set Task to Geometry Optimization

6. Go to Details → Engine Add-ons

7. Enable the D4 repulsion add-on

8. Go to Details → GeometryOptimization

9. Set Optimize lattice to Yes

10. Save the job as, for example, LiFePO4_opt

11. Start the calculation with File → Run

Next, create the delithiated structure FePO₄.

12. Reopen the LiFePO4 input, or continue from the existing setup

13. Select the lithium atoms in the structure view. To achieve this, either click the Li atoms holding the Shift key or click to select one Li atom then Select → Atoms of the Same → Type

14. Delete the selected lithium atoms with the Delete key

15. Keep the same Model, Task, D4 repulsion, and Optimize lattice settings

16. Save the new job as, for example, FePO4_opt

17. Run the calculation

Analyzing the Results

After both jobs have finished, collect the total energies and optimized cell volumes. A compact way to organize the results is shown below.

Calculation	Total energy (Ha)	Cell volume (Å 3)	Comment
Li metal	-0.070836 per atom	40.53114	bcc Li reference
LiFePO4	-7.21135362	293.76580	optimized lithiated structure
FePO4	-6.40276118	276.83367	optimized delithiated structure

Intercalation Potential and Volume Change

Use the total energies and volumes of LiFePO₄ and FePO₄ together with a lithium metal reference energy to compute the average intercalation potential and volume change.

For the reaction

\[\mathrm{LiFePO_4} \rightarrow \mathrm{FePO_4} + \mathrm{Li}\]

the benchmark calculation reported above gives the following LiFePO₄ values:

Property	Value
Average intercalation potential	3.573 V
Relative volume change	-5.764 %
Experimental intercalation potential	3.5 V
Experimental volume change	-6.534 %

You can repeat the workflow with other cathode materials to obtain Table 9.

Part B: Doped Material

In this part, replace a fraction of Fe by a different element and evaluate whether the modified material offers an improved trade-off between voltage and volume change.

Consider a composition of the form

\[\mathrm{LiFe}_{0.875}\mathrm{X}_{0.125}\mathrm{PO}_4\]

where X can be chosen from:

• Mg

• Ti

• Nb

• Si

Choose one dopant and repeat the same workflow as in Part A.

The goal is to identify a material with

• a small absolute volume change

• a high intercalation potential

• potentially improved energy density relative to LiFePO₄

Part C: Sodium Analogue

As a final exploratory exercise, adapt the same workflow from lithium to sodium.

Possible questions to investigate:

• How do the optimized lattice parameters change when Li is replaced by Na?

• How does the intercalation potential compare to the lithium system?

• Is the volume change larger or smaller than in the lithium case?

This part can be carried out by preparing the corresponding sodium structure and repeating the same geometry optimization and analysis procedure.

Summary

In this tutorial, you learned how to use AMSinput with a machine learning potential to:

• optimize lithiated and delithiated cathode structures

• extract total energies and cell volumes from the AMS GUI

• compute the average intercalation potential

• compute the relative volume change

• compare pristine and doped phosphate cathodes

The same approach can be extended to other battery materials and to larger screening studies.

References

[1] (1,2,3,4)

22. 12. Chevrier, S. P. Ong, R. Armiento, M. K. Y. Chan, G. Ceder. Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds. Phys. Rev. B 82, 075122 (2010).