# Should I add vdW interaction to estimate chemical potential of metallic elements?

I am considering layered oxides $$\ce{LiCoO2}$$. Previous papers suggested that vdW interaction should be added to get lattice parameters closer to experimental data. I would like to dope other elements to Co sites of layered $$\ce{LiCoO2}$$ and calculate the formation energy of the doped structure. In the formula for estimating formation energy, I need to know the chemical potentials of dopant elements. For example,

$$\textrm{formation energy} = E(\ce{LiCo}_{1-y}\ce{Na_yO_2})-[E(\ce{LiCoO2})+yE(\ce{Na})-yE(\ce{Co})]\tag{1}$$

The idea of adding vdW to estimate chemical potential seems to be strange, but I still wonder if I should add vdW interaction to calculate the chemical potentials of dopant elements? I found that when I add vdW interaction to calculated Na chemical potential, there is a big gap compared to results without adding vdW. For example, $$E(\ce{Na}_{\textrm{vdwD3}})$$ = -0.385 eV, E(Na_without vdW)= -1.283eV (using same ENCUT, K-POINTS).

• +1 but I'd like you to take a look at my edit and finish fixing the formatting issues that I started fixing. It would be appreciated! Can you tell us which papers you're referring to in the 2nd sentence of your question's body? Also, you got a big difference between using vdW and not using vdW for $\ce{Na}$, but what's the experimental value (i.e. which one is more accurate)? – Nike Dattani May 11 at 20:00
• @NikeDattani. Please take a look at the following paper for vdw adding while calculating LiCoO2. pubs.acs.org/doi/10.1021/acs.jpcc.5b06240. I checked chemical potential on this website job-stiftung.de/index.php?data-collection and I got the value of 0 in solid, but 0.5kG in liquid. – Binh Thien May 12 at 1:51