# What's the best way to compare two DFT codes?

What's the most efficient way to compare the two DFT codes in terms of computation time, basis sets (for example, one plane wave vs one atomic orbitals), functional performance, etc.?

• Welcome to our site! – Camps Dec 10 '20 at 11:53
• What exactly is your goal? Are there two codes you have in mind? What type of calculations are you doing? Are you asking this because you're wondering which code code to buy or which code to install or which code you want to use for an upcoming project? These are all good questions and it's good that you're trying to study the different codes available before delving deep into one particular code. – Nike Dattani Dec 10 '20 at 21:30

There are many options to answer your question.

Just to compare the computation time, the first condition is to run the simulations with the same hardware i.e. in the same system (two different set-ups even with the same type of hardware can perform differently). Also, both codes have to be compiled with the same compiler and with the same compiling optimization options. Finally, the physical system used should be the same.

For the other comparisons, you will need a third set of data. I strongly recommend to look for a system where the theoretical predictions are in accordance with experimental ones and then use the experimental data as a reference.

What's the best way to compare two DFT codes?

I assume here the DFT means Kohn-Sham density functional theory (KS-DFT). The central task of KS-DFT is to solve the following Kohn-Sham equation (atomic unit is adopted):

$$\left[-\dfrac{1}{2}\nabla^2+V_{ks}[\psi_i(\vec{r})]\right]\psi_i(\vec{r})=E_i\psi_i(\vec{r})$$

which is a nonlinear differential equation to be solved self-consistently. There are many elements that are related to solving the Kohn-Sham equation. For example:

• $$\psi_i$$: How to choose a basis to expand the wavefunction? plane-wave or local orbital?
• $$V_{ks}$$: How to treat effective potential? All electron or pseudopotential?
• $$-\dfrac{1}{2}\nabla^2$$: Is it necessary to consider spin-orbit coupling?
• How to choose the exchange-correlation functional?
• ....

Usually, different KS-DFT code will have their independent choice about these elements. Therefore, you can hardly find a general method to compare two KS-DFT codes. Although this task is untouchable, you can generate almost reasonable physical results based on different Kohn-Sham DFT codes, as discussed by this paper: Reproducibility in density functional theory calculations of solids

Although there is no absolute reference against which to compare two DFT codes due to each approach has its own intricacies and approximations, to quantify differences between two DFT codes, the $$\Delta$$ gauge is formulated by Lejaeghere et al..

• I gave you +1, but perhaps you could explain the paper more and rely less on screenshots and give more of your own text. This way the text is more "searchable" from search engines, unlike the text in the screenshots. – Nike Dattani Dec 11 '20 at 0:02
• @NikeDattani Later I will give a detailed answer. – Jack Dec 11 '20 at 0:52