I will talk about last today.

And the starting point is the energy functional, which is a function, the main equation which

class is dealing with.

Of course, we can do more than this, but it is not the focus of the talk today.

So what we have, we have the energy functional with different terms, which involve different

numerical algorithms depending on the basic set.

And this can change dramatically, but this is like the focus of our talk today.

So I'm going to talk about VAS.

The plane wave basis set, which is algorithm are almost fixed, is a popular code.

And also this basis is a popular choice in the community.

So what people, what VAS is doing is to minimize this energy functional for every orbital of

the system for these atmospheric simulations.

These orbitals are for electrons.

And then the charge entity is the main focus and the main physical observer of this system,

which is calculated at a summation of the orbital with the occupation number, which

depends if they are occupied or unoccupied or partially occupied.

So the energy is minimized for all orbital with the constraint of orthogonalization,

or to normalization actually.

So this is an important part.

And this regarding what basis set is being used, orthogonalization is part of this algorithm.

So the computational cost, the computational cost heavily depends on the number of electrons,

the number of orbitals we have and the type of basis set.

As we said, we have plane base here and also the size of the basis set, which is the same

as the number of grid points and plane base actually we have in our calculation.

But also, so what we have plane base, that means that we are dealing with discrete Fourier

transform and we use fast Fourier transform for that.

So this is a very important part of the scope.

So another factor is the exchange correlation functional, which is very important in the

cost of running this code.

Usually people use the conventional energy functional, the conventional ones, they depend

on the density and the gradient of the density in too much less extent.

People also use hybrid exchange correlation functional, which dealing with the orbitals,

these are a lot more expensive, even if they're not very common, but they're considered a

benchmark because they're a lot more costly.

So it's also important to have a good benchmark of these and run them efficiently.

As I said, we have different algorithms with different computational complexities, but

the dominant ones are quadratic and cubic.

Unfortunately, the quadratic is dominant for typical system sizes, which we are dealing

with in the past, also nowadays.

So this cubic term becomes dominant or actually is very important for system sizes larger

than thousands of atoms for this code.

So that means that we mainly dealing with these parts as a major part of the runtime.

So another point is the non-local part of the position, which can be cubic or quadratic,

but the test systems which we are interested in, we consider these real-space calculations,

which are quadratic.

So the previous argument that quadratic is dominant was with the assumption that I'm

running on a real-space for this non-local part.

Otherwise, the cubic would be also very important.

So this is also a very important point.

I should come back to it again.