I would like to ask about the calculation of mean squared displacement for binary alloy systems. In the case of binary alloy, there are two type of atoms, and it is possible to obtain the msd for two atoms, respectively, by using group ID command, while we can also get the msd for all atoms. I want to know the meaning of this msd for all atoms. Is it ok to think that this is connected to the mutual diffusion coefficient?

I would like to ask about the calculation of mean squared displacement
for binary alloy systems. In the case of binary alloy, there are two
type of atoms, and it is possible to obtain the msd for two atoms,
respectively, by using group ID command, while we can also get the msd
for all atoms. I want to know the meaning of this msd for all atoms. Is
it ok to think that this is connected to the mutual diffusion coefficient?

you are averaging over both atom types and thus simply computing
the average diffusion coefficient.

Then I would like to ask again whether LAMMPS whould have command option to obtain the velocity autocorrelation function, which is also related with diffusion constant as you know. Otherwise, do I have to make code to postprocess the data (maybe dump file?)?

I am sure many people have written scripts that post-process dump files to get the VACF functions that you want, but I donâ€™t think there is anything in the standard distribution that you could use. However, I believe that the Center-of_Mass fix could give you most of what you need. The mutual diffusion coefficient can be expressed as the mean square displacement of the vector joining the centers-of-mass of the two species.

The "m" in msd is for "mean" which simply
means it is averaged over whatever atoms are
in the group you specify. So if they are of one type,
it's the MSD for those atoms. If two types, it's
the MSD for both types of atoms together.