I just want to know why fftw and mpich should be installed before installing wien2k12.
Are they necessary for doing the calculation parallel?

For mpi-parallel calculations, you must have them.

For serial and k-point parallel calculations, they are not needed. The non-mpi calculations use WIEN2k's fftpack, but you can optionally use fftw, which might give some calculation speedup as described in section 11.1.1 on page 218 of the WIEN2k 16.1 usersguide [ http://susi.theochem.tuwien.ac.at/reg_user/textbooks/usersguide.pdf ].

The fftw is needed before the WIEN2k install so that its header and library files can be compiled and linked together with the WIEN2k code.

The mpich is needed before the WIEN2k install so that the environment, such as bin path, can configured during the WIEN2k installation.

should I install Mpich and Fftw according to this fact that I want to do the calculation in a single core?

No, a serial calculation is for a single core and it can be a waste of time to install them for two cores [ https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg03793.html ].
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