OpenMPI library compiled for gfortran for Macintosh using ARM with OSX 14.1:

openmpi-4.1.6_gfortran_arm.tgz

This should be put into /usr/local/ and /usr/local/openmpi/bin needs to be in the path. The MPI libraries here are provided for Nagfor compiler on OSX systems. The following MPI library works for Macintosh system using ARM chips:

mpich-4.1.2_nagfor_arm.tgz

As root (sudo -s), open the tar file inside NAG_fortran and link it

cd /usr/local/lib/NAG_Fortran
tar xzf mpich-4.1.2_nagfor_arm.tgz
cd /usr/local
rm -f mpi
ln -s /usr/local/lib/NAG_Fortran/mpich mpi
The following MPI library only works for 64-bit Macintosh system using Intel chips:

mpich-3.2.1_nagfor_fpp.tgz

As root (sudo -s), open the tar file and link it

cd /usr/local/
tar xzf mpich-3.2.1_nagfor_fpp.tgz
rm -f mpi
ln -s mpich-3.2.1 mpi
Exit from the super user mode (Ctrl-D or exit).

In both cases include /usr/local/mpi/bin into the path in the ~/.cshrc or similar file, then

source .cshrc
rehash
Then type
which mpif90
to see if it is found. Now you should be able to compile the code with NAG Fortran and MPICH. To avoid run time errors due to some security settings (software is not from Apple), it may be necessary to do the following:
xattr -d com.apple.quarantine /usr/local/mpi/bin/mpiexec
xattr -d com.apple.quarantine /usr/local/mpi/bin/hydra_pmi_prox
spctl --master-disable
Possibly the last command by itself is sufficient.

For some MPI implementations it may be necessary to create a public SSH key of the machine with

ssh-keygen 
(hit return to all questions) and the resulting public key file should be added to the authorized keys:
cat .ssh/id_rsa.pub >> .ssh/authorized_keys
Even if not needed for running MPI parallel code, the public key is useful for passwordless ssh/scp/rsync etc. access.