/usr/include/mpich/ is in libmpich-dev 3.0.4-6ubuntu1.
This file is owned by root:root, with mode 0o755.
..
/usr/include/mpich/mpi.h
/usr/include/mpich/mpi.mod
/usr/include/mpich/mpi_base.mod
/usr/include/mpich/mpi_constants.mod
/usr/include/mpich/mpi_sizeofs.mod
/usr/include/mpich/mpicxx.h
/usr/include/mpich/mpif.h
/usr/include/mpich/mpio.h
/usr/include/mpich/mpiof.h
/usr/include/mpich/opa_config.h
/usr/include/mpich/opa_primitives.h
/usr/include/mpich/opa_queue.h
/usr/include/mpich/opa_util.h
/usr/include/mpich/primitives/
/usr/include/mpich/primitives/opa_by_lock.h
/usr/include/mpich/primitives/opa_emulated.h
/usr/include/mpich/primitives/opa_gcc_ia64.h
/usr/include/mpich/primitives/opa_gcc_intel_32_64.h
/usr/include/mpich/primitives/opa_gcc_intel_32_64_barrier.h
/usr/include/mpich/primitives/opa_gcc_intel_32_64_ops.h
/usr/include/mpich/primitives/opa_gcc_intel_32_64_p3.h
/usr/include/mpich/primitives/opa_gcc_intel_32_64_p3barrier.h
/usr/include/mpich/primitives/opa_gcc_intrinsics.h
/usr/include/mpich/primitives/opa_gcc_ppc.h
/usr/include/mpich/primitives/opa_gcc_sicortex.h
/usr/include/mpich/primitives/opa_nt_intrinsics.h
/usr/include/mpich/primitives/opa_sun_atomic_ops.h
/usr/include/mpich/primitives/opa_unsafe.h