cmake - Could NOT find MPI_CXX

I am trying to compile the simulation software LAMMPS using CMake, and run into some trouble:
 

-- Could NOT find MPI_CXX (missing: MPI_CXX_LIB_NAMES) (found version "3.1")
CMake Error at /usr/share/cmake-3.16/Modules/FindPackageHandleStandardArgs.cmake:146 (message):
  Could NOT find MPI (missing: MPI_CXX_FOUND) (found version "3.1")
Call Stack (most recent call first):
  /usr/share/cmake-3.16/Modules/FindPackageHandleStandardArgs.cmake:393 (_FPHSA_FAILURE_MESSAGE)
  /usr/share/cmake-3.16/Modules/FindMPI.cmake:1688 (find_package_handle_standard_args)
  CMakeLists.txt:180 (find_package)

I do have the latest intel parallel studio

$ icc -V
Intel(R) C Intel(R) 64 Compiler for applications running on Intel(R) 64, Version 19.1.0.166 Build 20191121
Copyright (C) 1985-2019 Intel Corporation.  All rights reserved.

I'm on Archlinux, and the version of CMake I'm using is:

$ cmake --version
cmake version 3.16.3

CMake suite maintained and supported by Kitware (kitware.com/cmake).

My compilation options are:

-DCMAKE_C_COMPILER=mpiicc
-DCMAKE_C_FLAGS=-xHost -O2 -fp-model fast=2 -no-prec-div -qoverride-limits -qopt-zmm-usage=high
-DCMAKE_CXX_COMPILER=mpiicpc
-DCMAKE_CXX_FLAGS=-fp-model fast=2 -no-prec-div -qoverride-limits -qopt-zmm-usage=high -qno-offload -fno-alias -ansi-alias -O2 -std=c++11 -DLMP_INTEL_USELRT -DLMP_USE_MKL_RNG -I${MKLROOT}/include
-DCMAKE_Fortran_COMPILER=mpiifort

Am I doing something wrong?