Equations of motion based on an atomic group scaling scheme are described for a molecular system with bond constraints. The NPT ensemble extended system method is employed along with a numerical integration scheme using an operator technique. For parallelization of the integration scheme, a domain decomposition scheme is employed based on a group of atoms which share common constraints. This decomposition scheme fits well into the integration scheme and involves no extra inter-processor communication during the SHAKE/RATTLE procedures. An example is given for a solvated protein system containing a total of 23558 atoms on 64 processors.