# Extended System Dynamics Methods

## Grand Canonical Ensemble Molecular Dynamics

**
Extended system dynamics method for closed systems (with fixed number of
molecules) has been developed and widely used during 80's. A similar
approach is taken to extend a system with a variable number of molecules.
In this simulation method, the number of molecules become a variable (instead
of an integer, a real variable is used to represent the number of molecules
at any instant). Integer portion represents full atoms/molecules, whereas
the remainder represents the strength of coupling of a fractional atom/molecule
to the rest of the system. The chemical potential drives the number variable
through a dynamical equation of motion. At integer values of number variable
a new fractional atom/molecule is initiated while the old one either becomes
a full atom/molecule or decouples from the system.
**
Equations of motion for "*coordinates*" and "*momenta*" of atoms and
the additional extended system variables are obtained from the extended
hamiltonian.

Recent modifications to the hamiltonian approaches for GCMD simulations involved
addressing the ideal gas contribution [4,5].

### References

- T. Cagin and B. M. Pettitt,
*Molec. Simuln.* **6**, 5 (1991).
- T. Cagin and B. M. Pettitt,
*Mol. Phys.* **72**, 169 (1991).
- J. Ji, T. Cagin and B. M. Pettitt,
*J. Chem. Phys.* **96**, 1333 (1992).
- S. Wearingshe and B. M. Pettitt,
*Mol. Phys.* (1994)
- C. Lo and Palmer,
*J. Chem. Phys.* (1995).

tahir@wag.caltech.edu