Extended Systems for other Ensembles

OOPSE implements a number of extended system integrators for sampling from other ensembles relevant to chemical physics. The integrator can be selected with the ensemble keyword in the meta-data file:

Integrator	Ensemble	Meta-data instruction
NVE	microcanonical	`ensemble = NVE;`
NVT	canonical	`ensemble = NVT;`
NPTi	isobaric-isothermal	`ensemble = NPTi;`
	(with isotropic volume changes)
NPTf	isobaric-isothermal	`ensemble = NPTf;`
	(with changes to box shape)
NPTxyz	approximate isobaric-isothermal	`ensemble = NPTxyz;`
	(with separate barostats on each box dimension)

The relatively well-known Nosé-Hoover thermostat[45] is implemented in OOPSE's NVT integrator. This method couples an extra degree of freedom (the thermostat) to the kinetic energy of the system and it has been shown to sample the canonical distribution in the system degrees of freedom while conserving a quantity that is, to within a constant, the Helmholtz free energy.[46]

NPT algorithms attempt to maintain constant pressure in the system by coupling the volume of the system to a barostat. OOPSE contains three different constant pressure algorithms. The first two, NPTi and NPTf have been shown to conserve a quantity that is, to within a constant, the Gibbs free energy.[46] The Melchionna modification to the Hoover barostat is implemented in both NPTi and NPTf. NPTi allows only isotropic changes in the simulation box, while box shape variations are allowed in NPTf. The NPTxyz integrator has not been shown to sample from the isobaric-isothermal ensemble. It is useful, however, in that it maintains orthogonality for the axes of the simulation box while attempting to equalize pressure along the three perpendicular directions in the box.

Each of the extended system integrators requires additional keywords to set target values for the thermodynamic state variables that are being held constant. Keywords are also required to set the characteristic decay times for the dynamics of the extended variables.

variable	Meta-data instruction	units	default value
$T_{\mathrm{target}}$	`targetTemperature = 300;`	K	none
$P_{\mathrm{target}}$	`targetPressure = 1;`	atm	none
$\tau_T$	`tauThermostat = 1e3;`	fs	none
$\tau_B$	`tauBarostat = 5e3;`	fs	none
	`resetTime = 200;`	fs	none
	`useInitialExtendedSystemState = true;`	logical	true

Two additional keywords can be used to either clear the extended system variables periodically (resetTime), or to maintain the state of the extended system variables between simulations (useInitialExtendedSystemState). More details on these variables and their use in the integrators follows below.