Isobaric, isothermal ensemble

NPT ensemble isothermal-isobaric ensemble constant particle (N),... 

NPT NPT ensemble isothermal-isobaric ensemble constant particle (N), pressure (P), and temperature (T) simulation PBC Periodic boundary conditions... 

Evans D J and Morriss G P 1983 The Isothermal Isobaric molecular dynamics ensemble Phys. Lett. A 98 433-6... 

Wood W W 1968 Monte Carlo calculations for hard disks in the isothermal-isobaric ensemble J. Chem. Phys. 48 415-34... 

However, it is common practice to sample an isothermal isobaric ensemble NPT, constant pressure and constant temperature), which normally reflects standard laboratory conditions well. Similarly to temperature control, the system is coupled to an external bath with the desired target pressure Pq. By rescaling the dimensions of the periodic box and the atomic coordinates by the factor // at each integration step At according to Eq. (46), the volume of the box and the forces of the solvent molecules acting on the box walls are adjusted. 

In Ihc canonical, microcanonical and isothermal-isobaric ensembles the number of particles is constant but in a grand canonical simulation the composition can change (i.e. the number of particles can increase or decrease). The equilibrium states of each of these ensembles are cha racterised as follows ... 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

A macroscopic system maintains constant pressure by changing its volume. A simulation i the isothermal-isobaric ensemble also maintains constant pressure by changing the volurr... 

Umbrella sampling can give free-energy differences, but not absolute free energies Usually done in NPT—isothermal/isobaric ensembles, including a water box... 

Owicki, J. C. Scheraga, H. A., Monte Carlo calculations in the isothermal-isobaric ensemble. 1. Liquid water, J. Am. Chem. Soc. 1977, 99, 7403-7412... 

Vorontsov-Velyaminov, P. N. Elyashevich, A. M. Morgenshtem, L. A. Chasovskikh, V. P., Investigation of phase transitions in argon and coulomb gas by the Monte Carlo method using an isothermally isobaric ensemble, High Temp. USSR 1970, 8, 261-268... 

As an example [24, 25] consider calculation of ((W pAUa))0/ ((v))o inan isothermal-isobaric ensemble, for which the volume V fluctuates. In this formula V is a relic of the ensemble considered. A calculation using the rule of averages (9.14) then leads to [10]... 

The isothermal-isobaric ensemble (N,P,T) allows the simulation of chemical systems at a constant temperature and pressure, such as 298 K and 1 at. which are the most usual experimental conditions. At a given set of (N,P,T) the probability density is not only dependent of q N) but also of the volume V ... 

Monte Carlo simulations were carried out to determine the free energy curve for the reaction in solution. The simulations were executed for the solute surrounded by 250 water molecules (or 180 DMF molecules) in the isothermal-isobaric ensemble at 25 °C and 1 atm, including periodic boundary conditions. As a consequence, the Gibbs free energy is obtained in this case. There is sufficient solvent to adequately represent the bulk participation in the chemical reaction. 

The Claisen rearrangement of allyl vinyl ether in aqueous solution was studied by Gao et al. [157] by using the gas-phase ab initio MEP determined previously by the Jorgensen s group [60], In this case, 69 of the 143 frames were employed along the perturbation procedure in the isothermal-isobaric ensemble at 25 °C and 1 atm. The... 

Having developed a self-consistent treatment of the structure and interfacial energy of the Lennard-Jones droplet in a finite volume which avoids the usual assumptions by which homogeneous nucleation theory is implementedf we return to original question and examine how this new information alters the physical picture of nucleation. It is common to apply the analog of Equation 6 for an isothermal-isobaric ensemble,... 

G[T P] = G = —RTIn A, where A is the isothermal-isobaric partition function and U[T,n ] = —RTInE, where S is the grand canonical ensemble partition function. When a system involves several species, but only one can pass through a membrane to a reservoir, L/(7 jux] = — PTlnT, where T is the semigrand ensemble partition function. The last chapter of the book is on semigrand partition functions. 

There are many excellent reviews on the standard molecular dynamics method dealing with calculations in the microcanonical ensemble as well as on the Monte Carlo method involving calculations in the canonical, isothermal isobaric, and grand canonical ensemble (< ). In the present article, we shall limit ourselves exclusively to those developments that have taken place since the work of Andersen (4). In the molecular dynamics method, the developments are the constant-pressure, constant-temperature, constant-temperature-constant-pressure, variable shape simulation cell MD, and isostress calculations in the Monte Carlo method, it is the variable shape simulation cell calculation. 

The traditional MC method in the isothermal isobaric ensemble has been modified to include variations in size as well as the shape of the simulation cell (7). The... 

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