Rahman-Parrinello technique

Solid-state phase transitions often involve deformation of the unit cell along with rearrangements of the molecules inside the unit cell. Therefore a simple constant-pressure simulation which allows only isotropic expansion or contraction of the unit cell may not be able to reproduce all of the aspects of a solid-state phase transition. The technique of Parrinello and Rahman [160] introduces a time-dependent metric tensor in the Lagrangian of the system, which allows changes of both volume and shape of the xmit cells. As such, simple solid-state phase transitions can be directly simulated with this technique. However, this method cannot be used for solid phases with very different unit cells.[145] The orientational order-disorder transitions in the solid state in some cases occur with little change in the unit cell parameters or molecular rearrangements. These orientational transitions are suitable for the Parrinello-Rahman technique.[161]... 

Although the method is less rigorous than the alternative Rahman-Parrinello (RP) technique it does have at least one important practical advantage. This is that the pressure imbalance is coupled to the first derivative of the basis vectors rather than to the second derivative this means that motions of the box are overdamped and so there is little tendency for an unphysical oscillatory response to changes in the applied pressure. For this reason this method comes into its own for the calculation of nonequilibrium properties of dense highly viscoelastic systems. 

Constant Pressure MD. The conventional MD technique uses a fixed size for the simulation box, that is, the calculation is performed under constant volume conditions. Using methods developed by Parrinello and Rahman and by Berendsen and coworkers, it is now possible to undertake constant pressure simulations by allowing cell dimensions to vary dnring the simulation. Detailed discussions are given in Referenced . The most obvious field of application of this technique is to the study of phase transitions, and useful applications have been reported to the study of melting and glass formation as discussed below. 

A further consideration is the conditions under which the simulation is run. We have described the approach where the energy and volume are kept constant but there are well-established techniques that maintain constant temperature (Nose 1984, 1990) and constant pressure (Parrinello and Rahman 1981). 

For the majority of atomic and small molecule systems at equilibrium in the (N,P,T) ensemble (P is the pressure tensor) it is widely accepted that the most rigorous approach is to use the controlled pressure technique proposed by Rahman and Parrinello (RP) in conjunction with the Nose-Hoover thermostat.However, the choice of method must take careful account of the material we wish to study, how it is modeled and any external perturbations which we wish to apply. For polymers the Berendsen loose-coupling controlled pressure MD technique is a good compromise. Although the theoretical basis of this method has been criticised in practice it has been found that to within statistical uncertainties first-order properties are the same as those obtained by more rigorous approaches. 

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