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ParrinelloRahman dynamics
In the method of Parrinello and Rahman [79,80],
the equations of motion for atomic and lattice degrees of freedom
are derived from the following Lagrangian:

(6.35) 
where is a position vector in fractional coordinates for atom ,
is the matrix formed by lattice vectors, tensor is defined as
, is the external pressure, is the cell volume
(
), and is a constant with dimensionality of mass.
Integrating equations of motion based on Lagrangian defined in eq. 6.35
generates ensemble with enthalpy
being
the constant of motion. ParrinelloRahman method can be combined
with numerical thermostats such as Langevin thermostat (see Sec. 6.62.5),
or NoséPoincaré
method [65,72] to generate ensemble.
N.B. Requests for support are to be addressed to: vasp.materialphysik@univie.ac.at