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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:
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
the constant of motion. Parrinello-Rahman method can be combined
with numerical thermostats such as Langevin thermostat (see Sec. 6.62.5),
method [65,72] to generate ensemble.
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