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Pressure Control

Constant pressure simulation (and pressure calculation) require periodic boundary conditions. Pressure is controlled by dynamically adjusting the size of the unit cell and rescaling all atomic coordinates (other than those of fixed atoms) during the simulation.

Pressure values in NAMD output are in bar. PRESSURE is the pressure calculated based on individual atoms, while GPRESSURE incorporates hydrogen atoms into the heavier atoms to which they are bonded, producing smaller fluctuations. The TEMPAVG, PRESSAVG, and GPRESSAVG are the average of temperature and pressure values since the previous ENERGY output; for the first step in the simulation they will be identical to TEMP, PRESSURE, and GPRESSURE.

The phenomenological pressure of bulk matter reflects averaging in both space and time of the sum of a large positive term (the kinetic pressure, $ nRT/V$ ), and a large cancelling negative term (the static pressure). The instantaneous pressure of a simulation cell as simulated by NAMD will have mean square fluctuations (according to David Case quoting Section 114 of Statistical Physics by Landau and Lifshitz) of $ kT/(V \beta)$ , where $ \beta$ is the compressibility, which is RMS of roughly 100 bar for a 10,000 atom biomolecular system. Much larger fluctuations are regularly observed in practice.

The instantaneous pressure for a biomolecular system is well defined for ``internal'' forces that are based on particular periodic images of the interacting atoms, conserve momentum, and are translationally invariant. When dealing with externally applied forces such as harmonic constraints, fixed atoms, and various steering forces, NAMD bases its pressure calculation on the relative positions of the affected atoms in the input coordinates and assumes that the net force will average to zero over time. For time periods during with the net force is non-zero, the calculated pressure fluctuations will include a term proportional to the distance to the affected from the user-defined cell origin. A good way to observe these effects and to confirm that pressure for external forces is handled reasonably is to run a constant volume cutoff simulation in a cell that is larger than the molecular system by at least the cutoff distance; the pressure for this isolated system should average to zero over time.

Because NAMD's impluse-basd multiple timestepping system alters the balance between bonded and non-bonded forces from every timestep to an average balance over two steps, the calculated pressure on even and odd steps will be different. The PRESSAVG and GPRESSAVG fields provide the average over the non-printed intermediate steps. If you print energies on every timestep you will see the effect clearly in the PRESSURE field.

The following options affect all pressure control methods.

Berendsen pressure bath coupling

NAMD provides constant pressure simulation using Berendsen's method. The following parameters are used to define the algorithm.

Nosé-Hoover Langevin piston pressure control

NAMD provides constant pressure simulation using a modified Nosé-Hoover method in which Langevin dynamics is used to control fluctuations in the barostat. This method should be combined with a method of temperature control, such as Langevin dynamics, in order to simulate the NPT ensemble.

The Langevin piston Nose-Hoover method in NAMD is a combination of the Nose-Hoover constant pressure method as described in GJ Martyna, DJ Tobias and ML Klein, "Constant pressure molecular dynamics algorithms", J. Chem. Phys 101(5), 1994, with piston fluctuation control implemented using Langevin dynamics as in SE Feller, Y Zhang, RW Pastor and BR Brooks, "Constant pressure molecular dynamics simulation: The Langevin piston method", J. Chem. Phys. 103(11), 1995.

The equations of motion are:

$\displaystyle r'$ $\displaystyle =$ $\displaystyle p/m + e' r$  
$\displaystyle p'$ $\displaystyle =$ $\displaystyle F - e' p - g p + R$  
$\displaystyle V'$ $\displaystyle =$ $\displaystyle 3 V e'$  
$\displaystyle e''$ $\displaystyle =$ $\displaystyle 3V/W (P - P_0) - g_e e' + R_e/W$  
$\displaystyle W$ $\displaystyle =$ $\displaystyle 3 N \tau^2 k T$  
$\displaystyle <R^2>$ $\displaystyle =$ $\displaystyle 2 m g k T / h$  
$\displaystyle \tau$ $\displaystyle =$ $\displaystyle {\rm oscillation period}$  
$\displaystyle <R_e^2>$ $\displaystyle =$ $\displaystyle 2 W g_e k T / h$  

Here, $ W$ is the mass of piston, $ R$ is noise on atoms, and $ R_e$ is the noise on the piston.

The user specifies the desired pressure, oscillation and decay times of the piston, and temperature of the piston. The compressibility of the system is not required. In addition, the user specifies the damping coefficients and temperature of the atoms for Langevin dynamics.

The following parameters are used to define the algorithm.

next up previous contents index
Next: User Defined Forces Up: Standard Minimization and Dynamics Previous: Temperature Control and Equilibration   Contents   Index