A pressure coupling method

1. Molecular Dynamic: Parrinello Pressure
Coupling Method
Submitted To –
Dr. Sudip Chakraborty
Submitted By – Usha
16mslsbf16
M.sc Bioinformatics

2. Pressure Coupling:
The system can be coupled to a pressure bath as in temperature coupling
Weak coupling – Berendsen Pressure Coupling
exponential relaxations
Extended ensemble coupling – Parrinello Rahman Pressure Coupling
oscillatory relaxation

3. Berendsen pressure coupling
Rescales the coordinates and box vectors at every step
Yields a simulation with the correct average pressure
Equations of motion are modified with a first order relaxations of P
𝑑𝑃
𝑑𝑡
=
𝑃0 − 𝑃
Ƭ 𝑝
here Ƭ 𝑝 represents pressure coupling time constant

4. Parrinello Rahman Pressure Coupling
Based on constant NPT ensemble: constant number of particles, pressure, and
temperature
Volume and shape are allowed to fluctuate
Extra degree of freedom added similar to Nose Hoover temperature coupling
Useful for studying the stress strain relationship of material

5. Parrinello Rahman Pressure Coupling
Extra degree of freedom added, similar to Nose-Hoover temperature coupling, the
Hamiltonian is extended
𝑑2 𝑟 𝑖
𝑑𝑡2 =
𝐹 𝑖
𝑚 𝑖
- M
𝑑𝑟 𝑖
𝑑𝑡
𝑊−1 determines the strength of coupling and the box can be reformed
(𝑊−1)𝑖𝑗 =
4π2 β 𝑖𝑗
3 𝑇2
𝑝 𝐿

6. Parrinello Rahman Pressure Coupling
In most cases the Parrinello Rahman barostat is coupled with Nose- Hoover
thermostat
The extended methods are more difficult to program but safe
If system is far from equilibrium, it may be best to use weak coupling to reach target
pressure and then switch to Parrinello coupling method

7. References
Parrinello, M., Rahman, A. Polymorphic transitions in single crystals: A new molecular
Dynamics method. J. Appl. Phys. 52:7182–7190, 1981.
Nose, S., Klein, M. L. Constant pressure molecular dynamics for molecular systems.
Mol. Phys. 50:1055–1076, 1983.

8. Thankyou