Temperature%20and%20pressure%20coupling

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Temperature and pressure coupling

• MD workshops
• 26-10-2004

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Why control the temperature and pressure?

• isothermal and isobaric simulations (NPT) are
  most relevant to experimental data
• constant NPT ensemble constant number of
  particles, pressure, and temperature

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Causes of temperature and pressure fluctuations

• the temperature and pressure of a system tends to
  drift due to several factors
• drift as a result of integration errors
• drift during equilibration
• heating due to frictional forces
• heating due to external forces

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Temperature coupling methods in GROMACS

• weak coupling
• exponential relaxation Berendsen
  temperature coupling (Berendsen, 1984)
• extended system coupling
• oscillatory relaxation Nosé-Hoover
  temperature coupling (Nosé, 1984 Hoover, 1985)

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Berendsen temperature coupling

• there is weak coupling to an external heat bath
• deviation of system from a reference temperature
  To is corrected
• exponential decay of temperature deviation

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• the temperature of a system is related to its
  kinetic energy, therefore, the temperature can
  be easily altered by scaling the velocities vi by
  a factor ?
• is the temperature coupling time constant
• need to specify in input file (.mdp file)
  

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Some notes on Berendsen weak coupling algorithm

• very efficient for relaxing a system to the
  target temperature
• prolonged temperature differences of the separate
  components leads to a phenomenon called
  hot-solvent, cold-solute, even though the
  overall temperature is at the correct value
• Solutions
• apply temperature coupling separately to the
  solute and to the solvent problem with
  unequal distribution of energy between the
  different components

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solutions continued

• stochastic collisions (Anderson, 1980)
• - a random particles velocity is reassigned by
  random selection from the Maxwell-Boltzmann
  distribution at set intervals does not
  generate a smooth trajectory, less realistic
  dynamics
• extended system (Nosé, 1984 Hoover 1985)
• - the thermal reservoir is considered an
  integral part of the system and it is represented
  by an additional degree of freedom s
• - used in GROMACS

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Nosé-Hoover extended system

• canonical ensemble (NVT)
• more gentle than Anderson where particles
  suddenly gain new random velocities
• the Hamiltonian is extended by including a
  thermal reservoir term s and a friction parameter
  ?, in the equations of motion
• H K V Ks Vs

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Nosé-Hoover extended system

• The particles equation of motion
• ? is a dynamic quantity with its own equation of
  motion
• is proportional to the temperature coupling
  time constant (specified in .mdp file)

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• the strength of coupling between the reservoir
  and the system is determined by
• - when is too high slow energy
  flow between system and reservoir
• - when is too low rapid
  temperature fluctuations

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• Nosé-Hoover produces an oscillatory relaxation,
  it takes several times longer to relax with
  Nosé-Hoover coupling than with weak coupling
• can use Berendsen weak coupling for equilibration
  to reach desired target, then switch to
  Nosé-Hoover
• Nosé-Hoover chain the Nose-Hoover thermostat is
  coupled to another thermostat or a chain of
  thermostats and each are allowed to fluctuate

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Pressure coupling

• The system can be coupled to a pressure bath as
  in temperature coupling
• weak coupling
• exponential relaxation Berendsen pressure
  coupling
• extended ensemble coupling
• oscillatory relaxation Parrinello-Rahman
  pressure coupling (Parrinello and Rahman, 1980,
  1981, 1982)

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Berendsen pressure coupling

• equations of motion are modified with a
• first order relaxation of P towards a
  reference Po
• rescaling the edges and the atomic coordinates ri
  at each step by a factor u leads to volume change
• u is proportional to ß which is the isothermal
  compressibility of the system and which is the
  pressure coupling time constant. Both values
  must be specified in .mdp file

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• Berendsen scaling can be done
• 1. isotropically scaling factor is equal for
  all three directions i.e. in water
• 2. semi-isotropically where the x/y directions
  are scaled independently from the z direction
  i.e. lipid bilayer
• 3. anisotropically scaling factor is
  calculated independently for each of the three
  axes

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Parrinello-Rahman pressure coupling

• volume and shape are allowed to fluctuate
• extra degree of freedom added, similar to
  Nosé-Hoover temperature coupling, the Hamiltonian
  is extended
• box vectors and W-1 are functions of M
• W-1 determines the strength of coupling
• have to provide ß and
• in the input file (.mdp file)

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• if your system is far from equilibrium, it may be
  best to use weak coupling (Berendsen) to reach
  target pressure and then switch to
  Parrinello-Rahman as in temperature coupling
• in most cases the Parrinello-Rahman barostat is
  combined with the Nosé-Hoover thermostat
• the extended methods are more difficult to
  program but safer

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Weak coupling in .mdp file

• OPTIONS FOR WEAK COUPLING ALGORITHMS
• Temperature coupling
• tcoupl berendsen
• Groups to couple separately
• tc-grps Protein SOL_Na
• Time constant (ps) and reference temperature
  (K)
• tau-t 0.1 0.1
• ref-t 300 300
• Pressure coupling
• Pcoupl berendsen
• Pcoupltype isotropic
• Time constant (ps), compressibility (1/bar) and
  reference P (bar)
• tau-p 1.0
• compressibility 4.5E-5
• ref-p 1.0

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Extended system coupling in .mdp file

• OPTIONS FOR WEAK COUPLING ALGORITHMS
• Temperature coupling
• tcoupl nose-hoover
• Groups to couple separately
• tc-grps PROTEIN SOL_Na
• Time constant (ps) and reference temperature
  (K)
• tau-t 0.5 0.5
• ref-t 300 300
• Pressure coupling
• Pcoupl parrinello-rahman
• Pcoupltype isotropic
• Time constant (ps), compressibility (1/bar) and
  reference P (bar)
• tau-p 5.0
• compressibility 4.5E-5
• ref-p 1.0

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References

• Berendsen, H.J.C., Postma, J.P.M., DiNola, A.,
  Haak, J.R. Molecular dynamics with coupling to an
  external bath. J. Chem. Phys. 813684-3690, 1984
• Nosé, S. A molecular dynamics method for
  simulations in the canonical ensemble. Mol.
  Phys. 52255-268, 1984
• Hoover, W.G. Canonical dynamics equilibrium
  phase-space distributions. Phys. Rev. A
  311695-1697, 1985
• Berendsen, H.J.C. Transport properties computed
  by linear response through weak coupling to a
  bath. In Computer Simulations in Material
  Science. Meyer, M., Pontikis, V. eds. Kluwer
  1991, 139-155
• Parrinello, M., Rahman, A. Polymorphic
  transitions in single crystals A new molecular
  dynamics method. J. Appl. Phys. 527182-7190,
  1981
• Nosé, S., Klein, M.L. Constant pressure molecular
  dynamics for molecular systems. Mol. Phys. 50
  1055-1076, 1983

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