Transcript Temperature and pressure coupling

Temperature and pressure coupling
MD workshops
26-10-2004
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
Causes of temperature and pressure
fluctuations
the temperature and pressure of a system tends to drift due
to several factors:
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drift as a result of integration errors
drift during equilibration
heating due to frictional forces
heating due to external forces
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)
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
 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 λ
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is the temperature coupling time constant
 need to specify
in input file (*.mdp file)
Some notes on Berendsen weak coupling
algorithm
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1.
very efficient for relaxing a system to the target
temperature
prolonged temperature differences of the separate
components leads to a phenomenon called ‘hotsolvent, 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
solutions
2.
3.
continued …
stochastic collisions (Anderson, 1980)
- a random particle’s 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
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 ξ, in the
equations of motion
H = K + V + Ks + Vs
Nosé-Hoover extended system
 The particles’ equation of motion:
 ξ is a dynamic quantity with its own equation of motion:
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is proportional to the temperature coupling time
constant
(specified in *.mdp file)
 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
 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
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)
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 β 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
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 β and
in the input file (*.mdp file)
 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
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
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
References
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Berendsen, H.J.C., Postma, J.P.M., DiNola, A., Haak, J.R. Molecular
dynamics with coupling to an external bath. J. Chem. Phys. 81:3684-3690,
1984
Nosé, S. A molecular dynamics method for simulations in the canonical
ensemble. Mol. Phys. 52:255-268, 1984
Hoover, W.G. Canonical dynamics: equilibrium phase-space distributions.
Phys. Rev. A 31:1695-1697, 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. 52:7182-7190, 1981
Nosé, S., Klein, M.L. Constant pressure molecular dynamics for molecular
systems. Mol. Phys. 50: 1055-1076, 1983