Thermostats and Barostats PDF
Thermostats and Barostats PDF
Thermostats and Barostats PDF
Justin Finnerty
j.finnerty@grs-sim.de, 2011
Scientific theories of physical world
•Energy is invariant
•E = PV/nRT
• If we start in region with high P(q,p) energy conserving evolution over time will
continue to sample high P(q,p) phase space (note these are unique and non-
intersecting trajectories)
Molecular dynamics review
Time average of trajectories
• MD ansatz is starting from an initial low energy phase point (ie high P(q,p))
and moving along an iso-energetic time evolving trajectory will sample
properties of interest with high probability weights
�
• End of sampling uses property value convergence (�A� − A(ti ))2
Molecular dynamics review
pressure, temperature, volume
• Temperature:
N
1 � |pi |2
• T =
3N kB i=1 mi
• Volume:
• Biological reactions
• Stochastic methods
• Strong-coupling methods
• Weak-coupling methods
• τ is relaxation constant
Nosé-Hoover thermostat
• Hoover, Phys. Rev. A 31 (1985) 1695; S. Nosé, J. Chem. Phys. 81 (1984) 511;
S. Nosé, Mol. Phys. 52 (1984) 255
1.3
T (ε/kB)
1.2
1.1 LD
Berendsen
NoséHoover
1
0 1 2 3 4 5
*
t
p2ηM −1
ṗηM = − kB T. (6.135)
Nosé-Hoover thermostat
• The Parrinello-Rahman barostat (J. Appl. Phys. 52 (1981) 7182) extended this
further by making each unit vector of the unit-cell independent so that
• The additional terms in the equations of motion are of similar type to that
shown for the Nosé-Hoover thermostat (though somewhat more complex!)
does indic
might have been guessed by the title given to this subsection.
after quen
Figure 3 shows the details of the changes with the passage of
only the s
time. The MD cell, i.e., the h matrix, undergoes large and
but it also
swift changes which cannot possibly be described as elastic
shells sho
Parrinello-Rahman barostat deformations. In fact, as Fig. 3 shows, when equilibrium was
reached the average values of the components of h* were
cle positio
were pres
(h Tl) = 5.54 ± 0.03, (h!2) = 9.76 ± 0.06,
here that
the c axis
• Graph of MD simulation of a metal Havi
under a c
crystal after application of external .x TI = 20
stress. temperatu
was no st
veal the s
• Note second order decay of the ing the lo
three variables hii related to the quench te
unit-vectors ................. ,............................. "' .......
ff
8
6
(a)
...................... ........... .......... ''' ............. " ... ...... .............
o 500 1000
Consequences of control method
non-Hamiltonian
strong coupling canonical in phase space disturb dynamic
accuracy
maintain canonical
ensemble.
Nosé-Hoover thermostat considered most reliable
slow, second-order
and Parinello-Rahman for simulation at
approach to equilibrium
barostat equilibrium and for
predicting thermo-
dynamic properties
Group discussion: MD calculation process
• What impacts will the different control methods have on parallel MD code?
(steps in right square not necessarily shown in actual order)