Statistics
Stochastic thermostats
Sushmita Pal
Problems in molecular simulations (FB810)
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Experiments work at constant temp so NVT ensemble has to be incorporated
                NVE ensemble gives the correct dynamics
For NVT, we alter the newtons motion to reach the target temperature
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The velocity is altered in the system, it changes the dynamic properties and does not give the true
result
Thermostat
Constant Temperature
Kinetic energy
Velocity
Equation of motion
Changing the equation of motion
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       Changes in velocity by altering the newton’s equation of motion
Dampening of dynamic properties
Deviation from “true” dynamics
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Types of thermostats
Velocity Randomizing
Velocity rescaling
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COUPLING CONSTANT
Ƭt (coupling constant) determines how strongly the system is coupled to heat bath
More strongly coupled, Ƭt           0
Less strongly coupled, Ƭt          ∞
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Velocity randomizing thermostat
Andersen
Massive Andersen
Langevin Dynamics
randomly reassigning new velocities to all the molecules
randomly reassigning new velocities to a group of molecules
changing the Newtonian equation of motion by adding a frictional term and a random term for
collision of molecules
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Velocity rescaling thermostat
Stochastic rescaling
Berendsen
Nośe-Hoover
Temperature relaxation is exponential
Temperature relaxation is exponential with correct energy distribution by addition of properly
chosen stochastic factor that rescales the kinetic energy
Temperature relaxation in oscillatory manner
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Some dynamical properties
Short time scale dynamical properties
Diffusivity
Rotational correlation time
Viscosity
Long time scale dynamical properties
Dynamic structure factor using Dynamic light scattering experiments
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SOLUTIONS
¡ Use of velocity rescaling thermostats than velocity rescaling
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•Various thermostats with different   Ƭt
Table, Excel, calendar Description automatically generated
Simulations of TIP3P water model
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Graphical user interface Description automatically generated
                           Simulations of solvated polymer chain
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• Use of Non-invasive scheme ( only solvent is thermostatted and solute is connected to heat bath
i.e, solvent)
SOLUTIONS
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a) Simulations of solvated united-atom methane          b) a solvated polymer chain
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•Use of Global velocity rescaling thermostat rather than massive velocity rescaling thermostat
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•Global approach – the coupling constant is coupled to ensembled average Kinetic energy of the
system
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•Massive approach- the coupling constant is coupled to individual kinetic energy of the particle
SOLUTIONS
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Chart, bar chart, histogram Description automatically generated
Simulations of TIP3P water with coupling constants 0.1 ps, 1 ps, 10 ps and 100 ps respectively
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THANK YOU!!
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