Density Functional Calculations of Metal Clusters: Structure, Dynamics, and Reactivity - Metallic Systems: A Quantum Chemist's Perspective - page 290

600

T
< T >

500

400

300

200

100

0

5 1005 2005 3005 4005

Time (fs)

5005 6005 7005

(a)

4

3

2

1

0

-1

-2

-3

-4

4.24 4.26 4.28 4.3 4.32

q

4.34 4.36 4.38 4.4

(b)

FIGURE 9.4 Temperature. proile. (a). and. phase. space. distribution. (b). for. a. copper. dimer.
using.the.velocity.scaling.thermostat.for.the.BOMD.simulation.

points.visited.in.phase.space.are.not.the.ones.expected.for.the.canonical.sampling..
Therefore,.the.generated.trajectories.are.not.suited.for.the.calculation.of.thermody-
namic.averages.
An. alternative. way. to. maintain. the. temperature. is. to. couple. the. system. to. an.
external. heat. bath. that. is. ixed. at. the. desired. temperature. (Berendsen. thermostat.
[88])..The.bath.acts.as.a.source.of.thermal.energy,.supplying.or.removing.heat.from.
the.system.as.needed.
The.velocities.are.scaled.at.each.step,.such.that.the.rate.of.change.of.temperature.
is.proportional.to.the.difference.in.temperature.between.the.bath.and.the.system

dT t
dt

( ) 1

τ

= ( T T t − ( )). (9.69)

. .

Here,.τ.is.a.coupling.parameter.whose.magnitude.determines.how.tightly.the.bath.
and. the. system. are. coupled. together.. With. this. method,. the. system. temperature.
converges.exponentially.toward.the.desired.temperature..The.scaling.factor.for.the.
velocities.is