Density Functional Calculations of Metal Clusters: Structure, Dynamics, and Reactivity - Metallic Systems: A Quantum Chemist's Perspective - page 291

1 2 /

⎡
⎢

⎤
⎥

⎛
⎜

⎞
⎟

1 T

T t

λ = 1 + − 1 Δ t . (9.70)

τ ( )

. .

If.τ.is.large,.the.coupling.will.be.weak..If.τ.is.small,.the.coupling.will.be.strong,.and.
in.the.special.case.where.the.coupling.parameter.equals.the.time.step,.the.algorithm.
becomes. equivalent. to. the. simple. velocity. scaling. method.. The. advantage. of. this.
approach. is. that. it. does. permit. the. system. to. luctuate. about. the. desired. tempera-
ture..Because.of.its.exponential.convergence,.this.thermostat.is.well.suited.for.simu-
lated.annealing..Figure.9.5.shows.the.behavior.of.the.temperatures.along.the.BOMD.
simulation.of.a.copper.dimer,.the.same.system.used.in.Figure.9.4..The.exponential.
convergence.of.the.average.temperature.to.the.desired.one.(300.K).is.obvious.from.

500

450

400

350

300

250

200

150

T
< T >

100

50

0

5 1005 2005 3005 4005

Time (fs)

5005 6005 7005 8005 9005

(a)

5

4

3

2

1

0

-1

-2

-3

-4
-5

4.24 4.26 4.28 4.3 4.32

q

4.34 4.36 4.38 4.4

(b)

FIGURE 9.5 Temperature. proile. (a). and. phase. space. distribution. (b). for. a. copper. dimer.
using.the.Berendsen.thermostat.for.the.BOMD.simulation.