Density Functional Calculations of Metal Clusters: Structure, Dynamics, and Reactivity - Metallic Systems: A Quantum Chemist's Perspective - page 293

500

450

400

350

300

250

200

150

100

T
< T >

50

0

5 1005 2005 3005 4005

Time (fs)

5005 6005 7005

(a)

10
8
6
4
2
0
-2
-4
-6
-8
-10
-12

3 3.5 4 4.5 5 5.5 6

(b) q

FIGURE 9.6 Temperature. proile. (a). and. phase. space. distribution. (b). for. a. copper. dimer.
using.the.isokinetic.thermostat.for.the.BOMD.simulation.

For. some. systems,. the. Nosé-Hoover. method. described. above. does. not. yield. a.
canonical. distribution. in. phase. space,. even. for. very. long. simulations. [91,93].. The.
distribution.itself.has.a.dependence.on.the.particles.momenta,. p A ,.as.well.as.the.ther-
mostat.momenta,. p s ..While.the.luctuations.of. p A .are.driven.by.a.thermostat,.there.
is.nothing.to.drive.the.luctuations.of. p s ..These.luctuations,.which.clearly.occur.in.
ergodic.systems,.are.important.in.driving.the.system.to.ill.phase.space..This.sug-
gests.to.thermostat. p s .and,.by.analogy,.the.thermostat.of. p s .plus.its.thermostat,.etc.,.
thus.forming.a.chain.of.thermostats.
The.Hamiltonian.for.the.new.extended.system.is.then.given.by

N n n

2 2

1
2

p p

Q

N ln s

∑ ∑ ∑

A si f i

s

H = + V({ }) r + + ln + , (9.76)

A 1

2

m s 2 β β

A

.

A i = 1 i = 2

.