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c CCLRC

Section 3.2

Molecular dynamics simulations normally require properties that depend on position and velocity
at the same time (such as the sum of potential and kinetic energy). The velocity at time t is
obtained from the average of the velocities half a timestep either side of timestep t:

v(t)

1
2

v(t -

1
2

t) + v(t +

1
2

(3.8)

The instantaneous kinetic energy, for example, can then be obtained from the atomic velocities as

kin

(t) =

1
2

(t) ,

(3.9)

and assuming the system has no net momentum the instantaneous temperature is

T (t) =

kin

(t) ,

(3.10)

where i labels particles, N the number of particles in the system, k

the Boltzmann's constant and

f the number of degrees of freedom in the system.

f = 3N - 3 - 3N

f rozen

- 3N

shells

- N

constraints

- p .

(3.11)

Here N

f rozen

indicates the number of frozen atoms in the system, N

shells

number of core-shell units

and N

constraints

number of bond and pmf constraints. Three degrees of freedom are subtracted

for the centre of mass zero net momentum (we impose) and p is zero for periodic or three for
non-periodic systems.

The routines nve 1 vv and nve 1 lfv implement the Verlet algorithm in velocity and leapfrog
flavours respectively and calculate the instantaneous temperature. The conserved quantity is the
total energy of the system

NVE

= U + E

kin

(3.12)

where U is the potential energy of the system and E

kin

the kinetic energy at time t.

The full selection of integration algorithms, indicating both VV and LFV cast integration, within
DL POLY 3 is as follows:

nve 1 vv

nve 1 lfv

Constant E algorithm

nvt l1 vv