To use eq. (11.11) we need to obtain the velocities V_i(0) of all the molecule from a Maxwell-Boltzmann distribution of velocities,

f(v) dv = 4

(m / 2

k_BT )^{3/ 2} exp (-mv² / 2k_BT ) v² dv

(11.12)

An example of a 3 particle molecular dynamics (MD) is shown in Table 11.2. The initial coordinates are shown in fig 11.4. For simplicity, only the motion in the xy plane is considered.

Figure 11.4 Initial configuration of a three particle system.

Table 11.2

Components	Particle No. 1		Particle No.2		Particle No.3
	x	y	x	y	x	y

Step Number 0
Forces	55.47	55.47	-68.3	12.8	12.8	-68.3
Positions	0.00	00.00	4.00	0.0	0.0	4.0
Velocities	0.00	0.00	0.00	1.00	1.00	0.00

Step Number 1
Forces	+55.56	55.56	-68.8	13.23	13.23	-68.08
Positions	0.00174	0.00174	3.9979	0.0504	0.0504	3.9979
Velocities	0.0347	0.0347	-0.0427	1.008	1.008	-0.0427

Step Number 2
Forces	+54.3	54.3	-68.3	13.98	13.98	-68.3
Positions	0.00695	0.00695	3.9914	0.1016	0.1016	3.9914
Velocities	0.0695	0.0695	-0.0057	0.0163	0.0163	-0.0857

Step Number 3
Forces	51.4	51.4	-66.5	15.14	15.14	-66.5
Positions	0.0156	0.0156	3.9807	0.154	0.154	3.9807
Velocities	0.1383	0.1383	-0.172	1.0333	1.0333	-0.172

Table 11.2 coordinates of a three particle (Ar) system in the first three steps. The potential used is 4

[(

/r)¹² - (

/r)⁶] and

t = 0.05 ps. Initial velocities are (0,0), (0,1) and (1,0) for the x and y components for the three particles. The units are

/ps. The initial positions of the three particles 1,2 and 3 are, in

s, (0, 0), (4,0) and (0,4). The mass of Ar is 39.95 g/mol. With these units of mass and velocity, the unit of force becomes 10 J/ (mol

To use eq. (11.11) we need to obtain the velocities Vi(0) of all the molecule from a Maxwell-Boltzmann distribution of velocities,

To use eq. (11.11) we need to obtain the velocities V_i(0) of all the molecule from a Maxwell-Boltzmann distribution of velocities,