To carry out the reaction steps associated to the hydration of
ethylene to ethanol, firstly, a direction, forward or backward, to
take the reaction step, is randomly chosen. If the forward direction
of the reaction is chosen, then an ethylene molecule is randomly
selected, and its potential energy of interaction UðdÞ
1 with all the
other molecules is calculated before that molecule is deleted from
the simulation box. Following this deletion, a water molecule is
randomly chosen, and its potential energy of interaction UðdÞ
2 with
the remaining molecules is calculated before that molecule is
deleted. After this deletion, an ethanol molecule is created in the
same position as the water molecule that was deleted, and its
potential energy of interaction UðcÞ
3 with all the other molecules is
calculated. The change of configurational energy for the reaction
step in the forward direction is then given by the expression:
DUðfÞ
t ¼ UðcÞ
3 UðdÞ
1 UðdÞ
2 (4)
By setting z = +1, the product in Eq. (1) takes the form:
YC
i¼1
Ni!
ðNi þ nizÞ!
¼ N1N2
ðN3 þ 1Þ (5)
Substitution of n ¼ 1, z = +1, and Eq. (5) into Eq. (1) leads to the
following expression for the probability of acceptance of a reaction
step in the forward (f) direction:
PðfÞ
rx ¼ min 1;
kBT
P0V
Keq
N1N2
ðN3 þ 1Þ
exp DUðfÞ
t
kBT
( !)
(6)
where the change of configurational energy DUðfÞ
t is given by
Eq. (4).
If the backward direction of the reaction is chosen, then an
ethanol molecule is randomly selected, and its potential energy of
interaction UðdÞ
3 with all the other molecules is calculated before
that molecule is deleted from the simulation box. Following this
deletion, a water molecule is created in the same position as the
ethanol molecule that was deleted, and its potential energy of
interaction UðcÞ
2 with all the other molecules is calculated. Next, an
et