FATE OF MERCURY IN THE ARCTIC Michael Evan ... - COGCI

where Ri is the rate of population of HgBr(Ei) via reaction 4.1, ω is the frequency of collisions
between HgBr * and N2, and Pij is the probability of transfer of HgBr from grain j to grain i on
collision with N2. The individual Pij were estimated using the exponential down model (28). The
average energy for downward transitions (i < j), down, was set to be 400 cm -1 for N2 (28), and
assumed to be independent of temperature. The parameters σ and ε /k, which describe the
intermolecular potential between HgBr and N2 from which ω is calculated, were set to typical
values of 4 Å and 400 K, respectively (28). For upward transitions where j > i, Pij was calculated
by detailed balance. In order to simulate irreversible stabilization of HgBr via reaction 4.3, an
absorbing boundary was set 24 kJ mol -1 below the energy of the reactants, so that collisional
energization from the boundary to the threshold was highly improbable. The rate of population of
grain i, Ri, is given by detailed balance between reactions 4.1 and 4.2:
Ri = krec,∞ [Hg] [Br] ηi (II)
where krec,∞ is the limiting high-pressure association rate coefficient (reaction 4.1) and
η i =
k − 4 , i f i
∑ k − 4 , i f i
i
(III)
where fi is the equilibrium Boltzmann distribution of HgBr(Ei).
The microcanonical rate coefficients for dissociation of HgBr were determined using
inverse Laplace transformation (25), which links k-1(Ei) directly to krec,∞. In the present case, krec,∞
was expressed in the Arrhenius form A ∞ exp(-E ∞ /R T). Assuming that collisions between Hg and
Br are governed by the long-range attractive dispersion force, then A ∞ = 1.67 x 10 -10 cm 3 molecule -
1 -1 ∞ -1
s and E = -423 J mol .
The microcanonical rate coefficient for dissociation is then given by
∞
(
i
3/
2 E −E
−∆H
∞ o 0.
5
− ∆H0
) − x]
∞ o
A 2πµ
)
i
0
k−4, i =
N p(
x)[(
Ei
E
3 ∫
−
N(
E ) Γ(
1.
5)
h 0
where the density of states of HgBr at energy Ei, N(Ei), was calculated using a combination of the
Beyer-Swinehart algorithm for the vibrational modes (including a correction for anharmonicity)
dx
(V)
7