Copyright © 1998–2020 by A. Miyoshi
SSUMES - Quick Start step-4
SSUMES - Quick Start step-4
Example problem-4
Next example is the steady-state dissociation problem
of the adducts shown in Fig. Q2. For the multiple-well system,
the solution to the eigenvalue problem (1) is not always the solution
needed.
![](img/eqQ-1.gif)
(1)
where,
![](img/eqQ-2.gif)
(2)
The solution we want may be the solution of the eq (3), which is the
steady-state dissociation of
well-1 (2-phenylvinyl radical).
![](img/eqQ-3.gif)
(3)
The solution for this equation can be obtained by iteratively solve the
linear equation (4), starting from an initial guess,
n1(0).
![](img/eqQ-4.gif)
(4)
Control input
The contents of the control input file,
rc2h2ph_m_da.inp
,
is shown below.
# phenyl-c2h2 quadruple-well model - dissociation (from all wells)
tempList 1000
pressUnit atm
pressLog10Range -6 6 1
err3 1e-15
well{
index 1
filename rc2h2ph_mw1_mas
offset 27
connect 2 1 ! connect to well-2 via channel-1
connect 3 2 ! connect to well-3 via channel-2
}
well{
index 2
filename rc2h2ph_mw2_mas
offset 23
connect 1 1 ! connect to well-1 via channel-1
connect 4 2 ! connect to well-4 via channel-2
}
well{
index 3
filename rc2h2ph_mw3_mas
offset 71
connect 1 1 ! connect to well-1 via channel-1
connect 4 2 ! connect to well-4 via channel-2
}
well{
index 4
filename rc2h2ph_mw4_mas
offset 0
connect 2 1 ! connect to well-2 via channel-1
connect 3 2 ! connect to well-2 via channel-2
}
Compared to the previous example, the lines beginning with
'recombChan'
or
'truncate'
are missing since they are not needed for steady-state dissociation
problem. The line beginning with
'err3'
specifies
cut-off of the collisional energy transfer probability which determines
the band-width of the matrix of the master-equation.
Solving master-equation for dissociation
by an eigenvalue problem solver
- Run diseig as:
(This may take a few minutes.)
diseig rc2h2ph_m_da > rc2h2ph_m_da_diseig.log
- The program diseig gives solution to the eigenvalue problem (1)
as the least-negative eigenvalue.
A part of the results is shown below.
These are the rate of dissociation of a kind of mixture of four
intermediates.
Solving master-equation for dissociation
by an iterative linear equation solver
- Run dislit as:
(This may also take a few minutes.)
dislit rc2h2ph_m_d1 > rc2h2ph_m_d1_dislit.log
- The program dislit gives solution to the problem (3)
by iterative procedure (4).
A part of the results is shown below.
Note that the total rate constant,
(
'ktot'
), are different from the results obtained by
the eigenvalue problem solver, diseig.
- Run dislit as:
(This may also take a few minutes.)
dislit rc2h2ph_m_d4 > rc2h2ph_m_d4_dislit.log
- In this example, the solution to eq (5) is calculated by dislit.
![](img/eqQ-5.gif)
(5)
A part of the results is shown below.
- The results including that in example-2 are summarized in the plots below.
- The solution to eq (3),
![](img/eqQ-3.gif)
(3)
is the steady-state dissociation of well-1 (2-phenylvinyl), under
the condition that only 2-phenylvinly is produced but there is sufficiet
time to maintain the steady-state population of this molecule.
Even in this case, the rate of dissociation is much smaller than the solution
obtained in the example-2 where the all the other wells are ignored.
But it is larger than the steady-state solution obtained by diseig
for a kind of steady-state mixture of four wells. These results can be
understood by lookin at the steady-state population fractions in wells.
The right plot for 'f1'
shows the fraction of population in
well-1. Even when the 2-phenylvinyl is produced in the system,
there are wells more stable than it, and the buffering effect reduces
the steady-state population in well-1, resulting in the smaller overall
dissociation rate.
- Similarly, the solution to eq (5),
![](img/eqQ-5.gif)
(5)
is the steady-state dissociation of well-4 molecule.
- For the multiple-well system with fairly high barriers, as this example,
the independent solutions to each well are known to be able to reproduce
the phenomena. [N. Yamauchi, A. Miyoshi, K. Kosaka, M. Koshi, and H. Matsui,
J. Phys. Chem. A, 103, 2723–2733 (1999).].