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Performances of the SIGNATURE Program
Performances of the SIGNATURE Program
This example is a study case that was designed to quantify how
well the stochastic structure generator performs.
In the example, the potential energy distribution of the
isomers of C8H10 were analyzed using the deterministic and
the stochastic versions of the structure generator presented above.
One may notice that in the present example there is no need to
resolve the signature equation. In fact, the structures to be
generated are all composed of 8 carbon atoms and 10 hydrogen atoms;
these atoms constitute the list of molecular fragments.
The deterministic version of the structure generator computed
4008 different isomers of C8H10 (not including eventual stereoisomers).
To generate these isomers the deterministic version of the structure
generator ran for 353.0 s CPU time on a SGI Personal Iris Workstation.
For comparison, the stochastic version of the structure generator
estimated the number of isomers to be 3399. To calculate this number
the stochastic generator was run for 16.5 s CPU time until the deviation
between the estimates was lower than 1000.
To compute the energy distribution, the potential
energy of each isomer was calculated using
the MM simulations provided by Polygraf 3.21 (Molecular Simulations Inc.).
All energies were minimized using the DREIDING force field and using a
conjugate gradient algorithm for 500 steps or until the root mean square
between two successive conformations was lower than 0.1 (kcal/mol)/A.
The potential energy distribution of the 4008 isomers is shown in
the figure. This distribution was obtained in 114 285 s of CPU time
on a SGI Personal Iris Workstation. Most of the time was spent
minimizing the potential energy (as mentioned above, it took only
353 s to generate all the isomers without minimization).
Using the same hardware, it took 12 223 s to generate a potential
energy distribution from a random sample of 500 isomers, and 1 344 s
for a random sample of 50 isomers.
Let f be the fraction of isomers
of the total population having their potential energy in any given
range of the figure. Let f500 be the same fraction obtained from
the sample of 500 isomers, and let f50 be the fraction obtained from
the sample of 50 isomers. It can be shown from figure 2 that on
average | f500-f | = 0.17 f, and | f50-f | = 0.35 f.
Therefore, the sample of 50 isomers gives an acceptable
approximation of the potential energy distribution.
The same calculations were performed for all the hydrocarbons
CnHn+i, with n varying between 2 and 8, and i varying between 0 and 2.
For each of the previous hydrocarbons, it was concluded that a good
approximation of the potential energy distribution can be obtained
by generating a sample that represents only a small fraction of the
total population.
For more information e-mail to:
Jean-Loup Faulon /
January 12, 1996