Accurate molecular dynamics simulation of reactive multi-species systems
is important to the design of artificial molecular machines. For example,
the existing reactive hydrocarbon Brenner's potential has been used to
design gears, hinges, three-way junctions, and bearings and helped motivate
the design of a hydrocarbon assembler. Unfortunately, reactive multi-species
potentials are only available for C-H-nobel gas, Si-F, Si-C-Ge and a few
others. This is not sufficient to design molecular factories of the type
envisioned by Drexler. Furthermore, developing reactive multi-species potentials
is difficult, time consuming, tedious, failure prone and, thus, rarely
attempted.
There are two parts to developing any force field: finding a functional
form that reflects the physics and choosing the parameters required by
the form. Much of the tedium is in the parameterization. We hypothesize
that this step can be automated by large computations on cycle-harvested
desktop computers. By automating parameterization, exploration of functional
forms should be enhanced.
Given a functional form, the parameters are typically chosen to fit
experimental values and/or ab initio calculations. The fitting process
can be difficult because functional forms usually have many local minima
that tend to trap search algorithms. We are developing the JavaGenes genetic
algorithm to evolve force field parameters. Genetic algorithms are somewhat
less likely to fall into local minima than simulated annealing or hill
climbing. For proof of concept, we have evolved the (Stillinger and Weber
90) published parameters for Si and F separately with good, although not
yet perfect, results. Over the next few months we expect to evolve the
full, combined Si-F published parameters and compare the results with parameters
fitted to ab initio energy calculations.
Results
Table 1 shows results evolving the (Stillinger and Weber 90) Si parameters:
For two body parameters we fit the energies of 100 Si dimers spaced 0.5-3.7
angstroms apart. The three body parameters were evolved separately with
the two body parameters fixed to the best values from the two-body run
and fit to 400 Si tetrahedra randomized around the low energy conformation.
Table 1
Parameter
Published value
Evolved value
A
7.049556277
7.062138589233899
B
0.6022245584
0.6283594386627
C
1.0
0.9999066666678916
p
4.0
3.9970443831775535
q
0.0
0.005038128110635121
Three body parameters
alpha
0.0
-0.00476705603392214
lambda
21.0
21.030398353724657
gamma
1.2
1.2003753288365615
Table 2 shows results evolving the (Stillinger and Weber 90) F parameters.
For two body parameters we fit the energies of 100 F dimers spaced 0.5-5
angstroms apart. The three body parameters were evolved separately with
the two body parameters fixed and fit to 100 F2+F confomations.
Table 2
Parameter
Published value
Evolved Value
A
0.52276
0.536060720470749
B
0.11277
0.123804003816043856
C
0.579495
0.5794579857222181
p
8.0
7.884508889552029
q
4.0
4.055374744348555
Three body parameters
alpha
38.295
31.904841586417522
lambda
-19.1475
-23.848659093495885
gamma
1.738485
1.84226440597913
delta
0.0818182
6.711483050303828
m
4.0
2.2224104136309757
beta
0.579495
2.4738447463466304
Note: The functional form was transformed to give all terms an identical
form, except FFF where the last three parameters are unique. These three
parameters have not yet been accurately evolved by JavaGenes. Once the
proof of concept is complete, we will use the procedures developed to create
reactive force fields for new systems, e.g., BN nanotubes.
References
(Stillinger and Weber 90) Frank H. Stillinger and Thomas A. Weber, Dynamical
Branching during Fluorination of the Dimerized Si(100) Surface: A Molecular
Dynamic Study, Journal of Chemical Physics, 92(10), pages 6239-6245, 15
May 1990.