Chapter 3, Harder Questions, Answers
Q2
Do you think it is possible (in practical terms? In principle?) to develop a forcefield
that would accurately calculate the geometry of any kind of molecule?
It is intuitively apparent that with sufficient parameters a physical system, and
even a set of systems, can be simulated to any desired accuracy (although there does
not seem to a formal theorem in physics or mathematics to this effect). In this vein,
the mathematician John von Neumann said “With four parameters I can cover an
elephant, and with five I can make him wiggle his trunk” [1]. The logistics of
putting together such an enormous suite of algorithms apart, whether such a
forcefield would be practical is another matter.
Reference
- Speaking to Freeman Dyson, Enrico Fermi quoted von Neumann: Dyson F (2004) Nature
427 :297
Chapter 3, Harder Questions, Answers
Q3
What advantages or disadvantages are there to parameterizing a forcefield with the
results of “high-level” calculations rather than the results of experiments?
If you are a purist and regard molecular mechanics as a semiempirical method
(the theoretical part coming from the physics of springs and the theory of van der
Waals and electrostatic and nonbonded interactions) then you will be uncomfort-
able with any nonexperimental (nonempirical) parameterization. As a practical
matter, however, we simply want a method that works, and we can compare the
two approaches to parameterizing in this context.
Accurate force constants etc. can be obtained from high-level ab initio (Chapter
5) or DFT (Chapter 7) calculations. If we use these for a forcefield, then we are
parameterizing to match reality only to the extent that the high-level calculations
match experiment. Apart from a possible philosophical objection, which we essen-
tially dismissed, there is the question of the trustworthiness of the ab initio or DFT
results. For “normal” molecules, that is, species which are not in some way exotic
[1], these calculations do indeed deliver quite reliable results. The advantages they
offer over experimental acquisition of the required parameters is that these quan-
tities (1) can be obtained for a wide variety of compounds without regard to
synthetic difficulties or commercial availability, (2) are offered up transparently
Answers 603