Bearing in mind that MM algorithms are heavily parameterized, this does not
seem so surprising: the mathematician John von Neumann said “With four para-
meters I can cover an elephant, and with five I can make him wiggle his trunk.” [4].
MM uses more than four parameters. The accuracy is perhaps not surprising, but it
is nevertheless impressive.
References
- For a very detailed treatment of molecular vibrations, see Wilson EB Jr, Decius JC, Cross PC
(1955) Molecular vibrations. McGraw-Hill; Dover edition, 1980, New York. Particularly
relevant are chapters 1,2, and 8. - (a) Bader RFW (1990) Atoms in molecules. Clarendon Press, Oxford. (b), 1990. (b) Bader
RFW, Popelier PLA, Keith TA (1994) Angew Chem Int Ed Engl 33: 620 - Huber KP, Herzberg G (1979) Molecular spectra and molecular structure. IV. Constants of
diatomic molecules. Van Nostrand Reinhold, New York - Speaking to Freeman Dyson, Enrico Fermi quoted von Neumann: Dyson F (2004) Nature 427: 297
Chapter 1, Harder Questions, Answers
Q5
What kinds of properties might you expect MM to be unable to calculate?
Unassisted MM can’t calculate electronic properties, since MM knows nothing
about electrons. It is possible to use empirical parameters to elicit from a structure,
calculated by MM, electronic properties such as atomic charges: atoms in “standard
molecules” can be assigned charges based on electronic calculations like ab initio
or DFT, and these could be incorporated into a database. An MM program could
draw on these data to obtain a kind of educated guess of the atomic charges (which
might then be used to calculate dipole moments and indicate likely sites of nucleo-
philic and electrophilic attack).
Thus pure MM (MMby itself) can’t calculate UV spectra, the shapes and
energies of molecular orbitals, and electron distribution and derivative properties
of this, like atomic charges, dipole moments, and more arcane molecular features
like bond paths (associated with atoms-in-molecules theory, AIM [1]).
Reference
- (a) Bader RFW (1990) Atoms in molecules. Clarendon Press, Oxford. (b). Bader RFW,
Popelier PLA, Keith TA (1994) Angew Chem Int Ed Engl 33:620
Answers 589