However, a subterfuge enables MM molecular geometries to yield dipole
moments: the dipole moment of a molecule can be considered to be the vector
sum of bond moments, and like bond energies these are with a fair degree of
accuracy transferable between molecules. So from the geometry, which gives
the relative positions of the vectors in space, a dipole moment can be calculated,
purely empirically.
Delocalization energydenotes the energy by which a molecule is stabilized or
destabilized compared to a hypothetical reference compound in which electrons
(usuallypelectrons) are not as mobile. The canonical example is the energy of
benzene compared to the hypothetical 1,3,5-cyclohexatriene in which there are
three distinct double and three distinct triple bonds. With caveats, one measure
of this energy is the heat of hydrogenation of benzene compared to three times
the heat of hydrogenation of cyclohexene. As an electronic phenomenon, this
lies outside the purview of MM.
Transition state structures and energiesdiffer from those of molecules (i.e. from
those of relative minima on a potential energy surface) in that transition states
are not relative minima but rather are saddle points, and that they are not readily
observed experimentally (with molecular beam and laser technology simple
transition states can be, in effect, observed [1]). These differences should not,
in principle, make MM inapplicable to calculating geometries and energies of
transition states: an assembly of atoms connected by bonds (some of these would
be partial bonds for a transition state) of known force constants should permit its
geometry to be adjusted so that one of its normal-mode vibrations has a negative
force constant (the critical feature of a transition state), and for parameterization
force constants of transition states could be calculated by quantum mechanical
methods.^1 Indeed, MM has been used to calculate geometries and energies of
transition states, but these studies have used force fields developed for very
specific reactions, perhaps the best example being the dihdroxylation of alkenes
with osmium tetroxide under the influence of a chiral catalyst [2]. However, MM
is not at present a generally applicable tool for studying transition states. This is
probably because force constants are not as transferable between transition states
(are more variable from one transition state to another) as they are between
ordinary molecules, making a forcefield that works for one kind of reaction
inapplicable to another.
References
- (a) Lucht RP (2007) Science 316:207. (b) Rawls RL (2000) Chemical and Engineering News,
May 22, 35 - Norrby P-O, Rasmussen T, Haller J, Strassner T, Houk KN (1999) J Am Chem Soc 121:10186
(^1) Such as ab initio, density functional, and semiempirical methods. The reliability of the geometries
and energies of calculated transition states can be gauged by comparing activation energies
calculated from them with experimental activation energies.
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