Page 275 - Academic Press Encyclopedia of Physical Science and Technology 3rd Organic Chemistry

P1: LDK/GJK P2: GQT/Final Pages
Encyclopedia of Physical Science and Technology EN012G-576 July 28, 2001 12:44

Physical Organic Chemistry 221

conformer (59) that is the enantiomer of 58, so that this isomeric molecules and to calculate how the energy varies
will always be present as a racemic mixture. as the molecule is distorted to some other geometry.

III. CHEMICAL REACTIVITY
There are two aspects of chemical reactivity, static and dy-
namic. The static aspect relates to the question of chemical
equilibrium, determined by the stability of reactants and
products. The dynamic aspect relates to the question of
chemical kinetics, or rates of reactions. This is more com-
F. Molecular Mechanics plicated, but it can be converted into static terms.
Eachmoleculehasitsownpreferredgeometry,determined
by the various interatomic forces. If the preferences for A. Chemical Equilibrium
optimum bond distances and bond angles and for mini-
mum torsional strain and steric repulsion are character- For a general reaction, written as Eq. (13), the equilibrium
istic of the atoms involved and independent of the rest constant is related to concentrations and to free energies by
Eq. (14), where G = G − G , R is the gas constant,
◦
◦
◦
of the molecule, then it becomes possible to extend our B A
8.314 J/mole or 0.001987 kcal/mole, and T is the absolute
understanding from one set of molecules to others. It is
temperature:
necessary to express the dependence of energy on molec-
ular geometry in a form like Eq. (9), where V ({x i , y i , z i }) A (13)
B,
depends on the positions of all the individual atoms, and
◦
where V stretch [Eq. (10)] represents the energy to distort K = [B]/[A] = exp(− G /RT ). (14)
0
the distance between atoms i and j from the optimum d , Much of our understanding of chemical reactions comes
i j
V bend [Eq. (11)] and V torsion [Eq. (12)] represent the energy
from reasoning by analogy. If the equilibrium constant K
to distort the ijk bond angle or the ijkl dihedral angle from
is known for some standard reaction, it is often possible
its optimum, and V es and V vdW are electrostatic and van
to predict, at least qualitatively, the equilibrium constant
der Waals (steric) energies, respectively, which depend on
K for a related reaction, involving some modification of
the distance between atoms i and j:
the molecular structure. To do so, it is necessary to know

V ({x i , y i , z i }) = V stretch (d i j ) + V bend (θ i jk ) how the modification affects energies.
For the modified reaction of Eq. (13 ) if the modification

+ V torsion (θ i jkl ) + V es (d i j ) stabilizes B (distinguished with a prime) relative to B,

then it follows from Eq. (14) that K > K and that the

+ V vdW (d i j ), (9) equilibrium is shifted to the right:
1

V stretch (d i j ) = k ij d ij − d 0 2 , (10) A B . (13 )

2 ij
1 0 2
V bend (θ i jk ) = k i jk θ i jk − θ , (11) Likewise, if the modification destabilizes A, or raises its
2 i jk
energy relative to A, then K > K and the equilibrium

1

V torsion (θ i jkl ) = k i jkl θ i jkl − θ 0 2 . (12) is again shifted toward the right. If the modification sta-
2 i jkl

bilizes A relative to A or destabilizes B relative to B,

The sums are over all bonds, angles, and atom pairs. The then K < K and the equilibrium is shifted toward the left.
parameters that enter each of these terms can be cal- These conclusions are made graphic in Fig. 10.
culated for model compounds by quantum mechanics. Bondstrengthsrepresentasimplecaseofenergeticsthat
Alternatively they can be calibrated to give the best fit affect equilibrium. They are usually expressed as bond-
to an extensive set of experimental data on molecular ge- dissociation energies (BDEs), positive numbers that cor-
ometries, stabilities, and infrared vibrational frequencies. respond to the energy required to break a molecule into
These calculations are formidable, but they are easy on its constituent fragments, or the energy released when the
a computer. Moreover, programs are available, complete bond forms. Table I lists some representative values.
with parametrization. Thus it is possible to calculate the Such values can be used to understand equilibria. For
energy for any arbitrary molecule in any geometry and to the reaction of Eq. (15) the total bond-dissociation energy
seek the geometry that minimizes that energy. It is further of the C H and Cl Cl bonds on the left is 162 kcal/mole
possible to compare that minimum with the energies of (104 + 58), whereas that on the right is 187 kcal/mole