Content: Chemical Structure, 2nd part: “Must a Molecule have a Shape?”, R.G. Woolley, J.Am.Chem.Soc. 1978, 100(4),1073
How does Kimball’s model deal with the “classical” notion of molecular structure?
ES 18 August 2017/30 Dec 2016//24 Mar 2015//2002//1982
“Must a Molecule have a Shape ?”
I like to address the provocative statement of R.G.Woolley.
For most chemists his question sounds absolutely absurd, since for them
“shape” is the most chemical attribute of matter. How could e.g. the
genetic code survive decades, or millenia of years, if it was not
preserved in the “shape” of a stable double helix of complementary
nucleotide strands (of course, it is recreated at every cell division, but
the pattern=shape prevails)? How could chemists correctly synthesize
molecules with several chiral centers by cleverly making use of tiny
differences of reaction velocities, if the “shape” would not hold them
from loosing the target into a statistical mix of dozens of enantiomers
(did you ever read the synthesis of VitaminB12 with 9 chiral centers by
Albert Eschenmoser and Robert B. Woodward, finished 1972, a classic)?
I told you earlier that in atoms, molecules and solid
lattices nuclei have a “probability” cloud of positions which is for the
proton in the H-atom about 2000 times smaller than the electron cloud, and
for the same quantum mechanical cause. This is well known for the
vibrations of nuclei “clamped” to a certain position in a molecule, the
left-over mode of motion when a nucleus has lost its “freedom” by engaging
in a bond (a dog on a leash can only waggle his tail). In the picture,
below, we look at a diatomic molecule. The red curve is called the potential curve. It traces the energy of
the bond as function of the bond distance. One nucleus is held fixed at
the origin, left, the other moves away from it to the right. The
equilibrium distance is at the lowest energy point, designated as Re. Far
out to the right, the molecule dissociates into two atoms. Left of Re we
push the nuclei together which produces a steep increase in energy and a
strong repulsion - the bonding electron cloud is compressed and the nuclei
repel each other electrostatically.-
This picture of an anharmonic oscillator can be found at www.chemsoft.ch/chemed/linbox0.htm, Potential 5, together with the Pascal program, p.8-9 to calculate the quantum mechanical eigenvalues and eigenfunctions = wavefunctions of the anharmonic oscillator, and several other potentials, which you may click.>
This picture shows the nuclear wavefunction belonging to the 8th eigenvalue of the
anharmonic oscillator above.
What is the size of the zero point vibrational energy, e.g. in methane ? 23.9 kcal/mol = 100 kJ/mol. If we look at a small protein, Crambin with 46 amino acid residues, this sums up to about kcal/mol. If this energy was allowed to percolate through the molecule it could easily break some 100 C-C or C-H bonds! Hence, no “shape” would be stable. Fortunately, zero point energy is localised to a high degree and unavailable for transport elsewhere (this article describes a patent(!) for making use of zero point energy, getting loose!).
You see now Woolley’s argument: If all nuclei in molecules and solids jiggle around some percents of their distances to neighbors, how could we describe structure or talk about shape? Experimentally, there is no difficulty. Look at a recent X-ray crystallographically determined skeleton of a molecule. There is a “thermal ellipsoid” at the points of highest electron density.
The centers of the thermal ellipsoids define the position
of nuclei in the measured “shape”, the “Re” (actually Ro, see below)
points. The ellipsoids become smaller, the lower the temperature. Near 0
Kelvin, perhaps at 4 K in liquid He, the ellipsoid shrinks to the extent
of the average zero point motion of every nucleus. Very accurate X-ray
structures are, therefore, measured near 0 K.- BTW, the electronic kinetic
energy, e.g. in a Kimball free cloud, is practically not dependent on
temperature. The electrons move so fast around that several 100 to some
1000 K do not measurably change their kinetic energy! The zero point
energy makes them already very hot, several 104 K, if it was
I’ve written Re sometimes as “Re”, above. There are other
structural measures than the bond length: Angles between bond directions,
involving three nuclei, and dihedral angles ϑ, the angles between two
planes spanned by four nuclei, also, a triangle and a 4th
nucleus not in that plane (or in that plane, then ϑ =180°, otherwise
different from 180°).