Chapter 1, Harder Questions, Answers
Q4
Is it surprising that the geometry and energy (compared to that of other isomers) of a
molecule can often be accurately calculated by a ball-and springs model (MM)?
Since in some ways molecules really do behave like ball-and-springs toys, it is
not surprising that such a model enables one to calculate geometries and energies,
but what is surprising is the accuracy possible with such calculations. Let’s explore
these two assertions.
In some ways molecules really do behave like ball-and-springs toys.
There are two assumptions here: that molecules have definite bonds, and that
these bonds behave like springs.
- Do molecules have definite bonds? A molecule is a collection of relatively
immobile atomic nuclei and rapidly moving electrons, with the “relatively
immobile” nuclei vibrating about equilibrium positions. At first sight this
picture offers no hint of the existenceofbonds.ItmightseemthatIRspectra
show that molecules have definite bonds, since these spectra are interpreted in
terms of bond vibrations (stretching, bending, and torsional motions). Do the
fundamental vibrations, the normal-modevibrations (which in principle can be
calculated by any of the standard computational chemistry methods used to
optimize molecular geometry, and fromwhich the experimentally observed
vibrations can be “synthesized”) really show the presence of the conventional,
standard bonds of simple valence theory? Actually, the vibrational spectra
show only that nuclei are vibrating along certain directions, relative to the axes
of a coordinate system in which the molecule is placed. An IR spectrum
computed by assigning to the conventional bonds stretching and bending
force constants is said to correspond to avalence forcefield.Suchaforcefield
often serves to create a good Hessian (Chapter 2) to initiate optimization of an
input structure to a minimum (but not a transition state), but does not always
account for the observed IR bands, due to coupling of normal-mode vibra-
tions [1].
That molecules do have definite bonds, and that these tend to correspond in
direction and number to the conventional bonds of simple valence theory, is
indicated by the quantum theory of atoms-in-molecules (AIM, or QTAIM) [2].
This is based on an analysis of the variation of electron density in molecules. - Do bonds behave like springs? It is well-established that for the small vibrational
amplitudes of the bonds of most molecules at or below room temperature, the
spring approximation, i.e. the simple harmonic vibration approximation, is fairly
good, although for high accuracy one must recognize that molecules are actually
anharmonic oscillators [3].
Is the accuracy of geometries and relative energies obtainable from MM
surprising?
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