are missing something in their three-dimensional perception. The visual-tactile link
is so strong, and so direct – when we handle a model of a molecule in our hands as
we struggle to draw down on paper, in some primitive visual code its structure, the
molecule’s three-dimensionality forever enters our mind. As long as we are alive
we will see it and feel it”.^5 Hoffmann and Laszlo point out that for most chemists
“the real, physical handling of models” imprints better the “full glory” of a three-
dimensional structure than do the (somewhat problematically) direct results of, say,
X-ray crystallography [ 319 ].
5.5.6.1 Molecular Vibrations
Animation of normal-mode frequencies usually readily enables one to ascribe a
band in the calculated vibrational (i.e. IR) spectrum to a particular molecular
motion (a stretching, bending, or torsional mode, involving particular atoms). It
sometimes requires a little ingenuity todescribeclearly the motion involved, but
animation is far superior to trying to discern the motion by the presumably now
obsolete method of examining printed direction vectors (Section 2.5; these show the
extent of motion in thex,y, andzdirections). Useful, however, are the visualized
direction vectors that some programs, e. g. GaussView [ 320 ], can attach to a picture
of the molecule, catching the vibration in the act so to speak.
Animating vibrations is useful not only for predicting or interpreting an IR
spectrum; it can be extremely valuable in probing a potential energy surface.
Suppose we wish to locate computationally the intermediate through which the
chair conformers of cyclohexane interconvert 1 ⇆ 10 , Fig.5.45). This reaction,
although degenerate, can be studied by NMR spectroscopy [ 321 ]. One might
surmise that the intermediate is the boat conformation 2 , but a geometry optimiza-
tion and frequencies calculation on this C2vstructure (note that in a quantum
mechanical calculation, whether ab initio or otherwise, the input symmetry is
normally preserved) followed by animation of the vibrations, shows otherwise.
There is one imaginary vibration (Section 2.5), and the transition state wants to
escape from its saddle point by twisting to a D 2 structure 3 , called the twist or twist-
boat, which latter is the true intermediate. The enantiomeric twist structures 3 and 30
go to 1 and 10 , respectively, over a high-energy form 4 (or 40 ) called the half-chair.
A geometry optimization starting with a D 2 structure leads to the desired relative
minimum. Similarly, if one obtains a second-order saddle point (one kind of
hilltop), animation of the two imaginary frequencies often indicates what the
species seeks to do to escape from the hilltop to a become a first-order saddle
point (a transition state) or a minimum, and it often possible to obtain the desired
transition state or minimum by altering the shape of the input structure so that it has
the symmetry and approximates the shape of the desired structure.
(^5) R. Hoffmann, personal communication, 2009 August 12.
366 5 Ab initio Calculations