8.2 Singlet Diradicals........................................................
For “Is” and “Is-not” though with Rule and Line,
And “Up-and-down” by Logic, I define,...
Ah, but my Computations, People say,...- The Rubaiyat of Omar Khayyam, ca. 1100; translated by Edward Fitzgerald, 1859;
Stanzas 56 and 57.
8.2.1 Perspective.......................................................
The electrons in molecules, usually designated alpha and beta, but drawn as up
and down arrows in energy level diagrams and occasionally verbally bestowed
with those directional terms, are commonly neatly paired in orbitals and subject to
tolerably good computations by what Pople called a model chemistry [ 55 ]. This is a
sharply-defined procedure that, once settled upon, does not require judgement to
execute and will not vary from one worker to another. Examples are a HF/6-31G*
geometry optimization or a B3LYP/6-31þG** single-point calculation on a speci-
fied molecule. Almost all the molecular mechanics, ab initio, semiempirical and
DFT calculations discussed in this book have used model chemistries. In contrast
to these, some calculations demand judgement regarding the choice of which set of
orbitals and electrons is or is not to be considered. The most important class of such
calculations is on singlet diradicals (other open shell species, like radicals and
excited states, can present related problems).
A singlet diradical is a molecule with an even number of electrons in which
all but two are paired in orbitals in the familiar manner; each of the “last” two
electrons has one orbital to itself, and their spins are opposite, giving the spectro-
scopic state of a singlet (Fig.8.6). Simple examples of singlet diradicals are singlet
.CH
2 –CH 2 –CH 2
.(1,3-propanediyl, the trimethylene diradical) and the transition
state for rotation around the CC double bond of ethene, in which thep-bond has
been broken by twisting through 90. The reason for focussing on thesinglet
diradical will emerge from the examples below. Routine quantum calculations –
model chemistries – do not as a rule work with such species. The reasons for this,
and the techniques that are used on such molecules, are discussed below.
8.2.2 Problems with Singlet Diradicals and Model Chemistries......
Let us first do a reality check: we’ll test the ability of some model chemistry
methods to perform geometry optimizations on singlet 1,3-propanediyl or tri-
methylene (CH 2 –CH 2 –CH 2 .) and on singlet 1,4-butanediyl or tetramethylene
(.CH 2 CH 2 CH 2 CH 2 .), simple singlet diradicals.
8.2 Singlet Diradicals 535