Chemistry Reference
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but alas it is not, due to a number of intervening obstacles, some of which are
discussed below.
The survey of possible structures may easily run into tens of thousands, espe-
cially when the generating molecule has flexible torsional degrees of freedom that
add complexity to the landscape of crystal degrees of freedom, cell parameters, and
space group. Then, it is by now firmly established that energy differences between
polymorphic crystal structures are extremely small, sometimes almost vanishing,
posing a severe accuracy problem to any computational scheme, especially so
considering that for such large number of candidates, only approximate methods
are affordable. The balance between intra- and intermolecular energy calculations
may be problematic when, for example, atom-atom formulations must be used. A
common approximation is to run the intermolecular search only for a small number
of most likely conformations, as determined by a separate search of the gas-phase
energy landscape: this obviously neglects the direct interplay between intra- and
intermolecular terms in the global optimization of the energy of the system.
The most serious obstacle to consistent crystal structure prediction seems how-
ever the fact that kinetics of crystallization has an unknown, but certainly relevant,
influence, even more relevant because the energy differences between polymorphs
are relatively small. Yields of different polymorphs have been shown to depend as
expected on solvent and temperature, but even on hardly traceable contingencies
such as impurities, heterogeneous nucleation centers, heat and mass flow, stirring,
and seeding. In presence of kinetically favored, metastable structures, when predic-
tion is checked against experiment a “correct” prediction may actually be wrong in
a thermodynamic sense, or a “wrong” prediction may actually be correct in pointing
out the presence of an unknown more stable crystal phase. This point is particularly
crucial, also because no crystal structure prediction method to date is able to take
into account the effect of temperature, all calculations being carried out on potential
energies alone, and of course, in the real world, stability is also a function of
temperature (kinetic energy). In parallel, the neglect of the temperature dependence
implies the assumption that enthalpy is equal to free energy, or that
T
D
S
¼
0, either
because
T
¼
0 or because entropy differences among polymorphs vanish. Thus the
ultimate validation of a crystal structure prediction should involve an infinite
sampling of the crystal energy landscape
and
an infinitely extensive screening of
experimental forms in all conditions of solvent and temperature. The product of
these two infinities makes robust structure prediction and control impossible.
Success or failure must depend on computational effort but also (to the simulator's
frustration) on a certain amount of unpredictable side effects - in one word, chance.
This much said, one may come to terms with reality by considering that in many
cases a given compound reproducibly gives rise to only one crystal structure, and
that in many cases an accurate energy evaluation recipe will predict that structure as
the most stable one, thus verifying all the temperature-dependent assumptions.
Although no sensible author would risk presenting a numerical estimate of per-
centage of such cases, over the last few years the theoretical chemistry community
has had a glimpse of a statistical assessment through a series of blindfold tests
organized by the Cambridge Crystallographic Data Center. Participants in the test
