Grabowsky et al.
JOCArticle
2
cycloaddition reactions). The application of epoxides is so
broad and straightforward that they are a key element of the
3
so-called click-chemistry. There is also a pharmaceutical
properties by means of a topological analysis according to
12
Bader (Quantum Theory of Atoms in Molecules ). With
this method, the degree of covalency/ionicity of a bond can
be measured, local charge concentrations and depletions can
be found, atomic volumes and charges can be calculated,
and electronic communication throughout the molecule can be
quantified. This knowledge contributes to a further understand-
ing of reactivity and reaction mechanisms in epoxide chemistry.
The geometrical arrangement of the bonds in the epoxide
ring owing to mechanical forces within a ball-and-stick
model suggests that the bonds must bend outward to master
4
relevance of epoxides as potential protease inhibitors
against various diseases like cancer, stroke, and parasitic or
viral diseases. These applications are based on the ring-
opening reaction of epoxide derivatives with nucleophilic
amino acids (e.g., cysteine, aspartate ) of enzymes involved
in these diseases, namely proteases responsible for tumor
4
5
6
progression and metastasis (e.g., cathepsins B, D, and L),
7
ischemic cell death (calpains), or enzymes essential for the
8
9
13
life cycle of the parasites or viruses. We use acceptor-
substituted epoxides as model compounds for biologically
active agents in this field as the mode of action regarding the
recognition and inhibition process with the target enzymes is
not sufficiently understood. There are several factors that
explain the enzymatic activity of the epoxide agents. Besides
the electronic nature of the epoxide ring as the biologically
active center of the molecules, the steric interactions of the
entire enzyme-ligand aggregation alter the activity by low-
ering or raising the transition state of the reaction including
solvent interactions in the aqueous biological environment.
Electron-density investigations can contribute to an expla-
nation of the activity because they provide electronic proper-
ties which are important in the molecular association
process, e.g., properties describing electrostatic complemen-
the high strain (so-called banana bonds ). Similar consid-
erations apply for molecular-orbital (MO) and valence-bond
(VB) theories, respectively: A nonbent bond scenario is not
possible because overlap of ordinary atomic hybrid orbitals
can only produce 90° (pure p character) and not 60° as would
be necessary for a nonbent bond description. Therefore,
3
2
ordinary hybridization states, e.g., sp or sp , are modified
with increased or decreased s-orbital character in order to
accommodate a particular molecular geometry. Corresponding
models were developed for cyclopropane, but can also be
1
4-16
considered for epoxide.
1
The F o€ rster-Coulson-Moffitt
model makes use of hybrid orbitals with a relation between
7
2
s- and p-character similar to sp -hybridization. This leads to
an orbital overlapping outside the direct bond axis forming
three σ-type bonds. An alternative model is the Walsh
model, in which a stable central three-center bond is
1
8
1
0
tarity. High-resolution X-ray diffraction experiments at
ultralow temperatures on single crystals resulting in the
experimental electron-density distribution are most helpful
because the effects of molecular associations are present in a
crystalline environment as well as in a protein environment
under physiological conditions and can be expected to be
2
formed from inward-directed sp atomic orbitals. Addition-
ally, two weak peripheral three-center bonds are formed
from the tangential in-plane p-π orbitals of the CH frag-
2
ments. The Walsh model does not correspond to the ground
state of cyclopropane/epoxide, so that the bent-bond de-
scription of the F o€ rster-Coulson-Moffitt model is the
1
1
comparable in size. On the other hand, electron-density
investigations yield deep insight about atomic and bond
1
6
commonly considered one. But one could also state that
the models describe two different aspects of ring strain.
2
However, the involvement of sp -type orbitals in the epoxide
(3) (a) Kolb, H. C.; Finn, M. G.; Sharpless, K. B. Angew. Chem., Int. Ed.
001, 40, 2004. (b) Fokin, V. V.; Wu, P. Aziridines and Epoxides in Organic
3
ring instead of sp like in a normal single bond suggests that
2
Synthesis; Wiley-VCH: Weinheim, 2006; Chapter Epoxides and Aziridines in
the bonds are not saturated and can interact with π-electron
systems. Evidence by various methods (UV spectroscopy,
heat of combustion, MO calculations) has been found for
Click Chemistry, p 443.
(
€
4) (a) Powers, J. C.; Asgian, J. L.; Ekici, O. D.; James, K. E. Chem. Rev.
2
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14,19
such conjugation of the epoxide ring with substituents.
(
Therefore, we are interested to investigate these conjuga-
tion effects with electron-density means. We synthesized and
crystallized a row of acceptor-substituted epoxide deriva-
tives (see Figure 1a) to study substituent effects caused by
conjugation. The resonance formulas that express the con-
jugation effects with the present electron-withdrawing sub-
stituents (cyano, methyl ester and nitrophenyl groups) are
given in Figure 1b. The substituents can accept a formal
negative charge causing the epoxide ring to open and leaving
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