Electron-density determination of electrophilic building blocks as model compounds for protease inhibitors

Article abstract of DOI:10.1002/ejoc.200601074

Three types of synthesised compounds, the aziridine 1, the epoxide 2 and the acceptor-substituted olefin 3, were chosen as model compounds for electrophilic building blocks, which can covalently block the nucleophilic amino acids of the active sites of pr

Full text of DOI:10.1002/ejoc.200601074

FULL PAPER
DOI: 10.1002/ejoc.200601074
Electron-Density Determination of Electrophilic Building Blocks as Model
Compounds for Protease Inhibitors
Simon Grabowsky,[a] Thomas Pfeuffer,[b] Lilianna Checin´ska,[a] Manuela Weber,[a]
˛
Wolfgang Morgenroth,[c–e] Peter Luger,[a] and Tanja Schirmeister*[b]
Keywords: Aziridine / Charge density / Electron density / Nucleophile / Protease
Three types of synthesised compounds, the aziridine 1, the
epoxide 2 and the acceptor-substituted olefin 3, were chosen
as model compounds for electrophilic building blocks, which
can covalently block the nucleophilic amino acids of the
active sites of proteases (Cys in cysteine proteases or Asp in
aspartate proteases). In order to rationally design optimised
inhibitors and to understand the differences in inhibition
properties of the scrutinised building blocks their structural
and electronic properties were studied by ultra-high resolu-
tion X-ray diffraction and ab initio calculations to yield the
experimental electron-density distribution. It could be shown
that the carbon atom C1 of the three-membered heterocycle
is the preferred electrophilic centre for attack of the nucleo-
philes, which is consistent with the results of corresponding
chemical experiments with sulfur and oxygen nucleophiles.
(© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim,
Germany, 2007)
cluding charge transfer in co-crystals with more than one
molecule. Since molecules are found to have different dipole
moments in different crystalline environments due to pola-
risation effects of the crystal field, an advantage of the ex-
perimental electrostatic potential over the potential from
isolated molecule calculations is that effects arising from the
crystal packing are accounted for. Due to the nature of the
molecular interactions these effects will generally cause the
molecules to pack in a characteristic way, i.e. the molecules
will pack in a key-lock arrangement in which regions of
charge concentration face electron-deficient regions in adja-
cent molecules in the crystal, and in which hydrogen-bond
donors will face hydrogen-bond acceptors.[4] Thus, the X-
ray charge density contains quantitative information on the
electrostatic interactions and the hydrogen bonding net-
work between molecules. These influences can be assumed
to be quite often similar to the influence of a protein envi-
ronment, since the interactions within the crystals are based
on the same types of effects as the ligand-target-interactions
(steric, electrostatic, hydrogen bonding, van der Waals ef-
fects) and are expected to be comparable in size. Due to
these similarities the polarisation of the ligand within the
crystal and the protein environment should also be compar-
able. As a consequence the properties extracted from ultra-
high resolution X-ray data of a ligand are often much better
suited to simulate physiological conditions than those cal-
culated for an isolated ligand molecule. This has already
been shown for the antithrombotic drug terbogrel,[5] the
neurotransmitter taurine,[6] and the anti-leukemia drug bus-
ulfan.[7] For the latter the topological electron-density de-
scriptors were also used to explain its chemical reactivity,
namely its alkylating property.
Introduction
Most biological processes as well as the pharmacological
action of most drugs are initiated by a preliminary step in
which two molecular species, e.g. a macromolecular target
protein and a low-molecular weight ligand, recognise each
other and form a complex. Steric as well as electrostatic
properties of the two species play dominant roles in these
recognition processes.
Ultra-high resolution X-ray diffraction experiments at
low temperature cannot only be used to determine atomic
connectivity and conformation of compounds, but also to
analyse electron-density distribution.[1,2] Bond topological
and atomic properties are quantitatively accessible from the
three-dimensional distribution of the electron density by
application of Bader’s QTAIM-theory (QTAIM = Quan-
tum Theory of Atoms in Molecules).[3]
Additionally, the crystallographic experiment yields in-
formation on the nature of intermolecular interactions, in-
[a] Freie Universität Berlin, Institut für Chemie und Biochemie/
Kristallographie,
Fabeckstr. 36a, 14195 Berlin, Germany
[b] University of Würzburg, Institute for Pharmacy and Food
Chemistry,
Am Hubland, 97074 Würzburg, Germany
Fax: +49-9318885494
E-mail: schirmei@pzlc.uni-wuerzburg.de
[c] Institut für Anorganische Chemie, Georg-August-Universität,
Tammannstraße 4, 37077 Göttingen, Germany
[d] Department of Chemistry, Aarhus University,
Langelandsgade 140, 8000 Aarhus C, Denmark
[e] c/o DESY/HASYLAB,
Notkestraße 85, 22603 Hamburg, Germany
Supporting information for this article is available on the
WWW under http://www.eurjoc.org or from the author.
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Besides information on reversible target ligand binding
processes which are mainly based on electrostatic interac-
tions, high resolution X-ray data can also give valuable in-
sight into irreversible binding mechanisms which are always
based on the forming of a covalent bond between ligand
and target. Since the first stage of a chemical reaction, i.e.
the alignment of the involved molecules, is determined by
their electrostatic potentials the measured electron density
of the ligand allows estimates where the chemical bond is
formed if the nature of the attacking centre of the active
site is known (e.g. nucleophilic attack by a negatively
charged centre of the active site of an enzyme). Even de-
tailed information about the reactivity, the reaction mecha-
nisms, and the reaction rates may be possible. Here, the
proof of principle was given already by the electron-density
analysis of busulfan,[7] and penicillin derivatives.[8]
Results and Discussion
Geometric Results
The experimental conformation of the examined azirid-
ine 1 including thermal ellipsoids at 9 K and the atom num-
bering scheme chosen is shown in Figure 1. A summary of
selected geometric data for both molecules of the asymmet-
ric unit (Table 1) shows that the average difference of bond
lengths and angles is 0.003 Å and 0.7°, respectively. More-
over, topological properties do not differ significantly, so
that the following discussion is based on the quantitative
results obtained from molecule 1 if not otherwise stated.
Our efforts direct to the development of cysteine[9] and
aspartic protease inhibitors[10] consisting of an electrophilic
building block (aziridine,[11,12,15] epoxide[13,14] or acceptor-
substituted olefin[15,16]) which can covalently block the nu-
cleophilic amino acids of the enzymes’ active sites (Cys in
cysteine proteases or Asp in aspartate proteases). In order
to rationally design optimised inhibitors and to understand
the differences in inhibition properties of the scrutinised
building blocks we synthesised and crystallised three model
compounds 1, 2, and 3. These compounds contain the same
substituents (two methyl ester groups at C2, p-nitrophenyl
moiety at C1), but differ in the type of electrophile: azirid-
ine 1, epoxide 2, acceptor-substituted olefin 3. The nitro-
substituted compounds were chosen due to their enhanced
Figure 1. ORTEP[17] representation with displacement ellipsoids at
9 K (50% probability) of aziridine 1 with atom numbering scheme.
Hydrogen atoms represented by small spheres of arbitrary radii.
Due to the highly strained three-membered aziridine ring
crystallisation properties in comparison to the derivatives the intra-ring angles are far apart from the normal tetrahe-
lacking the nitro group. The electron densities of the com- dral angles as Table 1 shows. Inside the ring the angles are
pounds were derived from both, high-resolution X-ray dif- about 60°, outside between 115.5 and 118° without differ-
fraction experiments at ultra-low temperature (for 1), and ences whether an aryl group is connected to the carbon
ab initio calculations (for 1–3). The results of the experi- atom (C3–C1–N1 116.5°) or an ester group (e.g. C11–C2–
mentally and theoretically obtained electronic properties as N1 115.8°). But considering the bond lengths there is a
well as the electronic properties of the three different types small difference between the bond to the aryl group (C1–
of electrophiles are compared. In addition, these data are C3 1.49 Å) or to the ester groups (C2–C9, C2–C11 1.51 Å).
compared with the reactions of aziridine 1 with sulfur, and The bonds and angles inside the aziridine ring can be com-
oxygen nucleophiles, as model reactions for the inhibition pared to the corresponding values of the unsubstituted
of cysteine and aspartic proteases, respectively.
(free) aziridine by a study from Mitzel et al. at 145 K.[18]
Table 1. Bond lengths [Å], angles [°] and torsion angles [°] for the aziridine ring of aziridine 1 and its direct environment (first–second
line: molecule 1–2 of the asymmetric unit; third line: free aziridine, taken from ref.[18]).
C1–N1
C2–N1
C1–C2
1.4558(4)
1.4609(7)
1.4640(18)
1.4573(4)
1.4621(7)
1.4628(18)
1.5100(4)
1.5076(6)
1.4600(20)
1.4907(5)
1.4920(7)
1.5059(4)
1.5096(6)
1.5051(4)
1.5022(6)
C1–N1–C2
N1–C1–C2
N1–C2–C1
62.45(2)
62.07(3)
59.83(9)
58.83(2)
59.04(3)
60.05(9)
58.81(3)
58.89(3)
60.12(9)
115.71(3)
117.19(4)
118.12(3)
116.46(3)
115.55(3)
116.14(3)
C4–C3–C1–N1
N1–C2–C9–O4
N1–C2–C11–O6
3.8(1)
21.5(1)
141.0(1)
140.6(1)
143.6(1)
152.5(1)
C1–C3
C2–C9
C2–C11
C3–C1–N1
C9–C2–N1
C11–C2–N1
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Electron-Density Determination
FULL PAPER
These values are likewise given in Table 1. In the free azirid- distance criteria but are known in the literature[21] to be
ine the three bond lengths and the three angles are almost weak interactions that help stabilising the crystal. They
equal within the error margins (1.46 Å and 60.0°). In the have been shown to be important in several drug binding
substituted aziridine the C1–C2 distance increases by processes.[21] For the present structure they will be discussed
0.05 Å, the C–N distances decrease by about 0.01 Å, so that later in this article with the aid of Hirshfeld surfaces and
one side of the triangle is lengthened and the angle opposite topological analyses.
to this side has to expand. This effect is evident here: The
angle C1–N1–C2 increases from 59.8 to 62.2° and the other
angles decrease from 60.1 to 58.9°. The three torsion angles
listed in Table 1 are the most representative for the confor-
mation of the molecule because the aryl group including
the nitro group being in resonance with the phenyl ring is
very planar and rigid in its conformation. The two chains
consisting of an ester and a methyl group are rigid, too.
Therefore significant torsions should only occur at connec-
tions of the substituents to the aziridine ring. Comparing
the conformation of the molecule shown in Figure 1 to that
of the second molecule in the asymmetric unit and to the
optimised geometry one can state that the overall confor-
mation is very rigid and that the experimental geometry is
very near the gas phase geometry with minimum molecular
energy. The energy of a single-point calculation at the ex-
perimental geometry differs only by 3.7 kcalmol–1 from the
energy of a geometry optimisation. All the geometrical pa-
rameters only differ slightly when going from one molecule
of the asymmetric unit to the other or to the optimised
geometry. Due to the molecule’s small structural changes
when changing the environment, all the results derived from
Figure 2. Crystal packing and hydrogen bonding network
the experimental and theoretical electron-density distribu-
tion should be a good estimate for the molecule’s properties
in biological systems, too.
(SCHAKAL[20] representation).
Figure 2 shows an extract from the crystal packing. The
aziridine compound tends to build up layers. The molecules
inside a layer are held together by electrostatic contacts like
the C11–O3A contact (see below) whereas the molecules in
two different layers are connected by hydrogen bonds. In
Electron Deformation and Laplacian Density
Figure 3 shows the experimental negative Laplacian dis-
one layer the nitrogen atom of the aziridine ring alternates tribution in the plane of the aryl group of aziridine 1. It is
with the oxygen atom of a carbonyl group. Thus, the sta- obvious that all bonds are open-shell interactions, i.e. coval-
bilising hydrogen bonds N1A–H1NA···O5A and N1– ent bonds, as the typical saddle shape distributions in the
H1N···N1A must alternate, too, forming an angle of about bond regions indicate. Since Figure 3 shows all expected
90° between each other. Table 2 shows the geometric pa- features in the bonding and non-bonding regions it can be
rameters of these two hydrogen bonds and several C– concluded that the density distribution was adequately
H···acceptor contacts. These contacts are not just found by modelled by the multipole formalism.
Table 2. Hydrogen bond geometries, topological parameters and energies.
r(don···acc) /Å a(don–H···acc) /° ρ /eÅ–3
ٌ2ρ /eÅ–5
EHB /kJmol–1 a0
[j]
–3
donor–H···acceptor
r(H···acc) /Å
N1A[a]–H1NA···O5A[c]
N1–H1N···N1A
2.232(9)
2.220(9)
2.432(10)
2.441(10)
2.335(9)
2.341(9)
2.458(9)
2.415(10)
2.387(10)
3.113(9)
3.113(9)
3.437(10)
3.470(10)
3.244(9)
3.148(9)
3.224(9)
3.428(10)
3.383(10)
145.1(1)
168.8(1)
153.8(1)
158.4(1)
140.4(1)
130.0(1)
126.7(1)
158.3(1)
155.1(1)
0.088(9)
0.092(9)
0.043(11)
0.040(11)
0.067(10)
0.074(13)
0.065(12)
0.057(11)
0.078(9)
1.6(1)
1.6(1)
0.8(1)
0.8(1)
1.1(1)
1.1(1)
0.9(1)
1.0(1)
1.2(1)
9.54
9.46
4.79
4.85
6.43
6.30
5.07
5.92
6.92
C5–H5···O1[d]
C5A–H5A···O1A[e]
C6–H6···O4[f]
C7–H7···O5[g]
C7A–H7A···O5A[h]
C10–H10B···O6A[i]
C12A–H12D[b]···N1[d]
[a] Labels A refer to the second molecule of the asymmetric unit. [b] Atom H12D belongs to the second molecule of the asymmetric
unit. Symmetry operations. [c] –x, 1–y, 1–z (A). [d] –1+x, y, z. [e] –1+x, y, z (A). [f] 2–x, 2–y, 1–z. [g] 1+x, y, z. [h] 1+x, y, z (A). [i]
1–x, 1–y, 1–z (A). [j] Hydrogen bond energy calculated according to Espinosa et al.[19]
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T. Schirmeister et al.
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tween the nuclei. This so called banana bonding phenome-
non in highly strained systems has been reported for cyclo-
propanes and oxiranes in the literature.[1,24] The aziridine
three-membered ring differs from the oxirane three-mem-
bered ring with respect to the theoretical maps in two ways:
First, there is higher loss of density at the oxygen atom than
at the nitrogen atom; second, there is a somewhat higher
density at the maxima of the C–N bonds in the aziridine
than in the C–O bonds of the oxirane. The amount of den-
sity between the carbon atoms is about the same. The theo-
retical and the experimental maps agree well, but the latter
reflects the asymmetrical substitution better than the theo-
retical map. The heightfield representation (Figure 4, d)
shows the distribution of the experimental negative Lapla-
cian of the aziridine ring in the bonding regions. The typi-
cally saddle shaped bonding region of the homopolar coval-
ent C–C bond with a symmetrical Laplacian distribution
and the regions of the heteropolar covalent C–N bonds
with unsymmetrical Laplacian distributions can be iden-
tified unambiguously. Even the lone pair region of the ni-
trogen atom is visible behind its core region.
Figure 3. Experimental negative Laplacian distribution in the plane
of the aryl ring of aziridine 1, contour interval: 25 e/Å5, blue: nega-
tive, red: positive (XDGRAPH[22] representation).
Topological Analysis
The most eye-catching feature of the deformation density
According to Bader’s theory[3] an atom is the union of a
maps in Figure 4 is that the maxima of the deformation nuclear critical point ((3;-3) critical point) and its associated
density do not correspond to the straight connections be- basin of attracted trajectories of the electron-density gradi-
Figure 4. Static deformation density distribution (contour interval: 0.1 e/Å3, blue: positive, red: negative) of a) aziridine ring of 1 (experi-
ment), b) aziridine ring of 1 (theory), c) oxirane ring of 2 (theory) and the heightfield representation of the experimental negative
Laplacian of the aziridine ring of 1 (d)) (XDGRAPH[22] and MOLDEN[23] representations).
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Electron-Density Determination
FULL PAPER
ent vector field ٌρ(r) with zero flux surfaces (ZFS) as points in the reactive regions of compounds 1–3. The theo-
boundaries, i.e. surfaces that cannot be crossed by any gra- retical values for the optimised geometry of 1 differ only
dient vector except for the bond path. The intersection of a slightly from the theoretical values for the experimental ge-
zero-flux surface and a bond path is a bond critical point, ometry due to very small changes in the geometry (see
a three dimensional saddle point, minimum of the density above) so that the latter are omitted in the Table.
along the bond path but maximum in two other directions
The values for the experimental density of the N–C bond
perpendicular to the bond path. A ring critical point is a critical points (bcp) in the aziridine ring are equal to each
density minimum in two directions inside the ring’s plane other with respect to the error margins. The C–C bond of
being perpendicular to each other and a density maximum the aziridine contains 0.15 e/Å3 lower density than the N–
perpendicular to the ring’s plane. All these properties of C bonds. In the oxirane ring the density loss of the C–C
Bader’s partitioning scheme are visualised in Figure 5 repre- bond is smaller. The qualitative results of the comparison
senting the experimental gradient vector fields of the aryl of the theoretical maps in Figure 4 (see above) can be con-
group and the aziridine ring of aziridine 1.
firmed here: There is slightly higher density at the C–N bcp
than at the C–O bcp. The density of the C1–C2 bcp in the
olefin compound has the highest value of all C–C bonds as
it consists of a double bond. But there seems to be no influ-
ence on the densities of the bonds C1–C3, C2–C9 and C2–
C11 connecting the substituents to the rings or to the
double bond, because they are very similar when comparing
all three compounds. The values of the Laplacian for all bcp
are negative indicating that all bonds are covalent bonds.
The density of the ring critical point (rcp) of the phenyl
ring is about 1.2 e/Å3 lower than the density of the rcp of
the aziridine or oxirane ring because the centre of a smaller
ring is much closer to the atoms. The values of the density
of the rcp of the aziridine and oxirane ring are almost
equal.
Figure 5. Experimental gradient vector fields of a) the aryl group
and b) the aziridine ring. Bond paths and bond critical points are
plotted.
The ellipticity is defined as the ratio of the two negative
curvatures λ1 and λ2 of the Laplace function: ε = λ1/λ2–1.
Using Bader’s theory of atoms in molecules,[3] a topologi- It describes the deviation from a cylindrical symmetry of
cal analysis of the experimentally and theoretically obtained the electron-density distribution at the bcp. For an ideal
electron-density distribution was performed. Table 3 lists single bond the value of ε equals 0.0, for a conjugated bond
the topological properties of the bond and ring critical like in benzene ε equals 0.23 and for a double bond like in
Table 3. Density (ρ in e/Å3), Laplacian (ٌ2ρ in e/Å5) and ellipticity (ε) of bond and ring critical points; theoretical values from geometry
optimisations.
Bond/ring
Compound
ρexp
ρtheor
ٌ2ρexp
ٌ2ρtheor
εexp
εtheor
N1–C1
O7–C1
N1–C2
O7–C2
N1–H1N
C1–C2
aziridine 1
oxirane 2
aziridine 1
oxirane 2
aziridine 1
aziridine 1
oxirane 2
olefin 3
aziridine 1
oxirane 2
olefin 3
aziridine 1
oxirane 2
aziridine 1
oxirane 2
olefin 3
1.762(14)
1.765
1.690
1.766
1.733
2.329
1.557
1.644
2.253
1.772
1.779
1.836
1.869
1.943
1.771
1.745
1.762
1.759
1.719
1.767
0.149
0.149
0.147
1.379
1.394
–10.2(1)
–13.0
–8.9
–12.2
–10.1
–40.1
–9.3
–11.5
–23.2
–15.7
–15.8
–16.8
–22.4
–24.2
–15.8
–15.2
–15.7
–15.2
–14.8
–15.4
3.8
0.45
0.34
0.52
0.34
0.50
0.02
0.49
0.27
0.31
0.07
0.08
0.08
0.03
0.03
0.06
0.08
0.03
0.12
0.10
0.13
1.770(14)
–8.6(1)
0.56
2.135(10)
1.595(12)
–23.6(1)
–9.4(1)
0.03
0.70
C1–C3
1.815(14)
–18.1(1)
0.09
C1–H1
C2–C9
1.791(13)
1.835(11)
–18.4(1)
–16.8(1)
0.05
0.06
C2–C11
aziridine 1
oxirane 2
olefin 3
aziridine 1
oxirane 2
olefin 3
1.804(12)
0.231(19)
1.416(18)
–15.6(1)
3.1(1)
0.07
phenyl ring
3.8
3.8
4.8
7.4
three-membered ring
aziridine 1
oxirane 2
6.6(1)
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T. Schirmeister et al.
FULL PAPER
ethene ε equals 0.45.[25] In our case ε varies from 0.0 to 0.09 2.856 Å, symmetry operation: 1–x, 1–y, 1–z, ρ = 0.087(14)
for all single bonds. There are values of ε that are in the eÅ–3, ٌ2ρ = 1.1(1) eÅ–5). This example shows that the
region of double bonds: 0.34 to 0.70 for N1/O7–C1, N1/ Hirshfeld surface is not only a useful tool to visualise the
O7–C2 and C1–C2. This finding does not indicate that molecule’s steric demand in the crystal but also to localise
there are double bonds in the aziridine ring but that there all intermolecular interactions with their strength and direc-
are highly bent single bonds that cause the deviation from tion. The hydrogen bonds beginning or ending at the first
a cylindrical symmetry.
molecule of the asymmetric unit (Figure 6), namely N1–
Comparing experiment with theory for all bonds of the H1N···N1A (at H1N), C7–H7···O5 (at H7 and O5), C6–
aziridine compound (cf. electronic Supporting Information) H6···O4 (at H6 and O4) and C12A–H12D···N1 (at N1), can
the average deviations are 0.09 e/Å3 and 5.1 e/Å5. This is a be identified on the Hirshfeld surface and density values of
good agreement between experiment and theory compared about 0.06 e/Å3 can be read off the scale. This approxi-
to the deviations of 0.08 e/Å3 and 3.7 e/Å5 from literature[26] mated value is in very good agreement with the values of
and 0.14(9) e/Å3 from literature.[27]
the density at the bcp listed in Table 2 if one considers that
The topological analysis of the hydrogen bonds and con- a different partitioning scheme to generate Hirshfeld sur-
tacts yielded the values listed in Table 2. Both classical hy- faces is used.[28]
drogen bonds (N1A–H1NA···O5A and N1–H1N···N1A)
are weak not only regarding the geometrical parameters but
also regarding their topology. For strong hydrogen bonds
Atomic Charges and Volumes
electron-density values of about 0.2 e/Å3 and more are com-
mon.[30] On the other hand, there are several parameters
Integrating over the atomic basins yields the atomic vol-
defining a hydrogen bond referring to its topology: There
has to be a bond critical point between hydrogen atom and
acceptor, the density at the bcp has to be between 0.014
and 0.236 e/Å3 and the Laplacian at the bcp has to vary
between 0.58 and 3.35 e/Å5.[31] Referring to these criteria
all the other C–H···acceptor contacts are weak hydrogen
bonds, too. In the literature[5] donor–H···O interactions are
referred to as hydrogen bonds even though they are lower
in density at the bcp (e.g. 0.03 e/Å3) and of unfavourable
angles (e.g. 108°), but fulfil the conditions given in ref.[31]
Thus, one can state that the aziridine compound builds very
stable crystals (mechanically and chemically stable) because
of its weak but numerous hydrogen bonds stabilising the
molecules in the crystal enormously. Figure 6 shows that
there are even more interactions than the listed hydrogen
bonds. The strongest interaction of 0.085 e/Å3 on the Hirsh-
feld surface originates from the contact C11···O3A. The
umes and charges. The values from the analysis of the ex-
perimentally obtained electron-density distribution of the
aziridine ring are summarised in Table 4.
Table 4. Experimental atomic charges (Qtot) and atomic volumes
(Vtot) of the aziridine ring and environment of aziridine 1.
Atom
Qtot (e)
Vtot [Å3]
N1
C1
C2
C3
C9
C11
H1
H1N
–0.89
0.10
0.11
0.15
1.67
1.72
0.16
0.37
14.61
9.01
7.39
8.89
4.53
5.05
5.53
3.24
The aziridine ring as a functional group is negatively
value of this interaction’s density on the Hirshfeld surface charged (–0.15 e) due to the large atomic charge of the ni-
and at the bcp agree very well (C11···O3A distance: trogen atom. The carbon atoms C1 and C2 that can be
attacked from a nucleophile in a ring opening reaction are
positively charged as they should be. Thanks to the volume
being significantly larger for atom C1, one can assume that
an attack is directed towards this carbon atom. Regarding
the electrostatic potential (next chapter) this assumption
will be confirmed. The carbon atoms C9 and C11 are highly
positively charged because they are bound to two oxygen
atoms in the ester group. Each of their volumes is about
half of the volumes of the carbon atoms C1 and C2 in the
aziridine ring that are charged slightly positively. Another
striking example for the relationship between atomic vol-
ume and charge is the hydrogen atom H1N compared to all
the other hydrogen atoms. It carries more than 0.2 e more
positive charge than the other hydrogen atoms due to the
fact that it is bound to the singly negatively charged nitro-
gen atom N1 instead of a carbon atom. Consequently, the
volume of H1N is about half of the volume of each of the
other hydrogen atoms (see electronic Supporting Infor-
mation).
Figure 6. Hirshfeld surface[28] of aziridine 1, electron density
mapped on it, scale in e/Å3 (MolIso[29] representation, © 2006
Christian B. Hübschle).
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Electron-Density Determination
FULL PAPER
Figure 7. Electrostatic potential mapped on an iso-surface of the density at 0.5 e/Å3, a) aziridine ring of 1 (experiment), b) aziridine ring
of 1 (theory), c) oxirane ring of 2 (theory), d) olefin 3 (theory). Scale in e/Å for experiment, e/a0 for theory, converted into each other
for comparability (MolIso[29] representation).
Electrostatic Potentials
double bond of the olefin compound generates a more
negative potential than the conjugated bonds of the phenyl
ring do, but the carbon atoms of the double bond are posi-
tively polarised. This explains why a nucleophilic addition
reaction takes place instead of an electrophilic addition re-
action as far as conclusions can be drawn at present from
the theoretical results. It is therefore necessary to carry out
experimental studies also for oxirane 2 and olefin 3 which
are planned as soon as suitable single-crystals are obtained
and they will be reported in a forthcoming paper.
The representation of the electrostatic potential mapped
on an iso-surface of the density is very helpful in order to
get a deeper insight into the reactivity of the molecules.
Figure 7 shows a comparison of the electrostatic potentials
of all three compounds. Red coloured regions of the mole-
cules can be regarded as nucleophilic centres while blue re-
gions can be regarded as electrophilic centres. One can see
that the distribution of the potential is correlated with the
electronegativity of the atoms, as expected. Comparing sim-
ilar regions of the molecules in theory and experiment it is
obvious that charge separation is much more pronounced
in the experimental results. This is due to intermolecular
interactions in the crystal which can be assumed to be very
Zero Laplacian Iso-Surfaces
The zero Laplacian iso-surface (also called “reactive sur-
similar to interactions in biological systems. Thus, the ex- face” after Bader[3]) of the aziridine ring (Figure 8) allows
perimental determination of the electron-density distribu- an additional insight into the reaction mechanism. Each
tion is superior to the results of theoretical calculations of hole in the iso-surface depicts an electrophilic centre be-
isolated molecules in the gas phase if intermolecular inter- cause wherever the value of zero for the Laplacian cannot
actions are important for the system scrutinised.
be reached a reduced valence shell charge concentration is
Figure 7 allows a close look at the situation in the reac- located. So, these holes are the centres where a nucleophilic
tive region of the three-membered rings. The differences be-
tween theoretically and experimentally determined electron-
density distribution are obvious. In the experimentally de-
rived map (Figure 7, a) the carbon atom C1 is much more
positively polarised so that it will be the preferred site for a
nucleophilic attack. This finding can be confirmed by chem-
ical experiments (see Scheme 1). Regiospecificity for the at-
tack at C1 can be found. Steric hindrance at C2 also directs
the nucleophile to attack at C1. This finding cannot be con-
firmed by the theoretically derived map (Figure 7, b). No
discrimination between the carbon atoms C1 and C2 is pos-
sible as it is also not possible for the theoretically derived
Figure 8. Experimental zero Laplacian iso-surface of aziridine 1.
View from different directions: perspective b) is rotated by about
maps of oxirane and olefin (see parts c,d in Figure 7). The 180° against perspective a). MolIso © 2006 Christian B. Hübschle.
Eur. J. Org. Chem. 2007, 2759–2768
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T. Schirmeister et al.
FULL PAPER
attack is most probable. Looking at carbon atom C1 from We applied this method to dimethyl 3-(4-nitrophenyl)azirid-
two different directions three holes can be found. None of ine-2,2-dicarboxylate (1), which, together with the corre-
these holes is preferred regarding their dimensions because sponding epoxide 2 and the acceptor-substituted olefin 3,
the bigger a hole, the greater the electrophilicity. One can serves as model compound for irreversible cysteine and as-
assume that the attack will occur from the side of the least partic protease inhibitors consisting of an electrophilic “war
steric hindrance, that is from the side of the hydrogen atom head”. The detailed geometrical properties, bonding situa-
H1 instead of the aryl group. Next to the atom H1 there tions, hydrogen bonding properties, topological properties,
are two holes (Figure 8, b), none of which seems to be the atomic charges, and the electrostatic potential of aziridine
preferred reaction site.
1 are determined. With these detailed information it is pos-
sible to predict the positions and types of intermolecular
non-covalent interactions, as well as the reactive centres of
the molecule concerning covalent reactions. A comparison
with model reactions with oxygen and sulfur nucleophiles
revealed that aziridine 1 reacts according to its determined
electronic properties: Attack of the nucleophiles exclusively
takes place at C1 which is the more positively polarised car-
bon atom of the three-membered ring. A comparison of the
theoretically and experimentally obtained charge density
shows that the experimentally derived properties are much
better suited to explain the chemical reactivity of the scruti-
nised compound. The charge separation is much more pro-
nounced in the experimental results due to intermolecular
interactions between the molecules in the crystal. These in-
teractions are generally based on the same forces as com-
plex formation between a biologically active ligand and its
macromolecular target. Thus, the experimental electron-
density determination is a valid tool to get access to the
structural and electronic properties of biologically active
molecules, and can be used to understand their non-coval-
ent and covalent modes of action. Therefore experimental
studies for oxirane 2 and olefin 3 are planned as soon as
suitable single-crystals are obtained.
Reactions with Nucleophiles
Aziridine 1 is known to undergo nucleophilic ring open-
ing with acetate under cleavage of the C1–C2 bond of the
aziridine ring after acylation with acetic acid anhydride
leading to the open-chain product 4a (Scheme 1).[32] This
reaction, which may proceed through the azomethine ylide
1a, also occurs with propionic acid anhydride leading to
the corresponding product 4b (Scheme 1). In both cases, the
nucleophile attacks exclusively at C1 of the aziridine ring.
In order to examine if such ring opening reactions also take
place without preceeding activation by N-acylation, 1 was
treated with benzyl mercaptan (Scheme 1). The product 5
obtained hereby also results from C1–C2 bond cleavage
with attack of the nucleophilic thiol at C1. No product from
attack at C2 could be detected. These results are in a good
agreement with the properties of the compound derived
from the experimental charge-density determination.
Experimental Section and Computational Details
Syntheses and Crystallisation: The compounds were synthesised as
follows (Scheme 2): olefin 3 was obtained by Knoevenagel conden-
sation of malonate with p-nitro benzaldehyde. Epoxidation of 3
with hypochlorite yielded epoxide 2, and reaction of 3 with di-
phenylsulfimide led to aziridine 1.[32]
Scheme 1. Reactions of aziridine 1 with nucleophiles. In both cases
(reaction with oxygen and sulfur nucleophile) the ring-opened
product results from attack at C1 of the aziridine ring.
Conclusions
Scheme 2. Synthesis of electrophilic building blocks: acceptor-sub-
stituted olefin 3, epoxide 2, aziridine 1.
Experimental electron-density determination by means
of ultra-high resolution X-ray diffraction at low tempera-
ture is a hitherto rarely exploited tool for the development,
Compounds 1–3 were recrystallised from dichloromethane/meth-
optimisation, and analysis of biologically active molecules. anol. Originally, in no case the crystal quality was sufficient for
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Electron-Density Determination
FULL PAPER
single-crystal diffraction experiments because all compounds tend
to form poor diffracting, twinned crystals to a very high degree.
After several recrystallisation attempts only from aziridine 1 an ap-
propriate red shining single-crystal with dimensions of
0.45ϫ0.25ϫ0.15 mm3 could be obtained which was suited for
high-resolution X-ray diffraction experiments.
ring and environment, and a description of the syntheses and ana-
lytical data of compounds 1, 2, 3, 4b, 5.
Acknowledgments
Financial support by Deutsche Forschungsgemeinschaft (DFG) is
gratefully acknowledged.
X-ray Data Collection: X-ray synchrotron measurements of the sin-
gle-crystal were performed at the beamline D3 of storage ring
DORIS III at HASYLAB/DESY in Hamburg which is equipped
with a Huber four circle diffractometer and a MarCCD 165 area
detector. A wavelength of 0.56 Å for the primary radiation was
chosen. The temperature was maintained at 9 K during the mea-
surement by using an open helium gas flow cooling device (Helijet,
oxford diffraction). Although several geometric restrictions at the
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