68
P.S. Pereira Silva et al. / Journal of Molecular Structure 995 (2011) 66–71
Table 3
H-bond geometry (Å, °).
there is also an intramolecular N–Hꢀ ꢀ ꢀO hydrogen bond with
geometry similar to that found in form I [see Table 3], forming
six-membered rings with graph-set symbol S(6) [19,20]. Of the
two intramolecular C–Hꢀ ꢀ ꢀO hydrogen bonds present in form I
(C13–H13ꢀ ꢀ ꢀO2; C20–H20ꢀ ꢀ ꢀO2) only the C20–H20ꢀ ꢀ ꢀO2 is present
in this polymorph since the ring C9–C14 is considerably out of the
biuret plane, not allowing a conventional hydrogen bond between
the atoms C13 and O2.
D–H
Hꢀ ꢀ ꢀA
2.55
1.91
2.37
Dꢀ ꢀ ꢀA
3.162(2)
2.593(2)
2.903(2)
D–Hꢀ ꢀ ꢀA
124
135
116
C16–H16ꢀ ꢀ ꢀO2i
0.93
0.86
0.93
N3–H3ꢀ ꢀ ꢀO1 (intra)
C20–H20ꢀ ꢀ ꢀO2 (intra)
Symmetry code i: 1 ꢂ x, y ꢂ 1/2, 3/2 ꢂ z.
The use of available strong hydrogen bond donors and acceptors
is almost axiomatic [19], so an unusual structural feature in form II
is the absence of the expected N2–H2ꢀ ꢀ ꢀO1 hydrogen bond, that is
present in form I.
(2) The single point energy for the X-ray geometries with the
positions of the hydrogen atoms in form I modified to be like
those in form II (D
E1), i.e., with the same distances to the
parent atoms as in form II;
The molecular packing is also influenced by several C–Hꢀ ꢀ ꢀ
p
(3) Energy for the structures with all parameters optimised
except the torsion angles chosen to define each conformer
interactions. The strongest C–Hꢀ ꢀ ꢀ
p interaction is of the type II as
described by Malone et al. [21], with a Hꢀ ꢀ ꢀpi distance of 2.81 Å,
(D
E2).
and a C–Hꢀ ꢀ ꢀ
p angle of 162° [symmetry code: (i) 1 + x, y, z]; the
H8 atom is being attracted in the direction of the centre of the aro-
These calculations were performed with the molecular orbital
HF method and within DFT using B3LYP (Becke three-parameter
Lee–Yang–Parr) for exchange and correlation, which combines
the hybrid exchange functional of Becke [15,16] with the correla-
tion functional of Lee, Yang and Parr [17]. The calculations were
matic ring C15–C20. In the other two relevant C–Hꢀ ꢀ ꢀ
p
interac-
tions, the hydrogen atoms H17 and H12 are above the centre of
the phenyl ring C3–C8 but the C–H bonds point towards the ring
edge. These two interactions are of the type III according to the
classification of Malone et al. [21], the first with a H17ꢀ ꢀ ꢀpii dis-
performed with a 6-31G(d,p) basis set. For the method
D
E1 we also
tance of 2.83 Å, and a C17–H17ꢀ ꢀ ꢀ
p angle of 149° [symmetry code:
performed HF and DFT calculations with the augmented basis set
6-311+G(d,p).
(ii) 1 ꢂ x, ꢂ1/2 + y, 3/2 ꢂ z] and the second with a H12ꢀ ꢀ ꢀpiii dis-
tance of 3.02 Å, and a C12–H12ꢀ ꢀ ꢀ
(iii) 3 ꢂ x, 1 ꢂ y, 2 ꢂ z].
p angle of 143° [symmetry code:
We performed also geometry optimizations starting from the
experimental X-ray geometries of the two conformers. These opti-
mizations were performed only within DFT (B3LYP for exchange
and correlation and 6-31G(d,p) basis set). Tight conditions for con-
vergence of both the self-consistent field cycles and the maximum
density and energy gradient variations were imposed (10ꢂ5 atomic
units) in both calculations. At the end of these geometry optimiza-
tions we conducted Hessian calculations to guarantee that the final
structures correspond to true minima, using the same level of the-
ory as in the geometry optimizations.
3.2. Fingerprint plots
When comparing the same molecule in different crystal envi-
ronments, Hirshfeld surfaces and fingerprint plots [4–7] have been
shown to be a powerful tool for elucidating and comparing inter-
molecular interactions, complementing other tools currently avail-
able for the visualization of crystal structures and for their
systematic description and analysis, e.g. graph-set analysis [19]
and topological analysis [22].
3. Results and discussion
The intermolecular interactions of this new polymorph and of
the previously reported [2] were analyzed using the two-
dimensional fingerprint plots [6,7] derived from Hirshfeld surfaces
[4,5], using the software CrystalExplorer, version 2.1 [3]. 2D-finger-
print plots were generated by using the di and de pairs measured on
each individual spot of the calculated Hirshfeld surface. Fig. 3
shows unambiguously that different intermolecular interactions
are present in the polymorphs form II and form I, which result in
different packing modes. In the plot of form II the ‘wings’ are more
3.1. Crystal structure
In an attempt to synthesize a totally different compound we ob-
tained serendipitously a second polymorph, form II, of N0,N00,N000-
triphenylbiuret. It is monoclinic, like the already known form [2],
form I, and has the same space group (P21/c) but a less extensive
hydrogen-bonding arrangement. In the biuret moiety the individ-
ual –NH–CO–N– groups are planar within the standard error and
the angle between these groups is considerably smaller [5.8(1)°]
than the corresponding angle in form I [12.8(2)°]. The N1–C3 bond
is significantly longer [1.4463(17) Å] than the N2–C9 and N3–C15
bonds [1.4190(18) and 1.4136(17) Å] (see Fig. 1).
pronounced which indicate aromatic interactions, namely C–Hꢀ ꢀ ꢀ
p
contacts. Only the 2D-fingerprint plot of the form I shows the pres-
ence of a pair of long sharp spikes, a characteristic of the strong
hydrogen bonds, in this case the N–Hꢀ ꢀ ꢀO hydrogen bonds. There
is evidence of close intermolecular Hꢀ ꢀ ꢀH contacts in both poly-
The N3–C2 [1.3404(17) Å] and N2–C1 [1.3540(17) Å] bond
lengths are in the expected range for delocalized C–N bonds [18].
The geometry around the N1 atom is the expected for a hybridized
sp2 atom.
morphs, that occur as a characteristic hump in the region
di = de = 1.2 Å of the plot.
3.3. Results of the ab initio calculations
While in the form I the phenyl rings C9–C14 and C15–C20 are
roughly coplanar with the least squares plane of the biuret moiety
[with dihedral angles of 11.6 (2)° and 10.9 (2)°, respectively], in
this new polymorph they are considerably out of this plane, with
the dihedral angles being 50.31(5)° and 21.58(6)° respectively.
The ring C3–C8 is almost perpendicular to the biuret fragment
[dihedral angle of 87.98(5)° between the two planes] and this
can be explained by the steric hindrance of N2–H2.
The molecules are linked in infinite chains running parallel to
the b axis, via C–Hꢀ ꢀ ꢀO hydrogen bonds [Fig. 2; Table 3]. These
chains have a periodicity of six atoms, graph-set symbol C(6)
according to Etter’s graph-set theory [19,20]. In this polymorph
Using the three methods described previously we have per-
formed the calculation of the energy differences between the two
conformers of the title compound. The results are presented on
Table 4. As expected, the results obtained using method
DE
crys (sin-
gle point energy for the experimental X-ray geometries) lead to
very large differences of energy between the two conformations,
and the major source of these differences seems to be the hydrogen
atomic positions, since in our structure the hydrogen atoms were
positioned geometrically and in the previously reported poly-
morph they were refined freely, leading to large differences in
the X–H bond lengths between the two structures. The energy dif-