Dihydrogen phosphate and hydrogen sulphate of 1,4-dimethyl-1,4- diazabicyclo[2.2.2]octane-1,4-diium: Crystal structures, hydrogen bonding and infrared spectra

Article abstract of DOI:10.1007/s10870-011-0137-0

The crystal structures of the title compounds consist of 1,4-dimethyl-1,4-diazabicyclo[2.2.2]octane-1,4-diium cation [C₈H ₁₈N₂]²⁺ and [H₂PO₄] ^- or [HSO₄]^- anions. Both crystal structures are monoclinic, the structure of the dihydrogen phosphate (I) is non-centrosymmetric (P2₁) with a = 6.4090(2) A, b = 13.6920(5) A, c = 7.6140(3) A, β = 94.620(2)°, V = 665.97(4) A³, Z = 2; whereas the unit cell of the hydrogen sulphate (II) is centrosymmetric (P2₁/c) with a = 13.8460(2) A, b = 12.6610(2) A, c = 8.0360(2) A, β = 99.5800(12)°, V = 1389.10(5) A³, Z = 4. Both the structures are formed by the different bonding patterns of the anions interlinked by strong and moderate O-H???O hydrogen bonds. While the structure of (I) consists of a two-dimensional network of the hydrogen bonded dihydrogen phosphates, the infinite chains of the hydrogen bonded hydrogen sulphates are the basic building unit of the structure (II). In addition to the dominant electrostatic interaction the divalent cations stabilize themselves in the structures by forming several C-H???O hydrogen bonds to the oxygen atoms of the anions. The IR spectra of both the compounds are strongly affected by the hydrogen bonds whose influence on OH stretching vibrations is analysed by means of the DFT calculations in the solid state.

Full text of DOI:10.1007/s10870-011-0137-0

J Chem Crystallogr (2011) 41:1539–1546
DOI 10.1007/s10870-011-0137-0
ORIGINAL PAPER
Dihydrogen Phosphate and Hydrogen Sulphate of 1,4-Dimethyl-
1,4-diazabicyclo[2.2.2]octane-1,4-diium: Crystal Structures,
Hydrogen Bonding and Infrared Spectra
ˇ
Ondrej Kaman Lubomır Smrcok
•
•
ˇ
Ivana Cısarova David Havlıcek
´
ˇ
•
´
ˇ
´
´ˇ
Received: 8 October 2010 / Accepted: 28 May 2011 / Published online: 9 June 2011
Ó Springer Science+Business Media, LLC 2011
Abstract The crystal structures of the title compounds
consist of 1,4-dimethyl-1,4-diazabicyclo[2.2.2]octane-1,
4-diium cation [C8H18N2]2? and [H2PO4]- or [HSO4]-
anions. Both crystal structures are monoclinic, the structure
of the dihydrogen phosphate (I) is non-centrosymmetric
Keywords 1,4-Dimethyl-1,4-diazabicyclo[2.2.2]octane Á
Short hydrogen bonds Á Dihydrogen phosphate Á Hydrogen
sulphate Á DFT molecular dynamics
˚
(P21) with a = 6.4090(2) A, b = 13.6920(5) A, c =
˚
Introduction
3
˚
˚
7.6140(3) A, b = 94.620(2)°, V = 665.97(4) A , Z = 2;
whereas the unit cell of the hydrogen sulphate (II) is
The interest in compounds forming strong hydrogen bonds
in the solid state stems from their valuable physical prop-
erties such as ferroelectric or non-linear optical properties
or proton conductivity. Good proton conduction depends
on both the architecture of the hydrogen bonds and on their
bonding energies. While the former is responsible for
creation of suitable pathways enabling long range transport
of protons, an appropriate value of the latter facilitates the
dynamics including local proton transfer along the hydro-
gen bond followed by the reorientation movement of the
species involved in the hydrogen bond. These two pro-
cesses constitute so called Grotthuss mechanism of the
proton conductivity [1]. It should be stressed that this
mechanism is based on two contradicting claims: on one
hand the proton transfer is aided by low energy barriers
typical for short hydrogen bonds, on the other hand very
strong hydrogen bonds can hinder reorientations changing
the positions of the proton donor and the acceptor [2, 3].
We have recently reported the X-ray and neutron
structure analysis of the diazabicyclo[2.2.2]octane-1,4-diium
dihydrogen phosphate monohydrate comprising very short
O–HÁÁÁO hydrogen bonds [4]. Crystals of this compound
exhibit noticeable anisotropy in AC conductivity attributed
to the different proton conduction ability in different
crystal directions. Unfortunately, the compound proved to
be relatively unstable and to loose water at around 60 °C
[5]. Because the water molecules in the structure inter-
link hydrogen phosphate groups and thus most probably
˚
centrosymmetric (P21/c) with a = 13.8460(2) A, b =
˚
˚
12.6610(2) A, c = 8.0360(2) A, b = 99.5800(12)°, V =
3
1389.10(5) A , Z = 4. Both the structures are formed by
˚
the different bonding patterns of the anions interlinked by
strong and moderate O–HÁÁÁO hydrogen bonds. While the
structure of (I) consists of a two-dimensional network of
the hydrogen bonded dihydrogen phosphates, the infinite
chains of the hydrogen bonded hydrogen sulphates are the
basic building unit of the structure (II). In addition to the
dominant electrostatic interaction the divalent cations sta-
bilize themselves in the structures by forming several
C–HÁÁÁO hydrogen bonds to the oxygen atoms of the
anions. The IR spectra of both the compounds are strongly
affected by the hydrogen bonds whose influence on OH
stretching vibrations is analysed by means of the DFT
calculations in the solid state.
´
ˇ
´
´ˇ
O. Kaman (&) Á I. Cısarova Á D. Havlıcek
Department of Inorganic Chemistry, Faculty of Science,
Charles University in Prague, Hlavova 8, 128 40 Prague 2,
Czech Republic
e-mail: kamano@seznam.cz
ˇ
L. Smrcok
ˇ
Institute of Inorganic Chemistry, Slovak Academy of Sciences,
´
´
Dubravska cesta 9, 845 36 Bratislava, Slovak Republic
123

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J Chem Crystallogr (2011) 41:1539–1546
facilitate the proton transfer, even their partial lost could
result in a remarkable decrease of conductivity. It was
therefore assumed that a replacement of the cation by a
more bulky one could lead to an anhydrous compound with
the desired arrangement of the dihydrogen phosphate
anions preserved. The methylation of the original base,
the diazabicyclo[2.2.2]octane, leading to the title cation,
seemed to be the best solution.
Scheme 1 Preparation of (I) and (II) from 1,4-diazabicyclo[2.2.2]
octane as a starting material (a) CH3I, ethyl acetate, reflux; (b) Ag2O,
water; (c) H3PO4 or H2SO4, stoichiometric amount
In addition to the dihydrogen phosphate also the
hydrogen sulphate was synthesized in order to obtain a
structure based on the same stoichiometry (one cation and
two anions) and similar building blocks (the PO4 and SO4
tetrahedra are of comparable sizes) whose anions have,
however, only one proton donor. The system of hydrogen
bonds in such a structure has to exhibit lower dimension-
ality than the system in dihydrogen phosphate with two
proton donors. The comparison of both the compounds was
believed to enable the study of the cation behaviour in two
distinct hydrogen bonded structures and to see its influence
on the geometry of hydrogen bonds. Moreover, the latter
compound could be interesting from the viewpoint of
proton conductivity as several superprotonic phases based
on hydrogen sulphates have already been reported [6, 7].
We herein report the crystal structures of the title
compounds and analyze the impact of the short hydrogen
bonds on their vibrational spectra using the first principle
calculations in the solid state.
the modification that the synthesized iodide was not re-
crystallized but only washed twice with hot ethyl acetate and
its purity was confirmed by 1H NMR.
Structures Determination and Refinement
The crystals were measured on a Nonius KappaCCD dif-
fractometer equipped with a graphite monochromator using
MoKa radiation. Data were collected and the unit cells
determined using the HKL program package [9], multi-scan
absorption corrections were carried out in Sortav [10]. The
phase problem was solved by direct methods in SIR-92 [11]
and the positions of hydrogen atoms were located from
difference Fourier maps. The full matrix least square
refinements on |F2| were carried out using SHELXL-97
[12]. All non-hydrogen atoms were refined with anisotropic
displacement parameters. The hydrogen atoms were con-
strained to the ideal geometry using an appropriate riding
model and assigned displacement parameters Hiso(H) =
1.2 Ueq(pivot atom) or 1.5 Ueq(pivot atom) for (CH2) or
(CH3, OH), respectively. Geometrical analysis of the
structures was done by means of the PLATON [13] and
DIAMOND programs [14].
Methods
Synthesis
Colourless single crystals of both the salts (I and II) were
grown from their concentrated and viscous aqueous solu-
tions by evaporation of water after few weeks of storage over
KOH in desiccator. The crystals of (II) are hygroscopic and
dissolve due to the air moisture, while the crystals of (I)
are stable in the air. The solutions were prepared by the
neutralization of 1,4-dimethyl-1,4-diazabicyclo[2.2.2]octane-1,
4-diium hydroxide (0.06 mol dm-3) adding the stoichiom-
etric amount (molar ratio 1:2) of the corresponding diluted
acid (0.3 mol dm-3) (Scheme 1). The exact concentrations
of the base and both the acids were determined by titration
on methyl orange. The hydroxide was obtained in the form
of aqueous solution resulting in the conversion reaction of
1,4-diazabicyclo[2.2.2]octane-1,4-diium iodide and freshly
precipitated silver oxide present in stoichiometric excess
(1:1.15). The reaction mixture was exposed to ultrasound
irradiation for 30 min and then the precipitate was removed
by filtration. The starting iodide was prepared performing
exhaustive methylation of 1,4-diazabicyclo[2.2.2]octane by
iodomethane according to the published procedure [8] with
Additional material available from the Cambridge Crys-
tallographic Data Center comprises the final atomic coor-
dinates for all atoms, thermal parameters and a complete
listing of bond distances and angles. These data can be
obtained free of charge at www.ccdc.cam.ac.uk/conts/
retrieving.html or from the Cambridge Crystallographic
Data Center, 12, Union Road, Cambridge CB2 1EZ, E-mail:
deposit@ccdc.cam.ac.uk using the deposition numbers
CCDC 771666 (I) and 771667 (II) .
Vibrational Spectra
The infrared spectra (Happ-Genzel apodization, 4 cm-1
resolution) were recorded at the temperature of 298 K on
the FTIR spectrometer Nicolet 6700 FT-IR using DRIFTS
technique in optically pure KBr. Before the measurement
the corresponding samples were stored in desiccator over
KOH.
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J Chem Crystallogr (2011) 41:1539–1546
Theoretical Calculations
1541
Table 1 Crystal data and structure refinement details for (I) and (II)
(I)
(II)
Prior to the calculations of the vibrational modes the
positions of the atoms in the structures were optimized in
the solid state DFT calculations performed using the
computer code VASP [15–17] in the GGA approximation.
The structures were expanded to the P1 symmetry and the
unit cell parameters were not optimized. Plane waves
formed a basis set and the calculations were performed
using the projector-augmented wave method [18, 19] and
atomic pseudo-potentials [20]. The energy cutoff control-
ling the accuracy of the calculation was set to 500 eV,
representing an extended basis set and consequently highly
accurate calculations. The optimizations of the structures
were achieved by means of conjugated gradient method in
four k-points [21, 22]. Normal modes of vibrations were
calculated from the normal mode analysis using the har-
monic approximation without considering any selection
rules. The total energy was converged to 10-7 eV and
Empirical formula
Formula weight
C8H22N2O8P2
336.22
C8H20N2O8S2
336.38
Crystal color, shape
Crystal size (mm)
Temperature (K)
Colourless, prism
Colourless, prism
0.38 9 0.75 9 0.25 0.42 9 0.38 9 0.28
150
150
˚
Wawelength (A)
0.71073
Monoclinic
P21 (No. 4)
0.71073
Crystal system
Space group
Monoclinic
P21/c (No. 14)
˚
a = 6.4090(2) A
˚
a = 13.8460(2) A
Unit cell dimensions
˚
b = 13.6920(5) A
˚
b = 12.6610(2) A
˚
c = 7.6140(3) A
˚
c = 8.0360(2) A
b = 94.620(2)°
665.97(4)
2
b = 99.5800(12)
3
Volume (A )
˚
1389.10(5)
4
Z
Dcalc (gcm-3
)
1.677
1.609
0.423
Absorption coefficient
(mm-1
0.368
˚
residual forces on the atoms were \0.005 eV/A. The
)
Hessian was constructed from the single-point energy
calculations of the 6n structures generated from the opti-
mized structures by displacing each of the n atoms in the
cell in the positive and negative senses along the Cartesian
directions x, y, and z [23]. Calculated modes were analyzed
with the help of the MOLEKEL program [24]. These cal-
culations were complemented by the molecular dynamics
calculations (MD) as implemented in the VASP code.
Owing to the large computational demands the MD cal-
culations were restricted to the gamma point of the Brill-
ouin zone, the energy cutoff set to 400 eV and the required
convergence in total energy to 10-4 eV. The finite tem-
perature calculations were performed on a canonical
F(000)
356
712
h range for data
collection (°)
Index ranges
2.68°–27.42°
1.49°–27.51°
-8 \ h \ 8
-17 \ k \ 17
-9 \ l \ 9
11696
-17 \ h \ 17
-16 \ k \ 16
-10 \ l \ 10
24613
Reflections collected
Independent reflections 3031
3191
Reflections with
I [ 2r(I)
R(int)
3003
2973
0.0232
0.0173
Absorption correction
Multi-scan
0.861, 0.904
3031/1/183
Multi-scan
0.689, 0.917
3191/0/184
Tmin, Tmax
Data/restraints/
parameters
´
ensemble with a Nose thermostat procedure [25] at the
simulation temperature of 300 K. The Verlet velocity
algorithm [26] with a time step of 1 fs was chosen. The
results of the MD calculations were interpreted in the fre-
quency space by calculating the Fourier transform of the
velocity autocorrelation functions and presented in the
form of power spectra. Partial vibrational densities of states
for the selected hydrogen atoms were calculated using the
aClimax code [27].
Goodness-of-fit on F2
1.048
1.013
Final R indices
(I [ 2r(I))
R1 = 0.0227,
wR2 = 0.0595
R1 = 0.0230,
wR2 = 0.0598
-0.056(57)
R1 = 0.0282,
wR2 = 0.0806
R1 = 0.0305,
wR2 = 0.0825
–
R indices (all data)
Absolute structure
parameter
Largest diff. peak and
-3
0.227 and 0.274
0.308 and 0.512
˚
hole (eA
)
Results and Discussion
Crystal Structures
1,4-dimethyl-1,4-diazabicyclo[2.2.2]octane-1,4-diium cation
and protonated anions of the respective inorganic acid,
dihydrogen phosphate or hydrogen sulphate (Figs. 2, 3).
By and large, the skeletons of both structures are formed by
the different bonding patterns of the anions interlinked by
strong and moderate O–HÁÁÁO hydrogen bonds (Table 3).
While the structure of (I) consists of a two-dimensional
The basic crystallographic data, measurement and refine-
ment details are summarised in Table 1, atoms numbering
for the structures is in Fig. 1 and the essential bond dis-
tances, bond angles and torsional angles are in Table 2.
Both the structures of (I) and (II) consist of the
123

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J Chem Crystallogr (2011) 41:1539–1546
Fig. 1 Atom numbering
schemes and molecular
conformations in (I) (a) and (II)
(b). The hydrogen atoms of the
cation are omitted for the sake
of clarity. Probability
displacement ellipsoids are
drawn at the 50% level
network of hydrogen bonded dihydrogen phosphates, the
infinite chains of the hydrogen bonded sulphates are the
basic building units of the structure (II). In addition to
the dominant electrostatic interactions the divalent cations
stabilize themselves in the structures by forming several
C–HÁÁÁO hydrogen bonds with the respective anions.
bonded chains of the hydrogen sulphates anions running
along the c-axis (Fig. 3). The OÁÁÁO contact distances of the
strong hydrogen bonds (O2ÁÁÁO1 and O5ÁÁÁO6) are of sim-
ilar lengths, but larger than the OÁÁÁO contacts in (I). The
corresponding O–HÁÁÁO bond angles are close to the linear
as expected for such short OÁÁÁO contacts. The chains of
[HSO4]- form a skeleton of the structure to which the
organic cations are linked by the C–HÁÁÁO bonds of dif-
ferent strengths (Table 3).
In the structure of (I) the dihydrogen phosphate anions
form layers perpendicular to (100) in which the phosphate
units are coupled to the six member rings by four O–HÁÁÁO
hydrogen bonds with OÁÁÁO separations ranging from
The geometry of sulphate tetrahedra is predetermined by
the bonding state of the oxygen atoms. The S–O bond dis-
tances are remarkably differentiated with the S–O(H) dis-
tances considerably larger than those of S=O (Table 2). The
distorted tetrahedral environments, as documented by the
variations of the O–S–O bond angles, are then obviously
caused by the heterogeneous coordination spheres of the
central sulphur atoms. Refined values of the S–O bond lengths
are in good agreement with the values in the structure of
potassium hydrogen sulphate arsenate [30], where the
unprotonated oxygen atoms of [HSO4]- anion bond to the
˚
2.504(2) to 2.533(2) A. All oxygen atoms of the dihydro-
gen phosphate anions are involved in these bonds playing
either the roles of donors or acceptors. The bonds with the
O5/O10 atoms acting as donors are shorter and they should
be classified as very strong hydrogen bonds [28]. The
bonds with the O3/O4 donor atoms, though weaker, still
belong among the ‘‘moderately strong’’ hydrogen bonds. In
all the cases the O–HÁÁÁO bond angles are very close to the
linear angle.
The geometries of the PO4 units in (I) are deformed tet-
rahedra with a minimum spread of the O–P–O bond angles
(Table 2). The P–O bond distances fall into two groups; the
protonated P–O vertices show the expected lengthening
compared to the other P–O bonds. This spread of the P–O
˚
sulphur atoms within the interval 1.4357(19) to 1.4468(18) A,
while the S–O(H) bonds are considerably longer, i.e.
˚
1.5658(18) and 1.5562(18) A, respectively. Similar spread of
˚
the S–O bond distances, 1.4470(12) to 1.4599(11) A vs.
˚
bond distances is in line with e.g. 1.491(2) to 1.523(15) A
˚
1.5602(11) A, is found in 2-amino-4,6-dimethylpyrimidini-
interval found in the aducts of the phenylphosphoric acid
˚
[29] or with the 1.497(1) to 1.565(1) A interval in diazabi-
um hydrogen sulphate [31]. Of similar lengths are also the
S–O (S–OH) bonds in guanidinium hydrogen sulphate [32].
Examination of the organic moieties shows that the
cation has significantly distorted conformation from the
ideal C3v geometry in both structures as documented by
the N–C–C–N torsional angles that are within 18.22 (14) to
19.53 (15)° for (I) and 20.93(13) to 21.36(13)° for (II). The
range of N–C–C–N torsion angles is substantially larger
cyclo[2.2.2]octane-1,4-diium dihydrogen phosphate mono-
hydrate [4]. The organic cations occupy the voids created by
two phosphate hexagons of the neighbouring layers, being
thus the guests in the anionic framework.
The architecture of hydrogen bonds in the structure (II)
differs from (I) as it comprises two distinct hydrogen
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J Chem Crystallogr (2011) 41:1539–1546
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˚
Table 2 Essential bond distances (A), angles and torsional angles (°)
for (I) and (II)
Table 2 continued
Torsional angles
Bond distances
(I)
(I)
N1–C15–
C14–N2
-18.13(17) N1–C20–C13–N2 -19.58(16)
-18.99(16)
P1–O11
P1–O8
P1–O3
P1–O5
P2–O6
P2–O7
P2–O10
P2–O4
1.510(1)
1.517(1)
1.568(1)
1.569(1)
1.506(1)
1.508(1)
1.566(2)
1.576(2)
N2–C19–
C18–N1
(II)
N1–C5–C6–N2 20.93(14)
N2–C4–C3–N1 21.79(13)
N2–C2–C1–N1
21.50(13)
(II)
than that reported for the tetrachlorocuprate of the title
cation (5.5 (5) to 7.9 (5)°, [33] or for the tetrachloroco-
baltate (3.0 (4) to 8.7(4)°, [34]. Larger torsional angles
have also been found, e.g. 10.1 (10) to 17.2 (8)° in the
octasilicate hydrate [35]. The flexibility of the cation is
further documented by the zero torsion angles in its
bis(iodide) acetonitrile solvate where the nitrogen atoms
and one of the connecting ethylene bridges lie on a special
position with a mirror symmetry [36].
S1–O4
S1–O3
S1–O1
S1–O2
S2–O8
S2–O7
S2–O6
S2–O5
Bond angles
(I)
1.444(1)
1.445(1)
1.471(1)
1.570(1)
1.443(1)
1.448(1)
1.466(1)
1.568(1)
Infrared Spectra
O11–P1–O8
113.82(7)
109.04(7)
110.35(6)
107.02(7)
109.60(7)
106.73(6)
115.38(6)
110.24(7)
107.57(7)
107.42(7)
109.56(7)
106.31(7)
O11–P1–O3
O8–P1–O3
O11–P1–O5
O8–P1–O5
O3–P1–O5
O6–P2–O7
O6–P2–O10
O7–P2–O10
O6–P2–O4
O7–P2–O4
O10–P2–O4
The measured infrared spectra (Fig. 4) of both the com-
pounds exhibit complicated absorption profiles in the high
energy transfer regions ([1500 cm-1). Whilst the broad
bands are obviously related to OH stretching modes, the
well-recognized clusters of sharp peaks correspond to the
C–H stretching modes. The mentioned broad bands in
the spectrum of (I) can be described as a trio ‘‘ABC’’ with
the maxima in the range 2800–1600 cm-1. Its occurrence
is typical for the strong hydrogen bonds and its origin is
usually explained on the basis of coupling of the OH
stretching mode and some low energy modes, although
other effects could influence the band shapes and positions
as well [30, 32, 37–43]. Similarly, the ‘‘AB’’ broad bands
of medium intensities are clearly observed in (II), exhib-
iting maxima in the range of 3000–2500 cm-1. According
to the theoretical prediction the region below 1500 cm-1
starts with C–H bending modes and with the decreasing
energy transfer it contains the P–O (S–O) stretching and
bending modes involving both the atoms of the anions and
the cation. From *920 cm-1 downwards the spectrum is
populated with tetrahedral and cation deformation modes.
While the spectrum of (II) has in the middle and the low
energy transfer region several well-assignable peaks, the
spectrum of (I) is its caricature having at least the contri-
butions from the cation at the very similar positions as in
(II)
O4–S1–O3
O4–S1–O1
O3–S1–O1
O4–S1–O2
O3–S1–O2
O1–S1–O2
O8–S2–O7
O8–S2–O6
O7–S2–O6
O8–S2–O5
O7–S2–O5
O6–S2–O5
114.84(6)
111.62(6)
111.85(6)
104.41(6)
107.71(6)
105.63(6)
114.96(6)
112.05(6)
111.17(6)
104.52(6)
107.68(6)
105.71(6)
123

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J Chem Crystallogr (2011) 41:1539–1546
Fig. 2 Unit cell packing in
(I) viewed down the a (a) and
b (b) axis. Hydrogen atoms of
the organic moiety are omitted
for the sake of clarity. O–HÁÁÁO
hydrogen bonds are depicted as
broken lines
Fig. 3 Unit cell packing in (II)
viewed down the a (a) and
b (b) axis. Hydrogen atoms of
the organic moiety are omitted
for the sake of clarity. O–HÁÁÁO
hydrogen bonds are depicted as
broken lines
(II), but the corresponding bands are severally distorted
and obscured due to the intense absorption bands of the
strongly hydrogen bonded dihydrogen phosphate anions.
Our first attempt to clarify the nature of the broad bands in
the high energy region was based on the partial vibrational
densities of the states theoretically predicted for all hydrogen
atoms involved in the strong O–HÁÁÁO bonds. The calcula-
tions were believed to track the contributions of the partic-
ular hydrogen atoms to the resulting bands and to describe
the basis of the corresponding vibrations. The results
obtained for the individual hydrogen atoms are depicted in
Fig. 5. Unfortunately, the calculations predicting vibrational
modes using harmonic approximation have provided for (I) a
misleading picture of the nature on the modes above
*2000 cm-1. On one side, the calculations have in accord
with the strength of the hydrogen bonds predicted very large
red and blue shifts of the stretching OH and bending P–OH
modes and grouped them all to the region of energy transfer
between 2000 and 2500 cm-1. On the other side, a closer
inspection of the predicted modes reveals that the stretching
movements are predicted exclusively for the H3 and H10
atoms, while the H4 and H5 atoms are predicted to execute
only the bending movements. These confusing and incorrect
results can be explained by the inherent limits of the method
based on the harmonic approximation, which evidently
cannot correctly handle very strong hydrogen bonds causing
extreme shifts of both stretching and bending modes. Simi-
larly, all the modes in (II) obtained above 2400 cm-1 are
predicted to be the only extremely red shifted pure O–H
stretching modes. In contrast, the modes below 1600 cm-1
are in both the cases consistently identified as bending modes
(‘‘tetrahedral deformation’’) with hydrogen atoms moving
either in the plane (‘‘in-plane bending’’) defined by O(H)–S–O
or O(H)–P–O(H) atoms (the modes above *1250 cm-1) or
perpendicular (‘‘out-of-plane bending’’) to these planes (the
modes below *1250 cm-1).
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J Chem Crystallogr (2011) 41:1539–1546
1545
˚
Table 3 Hydrogen bonding geometry (A, °) for (I) and (II)
D–HÁÁÁA
d(D–H)
d(HÁÁÁA)
d(DÁÁÁA) \(DHA)
(I)
O3–H3ÁÁÁO7i
0.84
0.84
0.84
0.84
0.99
0.99
0.98
0.99
1.70
2.533(2)
2.504(2)
2.516(2)
2.507(2)
3.184(2)
3.301(2)
3.268(2)
3.295(2)
170.3
165.0
169.3
168.4
143.8
149.2
169.1
161.3
O5–H5ÁÁÁO6
1.68
O4–H4ÁÁÁO8ii
O10–H10ÁÁÁO11iii
C13–H13BÁÁÁO11iv
C15–H15BÁÁÁO4
C17–H17CÁÁÁO6v
C19–H19AÁÁÁO11vi
(II)
1.69
1.68
2.331
2.411
2.299
2.343
O5–H5CÁÁÁO6i
O2–H2CÁÁÁO1i
C3–H3AÁÁÁO4i
C3–H3BÁÁÁO3ii
C5–H5BÁÁÁO7iii
C6–H6AÁÁÁO8i
C7–H7AÁÁÁO7iii
C7–H7CÁÁÁO4i
C8–H8AÁÁÁO6
0.84
0.84
0.99
0.99
0.99
0.99
0.98
0.98
0.98
1.76
2.593(1)
2.574(1)
3.257(2)
3.308(2)
3.311(2)
3.297(2)
3.306(2)
3.268(2)
3.263(2)
169.3
164.1
139.2
150.3
155.6
149.0
142.1
144.1
151.0
1.76
2.443
2.412
2.384
2.408
2.478
2.424
2.371
Fig. 5 Projected vibrational densities of states calculated for the
hydrogen atoms involved in the strong O–HÁÁÁO hydrogen bonds. The
upper two projections were obtained for the atoms of (II), the four
bottom for the atoms from (I). The individual traces are scaled to their
respective maximum values and offset for the sake of clarity
Symmetry operations for (I): (i) 1 - x, -1/2 ? y, 1 - z; (ii) 1 - x,
1/2 ? y, 1 - z; (iii) x, y, 1 ? z; (iv) 1 - x, 1/2 ? y, -z; (v) -x,
1/2 ? y, 1 - z; (vi) -x, 1/2 ? y, -z
Symmetry operations for (II): (i) x, 1/2 - y, 1/2 ? z; (ii) -x, 1 - y,
1 - z; (iii) 1 - x, 1/2 ? y, 3/2 - z
Fig. 6 Calculated power spectra for (I) and (II). The individual
traces are scaled to their respective maximum values and offset for the
sake of clarity
positions of the pure bending modes (1000–1500 cm-1
)
appearing due to tetrahedral deformation showing, that
they are not influenced by anharmonicities in the respective
hydrogen atoms movements. Interestingly, the main sharp
maxima (\1500 cm-1) corresponding to the bending
modes obtained for the H2C in (II) are, compared to those
of the H5C atom blue, and the broad band assumed to
represent the stretching modes red shifted in accordance
with the different strengths of the hydrogen bonds.
Fig. 4 IR spectra of (I) and (II) as measured by DRIFTS technique
The problem of the wrongly predicted modes was par-
tially elucidated by the molecular dynamics calculations
lasting for 90 ps (I) and 70 ps (II), respectively (Fig. 6).
These calculations going beyond the harmonic approxi-
mation have on one side preserved for both (I) and (II) the
123

1546
J Chem Crystallogr (2011) 41:1539–1546
10. Blessing RH (1995) Acta Cryst A51:33
On the contrary, the most problematic regions between
1500 and 3500 cm-1 are now described in two different
ways. For (II) with slightly weaker hydrogen bonds two
broad, but recognizable maxima centred at *2600 and
2800 cm-1 are obtained. The positions of these bands
fairly correlate with the position of the weak band in the IR
spectrum recognizable at *2500 cm-1. In contrast,
stronger O–HÁÁÁO bonds in (I) lead to smeared, almost
featureless and low peak intensity bands completely van-
ishing at *3000 cm-1. The shapes of these contributions
to the total spectrum of (I) clearly indicates significantly
larger anharmonicities in the respective vibrations com-
pared to (II). Detailed analysis of the vibrational spectra is
however beyond the scope of this paper mainly because
such an analysis would require a vibrational spectrum
obtained by inelastic neutron scattering (INS) generated by
the compounds with all C–H deuterated rather than the
standard IR or Raman spectra.
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Acknowledgments Financial support by the Charles University in
Prague, through the project GAUK 133508 and by the Long term
research plan of the Ministry of Education of the Czech Republic
through the project No. MSM 0021620857 is acknowledged. The
work was partially supported by the Slovak Grant Agency VEGA
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