Strong coupling effects in the polarized IR spectra of the chain hydrogen bond systems in imidazole crystals: H/D isotopic 'self-organization' effects in the IR spectra of isotopically diluted imidazole single crystals

Article abstract of DOI:10.1016/j.molstruc.2004.03.054

This paper presents the investigation results of the polarized IR spectra of H1245 imidazole crystals and of D1H245, D1245 and H1D245 imidazole deuterium derivative crystals. The spectra were measured using polarized light at the room temperature and at 77 K by a transmission method, for two different crystalline faces. Theoretical analysis of the results concerned linear dichroic effects, H/D isotopic and temperature effects, observed in the spectra of the hydrogen and of the deuterium bonds in imidazole crystals, at the frequency ranges of ν_N-H and ν_N-D bands. The basic crystal spectral properties can be satisfactorily interpreted in a quantitative way for a hydrogen bond linear dimer model. Such a model explains not only a two-branch structure of the ν_N-H and ν_N-D bands in crystalline spectra, but also some essential linear dichroic effects in the band frequency ranges, for isotopically diluted crystals. Model calculations, performed within the limits of the strong-coupling model, allowed for quantitative interpretation and for understanding of the basic properties of the hydrogen bond IR spectra of imidazole crystals, H/D isotopic, temperature and dichroic effects included. The results allowed verification of theoretical models proposed recently for the imidazole crystal spectra generation mechanisms. In the scope of our studies, the mechanism of H/D isotopic self-organization processes, taking place in the crystal hydrogen bond lattices, was also recognized. It was proved that for isotopically diluted crystalline samples of imidazole, a non-random distribution of protons and deuterons exclusively occurs in some restricted fragments (domains) of open chains of the hydrogen-bonded molecules. Nevertheless, these co-operative interactions between the hydrogen bonds do not concern adjacent fragments of neighboring hydrogen bond chains in the lattice. Analysis of the isotopic self-organization effects in the spectra of imidazole crystals delivered crucial arguments for understanding of the nature of the hydrogen bond spectra generation mechanisms.

Full text of DOI:10.1016/j.molstruc.2004.03.054

Journal of Molecular Structure 707 (2004) 17–31
www.elsevier.com/locate/molstruc
Strong coupling effects in the polarized IR spectra of the chain
hydrogen bond systems in imidazole crystals: H/D isotopic
‘self-organization’ effects in the IR spectra of isotopically
diluted imidazole single crystals
*
Henryk T. Flakus , Anna Michta
Institute of Chemistry, University of Silesia, 9 Szkolna Street, Katowice Pl40-006, Poland
Received 4 February 2004; revised 23 March 2004; accepted 23 March 2004
Available online 27 September 2004
Abstract
This paper presents the investigation results of the polarized IR spectra of H1245 imidazole crystals and of D1H245, D1245 and H1D245
imidazole deuterium derivative crystals. The spectra were measured using polarized light at the room temperature and at 77 K by a
transmission method, for two different crystalline faces. Theoretical analysis of the results concerned linear dichroic effects, H/D isotopic and
temperature effects, observed in the spectra of the hydrogen and of the deuterium bonds in imidazole crystals, at the frequency ranges of nN–H
and nN–D bands. The basic crystal spectral properties can be satisfactorily interpreted in a quantitative way for a hydrogen bond linear dimer
model. Such a model explains not only a two-branch structure of the nN–H and nN–D bands in crystalline spectra, but also some essential
linear dichroic effects in the band frequency ranges, for isotopically diluted crystals. Model calculations, performed within the limits of the
strong-coupling model, allowed for quantitative interpretation and for understanding of the basic properties of the hydrogen bond IR spectra
of imidazole crystals, H/D isotopic, temperature and dichroic effects included. The results allowed verification of theoretical models
proposed recently for the imidazole crystal spectra generation mechanisms. In the scope of our studies, the mechanism of H/D isotopic self-
organization processes, taking place in the crystal hydrogen bond lattices, was also recognized. It was proved that for isotopically diluted
crystalline samples of imidazole, a non-random distribution of protons and deuterons exclusively occurs in some restricted fragments
(domains) of open chains of the hydrogen-bonded molecules. Nevertheless, these co-operative interactions between the hydrogen bonds do
not concern adjacent fragments of neighboring hydrogen bond chains in the lattice. Analysis of the isotopic self-organization effects in the
spectra of imidazole crystals delivered crucial arguments for understanding of the nature of the hydrogen bond spectra generation
mechanisms.
q 2004 Elsevier B.V. All rights reserved.
Keywords: Hydrogen bond; Molecular crystals; Polarized IR spectra; H/D isotopic effects; Linear dichroic effects; Temperature effects; Model calculations;
Isotopic dilution; H/D isotopic ‘self-organization’ effects
1. Introduction
[1–5]. The subsequently proposed theoretical approaches
tried to explain a strong increase of the nX–H band integral
intensities, a considerable decrease of the band frequencies
and their considerable widening, when compared with the
corresponding band parameters for the non-associated X–H
groups. The main effort of the researchers was focussed on
understanding of the nature of mechanisms, responsible for
the appearance of the nX–H band fine structure and of the
rules, governing the intensity distribution in these bands.
These bands are considered to be the main attribute of the
hydrogen bond, formed in molecular systems [1–5].
Infrared spectroscopy is still being considered to be the
most powerful tool for the hydrogen bond research. In this
area the unique properties of the high-frequency nX–H
bands, generated by the proton stretching vibrations in the
X–H· · ·Y hydrogen bonds, is the subject of the interest of
many researchers, of theoreticians and of experimenters
*
Corresponding author. Fax: þ48-32-2599-978.
E-mail address: flakus@ich.us.edu.pl (H.T. Flakus).
0022-2860/$ - see front matter q 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2004.03.054

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H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
Theoretical models developed to quantitatively interpret IR
spectra of hydrogen bonds, namely the so-called ‘strong-
coupling’ theory [6–8], the elder, as well as the ‘relaxation’
theory [9–12], the latest, see the source of these effects in
anharmonic couplings, involving the proton stretching
vibrations and the low-energy X· · ·Y bond stretching
vibrations. A unique dynamics of the hydrogen bridge
atoms is considered by the both theoretical models as
responsible for the basic spectral properties, not only for
single hydrogen bonds, but also for simple aggregates like
hydrogen bond dimers. Even for these latest systems,
characterized by a relatively low complexity degree, the
spectral behavior does not seem completely understood,
although their basic properties were intensively studied with
the help of many theoretical approaches [6,7,10–16].
However, the greatest challenge in this area is to deliver
adequate theories, to describe coupling mechanism in more
complex hydrogen bond systems than dimers, molecular
crystals included. From these models fine structure patterns
of the nX–H and nX–D bands in the crystalline spectra could
be calculated. Therefore, the experiment stimulates further
development in the theory and on the other hand, the theory
inspires seeking for new experimental methods, able to
deliver most reliable data for testing newly introduce
theoretical models.
only a spectral, but also of a thermodynamic nature. Some
of these effects were connected with breaking of vibrational
dipole selection rules in the spectra of centrosymmetric
hydrogen bond dimeric systems [17]. To the group of new
spectral effects also belonged diverse, non-traditional H/D
isotopic effects in IR spectra of the hydrogen bond in
crystals [18]. A part of the newly revealed effects were
considered as a manifestation of non-conventional, phe-
nomenological interactions, in the area of the hydrogen
bond thermodynamics. The so-called H/D isotopic ‘self-
organization’ effects, depend on a non-random distribution
of proton and deuterons between the hydrogen bridges, in
cyclic and in chain systems of associated molecules, in
mixture systems of hydrogen and deuterium bonds in
crystals [19–21]. Identification of these effects was possible
only when based on a quantitative analysis of the polarized
IR spectra of hydrogen bonded molecular crystals [20,21].
Although the basic principles of the H/D isotopic ‘self-
organization’ mechanism have been recognized only
recently for cyclic dimeric systems of hydrogen bonds
[22], the nature of these co-operative interactions between
hydrogen bonds needs further intensive studies, especially
for open chain hydrogen bond systems. These latter system
spectra not always exhibit effects, confirming a non-random
distribution of protons and deuterons in their hydrogen bond
lattices [20,21,23–25].
From this point of view it seems, however, that
traditional experimental methods of IR spectroscopy,
applied in the area of the hydrogen bond research, have
exhausted most of their potential abilities. This time, the IR
spectroscopy of hydrogen bonded molecular crystals in
polarized light, seems to be a most promising experimental
method for studying diverse aspects of inter-hydrogen bond
interactions. Measurements of the polarized IR spectra of
spatially oriented hydrogen bond systems, in the lattices of
molecular crystals, can deliver data, allowing estimating the
vibrational transition moment directions to the excited states
of the proton vibrations in the crystals, as well as the
symmetry of the proton vibration exciton states.
In this article, we present the results of our studies on the
hydrogen bond IR polarized spectra of imidazole crystals.
Although during the recent 30 years, this crystalline system
was several times the object of spectroscopic studies, as well
as of theoretical considerations [7,26–31], some basic
problems, concerning the band fine structure generation
mechanisms seemed to be still far from a satisfactory
solving. Imidazole crystal IR hydrogen bond spectrum is
characterized by a wide and a well-developed nN–H band
contour. In the spectra, an extremely strong H/D isotopic
effect can be observed, expressed by reduction of the nN–D
band fine structure pattern, practically to a single narrow
line [26–29]. So far no systematic studies of the polarized
IR spectra of imidazole crystals have been published.
Similar remark also concerns the polarized crystalline
spectra of the deuterium isotopomers of imidazole. There-
fore, at this stage a full understanding of the band structure
generation mechanisms for imidazole crystals seems to be
rather impossible.
The solid state, however, is responsible for a substantial
complication of the coupling mechanisms, involving the
hydrogen bond atom vibrations that implies a considerable
growth in difficulties, when interpreting the hydrogen bond
vibrational spectra of crystals, especially their fine structure
patterns. Therefore, elucidation of the nature of the inter-
and the intra-hydrogen bond interactions, based on the
polarized IR spectra, measured in the nX–H band range,
needs solving of a number of theoretical problems within
one of the quantitative theoretical models, elaborated for
interpretation of the hydrogen bond spectra. Unfortunately,
only extremely few researchers undertook this challenge.
Thus, investigations of polarized IR spectra of hydrogen
bonded molecular crystals, accompanied with an advanced
theoretical interpretation, were so far extremely rare.
Studies on polarized IR spectra of hydrogen bonded
crystals, performed in the recent 5 years, allowed revealing
a number of new and highly non-conventional effects, of not
The highly non-regular spectral effects in the crystalline
spectra of imidazole are still considered to be a serious
challenge for the theory. Solving these problems might be
crucial for deeper understanding of the nature of mutual
interactions in the hydrogen bond systems in the lattices of
molecular crystals. Therefore, it seemed justified to measure
reliable high quality, temperature dependent, polarized
spectra of imidazole crystals and also similar quality spectra
of the imidazole deuterium derivative crystals.
In the lattice of imidazole crystal hydrogen bonded
molecules form infinite open chains and in one chain

H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
19
the hydrogen bonds are arranged as a ‘zig–zag’ [32–35].
Investigation of the polarized IR spectra of partially
deuterated imidazole crystals should also provide a valuable
information about the H/D isotopic ‘self-organization’
effects in these hydrogen bond chains. Existence, or lack
of linear dichroic effects, differentiating spectral properties
of the longer- and the shorter-wave branch of the ‘residual’
nN–H band, should allow recognition of the way of
distribution of protons and deuterons in the crystal lattice.
Lack of the dichroic effect would indicate a totally random
distribution of the protons and of the deuterons. On the other
hand, polarization effects in the ‘residual’ nN–H band should
prove a non-random distribution of the hydrogen isotopes,
due to the H/D isotopic ‘self-organization’ effects. How-
ever, a full understanding of the problem, based on the
spectra, should be preceded by theoretical studies on the
hydrogen bond spectra generation mechanism for ‘pure’
imidazole crystals. At this stage of our knowledge about
hydrogen-bonded crystal spectra investigation of these non-
conventional co-operative effects may demand developing
of theoretical models, useful for a quantitative interpretation
of the hydrogen bond IR spectra. Therefore, spectral studies
on the H/D isotopic ‘self-organization’ effects in the crystals
might effectively facilitate understanding the nature of the
vibrational exciton coupling mechanism, involving the
crystal hydrogen bonds, responsible for generation of the
nN–H band fine structure.
the temperature of liquid nitrogen, using polarized radiation,
with two different orientations of the electric field vector E,
with respect to the crystal lattice.
The solid-state spectra were measured by a transmission
method, for the normal orientation of the beam with respect
to a given crystalline face, with the help of the FT-IR
Nicolet Magna 560 spectrometer, for two different, mutually
perpendicular polarization directions of IR beam. In each
case, the electric field vector E was parallel to one unit cell
period, b or c; when crystals developed the bc face. For
crystals with the ac face developed, the electric field vector
E of the polarized radiation was polarized parallel to the ap;
or to the c identity period. All the spectra were measured at
2 cm21 resolution.
In a similar way measurements of spectra were
completed for crystals of imidazole D1H245, H1D245 and
D1245 deuterium derivatives.
3. Results
Spectra of polycrystalline samples of H1245 imidazole
and H1D245 imidazole, measured at 298 and 77 K, in the
nN–H band frequency ranges, for KBr pellets, are shown in
Fig. 1. In Fig. 1a, there is also presented the Raman
spectrum of H1245 imidazole, in order to identify the nCH
2. Experimental
Imidazole H1245 used for our studies was the commer-
cial substance (Sigma-Aldrich). For our studies it was used
without further purification. Imidazole D1245—the per-
deuterated isotopomer of the compound, was obtained by
heating of imidazole H1245 solution in heavy water at
250 8C, in a pressure reactor.
Imidazole D1H245 was obtained by evaporation under a
reduced pressure of imidazole H1245 solution in D2O, at the
room temperature. It was found that the deuterium exchange
rate for the amine groups varied from 50% till 95% for
different samples. The H1D245 isotopomer was synthesized
by evaporation of imidazole D1245 solution in H2O, also
under a reduced pressure.
Crystals of imidazole, suitable for the spectral studies,
were obtained by crystallization from melt, between two
closely spaced CaF2 windows. In this way sufficiently thin
crystals could be obtained, characterized by their maximum
absorbance at the nN–H band frequency range, being close to
0.5. From the crystal mosaic, suitable monocrystalline
fragments were selected and then spatially oriented, with the
help of a polarization microscope. It was found that most
frequently the crystals developed the bc, or the ac crystal-
line faces. These crystals were exposed for the experiment
by use of a tin diaphragm, with a 1.5 mm hole diameter. IR
spectra were measured at room temperature and at
Fig. 1. The nN–H bands in the IR spectra of the polycrystalline samples of
imidazole dispersed in KBr pellets, measured at 298 and at 77 K. (a) H1245
imidazole. The Raman spectrum of the polycrystalline samples is also being
drawn in order to indicate the nC–H band influence on the spectra.
(b) H1D245 imidazole.

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H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
4. Discussion
4.1. The ‘state of the art’ in recent studies on imidazole
crystal spectra
The polarized spectra of imidazole crystals shown in
Figs. 3–7 prove a very wealthy structure of the nN–H and
nN–D bands. The crystalline spectra exhibit complex
temperature and linear dichroic effects, differentiating
properties of the longer- and the shorter-wave branches of
the bands. These spectral properties suggest that at least
three subbands participate in the nN–H and nN–D band
generation.
Investigations of imidazole crystal spectral properties
have a relatively long history; thus our discussion must be
related to the recent studies, performed by predecessors. In
the most recent approach the model, applied for describing
of the imidazole crystal spectral properties, was restricted to
one-dimensional, chain lattice of the N–H· · ·N hydrogen
bonds. For this model, the first trial was undertaken, in the
limits of the ‘strong-coupling’ theory, to reconstitute the
nN–H and nN–D band fine structures. These calculation
results were related to the room temperature spectra of
polycrystalline imidazole samples [7]. However, the latter
and more sophisticated experimental studies by Excoffon
and Marechal have shown that such a simple model was
insufficient for explaining of the band generation mechan-
isms. These bands appeared to be of a much more
complex nature, due to some temperature, as well as to
polarization effects, registered in these bands [26–29].
These results suggested that some vibrational exciton
couplings took part in the general ‘strong-coupling’
mechanism [3,7,26–29,36], which were responsible for
the basic spectral properties of the hydrogen-bonded
system.
Fig. 2. The nN–D bands in the IR spectra of polycrystalline samples of
imidazole. KBr pellets, measured at 298 and at 77 K. (a) D1H245
imidazole. (b) D1245 imidazole. The Raman spectrum indicates the nC–D
band positions in the spectra.
bands, corresponding to the C–H bond stretching vibrations
in the imidazole rings.
Fig. 2 presents the nN–D bands from the spectra of
polycrystalline samples of D1H245 imidazole and of
imidazole D1245, measured in similar conditions. In
Fig. 2b, there is also drawn the Raman spectrum of a
polycrystalline sample of D1245 imidazole, indicating
location of the nC–D bands.
Polarized IR spectra of H1245 imidazole and H1D245
imidazole crystals, measured at room temperature, in the
nN–H band frequency ranges, for the two different
crystalline faces bc and ab, are shown in Fig. 3.
In turn, the low temperature spectra of the same
crystals are presented in Fig. 4.
For quantitative describing of the spectral properties of
imidazole crystal an extended ‘strong-coupling’ model was
recently proposed [30,31], assuming an extremely strong
vibrational exciton coupling between these hydrogen bonds
in a unit cell, which were related by the inversion center
operation. These hydrogen bonds belonged to the adjacent
hydrogen bond chains. Much weaker interactions were
assumed for these hydrogen bonds from the unit cell, which
belonged to one chain. Such approach seemed justified due
to geometric relations, concerning hydrogen bonds from one
unit cell [32–35]. This model seemed adequate that time,
as it quantitatively explained the basic source of the
extremely abnormal H/D isotopic effect in the crystalline
spectra [30,31] and the intensity distribution patterns in the
analyzed spectra. However, in our further proceedings we
will show that some assumptions of the latest model must be
verified in confrontation with our experimental results.
Nevertheless, we will utilize this model for as a starting
point for our actualized interpretation of the temperature, of
the polarization and of the isotopic effects in the spectra of
imidazole crystals. We will also show that based on
In Fig. 5, polarized spectra of D1H245 and D1245
deuterium isotopomers crystals of imidazole, measured at
room temperature, in the nN–D band frequency ranges,
for the two different faces bc and ab, are being shown
and in Fig. 6 we present the corresponding low
temperature spectra.
Effects of isotopic dilution by deuterium, of the hydrogen
bonds in crystalline lattices of H1245 imidazole and
H1D245 imidazole, are shown in Fig. 7. The picture
presents the polarized ‘residual’ nN–H bands, corresponding
to the residual protons, i.e. those, which were non-replaced
by deuterons, measured at 77 K.

H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
21
Fig. 3. Polarized IR spectra of H1245 imidazole and H1D245 imidazole single crystals, measured at the room temperature in the nN–H and the nC–H band
frequency range. The IR beam of normal incidence with respect to different crystal faces ac and bc was applied. In each case the component spectra were
obtained for two orientations of the electric field vector E: (a) H1245 imidazole, ac plane, (I) Ekc; (II) E ’ c ðEkapÞ: (b) H1245 imidazole, bc plane, (I) Ekc; (II)
*
E ’ c ðEkbÞ: (c) H1D245 imidazole, ac plane, (I) Ekc; (II) E ’ c ðEkapÞ: (d) H1D245 imidazole, bc plane, (I) Ekc; (II) E ’ c ðEkbÞ: The a symbol denotes
the vector in the reciprocal lattice. In each case the spectrum (III) is the spectrum (II) re-normalized to full scale with the spectrum (I) Spectra (I) and (II) were
drawn on a common scale.
the modified model, also the H/D isotopic ‘self-organiz-
ation’ interaction mechanisms [19,22] in the hydrogen bond
lattices may be much more convincingly discussed.
differentiate polarization properties of the two spectral
branches of the nN–H band [17]. According to this approach,
the observed strong linear dichroic effect in the imidazole
crystal spectra should be rather ascribed to the weaker
exciton interactions, concerning hydrogen bonds from each
unit cell, related by the screw-axis rotation operation
[32–35]. Such theoretical interpretation of the imidazole
crystal spectra has found no counterpart as yet, due to the
highly incomplete experimental data [7,26–29].
From the recent works it also resulted that the nN–H band
structure in the solid-state spectra was a superposition of
four component bands, each of a different transition
frequencies and of a different intensity distribution pattern
[30,31]. Each of these subbands was connected with the
dipole transition to one from four exciton states, of the
proton vibrations in one unit cell, differing with respect to
their symmetries. The two-branch nN–H band structure
pattern was determined by the exciton coupling, involving
two closely spaced hydrogen bonds, from adjacent hydro-
gen bond chains. This kind of interaction was considered
responsible for the observed splitting between the spectral
branches and it was also responsible for the temperature-
induced evolution of the band shapes [30,31]. This latter
property was ascribed to the temperature impact on the
magnitude of the symmetry forbidden transition probability,
for centrosymmetric hydrogen bond dimers [17]. However,
exciton interactions between the N–H· · ·N hydrogen bonds
in a model centrosymmetric dimer should not substantially
In confrontation with our experimental results, the
theoretical model describing the crystal spectral propertied
has to be modified. The new approach should take into the
account a detailed analysis of the polarized spectra of
imidazole crystals, measured at two extreme temperatures,
for two different crystalline faces. The crystalline spectra
of three deuterium substituted imidazole isotopomers
should provide a most complete data system for
elaboration of an adequate theoretical model. Also the
spectra of solid-state samples of imidazole H1245 and
imidazole H1D245, isotopically diluted with deuterium,
have to be considered in order to elucidate the band
generation mechanisms.

22
H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
Fig. 4. Polarized IR spectra of H1245 imidazole and H1D245 imidazole single crystals, measured at 77 K in the nN–H and the nC–H band frequency range. Other
experimental conditions and the way of presentation is identical with those given in Fig. 3.
4.2. Linear dichroic effect in the nN–H and N –D bands
Generally, the fine nN–H band structure is more compact
in the spectra of H1D245 imidazole crystals, when
compared with the nN–H band structure for crystals of
H1245 imidazole. Undoubtedly, in these bands the Davy-
dow-splitting effects can be identified which are the attributes
of relatively strong exciton couplings, involving the hydrogen
bonds in the lattice. In the case of the different crystal-
lographic planes, these doublet components also differ by
their relative intensities, in relation to the shorter-wave
branch intensities of the nN–H bands. The above mentioned
polarization effects seem prove that the nN–H band fine
structures are composed with at least three component bands
of a different origin.
Linear dichroic effects, observed in the crystalline
spectra, in the frequency ranges of the nN–H and nN–D
bands, are very complex. The basic polarization effect in the
spectra are related to the orientation of the electric field
vector E of the incident beam, with respect to the spatially
oriented hydrogen bond chains in the lattice, for an
individual crystalline face. In the case of each face, bc or
ac, the most intense polarized component of the nN–H and
nN–D band corresponds to the orientation of the E vector,
parallel to the c identity period of the lattice. For each crystal
plane, i.e. for bc or ac; the much weaker polarized component
of the bands was measured for the perpendicular orientation
of the electric field vector E; with respect to the c direction.
In the spectra also more complex polarization effects can
be identified. For the longer-wave branch of the nN–H band,
in the spectra of imidazole H1245, strong dichroic effects
differentiate properties of intense doublet structures, located
at the frequency ranges of 2760–2795, 2664–2702 and of
2596–2630 cm21 (see Figs. 3 and 4). In the spectra of
H1D245 imidazole crystals doublet structures can be
observed, with different polarization properties of their
components, in the lower-frequency branch of the nN–H
band. The doublets are being observed at the frequency
The Davydow-splitting effects from the longer-wave
nN–H band branches practically vanish due to isotopic
dilution, as the doublet structures are absent in the ‘residual’
n
N–H bands. It seems prove a considerable weakening of the
exciton coupling mechanisms between the proton stretching
vibrations, for mixed H/D hydrogen isotope contents in
solid-state samples of imidazole. At this stage of our studies
we consider this effect as related with exciton coupling
weakening, involving only selected pairs of the hydrogen
bonds from a unit cell. This statement is strongly supported
by the fact that the ‘residual’ nN–H bands still exhibit an
essential difference in polarization properties, between the
band longer- and the shorter-wave branches (see Fig. 7).
ranges of 2615–2660 cm21 and of 2785–2845 cm21
.

H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
23
Fig. 5. Polarized IR spectra of D1H245 imidazole and D1245 imidazole single crystals, measured at the room temperature, in the nN–D and the nC–D band
frequency range. The IR beam of normal incidence with respect to different crystal faces ac and bc was applied. In each case the component spectra were
obtained for two orientations of the electric field vector E: (a) H1245 imidazole, ac plane, (I) Ekc; (II) E ’ c ðEkapÞ: (b) H1245 imidazole, bc plane, (I) Ekc; (II)
E ’ c ðEkbÞ: (c) H1D245 imidazole, ac plane, (I) Ekc; (II) E ’ c ðEkapÞ: (d) H1D245 imidazole, bc plane, (I) Ekc; (II) E ’ c ðEkbÞ: In each case spectrum (III)
is the spectrum (II) re-normalized to full scale with spectrum (I). Spectra (I) and (II) were drawn on a common scale.
When analyzing polarization properties of the crystal
spectra, measured in the frequency range of the nN–D bands,
one can find that also in these cases the Davydow-splitting
effects are being identifiable (see Figs. 4 and 5). In the case
of D1H245 imidazole crystal spectra, the nN–D band
exhibits a very simple band fine structure, reduced to
practically one intense line. In this case the nN–D band
features no shorter-wave branch of the band contour, which

24
H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
Fig. 6. Polarized IR spectra of D1H245 imidazole and D1245 imidazole single crystals, measured at 77 K in the nN–D and the nC–D band frequency range. Other
experimental conditions and the way of presentation is identical with those given in Fig. 5.
would correspond to the shorter-wave branch of the nN–H
band from the spectra of H1245 crystals. The nN–D bands
are characterized by the Davydow-splitting effect of the
magnitude of ca. 50 cm21. With respect to dichroic
properties, these bands resemble the longer-wave branch
of the nN–H bands. The two corresponding fragments of the
two compared bands nN–H and nN–D are related by the
frequency ratio equal to 1.3. It expresses a typical H/D
isotopic effect, usually observed in IR spectra of hydrogen
bonded systems [1–4].

H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
25
Fig. 7. Residual nN–H bands in polarized IR spectra of isotopically diluted H1245 imidazole and H1D245 imidazole single crystals, measured at 77 K, in the
nN–H band range. Other experimental conditions and the way of presentation are identical with those given in Fig. 4.
The nN–D band from the spectra of D1245 imidazole
crystals is noticeably wider, when compared with the
corresponding bandwidth from the spectra of D1H245
imidazole crystals (see Figs. 4 and 5). For imidazole
D1H245, the nN–D band, besides the intense longer-wave
branch, also exhibits presence of a shorter-wave branch,
which could be treated as a counterpart of the shorter-wave
branch of the nN–H band, from the spectra of imidazole
H1245. This nN–D band is also Davydow-split by ca.
4.4. Qualitative analysis of the nN–H and the
shapes
band
N –D
Comparison of the nN–H band contour shapes, from the
spectra of H1245 imidazole and H1D245 imidazole crystals,
leads to the conclusion that in contrast to our intuition based
expectations, these bands are of essentially different shapes,
although some common elements of these bands can be
found. For H1D245 imidazole, the nN–H band is narrower,
with a smaller number of lines in the both band branches.
However, the spectra of the two different imidazole
isotopomer crystals, corresponding to a given individual
crystal face, exhibit similar polarization effects in the nN–H
band longer-wave branches and also similar relations
between the intensities of the band polarized components.
In general, there is also very similar temperature effect in
the compared spectra.
50 cm21
.
4.3. Temperature effects
Decrease in temperature causes the intensity growth of
the longer-wave branches of the nN–H bands by ca. 30%,
when the intensity of the band shorter-wave branches
remain practically unchanged. Such effects can be observed
not only for the spectra measured for polycrystalline
samples of imidazole in KBr pellets, but also in the
polarized spectra, recorded for the different crystalline
faces, bc and ac.
The shapes of the nN–D bands in the spectra of D1H245
imidazole and D1245 imidazole crystals differ stronger and
in a different way than the compared earlier nN–H bands.
The nN–D band in the spectra of D1245 imidazole crystal is
considerably wider when compared with the
corresponding band from the spectra of D1H245 imidazole
crystal. In the nN–D band frequency range also two branches
can be distinguished, differing by the way of the
temperature-induced evolution. The intensity of this
In the case of the nN–D bands only a slight growth of
intensity on the band shorter-wave sides is being observed,
along with temperature diminution. In contrast, on the
longer-wave part of these bands a relatively strong increase
of the intensity can be noticed.

26
H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
spectral longer-wave branch of the nN–D band grows when
temperature decreases. On the other hand, in the spectra of
D1H245 imidazole crystals this branch reduces to a single,
intense line, forming the band fine structure. It also exhibits
relatively strong temperature effect.
properties of such dimers have been sufficiently well
established [16,17]. A typical cyclic dimer spectrum is
characterized by two transitions in the nX–H band frequency
region, corresponding to the two spectral branches in the
spectrum. The higher energy component band corresponds
to the symmetry-allowed transition to the excited state of the
anti-symmetric proton stretching vibrations. The lower
energy subband is connected with the symmetry forbidden
totally symmetric proton vibrations, activated by a vibronic
mechanism [17], as well as by lowering of the dimer
symmetry, due to structural deformations. When compared
with the cyclic dimer spectral properties, an open-chain
dimer exhibits some essential differences in its spectral
behavior. The nX–H band component, attributed to the
totally symmetric proton vibrations, is of the lower
frequency. This vibration takes the form of a simultaneous
stretching of all of the X–H bonds in a hydrogen bond chain
and should be active in IR even for the ideally axial
symmetry of a linear dimer. The anti-symmetric proton
vibration band, forbidden by the symmetry rules, should
appear at the higher frequencies, due to structural
deformations of the dimer, or due to the vibronic promotion
mechanism.
4.5. Choice of the model
All the facts presented above seem crucial for under-
standing of generation mechanisms of the hydrogen bond
spectra of imidazole crystals. They seem prove that the
strongest couplings in the lattice concern the adjacent
hydrogen bonds from an individual chain. This conclusion
results from comparing of the spectra of isotopically
undiluted crystals, with the crystal spectra in isotopic
dilution. The band analysis must also be confronted with the
theory of the newly revealed H/D isotopic ‘self-organiz-
ation’ effects, in the IR spectra of hydrogen bonded systems
[22]. Therefore, taking into the account the lattice
symmetry, an adequate simplest model for quantitative
description of the crystal spectra, measured in isotopic
dilution with deuterium, is a quasi-axial, linear dimer,
composed with the N–H·N hydrogen bonds. Such a reduced
model represents basic spectral properties of the crystal,
instead of the more complete model, considering exciton
coupling, between the four hydrogen bonds from a unit cell
of the crystal. We will show that this simple model is
sufficient for description of the basic spectral properties of
the analyzed spectra, the fine structure and the polarization
properties of the ‘residual’ nN–H bands included. It is also
able to explain the basic ‘classical’ H/D isotopic effects in
the spectra of the deuterium-bonded crystals.
Acceptation of the linear dimer as a model system, for
describing of the spectral properties of isotopically diluted
imidazole crystals, remains in agreement with the results of
the earlier published works, concerning H/D isotopic self-
organization processes, in chain systems of hydrogen bonds
[18,19]. For imidazole crystals, the unit cell containing four
hydrogen bonds, determines their basic spectral properties.
For solid-state samples of imidazole, characterized by very
high deuterium dilution rate, the remaining protons in a
sample are most probably grouped in some fragments of a
chain, i.e. domains, due to cooperative interactions,
involving hydrogen bonds with identical hydrogen isotope
atoms. There is probably no coordination between domains
in adjacent chains, trespassing one unit cell. When in a unit
cell there are two protons in one chain, the remaining
neighboring chain fragment in this cell most probably
contains two deuterium bonds. In this way, part of the
exciton couplings between the vibrationally excited hydro-
gen bonds from one unit cell vanishes. Only the couplings,
concerning the neighboring hydrogen bonds from a chain
domain, remain still active. Therefore, isotopic dilution
simplifies the nN–H band structure pattern due to decoupling
of hydrogen bonds, belonging to the two adjacent chains
from one unit cell. This justifies acceptation of the model for
our quantitative considerations.
When assuming the strong-coupling model [6–8] for a
linear, quasi-axial hydrogen bond dimer, the longer-wave
branch of the ‘residual’ nN–H band should correspond with
the totally symmetric ‘in-phase’ proton vibration. Excitation
of this vibration is symmetry-allowed. The shorter-wave
branch of the ‘residual’ nN–H band relates to the ‘out-of-
phase’ proton vibration in the dimer. Such a vibrational
transition is symmetry-forbidden for an ideally axial, linear
hydrogen bond dimer. In the case, when the dimer structure
declines from the ideal axial symmetry, the selection rule
should become weakened. For spatially oriented zig–zag
chains, the two transition spectra differ by their polarization
properties.
For the ideal axial symmetry of a linear dimer, the ‘plus’
band should be theoretically symmetry-forbidden. It may
appear in the crystal spectra for a number of reasons,
declining from the ideal axial symmetry included first. Also
some much more sophisticated band generation vibronic
mechanisms may be active in the forbidden transition
promotion process in the IR [17]. This latter mechanism
effectively acts even for the ideal axial symmetry for a
dimeric system [17].
Very similar model can be assumed for interpretation of
the nN–D band properties in the spectra of crystals of
D1H245 imidazole and D1245 imidazole, isotopically
diluted by hydrogen.
A consequence of the assumed model should be the
peculiar shape of the nN–H band fine structure in the
theoretically derived spectra. In its shorter-wave part, the
band should be of o form of a regular, well-developed
The most frequently investigated hydrogen bond dimers
were of a cyclic, centrosymmetric structure. Spectral

H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
27
progression of the low-energy nN–N vibration quantum. In
the longer-wave branch, the band should be of a compact
and of a more irregular fine structure pattern, with a
tendency of the band structure blurring [20].
parameter value for deuterium bond systems, according to
the relation:
pffiffi
bH ¼ 2bD:
4.6. Model calculations of the ‘residual’ nN–H and the
band shapes
For the C0 and C1 resonance interaction parameters, the
theory predicts the isotopic effect, expressed by diminution
by 1.0 to 2 times of the parameter values.
N –D
pffiffi
Model calculations, aiming to reconstitute the
‘residual’ nN–H and nN–D band shapes, were performed
in the limits of the ‘strong-coupling’ model [6–8,16] for a
quasi-axial, linear hydrogen bond dimer. For this model,
the nN–H and nN–D band structures were treated as
superposition of two component bands, corresponding to
excitation of two kinds of the proton stretching vibrations,
i.e. the totally symmetric ‘in-phase’ and the non-totally
symmetric ‘out-of-phase’ vibrations. The first of the
above-mentioned bands is of a lower frequency, in
comparison with the frequency of the second band. The
transition to the excited state of the totally symmetric
proton vibration, in a zig–zag chain, is polarized parallel
to the chain axis direction, whereas for the non-totally
symmetric vibration it should be polarized perpendicularly
to the chain axis and parallel to the inter-hydrogen-bond
angle bisector. As the forbidden transition promotion
mechanism is partially of a vibronic nature [17], the
higher-frequency band dichroic properties may be inter-
mediate between these two cases.
In Fig. 8, the model calculation results are being shown,
aiming to quantitatively reconstitute ‘residual’ nN–H band
contour shapes, from the spectra of isotopically diluted by
deuterium crystals of imidazole H1245 and crystals of
imidazole H1D245.
Quantitative reproduction of the nN–D band contour
shapes from the spectra of crystals of imidazole D1H245
and crystals of imidazole D1245, isotopically diluted by
hydrogen, is being presented in Fig. 9.
A strong narrowing of the nN–D bands in the spectra
of D1H245 imidazole crystals is thus a result of an
extremely strong coupling between vibrations in a dimer.
It is expressed by a linear dependence of the resonance
interaction integral, for vibrationally excited hydrogen
bonds in the dimer, upon the normal coordinates of the
low-frequency hydrogen bond vibrations [17]. Our
calculation results reproduce only some general properties
of the analyzed bands. In the case of reconstitution of
the ‘residual’ nN–H bands it was necessary to take into the
account, with a relatively high statistical weight, of the
dimeric ‘minus’ sub-band, corresponding to the ‘out-of-
phase’ proton vibrations, reproducing the shorter-wave
branches of the bands. When reconstituting the spectra,
measured for the two different crystal faces, the
component subband statistical weights should be appro-
priately varied. When performing the model calculations
for the nN–D bands, taking into the account of the ‘minus’
band was particularly necessary in the case of the spectra
of D1245 imidazole crystals, isotopically diluted by
hydrogen. It means that in D1245 imidazole crystal
spectra, the quasi-forbidden transition participates with
relatively high statistical weight, in generation of the nN–D
band fine structure pattern. The model calculations also
showed that in the ‘residual’ nN–D bands of D1H245
imidazole, crystal spectra the quasi-forbidden transition
contributes with a negligible statistical weight.
Within the ‘strong-coupling’ model, the nO–H band shape
for a dimer, composed with two N–H· · ·N hydrogen bonds,
basically depends on the following system of coupling
parameters: (i) on the distortion parameter bH; and on (ii) the
resonance interaction parameters C0 and C1 [6,7,16]. Each
parameter has a precisely defined physical meaning: the bH
parameter describes the change in the equilibrium geometry
for the low-energy hydrogen bond stretching vibrations,
accompanied the excitation of the high-frequency proton
stretching vibrations nO–H: The C0 and C1 parameters are
responsible for mutual interactions between the hydrogen
bonds in a dimer, in its vibrationally excited state. They
denote subsequent expansion coefficients in the series, when
developing the resonance interaction integral C; with
respect to the normal coordinates of the low frequency,
hydrogen bond stretching vibrations nN· · ·N
:
The model calculations have proved that the assumed
quasi-axial, linear dimeric hydrogen bond model explains
the basic spectral properties of the imidazole crystals,
with an essential difference in the polarization properties
between the spectral branches, retained even for iso-
topically diluted sample spectra. In the case of the ‘pure’
crystalline system spectra, Davydow-splitting additively
modifies the two branch band structures, generated
by exciton couplings between the proton vibrations in
the hydrogen bonds, belonging to two adjacent
chains, trespassing each individual unit cell of imidazole
crystals.
C ¼ C0 þ C1Q1;
where Q1 represents the totally symmetric normal coordi-
nate for the low-frequency stretching vibration in the dimer.
This parameter system remains in a close relation with the
intensity distribution in the dimeric nO–H band: The bH and
C1 parameters are directly connected with the dimeric nO–H
bandwidth. The C0 parameter determines the splitting of the
component bands of the dimeric spectrum, corresponding to
excitation of the proton vibrational motions of different-
symmetry [6,7,16]. In its original version the ‘strong-
coupling’ model predicts diminution of the distortion

28
H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
Fig. 8. Theoretical reconstitution of the most intense nN–H band component from the low- temperature spectra of imidazole crystals. (I) The ‘plus’ dimeric band
reconstituting the symmetry-allowed transition, (II) the ‘minus’ dimeric band reproducing the forbidden transition and, (III) the superposition of the ‘plus’ and
‘minus’ bands taken with their statistical weight parameters F2 and F2: The coupling parameter values: (a) H1245: bH ¼ 1:4; C0 ¼ 1:8; C1 ¼ 20:2;
Fþ ¼ 1:0; F2 ¼ 0:6; VN…N ¼ 90 cm21. (b) H1D245: bH ¼ 1:2; C0 ¼ 1:8; C1 ¼ 20:2; Fþ ¼ 1:0; F2 ¼ 0:6; VN· · ·N ¼ 90 cm21. The corresponding
experimental spectrum is presented at the right upper edge of the picture.
Based on the results of our model calculations and also
accepting our interpretation of the generation mechanisms
of the crystal spectra, the temperature effect may be
explained, recorded in the frequency ranges of the nN–H
and the nN–D bands. The intensity diminution of the longer-
wave branch of each band, when temperature grows, is most
probably connected with declining of the hydrogen bond
chain geometry from the low-temperature structure, towards
the more deformed one, due to large-amplitude libration
motions. This might be reflected in the observed tempera-
ture-induced change in the structural constants of the
imidazole crystal [33–35].

H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
29
Fig. 9. Theoretical prediction of the most intense nN–D band component from the low-temperature spectra of imidazole crystals. (I) The ‘plus’ dimeric band,
(II) the ‘minus’ dimeric band reproducing the forbidden transition. The coupling parameter values: (a) D1H245: bD ¼ 0:9; C0 ¼ 1:3; C1 ¼ 20:1; Fþ ¼ 1:0;
F2 ¼ 0:1; VN…N ¼ 90 cm21. (b) D1245 : bD ¼ 0:9; C0 ¼ 1:3; C1 ¼ 20:1; Fþ ¼ 1:0; F2 ¼ 1:0; VN· · ·N ¼ 90 cm21. The corresponding experimental
spectrum is presented at the right upper edge of the picture.
The adequacy of the accepted model may also be
supported by the observed difference between the ‘residual’
nN–D band shapes, in the spectra of isotopically diluted
crystals of D1H245 imidazole and D1245 imidazole. In the
latter case, the intense shorter-wave branch of the
band appears due to an effective enough promotion of
the symmetry-forbidden transition, in the quasi-axial linear
deuterium bond dimer. This effect of the vibrational
selection rule breaking has its source in dynamic couplings,
involving the deuteron stretching vibrations and the C–D
bond stretching vibrations, via the easy-polarizable ‘p’
electrons of the imidazole aromatic rings. It represents a

30
H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
kind of the so-called ‘long-range’ H/D isotopic effects. The
formalism of the coupling mechanism was elaborated
recently [18].
in the lattices. In the scope of our spectroscopic results, the
distribution of protons and deuterons among the hydrogen
bonds remains non-random, even for very high deuterium
substitution rates of the samples. The ‘self-organization’
processes are responsible for grouping of identical hydrogen
isotope atoms, i.e. protons or deuterons, in some fragments
of the associated molecular chains. These processes do not
involve more distant fragments of the lattices, including
adjacent fragments of the neighboring hydrogen bond
chains. Particularly, the ‘self-organization’ does not involve
all of the hydrogen bonds from each unit cell. Such an
interpretation of the H/D isotopic ‘self-organization’
processes may be deduced when based on the polarization
properties of the spectra, on the observed temperature
effects and on the quantitative analysis of the fine structure
patterns, of the hydrogen and of the deuterium bond spectra
of imidazole crystals.
5. H/D isotopic ‘self-organization’ processes
in the lattices of imidazole crystals in the scope
of the experiment and of the model calculations
Isotopic dilution of solid-state samples of H1245
imidazole and H1D245 imidazole crystals with deuterium
leads to very characteristic changes in the shapes and in the
polarization properties of the nN–H bands in the IR. The so-
called ‘residual’ nN–H bands still exhibit two-branch
structures, with almost identical differences in the tempera-
ture and linear dichroic effects, characterizing the spectral
branches, when compared with the properties of the nN–H
bands measured for ‘pure’ samples of H1245 imidazole and
H1D245 imidazole. Also the ‘residual’ nN–H bands,
measured for an individual system, for the two individual
crystal faces, differ one with respect to the other, by the
intensity distribution.
With regard to the H/D isotopic ‘self-organization’
effects imidazole crystal spectra fairly resemble IR spectra
of hydrogen-bonded pyrazole [21] and 4-thiopyridone [20]
crystals.
As a result of isotopic dilution, the doublet structures,
characterized in the spectra of ‘pure’ crystalline samples by
strong linear dichroic effects, vanish. It means, that isotopic
dilution is responsible for annihilation of not all, but only of
selected Davydow couplings. A precise analysis of dichroic
properties of the ‘residual’ nN–H bands allows identifying a
difference in polarization properties of the band branches,
i.e. the longer- and the shorter-wave ones. The two parts of
the ‘residual’ nN–H bands correspond with different
transition moment directions. This fact proves that some
exciton couplings still remain active for isotopically diluted
solid-state samples of imidazole and that distribution of
protons and deuterons in the hydrogen bond system is non-
random. The band polarization properties suggest that this
coupling concerns the non-parallel, neighboring hydrogen
bonds in chain fragments of associated imidazole mol-
ecules, in the crystal lattice. It is a strong evidence of
occurring of the H/D isotopic ‘self-organization’ effects
[22] in chain systems of hydrogen and deuterium bonds, in
isotopically diluted crystals of imidazole isotopomers.
For D1245 imidazole crystals, strongly diluted by
hydrogen, in the frequency range of the ‘residual’ nN–D
bands, some qualitatively similar effects can be identified,
namely disappearance of the Davydow-splitting. Also a
temperature impact on the band appears qualitatively
similar, when compared with the ‘residual’ nN–H band
properties. On the other hand, with regard to a simple and
reduced fine structure pattern of the ‘residual’ nN–D bands,
in the spectra of isotopically diluted with hydrogen D1H245
imidazole crystals, disappearance of the Davydow-splitting
effects, accompanying to the isotopic dilution, can be noticed.
The isotopic dilution effects, from the spectra of
imidazole crystals, provide weighty evidence, concerning
occurrence of the H/D isotopic ‘self-organization’ processes
6. Conclusion
The imidazole crystal IR spectra investigation results,
presented in this paper, allowed identifying most completely
the nature of vibrational transitions, occurring in the
hydrogen bond system, responsible for generation of the
nN–H and nN–D band fine structure pattern. Complementary
studies of polarization, of temperature and of H/D isotopic
effects, as well as of isotopic dilution effects in the
crystalline spectra, in confrontation with the model
calculations, allowed ascribing of these effects to a linear
hydrogen bond dimer, as a proper effective model system.
Such a dimer system is the source of the basic spectral
properties of imidazole crystals, determining the basic, two-
branch structure of the analyzed bands. Exciton interactions,
involving hydrogen bonds of the adjacent hydrogen bonds
of neighboring chains, are responsible for generation of
secondary effects, as for appearance of doublet structures in
nN–H and nN–D bands, due to Davydow couplings.
A quantitative analysis of the imidazole crystal spectra
allowed verifying of the recently proposed interpretation of
the crystal spectral properties. It was connected with
modification of the previously accepted model, assuming
that just a centrosymmetric dimer, composed with two
N–H· · ·N hydrogen bonds, belonging to two neighboring
chains, was responsible for generation of the basic spectral
properties of the imidazole crystal. The previous model was
simply based on the unit cell geometry criterion. The recent
interpretation was based on highly incomplete experimental
data that time [26–31].
The results of our consideration do not negate the nature
of the classical H/D isotopic effects in the spectra,
considered as a result of extremely strong coupling between

H.T. Flakus, A. Michta / Journal of Molecular Structure 707 (2004) 17–31
31
[4] P. Schuster, W. Mikenda (Eds.), Hydrogen Bond Research,
ˆ
Monatshefte fur Chemie, Chemical Monthly, 130/No.8, Springer,
vibrations in the hydrogen bond dimer [16]. Also the
explanation of the so-called ‘long-distance’ H/D isotopic
effects in the crystalline spectra remains still valid [18].
Our studies have provided data, confirming the H/D
‘self-organization’ process scheme, for the hydrogen bond
lattices of isotopically diluted imidazole crystals. In the case
of high deuterium exchange rates in imidazole crystals, the
remaining protons are grouped together in some fragments
of hydrogen bond chains, i.e. in domains. In turn, the
isotopic dilution effects in the spectra have provided data,
crucial for understanding of the nN–H and the nN–D band fine
structure generation mechanisms, as selected Davydow-
coupling effects in the crystal spectra vanished. Such
decoupling of the hydrogen bonds noticeably simplified
the spectrum fine structure patterns, facilitating theoretical
treatment of the problem.
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